## Begin on: Mon Jan 20 16:52:21 CET 2020

ENUMERATION
No. of records: 2364

FAMILY (oriented family) : isomorphism classes
1     [ E1b] : 32 (28 non-degenerate)
2     [ E3b] : 217 (185 non-degenerate)
2*    [E3*b] : 217 (185 non-degenerate)
2ex   [E3*c] : 2 (2 non-degenerate)
2*ex  [ E3c] : 2 (2 non-degenerate)
2P    [  E2] : 37 (30 non-degenerate)
2Pex  [ E1a] : 13 (13 non-degenerate)
3     [ E5a] : 1483 (1016 non-degenerate)
4     [  E4] : 126 (87 non-degenerate)
4*    [ E4*] : 126 (87 non-degenerate)
4P    [  E6] : 35 (14 non-degenerate)
5     [ E3a] : 35 (22 non-degenerate)
5*    [E3*a] : 35 (22 non-degenerate)
5P    [ E5b] : 4 (3 non-degenerate)

E27.1 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ B, A, B, A, B, A, A, B, A, B, A, B, A, A, B, A, B, A, B, B, A, B, A, B, A, B, B, A, B, A, B, A, A, B, A, B, A, B, A, A, B, A, B, A, B, B, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^27, (Z^-1 * A * B^-1 * A^-1 * B)^27 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 41, 68, 95, 14, 50, 77, 104, 23, 40, 67, 94, 13, 45, 72, 99, 18, 52, 79, 106, 25, 54, 81, 108, 27, 47, 74, 101, 20, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 42, 69, 96, 15, 49, 76, 103, 22, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 43, 70, 97, 16, 51, 78, 105, 24, 53, 80, 107, 26, 46, 73, 100, 19, 36, 63, 90, 9, 44, 71, 98, 17, 48, 75, 102, 21, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 55)(2, 56)(3, 57)(4, 58)(5, 59)(6, 60)(7, 61)(8, 62)(9, 63)(10, 64)(11, 65)(12, 66)(13, 67)(14, 68)(15, 69)(16, 70)(17, 71)(18, 72)(19, 73)(20, 74)(21, 75)(22, 76)(23, 77)(24, 78)(25, 79)(26, 80)(27, 81)(28, 82)(29, 83)(30, 84)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 91)(38, 92)(39, 93)(40, 94)(41, 95)(42, 96)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 103)(50, 104)(51, 105)(52, 106)(53, 107)(54, 108)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.2 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, B^3, A^3, (S * Z)^2, S * A * S * B, (A^-1, Z), Z^5 * B^-1 * Z^4 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 39, 66, 93, 12, 45, 72, 99, 18, 51, 78, 105, 24, 48, 75, 102, 21, 42, 69, 96, 15, 36, 63, 90, 9, 30, 57, 84, 3, 34, 61, 88, 7, 40, 67, 94, 13, 46, 73, 100, 19, 52, 79, 106, 25, 54, 81, 108, 27, 50, 77, 104, 23, 44, 71, 98, 17, 38, 65, 92, 11, 32, 59, 86, 5, 35, 62, 89, 8, 41, 68, 95, 14, 47, 74, 101, 20, 53, 80, 107, 26, 49, 76, 103, 22, 43, 70, 97, 16, 37, 64, 91, 10, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 59)(4, 63)(5, 55)(6, 67)(7, 62)(8, 56)(9, 65)(10, 69)(11, 58)(12, 73)(13, 68)(14, 60)(15, 71)(16, 75)(17, 64)(18, 79)(19, 74)(20, 66)(21, 77)(22, 78)(23, 70)(24, 81)(25, 80)(26, 72)(27, 76)(28, 86)(29, 89)(30, 82)(31, 92)(32, 84)(33, 95)(34, 83)(35, 88)(36, 85)(37, 98)(38, 90)(39, 101)(40, 87)(41, 94)(42, 91)(43, 104)(44, 96)(45, 107)(46, 93)(47, 100)(48, 97)(49, 108)(50, 102)(51, 103)(52, 99)(53, 106)(54, 105)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.3 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, A * B^-1, A^-1 * B^-2, A^3, A * Z^-1 * B^-1 * Z, Z * B^-1 * Z^-1 * A, (S * Z)^2, S * A * S * B, Z^-3 * B^-1 * Z^-6 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 39, 66, 93, 12, 45, 72, 99, 18, 51, 78, 105, 24, 50, 77, 104, 23, 44, 71, 98, 17, 38, 65, 92, 11, 32, 59, 86, 5, 35, 62, 89, 8, 41, 68, 95, 14, 47, 74, 101, 20, 53, 80, 107, 26, 54, 81, 108, 27, 48, 75, 102, 21, 42, 69, 96, 15, 36, 63, 90, 9, 30, 57, 84, 3, 34, 61, 88, 7, 40, 67, 94, 13, 46, 73, 100, 19, 52, 79, 106, 25, 49, 76, 103, 22, 43, 70, 97, 16, 37, 64, 91, 10, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 59)(4, 63)(5, 55)(6, 67)(7, 62)(8, 56)(9, 65)(10, 69)(11, 58)(12, 73)(13, 68)(14, 60)(15, 71)(16, 75)(17, 64)(18, 79)(19, 74)(20, 66)(21, 77)(22, 81)(23, 70)(24, 76)(25, 80)(26, 72)(27, 78)(28, 86)(29, 89)(30, 82)(31, 92)(32, 84)(33, 95)(34, 83)(35, 88)(36, 85)(37, 98)(38, 90)(39, 101)(40, 87)(41, 94)(42, 91)(43, 104)(44, 96)(45, 107)(46, 93)(47, 100)(48, 97)(49, 105)(50, 102)(51, 108)(52, 99)(53, 106)(54, 103)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.4 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B * A^-1, A * Z^-3, (S * Z)^2, S * B * S * A, (A^-1, Z^-1), A^9 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 30, 57, 84, 3, 34, 61, 88, 7, 39, 66, 93, 12, 36, 63, 90, 9, 40, 67, 94, 13, 45, 72, 99, 18, 42, 69, 96, 15, 46, 73, 100, 19, 51, 78, 105, 24, 48, 75, 102, 21, 52, 79, 106, 25, 54, 81, 108, 27, 50, 77, 104, 23, 53, 80, 107, 26, 49, 76, 103, 22, 44, 71, 98, 17, 47, 74, 101, 20, 43, 70, 97, 16, 38, 65, 92, 11, 41, 68, 95, 14, 37, 64, 91, 10, 32, 59, 86, 5, 35, 62, 89, 8, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 60)(5, 55)(6, 66)(7, 67)(8, 56)(9, 69)(10, 58)(11, 59)(12, 72)(13, 73)(14, 62)(15, 75)(16, 64)(17, 65)(18, 78)(19, 79)(20, 68)(21, 77)(22, 70)(23, 71)(24, 81)(25, 80)(26, 74)(27, 76)(28, 86)(29, 89)(30, 82)(31, 91)(32, 92)(33, 85)(34, 83)(35, 95)(36, 84)(37, 97)(38, 98)(39, 87)(40, 88)(41, 101)(42, 90)(43, 103)(44, 104)(45, 93)(46, 94)(47, 107)(48, 96)(49, 108)(50, 102)(51, 99)(52, 100)(53, 106)(54, 105)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.5 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, Z^-2 * A^-1 * Z^-1, (S * Z)^2, S * B * S * A, A^9, Z^-1 * A^4 * Z * A^-4 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 32, 59, 86, 5, 35, 62, 89, 8, 39, 66, 93, 12, 38, 65, 92, 11, 41, 68, 95, 14, 45, 72, 99, 18, 44, 71, 98, 17, 47, 74, 101, 20, 51, 78, 105, 24, 50, 77, 104, 23, 53, 80, 107, 26, 54, 81, 108, 27, 48, 75, 102, 21, 52, 79, 106, 25, 49, 76, 103, 22, 42, 69, 96, 15, 46, 73, 100, 19, 43, 70, 97, 16, 36, 63, 90, 9, 40, 67, 94, 13, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 58)(7, 67)(8, 56)(9, 69)(10, 70)(11, 59)(12, 60)(13, 73)(14, 62)(15, 75)(16, 76)(17, 65)(18, 66)(19, 79)(20, 68)(21, 77)(22, 81)(23, 71)(24, 72)(25, 80)(26, 74)(27, 78)(28, 86)(29, 89)(30, 82)(31, 87)(32, 92)(33, 93)(34, 83)(35, 95)(36, 84)(37, 85)(38, 98)(39, 99)(40, 88)(41, 101)(42, 90)(43, 91)(44, 104)(45, 105)(46, 94)(47, 107)(48, 96)(49, 97)(50, 102)(51, 108)(52, 100)(53, 106)(54, 103)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.6 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, A^-1 * B, (A^-1, Z^-1), (S * Z)^2, Z^-1 * B * Z * A^-1, S * B * S * A, Z^-1 * A * Z * B^-1, Z^2 * A^-1 * Z * A^-3, B^-2 * Z * B^-1 * Z * B^-1 * Z, Z^3 * B * Z^3, A^-2 * Z^-2 * A^-3 * Z^-1 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 41, 68, 95, 14, 50, 77, 104, 23, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 43, 70, 97, 16, 46, 73, 100, 19, 54, 81, 108, 27, 51, 78, 105, 24, 40, 67, 94, 13, 45, 72, 99, 18, 47, 74, 101, 20, 36, 63, 90, 9, 44, 71, 98, 17, 53, 80, 107, 26, 52, 79, 106, 25, 48, 75, 102, 21, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 42, 69, 96, 15, 49, 76, 103, 22, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 69)(7, 71)(8, 56)(9, 73)(10, 74)(11, 75)(12, 58)(13, 59)(14, 76)(15, 80)(16, 60)(17, 81)(18, 62)(19, 68)(20, 70)(21, 72)(22, 79)(23, 65)(24, 66)(25, 67)(26, 78)(27, 77)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 97)(34, 83)(35, 99)(36, 84)(37, 85)(38, 104)(39, 105)(40, 106)(41, 100)(42, 87)(43, 101)(44, 88)(45, 102)(46, 90)(47, 91)(48, 92)(49, 95)(50, 108)(51, 107)(52, 103)(53, 96)(54, 98)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.7 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, A * B^-1, A * B^-1, (A, Z), (S * Z)^2, S * B * S * A, Z^-1 * A * Z * B^-1, A * Z^-1 * B^-1 * Z, B^3 * A * Z^3, A * B * Z * B * Z * A * Z, Z^2 * B^-1 * Z^4 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 41, 68, 95, 14, 48, 75, 102, 21, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 42, 69, 96, 15, 52, 79, 106, 25, 54, 81, 108, 27, 47, 74, 101, 20, 36, 63, 90, 9, 44, 71, 98, 17, 51, 78, 105, 24, 40, 67, 94, 13, 45, 72, 99, 18, 53, 80, 107, 26, 46, 73, 100, 19, 50, 77, 104, 23, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 43, 70, 97, 16, 49, 76, 103, 22, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 69)(7, 71)(8, 56)(9, 73)(10, 74)(11, 75)(12, 58)(13, 59)(14, 79)(15, 78)(16, 60)(17, 77)(18, 62)(19, 76)(20, 80)(21, 81)(22, 68)(23, 65)(24, 66)(25, 67)(26, 70)(27, 72)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 97)(34, 83)(35, 99)(36, 84)(37, 85)(38, 104)(39, 105)(40, 106)(41, 103)(42, 87)(43, 107)(44, 88)(45, 108)(46, 90)(47, 91)(48, 92)(49, 100)(50, 98)(51, 96)(52, 95)(53, 101)(54, 102)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.8 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, B^-1 * A, A^-1 * B, (Z, A^-1), (S * Z)^2, S * A * S * B, Z^-3 * A^2, A^9, A^-3 * B^-1 * A^-4 * B^-1, A^9, (A^-1 * B^-1)^9 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 36, 63, 90, 9, 42, 69, 96, 15, 47, 74, 101, 20, 49, 76, 103, 22, 54, 81, 108, 27, 51, 78, 105, 24, 46, 73, 100, 19, 44, 71, 98, 17, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 41, 68, 95, 14, 43, 70, 97, 16, 48, 75, 102, 21, 53, 80, 107, 26, 52, 79, 106, 25, 50, 77, 104, 23, 45, 72, 99, 18, 40, 67, 94, 13, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 68)(7, 69)(8, 56)(9, 70)(10, 60)(11, 62)(12, 58)(13, 59)(14, 74)(15, 75)(16, 76)(17, 65)(18, 66)(19, 67)(20, 80)(21, 81)(22, 79)(23, 71)(24, 72)(25, 73)(26, 78)(27, 77)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 91)(34, 83)(35, 92)(36, 84)(37, 85)(38, 98)(39, 99)(40, 100)(41, 87)(42, 88)(43, 90)(44, 104)(45, 105)(46, 106)(47, 95)(48, 96)(49, 97)(50, 108)(51, 107)(52, 103)(53, 101)(54, 102)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.9 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, A^-1 * B, (B^-1, Z), A * Z^-1 * B^-1 * Z, (S * Z)^2, S * A * S * B, Z * B^-1 * Z^-1 * A, Z * B^2 * Z^2, A^9, A * Z^-1 * B^3 * A^2 * Z^-1 * B * Z^-1 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 40, 67, 94, 13, 42, 69, 96, 15, 47, 74, 101, 20, 52, 79, 106, 25, 54, 81, 108, 27, 50, 77, 104, 23, 43, 70, 97, 16, 45, 72, 99, 18, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 41, 68, 95, 14, 46, 73, 100, 19, 48, 75, 102, 21, 53, 80, 107, 26, 49, 76, 103, 22, 51, 78, 105, 24, 44, 71, 98, 17, 36, 63, 90, 9, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 66)(7, 65)(8, 56)(9, 70)(10, 71)(11, 72)(12, 58)(13, 59)(14, 60)(15, 62)(16, 76)(17, 77)(18, 78)(19, 67)(20, 68)(21, 69)(22, 79)(23, 80)(24, 81)(25, 73)(26, 74)(27, 75)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 95)(34, 83)(35, 96)(36, 84)(37, 85)(38, 88)(39, 87)(40, 100)(41, 101)(42, 102)(43, 90)(44, 91)(45, 92)(46, 106)(47, 107)(48, 108)(49, 97)(50, 98)(51, 99)(52, 103)(53, 104)(54, 105)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.10 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, Z^-1 * A^-1, B^-1 * Z^-1, (S * Z)^2, S * A * S * B, B^27, Z^27, Z^13 * A^-14 ]
Map::
	R = (1, 29, 56, 83, 2, 31, 58, 85, 4, 33, 60, 87, 6, 35, 62, 89, 8, 37, 64, 91, 10, 39, 66, 93, 12, 45, 72, 99, 18, 43, 70, 97, 16, 41, 68, 95, 14, 42, 69, 96, 15, 44, 71, 98, 17, 46, 73, 100, 19, 47, 74, 101, 20, 48, 75, 102, 21, 49, 76, 103, 22, 54, 81, 108, 27, 53, 80, 107, 26, 51, 78, 105, 24, 52, 79, 106, 25, 50, 77, 104, 23, 40, 67, 94, 13, 38, 65, 92, 11, 36, 63, 90, 9, 34, 61, 88, 7, 32, 59, 86, 5, 30, 57, 84, 3, 28, 55, 82)
	L = (1, 57)(2, 55)(3, 59)(4, 56)(5, 61)(6, 58)(7, 63)(8, 60)(9, 65)(10, 62)(11, 67)(12, 64)(13, 77)(14, 70)(15, 68)(16, 72)(17, 69)(18, 66)(19, 71)(20, 73)(21, 74)(22, 75)(23, 79)(24, 80)(25, 78)(26, 81)(27, 76)(28, 83)(29, 85)(30, 82)(31, 87)(32, 84)(33, 89)(34, 86)(35, 91)(36, 88)(37, 93)(38, 90)(39, 99)(40, 92)(41, 96)(42, 98)(43, 95)(44, 100)(45, 97)(46, 101)(47, 102)(48, 103)(49, 108)(50, 94)(51, 106)(52, 104)(53, 105)(54, 107)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.11 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, (S * Z)^2, (Z, A^-1), S * B * S * A, Z^2 * A * Z^2, A^5 * Z * A^2, (A^-2 * Z)^3, A^-1 * Z * A^-1 * Z * B^-1 * A^-3 * Z ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 41, 68, 95, 14, 47, 74, 101, 20, 40, 67, 94, 13, 43, 70, 97, 16, 49, 76, 103, 22, 52, 79, 106, 25, 48, 75, 102, 21, 51, 78, 105, 24, 53, 80, 107, 26, 44, 71, 98, 17, 50, 77, 104, 23, 54, 81, 108, 27, 45, 72, 99, 18, 36, 63, 90, 9, 42, 69, 96, 15, 46, 73, 100, 19, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 65)(7, 69)(8, 56)(9, 71)(10, 72)(11, 73)(12, 58)(13, 59)(14, 60)(15, 77)(16, 62)(17, 79)(18, 80)(19, 81)(20, 66)(21, 67)(22, 68)(23, 75)(24, 70)(25, 74)(26, 76)(27, 78)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 95)(34, 83)(35, 97)(36, 84)(37, 85)(38, 87)(39, 101)(40, 102)(41, 103)(42, 88)(43, 105)(44, 90)(45, 91)(46, 92)(47, 106)(48, 104)(49, 107)(50, 96)(51, 108)(52, 98)(53, 99)(54, 100)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.12 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B * A^-1, Z^-1 * B * Z * A^-1, Z^-1 * A * Z * B^-1, S * B * S * A, (S * Z)^2, Z * A^2 * B * A, A^2 * Z * B^2, Z^-1 * B^-1 * Z^-6 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 41, 68, 95, 14, 49, 76, 103, 22, 48, 75, 102, 21, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 43, 70, 97, 16, 51, 78, 105, 24, 53, 80, 107, 26, 45, 72, 99, 18, 36, 63, 90, 9, 40, 67, 94, 13, 44, 71, 98, 17, 52, 79, 106, 25, 54, 81, 108, 27, 46, 73, 100, 19, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 42, 69, 96, 15, 50, 77, 104, 23, 47, 74, 101, 20, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 69)(7, 67)(8, 56)(9, 66)(10, 72)(11, 73)(12, 58)(13, 59)(14, 77)(15, 71)(16, 60)(17, 62)(18, 75)(19, 80)(20, 81)(21, 65)(22, 74)(23, 79)(24, 68)(25, 70)(26, 76)(27, 78)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 97)(34, 83)(35, 98)(36, 84)(37, 85)(38, 102)(39, 90)(40, 88)(41, 105)(42, 87)(43, 106)(44, 96)(45, 91)(46, 92)(47, 103)(48, 99)(49, 107)(50, 95)(51, 108)(52, 104)(53, 100)(54, 101)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.13 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {27, 27})
Quotient :: toric
Aut^+ = C27 (small group id <27, 1>)
Aut   = D54 (small group id <54, 1>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, (A^-1, Z^-1), Z^-1 * A * Z * B^-1, A^-1 * Z^-1 * B * Z, S * B * S * A, (S * Z)^2, Z^2 * B * A * Z * B, Z * B^-2 * Z * B^-1 * Z * B^-2 * Z, Z^3 * B^-5 * Z, Z^27 ]
Map::
	R = (1, 29, 56, 83, 2, 33, 60, 87, 6, 41, 68, 95, 14, 49, 76, 103, 22, 54, 81, 108, 27, 47, 74, 101, 20, 36, 63, 90, 9, 44, 71, 98, 17, 39, 66, 93, 12, 32, 59, 86, 5, 35, 62, 89, 8, 43, 70, 97, 16, 50, 77, 104, 23, 52, 79, 106, 25, 48, 75, 102, 21, 37, 64, 91, 10, 30, 57, 84, 3, 34, 61, 88, 7, 42, 69, 96, 15, 40, 67, 94, 13, 45, 72, 99, 18, 51, 78, 105, 24, 53, 80, 107, 26, 46, 73, 100, 19, 38, 65, 92, 11, 31, 58, 85, 4, 28, 55, 82)
	L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 69)(7, 71)(8, 56)(9, 73)(10, 74)(11, 75)(12, 58)(13, 59)(14, 67)(15, 66)(16, 60)(17, 65)(18, 62)(19, 79)(20, 80)(21, 81)(22, 72)(23, 68)(24, 70)(25, 76)(26, 77)(27, 78)(28, 86)(29, 89)(30, 82)(31, 93)(32, 94)(33, 97)(34, 83)(35, 99)(36, 84)(37, 85)(38, 98)(39, 96)(40, 95)(41, 104)(42, 87)(43, 105)(44, 88)(45, 103)(46, 90)(47, 91)(48, 92)(49, 106)(50, 107)(51, 108)(52, 100)(53, 101)(54, 102)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.14 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = C4 x D14 (small group id <56, 4>)
|r| :: 2
Presentation :: [ S^2, A^-1 * B^-1, Z * A^-1 * Z^-1 * B^-1, S * A * S * B, (S * Z)^2, Z * B^-1 * Z^-1 * A^-1, B * A^-3, Z^3 * A^-1 * Z^4 * A^-1, Z^3 * B^-1 * Z^4 * B^-1, Z^14 ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 41, 69, 97, 13, 49, 77, 105, 21, 53, 81, 109, 25, 45, 73, 101, 17, 37, 65, 93, 9, 44, 72, 100, 16, 52, 80, 108, 24, 56, 84, 112, 28, 48, 76, 104, 20, 40, 68, 96, 12, 33, 61, 89, 5, 29, 57, 85)(3, 35, 63, 91, 7, 42, 70, 98, 14, 50, 78, 106, 22, 55, 83, 111, 27, 47, 75, 103, 19, 39, 67, 95, 11, 32, 60, 88, 4, 36, 64, 92, 8, 43, 71, 99, 15, 51, 79, 107, 23, 54, 82, 110, 26, 46, 74, 102, 18, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 65)(4, 57)(5, 66)(6, 70)(7, 72)(8, 58)(9, 60)(10, 73)(11, 61)(12, 74)(13, 78)(14, 80)(15, 62)(16, 64)(17, 67)(18, 81)(19, 68)(20, 82)(21, 83)(22, 84)(23, 69)(24, 71)(25, 75)(26, 77)(27, 76)(28, 79)(29, 87)(30, 91)(31, 93)(32, 85)(33, 94)(34, 98)(35, 100)(36, 86)(37, 88)(38, 101)(39, 89)(40, 102)(41, 106)(42, 108)(43, 90)(44, 92)(45, 95)(46, 109)(47, 96)(48, 110)(49, 111)(50, 112)(51, 97)(52, 99)(53, 103)(54, 105)(55, 104)(56, 107)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.15 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = C4 x D14 (small group id <56, 4>)
|r| :: 2
Presentation :: [ S^2, Z * A^2, Z * B^2, (B^-1, A), (A^-1 * B)^2, S * B * S * A, (S * Z)^2, B * Z^-2 * A * Z^-4 ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 36, 64, 92, 8, 45, 73, 101, 17, 53, 81, 109, 25, 49, 77, 105, 21, 39, 67, 95, 11, 41, 69, 97, 13, 44, 72, 100, 16, 48, 76, 104, 20, 56, 84, 112, 28, 52, 80, 108, 24, 43, 71, 99, 15, 33, 61, 89, 5, 29, 57, 85)(3, 34, 62, 90, 6, 37, 65, 93, 9, 46, 74, 102, 18, 54, 82, 110, 26, 51, 79, 107, 23, 42, 70, 98, 14, 32, 60, 88, 4, 35, 63, 91, 7, 38, 66, 94, 10, 47, 75, 103, 19, 55, 83, 111, 27, 50, 78, 106, 22, 40, 68, 96, 12, 31, 59, 87)
	L = (1, 59)(2, 62)(3, 61)(4, 67)(5, 68)(6, 57)(7, 69)(8, 65)(9, 58)(10, 72)(11, 70)(12, 71)(13, 60)(14, 77)(15, 78)(16, 63)(17, 74)(18, 64)(19, 76)(20, 66)(21, 79)(22, 80)(23, 81)(24, 83)(25, 82)(26, 73)(27, 84)(28, 75)(29, 91)(30, 94)(31, 97)(32, 85)(33, 88)(34, 100)(35, 86)(36, 103)(37, 104)(38, 92)(39, 87)(40, 95)(41, 90)(42, 89)(43, 98)(44, 93)(45, 111)(46, 112)(47, 101)(48, 102)(49, 96)(50, 105)(51, 99)(52, 107)(53, 106)(54, 108)(55, 109)(56, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.16 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = C4 x D14 (small group id <56, 4>)
|r| :: 2
Presentation :: [ S^2, (B * A^-1)^2, A^-1 * B^2 * A^-1, (B^-1, Z^-1), (B, A), (S * Z)^2, (A^-1, Z^-1), S * A * S * B, A^-1 * Z * B^-1 * A^-2, B^2 * Z^-1 * B * A, Z * A * Z * A * Z, B^-3 * Z * A^-1, Z * B * Z^2 * B ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 36, 64, 92, 8, 49, 77, 105, 21, 42, 70, 98, 14, 53, 81, 109, 25, 55, 83, 111, 27, 44, 72, 100, 16, 54, 82, 110, 26, 56, 84, 112, 28, 50, 78, 106, 22, 41, 69, 97, 13, 46, 74, 102, 18, 33, 61, 89, 5, 29, 57, 85)(3, 37, 65, 93, 9, 47, 75, 103, 19, 34, 62, 90, 6, 39, 67, 95, 11, 51, 79, 107, 23, 45, 73, 101, 17, 32, 60, 88, 4, 38, 66, 94, 10, 48, 76, 104, 20, 35, 63, 91, 7, 40, 68, 96, 12, 52, 80, 108, 24, 43, 71, 99, 15, 31, 59, 87)
	L = (1, 59)(2, 65)(3, 69)(4, 70)(5, 71)(6, 57)(7, 72)(8, 75)(9, 74)(10, 81)(11, 58)(12, 82)(13, 68)(14, 67)(15, 78)(16, 60)(17, 77)(18, 80)(19, 61)(20, 83)(21, 62)(22, 63)(23, 64)(24, 84)(25, 79)(26, 66)(27, 73)(28, 76)(29, 91)(30, 96)(31, 100)(32, 85)(33, 104)(34, 106)(35, 105)(36, 108)(37, 110)(38, 86)(39, 97)(40, 98)(41, 88)(42, 87)(43, 111)(44, 90)(45, 89)(46, 94)(47, 112)(48, 92)(49, 99)(50, 101)(51, 102)(52, 109)(53, 93)(54, 95)(55, 103)(56, 107)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.17 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ A^2, B^2, S^2, Z * B * Z^-1 * B, S * A * S * B, Z^-1 * A * Z * A, (S * Z)^2, (B * A)^2, Z^2 * B * Z^5 * A, Z^-4 * A * Z^2 * B * A * Z^2 * B ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 41, 69, 97, 13, 49, 77, 105, 21, 53, 81, 109, 25, 45, 73, 101, 17, 37, 65, 93, 9, 44, 72, 100, 16, 52, 80, 108, 24, 56, 84, 112, 28, 48, 76, 104, 20, 40, 68, 96, 12, 33, 61, 89, 5, 29, 57, 85)(3, 35, 63, 91, 7, 42, 70, 98, 14, 50, 78, 106, 22, 55, 83, 111, 27, 47, 75, 103, 19, 39, 67, 95, 11, 32, 60, 88, 4, 36, 64, 92, 8, 43, 71, 99, 15, 51, 79, 107, 23, 54, 82, 110, 26, 46, 74, 102, 18, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 57)(4, 65)(5, 66)(6, 70)(7, 58)(8, 72)(9, 60)(10, 61)(11, 73)(12, 74)(13, 78)(14, 62)(15, 80)(16, 64)(17, 67)(18, 68)(19, 81)(20, 82)(21, 83)(22, 69)(23, 84)(24, 71)(25, 75)(26, 76)(27, 77)(28, 79)(29, 88)(30, 92)(31, 93)(32, 85)(33, 95)(34, 99)(35, 100)(36, 86)(37, 87)(38, 101)(39, 89)(40, 103)(41, 107)(42, 108)(43, 90)(44, 91)(45, 94)(46, 109)(47, 96)(48, 111)(49, 110)(50, 112)(51, 97)(52, 98)(53, 102)(54, 105)(55, 104)(56, 106)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.18 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ S^2, B^-2 * A^2, Z^-2 * B^-2, (B, A^-1), (Z^-1, B), (A, Z^-1), Z^-1 * A^-2 * Z^-1, S * B * S * A, (S * Z)^2, A^-1 * Z * B^-1 * A * Z^-1 * B, B^-2 * A^-1 * B^-1 * Z * A^-2, B^14 ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 36, 64, 92, 8, 47, 75, 103, 19, 56, 84, 112, 28, 42, 70, 98, 14, 50, 78, 106, 22, 44, 72, 100, 16, 51, 79, 107, 23, 46, 74, 102, 18, 52, 80, 108, 24, 55, 83, 111, 27, 41, 69, 97, 13, 33, 61, 89, 5, 29, 57, 85)(3, 37, 65, 93, 9, 34, 62, 90, 6, 39, 67, 95, 11, 48, 76, 104, 20, 54, 82, 110, 26, 45, 73, 101, 17, 32, 60, 88, 4, 38, 66, 94, 10, 35, 63, 91, 7, 40, 68, 96, 12, 49, 77, 105, 21, 53, 81, 109, 25, 43, 71, 99, 15, 31, 59, 87)
	L = (1, 59)(2, 65)(3, 69)(4, 70)(5, 71)(6, 57)(7, 72)(8, 62)(9, 61)(10, 78)(11, 58)(12, 79)(13, 81)(14, 82)(15, 83)(16, 60)(17, 84)(18, 63)(19, 67)(20, 64)(21, 74)(22, 73)(23, 66)(24, 68)(25, 80)(26, 75)(27, 77)(28, 76)(29, 91)(30, 96)(31, 100)(32, 85)(33, 94)(34, 102)(35, 92)(36, 105)(37, 107)(38, 86)(39, 108)(40, 103)(41, 88)(42, 87)(43, 106)(44, 90)(45, 89)(46, 104)(47, 109)(48, 111)(49, 112)(50, 93)(51, 95)(52, 110)(53, 98)(54, 97)(55, 101)(56, 99)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.19 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ S^2, Z * A * B, Z * B * A, A * B^-2 * A, S * A * S * B, (S * Z)^2, A * Z^-2 * A * Z^-4 ]
Map:: non-degenerate
	R = (1, 30, 58, 86, 2, 36, 64, 92, 8, 45, 73, 101, 17, 53, 81, 109, 25, 49, 77, 105, 21, 39, 67, 95, 11, 41, 69, 97, 13, 44, 72, 100, 16, 48, 76, 104, 20, 56, 84, 112, 28, 52, 80, 108, 24, 43, 71, 99, 15, 33, 61, 89, 5, 29, 57, 85)(3, 35, 63, 91, 7, 38, 66, 94, 10, 47, 75, 103, 19, 55, 83, 111, 27, 51, 79, 107, 23, 42, 70, 98, 14, 32, 60, 88, 4, 34, 62, 90, 6, 37, 65, 93, 9, 46, 74, 102, 18, 54, 82, 110, 26, 50, 78, 106, 22, 40, 68, 96, 12, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 67)(4, 61)(5, 68)(6, 57)(7, 69)(8, 66)(9, 58)(10, 72)(11, 70)(12, 77)(13, 60)(14, 71)(15, 78)(16, 62)(17, 75)(18, 64)(19, 76)(20, 65)(21, 79)(22, 81)(23, 80)(24, 82)(25, 83)(26, 73)(27, 84)(28, 74)(29, 91)(30, 94)(31, 97)(32, 85)(33, 87)(34, 86)(35, 100)(36, 103)(37, 92)(38, 104)(39, 88)(40, 95)(41, 90)(42, 89)(43, 96)(44, 93)(45, 111)(46, 101)(47, 112)(48, 102)(49, 98)(50, 105)(51, 99)(52, 106)(53, 107)(54, 109)(55, 108)(56, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.20 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, Z^-1 * A * Z * B^-1, A^4, Z^-1 * B * Z * A^-1, (S * Z)^2, S * A * S * B, A^-2 * Z * A^-2 * Z^-1, Z^3 * B * Z * A * Z^3, Z^3 * B^-1 * Z^3 * B^-1 * Z ]
Map::
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 41, 69, 97, 13, 49, 77, 105, 21, 53, 81, 109, 25, 45, 73, 101, 17, 37, 65, 93, 9, 44, 72, 100, 16, 52, 80, 108, 24, 55, 83, 111, 27, 47, 75, 103, 19, 39, 67, 95, 11, 32, 60, 88, 4, 29, 57, 85)(3, 35, 63, 91, 7, 42, 70, 98, 14, 50, 78, 106, 22, 56, 84, 112, 28, 48, 76, 104, 20, 40, 68, 96, 12, 33, 61, 89, 5, 36, 64, 92, 8, 43, 71, 99, 15, 51, 79, 107, 23, 54, 82, 110, 26, 46, 74, 102, 18, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 70)(7, 72)(8, 58)(9, 61)(10, 73)(11, 74)(12, 60)(13, 78)(14, 80)(15, 62)(16, 64)(17, 68)(18, 81)(19, 82)(20, 67)(21, 84)(22, 83)(23, 69)(24, 71)(25, 76)(26, 77)(27, 79)(28, 75)(29, 89)(30, 92)(31, 85)(32, 96)(33, 93)(34, 99)(35, 86)(36, 100)(37, 87)(38, 88)(39, 104)(40, 101)(41, 107)(42, 90)(43, 108)(44, 91)(45, 94)(46, 95)(47, 112)(48, 109)(49, 110)(50, 97)(51, 111)(52, 98)(53, 102)(54, 103)(55, 106)(56, 105)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.21 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, A * B * Z, Z * B * A, S * A * S * B, (S * Z)^2, Z^14, B^28 ]
Map::
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 38, 66, 94, 10, 42, 70, 98, 14, 46, 74, 102, 18, 50, 78, 106, 22, 54, 82, 110, 26, 53, 81, 109, 25, 49, 77, 105, 21, 45, 73, 101, 17, 41, 69, 97, 13, 37, 65, 93, 9, 32, 60, 88, 4, 29, 57, 85)(3, 33, 61, 89, 5, 35, 63, 91, 7, 39, 67, 95, 11, 43, 71, 99, 15, 47, 75, 103, 19, 51, 79, 107, 23, 55, 83, 111, 27, 56, 84, 112, 28, 52, 80, 108, 24, 48, 76, 104, 20, 44, 72, 100, 16, 40, 68, 96, 12, 36, 64, 92, 8, 31, 59, 87)
	L = (1, 59)(2, 61)(3, 60)(4, 64)(5, 57)(6, 63)(7, 58)(8, 65)(9, 68)(10, 67)(11, 62)(12, 69)(13, 72)(14, 71)(15, 66)(16, 73)(17, 76)(18, 75)(19, 70)(20, 77)(21, 80)(22, 79)(23, 74)(24, 81)(25, 84)(26, 83)(27, 78)(28, 82)(29, 89)(30, 91)(31, 85)(32, 87)(33, 86)(34, 95)(35, 90)(36, 88)(37, 92)(38, 99)(39, 94)(40, 93)(41, 96)(42, 103)(43, 98)(44, 97)(45, 100)(46, 107)(47, 102)(48, 101)(49, 104)(50, 111)(51, 106)(52, 105)(53, 108)(54, 112)(55, 110)(56, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.22 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ S^2, A * B^-1, S * A * S * B, (S * Z)^2, A * Z^-1 * B^-1 * Z, Z * B^-1 * Z^-1 * A, Z * B^2 * Z^2, Z^-1 * B^8 * Z^-1, A * Z^-1 * B^3 * A^3 * Z^-1 * B ]
Map::
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 41, 69, 97, 13, 43, 71, 99, 15, 48, 76, 104, 20, 53, 81, 109, 25, 55, 83, 111, 27, 50, 78, 106, 22, 52, 80, 108, 24, 45, 73, 101, 17, 37, 65, 93, 9, 39, 67, 95, 11, 32, 60, 88, 4, 29, 57, 85)(3, 35, 63, 91, 7, 40, 68, 96, 12, 33, 61, 89, 5, 36, 64, 92, 8, 42, 70, 98, 14, 47, 75, 103, 19, 49, 77, 105, 21, 54, 82, 110, 26, 56, 84, 112, 28, 51, 79, 107, 23, 44, 72, 100, 16, 46, 74, 102, 18, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 68)(7, 67)(8, 58)(9, 72)(10, 73)(11, 74)(12, 60)(13, 61)(14, 62)(15, 64)(16, 78)(17, 79)(18, 80)(19, 69)(20, 70)(21, 71)(22, 82)(23, 83)(24, 84)(25, 75)(26, 76)(27, 77)(28, 81)(29, 89)(30, 92)(31, 85)(32, 96)(33, 97)(34, 98)(35, 86)(36, 99)(37, 87)(38, 88)(39, 91)(40, 90)(41, 103)(42, 104)(43, 105)(44, 93)(45, 94)(46, 95)(47, 109)(48, 110)(49, 111)(50, 100)(51, 101)(52, 102)(53, 112)(54, 106)(55, 107)(56, 108)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.23 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ A^2, S^2, B^-1 * A, Z^-1 * A * Z * B^-1, (S * Z)^2, Z^-1 * B * Z * A, S * B * S * A, Z^14 ]
Map::
	R = (1, 30, 58, 86, 2, 33, 61, 89, 5, 37, 65, 93, 9, 41, 69, 97, 13, 45, 73, 101, 17, 49, 77, 105, 21, 53, 81, 109, 25, 52, 80, 108, 24, 48, 76, 104, 20, 44, 72, 100, 16, 40, 68, 96, 12, 36, 64, 92, 8, 32, 60, 88, 4, 29, 57, 85)(3, 34, 62, 90, 6, 38, 66, 94, 10, 42, 70, 98, 14, 46, 74, 102, 18, 50, 78, 106, 22, 54, 82, 110, 26, 56, 84, 112, 28, 55, 83, 111, 27, 51, 79, 107, 23, 47, 75, 103, 19, 43, 71, 99, 15, 39, 67, 95, 11, 35, 63, 91, 7, 31, 59, 87)
	L = (1, 59)(2, 62)(3, 57)(4, 63)(5, 66)(6, 58)(7, 60)(8, 67)(9, 70)(10, 61)(11, 64)(12, 71)(13, 74)(14, 65)(15, 68)(16, 75)(17, 78)(18, 69)(19, 72)(20, 79)(21, 82)(22, 73)(23, 76)(24, 83)(25, 84)(26, 77)(27, 80)(28, 81)(29, 87)(30, 90)(31, 85)(32, 91)(33, 94)(34, 86)(35, 88)(36, 95)(37, 98)(38, 89)(39, 92)(40, 99)(41, 102)(42, 93)(43, 96)(44, 103)(45, 106)(46, 97)(47, 100)(48, 107)(49, 110)(50, 101)(51, 104)(52, 111)(53, 112)(54, 105)(55, 108)(56, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.24 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ S^2, B * A^-1, A * B^-1, (A * Z)^2, S * B * S * A, Z^-2 * A^-2, (S * Z)^2, Z^-2 * A^6 * Z^-6, A^14 ]
Map::
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 39, 67, 95, 11, 43, 71, 99, 15, 47, 75, 103, 19, 51, 79, 107, 23, 55, 83, 111, 27, 53, 81, 109, 25, 50, 78, 106, 22, 45, 73, 101, 17, 42, 70, 98, 14, 37, 65, 93, 9, 32, 60, 88, 4, 29, 57, 85)(3, 35, 63, 91, 7, 33, 61, 89, 5, 36, 64, 92, 8, 40, 68, 96, 12, 44, 72, 100, 16, 48, 76, 104, 20, 52, 80, 108, 24, 56, 84, 112, 28, 54, 82, 110, 26, 49, 77, 105, 21, 46, 74, 102, 18, 41, 69, 97, 13, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 61)(7, 60)(8, 58)(9, 69)(10, 70)(11, 64)(12, 62)(13, 73)(14, 74)(15, 68)(16, 67)(17, 77)(18, 78)(19, 72)(20, 71)(21, 81)(22, 82)(23, 76)(24, 75)(25, 84)(26, 83)(27, 80)(28, 79)(29, 89)(30, 92)(31, 85)(32, 91)(33, 90)(34, 96)(35, 86)(36, 95)(37, 87)(38, 88)(39, 100)(40, 99)(41, 93)(42, 94)(43, 104)(44, 103)(45, 97)(46, 98)(47, 108)(48, 107)(49, 101)(50, 102)(51, 112)(52, 111)(53, 105)(54, 106)(55, 110)(56, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.25 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {14, 14})
Quotient :: toric
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, (Z, A^-1), S * B * S * A, (S * Z)^2, Z^-1 * A^-1 * Z^-1 * A^-3, Z^-1 * A * Z^-1 * A * Z^-4 ]
Map::
	R = (1, 30, 58, 86, 2, 34, 62, 90, 6, 42, 70, 98, 14, 51, 79, 107, 23, 48, 76, 104, 20, 37, 65, 93, 9, 45, 73, 101, 17, 41, 69, 97, 13, 46, 74, 102, 18, 54, 82, 110, 26, 50, 78, 106, 22, 39, 67, 95, 11, 32, 60, 88, 4, 29, 57, 85)(3, 35, 63, 91, 7, 43, 71, 99, 15, 52, 80, 108, 24, 56, 84, 112, 28, 55, 83, 111, 27, 47, 75, 103, 19, 40, 68, 96, 12, 33, 61, 89, 5, 36, 64, 92, 8, 44, 72, 100, 16, 53, 81, 109, 25, 49, 77, 105, 21, 38, 66, 94, 10, 31, 59, 87)
	L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 71)(7, 73)(8, 58)(9, 75)(10, 76)(11, 77)(12, 60)(13, 61)(14, 80)(15, 69)(16, 62)(17, 68)(18, 64)(19, 67)(20, 83)(21, 79)(22, 81)(23, 84)(24, 74)(25, 70)(26, 72)(27, 78)(28, 82)(29, 89)(30, 92)(31, 85)(32, 96)(33, 97)(34, 100)(35, 86)(36, 102)(37, 87)(38, 88)(39, 103)(40, 101)(41, 99)(42, 109)(43, 90)(44, 110)(45, 91)(46, 108)(47, 93)(48, 94)(49, 95)(50, 111)(51, 105)(52, 98)(53, 106)(54, 112)(55, 104)(56, 107)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.26 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {5, 15})
Quotient :: toric
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ A^2, S^2, B^2, S * B * S * A, Z^-1 * B * Z * B, Z^-1 * A * Z * A, (S * Z)^2, Z^5, (B * A)^3, (B * Z^-1 * A)^15 ]
Map:: non-degenerate
	R = (1, 32, 62, 92, 2, 36, 66, 96, 6, 43, 73, 103, 13, 35, 65, 95, 5, 31, 61, 91)(3, 37, 67, 97, 7, 44, 74, 104, 14, 50, 80, 110, 20, 40, 70, 100, 10, 33, 63, 93)(4, 38, 68, 98, 8, 45, 75, 105, 15, 52, 82, 112, 22, 42, 72, 102, 12, 34, 64, 94)(9, 46, 76, 106, 16, 53, 83, 113, 23, 57, 87, 117, 27, 49, 79, 109, 19, 39, 69, 99)(11, 47, 77, 107, 17, 54, 84, 114, 24, 58, 88, 118, 28, 51, 81, 111, 21, 41, 71, 101)(18, 55, 85, 115, 25, 59, 89, 119, 29, 60, 90, 120, 30, 56, 86, 116, 26, 48, 78, 108)
	L = (1, 63)(2, 67)(3, 61)(4, 71)(5, 70)(6, 74)(7, 62)(8, 77)(9, 78)(10, 65)(11, 64)(12, 81)(13, 80)(14, 66)(15, 84)(16, 85)(17, 68)(18, 69)(19, 86)(20, 73)(21, 72)(22, 88)(23, 89)(24, 75)(25, 76)(26, 79)(27, 90)(28, 82)(29, 83)(30, 87)(31, 94)(32, 98)(33, 99)(34, 91)(35, 102)(36, 105)(37, 106)(38, 92)(39, 93)(40, 109)(41, 108)(42, 95)(43, 112)(44, 113)(45, 96)(46, 97)(47, 115)(48, 101)(49, 100)(50, 117)(51, 116)(52, 103)(53, 104)(54, 119)(55, 107)(56, 111)(57, 110)(58, 120)(59, 114)(60, 118)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.28
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.27 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {5, 15})
Quotient :: toric
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ S^2, (A^-1, Z^-1), (A * Z)^2, Z^-1 * B^-2 * Z^-1, A^-2 * B^2, S * A * S * B, Z^2 * A^2, (S * Z)^2, (B^-1 * Z^-1)^2, A^-1 * Z * B^-2 * A^-1, Z^-1 * B * Z^-1 * B * Z^-1, B * A^-1 * B * A * B^-1 * A^-1, (Z^-1 * B^-1 * A)^15 ]
Map:: non-degenerate
	R = (1, 32, 62, 92, 2, 38, 68, 98, 8, 43, 73, 103, 13, 35, 65, 95, 5, 31, 61, 91)(3, 39, 69, 99, 9, 36, 66, 96, 6, 41, 71, 101, 11, 45, 75, 105, 15, 33, 63, 93)(4, 40, 70, 100, 10, 37, 67, 97, 7, 42, 72, 102, 12, 48, 78, 108, 18, 34, 64, 94)(14, 52, 82, 112, 22, 46, 76, 106, 16, 53, 83, 113, 23, 50, 80, 110, 20, 44, 74, 104)(17, 54, 84, 114, 24, 49, 79, 109, 19, 55, 85, 115, 25, 51, 81, 111, 21, 47, 77, 107)(26, 59, 89, 119, 29, 57, 87, 117, 27, 60, 90, 120, 30, 58, 88, 118, 28, 56, 86, 116)
	L = (1, 63)(2, 69)(3, 73)(4, 77)(5, 75)(6, 61)(7, 79)(8, 66)(9, 65)(10, 84)(11, 62)(12, 85)(13, 71)(14, 86)(15, 68)(16, 87)(17, 72)(18, 81)(19, 64)(20, 88)(21, 67)(22, 89)(23, 90)(24, 78)(25, 70)(26, 83)(27, 74)(28, 76)(29, 80)(30, 82)(31, 97)(32, 102)(33, 106)(34, 91)(35, 100)(36, 110)(37, 98)(38, 108)(39, 113)(40, 92)(41, 104)(42, 103)(43, 94)(44, 93)(45, 112)(46, 96)(47, 117)(48, 95)(49, 118)(50, 105)(51, 119)(52, 99)(53, 101)(54, 120)(55, 116)(56, 107)(57, 109)(58, 111)(59, 114)(60, 115)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.29
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.28 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {5, 15})
Quotient :: toric
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ B^2, S^2, A^2, A * Z * B * Z^-1, S * A * S * B, (S * Z)^2, B * A * B * Z * A * Z^-1, B * Z * A * B * A * Z^-1, B * A * B * Z^-1 * B * Z, Z^5 * B * A ]
Map:: non-degenerate
	R = (1, 32, 62, 92, 2, 36, 66, 96, 6, 46, 76, 106, 16, 53, 83, 113, 23, 39, 69, 99, 9, 49, 79, 109, 19, 59, 89, 119, 29, 60, 90, 120, 30, 54, 84, 114, 24, 42, 72, 102, 12, 52, 82, 112, 22, 58, 88, 118, 28, 45, 75, 105, 15, 35, 65, 95, 5, 31, 61, 91)(3, 38, 68, 98, 8, 51, 81, 111, 21, 56, 86, 116, 26, 43, 73, 103, 13, 34, 64, 94, 4, 41, 71, 101, 11, 47, 77, 107, 17, 57, 87, 117, 27, 44, 74, 104, 14, 50, 80, 110, 20, 37, 67, 97, 7, 48, 78, 108, 18, 55, 85, 115, 25, 40, 70, 100, 10, 33, 63, 93)
	L = (1, 63)(2, 67)(3, 61)(4, 72)(5, 73)(6, 77)(7, 62)(8, 82)(9, 80)(10, 83)(11, 79)(12, 64)(13, 65)(14, 84)(15, 87)(16, 86)(17, 66)(18, 88)(19, 71)(20, 69)(21, 89)(22, 68)(23, 70)(24, 74)(25, 90)(26, 76)(27, 75)(28, 78)(29, 81)(30, 85)(31, 94)(32, 98)(33, 99)(34, 91)(35, 104)(36, 108)(37, 109)(38, 92)(39, 93)(40, 114)(41, 112)(42, 110)(43, 113)(44, 95)(45, 115)(46, 117)(47, 119)(48, 96)(49, 97)(50, 102)(51, 118)(52, 101)(53, 103)(54, 100)(55, 105)(56, 120)(57, 106)(58, 111)(59, 107)(60, 116)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.26
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.29 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {5, 15})
Quotient :: toric
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ S^2, (B * Z)^2, A^-1 * B^-1 * Z^-2, (A^-1 * Z^-1)^2, Z * B^-1 * Z^-1 * A, S * A * S * B, (S * Z)^2, B * A^-2 * B, A^-1 * B^-1 * Z * A^-2, A^-1 * Z * A^-1 * B^-1 * A^-1, Z^-1 * B^-1 * Z^2 * A * Z^-1, B^20 ]
Map:: non-degenerate
	R = (1, 32, 62, 92, 2, 38, 68, 98, 8, 43, 73, 103, 13, 56, 86, 116, 26, 46, 76, 106, 16, 59, 89, 119, 29, 54, 84, 114, 24, 44, 74, 104, 14, 57, 87, 117, 27, 50, 80, 110, 20, 60, 90, 120, 30, 52, 82, 112, 22, 48, 78, 108, 18, 35, 65, 95, 5, 31, 61, 91)(3, 40, 70, 100, 10, 37, 67, 97, 7, 53, 83, 113, 23, 49, 79, 109, 19, 34, 64, 94, 4, 47, 77, 107, 17, 55, 85, 115, 25, 41, 71, 101, 11, 51, 81, 111, 21, 58, 88, 118, 28, 39, 69, 99, 9, 36, 66, 96, 6, 42, 72, 102, 12, 45, 75, 105, 15, 33, 63, 93)
	L = (1, 63)(2, 69)(3, 73)(4, 78)(5, 79)(6, 61)(7, 80)(8, 85)(9, 86)(10, 65)(11, 62)(12, 90)(13, 83)(14, 72)(15, 84)(16, 88)(17, 87)(18, 71)(19, 68)(20, 64)(21, 82)(22, 66)(23, 89)(24, 67)(25, 76)(26, 75)(27, 81)(28, 74)(29, 77)(30, 70)(31, 97)(32, 102)(33, 106)(34, 91)(35, 107)(36, 98)(37, 112)(38, 111)(39, 119)(40, 92)(41, 103)(42, 108)(43, 94)(44, 93)(45, 117)(46, 96)(47, 120)(48, 118)(49, 116)(50, 115)(51, 95)(52, 105)(53, 104)(54, 109)(55, 114)(56, 100)(57, 99)(58, 110)(59, 101)(60, 113)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.27
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.30 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {3, 3})
Quotient :: toric
Aut^+ = C39 (small group id <39, 2>)
Aut   = C13 x S3 (small group id <78, 3>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A^-1, Z^3, (Z, B^-1), S * B * S * A, (Z, A^-1), (S * Z)^2, A^7 * B^-6 ]
Map:: non-degenerate
	R = (1, 41, 80, 119, 2, 44, 83, 122, 5, 40, 79, 118)(3, 45, 84, 123, 6, 48, 87, 126, 9, 42, 81, 120)(4, 46, 85, 124, 7, 50, 89, 128, 11, 43, 82, 121)(8, 51, 90, 129, 12, 54, 93, 132, 15, 47, 86, 125)(10, 52, 91, 130, 13, 56, 95, 134, 17, 49, 88, 127)(14, 57, 96, 135, 18, 60, 99, 138, 21, 53, 92, 131)(16, 58, 97, 136, 19, 62, 101, 140, 23, 55, 94, 133)(20, 63, 102, 141, 24, 66, 105, 144, 27, 59, 98, 137)(22, 64, 103, 142, 25, 68, 107, 146, 29, 61, 100, 139)(26, 69, 108, 147, 30, 72, 111, 150, 33, 65, 104, 143)(28, 70, 109, 148, 31, 74, 113, 152, 35, 67, 106, 145)(32, 75, 114, 153, 36, 77, 116, 155, 38, 71, 110, 149)(34, 76, 115, 154, 37, 78, 117, 156, 39, 73, 112, 151)
	L = (1, 81)(2, 84)(3, 86)(4, 79)(5, 87)(6, 90)(7, 80)(8, 92)(9, 93)(10, 82)(11, 83)(12, 96)(13, 85)(14, 98)(15, 99)(16, 88)(17, 89)(18, 102)(19, 91)(20, 104)(21, 105)(22, 94)(23, 95)(24, 108)(25, 97)(26, 110)(27, 111)(28, 100)(29, 101)(30, 114)(31, 103)(32, 112)(33, 116)(34, 106)(35, 107)(36, 115)(37, 109)(38, 117)(39, 113)(40, 120)(41, 123)(42, 125)(43, 118)(44, 126)(45, 129)(46, 119)(47, 131)(48, 132)(49, 121)(50, 122)(51, 135)(52, 124)(53, 137)(54, 138)(55, 127)(56, 128)(57, 141)(58, 130)(59, 143)(60, 144)(61, 133)(62, 134)(63, 147)(64, 136)(65, 149)(66, 150)(67, 139)(68, 140)(69, 153)(70, 142)(71, 151)(72, 155)(73, 145)(74, 146)(75, 154)(76, 148)(77, 156)(78, 152)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.31 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {3, 3})
Quotient :: toric
Aut^+ = C39 (small group id <39, 2>)
Aut   = D78 (small group id <78, 5>)
|r| :: 2
Presentation :: [ S^2, B^-1 * A, Z^3, S * A * S * B, (S * Z)^2, (A, Z^-1), A^6 * B * A^6 ]
Map::
	R = (1, 41, 80, 119, 2, 43, 82, 121, 4, 40, 79, 118)(3, 45, 84, 123, 6, 48, 87, 126, 9, 42, 81, 120)(5, 46, 85, 124, 7, 49, 88, 127, 10, 44, 83, 122)(8, 51, 90, 129, 12, 54, 93, 132, 15, 47, 86, 125)(11, 52, 91, 130, 13, 55, 94, 133, 16, 50, 89, 128)(14, 57, 96, 135, 18, 60, 99, 138, 21, 53, 92, 131)(17, 58, 97, 136, 19, 61, 100, 139, 22, 56, 95, 134)(20, 63, 102, 141, 24, 66, 105, 144, 27, 59, 98, 137)(23, 64, 103, 142, 25, 67, 106, 145, 28, 62, 101, 140)(26, 69, 108, 147, 30, 72, 111, 150, 33, 65, 104, 143)(29, 70, 109, 148, 31, 73, 112, 151, 34, 68, 107, 146)(32, 75, 114, 153, 36, 77, 116, 155, 38, 71, 110, 149)(35, 76, 115, 154, 37, 78, 117, 156, 39, 74, 113, 152)
	L = (1, 81)(2, 84)(3, 86)(4, 87)(5, 79)(6, 90)(7, 80)(8, 92)(9, 93)(10, 82)(11, 83)(12, 96)(13, 85)(14, 98)(15, 99)(16, 88)(17, 89)(18, 102)(19, 91)(20, 104)(21, 105)(22, 94)(23, 95)(24, 108)(25, 97)(26, 110)(27, 111)(28, 100)(29, 101)(30, 114)(31, 103)(32, 113)(33, 116)(34, 106)(35, 107)(36, 115)(37, 109)(38, 117)(39, 112)(40, 122)(41, 124)(42, 118)(43, 127)(44, 128)(45, 119)(46, 130)(47, 120)(48, 121)(49, 133)(50, 134)(51, 123)(52, 136)(53, 125)(54, 126)(55, 139)(56, 140)(57, 129)(58, 142)(59, 131)(60, 132)(61, 145)(62, 146)(63, 135)(64, 148)(65, 137)(66, 138)(67, 151)(68, 152)(69, 141)(70, 154)(71, 143)(72, 144)(73, 156)(74, 149)(75, 147)(76, 153)(77, 150)(78, 155)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.32 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C13 : C4 (small group id <52, 3>)
Aut   = C2 x (C13 : C4) (small group id <104, 12>)
|r| :: 2
Presentation :: [ Z^2, S^2, B^-1 * A^-1, (S * Z)^2, B^2 * A^-2, S * A * S * B, Z * B * Z * B * Z * A^-1 * Z * A^-1, B * Z * A * Z * A^-1 * B^-1 * Z * A^-1 * Z * A, Z * B * A * Z * B * Z * B^-1 * A^-1 * Z * B^-1, Z * A * Z * B * A^-1 * Z * B * Z * B^-1 * Z * A^-1 ]
Map:: non-degenerate
	R = (1, 54, 106, 158, 2, 53, 105, 157)(3, 59, 111, 163, 7, 55, 107, 159)(4, 61, 113, 165, 9, 56, 108, 160)(5, 62, 114, 166, 10, 57, 109, 161)(6, 64, 116, 168, 12, 58, 110, 162)(8, 67, 119, 171, 15, 60, 112, 164)(11, 72, 124, 176, 20, 63, 115, 167)(13, 74, 126, 178, 22, 65, 117, 169)(14, 76, 128, 180, 24, 66, 118, 170)(16, 79, 131, 183, 27, 68, 120, 172)(17, 70, 122, 174, 18, 69, 121, 173)(19, 82, 134, 186, 30, 71, 123, 175)(21, 85, 137, 189, 33, 73, 125, 177)(23, 87, 139, 191, 35, 75, 127, 179)(25, 89, 141, 193, 37, 77, 129, 181)(26, 91, 143, 195, 39, 78, 130, 182)(28, 93, 145, 197, 41, 80, 132, 184)(29, 88, 140, 192, 36, 81, 133, 185)(31, 94, 146, 198, 42, 83, 135, 187)(32, 92, 144, 196, 40, 84, 136, 188)(34, 96, 148, 200, 44, 86, 138, 190)(38, 99, 151, 203, 47, 90, 142, 194)(43, 100, 152, 204, 48, 95, 147, 199)(45, 102, 154, 206, 50, 97, 149, 201)(46, 101, 153, 205, 49, 98, 150, 202)(51, 104, 156, 208, 52, 103, 155, 207)
	L = (1, 107)(2, 109)(3, 112)(4, 105)(5, 115)(6, 106)(7, 117)(8, 108)(9, 120)(10, 122)(11, 110)(12, 125)(13, 127)(14, 111)(15, 129)(16, 132)(17, 113)(18, 133)(19, 114)(20, 135)(21, 138)(22, 116)(23, 118)(24, 140)(25, 142)(26, 119)(27, 143)(28, 121)(29, 123)(30, 139)(31, 147)(32, 124)(33, 144)(34, 126)(35, 149)(36, 150)(37, 128)(38, 130)(39, 137)(40, 131)(41, 152)(42, 134)(43, 136)(44, 151)(45, 146)(46, 141)(47, 155)(48, 156)(49, 145)(50, 148)(51, 154)(52, 153)(53, 159)(54, 161)(55, 164)(56, 157)(57, 167)(58, 158)(59, 169)(60, 160)(61, 172)(62, 174)(63, 162)(64, 177)(65, 179)(66, 163)(67, 181)(68, 184)(69, 165)(70, 185)(71, 166)(72, 187)(73, 190)(74, 168)(75, 170)(76, 192)(77, 194)(78, 171)(79, 195)(80, 173)(81, 175)(82, 191)(83, 199)(84, 176)(85, 196)(86, 178)(87, 201)(88, 202)(89, 180)(90, 182)(91, 189)(92, 183)(93, 204)(94, 186)(95, 188)(96, 203)(97, 198)(98, 193)(99, 207)(100, 208)(101, 197)(102, 200)(103, 206)(104, 205)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E27.33
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.33 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C13 : C4 (small group id <52, 3>)
Aut   = C2 x (C13 : C4) (small group id <104, 12>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^-1 * B^-1, A^2 * B^-2, S * A * S * B, (A * B^-1)^2, (S * Z)^2, Z * B * Z * B * Z * A^-1 * Z * B, Z * A^2 * Z * A * Z * A^-1 * Z * B^-1 * Z * A^-1, Z * B * Z * A * Z * A^-1 * Z * A^-2 * Z * B^-1 ]
Map:: non-degenerate
	R = (1, 54, 106, 158, 2, 53, 105, 157)(3, 59, 111, 163, 7, 55, 107, 159)(4, 61, 113, 165, 9, 56, 108, 160)(5, 62, 114, 166, 10, 57, 109, 161)(6, 64, 116, 168, 12, 58, 110, 162)(8, 67, 119, 171, 15, 60, 112, 164)(11, 72, 124, 176, 20, 63, 115, 167)(13, 74, 126, 178, 22, 65, 117, 169)(14, 76, 128, 180, 24, 66, 118, 170)(16, 79, 131, 183, 27, 68, 120, 172)(17, 70, 122, 174, 18, 69, 121, 173)(19, 82, 134, 186, 30, 71, 123, 175)(21, 85, 137, 189, 33, 73, 125, 177)(23, 87, 139, 191, 35, 75, 127, 179)(25, 89, 141, 193, 37, 77, 129, 181)(26, 91, 143, 195, 39, 78, 130, 182)(28, 93, 145, 197, 41, 80, 132, 184)(29, 94, 146, 198, 42, 81, 133, 185)(31, 88, 140, 192, 36, 83, 135, 187)(32, 96, 148, 200, 44, 84, 136, 188)(34, 92, 144, 196, 40, 86, 138, 190)(38, 99, 151, 203, 47, 90, 142, 194)(43, 98, 150, 202, 46, 95, 147, 199)(45, 100, 152, 204, 48, 97, 149, 201)(49, 102, 154, 206, 50, 101, 153, 205)(51, 104, 156, 208, 52, 103, 155, 207)
	L = (1, 107)(2, 109)(3, 112)(4, 105)(5, 115)(6, 106)(7, 117)(8, 108)(9, 120)(10, 122)(11, 110)(12, 125)(13, 127)(14, 111)(15, 129)(16, 132)(17, 113)(18, 133)(19, 114)(20, 135)(21, 138)(22, 116)(23, 118)(24, 140)(25, 142)(26, 119)(27, 143)(28, 121)(29, 123)(30, 141)(31, 147)(32, 124)(33, 148)(34, 126)(35, 149)(36, 134)(37, 128)(38, 130)(39, 152)(40, 131)(41, 137)(42, 154)(43, 136)(44, 153)(45, 155)(46, 139)(47, 146)(48, 144)(49, 145)(50, 156)(51, 150)(52, 151)(53, 159)(54, 161)(55, 164)(56, 157)(57, 167)(58, 158)(59, 169)(60, 160)(61, 172)(62, 174)(63, 162)(64, 177)(65, 179)(66, 163)(67, 181)(68, 184)(69, 165)(70, 185)(71, 166)(72, 187)(73, 190)(74, 168)(75, 170)(76, 192)(77, 194)(78, 171)(79, 195)(80, 173)(81, 175)(82, 193)(83, 199)(84, 176)(85, 200)(86, 178)(87, 201)(88, 186)(89, 180)(90, 182)(91, 204)(92, 183)(93, 189)(94, 206)(95, 188)(96, 205)(97, 207)(98, 191)(99, 198)(100, 196)(101, 197)(102, 208)(103, 202)(104, 203)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E27.32
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.34 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = D52 (small group id <52, 4>)
Aut   = C2 x C2 x D26 (small group id <104, 13>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^26 ]
Map::
	R = (1, 54, 106, 158, 2, 53, 105, 157)(3, 57, 109, 161, 5, 55, 107, 159)(4, 58, 110, 162, 6, 56, 108, 160)(7, 61, 113, 165, 9, 59, 111, 163)(8, 62, 114, 166, 10, 60, 112, 164)(11, 65, 117, 169, 13, 63, 115, 167)(12, 66, 118, 170, 14, 64, 116, 168)(15, 75, 127, 179, 23, 67, 119, 171)(16, 77, 129, 181, 25, 68, 120, 172)(17, 79, 131, 183, 27, 69, 121, 173)(18, 81, 133, 185, 29, 70, 122, 174)(19, 83, 135, 187, 31, 71, 123, 175)(20, 85, 137, 189, 33, 72, 124, 176)(21, 87, 139, 191, 35, 73, 125, 177)(22, 89, 141, 193, 37, 74, 126, 178)(24, 91, 143, 195, 39, 76, 128, 180)(26, 93, 145, 197, 41, 78, 130, 182)(28, 95, 147, 199, 43, 80, 132, 184)(30, 97, 149, 201, 45, 82, 134, 186)(32, 99, 151, 203, 47, 84, 136, 188)(34, 101, 153, 205, 49, 86, 138, 190)(36, 103, 155, 207, 51, 88, 140, 192)(38, 104, 156, 208, 52, 90, 142, 194)(40, 102, 154, 206, 50, 92, 144, 196)(42, 100, 152, 204, 48, 94, 146, 198)(44, 98, 150, 202, 46, 96, 148, 200)
	L = (1, 107)(2, 108)(3, 105)(4, 106)(5, 111)(6, 112)(7, 109)(8, 110)(9, 115)(10, 116)(11, 113)(12, 114)(13, 119)(14, 120)(15, 117)(16, 118)(17, 127)(18, 129)(19, 131)(20, 133)(21, 135)(22, 137)(23, 121)(24, 139)(25, 122)(26, 141)(27, 123)(28, 143)(29, 124)(30, 145)(31, 125)(32, 147)(33, 126)(34, 149)(35, 128)(36, 151)(37, 130)(38, 153)(39, 132)(40, 155)(41, 134)(42, 156)(43, 136)(44, 154)(45, 138)(46, 152)(47, 140)(48, 150)(49, 142)(50, 148)(51, 144)(52, 146)(53, 159)(54, 160)(55, 157)(56, 158)(57, 163)(58, 164)(59, 161)(60, 162)(61, 167)(62, 168)(63, 165)(64, 166)(65, 171)(66, 172)(67, 169)(68, 170)(69, 179)(70, 181)(71, 183)(72, 185)(73, 187)(74, 189)(75, 173)(76, 191)(77, 174)(78, 193)(79, 175)(80, 195)(81, 176)(82, 197)(83, 177)(84, 199)(85, 178)(86, 201)(87, 180)(88, 203)(89, 182)(90, 205)(91, 184)(92, 207)(93, 186)(94, 208)(95, 188)(96, 206)(97, 190)(98, 204)(99, 192)(100, 202)(101, 194)(102, 200)(103, 196)(104, 198)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.35 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = D52 (small group id <52, 4>)
Aut   = C2 x C2 x D26 (small group id <104, 13>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * B * S * A, (S * Z)^2, A * Z * B^-1 * Z, B^13 * A^-13 ]
Map:: non-degenerate
	R = (1, 54, 106, 158, 2, 53, 105, 157)(3, 58, 110, 162, 6, 55, 107, 159)(4, 57, 109, 161, 5, 56, 108, 160)(7, 62, 114, 166, 10, 59, 111, 163)(8, 61, 113, 165, 9, 60, 112, 164)(11, 66, 118, 170, 14, 63, 115, 167)(12, 65, 117, 169, 13, 64, 116, 168)(15, 70, 122, 174, 18, 67, 119, 171)(16, 69, 121, 173, 17, 68, 120, 172)(19, 74, 126, 178, 22, 71, 123, 175)(20, 73, 125, 177, 21, 72, 124, 176)(23, 78, 130, 182, 26, 75, 127, 179)(24, 77, 129, 181, 25, 76, 128, 180)(27, 82, 134, 186, 30, 79, 131, 183)(28, 81, 133, 185, 29, 80, 132, 184)(31, 86, 138, 190, 34, 83, 135, 187)(32, 85, 137, 189, 33, 84, 136, 188)(35, 90, 142, 194, 38, 87, 139, 191)(36, 89, 141, 193, 37, 88, 140, 192)(39, 94, 146, 198, 42, 91, 143, 195)(40, 93, 145, 197, 41, 92, 144, 196)(43, 98, 150, 202, 46, 95, 147, 199)(44, 97, 149, 201, 45, 96, 148, 200)(47, 102, 154, 206, 50, 99, 151, 203)(48, 101, 153, 205, 49, 100, 152, 204)(51, 104, 156, 208, 52, 103, 155, 207)
	L = (1, 107)(2, 109)(3, 111)(4, 105)(5, 113)(6, 106)(7, 115)(8, 108)(9, 117)(10, 110)(11, 119)(12, 112)(13, 121)(14, 114)(15, 123)(16, 116)(17, 125)(18, 118)(19, 127)(20, 120)(21, 129)(22, 122)(23, 131)(24, 124)(25, 133)(26, 126)(27, 135)(28, 128)(29, 137)(30, 130)(31, 139)(32, 132)(33, 141)(34, 134)(35, 143)(36, 136)(37, 145)(38, 138)(39, 147)(40, 140)(41, 149)(42, 142)(43, 151)(44, 144)(45, 153)(46, 146)(47, 155)(48, 148)(49, 156)(50, 150)(51, 152)(52, 154)(53, 159)(54, 161)(55, 163)(56, 157)(57, 165)(58, 158)(59, 167)(60, 160)(61, 169)(62, 162)(63, 171)(64, 164)(65, 173)(66, 166)(67, 175)(68, 168)(69, 177)(70, 170)(71, 179)(72, 172)(73, 181)(74, 174)(75, 183)(76, 176)(77, 185)(78, 178)(79, 187)(80, 180)(81, 189)(82, 182)(83, 191)(84, 184)(85, 193)(86, 186)(87, 195)(88, 188)(89, 197)(90, 190)(91, 199)(92, 192)(93, 201)(94, 194)(95, 203)(96, 196)(97, 205)(98, 198)(99, 207)(100, 200)(101, 208)(102, 202)(103, 204)(104, 206)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.36 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^2 * Y1^-1 * Y2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^9 * Y2, (Y3 * Y2^-1)^28, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 29, 2, 30, 6, 34, 12, 40, 18, 46, 24, 52, 23, 51, 17, 45, 11, 39, 5, 33, 8, 36, 14, 42, 20, 48, 26, 54, 28, 56, 27, 55, 21, 49, 15, 43, 9, 37, 3, 31, 7, 35, 13, 41, 19, 47, 25, 53, 22, 50, 16, 44, 10, 38, 4, 32)(57, 85, 59, 87, 64, 92, 58, 86, 63, 91, 70, 98, 62, 90, 69, 97, 76, 104, 68, 96, 75, 103, 82, 110, 74, 102, 81, 109, 84, 112, 80, 108, 78, 106, 83, 111, 79, 107, 72, 100, 77, 105, 73, 101, 66, 94, 71, 99, 67, 95, 60, 88, 65, 93, 61, 89)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.37 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-9, (Y3 * Y2^-1)^28, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 29, 2, 30, 6, 34, 12, 40, 18, 46, 24, 52, 22, 50, 16, 44, 10, 38, 3, 31, 7, 35, 13, 41, 19, 47, 25, 53, 28, 56, 27, 55, 21, 49, 15, 43, 9, 37, 5, 33, 8, 36, 14, 42, 20, 48, 26, 54, 23, 51, 17, 45, 11, 39, 4, 32)(57, 85, 59, 87, 65, 93, 60, 88, 66, 94, 71, 99, 67, 95, 72, 100, 77, 105, 73, 101, 78, 106, 83, 111, 79, 107, 80, 108, 84, 112, 82, 110, 74, 102, 81, 109, 76, 104, 68, 96, 75, 103, 70, 98, 62, 90, 69, 97, 64, 92, 58, 86, 63, 91, 61, 89)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.38 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2, Y1), (R * Y1)^2, (R * Y3)^2, Y1 * Y2^2 * Y1^-1 * Y2^-2, Y2^5 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-3, (Y3^-1 * Y1^-1)^28, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 29, 2, 30, 6, 34, 14, 42, 24, 52, 19, 47, 9, 37, 17, 45, 27, 55, 22, 50, 12, 40, 5, 33, 8, 36, 16, 44, 26, 54, 20, 48, 10, 38, 3, 31, 7, 35, 15, 43, 25, 53, 23, 51, 13, 41, 18, 46, 28, 56, 21, 49, 11, 39, 4, 32)(57, 85, 59, 87, 65, 93, 74, 102, 64, 92, 58, 86, 63, 91, 73, 101, 84, 112, 72, 100, 62, 90, 71, 99, 83, 111, 77, 105, 82, 110, 70, 98, 81, 109, 78, 106, 67, 95, 76, 104, 80, 108, 79, 107, 68, 96, 60, 88, 66, 94, 75, 103, 69, 97, 61, 89)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.39 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^-4, Y2^2 * Y1^-1 * Y2 * Y1^-4, (Y3 * Y2^-1)^28, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 29, 2, 30, 6, 34, 14, 42, 24, 52, 19, 47, 13, 41, 18, 46, 28, 56, 21, 49, 10, 38, 3, 31, 7, 35, 15, 43, 25, 53, 23, 51, 12, 40, 5, 33, 8, 36, 16, 44, 26, 54, 20, 48, 9, 37, 17, 45, 27, 55, 22, 50, 11, 39, 4, 32)(57, 85, 59, 87, 65, 93, 75, 103, 68, 96, 60, 88, 66, 94, 76, 104, 80, 108, 79, 107, 67, 95, 77, 105, 82, 110, 70, 98, 81, 109, 78, 106, 84, 112, 72, 100, 62, 90, 71, 99, 83, 111, 74, 102, 64, 92, 58, 86, 63, 91, 73, 101, 69, 97, 61, 89)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.40 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^2 * Y1^-1 * Y2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-2 * Y2, Y3 * Y2^2 * Y3 * Y2 * Y1^-1, Y2^-1 * Y1^5 * Y3, (Y1^-1 * Y2^-1)^7 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 7, 35, 17, 45, 23, 51, 11, 39, 21, 49, 28, 56, 16, 44, 6, 34, 10, 38, 20, 48, 25, 53, 13, 41, 4, 32, 9, 37, 19, 47, 24, 52, 12, 40, 3, 31, 8, 36, 18, 46, 26, 54, 14, 42, 22, 50, 27, 55, 15, 43, 5, 33)(57, 85, 59, 87, 66, 94, 58, 86, 64, 92, 76, 104, 63, 91, 74, 102, 81, 109, 73, 101, 82, 110, 69, 97, 79, 107, 70, 98, 60, 88, 67, 95, 78, 106, 65, 93, 77, 105, 83, 111, 75, 103, 84, 112, 71, 99, 80, 108, 72, 100, 61, 89, 68, 96, 62, 90)
	L = (1, 60)(2, 65)(3, 67)(4, 57)(5, 69)(6, 70)(7, 75)(8, 77)(9, 58)(10, 78)(11, 59)(12, 79)(13, 61)(14, 62)(15, 81)(16, 82)(17, 80)(18, 84)(19, 63)(20, 83)(21, 64)(22, 66)(23, 68)(24, 73)(25, 71)(26, 72)(27, 76)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.41 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), (Y1^-1, Y2^-1), Y2^2 * Y1 * Y2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y2)^2, Y1 * Y2^-2 * Y1^3 * Y3, (Y2^-1 * Y1)^7 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 7, 35, 17, 45, 23, 51, 15, 43, 22, 50, 26, 54, 13, 41, 3, 31, 8, 36, 18, 46, 27, 55, 14, 42, 4, 32, 9, 37, 19, 47, 24, 52, 11, 39, 6, 34, 10, 38, 20, 48, 25, 53, 12, 40, 21, 49, 28, 56, 16, 44, 5, 33)(57, 85, 59, 87, 67, 95, 61, 89, 69, 97, 80, 108, 72, 100, 82, 110, 75, 103, 84, 112, 78, 106, 65, 93, 77, 105, 71, 99, 60, 88, 68, 96, 79, 107, 70, 98, 81, 109, 73, 101, 83, 111, 76, 104, 63, 91, 74, 102, 66, 94, 58, 86, 64, 92, 62, 90)
	L = (1, 60)(2, 65)(3, 68)(4, 57)(5, 70)(6, 71)(7, 75)(8, 77)(9, 58)(10, 78)(11, 79)(12, 59)(13, 81)(14, 61)(15, 62)(16, 83)(17, 80)(18, 84)(19, 63)(20, 82)(21, 64)(22, 66)(23, 67)(24, 73)(25, 69)(26, 76)(27, 72)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.42 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ Y3^2, R^2, (Y1, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y1^3 * Y2^-1, Y2^-3 * Y1 * Y2^-2, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y3 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 7, 35, 12, 40, 21, 49, 24, 52, 11, 39, 20, 48, 26, 54, 27, 55, 17, 45, 6, 34, 10, 38, 14, 42, 4, 32, 9, 37, 13, 41, 3, 31, 8, 36, 19, 47, 23, 51, 28, 56, 18, 46, 22, 50, 25, 53, 15, 43, 16, 44, 5, 33)(57, 85, 59, 87, 67, 95, 78, 106, 66, 94, 58, 86, 64, 92, 76, 104, 81, 109, 70, 98, 63, 91, 75, 103, 82, 110, 71, 99, 60, 88, 68, 96, 79, 107, 83, 111, 72, 100, 65, 93, 77, 105, 84, 112, 73, 101, 61, 89, 69, 97, 80, 108, 74, 102, 62, 90)
	L = (1, 60)(2, 65)(3, 68)(4, 57)(5, 70)(6, 71)(7, 69)(8, 77)(9, 58)(10, 72)(11, 79)(12, 59)(13, 63)(14, 61)(15, 62)(16, 66)(17, 81)(18, 82)(19, 80)(20, 84)(21, 64)(22, 83)(23, 67)(24, 75)(25, 73)(26, 74)(27, 78)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.43 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, Y1 * Y3 * Y1^2 * Y2, Y2^-5 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 7, 35, 15, 43, 21, 49, 23, 51, 18, 46, 22, 50, 24, 52, 27, 55, 13, 41, 3, 31, 8, 36, 14, 42, 4, 32, 9, 37, 17, 45, 6, 34, 10, 38, 19, 47, 28, 56, 25, 53, 11, 39, 20, 48, 26, 54, 12, 40, 16, 44, 5, 33)(57, 85, 59, 87, 67, 95, 79, 107, 73, 101, 61, 89, 69, 97, 81, 109, 77, 105, 65, 93, 72, 100, 83, 111, 84, 112, 71, 99, 60, 88, 68, 96, 80, 108, 75, 103, 63, 91, 70, 98, 82, 110, 78, 106, 66, 94, 58, 86, 64, 92, 76, 104, 74, 102, 62, 90)
	L = (1, 60)(2, 65)(3, 68)(4, 57)(5, 70)(6, 71)(7, 73)(8, 72)(9, 58)(10, 77)(11, 80)(12, 59)(13, 82)(14, 61)(15, 62)(16, 64)(17, 63)(18, 84)(19, 79)(20, 83)(21, 66)(22, 81)(23, 75)(24, 67)(25, 78)(26, 69)(27, 76)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.44 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-2, (Y2, Y3), (Y2^-1, Y1), (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^2 * Y3 * Y2, Y3 * Y1^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3^-2, (Y1^-2 * Y3)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y1 * Y2^-1 * Y3^-1)^14 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 15, 43, 16, 44, 25, 53, 28, 56, 13, 41, 20, 48, 6, 34, 11, 39, 21, 49, 7, 35, 12, 40, 24, 52, 17, 45, 4, 32, 10, 38, 14, 42, 3, 31, 9, 37, 22, 50, 26, 54, 27, 55, 23, 51, 18, 46, 19, 47, 5, 33)(57, 85, 59, 87, 67, 95, 58, 86, 65, 93, 77, 105, 64, 92, 78, 106, 63, 91, 71, 99, 82, 110, 68, 96, 72, 100, 83, 111, 80, 108, 81, 109, 79, 107, 73, 101, 84, 112, 74, 102, 60, 88, 69, 97, 75, 103, 66, 94, 76, 104, 61, 89, 70, 98, 62, 90)
	L = (1, 60)(2, 66)(3, 69)(4, 72)(5, 73)(6, 74)(7, 57)(8, 70)(9, 76)(10, 81)(11, 75)(12, 58)(13, 83)(14, 84)(15, 59)(16, 65)(17, 71)(18, 68)(19, 80)(20, 79)(21, 61)(22, 62)(23, 63)(24, 64)(25, 78)(26, 67)(27, 77)(28, 82)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.53
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.45 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1), Y2^-2 * Y1^-1 * Y2^-1, (Y1, Y3^-1), (R * Y3)^2, (Y2^-1, Y3), (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y2 * Y3^-1 * Y1^-1 * Y3^-2, Y2^-2 * Y1^2 * Y3^-1, Y2 * Y3^4 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 19, 47, 23, 51, 26, 54, 27, 55, 22, 50, 15, 43, 3, 31, 9, 37, 18, 46, 4, 32, 10, 38, 24, 52, 21, 49, 7, 35, 12, 40, 13, 41, 6, 34, 11, 39, 14, 42, 25, 53, 28, 56, 17, 45, 16, 44, 20, 48, 5, 33)(57, 85, 59, 87, 69, 97, 61, 89, 71, 99, 68, 96, 76, 104, 78, 106, 63, 91, 72, 100, 83, 111, 77, 105, 73, 101, 82, 110, 80, 108, 84, 112, 79, 107, 66, 94, 81, 109, 75, 103, 60, 88, 70, 98, 64, 92, 74, 102, 67, 95, 58, 86, 65, 93, 62, 90)
	L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 80)(9, 81)(10, 72)(11, 79)(12, 58)(13, 64)(14, 82)(15, 67)(16, 59)(17, 71)(18, 84)(19, 77)(20, 65)(21, 61)(22, 62)(23, 63)(24, 76)(25, 83)(26, 68)(27, 69)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.46
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.46 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1^-1), (Y3^-1, Y1), (R * Y3)^2, (Y2^-1, Y3), (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1^-2 * Y2^2, Y3^-1 * Y2^-1 * Y3^-2 * Y1, Y2 * Y1 * Y2 * Y3 * Y2, Y3 * Y1 * Y2^3, Y1 * Y3^-1 * Y1^3, Y2^-1 * Y1^-2 * Y3^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 18, 46, 4, 32, 10, 38, 13, 41, 24, 52, 17, 45, 28, 56, 21, 49, 6, 34, 11, 39, 16, 44, 27, 55, 19, 47, 15, 43, 3, 31, 9, 37, 26, 54, 25, 53, 14, 42, 23, 51, 22, 50, 7, 35, 12, 40, 20, 48, 5, 33)(57, 85, 59, 87, 69, 97, 78, 106, 67, 95, 58, 86, 65, 93, 80, 108, 63, 91, 72, 100, 64, 92, 82, 110, 73, 101, 68, 96, 83, 111, 74, 102, 81, 109, 84, 112, 76, 104, 75, 103, 60, 88, 70, 98, 77, 105, 61, 89, 71, 99, 66, 94, 79, 107, 62, 90)
	L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 69)(9, 79)(10, 84)(11, 71)(12, 58)(13, 77)(14, 68)(15, 81)(16, 59)(17, 67)(18, 80)(19, 82)(20, 64)(21, 83)(22, 61)(23, 76)(24, 62)(25, 63)(26, 78)(27, 65)(28, 72)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.45
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.47 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y2^-1 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1^2, (R * Y2)^2, Y2^2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^7, Y2^-2 * Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y2^28 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 3, 31, 4, 32, 9, 37, 11, 39, 12, 40, 13, 41, 18, 46, 19, 47, 20, 48, 21, 49, 26, 54, 27, 55, 28, 56, 25, 53, 24, 52, 23, 51, 22, 50, 17, 45, 16, 44, 15, 43, 14, 42, 7, 35, 6, 34, 10, 38, 5, 33)(57, 85, 59, 87, 67, 95, 74, 102, 77, 105, 84, 112, 79, 107, 72, 100, 63, 91, 61, 89, 64, 92, 65, 93, 69, 97, 76, 104, 83, 111, 80, 108, 73, 101, 70, 98, 66, 94, 58, 86, 60, 88, 68, 96, 75, 103, 82, 110, 81, 109, 78, 106, 71, 99, 62, 90)
	L = (1, 60)(2, 65)(3, 68)(4, 69)(5, 59)(6, 58)(7, 57)(8, 67)(9, 74)(10, 64)(11, 75)(12, 76)(13, 77)(14, 61)(15, 66)(16, 62)(17, 63)(18, 82)(19, 83)(20, 84)(21, 81)(22, 70)(23, 71)(24, 72)(25, 73)(26, 80)(27, 79)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.52
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.48 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3^-1), Y1 * Y2 * Y3^-2, (Y2^-1, Y3), (R * Y2)^2, Y3^2 * Y1^-1 * Y2^-1, Y3 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y3^-1 * Y2^-2, Y1^4 * Y3^2, Y1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y3^7, Y1^-10 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 22, 50, 18, 46, 6, 34, 11, 39, 14, 42, 26, 54, 27, 55, 20, 48, 16, 44, 4, 32, 10, 38, 24, 52, 19, 47, 7, 35, 12, 40, 13, 41, 25, 53, 28, 56, 21, 49, 15, 43, 3, 31, 9, 37, 23, 51, 17, 45, 5, 33)(57, 85, 59, 87, 69, 97, 66, 94, 82, 110, 78, 106, 73, 101, 77, 105, 63, 91, 72, 100, 67, 95, 58, 86, 65, 93, 81, 109, 80, 108, 83, 111, 74, 102, 61, 89, 71, 99, 68, 96, 60, 88, 70, 98, 64, 92, 79, 107, 84, 112, 75, 103, 76, 104, 62, 90)
	L = (1, 60)(2, 66)(3, 70)(4, 65)(5, 72)(6, 68)(7, 57)(8, 80)(9, 82)(10, 79)(11, 69)(12, 58)(13, 64)(14, 81)(15, 67)(16, 59)(17, 76)(18, 63)(19, 61)(20, 71)(21, 62)(22, 75)(23, 83)(24, 73)(25, 78)(26, 84)(27, 77)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.49
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.49 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2), Y3^2 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y3^-1), Y2^-2 * Y1 * Y2^-1, (R * Y3)^2, Y1^2 * Y3 * Y1^2, Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y3^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 18, 46, 7, 35, 12, 40, 22, 50, 27, 55, 17, 45, 6, 34, 11, 39, 21, 49, 28, 56, 19, 47, 24, 52, 13, 41, 23, 51, 25, 53, 14, 42, 3, 31, 9, 37, 20, 48, 26, 54, 15, 43, 4, 32, 10, 38, 16, 44, 5, 33)(57, 85, 59, 87, 67, 95, 58, 86, 65, 93, 77, 105, 64, 92, 76, 104, 84, 112, 74, 102, 82, 110, 75, 103, 63, 91, 71, 99, 80, 108, 68, 96, 60, 88, 69, 97, 78, 106, 66, 94, 79, 107, 83, 111, 72, 100, 81, 109, 73, 101, 61, 89, 70, 98, 62, 90)
	L = (1, 60)(2, 66)(3, 69)(4, 65)(5, 71)(6, 68)(7, 57)(8, 72)(9, 79)(10, 76)(11, 78)(12, 58)(13, 77)(14, 80)(15, 59)(16, 82)(17, 63)(18, 61)(19, 62)(20, 81)(21, 83)(22, 64)(23, 84)(24, 67)(25, 75)(26, 70)(27, 74)(28, 73)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.48
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.50 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y3, Y2 * Y3 * Y1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-4, Y2^-3 * Y3^2 * Y2^-1, Y3^7, Y1 * Y2^-2 * Y1 * Y3^-3 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 15, 43, 4, 32, 6, 34, 9, 37, 20, 48, 14, 42, 16, 44, 18, 46, 21, 49, 27, 55, 23, 51, 25, 53, 26, 54, 28, 56, 24, 52, 11, 39, 13, 41, 19, 47, 22, 50, 12, 40, 3, 31, 7, 35, 10, 38, 17, 45, 5, 33)(57, 85, 59, 87, 67, 95, 79, 107, 70, 98, 71, 99, 73, 101, 78, 106, 84, 112, 77, 105, 65, 93, 58, 86, 63, 91, 69, 97, 81, 109, 72, 100, 60, 88, 61, 89, 68, 96, 80, 108, 83, 111, 76, 104, 64, 92, 66, 94, 75, 103, 82, 110, 74, 102, 62, 90)
	L = (1, 60)(2, 62)(3, 61)(4, 70)(5, 71)(6, 72)(7, 57)(8, 65)(9, 74)(10, 58)(11, 68)(12, 73)(13, 59)(14, 83)(15, 76)(16, 79)(17, 64)(18, 81)(19, 63)(20, 77)(21, 82)(22, 66)(23, 80)(24, 78)(25, 67)(26, 69)(27, 84)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.51
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.51 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y2^-1 * Y1^-1 * Y3, Y2^2 * Y1^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^7, Y3^-3 * Y1^-1 * Y3^-3 * Y2^-1, Y3 * Y2^24 * Y3, (Y3^-1 * Y1^-1)^28 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 11, 39, 12, 40, 18, 46, 25, 53, 27, 55, 24, 52, 23, 51, 21, 49, 14, 42, 7, 35, 6, 34, 10, 38, 3, 31, 4, 32, 9, 37, 17, 45, 19, 47, 20, 48, 26, 54, 28, 56, 22, 50, 16, 44, 15, 43, 13, 41, 5, 33)(57, 85, 59, 87, 64, 92, 65, 93, 68, 96, 75, 103, 81, 109, 82, 110, 80, 108, 78, 106, 77, 105, 71, 99, 63, 91, 61, 89, 66, 94, 58, 86, 60, 88, 67, 95, 73, 101, 74, 102, 76, 104, 83, 111, 84, 112, 79, 107, 72, 100, 70, 98, 69, 97, 62, 90)
	L = (1, 60)(2, 65)(3, 67)(4, 68)(5, 59)(6, 58)(7, 57)(8, 73)(9, 74)(10, 64)(11, 75)(12, 76)(13, 66)(14, 61)(15, 62)(16, 63)(17, 81)(18, 82)(19, 83)(20, 80)(21, 69)(22, 70)(23, 71)(24, 72)(25, 84)(26, 79)(27, 78)(28, 77)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.50
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.52 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y3^-1, Y2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1^-3, Y1 * Y2^-1 * Y1^2 * Y3^2, Y2^-3 * Y3^-2 * Y2^-1, Y3^7, Y1 * Y3^3 * Y1 * Y2^-2, Y3^-8 * Y2^-2 * Y1 * Y2^-1 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 16, 44, 7, 35, 6, 34, 10, 38, 20, 48, 19, 47, 18, 46, 17, 45, 22, 50, 28, 56, 23, 51, 24, 52, 26, 54, 27, 55, 25, 53, 11, 39, 12, 40, 14, 42, 21, 49, 13, 41, 3, 31, 4, 32, 9, 37, 15, 43, 5, 33)(57, 85, 59, 87, 67, 95, 79, 107, 75, 103, 72, 100, 71, 99, 77, 105, 83, 111, 78, 106, 66, 94, 58, 86, 60, 88, 68, 96, 80, 108, 74, 102, 63, 91, 61, 89, 69, 97, 81, 109, 84, 112, 76, 104, 64, 92, 65, 93, 70, 98, 82, 110, 73, 101, 62, 90)
	L = (1, 60)(2, 65)(3, 68)(4, 70)(5, 59)(6, 58)(7, 57)(8, 71)(9, 77)(10, 64)(11, 80)(12, 82)(13, 67)(14, 83)(15, 69)(16, 61)(17, 66)(18, 62)(19, 63)(20, 72)(21, 81)(22, 76)(23, 74)(24, 73)(25, 79)(26, 78)(27, 84)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.47
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.53 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1^-1), (R * Y3)^2, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y3^-1), Y2^2 * Y1 * Y3 * Y1, Y1 * Y3^-3 * Y2, Y2^28, Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y1^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 20, 48, 7, 35, 12, 40, 23, 51, 27, 55, 22, 50, 17, 45, 25, 53, 13, 41, 19, 47, 6, 34, 11, 39, 3, 31, 9, 37, 21, 49, 26, 54, 14, 42, 15, 43, 24, 52, 28, 56, 16, 44, 4, 32, 10, 38, 18, 46, 5, 33)(57, 85, 59, 87, 64, 92, 77, 105, 63, 91, 70, 98, 79, 107, 80, 108, 78, 106, 72, 100, 81, 109, 66, 94, 75, 103, 61, 89, 67, 95, 58, 86, 65, 93, 76, 104, 82, 110, 68, 96, 71, 99, 83, 111, 84, 112, 73, 101, 60, 88, 69, 97, 74, 102, 62, 90)
	L = (1, 60)(2, 66)(3, 69)(4, 71)(5, 72)(6, 73)(7, 57)(8, 74)(9, 75)(10, 80)(11, 81)(12, 58)(13, 83)(14, 59)(15, 65)(16, 70)(17, 68)(18, 84)(19, 78)(20, 61)(21, 62)(22, 63)(23, 64)(24, 77)(25, 79)(26, 67)(27, 76)(28, 82)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.44
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.54 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-2, Y1^2 * Y2 * Y1, Y1^2 * Y2 * Y1, Y1^3 * Y2, (R * Y1)^2, (Y3, Y1^-1), Y2^-1 * Y1^-3, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, Y3^2 * Y2 * Y3 * Y1^-1 * Y3, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 6, 34, 11, 39, 17, 45, 7, 35, 12, 40, 20, 48, 18, 46, 23, 51, 27, 55, 19, 47, 24, 52, 28, 56, 26, 54, 15, 43, 22, 50, 25, 53, 13, 41, 21, 49, 16, 44, 4, 32, 10, 38, 14, 42, 3, 31, 9, 37, 5, 33)(57, 85, 59, 87, 60, 88, 69, 97, 71, 99, 80, 108, 79, 107, 68, 96, 67, 95, 58, 86, 65, 93, 66, 94, 77, 105, 78, 106, 84, 112, 83, 111, 76, 104, 73, 101, 64, 92, 61, 89, 70, 98, 72, 100, 81, 109, 82, 110, 75, 103, 74, 102, 63, 91, 62, 90)
	L = (1, 60)(2, 66)(3, 69)(4, 71)(5, 72)(6, 59)(7, 57)(8, 70)(9, 77)(10, 78)(11, 65)(12, 58)(13, 80)(14, 81)(15, 79)(16, 82)(17, 61)(18, 62)(19, 63)(20, 64)(21, 84)(22, 83)(23, 67)(24, 68)(25, 75)(26, 74)(27, 73)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.55
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.55 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 28, 28, 28})
Quotient :: dipole
Aut^+ = C28 (small group id <28, 2>)
Aut   = D56 (small group id <56, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, (Y2^-1, Y1), (Y1, Y3), (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1), (R * Y1)^2, Y3^2 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-2 * Y1^-1, Y1^-5 * Y2, (Y1^-1 * Y3^-1)^28 ]
Map:: non-degenerate
	R = (1, 29, 2, 30, 8, 36, 22, 50, 14, 42, 3, 31, 9, 37, 23, 51, 21, 49, 16, 44, 4, 32, 10, 38, 24, 52, 20, 48, 28, 56, 13, 41, 26, 54, 19, 47, 7, 35, 12, 40, 15, 43, 27, 55, 18, 46, 6, 34, 11, 39, 25, 53, 17, 45, 5, 33)(57, 85, 59, 87, 60, 88, 69, 97, 71, 99, 81, 109, 64, 92, 79, 107, 80, 108, 75, 103, 74, 102, 61, 89, 70, 98, 72, 100, 84, 112, 68, 96, 67, 95, 58, 86, 65, 93, 66, 94, 82, 110, 83, 111, 73, 101, 78, 106, 77, 105, 76, 104, 63, 91, 62, 90)
	L = (1, 60)(2, 66)(3, 69)(4, 71)(5, 72)(6, 59)(7, 57)(8, 80)(9, 82)(10, 83)(11, 65)(12, 58)(13, 81)(14, 84)(15, 64)(16, 68)(17, 77)(18, 70)(19, 61)(20, 62)(21, 63)(22, 76)(23, 75)(24, 74)(25, 79)(26, 73)(27, 78)(28, 67)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.54
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.56 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y1, Y3^-1), (R * Y2)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^-3 * Y1^-2, Y1^10, Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y2^-1 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 24, 54, 23, 53, 28, 58, 14, 44, 26, 56, 19, 49, 5, 35)(3, 33, 9, 39, 22, 52, 21, 51, 7, 37, 12, 42, 25, 55, 30, 60, 18, 48, 15, 45)(4, 34, 10, 40, 13, 43, 20, 50, 6, 36, 11, 41, 16, 46, 27, 57, 29, 59, 17, 47)(61, 91, 63, 93, 73, 103, 79, 109, 78, 108, 64, 94, 74, 104, 85, 115, 89, 119, 83, 113, 67, 97, 76, 106, 68, 98, 82, 112, 66, 96)(62, 92, 69, 99, 80, 110, 65, 95, 75, 105, 70, 100, 86, 116, 90, 120, 77, 107, 88, 118, 72, 102, 87, 117, 84, 114, 81, 111, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 67)(5, 77)(6, 78)(7, 61)(8, 73)(9, 86)(10, 72)(11, 75)(12, 62)(13, 85)(14, 76)(15, 88)(16, 63)(17, 81)(18, 83)(19, 89)(20, 90)(21, 65)(22, 79)(23, 66)(24, 80)(25, 68)(26, 87)(27, 69)(28, 71)(29, 82)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.79
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.57 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y2^-1, Y3^-1), (Y3, Y1), (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, Y2^-3 * Y1^2, Y2^-1 * Y3 * Y2^-1 * Y1^-2, Y1^10, Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y2^-1 * Y3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 24, 54, 14, 44, 26, 56, 23, 53, 28, 58, 19, 49, 5, 35)(3, 33, 9, 39, 18, 48, 27, 57, 29, 59, 21, 51, 7, 37, 12, 42, 22, 52, 15, 45)(4, 34, 10, 40, 25, 55, 30, 60, 16, 46, 20, 50, 6, 36, 11, 41, 13, 43, 17, 47)(61, 91, 63, 93, 73, 103, 68, 98, 78, 108, 64, 94, 74, 104, 89, 119, 85, 115, 83, 113, 67, 97, 76, 106, 79, 109, 82, 112, 66, 96)(62, 92, 69, 99, 77, 107, 84, 114, 87, 117, 70, 100, 86, 116, 81, 111, 90, 120, 88, 118, 72, 102, 80, 110, 65, 95, 75, 105, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 67)(5, 77)(6, 78)(7, 61)(8, 85)(9, 86)(10, 72)(11, 87)(12, 62)(13, 89)(14, 76)(15, 84)(16, 63)(17, 81)(18, 83)(19, 73)(20, 69)(21, 65)(22, 68)(23, 66)(24, 90)(25, 82)(26, 80)(27, 88)(28, 71)(29, 79)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.81
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.58 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y2^-1, Y3), Y3 * Y1^-1 * Y2 * Y1^-1, (Y3^-1, Y1), Y1^-1 * Y3 * Y2 * Y1^-1, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3^-1 * Y2^-1, Y3 * Y1 * Y3 * Y2^-1 * Y1, Y3 * Y2^-5, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 26, 56, 30, 60, 25, 55, 27, 57, 16, 46, 5, 35)(3, 33, 9, 39, 21, 51, 29, 59, 19, 49, 24, 54, 15, 45, 18, 48, 7, 37, 12, 42)(4, 34, 10, 40, 14, 44, 23, 53, 13, 43, 22, 52, 28, 58, 17, 47, 6, 36, 11, 41)(61, 91, 63, 93, 73, 103, 85, 115, 75, 105, 64, 94, 68, 98, 81, 111, 88, 118, 76, 106, 67, 97, 74, 104, 86, 116, 79, 109, 66, 96)(62, 92, 69, 99, 82, 112, 87, 117, 78, 108, 70, 100, 80, 110, 89, 119, 77, 107, 65, 95, 72, 102, 83, 113, 90, 120, 84, 114, 71, 101)
	L = (1, 64)(2, 70)(3, 68)(4, 67)(5, 71)(6, 75)(7, 61)(8, 74)(9, 80)(10, 72)(11, 78)(12, 62)(13, 81)(14, 63)(15, 76)(16, 66)(17, 84)(18, 65)(19, 85)(20, 83)(21, 86)(22, 89)(23, 69)(24, 87)(25, 88)(26, 73)(27, 77)(28, 79)(29, 90)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.82
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.59 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (Y2^-1, Y3), (R * Y2)^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2^-1), Y3^-1 * Y2 * Y1 * Y3^-1 * Y1, Y2^-5 * Y3, Y2^-1 * Y3^-1 * Y1^8, Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 25, 55, 30, 60, 28, 58, 29, 59, 14, 44, 5, 35)(3, 33, 9, 39, 7, 37, 12, 42, 18, 48, 23, 53, 19, 49, 24, 54, 26, 56, 15, 45)(4, 34, 10, 40, 6, 36, 11, 41, 21, 51, 27, 57, 13, 43, 22, 52, 16, 46, 17, 47)(61, 91, 63, 93, 73, 103, 85, 115, 78, 108, 64, 94, 74, 104, 86, 116, 81, 111, 68, 98, 67, 97, 76, 106, 88, 118, 79, 109, 66, 96)(62, 92, 69, 99, 82, 112, 90, 120, 83, 113, 70, 100, 65, 95, 75, 105, 87, 117, 80, 110, 72, 102, 77, 107, 89, 119, 84, 114, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 67)(5, 77)(6, 78)(7, 61)(8, 66)(9, 65)(10, 72)(11, 83)(12, 62)(13, 86)(14, 76)(15, 89)(16, 63)(17, 69)(18, 68)(19, 85)(20, 71)(21, 79)(22, 75)(23, 80)(24, 90)(25, 81)(26, 88)(27, 84)(28, 73)(29, 82)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.80
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.60 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-1, (R * Y1)^2, (Y1, Y3^-1), R * Y2 * R * Y3^-1, (Y1, Y2^-1), Y1^-1 * Y2 * Y1^-1 * Y3^-2, Y1^10, Y1^4 * Y2 * Y1^4 * Y3^-2, Y2^15, Y3^-30, (Y3 * Y2^-1)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 20, 50, 26, 56, 25, 55, 19, 49, 13, 43, 5, 35)(3, 33, 7, 37, 15, 45, 21, 51, 27, 57, 29, 59, 23, 53, 17, 47, 11, 41, 10, 40)(4, 34, 8, 38, 9, 39, 16, 46, 22, 52, 28, 58, 30, 60, 24, 54, 18, 48, 12, 42)(61, 91, 63, 93, 69, 99, 66, 96, 75, 105, 82, 112, 80, 110, 87, 117, 90, 120, 85, 115, 83, 113, 78, 108, 73, 103, 71, 101, 64, 94)(62, 92, 67, 97, 76, 106, 74, 104, 81, 111, 88, 118, 86, 116, 89, 119, 84, 114, 79, 109, 77, 107, 72, 102, 65, 95, 70, 100, 68, 98)
	L = (1, 64)(2, 68)(3, 61)(4, 71)(5, 72)(6, 69)(7, 62)(8, 70)(9, 63)(10, 65)(11, 73)(12, 77)(13, 78)(14, 76)(15, 66)(16, 67)(17, 79)(18, 83)(19, 84)(20, 82)(21, 74)(22, 75)(23, 85)(24, 89)(25, 90)(26, 88)(27, 80)(28, 81)(29, 86)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.85
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.61 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-1, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), Y3^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1^-1 * Y3, Y1 * Y2^-1 * Y1^-2 * Y3^-1 * Y1, Y2 * Y1 * Y2^2 * Y1^3, Y3^-2 * Y1^-1 * Y3^-4 * Y1^-1, Y1^2 * Y3^2 * Y2^-4, (Y3 * Y2^-1)^15, (Y1^-1 * Y2)^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 28, 58, 19, 49, 25, 55, 13, 43, 5, 35)(3, 33, 7, 37, 15, 45, 23, 53, 11, 41, 18, 48, 27, 57, 30, 60, 21, 51, 10, 40)(4, 34, 8, 38, 16, 46, 26, 56, 29, 59, 20, 50, 9, 39, 17, 47, 24, 54, 12, 42)(61, 91, 63, 93, 69, 99, 79, 109, 87, 117, 76, 106, 66, 96, 75, 105, 84, 114, 73, 103, 81, 111, 89, 119, 82, 112, 71, 101, 64, 94)(62, 92, 67, 97, 77, 107, 85, 115, 90, 120, 86, 116, 74, 104, 83, 113, 72, 102, 65, 95, 70, 100, 80, 110, 88, 118, 78, 108, 68, 98)
	L = (1, 64)(2, 68)(3, 61)(4, 71)(5, 72)(6, 76)(7, 62)(8, 78)(9, 63)(10, 65)(11, 82)(12, 83)(13, 84)(14, 86)(15, 66)(16, 87)(17, 67)(18, 88)(19, 69)(20, 70)(21, 73)(22, 89)(23, 74)(24, 75)(25, 77)(26, 90)(27, 79)(28, 80)(29, 81)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.89
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.62 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3, Y3^-1 * Y2^-1, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y2^-1, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y1^3 * Y3 * Y2^-2 * Y1, Y1^2 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1^2 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1, Y1^-1 * Y3^3 * Y2^-1 * Y1^-1 * Y2^-2, Y2^15, (Y3 * Y2^-1)^15, (Y3^-1 * Y1^-1)^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 19, 49, 28, 58, 22, 52, 25, 55, 13, 43, 5, 35)(3, 33, 7, 37, 15, 45, 26, 56, 29, 59, 23, 53, 11, 41, 18, 48, 21, 51, 10, 40)(4, 34, 8, 38, 16, 46, 20, 50, 9, 39, 17, 47, 27, 57, 30, 60, 24, 54, 12, 42)(61, 91, 63, 93, 69, 99, 79, 109, 89, 119, 84, 114, 73, 103, 81, 111, 76, 106, 66, 96, 75, 105, 87, 117, 82, 112, 71, 101, 64, 94)(62, 92, 67, 97, 77, 107, 88, 118, 83, 113, 72, 102, 65, 95, 70, 100, 80, 110, 74, 104, 86, 116, 90, 120, 85, 115, 78, 108, 68, 98)
	L = (1, 64)(2, 68)(3, 61)(4, 71)(5, 72)(6, 76)(7, 62)(8, 78)(9, 63)(10, 65)(11, 82)(12, 83)(13, 84)(14, 80)(15, 66)(16, 81)(17, 67)(18, 85)(19, 69)(20, 70)(21, 73)(22, 87)(23, 88)(24, 89)(25, 90)(26, 74)(27, 75)(28, 77)(29, 79)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.88
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.63 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1, (Y1^-1, Y2), Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1^-2 * Y2^-1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y3^-5 * Y2^-1 * Y3^-2, (Y3^3 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y1^8 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 18, 48, 25, 55, 28, 58, 23, 53, 22, 52, 13, 43, 5, 35)(3, 33, 9, 39, 7, 37, 12, 42, 19, 49, 26, 56, 29, 59, 24, 54, 15, 45, 14, 44)(4, 34, 10, 40, 6, 36, 11, 41, 17, 47, 20, 50, 27, 57, 30, 60, 21, 51, 16, 46)(61, 91, 63, 93, 64, 94, 73, 103, 75, 105, 81, 111, 83, 113, 89, 119, 87, 117, 85, 115, 79, 109, 77, 107, 68, 98, 67, 97, 66, 96)(62, 92, 69, 99, 70, 100, 65, 95, 74, 104, 76, 106, 82, 112, 84, 114, 90, 120, 88, 118, 86, 116, 80, 110, 78, 108, 72, 102, 71, 101)
	L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 76)(6, 63)(7, 61)(8, 66)(9, 65)(10, 74)(11, 69)(12, 62)(13, 81)(14, 82)(15, 83)(16, 84)(17, 67)(18, 71)(19, 68)(20, 72)(21, 89)(22, 90)(23, 87)(24, 88)(25, 77)(26, 78)(27, 79)(28, 80)(29, 85)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.86
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.64 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y1^2 * Y3^-1 * Y2^-1, Y1^-2 * Y2 * Y3, (R * Y3)^2, (Y2, Y1^-1), Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y3^5 * Y2 * Y3^2, Y2 * Y3 * Y1^8, (Y3^-1 * Y1^-1)^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 18, 48, 21, 51, 28, 58, 25, 55, 22, 52, 14, 44, 5, 35)(3, 33, 9, 39, 13, 43, 20, 50, 27, 57, 30, 60, 23, 53, 16, 46, 7, 37, 12, 42)(4, 34, 10, 40, 19, 49, 26, 56, 29, 59, 24, 54, 17, 47, 15, 45, 6, 36, 11, 41)(61, 91, 63, 93, 64, 94, 68, 98, 73, 103, 79, 109, 81, 111, 87, 117, 89, 119, 85, 115, 83, 113, 77, 107, 74, 104, 67, 97, 66, 96)(62, 92, 69, 99, 70, 100, 78, 108, 80, 110, 86, 116, 88, 118, 90, 120, 84, 114, 82, 112, 76, 106, 75, 105, 65, 95, 72, 102, 71, 101)
	L = (1, 64)(2, 70)(3, 68)(4, 73)(5, 71)(6, 63)(7, 61)(8, 79)(9, 78)(10, 80)(11, 69)(12, 62)(13, 81)(14, 66)(15, 72)(16, 65)(17, 67)(18, 86)(19, 87)(20, 88)(21, 89)(22, 75)(23, 74)(24, 76)(25, 77)(26, 90)(27, 85)(28, 84)(29, 83)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.90
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.65 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-2, Y3 * Y2^-2, (Y3^-1, Y1), (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-4 * Y2, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 13, 43, 26, 56, 20, 50, 27, 57, 17, 47, 5, 35)(3, 33, 9, 39, 23, 53, 30, 60, 15, 45, 19, 49, 7, 37, 12, 42, 25, 55, 14, 44)(4, 34, 10, 40, 21, 51, 28, 58, 29, 59, 18, 48, 6, 36, 11, 41, 24, 54, 16, 46)(61, 91, 63, 93, 64, 94, 73, 103, 75, 105, 89, 119, 77, 107, 85, 115, 84, 114, 68, 98, 83, 113, 81, 111, 80, 110, 67, 97, 66, 96)(62, 92, 69, 99, 70, 100, 86, 116, 79, 109, 78, 108, 65, 95, 74, 104, 76, 106, 82, 112, 90, 120, 88, 118, 87, 117, 72, 102, 71, 101)
	L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 76)(6, 63)(7, 61)(8, 81)(9, 86)(10, 79)(11, 69)(12, 62)(13, 89)(14, 82)(15, 77)(16, 90)(17, 84)(18, 74)(19, 65)(20, 66)(21, 67)(22, 88)(23, 80)(24, 83)(25, 68)(26, 78)(27, 71)(28, 72)(29, 85)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.83
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.66 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2, (Y3^-1, Y1), (Y1^-1, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2, Y1^-1 * Y2 * Y3 * Y1^-3, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 14, 44, 26, 56, 21, 51, 28, 58, 17, 47, 5, 35)(3, 33, 9, 39, 20, 50, 27, 57, 29, 59, 19, 49, 7, 37, 12, 42, 25, 55, 15, 45)(4, 34, 10, 40, 23, 53, 30, 60, 13, 43, 18, 48, 6, 36, 11, 41, 24, 54, 16, 46)(61, 91, 63, 93, 73, 103, 77, 107, 85, 115, 83, 113, 81, 111, 67, 97, 64, 94, 74, 104, 89, 119, 84, 114, 68, 98, 80, 110, 66, 96)(62, 92, 69, 99, 78, 108, 65, 95, 75, 105, 90, 120, 88, 118, 72, 102, 70, 100, 86, 116, 79, 109, 76, 106, 82, 112, 87, 117, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 63)(5, 76)(6, 67)(7, 61)(8, 83)(9, 86)(10, 69)(11, 72)(12, 62)(13, 89)(14, 73)(15, 82)(16, 75)(17, 84)(18, 79)(19, 65)(20, 81)(21, 66)(22, 90)(23, 80)(24, 85)(25, 68)(26, 78)(27, 88)(28, 71)(29, 77)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.91
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.67 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-1, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y1), Y2^-2 * Y1^2 * Y2^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y2^-1 * Y1 * Y3 * Y1 * Y2^-2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 21, 51, 28, 58, 14, 44, 27, 57, 17, 47, 5, 35)(3, 33, 9, 39, 23, 53, 19, 49, 7, 37, 12, 42, 25, 55, 30, 60, 20, 50, 15, 45)(4, 34, 10, 40, 24, 54, 18, 48, 6, 36, 11, 41, 13, 43, 26, 56, 29, 59, 16, 46)(61, 91, 63, 93, 73, 103, 68, 98, 83, 113, 89, 119, 81, 111, 67, 97, 64, 94, 74, 104, 85, 115, 84, 114, 77, 107, 80, 110, 66, 96)(62, 92, 69, 99, 86, 116, 82, 112, 79, 109, 76, 106, 88, 118, 72, 102, 70, 100, 87, 117, 90, 120, 78, 108, 65, 95, 75, 105, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 63)(5, 76)(6, 67)(7, 61)(8, 84)(9, 87)(10, 69)(11, 72)(12, 62)(13, 85)(14, 73)(15, 88)(16, 75)(17, 89)(18, 79)(19, 65)(20, 81)(21, 66)(22, 78)(23, 77)(24, 83)(25, 68)(26, 90)(27, 86)(28, 71)(29, 80)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.87
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.68 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2 * Y3^-1, (Y1, Y3^-1), Y2 * Y3 * Y1^2, Y1 * Y2 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-3 * Y1)^2, Y2^6 * Y1^-2, (Y3^-1 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 18, 48, 25, 55, 28, 58, 21, 51, 24, 54, 14, 44, 5, 35)(3, 33, 9, 39, 7, 37, 12, 42, 17, 47, 20, 50, 27, 57, 30, 60, 22, 52, 15, 45)(4, 34, 10, 40, 6, 36, 11, 41, 19, 49, 26, 56, 29, 59, 23, 53, 13, 43, 16, 46)(61, 91, 63, 93, 73, 103, 81, 111, 87, 117, 79, 109, 68, 98, 67, 97, 64, 94, 74, 104, 82, 112, 89, 119, 85, 115, 77, 107, 66, 96)(62, 92, 69, 99, 76, 106, 84, 114, 90, 120, 86, 116, 78, 108, 72, 102, 70, 100, 65, 95, 75, 105, 83, 113, 88, 118, 80, 110, 71, 101)
	L = (1, 64)(2, 70)(3, 74)(4, 63)(5, 76)(6, 67)(7, 61)(8, 66)(9, 65)(10, 69)(11, 72)(12, 62)(13, 82)(14, 73)(15, 84)(16, 75)(17, 68)(18, 71)(19, 77)(20, 78)(21, 89)(22, 81)(23, 90)(24, 83)(25, 79)(26, 80)(27, 85)(28, 86)(29, 87)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.84
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.69 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2), (Y3^-1, Y1^-1), Y3 * Y2 * Y3 * Y1^-2, Y3^6, Y3^-2 * Y1^-5 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 30, 60, 21, 51, 13, 43, 3, 33, 6, 36, 10, 40, 15, 45, 24, 54, 27, 57, 18, 48, 5, 35)(4, 34, 9, 39, 23, 53, 29, 59, 19, 49, 7, 37, 11, 41, 12, 42, 17, 47, 25, 55, 28, 58, 26, 56, 14, 44, 20, 50, 16, 46)(61, 91, 63, 93, 65, 95, 73, 103, 78, 108, 81, 111, 87, 117, 90, 120, 84, 114, 82, 112, 75, 105, 68, 98, 70, 100, 62, 92, 66, 96)(64, 94, 72, 102, 76, 106, 71, 101, 80, 110, 67, 97, 74, 104, 79, 109, 86, 116, 89, 119, 88, 118, 83, 113, 85, 115, 69, 99, 77, 107)
	L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 83)(9, 84)(10, 85)(11, 62)(12, 68)(13, 71)(14, 63)(15, 88)(16, 70)(17, 82)(18, 80)(19, 65)(20, 66)(21, 67)(22, 89)(23, 87)(24, 86)(25, 90)(26, 73)(27, 74)(28, 81)(29, 78)(30, 79)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.74
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.70 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-2, (R * Y2)^2, (Y1^-1, Y3), (Y2, Y1^-1), (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^4, Y1^3 * Y2^-1 * Y1, (Y2^-1 * Y3 * Y1^-1)^2, Y2^-1 * Y1^-2 * Y2^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 15, 45, 3, 33, 9, 39, 22, 52, 21, 51, 13, 43, 25, 55, 17, 47, 6, 36, 11, 41, 20, 50, 5, 35)(4, 34, 10, 40, 23, 53, 30, 60, 14, 44, 7, 37, 12, 42, 24, 54, 28, 58, 16, 46, 26, 56, 19, 49, 27, 57, 29, 59, 18, 48)(61, 91, 63, 93, 73, 103, 71, 101, 62, 92, 69, 99, 85, 115, 80, 110, 68, 98, 82, 112, 77, 107, 65, 95, 75, 105, 81, 111, 66, 96)(64, 94, 74, 104, 88, 118, 87, 117, 70, 100, 67, 97, 76, 106, 89, 119, 83, 113, 72, 102, 86, 116, 78, 108, 90, 120, 84, 114, 79, 109)
	L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 83)(9, 67)(10, 66)(11, 87)(12, 62)(13, 88)(14, 65)(15, 90)(16, 63)(17, 86)(18, 85)(19, 82)(20, 89)(21, 84)(22, 72)(23, 71)(24, 68)(25, 76)(26, 69)(27, 81)(28, 75)(29, 73)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.75
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.71 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^2, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y3^2 * Y2^-1, Y3^6, Y2^5 * Y3^2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 9, 39, 19, 49, 21, 51, 23, 53, 30, 60, 26, 56, 24, 54, 15, 45, 11, 41, 13, 43, 3, 33, 5, 35)(4, 34, 8, 38, 17, 47, 14, 44, 18, 48, 7, 37, 10, 40, 20, 50, 22, 52, 29, 59, 28, 58, 25, 55, 27, 57, 12, 42, 16, 46)(61, 91, 63, 93, 71, 101, 84, 114, 90, 120, 81, 111, 69, 99, 62, 92, 65, 95, 73, 103, 75, 105, 86, 116, 83, 113, 79, 109, 66, 96)(64, 94, 72, 102, 85, 115, 89, 119, 80, 110, 67, 97, 74, 104, 68, 98, 76, 106, 87, 117, 88, 118, 82, 112, 70, 100, 78, 108, 77, 107)
	L = (1, 64)(2, 68)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 71)(9, 74)(10, 62)(11, 85)(12, 86)(13, 87)(14, 63)(15, 88)(16, 84)(17, 73)(18, 65)(19, 78)(20, 66)(21, 67)(22, 69)(23, 70)(24, 89)(25, 83)(26, 82)(27, 90)(28, 81)(29, 79)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.76
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.72 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^2, Y3 * Y1^-1 * Y3, (Y2^-1 * Y3^-1)^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^7 * Y2^-1, (Y3^-1 * Y1^-1)^10, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 17, 47, 25, 55, 21, 51, 12, 42, 3, 33, 6, 36, 10, 40, 19, 49, 27, 57, 23, 53, 15, 45, 5, 35)(4, 34, 9, 39, 18, 48, 26, 56, 29, 59, 22, 52, 13, 43, 11, 41, 14, 44, 20, 50, 28, 58, 30, 60, 24, 54, 16, 46, 7, 37)(61, 91, 63, 93, 65, 95, 72, 102, 75, 105, 81, 111, 83, 113, 85, 115, 87, 117, 77, 107, 79, 109, 68, 98, 70, 100, 62, 92, 66, 96)(64, 94, 71, 101, 67, 97, 73, 103, 76, 106, 82, 112, 84, 114, 89, 119, 90, 120, 86, 116, 88, 118, 78, 108, 80, 110, 69, 99, 74, 104)
	L = (1, 64)(2, 69)(3, 71)(4, 62)(5, 67)(6, 74)(7, 61)(8, 78)(9, 68)(10, 80)(11, 66)(12, 73)(13, 63)(14, 70)(15, 76)(16, 65)(17, 86)(18, 77)(19, 88)(20, 79)(21, 82)(22, 72)(23, 84)(24, 75)(25, 89)(26, 85)(27, 90)(28, 87)(29, 81)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.78
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.73 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y2^-1)^2, Y2^-1 * Y3^-2 * Y2^-1, (Y2^-1, Y3^-1), (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y2^-3 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1^3, Y3^-2 * Y1^-1 * Y3^-2, Y1^-2 * Y3 * Y1^-1 * Y3 * Y2^-1, (Y2^-1 * Y3)^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 15, 45, 3, 33, 9, 39, 23, 53, 17, 47, 13, 43, 26, 56, 21, 51, 6, 36, 11, 41, 20, 50, 5, 35)(4, 34, 10, 40, 24, 54, 29, 59, 14, 44, 27, 57, 30, 60, 22, 52, 7, 37, 12, 42, 25, 55, 19, 49, 16, 46, 28, 58, 18, 48)(61, 91, 63, 93, 73, 103, 71, 101, 62, 92, 69, 99, 86, 116, 80, 110, 68, 98, 83, 113, 81, 111, 65, 95, 75, 105, 77, 107, 66, 96)(64, 94, 74, 104, 67, 97, 76, 106, 70, 100, 87, 117, 72, 102, 88, 118, 84, 114, 90, 120, 85, 115, 78, 108, 89, 119, 82, 112, 79, 109)
	L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 84)(9, 87)(10, 73)(11, 76)(12, 62)(13, 67)(14, 66)(15, 89)(16, 63)(17, 82)(18, 83)(19, 75)(20, 88)(21, 85)(22, 65)(23, 90)(24, 86)(25, 68)(26, 72)(27, 71)(28, 69)(29, 81)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.77
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.74 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-2, Y2^-2 * Y1 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (Y3, Y1^-1), Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y2 * Y1^-3, (R * Y1)^2, Y3 * Y2^2 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y3^6, Y3^-3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3^-2 * Y2 * Y3^-2 * Y1 * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 3, 33, 9, 39, 7, 37, 12, 42, 18, 48, 13, 43, 19, 49, 17, 47, 22, 52, 27, 57, 23, 53, 28, 58, 24, 54, 29, 59, 26, 56, 30, 60, 25, 55, 14, 44, 20, 50, 16, 46, 21, 51, 15, 45, 4, 34, 10, 40, 6, 36, 11, 41, 5, 35)(61, 91, 63, 93, 72, 102, 79, 109, 87, 117, 84, 114, 90, 120, 80, 110, 75, 105, 66, 96)(62, 92, 69, 99, 78, 108, 77, 107, 83, 113, 89, 119, 85, 115, 76, 106, 64, 94, 71, 101)(65, 95, 68, 98, 67, 97, 73, 103, 82, 112, 88, 118, 86, 116, 74, 104, 81, 111, 70, 100)
	L = (1, 64)(2, 70)(3, 71)(4, 74)(5, 75)(6, 76)(7, 61)(8, 66)(9, 65)(10, 80)(11, 81)(12, 62)(13, 63)(14, 84)(15, 85)(16, 86)(17, 67)(18, 68)(19, 69)(20, 89)(21, 90)(22, 72)(23, 73)(24, 77)(25, 88)(26, 87)(27, 78)(28, 79)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.69
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.75 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3 * Y2 * Y3, Y3^2 * Y1 * Y2, (Y3^-1, Y2^-1), (R * Y2)^2, Y2 * Y3 * Y1 * Y3, Y2^-1 * Y3^-2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-3 * Y1^-3, Y1^-1 * Y2 * Y3 * Y1^-3, Y2^-1 * Y3 * Y2^-2 * Y1^2, (Y3 * Y2^-1 * Y1^-1)^2, Y2^2 * Y3 * Y2^2 * Y1^-1, Y2^10, Y3^12 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 14, 44, 7, 37, 12, 42, 26, 56, 15, 45, 3, 33, 9, 39, 23, 53, 21, 51, 30, 60, 16, 46, 28, 58, 19, 49, 29, 59, 13, 43, 27, 57, 17, 47, 6, 36, 11, 41, 25, 55, 18, 48, 4, 34, 10, 40, 24, 54, 20, 50, 5, 35)(61, 91, 63, 93, 73, 103, 84, 114, 72, 102, 88, 118, 78, 108, 82, 112, 81, 111, 66, 96)(62, 92, 69, 99, 87, 117, 80, 110, 86, 116, 79, 109, 64, 94, 74, 104, 90, 120, 71, 101)(65, 95, 75, 105, 89, 119, 70, 100, 67, 97, 76, 106, 85, 115, 68, 98, 83, 113, 77, 107)
	L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 84)(9, 67)(10, 66)(11, 89)(12, 62)(13, 90)(14, 65)(15, 82)(16, 63)(17, 88)(18, 87)(19, 83)(20, 85)(21, 86)(22, 80)(23, 72)(24, 71)(25, 73)(26, 68)(27, 76)(28, 69)(29, 81)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.70
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.76 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), Y1^-1 * Y2 * Y1^-1 * Y3^-1, Y3 * Y1^-1 * Y2^-2, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y2)^2, Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^6, Y3^2 * Y2^2 * Y3^2 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^3, Y2^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 6, 36, 11, 41, 7, 37, 12, 42, 18, 48, 16, 46, 21, 51, 17, 47, 22, 52, 27, 57, 26, 56, 30, 60, 25, 55, 29, 59, 24, 54, 28, 58, 23, 53, 15, 45, 20, 50, 14, 44, 19, 49, 13, 43, 4, 34, 10, 40, 3, 33, 9, 39, 5, 35)(61, 91, 63, 93, 73, 103, 80, 110, 88, 118, 85, 115, 87, 117, 81, 111, 72, 102, 66, 96)(62, 92, 69, 99, 64, 94, 74, 104, 83, 113, 89, 119, 86, 116, 77, 107, 78, 108, 71, 101)(65, 95, 70, 100, 79, 109, 75, 105, 84, 114, 90, 120, 82, 112, 76, 106, 67, 97, 68, 98)
	L = (1, 64)(2, 70)(3, 74)(4, 75)(5, 73)(6, 69)(7, 61)(8, 63)(9, 79)(10, 80)(11, 65)(12, 62)(13, 83)(14, 84)(15, 85)(16, 66)(17, 67)(18, 68)(19, 88)(20, 89)(21, 71)(22, 72)(23, 90)(24, 87)(25, 77)(26, 76)(27, 78)(28, 86)(29, 82)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.71
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.77 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y2, Y3), (Y1, Y2), (R * Y2)^2, (R * Y1)^2, Y2^2 * Y1^3 * Y2, Y1^-3 * Y2^-3, Y2^-1 * Y1^9, Y2^10, Y2^5 * Y3^15, (Y3^-1 * Y1^-1)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 28, 58, 25, 55, 21, 51, 10, 40, 3, 33, 7, 37, 15, 45, 13, 43, 18, 48, 24, 54, 30, 60, 27, 57, 20, 50, 9, 39, 17, 47, 12, 42, 5, 35, 8, 38, 16, 46, 23, 53, 29, 59, 26, 56, 19, 49, 11, 41, 4, 34)(61, 91, 63, 93, 69, 99, 79, 109, 85, 115, 90, 120, 83, 113, 74, 104, 73, 103, 65, 95)(62, 92, 67, 97, 77, 107, 71, 101, 81, 111, 87, 117, 89, 119, 82, 112, 78, 108, 68, 98)(64, 94, 70, 100, 80, 110, 86, 116, 88, 118, 84, 114, 76, 106, 66, 96, 75, 105, 72, 102)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 82)(15, 73)(16, 83)(17, 72)(18, 84)(19, 71)(20, 69)(21, 70)(22, 88)(23, 89)(24, 90)(25, 81)(26, 79)(27, 80)(28, 85)(29, 86)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.73
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.78 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2), Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y1^2, Y3 * Y2 * Y1^2, (R * Y3)^2, Y3^3 * Y2^-1, (Y3^-1, Y1), (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^4 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 29, 59, 27, 57, 17, 47, 4, 34, 10, 40, 6, 36, 11, 41, 21, 51, 13, 43, 23, 53, 16, 46, 24, 54, 18, 48, 25, 55, 19, 49, 26, 56, 15, 45, 3, 33, 9, 39, 7, 37, 12, 42, 22, 52, 30, 60, 28, 58, 14, 44, 5, 35)(61, 91, 63, 93, 73, 103, 80, 110, 72, 102, 84, 114, 77, 107, 88, 118, 79, 109, 66, 96)(62, 92, 69, 99, 83, 113, 89, 119, 82, 112, 78, 108, 64, 94, 74, 104, 86, 116, 71, 101)(65, 95, 75, 105, 81, 111, 68, 98, 67, 97, 76, 106, 87, 117, 90, 120, 85, 115, 70, 100)
	L = (1, 64)(2, 70)(3, 74)(4, 76)(5, 77)(6, 78)(7, 61)(8, 66)(9, 65)(10, 84)(11, 85)(12, 62)(13, 86)(14, 87)(15, 88)(16, 63)(17, 83)(18, 67)(19, 82)(20, 71)(21, 79)(22, 68)(23, 75)(24, 69)(25, 72)(26, 90)(27, 73)(28, 89)(29, 81)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.72
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.79 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^2 * Y2^-2, (R * Y2)^2, (Y1, Y2), (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (Y3^-1, Y2), Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-2, Y3^-1 * Y1^-5, (Y2^-1 * Y3)^10, Y1 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-1, Y2^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 21, 51, 19, 49, 7, 37, 12, 42, 24, 54, 29, 59, 15, 45, 4, 34, 10, 40, 23, 53, 17, 47, 5, 35)(3, 33, 9, 39, 22, 52, 20, 50, 28, 58, 14, 44, 26, 56, 30, 60, 16, 46, 27, 57, 13, 43, 25, 55, 18, 48, 6, 36, 11, 41)(61, 91, 63, 93, 68, 98, 82, 112, 79, 109, 88, 118, 72, 102, 86, 116, 89, 119, 76, 106, 64, 94, 73, 103, 83, 113, 78, 108, 65, 95, 71, 101, 62, 92, 69, 99, 81, 111, 80, 110, 67, 97, 74, 104, 84, 114, 90, 120, 75, 105, 87, 117, 70, 100, 85, 115, 77, 107, 66, 96)
	L = (1, 64)(2, 70)(3, 73)(4, 67)(5, 75)(6, 76)(7, 61)(8, 83)(9, 85)(10, 72)(11, 87)(12, 62)(13, 74)(14, 63)(15, 79)(16, 80)(17, 89)(18, 90)(19, 65)(20, 66)(21, 77)(22, 78)(23, 84)(24, 68)(25, 86)(26, 69)(27, 88)(28, 71)(29, 81)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.56
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.80 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2 * Y1 * Y2, (R * Y1)^2, (Y3, Y1^-1), (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y1^-5, (Y2^-1 * Y3)^10, Y1 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 18, 48, 7, 37, 11, 41, 23, 53, 29, 59, 15, 45, 4, 34, 9, 39, 21, 51, 17, 47, 5, 35)(3, 33, 6, 36, 10, 40, 22, 52, 28, 58, 14, 44, 19, 49, 25, 55, 30, 60, 26, 56, 12, 42, 16, 46, 24, 54, 27, 57, 13, 43)(61, 91, 63, 93, 65, 95, 73, 103, 77, 107, 87, 117, 81, 111, 84, 114, 69, 99, 76, 106, 64, 94, 72, 102, 75, 105, 86, 116, 89, 119, 90, 120, 83, 113, 85, 115, 71, 101, 79, 109, 67, 97, 74, 104, 78, 108, 88, 118, 80, 110, 82, 112, 68, 98, 70, 100, 62, 92, 66, 96)
	L = (1, 64)(2, 69)(3, 72)(4, 67)(5, 75)(6, 76)(7, 61)(8, 81)(9, 71)(10, 84)(11, 62)(12, 74)(13, 86)(14, 63)(15, 78)(16, 79)(17, 89)(18, 65)(19, 66)(20, 77)(21, 83)(22, 87)(23, 68)(24, 85)(25, 70)(26, 88)(27, 90)(28, 73)(29, 80)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.59
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.81 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y2, Y3), (Y3^-1, Y1), (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1^2 * Y2^2, Y2^-1 * Y1 * Y2^-3, Y1^3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 24, 54, 21, 51, 7, 37, 12, 42, 22, 52, 13, 43, 17, 47, 4, 34, 10, 40, 25, 55, 19, 49, 5, 35)(3, 33, 9, 39, 18, 48, 28, 58, 30, 60, 16, 46, 20, 50, 6, 36, 11, 41, 26, 56, 14, 44, 27, 57, 23, 53, 29, 59, 15, 45)(61, 91, 63, 93, 73, 103, 71, 101, 62, 92, 69, 99, 77, 107, 86, 116, 68, 98, 78, 108, 64, 94, 74, 104, 84, 114, 88, 118, 70, 100, 87, 117, 81, 111, 90, 120, 85, 115, 83, 113, 67, 97, 76, 106, 79, 109, 89, 119, 72, 102, 80, 110, 65, 95, 75, 105, 82, 112, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 67)(5, 77)(6, 78)(7, 61)(8, 85)(9, 87)(10, 72)(11, 88)(12, 62)(13, 84)(14, 76)(15, 86)(16, 63)(17, 81)(18, 83)(19, 73)(20, 69)(21, 65)(22, 68)(23, 66)(24, 79)(25, 82)(26, 90)(27, 80)(28, 89)(29, 71)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.57
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.82 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y1, Y3^-1), (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, Y2^-2 * Y3^-1 * Y1 * Y3^-1, Y2^-2 * Y1^-4, (Y2 * Y1^2)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-1 * Y3 * Y2^24 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 18, 48, 7, 37, 12, 42, 24, 54, 27, 57, 15, 45, 4, 34, 10, 40, 22, 52, 16, 46, 5, 35)(3, 33, 9, 39, 21, 51, 17, 47, 6, 36, 11, 41, 23, 53, 29, 59, 28, 58, 19, 49, 13, 43, 25, 55, 30, 60, 26, 56, 14, 44)(61, 91, 63, 93, 70, 100, 85, 115, 84, 114, 89, 119, 80, 110, 77, 107, 65, 95, 74, 104, 64, 94, 73, 103, 72, 102, 83, 113, 68, 98, 81, 111, 76, 106, 86, 116, 75, 105, 79, 109, 67, 97, 71, 101, 62, 92, 69, 99, 82, 112, 90, 120, 87, 117, 88, 118, 78, 108, 66, 96)
	L = (1, 64)(2, 70)(3, 73)(4, 67)(5, 75)(6, 74)(7, 61)(8, 82)(9, 85)(10, 72)(11, 63)(12, 62)(13, 71)(14, 79)(15, 78)(16, 87)(17, 86)(18, 65)(19, 66)(20, 76)(21, 90)(22, 84)(23, 69)(24, 68)(25, 83)(26, 88)(27, 80)(28, 77)(29, 81)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.58
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.83 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2, Y3 * Y2^2, (Y1^-1 * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-7 * Y1, (Y3 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 10, 40, 16, 46, 18, 48, 24, 54, 26, 56, 28, 58, 20, 50, 21, 51, 12, 42, 13, 43, 4, 34, 5, 35)(3, 33, 8, 38, 11, 41, 17, 47, 19, 49, 25, 55, 27, 57, 29, 59, 30, 60, 22, 52, 23, 53, 14, 44, 15, 45, 6, 36, 9, 39)(61, 91, 63, 93, 67, 97, 71, 101, 76, 106, 79, 109, 84, 114, 87, 117, 88, 118, 90, 120, 81, 111, 83, 113, 73, 103, 75, 105, 65, 95, 69, 99, 62, 92, 68, 98, 70, 100, 77, 107, 78, 108, 85, 115, 86, 116, 89, 119, 80, 110, 82, 112, 72, 102, 74, 104, 64, 94, 66, 96)
	L = (1, 64)(2, 65)(3, 66)(4, 72)(5, 73)(6, 74)(7, 61)(8, 69)(9, 75)(10, 62)(11, 63)(12, 80)(13, 81)(14, 82)(15, 83)(16, 67)(17, 68)(18, 70)(19, 71)(20, 86)(21, 88)(22, 89)(23, 90)(24, 76)(25, 77)(26, 78)(27, 79)(28, 84)(29, 85)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.65
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.84 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^15, (Y3 * Y2^-1)^10, (Y3^-1 * Y1^-1)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 10, 40, 14, 44, 18, 48, 22, 52, 26, 56, 29, 59, 25, 55, 21, 51, 17, 47, 13, 43, 9, 39, 4, 34)(3, 33, 5, 35, 7, 37, 11, 41, 15, 45, 19, 49, 23, 53, 27, 57, 30, 60, 28, 58, 24, 54, 20, 50, 16, 46, 12, 42, 8, 38)(61, 91, 63, 93, 64, 94, 68, 98, 69, 99, 72, 102, 73, 103, 76, 106, 77, 107, 80, 110, 81, 111, 84, 114, 85, 115, 88, 118, 89, 119, 90, 120, 86, 116, 87, 117, 82, 112, 83, 113, 78, 108, 79, 109, 74, 104, 75, 105, 70, 100, 71, 101, 66, 96, 67, 97, 62, 92, 65, 95)
	L = (1, 62)(2, 66)(3, 65)(4, 61)(5, 67)(6, 70)(7, 71)(8, 63)(9, 64)(10, 74)(11, 75)(12, 68)(13, 69)(14, 78)(15, 79)(16, 72)(17, 73)(18, 82)(19, 83)(20, 76)(21, 77)(22, 86)(23, 87)(24, 80)(25, 81)(26, 89)(27, 90)(28, 84)(29, 85)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.68
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.85 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^2, Y3 * Y2^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^7, (Y3 * Y1^-1)^5 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 16, 46, 24, 54, 21, 51, 13, 43, 4, 34, 7, 37, 11, 41, 19, 49, 27, 57, 22, 52, 14, 44, 5, 35)(3, 33, 9, 39, 17, 47, 25, 55, 29, 59, 23, 53, 15, 45, 6, 36, 10, 40, 18, 48, 26, 56, 30, 60, 28, 58, 20, 50, 12, 42)(61, 91, 63, 93, 67, 97, 70, 100, 62, 92, 69, 99, 71, 101, 78, 108, 68, 98, 77, 107, 79, 109, 86, 116, 76, 106, 85, 115, 87, 117, 90, 120, 84, 114, 89, 119, 82, 112, 88, 118, 81, 111, 83, 113, 74, 104, 80, 110, 73, 103, 75, 105, 65, 95, 72, 102, 64, 94, 66, 96)
	L = (1, 64)(2, 67)(3, 66)(4, 65)(5, 73)(6, 72)(7, 61)(8, 71)(9, 70)(10, 63)(11, 62)(12, 75)(13, 74)(14, 81)(15, 80)(16, 79)(17, 78)(18, 69)(19, 68)(20, 83)(21, 82)(22, 84)(23, 88)(24, 87)(25, 86)(26, 77)(27, 76)(28, 89)(29, 90)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.60
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.86 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^2, Y2 * Y1 * Y2, (Y3, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3^-7, (Y3 * Y1^-1)^5 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 9, 39, 15, 45, 17, 47, 23, 53, 25, 55, 28, 58, 20, 50, 21, 51, 12, 42, 13, 43, 4, 34, 5, 35)(3, 33, 6, 36, 8, 38, 14, 44, 16, 46, 22, 52, 24, 54, 29, 59, 30, 60, 26, 56, 27, 57, 18, 48, 19, 49, 10, 40, 11, 41)(61, 91, 63, 93, 65, 95, 71, 101, 64, 94, 70, 100, 73, 103, 79, 109, 72, 102, 78, 108, 81, 111, 87, 117, 80, 110, 86, 116, 88, 118, 90, 120, 85, 115, 89, 119, 83, 113, 84, 114, 77, 107, 82, 112, 75, 105, 76, 106, 69, 99, 74, 104, 67, 97, 68, 98, 62, 92, 66, 96)
	L = (1, 64)(2, 65)(3, 70)(4, 72)(5, 73)(6, 71)(7, 61)(8, 63)(9, 62)(10, 78)(11, 79)(12, 80)(13, 81)(14, 66)(15, 67)(16, 68)(17, 69)(18, 86)(19, 87)(20, 85)(21, 88)(22, 74)(23, 75)(24, 76)(25, 77)(26, 89)(27, 90)(28, 83)(29, 82)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.63
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.87 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, Y2^-4 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^6 * Y2, (Y3 * Y2^-1)^10, (Y3^-1 * Y1^-1)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 29, 59, 21, 51, 13, 43, 9, 39, 17, 47, 25, 55, 27, 57, 19, 49, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 23, 53, 28, 58, 20, 50, 12, 42, 5, 35, 8, 38, 16, 46, 24, 54, 30, 60, 26, 56, 18, 48, 10, 40)(61, 91, 63, 93, 69, 99, 68, 98, 62, 92, 67, 97, 77, 107, 76, 106, 66, 96, 75, 105, 85, 115, 84, 114, 74, 104, 83, 113, 87, 117, 90, 120, 82, 112, 88, 118, 79, 109, 86, 116, 89, 119, 80, 110, 71, 101, 78, 108, 81, 111, 72, 102, 64, 94, 70, 100, 73, 103, 65, 95)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 69)(14, 82)(15, 83)(16, 84)(17, 85)(18, 70)(19, 71)(20, 72)(21, 73)(22, 89)(23, 88)(24, 90)(25, 87)(26, 78)(27, 79)(28, 80)(29, 81)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.67
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.88 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (Y2, Y3^-1), (R * Y3)^2, Y2^-4 * Y3, Y3^-1 * Y2^4, Y2 * Y1^-1 * Y2 * Y1^-2 * Y3, Y2^-2 * Y1^-4, Y1^-1 * Y2^2 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 20, 50, 28, 58, 16, 46, 4, 34, 7, 37, 11, 41, 25, 55, 12, 42, 26, 56, 18, 48, 5, 35)(3, 33, 9, 39, 23, 53, 19, 49, 6, 36, 10, 40, 24, 54, 13, 43, 15, 45, 27, 57, 30, 60, 17, 47, 21, 51, 29, 59, 14, 44)(61, 91, 63, 93, 72, 102, 77, 107, 64, 94, 73, 103, 82, 112, 79, 109, 65, 95, 74, 104, 85, 115, 90, 120, 76, 106, 84, 114, 68, 98, 83, 113, 78, 108, 89, 119, 71, 101, 87, 117, 88, 118, 70, 100, 62, 92, 69, 99, 86, 116, 81, 111, 67, 97, 75, 105, 80, 110, 66, 96)
	L = (1, 64)(2, 67)(3, 73)(4, 65)(5, 76)(6, 77)(7, 61)(8, 71)(9, 75)(10, 81)(11, 62)(12, 82)(13, 74)(14, 84)(15, 63)(16, 78)(17, 79)(18, 88)(19, 90)(20, 72)(21, 66)(22, 85)(23, 87)(24, 89)(25, 68)(26, 80)(27, 69)(28, 86)(29, 70)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.62
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.89 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^2, Y2^-2 * Y1^2, (Y2, Y1), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y1^-7 * Y3, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 19, 49, 27, 57, 23, 53, 14, 44, 4, 34, 7, 37, 11, 41, 21, 51, 29, 59, 25, 55, 16, 46, 5, 35)(3, 33, 9, 39, 20, 50, 28, 58, 24, 54, 15, 45, 18, 48, 12, 42, 13, 43, 22, 52, 30, 60, 26, 56, 17, 47, 6, 36, 10, 40)(61, 91, 63, 93, 68, 98, 80, 110, 87, 117, 84, 114, 74, 104, 78, 108, 67, 97, 73, 103, 81, 111, 90, 120, 85, 115, 77, 107, 65, 95, 70, 100, 62, 92, 69, 99, 79, 109, 88, 118, 83, 113, 75, 105, 64, 94, 72, 102, 71, 101, 82, 112, 89, 119, 86, 116, 76, 106, 66, 96)
	L = (1, 64)(2, 67)(3, 72)(4, 65)(5, 74)(6, 75)(7, 61)(8, 71)(9, 73)(10, 78)(11, 62)(12, 70)(13, 63)(14, 76)(15, 77)(16, 83)(17, 84)(18, 66)(19, 81)(20, 82)(21, 68)(22, 69)(23, 85)(24, 86)(25, 87)(26, 88)(27, 89)(28, 90)(29, 79)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.61
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.90 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2, (Y3, Y2), (Y2, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2^-4, Y3^3 * Y2^-2 * Y1^-1, Y3^-1 * Y2 * Y3^-2 * Y2 * Y1, Y2^-1 * Y3^-3 * Y2^-1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 10, 40, 21, 51, 25, 55, 26, 56, 19, 49, 11, 41, 22, 52, 27, 57, 15, 45, 16, 46, 4, 34, 5, 35)(3, 33, 8, 38, 14, 44, 23, 53, 30, 60, 17, 47, 18, 48, 6, 36, 9, 39, 20, 50, 24, 54, 28, 58, 29, 59, 12, 42, 13, 43)(61, 91, 63, 93, 71, 101, 69, 99, 62, 92, 68, 98, 82, 112, 80, 110, 67, 97, 74, 104, 87, 117, 84, 114, 70, 100, 83, 113, 75, 105, 88, 118, 81, 111, 90, 120, 76, 106, 89, 119, 85, 115, 77, 107, 64, 94, 72, 102, 86, 116, 78, 108, 65, 95, 73, 103, 79, 109, 66, 96)
	L = (1, 64)(2, 65)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 73)(9, 78)(10, 62)(11, 86)(12, 88)(13, 89)(14, 63)(15, 82)(16, 87)(17, 83)(18, 90)(19, 85)(20, 66)(21, 67)(22, 79)(23, 68)(24, 69)(25, 70)(26, 81)(27, 71)(28, 80)(29, 84)(30, 74)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.64
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.91 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 15, 15, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3, (Y1, Y2^-1), Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^4 * Y2, Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y1 * Y2^-1 * Y3^2 * Y2^-5, (Y2^-1 * Y1)^10, (Y3^-1 * Y1^-1)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 6, 36, 14, 44, 13, 43, 18, 48, 24, 54, 27, 57, 30, 60, 29, 59, 20, 50, 9, 39, 17, 47, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 12, 42, 5, 35, 8, 38, 16, 46, 23, 53, 22, 52, 26, 56, 28, 58, 19, 49, 25, 55, 21, 51, 10, 40)(61, 91, 63, 93, 69, 99, 79, 109, 87, 117, 83, 113, 74, 104, 72, 102, 64, 94, 70, 100, 80, 110, 88, 118, 84, 114, 76, 106, 66, 96, 75, 105, 71, 101, 81, 111, 89, 119, 86, 116, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 85, 115, 90, 120, 82, 112, 73, 103, 65, 95)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 73)(15, 72)(16, 83)(17, 71)(18, 84)(19, 85)(20, 69)(21, 70)(22, 86)(23, 82)(24, 87)(25, 81)(26, 88)(27, 90)(28, 79)(29, 80)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.66
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.92 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^-1 * Y1^-3, Y2^-1 * Y1 * Y2^-2, (R * Y2)^2, (Y2, Y1), (Y3^-1, Y1), (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 6, 36, 11, 41, 21, 51, 14, 44, 3, 33, 9, 39, 5, 35)(4, 34, 10, 40, 20, 50, 17, 47, 25, 55, 29, 59, 27, 57, 13, 43, 23, 53, 16, 46)(7, 37, 12, 42, 22, 52, 19, 49, 26, 56, 30, 60, 28, 58, 15, 45, 24, 54, 18, 48)(61, 91, 63, 93, 71, 101, 62, 92, 69, 99, 81, 111, 68, 98, 65, 95, 74, 104, 66, 96)(64, 94, 73, 103, 85, 115, 70, 100, 83, 113, 89, 119, 80, 110, 76, 106, 87, 117, 77, 107)(67, 97, 75, 105, 86, 116, 72, 102, 84, 114, 90, 120, 82, 112, 78, 108, 88, 118, 79, 109)
	L = (1, 64)(2, 70)(3, 73)(4, 67)(5, 76)(6, 77)(7, 61)(8, 80)(9, 83)(10, 72)(11, 85)(12, 62)(13, 75)(14, 87)(15, 63)(16, 78)(17, 79)(18, 65)(19, 66)(20, 82)(21, 89)(22, 68)(23, 84)(24, 69)(25, 86)(26, 71)(27, 88)(28, 74)(29, 90)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.106
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.93 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2^3 * Y1^-3, Y2^3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-9, Y1^10, (Y3^-1 * Y1^-1)^10, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 28, 58, 25, 55, 19, 49, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 23, 53, 29, 59, 27, 57, 21, 51, 13, 43, 18, 48, 10, 40)(5, 35, 8, 38, 16, 46, 9, 39, 17, 47, 24, 54, 30, 60, 26, 56, 20, 50, 12, 42)(61, 91, 63, 93, 69, 99, 74, 104, 83, 113, 90, 120, 85, 115, 81, 111, 72, 102, 64, 94, 70, 100, 76, 106, 66, 96, 75, 105, 84, 114, 88, 118, 87, 117, 80, 110, 71, 101, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 82, 112, 89, 119, 86, 116, 79, 109, 73, 103, 65, 95)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.94 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2, Y1), (R * Y3)^2, Y2^3 * Y1^3, Y1^-3 * Y2^-3, Y2^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^10, Y1^-1 * Y2^9, (Y3^-1 * Y1^-1)^10, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 28, 58, 26, 56, 19, 49, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 13, 43, 18, 48, 24, 54, 30, 60, 25, 55, 21, 51, 10, 40)(5, 35, 8, 38, 16, 46, 23, 53, 29, 59, 27, 57, 20, 50, 9, 39, 17, 47, 12, 42)(61, 91, 63, 93, 69, 99, 79, 109, 85, 115, 89, 119, 82, 112, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 71, 101, 81, 111, 87, 117, 88, 118, 84, 114, 76, 106, 66, 96, 75, 105, 72, 102, 64, 94, 70, 100, 80, 110, 86, 116, 90, 120, 83, 113, 74, 104, 73, 103, 65, 95)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.95 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^3 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^10, (Y3^-1 * Y1^-1)^10, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 12, 42, 18, 48, 24, 54, 22, 52, 16, 46, 10, 40, 4, 34)(3, 33, 7, 37, 13, 43, 19, 49, 25, 55, 29, 59, 27, 57, 21, 51, 15, 45, 9, 39)(5, 35, 8, 38, 14, 44, 20, 50, 26, 56, 30, 60, 28, 58, 23, 53, 17, 47, 11, 41)(61, 91, 63, 93, 68, 98, 62, 92, 67, 97, 74, 104, 66, 96, 73, 103, 80, 110, 72, 102, 79, 109, 86, 116, 78, 108, 85, 115, 90, 120, 84, 114, 89, 119, 88, 118, 82, 112, 87, 117, 83, 113, 76, 106, 81, 111, 77, 107, 70, 100, 75, 105, 71, 101, 64, 94, 69, 99, 65, 95)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.96 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^10, (Y3^-1 * Y1^-1)^10, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 12, 42, 18, 48, 24, 54, 23, 53, 17, 47, 11, 41, 4, 34)(3, 33, 7, 37, 13, 43, 19, 49, 25, 55, 29, 59, 28, 58, 22, 52, 16, 46, 10, 40)(5, 35, 8, 38, 14, 44, 20, 50, 26, 56, 30, 60, 27, 57, 21, 51, 15, 45, 9, 39)(61, 91, 63, 93, 69, 99, 64, 94, 70, 100, 75, 105, 71, 101, 76, 106, 81, 111, 77, 107, 82, 112, 87, 117, 83, 113, 88, 118, 90, 120, 84, 114, 89, 119, 86, 116, 78, 108, 85, 115, 80, 110, 72, 102, 79, 109, 74, 104, 66, 96, 73, 103, 68, 98, 62, 92, 67, 97, 65, 95)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.97 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-2, (Y3, Y1), (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y2^-1, Y3^-1), (R * Y3)^2, Y3^5, Y3 * Y1^4, Y3 * Y1 * Y2^-3, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y1^-1 * Y2^-1 * Y1^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 7, 37, 12, 42, 4, 34, 10, 40, 18, 48, 5, 35)(3, 33, 9, 39, 23, 53, 21, 51, 16, 46, 27, 57, 14, 44, 26, 56, 30, 60, 15, 45)(6, 36, 11, 41, 24, 54, 29, 59, 22, 52, 28, 58, 17, 47, 13, 43, 25, 55, 19, 49)(61, 91, 63, 93, 73, 103, 70, 100, 86, 116, 82, 112, 67, 97, 76, 106, 71, 101, 62, 92, 69, 99, 85, 115, 78, 108, 90, 120, 88, 118, 72, 102, 87, 117, 84, 114, 68, 98, 83, 113, 79, 109, 65, 95, 75, 105, 77, 107, 64, 94, 74, 104, 89, 119, 80, 110, 81, 111, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 68)(5, 72)(6, 77)(7, 61)(8, 78)(9, 86)(10, 80)(11, 73)(12, 62)(13, 89)(14, 83)(15, 87)(16, 63)(17, 84)(18, 67)(19, 88)(20, 65)(21, 75)(22, 66)(23, 90)(24, 85)(25, 82)(26, 81)(27, 69)(28, 71)(29, 79)(30, 76)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.104
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.98 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^2, Y2^2 * Y1^-1 * Y2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^5, Y3^5, (Y3^2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 10, 40, 19, 49, 22, 52, 14, 44, 15, 45, 4, 34, 5, 35)(3, 33, 8, 38, 13, 43, 20, 50, 25, 55, 29, 59, 23, 53, 24, 54, 11, 41, 12, 42)(6, 36, 9, 39, 18, 48, 21, 51, 28, 58, 30, 60, 26, 56, 27, 57, 16, 46, 17, 47)(61, 91, 63, 93, 69, 99, 62, 92, 68, 98, 78, 108, 67, 97, 73, 103, 81, 111, 70, 100, 80, 110, 88, 118, 79, 109, 85, 115, 90, 120, 82, 112, 89, 119, 86, 116, 74, 104, 83, 113, 87, 117, 75, 105, 84, 114, 76, 106, 64, 94, 71, 101, 77, 107, 65, 95, 72, 102, 66, 96)
	L = (1, 64)(2, 65)(3, 71)(4, 74)(5, 75)(6, 76)(7, 61)(8, 72)(9, 77)(10, 62)(11, 83)(12, 84)(13, 63)(14, 79)(15, 82)(16, 86)(17, 87)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 85)(24, 89)(25, 73)(26, 88)(27, 90)(28, 78)(29, 80)(30, 81)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.103
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.99 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (Y2^-1, Y3), Y1^-1 * Y2^-3, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^5, Y3^5, (Y3^-1 * Y1^-1)^10 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 4, 34, 9, 39, 15, 45, 21, 51, 19, 49, 17, 47, 7, 37, 5, 35)(3, 33, 8, 38, 12, 42, 20, 50, 24, 54, 29, 59, 26, 56, 25, 55, 14, 44, 13, 43)(6, 36, 10, 40, 16, 46, 22, 52, 27, 57, 30, 60, 28, 58, 23, 53, 18, 48, 11, 41)(61, 91, 63, 93, 71, 101, 65, 95, 73, 103, 78, 108, 67, 97, 74, 104, 83, 113, 77, 107, 85, 115, 88, 118, 79, 109, 86, 116, 90, 120, 81, 111, 89, 119, 87, 117, 75, 105, 84, 114, 82, 112, 69, 99, 80, 110, 76, 106, 64, 94, 72, 102, 70, 100, 62, 92, 68, 98, 66, 96)
	L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 62)(6, 76)(7, 61)(8, 80)(9, 81)(10, 82)(11, 70)(12, 84)(13, 68)(14, 63)(15, 79)(16, 87)(17, 65)(18, 66)(19, 67)(20, 89)(21, 77)(22, 90)(23, 71)(24, 86)(25, 73)(26, 74)(27, 88)(28, 78)(29, 85)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.105
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.100 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y1, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1, Y3^5, Y1 * Y2^-3 * Y3, (Y3 * Y1 * Y3)^2, Y1 * Y3 * Y2 * Y3^2 * Y2^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 4, 34, 9, 39, 15, 45, 24, 54, 21, 51, 18, 48, 7, 37, 5, 35)(3, 33, 8, 38, 12, 42, 23, 53, 26, 56, 29, 59, 27, 57, 19, 49, 14, 44, 13, 43)(6, 36, 10, 40, 16, 46, 11, 41, 22, 52, 25, 55, 30, 60, 28, 58, 20, 50, 17, 47)(61, 91, 63, 93, 71, 101, 69, 99, 83, 113, 90, 120, 81, 111, 87, 117, 77, 107, 65, 95, 73, 103, 76, 106, 64, 94, 72, 102, 85, 115, 84, 114, 89, 119, 80, 110, 67, 97, 74, 104, 70, 100, 62, 92, 68, 98, 82, 112, 75, 105, 86, 116, 88, 118, 78, 108, 79, 109, 66, 96)
	L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 62)(6, 76)(7, 61)(8, 83)(9, 84)(10, 71)(11, 85)(12, 86)(13, 68)(14, 63)(15, 81)(16, 82)(17, 70)(18, 65)(19, 73)(20, 66)(21, 67)(22, 90)(23, 89)(24, 78)(25, 88)(26, 87)(27, 74)(28, 77)(29, 79)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.102
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.101 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3 * Y1, (Y1^-1, Y2^-1), (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^2 * Y1, Y3^5, (Y3^2 * Y1^-1)^2, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 10, 40, 21, 51, 24, 54, 15, 45, 16, 46, 4, 34, 5, 35)(3, 33, 8, 38, 14, 44, 19, 49, 22, 52, 29, 59, 27, 57, 28, 58, 12, 42, 13, 43)(6, 36, 9, 39, 20, 50, 23, 53, 30, 60, 25, 55, 26, 56, 11, 41, 17, 47, 18, 48)(61, 91, 63, 93, 71, 101, 76, 106, 88, 118, 90, 120, 81, 111, 82, 112, 69, 99, 62, 92, 68, 98, 77, 107, 64, 94, 72, 102, 85, 115, 84, 114, 89, 119, 80, 110, 67, 97, 74, 104, 78, 108, 65, 95, 73, 103, 86, 116, 75, 105, 87, 117, 83, 113, 70, 100, 79, 109, 66, 96)
	L = (1, 64)(2, 65)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 73)(9, 78)(10, 62)(11, 85)(12, 87)(13, 88)(14, 63)(15, 81)(16, 84)(17, 86)(18, 71)(19, 68)(20, 66)(21, 67)(22, 74)(23, 69)(24, 70)(25, 83)(26, 90)(27, 82)(28, 89)(29, 79)(30, 80)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.102 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1^-1), (Y2, Y3^-1), Y1^-1 * Y3^2 * Y1^-1, (R * Y3)^2, Y2^-3 * Y1^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, Y3^3 * Y1^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 19, 49, 7, 37, 12, 42, 4, 34, 10, 40, 18, 48, 5, 35)(3, 33, 9, 39, 21, 51, 30, 60, 16, 46, 24, 54, 14, 44, 23, 53, 29, 59, 15, 45)(6, 36, 11, 41, 22, 52, 28, 58, 20, 50, 26, 56, 17, 47, 25, 55, 27, 57, 13, 43)(61, 91, 63, 93, 73, 103, 65, 95, 75, 105, 87, 117, 78, 108, 89, 119, 85, 115, 70, 100, 83, 113, 77, 107, 64, 94, 74, 104, 86, 116, 72, 102, 84, 114, 80, 110, 67, 97, 76, 106, 88, 118, 79, 109, 90, 120, 82, 112, 68, 98, 81, 111, 71, 101, 62, 92, 69, 99, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 68)(5, 72)(6, 77)(7, 61)(8, 78)(9, 83)(10, 79)(11, 85)(12, 62)(13, 86)(14, 81)(15, 84)(16, 63)(17, 82)(18, 67)(19, 65)(20, 66)(21, 89)(22, 87)(23, 90)(24, 69)(25, 88)(26, 71)(27, 80)(28, 73)(29, 76)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.100
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.103 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^-1, (Y2^-1, Y1^-1), (Y2, Y3^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^5, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-2, (Y3^2 * Y1^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 7, 37, 10, 40, 21, 51, 24, 54, 15, 45, 16, 46, 4, 34, 5, 35)(3, 33, 8, 38, 14, 44, 23, 53, 27, 57, 30, 60, 26, 56, 19, 49, 12, 42, 13, 43)(6, 36, 9, 39, 20, 50, 11, 41, 22, 52, 25, 55, 28, 58, 29, 59, 17, 47, 18, 48)(61, 91, 63, 93, 71, 101, 70, 100, 83, 113, 88, 118, 75, 105, 86, 116, 78, 108, 65, 95, 73, 103, 80, 110, 67, 97, 74, 104, 85, 115, 84, 114, 90, 120, 77, 107, 64, 94, 72, 102, 69, 99, 62, 92, 68, 98, 82, 112, 81, 111, 87, 117, 89, 119, 76, 106, 79, 109, 66, 96)
	L = (1, 64)(2, 65)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 73)(9, 78)(10, 62)(11, 69)(12, 86)(13, 79)(14, 63)(15, 81)(16, 84)(17, 88)(18, 89)(19, 90)(20, 66)(21, 67)(22, 80)(23, 68)(24, 70)(25, 71)(26, 87)(27, 74)(28, 82)(29, 85)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.98
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.104 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2, (R * Y2)^2, (R * Y3)^2, (Y1, Y2), (Y2, Y3), (R * Y1)^2, Y2 * Y3 * Y2^2 * Y1, Y3^5, Y1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y3, Y1 * Y2^-2 * Y3^2 * Y2^-1 * Y3, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2, (Y3^-1 * Y1^-1)^10 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 4, 34, 9, 39, 15, 45, 22, 52, 21, 51, 18, 48, 7, 37, 5, 35)(3, 33, 8, 38, 12, 42, 19, 49, 24, 54, 30, 60, 28, 58, 27, 57, 14, 44, 13, 43)(6, 36, 10, 40, 16, 46, 23, 53, 29, 59, 26, 56, 25, 55, 11, 41, 20, 50, 17, 47)(61, 91, 63, 93, 71, 101, 78, 108, 87, 117, 89, 119, 75, 105, 84, 114, 70, 100, 62, 92, 68, 98, 80, 110, 67, 97, 74, 104, 86, 116, 82, 112, 90, 120, 76, 106, 64, 94, 72, 102, 77, 107, 65, 95, 73, 103, 85, 115, 81, 111, 88, 118, 83, 113, 69, 99, 79, 109, 66, 96)
	L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 62)(6, 76)(7, 61)(8, 79)(9, 82)(10, 83)(11, 77)(12, 84)(13, 68)(14, 63)(15, 81)(16, 89)(17, 70)(18, 65)(19, 90)(20, 66)(21, 67)(22, 78)(23, 86)(24, 88)(25, 80)(26, 71)(27, 73)(28, 74)(29, 85)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.97
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.105 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, (Y3^-1 * Y1)^2, Y2^-1 * Y1 * Y2^-2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^3 * Y1^2, Y2^-1 * Y3^2 * Y2^-2 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 19, 49, 7, 37, 12, 42, 4, 34, 10, 40, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 28, 58, 15, 45, 24, 54, 13, 43, 23, 53, 27, 57, 14, 44)(6, 36, 11, 41, 22, 52, 30, 60, 20, 50, 26, 56, 16, 46, 25, 55, 29, 59, 18, 48)(61, 91, 63, 93, 71, 101, 62, 92, 69, 99, 82, 112, 68, 98, 81, 111, 90, 120, 79, 109, 88, 118, 80, 110, 67, 97, 75, 105, 86, 116, 72, 102, 84, 114, 76, 106, 64, 94, 73, 103, 85, 115, 70, 100, 83, 113, 89, 119, 77, 107, 87, 117, 78, 108, 65, 95, 74, 104, 66, 96)
	L = (1, 64)(2, 70)(3, 73)(4, 68)(5, 72)(6, 76)(7, 61)(8, 77)(9, 83)(10, 79)(11, 85)(12, 62)(13, 81)(14, 84)(15, 63)(16, 82)(17, 67)(18, 86)(19, 65)(20, 66)(21, 87)(22, 89)(23, 88)(24, 69)(25, 90)(26, 71)(27, 75)(28, 74)(29, 80)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.99
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.106 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 10, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (R * Y3)^2, (Y3, Y1), (Y2^-1, Y3^-1), (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y2 * Y1^3 * Y3^-1, Y2 * Y1^-1 * Y2^2 * Y3^-1, (Y1^-2 * Y2)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 18, 48, 13, 43, 26, 56, 29, 59, 14, 44, 27, 57, 21, 51, 7, 37, 12, 42, 20, 50, 6, 36, 11, 41, 25, 55, 15, 45, 3, 33, 9, 39, 17, 47, 4, 34, 10, 40, 24, 54, 23, 53, 28, 58, 30, 60, 22, 52, 16, 46, 19, 49, 5, 35)(61, 91, 63, 93, 73, 103, 70, 100, 87, 117, 90, 120, 80, 110, 65, 95, 75, 105, 78, 108, 64, 94, 74, 104, 88, 118, 72, 102, 79, 109, 85, 115, 68, 98, 77, 107, 89, 119, 83, 113, 67, 97, 76, 106, 71, 101, 62, 92, 69, 99, 86, 116, 84, 114, 81, 111, 82, 112, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 67)(5, 77)(6, 78)(7, 61)(8, 84)(9, 87)(10, 72)(11, 73)(12, 62)(13, 88)(14, 76)(15, 89)(16, 63)(17, 81)(18, 83)(19, 69)(20, 68)(21, 65)(22, 75)(23, 66)(24, 80)(25, 86)(26, 90)(27, 79)(28, 71)(29, 82)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.92
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.107 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^5, Y2^2 * Y1 * Y2^3, Y1^6, Y3^-2 * Y2 * Y3^-2 * Y1^-1, (Y3 * Y2^-2)^15, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 15, 45, 5, 35)(3, 33, 9, 39, 21, 51, 30, 60, 17, 47, 7, 37)(4, 34, 10, 40, 22, 52, 29, 59, 16, 46, 6, 36)(11, 41, 23, 53, 28, 58, 27, 57, 19, 49, 12, 42)(13, 43, 24, 54, 26, 56, 25, 55, 18, 48, 14, 44)(61, 91, 63, 93, 71, 101, 85, 115, 76, 106, 65, 95, 67, 97, 72, 102, 86, 116, 89, 119, 75, 105, 77, 107, 79, 109, 84, 114, 82, 112, 80, 110, 90, 120, 87, 117, 73, 103, 70, 100, 68, 98, 81, 111, 88, 118, 74, 104, 64, 94, 62, 92, 69, 99, 83, 113, 78, 108, 66, 96)
	L = (1, 64)(2, 70)(3, 62)(4, 73)(5, 66)(6, 74)(7, 61)(8, 82)(9, 68)(10, 84)(11, 69)(12, 63)(13, 79)(14, 87)(15, 76)(16, 78)(17, 65)(18, 88)(19, 67)(20, 89)(21, 80)(22, 86)(23, 81)(24, 72)(25, 83)(26, 71)(27, 77)(28, 90)(29, 85)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^12 ), ( 60^60 ) }
Outer automorphisms :: reflexible
Dual of E27.113
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 12^5, 60 ]

E27.108 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3 * Y2, Y2 * Y3 * Y1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^5, Y1^6, Y1 * Y2^-5, Y3^2 * Y1^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y1^2)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 17, 47, 5, 35)(3, 33, 7, 37, 10, 40, 22, 52, 27, 57, 12, 42)(4, 34, 6, 36, 9, 39, 21, 51, 29, 59, 15, 45)(11, 41, 13, 43, 19, 49, 24, 54, 30, 60, 25, 55)(14, 44, 16, 46, 18, 48, 23, 53, 26, 56, 28, 58)(61, 91, 63, 93, 71, 101, 83, 113, 69, 99, 62, 92, 67, 97, 73, 103, 86, 116, 81, 111, 68, 98, 70, 100, 79, 109, 88, 118, 89, 119, 80, 110, 82, 112, 84, 114, 74, 104, 75, 105, 77, 107, 87, 117, 90, 120, 76, 106, 64, 94, 65, 95, 72, 102, 85, 115, 78, 108, 66, 96)
	L = (1, 64)(2, 66)(3, 65)(4, 74)(5, 75)(6, 76)(7, 61)(8, 69)(9, 78)(10, 62)(11, 72)(12, 77)(13, 63)(14, 79)(15, 88)(16, 84)(17, 89)(18, 90)(19, 67)(20, 81)(21, 83)(22, 68)(23, 85)(24, 70)(25, 87)(26, 71)(27, 80)(28, 73)(29, 86)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^12 ), ( 60^60 ) }
Outer automorphisms :: reflexible
Dual of E27.114
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 12^5, 60 ]

E27.109 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3^-1), Y2^-1 * Y3^-2 * Y1^-1, Y1 * Y3 * Y2 * Y3, Y1 * Y2 * Y3^2, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y1^2 * Y2 * Y3^-1 * Y2, Y3^5, Y1 * Y3^-2 * Y2 * Y3^-1, Y2^-3 * Y1 * Y2^-2, Y1^6, Y1 * Y3^-1 * Y2^3 * Y1 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 20, 50, 5, 35)(3, 33, 9, 39, 19, 49, 25, 55, 30, 60, 15, 45)(4, 34, 10, 40, 23, 53, 28, 58, 13, 43, 18, 48)(6, 36, 11, 41, 24, 54, 27, 57, 16, 46, 17, 47)(7, 37, 12, 42, 21, 51, 26, 56, 29, 59, 14, 44)(61, 91, 63, 93, 73, 103, 86, 116, 71, 101, 62, 92, 69, 99, 78, 108, 89, 119, 84, 114, 68, 98, 79, 109, 64, 94, 74, 104, 87, 117, 82, 112, 85, 115, 70, 100, 67, 97, 76, 106, 80, 110, 90, 120, 83, 113, 72, 102, 77, 107, 65, 95, 75, 105, 88, 118, 81, 111, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 83)(9, 67)(10, 66)(11, 85)(12, 62)(13, 87)(14, 65)(15, 89)(16, 63)(17, 69)(18, 76)(19, 72)(20, 73)(21, 68)(22, 88)(23, 71)(24, 90)(25, 81)(26, 82)(27, 75)(28, 84)(29, 80)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^12 ), ( 60^60 ) }
Outer automorphisms :: reflexible
Dual of E27.112
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 12^5, 60 ]

E27.110 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y3^-2, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y2)^2, Y3 * Y2^-1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y1^-1, Y2), Y3 * Y2 * Y3^2 * Y1, Y2 * Y1 * Y2 * Y3 * Y1, Y1^-1 * Y2^5, Y1^6, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1, (Y1^-1 * Y2 * Y3)^15 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 26, 56, 29, 59, 15, 45)(4, 34, 10, 40, 20, 50, 25, 55, 30, 60, 16, 46)(6, 36, 11, 41, 23, 53, 28, 58, 14, 44, 18, 48)(7, 37, 12, 42, 24, 54, 27, 57, 13, 43, 19, 49)(61, 91, 63, 93, 73, 103, 85, 115, 71, 101, 62, 92, 69, 99, 79, 109, 90, 120, 83, 113, 68, 98, 81, 111, 67, 97, 76, 106, 88, 118, 82, 112, 86, 116, 72, 102, 64, 94, 74, 104, 77, 107, 89, 119, 84, 114, 70, 100, 78, 108, 65, 95, 75, 105, 87, 117, 80, 110, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 69)(5, 76)(6, 72)(7, 61)(8, 80)(9, 78)(10, 81)(11, 84)(12, 62)(13, 77)(14, 79)(15, 88)(16, 63)(17, 90)(18, 67)(19, 65)(20, 86)(21, 66)(22, 85)(23, 87)(24, 68)(25, 89)(26, 71)(27, 82)(28, 73)(29, 83)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^12 ), ( 60^60 ) }
Outer automorphisms :: reflexible
Dual of E27.111
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 12^5, 60 ]

E27.111 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y1 * Y3, Y3^-2 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y2^2 * Y1, Y1 * Y2 * Y3^-1 * Y1 * Y2, Y2^3 * Y1^-3, Y2^30, (Y3 * Y2^-1)^30 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 28, 58, 14, 44, 7, 37, 12, 42, 21, 51, 26, 56, 15, 45, 3, 33, 9, 39, 19, 49, 25, 55, 30, 60, 27, 57, 16, 46, 17, 47, 6, 36, 11, 41, 24, 54, 13, 43, 18, 48, 4, 34, 10, 40, 23, 53, 29, 59, 20, 50, 5, 35)(61, 91, 63, 93, 73, 103, 82, 112, 85, 115, 70, 100, 67, 97, 76, 106, 80, 110, 86, 116, 71, 101, 62, 92, 69, 99, 78, 108, 88, 118, 90, 120, 83, 113, 72, 102, 77, 107, 65, 95, 75, 105, 84, 114, 68, 98, 79, 109, 64, 94, 74, 104, 87, 117, 89, 119, 81, 111, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 83)(9, 67)(10, 66)(11, 85)(12, 62)(13, 87)(14, 65)(15, 88)(16, 63)(17, 69)(18, 76)(19, 72)(20, 73)(21, 68)(22, 89)(23, 71)(24, 90)(25, 81)(26, 82)(27, 75)(28, 80)(29, 84)(30, 86)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.110
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.112 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2^-1), Y2^-1 * Y3 * Y1^-1 * Y3, Y2^-1 * Y3^2 * Y1^-1, (Y1^-1, Y2^-1), (Y1^-1, Y3^-1), (Y3^-1, Y2^-1), Y3^2 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^2 * Y2^2 * Y3, Y3 * Y2 * Y3^2 * Y1, Y1^-4 * Y2^2, Y2^5 * Y1^-1 * Y3^-1, (Y1^-1 * Y2 * Y3)^3, (Y1^-1 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 22, 52, 13, 43, 19, 49, 7, 37, 12, 42, 24, 54, 30, 60, 28, 58, 14, 44, 18, 48, 6, 36, 11, 41, 23, 53, 15, 45, 3, 33, 9, 39, 21, 51, 26, 56, 27, 57, 29, 59, 16, 46, 4, 34, 10, 40, 20, 50, 25, 55, 17, 47, 5, 35)(61, 91, 63, 93, 73, 103, 87, 117, 84, 114, 70, 100, 78, 108, 65, 95, 75, 105, 82, 112, 86, 116, 72, 102, 64, 94, 74, 104, 77, 107, 83, 113, 68, 98, 81, 111, 67, 97, 76, 106, 88, 118, 85, 115, 71, 101, 62, 92, 69, 99, 79, 109, 89, 119, 90, 120, 80, 110, 66, 96)
	L = (1, 64)(2, 70)(3, 74)(4, 69)(5, 76)(6, 72)(7, 61)(8, 80)(9, 78)(10, 81)(11, 84)(12, 62)(13, 77)(14, 79)(15, 88)(16, 63)(17, 89)(18, 67)(19, 65)(20, 86)(21, 66)(22, 85)(23, 90)(24, 68)(25, 87)(26, 71)(27, 83)(28, 73)(29, 75)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.109
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.113 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^5, Y3^-2 * Y2 * Y3^-2 * Y1^-1, Y1 * Y2 * Y1 * Y2^3, Y1^2 * Y3 * Y1^4, (Y3 * Y2^-2)^3, (Y1^-1 * Y2^-1 * Y1^-1)^10, Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 30, 60, 17, 47, 7, 37, 3, 33, 9, 39, 21, 51, 28, 58, 27, 57, 19, 49, 12, 42, 11, 41, 23, 53, 18, 48, 14, 44, 13, 43, 24, 54, 26, 56, 25, 55, 16, 46, 6, 36, 4, 34, 10, 40, 22, 52, 29, 59, 15, 45, 5, 35)(61, 91, 63, 93, 71, 101, 85, 115, 75, 105, 77, 107, 79, 109, 84, 114, 82, 112, 80, 110, 88, 118, 74, 104, 64, 94, 62, 92, 69, 99, 83, 113, 76, 106, 65, 95, 67, 97, 72, 102, 86, 116, 89, 119, 90, 120, 87, 117, 73, 103, 70, 100, 68, 98, 81, 111, 78, 108, 66, 96)
	L = (1, 64)(2, 70)(3, 62)(4, 73)(5, 66)(6, 74)(7, 61)(8, 82)(9, 68)(10, 84)(11, 69)(12, 63)(13, 79)(14, 87)(15, 76)(16, 78)(17, 65)(18, 88)(19, 67)(20, 89)(21, 80)(22, 86)(23, 81)(24, 72)(25, 83)(26, 71)(27, 77)(28, 90)(29, 85)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.107
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.114 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 30, 30, 30})
Quotient :: dipole
Aut^+ = C30 (small group id <30, 4>)
Aut   = D60 (small group id <60, 12>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^5, Y3^-2 * Y1^-1 * Y3^-2 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-3, Y1^4 * Y3 * Y1^2, (Y3 * Y2^2)^3 ]
Map:: non-degenerate
	R = (1, 31, 2, 32, 8, 38, 20, 50, 29, 59, 16, 46, 7, 37, 6, 36, 10, 40, 22, 52, 25, 55, 26, 56, 19, 49, 18, 48, 17, 47, 24, 54, 11, 41, 12, 42, 14, 44, 23, 53, 30, 60, 27, 57, 13, 43, 3, 33, 4, 34, 9, 39, 21, 51, 28, 58, 15, 45, 5, 35)(61, 91, 63, 93, 71, 101, 82, 112, 68, 98, 69, 99, 74, 104, 86, 116, 89, 119, 88, 118, 90, 120, 78, 108, 67, 97, 65, 95, 73, 103, 84, 114, 70, 100, 62, 92, 64, 94, 72, 102, 85, 115, 80, 110, 81, 111, 83, 113, 79, 109, 76, 106, 75, 105, 87, 117, 77, 107, 66, 96)
	L = (1, 64)(2, 69)(3, 72)(4, 74)(5, 63)(6, 62)(7, 61)(8, 81)(9, 83)(10, 68)(11, 85)(12, 86)(13, 71)(14, 79)(15, 73)(16, 65)(17, 70)(18, 66)(19, 67)(20, 88)(21, 90)(22, 80)(23, 78)(24, 82)(25, 89)(26, 76)(27, 84)(28, 87)(29, 75)(30, 77)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.108
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.115 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2, Y2^2 * Y1^-2, (Y2 * Y1^-1)^2, (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y3 * Y1, Y1^2 * Y2^6, Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 25, 57, 16, 48, 5, 37)(3, 35, 9, 41, 20, 52, 28, 60, 26, 58, 17, 49, 6, 38, 11, 43)(4, 36, 10, 42, 13, 45, 22, 54, 30, 62, 31, 63, 23, 55, 14, 46)(7, 39, 12, 44, 21, 53, 29, 61, 32, 64, 24, 56, 15, 47, 18, 50)(65, 97, 67, 99, 72, 104, 84, 116, 91, 123, 90, 122, 80, 112, 70, 102)(66, 98, 73, 105, 83, 115, 92, 124, 89, 121, 81, 113, 69, 101, 75, 107)(68, 100, 71, 103, 77, 109, 85, 117, 94, 126, 96, 128, 87, 119, 79, 111)(74, 106, 76, 108, 86, 118, 93, 125, 95, 127, 88, 120, 78, 110, 82, 114)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 78)(6, 79)(7, 65)(8, 77)(9, 76)(10, 75)(11, 82)(12, 66)(13, 67)(14, 81)(15, 80)(16, 87)(17, 88)(18, 69)(19, 86)(20, 85)(21, 72)(22, 73)(23, 90)(24, 89)(25, 95)(26, 96)(27, 94)(28, 93)(29, 83)(30, 84)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.144
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.116 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^2, Y1^-1 * Y2^-2 * Y1^-1, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), (R * Y2)^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y2^-2 * Y1^6, (Y1^2 * Y2^-1)^8, (Y1^-1 * Y3^-1)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 24, 56, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 21, 53, 29, 61, 23, 55, 14, 46)(4, 36, 10, 42, 20, 52, 28, 60, 31, 63, 26, 58, 15, 47, 16, 48)(7, 39, 12, 44, 17, 49, 22, 54, 30, 62, 32, 64, 25, 57, 18, 50)(65, 97, 67, 99, 77, 109, 87, 119, 91, 123, 85, 117, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 78, 110, 88, 120, 93, 125, 83, 115, 75, 107)(68, 100, 71, 103, 79, 111, 89, 121, 95, 127, 94, 126, 84, 116, 81, 113)(74, 106, 76, 108, 80, 112, 82, 114, 90, 122, 96, 128, 92, 124, 86, 118)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 80)(6, 81)(7, 65)(8, 84)(9, 76)(10, 75)(11, 86)(12, 66)(13, 79)(14, 82)(15, 67)(16, 73)(17, 72)(18, 69)(19, 92)(20, 85)(21, 94)(22, 83)(23, 89)(24, 90)(25, 77)(26, 78)(27, 95)(28, 93)(29, 96)(30, 91)(31, 87)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.146
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.117 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^2, (Y2^-1, Y1^-1), Y2^-2 * Y1^-2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2^-6, (Y1^-1 * Y3^-1)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 25, 57, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 20, 52, 28, 60, 23, 55, 15, 47)(4, 36, 10, 42, 18, 50, 22, 54, 30, 62, 32, 64, 24, 56, 16, 48)(7, 39, 12, 44, 21, 53, 29, 61, 31, 63, 26, 58, 14, 46, 17, 49)(65, 97, 67, 99, 77, 109, 87, 119, 91, 123, 84, 116, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 79, 111, 89, 121, 92, 124, 83, 115, 75, 107)(68, 100, 78, 110, 88, 120, 95, 127, 94, 126, 85, 117, 82, 114, 71, 103)(74, 106, 81, 113, 80, 112, 90, 122, 96, 128, 93, 125, 86, 118, 76, 108)
	L = (1, 68)(2, 74)(3, 78)(4, 67)(5, 80)(6, 71)(7, 65)(8, 82)(9, 81)(10, 73)(11, 76)(12, 66)(13, 88)(14, 77)(15, 90)(16, 79)(17, 69)(18, 70)(19, 86)(20, 85)(21, 72)(22, 75)(23, 95)(24, 87)(25, 96)(26, 89)(27, 94)(28, 93)(29, 83)(30, 84)(31, 91)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.143
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.118 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1), (Y2 * Y1^-1)^2, Y1^2 * Y2^-2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3, Y2^3 * Y3^2, Y2^-2 * Y3^4, Y2^2 * Y1^6 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 29, 61, 32, 64, 18, 50, 5, 37)(3, 35, 9, 41, 22, 54, 28, 60, 15, 47, 19, 51, 6, 38, 11, 43)(4, 36, 10, 42, 21, 53, 27, 59, 14, 46, 25, 57, 30, 62, 16, 48)(7, 39, 12, 44, 24, 56, 31, 63, 17, 49, 26, 58, 13, 45, 20, 52)(65, 97, 67, 99, 72, 104, 86, 118, 93, 125, 79, 111, 82, 114, 70, 102)(66, 98, 73, 105, 87, 119, 92, 124, 96, 128, 83, 115, 69, 101, 75, 107)(68, 100, 77, 109, 85, 117, 71, 103, 78, 110, 88, 120, 94, 126, 81, 113)(74, 106, 84, 116, 91, 123, 76, 108, 89, 121, 95, 127, 80, 112, 90, 122)
	L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 80)(6, 81)(7, 65)(8, 85)(9, 84)(10, 83)(11, 90)(12, 66)(13, 82)(14, 67)(15, 88)(16, 92)(17, 93)(18, 94)(19, 95)(20, 69)(21, 70)(22, 71)(23, 91)(24, 72)(25, 73)(26, 96)(27, 75)(28, 76)(29, 78)(30, 86)(31, 87)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.145
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.119 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-4 * Y1^-2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 14, 46, 23, 55, 22, 54, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 24, 56, 30, 62, 29, 61, 21, 53, 10, 42)(5, 37, 8, 40, 16, 48, 25, 57, 31, 63, 27, 59, 19, 51, 12, 44)(9, 41, 17, 49, 13, 45, 18, 50, 26, 58, 32, 64, 28, 60, 20, 52)(65, 97, 67, 99, 73, 105, 83, 115, 75, 107, 85, 117, 92, 124, 95, 127, 87, 119, 94, 126, 90, 122, 80, 112, 70, 102, 79, 111, 77, 109, 69, 101)(66, 98, 71, 103, 81, 113, 76, 108, 68, 100, 74, 106, 84, 116, 91, 123, 86, 118, 93, 125, 96, 128, 89, 121, 78, 110, 88, 120, 82, 114, 72, 104)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.120 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2^-4 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 14, 46, 23, 55, 20, 52, 11, 43, 4, 36)(3, 35, 7, 39, 15, 47, 24, 56, 30, 62, 27, 59, 19, 51, 10, 42)(5, 37, 8, 40, 16, 48, 25, 57, 31, 63, 28, 60, 21, 53, 12, 44)(9, 41, 17, 49, 26, 58, 32, 64, 29, 61, 22, 54, 13, 45, 18, 50)(65, 97, 67, 99, 73, 105, 80, 112, 70, 102, 79, 111, 90, 122, 95, 127, 87, 119, 94, 126, 93, 125, 85, 117, 75, 107, 83, 115, 77, 109, 69, 101)(66, 98, 71, 103, 81, 113, 89, 121, 78, 110, 88, 120, 96, 128, 92, 124, 84, 116, 91, 123, 86, 118, 76, 108, 68, 100, 74, 106, 82, 114, 72, 104)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.121 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1 * Y2^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 22, 54, 14, 46, 5, 37)(3, 35, 6, 38, 9, 41, 17, 49, 25, 57, 28, 60, 20, 52, 11, 43)(4, 36, 8, 40, 16, 48, 24, 56, 30, 62, 29, 61, 21, 53, 12, 44)(10, 42, 13, 45, 18, 50, 26, 58, 31, 63, 32, 64, 27, 59, 19, 51)(65, 97, 67, 99, 69, 101, 75, 107, 78, 110, 84, 116, 86, 118, 92, 124, 87, 119, 89, 121, 79, 111, 81, 113, 71, 103, 73, 105, 66, 98, 70, 102)(68, 100, 74, 106, 76, 108, 83, 115, 85, 117, 91, 123, 93, 125, 96, 128, 94, 126, 95, 127, 88, 120, 90, 122, 80, 112, 82, 114, 72, 104, 77, 109)
	L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 76)(6, 77)(7, 80)(8, 66)(9, 82)(10, 67)(11, 83)(12, 69)(13, 70)(14, 85)(15, 88)(16, 71)(17, 90)(18, 73)(19, 75)(20, 91)(21, 78)(22, 93)(23, 94)(24, 79)(25, 95)(26, 81)(27, 84)(28, 96)(29, 86)(30, 87)(31, 89)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.125
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.122 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, Y1^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 21, 53, 13, 45, 5, 37)(3, 35, 8, 40, 16, 48, 24, 56, 29, 61, 22, 54, 14, 46, 6, 38)(4, 36, 9, 41, 17, 49, 25, 57, 30, 62, 27, 59, 19, 51, 11, 43)(10, 42, 18, 50, 26, 58, 31, 63, 32, 64, 28, 60, 20, 52, 12, 44)(65, 97, 67, 99, 66, 98, 72, 104, 71, 103, 80, 112, 79, 111, 88, 120, 87, 119, 93, 125, 85, 117, 86, 118, 77, 109, 78, 110, 69, 101, 70, 102)(68, 100, 74, 106, 73, 105, 82, 114, 81, 113, 90, 122, 89, 121, 95, 127, 94, 126, 96, 128, 91, 123, 92, 124, 83, 115, 84, 116, 75, 107, 76, 108)
	L = (1, 68)(2, 73)(3, 74)(4, 65)(5, 75)(6, 76)(7, 81)(8, 82)(9, 66)(10, 67)(11, 69)(12, 70)(13, 83)(14, 84)(15, 89)(16, 90)(17, 71)(18, 72)(19, 77)(20, 78)(21, 91)(22, 92)(23, 94)(24, 95)(25, 79)(26, 80)(27, 85)(28, 86)(29, 96)(30, 87)(31, 88)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.126
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.123 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ Y3^2, R^2, (Y2^-1, Y1^-1), Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y1^2 * Y2 * Y1 * Y2, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 18, 50, 23, 55, 11, 43, 16, 48, 5, 37)(3, 35, 8, 40, 17, 49, 6, 38, 10, 42, 20, 52, 26, 58, 13, 45)(4, 36, 9, 41, 19, 51, 29, 61, 31, 63, 24, 56, 27, 59, 14, 46)(12, 44, 21, 53, 28, 60, 15, 47, 22, 54, 30, 62, 32, 64, 25, 57)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 81, 113, 69, 101, 77, 109, 87, 119, 74, 106, 66, 98, 72, 104, 80, 112, 90, 122, 82, 114, 70, 102)(68, 100, 76, 108, 88, 120, 94, 126, 83, 115, 92, 124, 78, 110, 89, 121, 95, 127, 86, 118, 73, 105, 85, 117, 91, 123, 96, 128, 93, 125, 79, 111)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 83)(8, 85)(9, 66)(10, 86)(11, 88)(12, 67)(13, 89)(14, 69)(15, 70)(16, 91)(17, 92)(18, 93)(19, 71)(20, 94)(21, 72)(22, 74)(23, 95)(24, 75)(25, 77)(26, 96)(27, 80)(28, 81)(29, 82)(30, 84)(31, 87)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.127
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.124 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2, Y1), Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, Y2^-2 * Y1^3, Y2^-4 * Y1^-2, Y1^2 * Y2^4, (Y2^-2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 11, 43, 21, 53, 18, 50, 16, 48, 5, 37)(3, 35, 8, 40, 19, 51, 24, 56, 17, 49, 6, 38, 10, 42, 13, 45)(4, 36, 9, 41, 20, 52, 25, 57, 31, 63, 29, 61, 27, 59, 14, 46)(12, 44, 22, 54, 30, 62, 32, 64, 28, 60, 15, 47, 23, 55, 26, 58)(65, 97, 67, 99, 75, 107, 88, 120, 80, 112, 74, 106, 66, 98, 72, 104, 85, 117, 81, 113, 69, 101, 77, 109, 71, 103, 83, 115, 82, 114, 70, 102)(68, 100, 76, 108, 89, 121, 96, 128, 91, 123, 87, 119, 73, 105, 86, 118, 95, 127, 92, 124, 78, 110, 90, 122, 84, 116, 94, 126, 93, 125, 79, 111)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 84)(8, 86)(9, 66)(10, 87)(11, 89)(12, 67)(13, 90)(14, 69)(15, 70)(16, 91)(17, 92)(18, 93)(19, 94)(20, 71)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 77)(27, 80)(28, 81)(29, 82)(30, 83)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.128
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.125 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1^-1 * Y2^-2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2^-2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^8, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^2, Y1^-1 * Y2^12 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 22, 54, 14, 46, 5, 37)(3, 35, 8, 40, 16, 48, 24, 56, 30, 62, 29, 61, 21, 53, 13, 45)(4, 36, 9, 41, 17, 49, 25, 57, 31, 63, 28, 60, 20, 52, 11, 43)(6, 38, 10, 42, 18, 50, 26, 58, 32, 64, 27, 59, 19, 51, 12, 44)(65, 97, 67, 99, 75, 107, 83, 115, 78, 110, 85, 117, 92, 124, 96, 128, 87, 119, 94, 126, 89, 121, 82, 114, 71, 103, 80, 112, 73, 105, 70, 102)(66, 98, 72, 104, 68, 100, 76, 108, 69, 101, 77, 109, 84, 116, 91, 123, 86, 118, 93, 125, 95, 127, 90, 122, 79, 111, 88, 120, 81, 113, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 75)(6, 72)(7, 81)(8, 70)(9, 66)(10, 80)(11, 69)(12, 67)(13, 83)(14, 84)(15, 89)(16, 74)(17, 71)(18, 88)(19, 77)(20, 78)(21, 91)(22, 92)(23, 95)(24, 82)(25, 79)(26, 94)(27, 85)(28, 86)(29, 96)(30, 90)(31, 87)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.121
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.126 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^-1 * Y3 * Y2, Y2^2 * Y3 * Y1^-1, (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^8, (Y3 * Y1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 23, 55, 21, 53, 13, 45, 5, 37)(3, 35, 8, 40, 16, 48, 24, 56, 30, 62, 27, 59, 19, 51, 11, 43)(4, 36, 9, 41, 17, 49, 25, 57, 31, 63, 28, 60, 20, 52, 12, 44)(6, 38, 10, 42, 18, 50, 26, 58, 32, 64, 29, 61, 22, 54, 14, 46)(65, 97, 67, 99, 73, 105, 82, 114, 71, 103, 80, 112, 89, 121, 96, 128, 87, 119, 94, 126, 92, 124, 86, 118, 77, 109, 83, 115, 76, 108, 70, 102)(66, 98, 72, 104, 81, 113, 90, 122, 79, 111, 88, 120, 95, 127, 93, 125, 85, 117, 91, 123, 84, 116, 78, 110, 69, 101, 75, 107, 68, 100, 74, 106)
	L = (1, 68)(2, 73)(3, 74)(4, 65)(5, 76)(6, 75)(7, 81)(8, 82)(9, 66)(10, 67)(11, 70)(12, 69)(13, 84)(14, 83)(15, 89)(16, 90)(17, 71)(18, 72)(19, 78)(20, 77)(21, 92)(22, 91)(23, 95)(24, 96)(25, 79)(26, 80)(27, 86)(28, 85)(29, 94)(30, 93)(31, 87)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.122
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.127 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y3 * Y2 * Y3, (Y2, Y1), (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^-2 * Y3 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y1, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y2^2 * Y3 * Y2^2 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 19, 51, 30, 62, 27, 59, 16, 48, 5, 37)(3, 35, 8, 40, 20, 52, 15, 47, 25, 57, 32, 64, 29, 61, 13, 45)(4, 36, 9, 41, 21, 53, 18, 50, 26, 58, 11, 43, 23, 55, 14, 46)(6, 38, 10, 42, 22, 54, 31, 63, 28, 60, 12, 44, 24, 56, 17, 49)(65, 97, 67, 99, 75, 107, 86, 118, 71, 103, 84, 116, 78, 110, 92, 124, 94, 126, 89, 121, 73, 105, 88, 120, 80, 112, 93, 125, 82, 114, 70, 102)(66, 98, 72, 104, 87, 119, 95, 127, 83, 115, 79, 111, 68, 100, 76, 108, 91, 123, 96, 128, 85, 117, 81, 113, 69, 101, 77, 109, 90, 122, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 85)(8, 88)(9, 66)(10, 89)(11, 91)(12, 67)(13, 92)(14, 69)(15, 70)(16, 87)(17, 84)(18, 83)(19, 82)(20, 81)(21, 71)(22, 96)(23, 80)(24, 72)(25, 74)(26, 94)(27, 75)(28, 77)(29, 95)(30, 90)(31, 93)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.123
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.128 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y3 * Y2^-1 * Y3, (Y2^-1, Y1^-1), Y3 * Y1^-1 * Y3 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^-2 * Y3 * Y2^2 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y2^2 * Y1^5 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 19, 51, 30, 62, 29, 61, 16, 48, 5, 37)(3, 35, 8, 40, 20, 52, 31, 63, 28, 60, 15, 47, 25, 57, 13, 45)(4, 36, 9, 41, 21, 53, 11, 43, 23, 55, 18, 50, 26, 58, 14, 46)(6, 38, 10, 42, 22, 54, 12, 44, 24, 56, 32, 64, 27, 59, 17, 49)(65, 97, 67, 99, 75, 107, 91, 123, 80, 112, 89, 121, 73, 105, 88, 120, 94, 126, 92, 124, 78, 110, 86, 118, 71, 103, 84, 116, 82, 114, 70, 102)(66, 98, 72, 104, 87, 119, 81, 113, 69, 101, 77, 109, 85, 117, 96, 128, 93, 125, 79, 111, 68, 100, 76, 108, 83, 115, 95, 127, 90, 122, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 85)(8, 88)(9, 66)(10, 89)(11, 83)(12, 67)(13, 86)(14, 69)(15, 70)(16, 90)(17, 92)(18, 93)(19, 75)(20, 96)(21, 71)(22, 77)(23, 94)(24, 72)(25, 74)(26, 80)(27, 95)(28, 81)(29, 82)(30, 87)(31, 91)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.124
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.129 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y2^-1 * Y3 * Y2, (Y1, Y2), (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y2)^2, Y1^4 * Y3, Y2^-1 * Y1^-1 * Y2^-3 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 14, 46, 4, 36, 9, 41, 16, 48, 5, 37)(3, 35, 8, 40, 19, 51, 28, 60, 12, 44, 22, 54, 29, 61, 13, 45)(6, 38, 10, 42, 20, 52, 30, 62, 15, 47, 23, 55, 25, 57, 17, 49)(11, 43, 21, 53, 18, 50, 24, 56, 26, 58, 32, 64, 31, 63, 27, 59)(65, 97, 67, 99, 75, 107, 89, 121, 80, 112, 93, 125, 95, 127, 79, 111, 68, 100, 76, 108, 90, 122, 84, 116, 71, 103, 83, 115, 82, 114, 70, 102)(66, 98, 72, 104, 85, 117, 81, 113, 69, 101, 77, 109, 91, 123, 87, 119, 73, 105, 86, 118, 96, 128, 94, 126, 78, 110, 92, 124, 88, 120, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 80)(8, 86)(9, 66)(10, 87)(11, 90)(12, 67)(13, 92)(14, 69)(15, 70)(16, 71)(17, 94)(18, 95)(19, 93)(20, 89)(21, 96)(22, 72)(23, 74)(24, 91)(25, 84)(26, 75)(27, 88)(28, 77)(29, 83)(30, 81)(31, 82)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.130 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4 * Y3, Y2^3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, Y2^3 * Y1 * Y2 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 14, 46, 4, 36, 9, 41, 16, 48, 5, 37)(3, 35, 8, 40, 19, 51, 26, 58, 12, 44, 22, 54, 27, 59, 13, 45)(6, 38, 10, 42, 20, 52, 28, 60, 15, 47, 23, 55, 30, 62, 17, 49)(11, 43, 21, 53, 29, 61, 32, 64, 25, 57, 31, 63, 18, 50, 24, 56)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 83, 115, 93, 125, 79, 111, 68, 100, 76, 108, 89, 121, 94, 126, 80, 112, 91, 123, 82, 114, 70, 102)(66, 98, 72, 104, 85, 117, 92, 124, 78, 110, 90, 122, 96, 128, 87, 119, 73, 105, 86, 118, 95, 127, 81, 113, 69, 101, 77, 109, 88, 120, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 80)(8, 86)(9, 66)(10, 87)(11, 89)(12, 67)(13, 90)(14, 69)(15, 70)(16, 71)(17, 92)(18, 93)(19, 91)(20, 94)(21, 95)(22, 72)(23, 74)(24, 96)(25, 75)(26, 77)(27, 83)(28, 81)(29, 82)(30, 84)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.131 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, Y3^4, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y2, Y3), (R * Y1)^2, Y2^-4 * Y3^-1, Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 15, 47, 18, 50, 7, 39, 5, 37)(3, 35, 8, 40, 12, 44, 22, 54, 27, 59, 28, 60, 14, 46, 13, 45)(6, 38, 10, 42, 16, 48, 23, 55, 29, 61, 31, 63, 20, 52, 17, 49)(11, 43, 21, 53, 19, 51, 24, 56, 30, 62, 32, 64, 26, 58, 25, 57)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 78, 110, 90, 122, 93, 125, 79, 111, 91, 123, 94, 126, 80, 112, 68, 100, 76, 108, 83, 115, 70, 102)(66, 98, 72, 104, 85, 117, 81, 113, 69, 101, 77, 109, 89, 121, 95, 127, 82, 114, 92, 124, 96, 128, 87, 119, 73, 105, 86, 118, 88, 120, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 66)(6, 80)(7, 65)(8, 86)(9, 82)(10, 87)(11, 83)(12, 91)(13, 72)(14, 67)(15, 71)(16, 93)(17, 74)(18, 69)(19, 94)(20, 70)(21, 88)(22, 92)(23, 95)(24, 96)(25, 85)(26, 75)(27, 78)(28, 77)(29, 84)(30, 90)(31, 81)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.134
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.132 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1, (Y2, Y3^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^4, Y2^4 * Y3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 15, 47, 16, 48, 4, 36, 5, 37)(3, 35, 8, 40, 14, 46, 22, 54, 26, 58, 27, 59, 12, 44, 13, 45)(6, 38, 9, 41, 20, 52, 24, 56, 28, 60, 29, 61, 17, 49, 18, 50)(11, 43, 21, 53, 25, 57, 32, 64, 30, 62, 31, 63, 19, 51, 23, 55)(65, 97, 67, 99, 75, 107, 84, 116, 71, 103, 78, 110, 89, 121, 92, 124, 79, 111, 90, 122, 94, 126, 81, 113, 68, 100, 76, 108, 83, 115, 70, 102)(66, 98, 72, 104, 85, 117, 88, 120, 74, 106, 86, 118, 96, 128, 93, 125, 80, 112, 91, 123, 95, 127, 82, 114, 69, 101, 77, 109, 87, 119, 73, 105)
	L = (1, 68)(2, 69)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 77)(9, 82)(10, 66)(11, 83)(12, 90)(13, 91)(14, 67)(15, 71)(16, 74)(17, 92)(18, 93)(19, 94)(20, 70)(21, 87)(22, 72)(23, 95)(24, 73)(25, 75)(26, 78)(27, 86)(28, 84)(29, 88)(30, 89)(31, 96)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.133
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.133 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (Y1^-1, Y2), Y3^4, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, Y2^-4 * Y3, (Y2^2 * Y3)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 15, 47, 16, 48, 4, 36, 5, 37)(3, 35, 8, 40, 14, 46, 22, 54, 27, 59, 28, 60, 12, 44, 13, 45)(6, 38, 9, 41, 20, 52, 24, 56, 29, 61, 30, 62, 17, 49, 18, 50)(11, 43, 21, 53, 19, 51, 23, 55, 31, 63, 32, 64, 25, 57, 26, 58)(65, 97, 67, 99, 75, 107, 81, 113, 68, 100, 76, 108, 89, 121, 93, 125, 79, 111, 91, 123, 95, 127, 84, 116, 71, 103, 78, 110, 83, 115, 70, 102)(66, 98, 72, 104, 85, 117, 82, 114, 69, 101, 77, 109, 90, 122, 94, 126, 80, 112, 92, 124, 96, 128, 88, 120, 74, 106, 86, 118, 87, 119, 73, 105)
	L = (1, 68)(2, 69)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 77)(9, 82)(10, 66)(11, 89)(12, 91)(13, 92)(14, 67)(15, 71)(16, 74)(17, 93)(18, 94)(19, 75)(20, 70)(21, 90)(22, 72)(23, 85)(24, 73)(25, 95)(26, 96)(27, 78)(28, 86)(29, 84)(30, 88)(31, 83)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.132
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.134 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y3), Y3^4, Y2^4 * Y3^-1, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 15, 47, 18, 50, 7, 39, 5, 37)(3, 35, 8, 40, 12, 44, 22, 54, 26, 58, 27, 59, 14, 46, 13, 45)(6, 38, 10, 42, 16, 48, 23, 55, 28, 60, 30, 62, 20, 52, 17, 49)(11, 43, 21, 53, 25, 57, 32, 64, 31, 63, 29, 61, 19, 51, 24, 56)(65, 97, 67, 99, 75, 107, 80, 112, 68, 100, 76, 108, 89, 121, 92, 124, 79, 111, 90, 122, 95, 127, 84, 116, 71, 103, 78, 110, 83, 115, 70, 102)(66, 98, 72, 104, 85, 117, 87, 119, 73, 105, 86, 118, 96, 128, 94, 126, 82, 114, 91, 123, 93, 125, 81, 113, 69, 101, 77, 109, 88, 120, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 66)(6, 80)(7, 65)(8, 86)(9, 82)(10, 87)(11, 89)(12, 90)(13, 72)(14, 67)(15, 71)(16, 92)(17, 74)(18, 69)(19, 75)(20, 70)(21, 96)(22, 91)(23, 94)(24, 85)(25, 95)(26, 78)(27, 77)(28, 84)(29, 88)(30, 81)(31, 83)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.131
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.135 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^-4, (Y3, Y2), (Y1^-1, Y3), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^-4 * Y3^2, Y1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1, Y1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 15, 47, 25, 57, 18, 50, 5, 37)(3, 35, 6, 38, 10, 42, 23, 55, 28, 60, 32, 64, 30, 62, 13, 45)(4, 36, 9, 41, 22, 54, 19, 51, 7, 39, 11, 43, 24, 56, 16, 48)(12, 44, 17, 49, 26, 58, 31, 63, 14, 46, 20, 52, 27, 59, 29, 61)(65, 97, 67, 99, 69, 101, 77, 109, 82, 114, 94, 126, 89, 121, 96, 128, 79, 111, 92, 124, 85, 117, 87, 119, 72, 104, 74, 106, 66, 98, 70, 102)(68, 100, 76, 108, 80, 112, 93, 125, 88, 120, 91, 123, 75, 107, 84, 116, 71, 103, 78, 110, 83, 115, 95, 127, 86, 118, 90, 122, 73, 105, 81, 113)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 86)(9, 89)(10, 90)(11, 66)(12, 92)(13, 93)(14, 67)(15, 71)(16, 85)(17, 96)(18, 88)(19, 69)(20, 70)(21, 83)(22, 82)(23, 95)(24, 72)(25, 75)(26, 94)(27, 74)(28, 78)(29, 87)(30, 91)(31, 77)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.140
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.136 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-2, Y3^4, (Y2^-1, Y3), (R * Y2)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^4, Y1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 14, 46, 27, 59, 17, 49, 5, 37)(3, 35, 9, 41, 22, 54, 29, 61, 28, 60, 31, 63, 18, 50, 6, 38)(4, 36, 10, 42, 23, 55, 19, 51, 7, 39, 11, 43, 24, 56, 15, 47)(12, 44, 25, 57, 32, 64, 20, 52, 13, 45, 26, 58, 30, 62, 16, 48)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 86, 118, 85, 117, 93, 125, 78, 110, 92, 124, 91, 123, 95, 127, 81, 113, 82, 114, 69, 101, 70, 102)(68, 100, 76, 108, 74, 106, 89, 121, 87, 119, 96, 128, 83, 115, 84, 116, 71, 103, 77, 109, 75, 107, 90, 122, 88, 120, 94, 126, 79, 111, 80, 112)
	L = (1, 68)(2, 74)(3, 76)(4, 78)(5, 79)(6, 80)(7, 65)(8, 87)(9, 89)(10, 91)(11, 66)(12, 92)(13, 67)(14, 71)(15, 85)(16, 93)(17, 88)(18, 94)(19, 69)(20, 70)(21, 83)(22, 96)(23, 81)(24, 72)(25, 95)(26, 73)(27, 75)(28, 77)(29, 84)(30, 86)(31, 90)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.142
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.137 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1^-1), Y3^4, (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (Y3, Y2), (R * Y2)^2, Y2^2 * Y1^3, Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 17, 49, 13, 45, 20, 52, 5, 37)(3, 35, 9, 41, 21, 53, 6, 38, 11, 43, 26, 58, 30, 62, 15, 47)(4, 36, 10, 42, 25, 57, 22, 54, 7, 39, 12, 44, 27, 59, 18, 50)(14, 46, 28, 60, 31, 63, 19, 51, 16, 48, 29, 61, 32, 64, 24, 56)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 85, 117, 69, 101, 79, 111, 81, 113, 75, 107, 66, 98, 73, 105, 84, 116, 94, 126, 87, 119, 70, 102)(68, 100, 78, 110, 76, 108, 93, 125, 89, 121, 95, 127, 82, 114, 88, 120, 71, 103, 80, 112, 74, 106, 92, 124, 91, 123, 96, 128, 86, 118, 83, 115)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 89)(9, 92)(10, 77)(11, 80)(12, 66)(13, 76)(14, 75)(15, 88)(16, 67)(17, 71)(18, 87)(19, 79)(20, 91)(21, 95)(22, 69)(23, 86)(24, 70)(25, 84)(26, 93)(27, 72)(28, 90)(29, 73)(30, 96)(31, 94)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.139
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.138 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y3), (Y1^-1, Y2), Y3^4, Y1^3 * Y2^-2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3 * Y1 * Y3 * Y2^2, Y2^-4 * Y1^-2, Y1^2 * Y2^4, Y2^4 * Y1^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 13, 45, 17, 49, 23, 55, 20, 52, 5, 37)(3, 35, 9, 41, 25, 57, 30, 62, 21, 53, 6, 38, 11, 43, 15, 47)(4, 36, 10, 42, 26, 58, 22, 54, 7, 39, 12, 44, 27, 59, 18, 50)(14, 46, 24, 56, 29, 61, 32, 64, 16, 48, 19, 51, 28, 60, 31, 63)(65, 97, 67, 99, 77, 109, 94, 126, 84, 116, 75, 107, 66, 98, 73, 105, 81, 113, 85, 117, 69, 101, 79, 111, 72, 104, 89, 121, 87, 119, 70, 102)(68, 100, 78, 110, 86, 118, 96, 128, 91, 123, 92, 124, 74, 106, 88, 120, 71, 103, 80, 112, 82, 114, 95, 127, 90, 122, 93, 125, 76, 108, 83, 115)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 90)(9, 88)(10, 87)(11, 92)(12, 66)(13, 86)(14, 85)(15, 95)(16, 67)(17, 71)(18, 77)(19, 73)(20, 91)(21, 80)(22, 69)(23, 76)(24, 70)(25, 93)(26, 84)(27, 72)(28, 89)(29, 75)(30, 96)(31, 94)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.141
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.139 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^-4, (Y2, Y1), (Y3^-1, Y1^-1), Y2^-1 * Y3 * Y1 * Y2^-1, Y3^4, (R * Y2)^2, (R * Y3)^2, (Y3, Y2), (R * Y1)^2, Y3^2 * Y1^4, Y3^-1 * Y2^-1 * Y1^-3 * Y2^-1, Y2^10 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 15, 47, 27, 59, 17, 49, 5, 37)(3, 35, 9, 41, 22, 54, 20, 52, 28, 60, 32, 64, 30, 62, 14, 46)(4, 36, 10, 42, 23, 55, 19, 51, 7, 39, 12, 44, 25, 57, 16, 48)(6, 38, 11, 43, 24, 56, 31, 63, 29, 61, 13, 45, 26, 58, 18, 50)(65, 97, 67, 99, 74, 106, 90, 122, 81, 113, 94, 126, 80, 112, 93, 125, 79, 111, 92, 124, 76, 108, 88, 120, 72, 104, 86, 118, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 82, 114, 69, 101, 78, 110, 68, 100, 77, 109, 91, 123, 96, 128, 89, 121, 95, 127, 85, 117, 84, 116, 71, 103, 75, 107)
	L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 80)(6, 78)(7, 65)(8, 87)(9, 90)(10, 91)(11, 67)(12, 66)(13, 92)(14, 93)(15, 71)(16, 85)(17, 89)(18, 94)(19, 69)(20, 70)(21, 83)(22, 82)(23, 81)(24, 73)(25, 72)(26, 96)(27, 76)(28, 75)(29, 84)(30, 95)(31, 86)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.137
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.140 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^-4, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y1^-1, Y2), (Y1, Y3^-1), (Y3^-1, Y2^-1), (R * Y1)^2, Y3^4, (R * Y2)^2, Y1^4 * Y3^2, Y3 * Y2 * Y1^-1 * Y2 * Y1^-2, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-2 * Y2^-1, Y1 * Y3 * Y2^10 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 17, 49, 27, 59, 18, 50, 5, 37)(3, 35, 9, 41, 22, 54, 31, 63, 29, 61, 20, 52, 28, 60, 15, 47)(4, 36, 10, 42, 23, 55, 19, 51, 7, 39, 12, 44, 25, 57, 13, 45)(6, 38, 11, 43, 24, 56, 14, 46, 26, 58, 32, 64, 30, 62, 16, 48)(65, 97, 67, 99, 77, 109, 88, 120, 72, 104, 86, 118, 74, 106, 90, 122, 81, 113, 93, 125, 83, 115, 94, 126, 82, 114, 92, 124, 76, 108, 70, 102)(66, 98, 73, 105, 68, 100, 78, 110, 85, 117, 95, 127, 87, 119, 96, 128, 91, 123, 84, 116, 71, 103, 80, 112, 69, 101, 79, 111, 89, 121, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 77)(6, 73)(7, 65)(8, 87)(9, 90)(10, 91)(11, 86)(12, 66)(13, 85)(14, 93)(15, 88)(16, 67)(17, 71)(18, 89)(19, 69)(20, 70)(21, 83)(22, 96)(23, 82)(24, 95)(25, 72)(26, 84)(27, 76)(28, 75)(29, 80)(30, 79)(31, 94)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.135
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.141 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^4, (Y2, Y1^-1), Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3, Y1), Y3 * Y2^2 * Y1, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^2 * Y1^-4, Y1 * Y2 * Y3^-1 * Y2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 17, 49, 27, 59, 20, 52, 5, 37)(3, 35, 9, 41, 22, 54, 31, 63, 29, 61, 19, 51, 28, 60, 15, 47)(4, 36, 10, 42, 23, 55, 13, 45, 7, 39, 12, 44, 25, 57, 18, 50)(6, 38, 11, 43, 24, 56, 16, 48, 26, 58, 32, 64, 30, 62, 14, 46)(65, 97, 67, 99, 77, 109, 88, 120, 72, 104, 86, 118, 76, 108, 90, 122, 81, 113, 93, 125, 82, 114, 94, 126, 84, 116, 92, 124, 74, 106, 70, 102)(66, 98, 73, 105, 71, 103, 80, 112, 85, 117, 95, 127, 89, 121, 96, 128, 91, 123, 83, 115, 68, 100, 78, 110, 69, 101, 79, 111, 87, 119, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 87)(9, 70)(10, 91)(11, 92)(12, 66)(13, 69)(14, 93)(15, 94)(16, 67)(17, 71)(18, 85)(19, 90)(20, 89)(21, 77)(22, 75)(23, 84)(24, 79)(25, 72)(26, 73)(27, 76)(28, 96)(29, 80)(30, 95)(31, 88)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.138
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.142 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3^4, (Y3^-1, Y2), (Y1, Y3^-1), Y1^-1 * Y2 * Y3 * Y2, Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y3^4, (R * Y1)^2, Y1^-1 * Y3 * Y2^2, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y1^-4, Y2^-2 * Y1^-1 * Y3 * Y1^-2, Y2^8 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 15, 47, 27, 59, 18, 50, 5, 37)(3, 35, 9, 41, 22, 54, 17, 49, 28, 60, 32, 64, 29, 61, 13, 45)(4, 36, 10, 42, 23, 55, 20, 52, 7, 39, 12, 44, 25, 57, 16, 48)(6, 38, 11, 43, 24, 56, 31, 63, 30, 62, 14, 46, 26, 58, 19, 51)(65, 97, 67, 99, 76, 108, 90, 122, 82, 114, 93, 125, 84, 116, 94, 126, 79, 111, 92, 124, 74, 106, 88, 120, 72, 104, 86, 118, 80, 112, 70, 102)(66, 98, 73, 105, 89, 121, 83, 115, 69, 101, 77, 109, 71, 103, 78, 110, 91, 123, 96, 128, 87, 119, 95, 127, 85, 117, 81, 113, 68, 100, 75, 107)
	L = (1, 68)(2, 74)(3, 75)(4, 79)(5, 80)(6, 81)(7, 65)(8, 87)(9, 88)(10, 91)(11, 92)(12, 66)(13, 70)(14, 67)(15, 71)(16, 85)(17, 94)(18, 89)(19, 86)(20, 69)(21, 84)(22, 95)(23, 82)(24, 96)(25, 72)(26, 73)(27, 76)(28, 78)(29, 83)(30, 77)(31, 93)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.136
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.143 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y3^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3^2 * Y1^-2, Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y3^2 * Y1^14, Y3^-2 * Y2^14, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 6, 38, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 30, 62, 25, 57, 22, 54, 17, 49, 14, 46, 9, 41, 5, 37)(3, 35, 7, 39, 4, 36, 8, 40, 12, 44, 16, 48, 20, 52, 24, 56, 28, 60, 32, 64, 29, 61, 26, 58, 21, 53, 18, 50, 13, 45, 10, 42)(65, 97, 67, 99, 73, 105, 77, 109, 81, 113, 85, 117, 89, 121, 93, 125, 95, 127, 92, 124, 87, 119, 84, 116, 79, 111, 76, 108, 70, 102, 68, 100)(66, 98, 71, 103, 69, 101, 74, 106, 78, 110, 82, 114, 86, 118, 90, 122, 94, 126, 96, 128, 91, 123, 88, 120, 83, 115, 80, 112, 75, 107, 72, 104)
	L = (1, 68)(2, 72)(3, 65)(4, 70)(5, 71)(6, 76)(7, 66)(8, 75)(9, 67)(10, 69)(11, 80)(12, 79)(13, 73)(14, 74)(15, 84)(16, 83)(17, 77)(18, 78)(19, 88)(20, 87)(21, 81)(22, 82)(23, 92)(24, 91)(25, 85)(26, 86)(27, 96)(28, 95)(29, 89)(30, 90)(31, 93)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.117
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.144 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, (Y2^-1, Y1^-1), R * Y2 * R * Y3^-1, (Y3^-1, Y1^-1), (R * Y1)^2, Y2^4 * Y1^4, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-2 * Y1^-2, Y2^4 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y2 * Y1^-1 * Y2 * Y3^-4 * Y1^-1, Y3^3 * Y1^-4 * Y3, (Y3 * Y1)^8, Y2^16, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 20, 52, 9, 41, 17, 49, 29, 61, 23, 55, 11, 43, 18, 50, 30, 62, 25, 57, 13, 45, 5, 37)(3, 35, 7, 39, 15, 47, 27, 59, 22, 54, 32, 64, 19, 51, 31, 63, 24, 56, 12, 44, 4, 36, 8, 40, 16, 48, 28, 60, 21, 53, 10, 42)(65, 97, 67, 99, 73, 105, 83, 115, 94, 126, 80, 112, 70, 102, 79, 111, 93, 125, 88, 120, 77, 109, 85, 117, 90, 122, 86, 118, 75, 107, 68, 100)(66, 98, 71, 103, 81, 113, 95, 127, 89, 121, 92, 124, 78, 110, 91, 123, 87, 119, 76, 108, 69, 101, 74, 106, 84, 116, 96, 128, 82, 114, 72, 104)
	L = (1, 68)(2, 72)(3, 65)(4, 75)(5, 76)(6, 80)(7, 66)(8, 82)(9, 67)(10, 69)(11, 86)(12, 87)(13, 88)(14, 92)(15, 70)(16, 94)(17, 71)(18, 96)(19, 73)(20, 74)(21, 77)(22, 90)(23, 91)(24, 93)(25, 95)(26, 85)(27, 78)(28, 89)(29, 79)(30, 83)(31, 81)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.115
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.145 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-3, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y1, Y2), Y1^-2 * Y3^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^4 * Y3, Y3^-2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-2 * Y2^-1 * Y1^-2, Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2, (Y3 * Y2)^4 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 20, 52, 28, 60, 13, 45, 25, 57, 32, 64, 30, 62, 16, 48, 27, 59, 14, 46, 26, 58, 17, 49, 5, 37)(3, 35, 9, 41, 22, 54, 19, 51, 7, 39, 12, 44, 4, 36, 10, 42, 23, 55, 18, 50, 6, 38, 11, 43, 24, 56, 31, 63, 29, 61, 15, 47)(65, 97, 67, 99, 77, 109, 68, 100, 78, 110, 88, 120, 72, 104, 86, 118, 96, 128, 87, 119, 81, 113, 93, 125, 84, 116, 71, 103, 80, 112, 70, 102)(66, 98, 73, 105, 89, 121, 74, 106, 90, 122, 95, 127, 85, 117, 83, 115, 94, 126, 82, 114, 69, 101, 79, 111, 92, 124, 76, 108, 91, 123, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 77)(7, 65)(8, 87)(9, 90)(10, 85)(11, 89)(12, 66)(13, 88)(14, 86)(15, 91)(16, 67)(17, 71)(18, 92)(19, 69)(20, 70)(21, 82)(22, 81)(23, 84)(24, 96)(25, 95)(26, 83)(27, 73)(28, 75)(29, 80)(30, 79)(31, 94)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.118
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.146 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 x C2 (small group id <32, 16>)
Aut   = C2 x D32 (small group id <64, 186>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y2^-1)^2, Y3^3 * Y2^-1, (R * Y3)^2, Y2^-2 * Y1^-2, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y2^2 * Y3 * Y2 * Y1^-1, Y3^-2 * Y2^-1 * Y3^-1 * Y1^-2, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, (Y2^-1 * Y1^2 * Y3)^2, (Y1^-1 * Y3^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 14, 46, 25, 57, 18, 50, 27, 59, 32, 64, 30, 62, 16, 48, 26, 58, 20, 52, 28, 60, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 23, 55, 17, 49, 4, 36, 10, 42, 22, 54, 31, 63, 29, 61, 19, 51, 7, 39, 12, 44, 24, 56, 15, 47)(65, 97, 67, 99, 77, 109, 88, 120, 84, 116, 71, 103, 80, 112, 93, 125, 96, 128, 86, 118, 82, 114, 68, 100, 78, 110, 87, 119, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 79, 111, 92, 124, 76, 108, 90, 122, 83, 115, 94, 126, 95, 127, 91, 123, 74, 106, 89, 121, 81, 113, 85, 117, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 80)(5, 81)(6, 82)(7, 65)(8, 86)(9, 89)(10, 90)(11, 91)(12, 66)(13, 87)(14, 93)(15, 85)(16, 67)(17, 94)(18, 71)(19, 69)(20, 70)(21, 95)(22, 84)(23, 96)(24, 72)(25, 83)(26, 73)(27, 76)(28, 75)(29, 77)(30, 79)(31, 92)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.116
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.147 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 16, 16})
Quotient :: edge^2
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-3, Y2^2 * Y1^-2, (Y2, Y1^-1), (Y2 * Y1^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-2, Y2^8, Y3^-3 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-3 ]
Map:: non-degenerate
	R = (1, 33, 4, 36, 15, 47, 24, 56, 9, 41, 23, 55, 32, 64, 27, 59, 11, 43, 26, 58, 31, 63, 22, 54, 8, 40, 21, 53, 20, 52, 7, 39)(2, 34, 10, 42, 25, 57, 18, 50, 5, 37, 17, 49, 30, 62, 14, 46, 3, 35, 13, 45, 29, 61, 19, 51, 6, 38, 16, 48, 28, 60, 12, 44)(65, 66, 72, 70, 75, 67, 73, 69)(68, 77, 85, 81, 90, 74, 87, 80)(71, 78, 86, 82, 91, 76, 88, 83)(79, 89, 84, 92, 95, 93, 96, 94)(97, 99, 104, 101, 107, 98, 105, 102)(100, 106, 117, 112, 122, 109, 119, 113)(103, 108, 118, 115, 123, 110, 120, 114)(111, 125, 116, 126, 127, 121, 128, 124)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.150
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.148 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 16, 16})
Quotient :: edge^2
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-3, Y2^-1 * Y3 * Y1 * Y3^-1, (Y2, Y1^-1), Y3 * Y2^-1 * Y3^-1 * Y1, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, Y3 * Y1^-1 * Y3^3 * Y2^-1, Y3^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-1, Y3^-4 * Y2^-1 * Y1^-1, Y2^8, Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 4, 36, 15, 47, 22, 54, 8, 40, 21, 53, 31, 63, 27, 59, 11, 43, 26, 58, 32, 64, 24, 56, 9, 41, 23, 55, 20, 52, 7, 39)(2, 34, 10, 42, 25, 57, 19, 51, 6, 38, 16, 48, 30, 62, 14, 46, 3, 35, 13, 45, 29, 61, 18, 50, 5, 37, 17, 49, 28, 60, 12, 44)(65, 66, 72, 70, 75, 67, 73, 69)(68, 77, 85, 81, 90, 74, 87, 80)(71, 78, 86, 82, 91, 76, 88, 83)(79, 89, 95, 94, 96, 93, 84, 92)(97, 99, 104, 101, 107, 98, 105, 102)(100, 106, 117, 112, 122, 109, 119, 113)(103, 108, 118, 115, 123, 110, 120, 114)(111, 125, 127, 124, 128, 121, 116, 126)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.149
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.149 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 16, 16})
Quotient :: loop^2
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-3, Y2^2 * Y1^-2, (Y2, Y1^-1), (Y2 * Y1^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-2, Y2^8, Y3^-3 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-3 ]
Map:: non-degenerate
	R = (1, 33, 65, 97, 4, 36, 68, 100, 15, 47, 79, 111, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 32, 64, 96, 128, 27, 59, 91, 123, 11, 43, 75, 107, 26, 58, 90, 122, 31, 63, 95, 127, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 25, 57, 89, 121, 18, 50, 82, 114, 5, 37, 69, 101, 17, 49, 81, 113, 30, 62, 94, 126, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 29, 61, 93, 125, 19, 51, 83, 115, 6, 38, 70, 102, 16, 48, 80, 112, 28, 60, 92, 124, 12, 44, 76, 108)
	L = (1, 34)(2, 40)(3, 41)(4, 45)(5, 33)(6, 43)(7, 46)(8, 38)(9, 37)(10, 55)(11, 35)(12, 56)(13, 53)(14, 54)(15, 57)(16, 36)(17, 58)(18, 59)(19, 39)(20, 60)(21, 49)(22, 50)(23, 48)(24, 51)(25, 52)(26, 42)(27, 44)(28, 63)(29, 64)(30, 47)(31, 61)(32, 62)(65, 99)(66, 105)(67, 104)(68, 106)(69, 107)(70, 97)(71, 108)(72, 101)(73, 102)(74, 117)(75, 98)(76, 118)(77, 119)(78, 120)(79, 125)(80, 122)(81, 100)(82, 103)(83, 123)(84, 126)(85, 112)(86, 115)(87, 113)(88, 114)(89, 128)(90, 109)(91, 110)(92, 111)(93, 116)(94, 127)(95, 121)(96, 124)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.148
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.150 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 16, 16})
Quotient :: loop^2
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-3, Y2^-1 * Y3 * Y1 * Y3^-1, (Y2, Y1^-1), Y3 * Y2^-1 * Y3^-1 * Y1, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, Y3 * Y1^-1 * Y3^3 * Y2^-1, Y3^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-1, Y3^-4 * Y2^-1 * Y1^-1, Y2^8, Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1 * Y3^-2 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 65, 97, 4, 36, 68, 100, 15, 47, 79, 111, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 31, 63, 95, 127, 27, 59, 91, 123, 11, 43, 75, 107, 26, 58, 90, 122, 32, 64, 96, 128, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 25, 57, 89, 121, 19, 51, 83, 115, 6, 38, 70, 102, 16, 48, 80, 112, 30, 62, 94, 126, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 29, 61, 93, 125, 18, 50, 82, 114, 5, 37, 69, 101, 17, 49, 81, 113, 28, 60, 92, 124, 12, 44, 76, 108)
	L = (1, 34)(2, 40)(3, 41)(4, 45)(5, 33)(6, 43)(7, 46)(8, 38)(9, 37)(10, 55)(11, 35)(12, 56)(13, 53)(14, 54)(15, 57)(16, 36)(17, 58)(18, 59)(19, 39)(20, 60)(21, 49)(22, 50)(23, 48)(24, 51)(25, 63)(26, 42)(27, 44)(28, 47)(29, 52)(30, 64)(31, 62)(32, 61)(65, 99)(66, 105)(67, 104)(68, 106)(69, 107)(70, 97)(71, 108)(72, 101)(73, 102)(74, 117)(75, 98)(76, 118)(77, 119)(78, 120)(79, 125)(80, 122)(81, 100)(82, 103)(83, 123)(84, 126)(85, 112)(86, 115)(87, 113)(88, 114)(89, 116)(90, 109)(91, 110)(92, 128)(93, 127)(94, 111)(95, 124)(96, 121)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.147
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.151 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2^-1, (Y1 * Y2^-1)^2, Y2^2 * Y1^-2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y1 * Y2^2 * Y3^-1 * Y1 * Y3, Y2^3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^8, (Y1^2 * Y2)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 32, 64, 30, 62, 18, 50, 5, 37)(3, 35, 9, 41, 24, 56, 29, 61, 31, 63, 19, 51, 6, 38, 11, 43)(4, 36, 14, 46, 13, 45, 17, 49, 27, 59, 10, 42, 26, 58, 15, 47)(7, 39, 21, 53, 25, 57, 20, 52, 28, 60, 12, 44, 16, 48, 22, 54)(65, 97, 67, 99, 72, 104, 88, 120, 96, 128, 95, 127, 82, 114, 70, 102)(66, 98, 73, 105, 87, 119, 93, 125, 94, 126, 83, 115, 69, 101, 75, 107)(68, 100, 71, 103, 77, 109, 89, 121, 91, 123, 92, 124, 90, 122, 80, 112)(74, 106, 76, 108, 79, 111, 86, 118, 78, 110, 85, 117, 81, 113, 84, 116)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 81)(6, 80)(7, 65)(8, 77)(9, 76)(10, 75)(11, 84)(12, 66)(13, 67)(14, 93)(15, 73)(16, 82)(17, 83)(18, 90)(19, 85)(20, 69)(21, 94)(22, 87)(23, 79)(24, 89)(25, 72)(26, 95)(27, 88)(28, 96)(29, 86)(30, 78)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.182
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.152 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-2, Y1^-2 * Y2^-2, (Y2, Y1), (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y1 * Y3 * Y2^-1 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 32, 64, 30, 62, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 25, 57, 31, 63, 29, 61, 14, 46)(4, 36, 16, 48, 24, 56, 19, 51, 26, 58, 10, 42, 15, 47, 17, 49)(7, 39, 21, 53, 18, 50, 20, 52, 28, 60, 12, 44, 27, 59, 22, 54)(65, 97, 67, 99, 77, 109, 93, 125, 96, 128, 89, 121, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 78, 110, 94, 126, 95, 127, 87, 119, 75, 107)(68, 100, 71, 103, 79, 111, 91, 123, 90, 122, 92, 124, 88, 120, 82, 114)(74, 106, 76, 108, 83, 115, 84, 116, 80, 112, 85, 117, 81, 113, 86, 118)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 83)(6, 82)(7, 65)(8, 88)(9, 76)(10, 75)(11, 86)(12, 66)(13, 79)(14, 84)(15, 67)(16, 78)(17, 95)(18, 72)(19, 73)(20, 69)(21, 94)(22, 87)(23, 81)(24, 89)(25, 92)(26, 93)(27, 77)(28, 96)(29, 91)(30, 80)(31, 85)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.179
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.153 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2, (Y1, Y2^-1), (R * Y1)^2, Y2^2 * Y1^-2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y2^2 * Y1^6 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 32, 64, 29, 61, 17, 49, 5, 37)(3, 35, 9, 41, 24, 56, 30, 62, 31, 63, 18, 50, 6, 38, 11, 43)(4, 36, 14, 46, 25, 57, 16, 48, 26, 58, 10, 42, 20, 52, 15, 47)(7, 39, 21, 53, 13, 45, 19, 51, 28, 60, 12, 44, 27, 59, 22, 54)(65, 97, 67, 99, 72, 104, 88, 120, 96, 128, 95, 127, 81, 113, 70, 102)(66, 98, 73, 105, 87, 119, 94, 126, 93, 125, 82, 114, 69, 101, 75, 107)(68, 100, 77, 109, 89, 121, 92, 124, 90, 122, 91, 123, 84, 116, 71, 103)(74, 106, 86, 118, 79, 111, 85, 117, 78, 110, 83, 115, 80, 112, 76, 108)
	L = (1, 68)(2, 74)(3, 77)(4, 67)(5, 80)(6, 71)(7, 65)(8, 89)(9, 86)(10, 73)(11, 76)(12, 66)(13, 72)(14, 82)(15, 94)(16, 75)(17, 84)(18, 83)(19, 69)(20, 70)(21, 93)(22, 87)(23, 79)(24, 92)(25, 88)(26, 95)(27, 81)(28, 96)(29, 78)(30, 85)(31, 91)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.180
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.154 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^-2, (R * Y3)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2), Y1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1, Y3^-2 * Y2^-3, Y1 * Y3 * Y1 * Y2 * Y3, Y1 * Y2^-1 * Y1 * Y3^-2, Y3^-4 * Y2^2, Y2^2 * Y3^-4, Y1^-1 * Y3^-4 * Y1^-1, Y1^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 27, 59, 32, 64, 31, 63, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 18, 50, 29, 61, 26, 58, 15, 47)(4, 36, 17, 49, 28, 60, 21, 53, 16, 48, 10, 42, 23, 55, 19, 51)(7, 39, 24, 56, 14, 46, 22, 54, 20, 52, 12, 44, 30, 62, 25, 57)(65, 97, 67, 99, 77, 109, 90, 122, 96, 128, 82, 114, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 79, 111, 95, 127, 93, 125, 91, 123, 75, 107)(68, 100, 78, 110, 87, 119, 71, 103, 80, 112, 94, 126, 92, 124, 84, 116)(74, 106, 89, 121, 85, 117, 76, 108, 81, 113, 86, 118, 83, 115, 88, 120)
	L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 85)(6, 84)(7, 65)(8, 92)(9, 89)(10, 93)(11, 88)(12, 66)(13, 87)(14, 72)(15, 76)(16, 67)(17, 73)(18, 94)(19, 79)(20, 96)(21, 75)(22, 69)(23, 70)(24, 95)(25, 91)(26, 71)(27, 83)(28, 90)(29, 86)(30, 77)(31, 81)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.181
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.155 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-3 * Y2 * Y1^-1, Y2 * Y1^-3 * Y2^-1 * Y1^-1, Y2^4 * Y1^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, (Y2, Y1^-1)^2, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 18, 50, 30, 62, 28, 60, 13, 45, 4, 36)(3, 35, 9, 41, 19, 51, 12, 44, 23, 55, 7, 39, 21, 53, 11, 43)(5, 37, 15, 47, 20, 52, 14, 46, 25, 57, 8, 40, 24, 56, 16, 48)(10, 42, 22, 54, 17, 49, 26, 58, 31, 63, 27, 59, 32, 64, 29, 61)(65, 97, 67, 99, 74, 106, 88, 120, 77, 109, 85, 117, 96, 128, 89, 121, 94, 126, 87, 119, 95, 127, 84, 116, 70, 102, 83, 115, 81, 113, 69, 101)(66, 98, 71, 103, 86, 118, 78, 110, 68, 100, 76, 108, 93, 125, 79, 111, 92, 124, 73, 105, 91, 123, 80, 112, 82, 114, 75, 107, 90, 122, 72, 104)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.156 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^3 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^4 * Y1^-2, (Y2^2 * Y1^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^-2 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 18, 50, 30, 62, 28, 60, 13, 45, 4, 36)(3, 35, 9, 41, 19, 51, 12, 44, 23, 55, 7, 39, 21, 53, 11, 43)(5, 37, 15, 47, 20, 52, 14, 46, 25, 57, 8, 40, 24, 56, 16, 48)(10, 42, 22, 54, 31, 63, 29, 61, 32, 64, 27, 59, 17, 49, 26, 58)(65, 97, 67, 99, 74, 106, 84, 116, 70, 102, 83, 115, 95, 127, 89, 121, 94, 126, 87, 119, 96, 128, 88, 120, 77, 109, 85, 117, 81, 113, 69, 101)(66, 98, 71, 103, 86, 118, 80, 112, 82, 114, 75, 107, 93, 125, 79, 111, 92, 124, 73, 105, 91, 123, 78, 110, 68, 100, 76, 108, 90, 122, 72, 104)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.157 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, Y3 * Y1^-4, Y1^-1 * Y3 * Y2^-1 * Y1 * Y2, Y1 * Y3 * Y2 * Y1^-1 * Y2^-1, (Y2^-2 * Y1^-1)^2, Y1 * Y2^-3 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 4, 36, 9, 41, 18, 50, 5, 37)(3, 35, 11, 43, 23, 55, 17, 49, 13, 45, 8, 40, 25, 57, 14, 46)(6, 38, 20, 52, 24, 56, 19, 51, 16, 48, 10, 42, 27, 59, 21, 53)(12, 44, 26, 58, 22, 54, 28, 60, 30, 62, 29, 61, 32, 64, 31, 63)(65, 97, 67, 99, 76, 108, 91, 123, 82, 114, 89, 121, 96, 128, 80, 112, 68, 100, 77, 109, 94, 126, 88, 120, 71, 103, 87, 119, 86, 118, 70, 102)(66, 98, 72, 104, 90, 122, 83, 115, 69, 101, 81, 113, 95, 127, 84, 116, 73, 105, 75, 107, 93, 125, 85, 117, 79, 111, 78, 110, 92, 124, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 80)(7, 82)(8, 75)(9, 66)(10, 84)(11, 72)(12, 94)(13, 67)(14, 81)(15, 69)(16, 70)(17, 78)(18, 71)(19, 85)(20, 74)(21, 83)(22, 96)(23, 89)(24, 91)(25, 87)(26, 93)(27, 88)(28, 95)(29, 90)(30, 76)(31, 92)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.158 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y1^4 * Y3, Y1 * Y3 * Y2^-1 * Y1^-1 * Y2, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2, (Y2^-1 * Y1 * Y2^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 15, 47, 4, 36, 9, 41, 18, 50, 5, 37)(3, 35, 11, 43, 23, 55, 17, 49, 13, 45, 8, 40, 25, 57, 14, 46)(6, 38, 20, 52, 24, 56, 19, 51, 16, 48, 10, 42, 27, 59, 21, 53)(12, 44, 26, 58, 32, 64, 31, 63, 30, 62, 29, 61, 22, 54, 28, 60)(65, 97, 67, 99, 76, 108, 88, 120, 71, 103, 87, 119, 96, 128, 80, 112, 68, 100, 77, 109, 94, 126, 91, 123, 82, 114, 89, 121, 86, 118, 70, 102)(66, 98, 72, 104, 90, 122, 85, 117, 79, 111, 78, 110, 95, 127, 84, 116, 73, 105, 75, 107, 93, 125, 83, 115, 69, 101, 81, 113, 92, 124, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 80)(7, 82)(8, 75)(9, 66)(10, 84)(11, 72)(12, 94)(13, 67)(14, 81)(15, 69)(16, 70)(17, 78)(18, 71)(19, 85)(20, 74)(21, 83)(22, 96)(23, 89)(24, 91)(25, 87)(26, 93)(27, 88)(28, 95)(29, 90)(30, 76)(31, 92)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.159 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1 * Y2^2, Y1 * Y3 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^2, Y1^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 17, 49, 32, 64, 30, 62, 15, 47, 5, 37)(3, 35, 6, 38, 9, 41, 19, 51, 26, 58, 29, 61, 25, 57, 11, 43)(4, 36, 8, 40, 18, 50, 22, 54, 24, 56, 31, 63, 28, 60, 13, 45)(10, 42, 16, 48, 21, 53, 27, 59, 12, 44, 14, 46, 20, 52, 23, 55)(65, 97, 67, 99, 69, 101, 75, 107, 79, 111, 89, 121, 94, 126, 93, 125, 96, 128, 90, 122, 81, 113, 83, 115, 71, 103, 73, 105, 66, 98, 70, 102)(68, 100, 76, 108, 77, 109, 91, 123, 92, 124, 85, 117, 95, 127, 80, 112, 88, 120, 74, 106, 86, 118, 87, 119, 82, 114, 84, 116, 72, 104, 78, 110)
	L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 77)(6, 80)(7, 82)(8, 66)(9, 85)(10, 67)(11, 87)(12, 90)(13, 69)(14, 93)(15, 92)(16, 70)(17, 86)(18, 71)(19, 91)(20, 89)(21, 73)(22, 81)(23, 75)(24, 96)(25, 84)(26, 76)(27, 83)(28, 79)(29, 78)(30, 95)(31, 94)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.166
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.160 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1^-1 * Y2^2, Y1 * Y3 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3, Y1^2 * Y3 * Y2 * Y3 * Y2 * Y1, Y1^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 17, 49, 32, 64, 28, 60, 14, 46, 5, 37)(3, 35, 8, 40, 18, 50, 27, 59, 24, 56, 29, 61, 15, 47, 6, 38)(4, 36, 9, 41, 19, 51, 31, 63, 23, 55, 22, 54, 25, 57, 12, 44)(10, 42, 20, 52, 26, 58, 13, 45, 11, 43, 21, 53, 30, 62, 16, 48)(65, 97, 67, 99, 66, 98, 72, 104, 71, 103, 82, 114, 81, 113, 91, 123, 96, 128, 88, 120, 92, 124, 93, 125, 78, 110, 79, 111, 69, 101, 70, 102)(68, 100, 75, 107, 73, 105, 85, 117, 83, 115, 94, 126, 95, 127, 80, 112, 87, 119, 74, 106, 86, 118, 84, 116, 89, 121, 90, 122, 76, 108, 77, 109)
	L = (1, 68)(2, 73)(3, 74)(4, 65)(5, 76)(6, 80)(7, 83)(8, 84)(9, 66)(10, 67)(11, 88)(12, 69)(13, 91)(14, 89)(15, 94)(16, 70)(17, 95)(18, 90)(19, 71)(20, 72)(21, 93)(22, 92)(23, 96)(24, 75)(25, 78)(26, 82)(27, 77)(28, 86)(29, 85)(30, 79)(31, 81)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.164
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.161 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1), Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, R * Y2 * Y1^-1 * R * Y2^-1, Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1^-1 * Y2 * Y3 * Y2, Y1 * Y2^-1 * Y1 * Y2^-3, Y2^2 * Y3 * Y2^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 20, 52, 25, 57, 11, 43, 17, 49, 5, 37)(3, 35, 8, 40, 18, 50, 6, 38, 10, 42, 22, 54, 28, 60, 13, 45)(4, 36, 9, 41, 21, 53, 31, 63, 27, 59, 26, 58, 29, 61, 15, 47)(12, 44, 23, 55, 32, 64, 19, 51, 14, 46, 24, 56, 30, 62, 16, 48)(65, 97, 67, 99, 75, 107, 86, 118, 71, 103, 82, 114, 69, 101, 77, 109, 89, 121, 74, 106, 66, 98, 72, 104, 81, 113, 92, 124, 84, 116, 70, 102)(68, 100, 78, 110, 90, 122, 87, 119, 85, 117, 94, 126, 79, 111, 83, 115, 91, 123, 76, 108, 73, 105, 88, 120, 93, 125, 96, 128, 95, 127, 80, 112)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 83)(7, 85)(8, 87)(9, 66)(10, 78)(11, 90)(12, 67)(13, 80)(14, 74)(15, 69)(16, 77)(17, 93)(18, 96)(19, 70)(20, 95)(21, 71)(22, 88)(23, 72)(24, 86)(25, 91)(26, 75)(27, 89)(28, 94)(29, 81)(30, 92)(31, 84)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.165
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.162 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y1^-1 * Y3 * Y1 * Y3, Y2^-2 * Y1^3, R * Y2 * Y1 * R * Y2^-1, Y3 * Y1 * Y2 * Y3 * Y2, Y2^-4 * Y1^-2, Y1^2 * Y2^4, Y2^-1 * Y1^-1 * Y2^-3 * Y1^-1, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 11, 43, 23, 55, 20, 52, 17, 49, 5, 37)(3, 35, 8, 40, 21, 53, 26, 58, 18, 50, 6, 38, 10, 42, 13, 45)(4, 36, 9, 41, 22, 54, 27, 59, 29, 61, 32, 64, 31, 63, 15, 47)(12, 44, 16, 48, 24, 56, 30, 62, 14, 46, 19, 51, 25, 57, 28, 60)(65, 97, 67, 99, 75, 107, 90, 122, 81, 113, 74, 106, 66, 98, 72, 104, 87, 119, 82, 114, 69, 101, 77, 109, 71, 103, 85, 117, 84, 116, 70, 102)(68, 100, 78, 110, 91, 123, 92, 124, 95, 127, 88, 120, 73, 105, 83, 115, 93, 125, 76, 108, 79, 111, 94, 126, 86, 118, 89, 121, 96, 128, 80, 112)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 83)(7, 86)(8, 80)(9, 66)(10, 89)(11, 91)(12, 67)(13, 92)(14, 82)(15, 69)(16, 72)(17, 95)(18, 78)(19, 70)(20, 96)(21, 88)(22, 71)(23, 93)(24, 85)(25, 74)(26, 94)(27, 75)(28, 77)(29, 87)(30, 90)(31, 81)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.163
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.163 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y1^-1 * Y2^-2, Y3 * Y1^-1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-2, Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, (Y2, Y1^-1)^2, Y2^-1 * Y1 * Y2^11 * Y3, Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 19, 51, 30, 62, 28, 60, 17, 49, 5, 37)(3, 35, 11, 43, 20, 52, 16, 48, 25, 57, 8, 40, 23, 55, 14, 46)(4, 36, 9, 41, 21, 53, 31, 63, 27, 59, 32, 64, 29, 61, 12, 44)(6, 38, 18, 50, 22, 54, 15, 47, 24, 56, 10, 42, 26, 58, 13, 45)(65, 97, 67, 99, 76, 108, 90, 122, 81, 113, 87, 119, 96, 128, 88, 120, 94, 126, 89, 121, 95, 127, 86, 118, 71, 103, 84, 116, 73, 105, 70, 102)(66, 98, 72, 104, 68, 100, 79, 111, 69, 101, 80, 112, 93, 125, 82, 114, 92, 124, 75, 107, 91, 123, 77, 109, 83, 115, 78, 110, 85, 117, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 76)(6, 75)(7, 85)(8, 88)(9, 66)(10, 87)(11, 70)(12, 69)(13, 67)(14, 90)(15, 89)(16, 86)(17, 93)(18, 84)(19, 95)(20, 82)(21, 71)(22, 80)(23, 74)(24, 72)(25, 79)(26, 78)(27, 94)(28, 96)(29, 81)(30, 91)(31, 83)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.162
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.164 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^3 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-3, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-1)^2, (Y2, Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 21, 53, 32, 64, 31, 63, 17, 49, 5, 37)(3, 35, 11, 43, 22, 54, 16, 48, 27, 59, 8, 40, 25, 57, 13, 45)(4, 36, 9, 41, 23, 55, 20, 52, 30, 62, 12, 44, 26, 58, 15, 47)(6, 38, 14, 46, 24, 56, 18, 50, 29, 61, 10, 42, 28, 60, 19, 51)(65, 97, 67, 99, 76, 108, 88, 120, 71, 103, 86, 118, 79, 111, 93, 125, 96, 128, 91, 123, 73, 105, 92, 124, 81, 113, 89, 121, 84, 116, 70, 102)(66, 98, 72, 104, 90, 122, 83, 115, 85, 117, 77, 109, 68, 100, 78, 110, 95, 127, 75, 107, 87, 119, 82, 114, 69, 101, 80, 112, 94, 126, 74, 106)
	L = (1, 68)(2, 73)(3, 74)(4, 65)(5, 79)(6, 80)(7, 87)(8, 88)(9, 66)(10, 67)(11, 92)(12, 95)(13, 93)(14, 91)(15, 69)(16, 70)(17, 90)(18, 89)(19, 86)(20, 85)(21, 84)(22, 83)(23, 71)(24, 72)(25, 82)(26, 81)(27, 78)(28, 75)(29, 77)(30, 96)(31, 76)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.160
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.165 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1 * Y3 * Y1^-1 * Y3, Y2^-2 * Y1 * Y3, Y2^-1 * Y3 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y2 * Y1^-2, Y2 * Y1 * Y2^-1 * Y1^3, (R * Y2 * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-3, Y2^-1 * R * Y1^-1 * Y3 * R * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y1^-2, Y2 * Y1^2 * Y2^11, (Y1^-1 * Y2)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 19, 51, 30, 62, 28, 60, 16, 48, 5, 37)(3, 35, 11, 43, 20, 52, 15, 47, 25, 57, 8, 40, 23, 55, 13, 45)(4, 36, 9, 41, 21, 53, 31, 63, 29, 61, 32, 64, 27, 59, 14, 46)(6, 38, 12, 44, 22, 54, 17, 49, 26, 58, 10, 42, 24, 56, 18, 50)(65, 97, 67, 99, 73, 105, 86, 118, 71, 103, 84, 116, 95, 127, 90, 122, 94, 126, 89, 121, 96, 128, 88, 120, 80, 112, 87, 119, 78, 110, 70, 102)(66, 98, 72, 104, 85, 117, 82, 114, 83, 115, 77, 109, 93, 125, 76, 108, 92, 124, 75, 107, 91, 123, 81, 113, 69, 101, 79, 111, 68, 100, 74, 106)
	L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 77)(7, 85)(8, 88)(9, 66)(10, 89)(11, 86)(12, 67)(13, 70)(14, 69)(15, 90)(16, 91)(17, 84)(18, 87)(19, 95)(20, 81)(21, 71)(22, 75)(23, 82)(24, 72)(25, 74)(26, 79)(27, 80)(28, 96)(29, 94)(30, 93)(31, 83)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.161
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.166 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y1 * Y2, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y2^2 * Y3 * Y1^-3, (R * Y2 * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-2, Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 21, 53, 32, 64, 31, 63, 18, 50, 5, 37)(3, 35, 11, 43, 22, 54, 17, 49, 27, 59, 8, 40, 25, 57, 14, 46)(4, 36, 9, 41, 23, 55, 12, 44, 26, 58, 20, 52, 30, 62, 16, 48)(6, 38, 19, 51, 24, 56, 13, 45, 28, 60, 10, 42, 29, 61, 15, 47)(65, 97, 67, 99, 76, 108, 93, 125, 82, 114, 89, 121, 73, 105, 92, 124, 96, 128, 91, 123, 80, 112, 88, 120, 71, 103, 86, 118, 84, 116, 70, 102)(66, 98, 72, 104, 90, 122, 77, 109, 69, 101, 81, 113, 87, 119, 83, 115, 95, 127, 75, 107, 68, 100, 79, 111, 85, 117, 78, 110, 94, 126, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 80)(6, 72)(7, 87)(8, 70)(9, 66)(10, 86)(11, 92)(12, 85)(13, 67)(14, 88)(15, 91)(16, 69)(17, 93)(18, 94)(19, 89)(20, 95)(21, 76)(22, 74)(23, 71)(24, 78)(25, 83)(26, 96)(27, 79)(28, 75)(29, 81)(30, 82)(31, 84)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.159
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.167 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^-1, (R * Y3)^2, (Y2, Y3^-1), (R * Y2)^2, Y3^4, (R * Y1)^2, Y2^-4 * Y3^-1, Y2 * Y3 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y1 * Y2 * Y1, (Y2^-2 * Y1^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 16, 48, 20, 52, 7, 39, 5, 37)(3, 35, 11, 43, 13, 45, 18, 50, 26, 58, 8, 40, 15, 47, 14, 46)(6, 38, 21, 53, 17, 49, 19, 51, 27, 59, 10, 42, 24, 56, 22, 54)(12, 44, 25, 57, 23, 55, 28, 60, 32, 64, 29, 61, 31, 63, 30, 62)(65, 97, 67, 99, 76, 108, 88, 120, 71, 103, 79, 111, 95, 127, 91, 123, 80, 112, 90, 122, 96, 128, 81, 113, 68, 100, 77, 109, 87, 119, 70, 102)(66, 98, 72, 104, 89, 121, 83, 115, 69, 101, 82, 114, 94, 126, 85, 117, 84, 116, 75, 107, 93, 125, 86, 118, 73, 105, 78, 110, 92, 124, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 80)(5, 66)(6, 81)(7, 65)(8, 78)(9, 84)(10, 86)(11, 82)(12, 87)(13, 90)(14, 75)(15, 67)(16, 71)(17, 91)(18, 72)(19, 74)(20, 69)(21, 83)(22, 85)(23, 96)(24, 70)(25, 92)(26, 79)(27, 88)(28, 93)(29, 94)(30, 89)(31, 76)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.170
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.168 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^-1, (R * Y3)^2, Y3^4, (Y2, Y3), (R * Y1)^2, (R * Y2)^2, Y2^4 * Y3, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1^-1 * Y2)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 16, 48, 17, 49, 4, 36, 5, 37)(3, 35, 11, 43, 15, 47, 19, 51, 26, 58, 8, 40, 13, 45, 14, 46)(6, 38, 21, 53, 24, 56, 20, 52, 27, 59, 9, 41, 18, 50, 22, 54)(12, 44, 25, 57, 30, 62, 31, 63, 32, 64, 29, 61, 23, 55, 28, 60)(65, 97, 67, 99, 76, 108, 88, 120, 71, 103, 79, 111, 94, 126, 91, 123, 80, 112, 90, 122, 96, 128, 82, 114, 68, 100, 77, 109, 87, 119, 70, 102)(66, 98, 72, 104, 89, 121, 86, 118, 74, 106, 78, 110, 95, 127, 85, 117, 81, 113, 75, 107, 93, 125, 84, 116, 69, 101, 83, 115, 92, 124, 73, 105)
	L = (1, 68)(2, 69)(3, 77)(4, 80)(5, 81)(6, 82)(7, 65)(8, 83)(9, 84)(10, 66)(11, 78)(12, 87)(13, 90)(14, 72)(15, 67)(16, 71)(17, 74)(18, 91)(19, 75)(20, 85)(21, 86)(22, 73)(23, 96)(24, 70)(25, 92)(26, 79)(27, 88)(28, 93)(29, 95)(30, 76)(31, 89)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.169
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.169 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), (R * Y2)^2, Y3^4, Y2^-4 * Y3, Y3^-1 * Y1 * Y2^-1 * Y1 * Y2, Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2 * Y3^2 * Y2^-1, (Y1 * Y2^2)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 16, 48, 17, 49, 4, 36, 5, 37)(3, 35, 11, 43, 15, 47, 19, 51, 26, 58, 8, 40, 13, 45, 14, 46)(6, 38, 21, 53, 24, 56, 20, 52, 27, 59, 9, 41, 18, 50, 22, 54)(12, 44, 25, 57, 23, 55, 28, 60, 32, 64, 29, 61, 30, 62, 31, 63)(65, 97, 67, 99, 76, 108, 82, 114, 68, 100, 77, 109, 94, 126, 91, 123, 80, 112, 90, 122, 96, 128, 88, 120, 71, 103, 79, 111, 87, 119, 70, 102)(66, 98, 72, 104, 89, 121, 84, 116, 69, 101, 83, 115, 95, 127, 85, 117, 81, 113, 75, 107, 93, 125, 86, 118, 74, 106, 78, 110, 92, 124, 73, 105)
	L = (1, 68)(2, 69)(3, 77)(4, 80)(5, 81)(6, 82)(7, 65)(8, 83)(9, 84)(10, 66)(11, 78)(12, 94)(13, 90)(14, 72)(15, 67)(16, 71)(17, 74)(18, 91)(19, 75)(20, 85)(21, 86)(22, 73)(23, 76)(24, 70)(25, 95)(26, 79)(27, 88)(28, 89)(29, 92)(30, 96)(31, 93)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.168
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.170 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4, (Y2^-1, Y3), Y2^4 * Y3^-1, Y2 * Y3 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y1 * Y2 * Y1, (Y1 * Y2^-2)^2, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 16, 48, 20, 52, 7, 39, 5, 37)(3, 35, 11, 43, 13, 45, 18, 50, 26, 58, 8, 40, 15, 47, 14, 46)(6, 38, 21, 53, 17, 49, 19, 51, 27, 59, 10, 42, 24, 56, 22, 54)(12, 44, 25, 57, 30, 62, 31, 63, 32, 64, 29, 61, 23, 55, 28, 60)(65, 97, 67, 99, 76, 108, 81, 113, 68, 100, 77, 109, 94, 126, 91, 123, 80, 112, 90, 122, 96, 128, 88, 120, 71, 103, 79, 111, 87, 119, 70, 102)(66, 98, 72, 104, 89, 121, 86, 118, 73, 105, 78, 110, 95, 127, 85, 117, 84, 116, 75, 107, 93, 125, 83, 115, 69, 101, 82, 114, 92, 124, 74, 106)
	L = (1, 68)(2, 73)(3, 77)(4, 80)(5, 66)(6, 81)(7, 65)(8, 78)(9, 84)(10, 86)(11, 82)(12, 94)(13, 90)(14, 75)(15, 67)(16, 71)(17, 91)(18, 72)(19, 74)(20, 69)(21, 83)(22, 85)(23, 76)(24, 70)(25, 95)(26, 79)(27, 88)(28, 89)(29, 92)(30, 96)(31, 93)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.167
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.171 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^4, Y3^-4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^-4, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 15, 47, 25, 57, 18, 50, 5, 37)(3, 35, 6, 38, 10, 42, 23, 55, 28, 60, 32, 64, 30, 62, 13, 45)(4, 36, 9, 41, 22, 54, 19, 51, 7, 39, 11, 43, 24, 56, 16, 48)(12, 44, 20, 52, 27, 59, 31, 63, 14, 46, 17, 49, 26, 58, 29, 61)(65, 97, 67, 99, 69, 101, 77, 109, 82, 114, 94, 126, 89, 121, 96, 128, 79, 111, 92, 124, 85, 117, 87, 119, 72, 104, 74, 106, 66, 98, 70, 102)(68, 100, 78, 110, 80, 112, 95, 127, 88, 120, 91, 123, 75, 107, 84, 116, 71, 103, 76, 108, 83, 115, 93, 125, 86, 118, 90, 122, 73, 105, 81, 113)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 80)(6, 84)(7, 65)(8, 86)(9, 89)(10, 91)(11, 66)(12, 92)(13, 93)(14, 67)(15, 71)(16, 85)(17, 70)(18, 88)(19, 69)(20, 96)(21, 83)(22, 82)(23, 95)(24, 72)(25, 75)(26, 74)(27, 94)(28, 78)(29, 87)(30, 90)(31, 77)(32, 81)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.176
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.172 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-2, Y3^4, Y3^4, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (Y3^-1, Y1^-1), (R * Y1^-1)^2, Y3^2 * Y1^4, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 14, 46, 27, 59, 17, 49, 5, 37)(3, 35, 9, 41, 22, 54, 29, 61, 28, 60, 31, 63, 18, 50, 6, 38)(4, 36, 10, 42, 23, 55, 19, 51, 7, 39, 11, 43, 24, 56, 15, 47)(12, 44, 25, 57, 30, 62, 16, 48, 13, 45, 26, 58, 32, 64, 20, 52)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 86, 118, 85, 117, 93, 125, 78, 110, 92, 124, 91, 123, 95, 127, 81, 113, 82, 114, 69, 101, 70, 102)(68, 100, 77, 109, 74, 106, 90, 122, 87, 119, 96, 128, 83, 115, 84, 116, 71, 103, 76, 108, 75, 107, 89, 121, 88, 120, 94, 126, 79, 111, 80, 112)
	L = (1, 68)(2, 74)(3, 76)(4, 78)(5, 79)(6, 84)(7, 65)(8, 87)(9, 89)(10, 91)(11, 66)(12, 92)(13, 67)(14, 71)(15, 85)(16, 70)(17, 88)(18, 96)(19, 69)(20, 93)(21, 83)(22, 94)(23, 81)(24, 72)(25, 95)(26, 73)(27, 75)(28, 77)(29, 80)(30, 82)(31, 90)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.175
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.173 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), Y3 * Y2 * Y3 * Y2^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y3^4, (R * Y3)^2, Y2^2 * Y1^3, Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y3 * Y1 * Y3 * Y2^-2, Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, Y2 * Y1^-1 * R * Y2^-1 * R, Y2^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 24, 56, 17, 49, 13, 45, 20, 52, 5, 37)(3, 35, 9, 41, 21, 53, 6, 38, 11, 43, 26, 58, 30, 62, 15, 47)(4, 36, 10, 42, 25, 57, 22, 54, 7, 39, 12, 44, 27, 59, 18, 50)(14, 46, 28, 60, 32, 64, 23, 55, 16, 48, 29, 61, 31, 63, 19, 51)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 85, 117, 69, 101, 79, 111, 81, 113, 75, 107, 66, 98, 73, 105, 84, 116, 94, 126, 88, 120, 70, 102)(68, 100, 80, 112, 76, 108, 92, 124, 89, 121, 95, 127, 82, 114, 87, 119, 71, 103, 78, 110, 74, 106, 93, 125, 91, 123, 96, 128, 86, 118, 83, 115)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 87)(7, 65)(8, 89)(9, 92)(10, 77)(11, 80)(12, 66)(13, 76)(14, 75)(15, 83)(16, 67)(17, 71)(18, 88)(19, 70)(20, 91)(21, 96)(22, 69)(23, 79)(24, 86)(25, 84)(26, 93)(27, 72)(28, 90)(29, 73)(30, 95)(31, 85)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.178
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.174 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2^-1), Y3^4, (R * Y3)^2, (Y1^-1, Y3^-1), Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, Y1^3 * Y2^-2, Y3^-1 * Y2^2 * Y1 * Y3^-1, Y3^2 * Y1 * Y2^2, (R * Y2 * Y3^-1)^2, Y2^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 13, 45, 17, 49, 24, 56, 20, 52, 5, 37)(3, 35, 9, 41, 25, 57, 30, 62, 21, 53, 6, 38, 11, 43, 15, 47)(4, 36, 10, 42, 26, 58, 22, 54, 7, 39, 12, 44, 27, 59, 18, 50)(14, 46, 19, 51, 28, 60, 32, 64, 16, 48, 23, 55, 29, 61, 31, 63)(65, 97, 67, 99, 77, 109, 94, 126, 84, 116, 75, 107, 66, 98, 73, 105, 81, 113, 85, 117, 69, 101, 79, 111, 72, 104, 89, 121, 88, 120, 70, 102)(68, 100, 80, 112, 86, 118, 95, 127, 91, 123, 92, 124, 74, 106, 87, 119, 71, 103, 78, 110, 82, 114, 96, 128, 90, 122, 93, 125, 76, 108, 83, 115)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 87)(7, 65)(8, 90)(9, 83)(10, 88)(11, 93)(12, 66)(13, 86)(14, 85)(15, 95)(16, 67)(17, 71)(18, 77)(19, 70)(20, 91)(21, 80)(22, 69)(23, 73)(24, 76)(25, 92)(26, 84)(27, 72)(28, 75)(29, 89)(30, 96)(31, 94)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.177
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.175 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2 * Y3 * Y2, (Y3, Y1^-1), Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3 * Y2^-2 * Y1, (R * Y3)^2, Y3^4, Y2 * Y1^-1 * Y3^-1 * Y2, (R * Y1)^2, Y3^2 * Y1^-4, Y2^3 * Y1^2 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2 * Y3, Y2 * Y1 * Y3^-1 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 16, 48, 31, 63, 19, 51, 5, 37)(3, 35, 13, 45, 24, 56, 18, 50, 29, 61, 9, 41, 28, 60, 14, 46)(4, 36, 10, 42, 25, 57, 21, 53, 7, 39, 12, 44, 27, 59, 17, 49)(6, 38, 15, 47, 26, 58, 20, 52, 32, 64, 11, 43, 30, 62, 22, 54)(65, 97, 67, 99, 74, 106, 94, 126, 83, 115, 92, 124, 81, 113, 96, 128, 80, 112, 93, 125, 76, 108, 90, 122, 72, 104, 88, 120, 85, 117, 70, 102)(66, 98, 73, 105, 89, 121, 84, 116, 69, 101, 82, 114, 68, 100, 79, 111, 95, 127, 77, 109, 91, 123, 86, 118, 87, 119, 78, 110, 71, 103, 75, 107)
	L = (1, 68)(2, 74)(3, 75)(4, 80)(5, 81)(6, 78)(7, 65)(8, 89)(9, 90)(10, 95)(11, 93)(12, 66)(13, 94)(14, 96)(15, 67)(16, 71)(17, 87)(18, 70)(19, 91)(20, 88)(21, 69)(22, 92)(23, 85)(24, 86)(25, 83)(26, 77)(27, 72)(28, 84)(29, 79)(30, 73)(31, 76)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.172
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.176 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2 * Y3^-1, Y1 * Y3 * Y2^2, Y3^4, (R * Y1)^2, Y1^-1 * Y3^-1 * Y2^-2, (Y3, Y1^-1), Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2^2 * Y1^-2, R * Y2^-1 * Y3^-2 * R * Y2^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 18, 50, 31, 63, 21, 53, 5, 37)(3, 35, 13, 45, 24, 56, 20, 52, 30, 62, 9, 41, 28, 60, 16, 48)(4, 36, 10, 42, 25, 57, 14, 46, 7, 39, 12, 44, 27, 59, 19, 51)(6, 38, 22, 54, 26, 58, 17, 49, 29, 61, 11, 43, 32, 64, 15, 47)(65, 97, 67, 99, 78, 110, 90, 122, 72, 104, 88, 120, 76, 108, 93, 125, 82, 114, 94, 126, 83, 115, 96, 128, 85, 117, 92, 124, 74, 106, 70, 102)(66, 98, 73, 105, 71, 103, 79, 111, 87, 119, 80, 112, 91, 123, 86, 118, 95, 127, 77, 109, 68, 100, 81, 113, 69, 101, 84, 116, 89, 121, 75, 107)
	L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 83)(6, 73)(7, 65)(8, 89)(9, 93)(10, 95)(11, 88)(12, 66)(13, 70)(14, 69)(15, 94)(16, 96)(17, 67)(18, 71)(19, 87)(20, 90)(21, 91)(22, 92)(23, 78)(24, 86)(25, 85)(26, 80)(27, 72)(28, 75)(29, 77)(30, 81)(31, 76)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.171
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.177 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^4, Y2^-1 * Y1^-1 * Y3 * Y2^-1, (Y3, Y1), Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y3^2 * Y1^-4, Y3^-1 * Y2^-2 * Y3^-2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y2 * Y1^-2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y2^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 18, 50, 31, 63, 20, 52, 5, 37)(3, 35, 13, 45, 24, 56, 19, 51, 29, 61, 9, 41, 28, 60, 16, 48)(4, 36, 10, 42, 25, 57, 21, 53, 7, 39, 12, 44, 27, 59, 14, 46)(6, 38, 22, 54, 26, 58, 15, 47, 30, 62, 11, 43, 32, 64, 17, 49)(65, 97, 67, 99, 78, 110, 90, 122, 72, 104, 88, 120, 74, 106, 94, 126, 82, 114, 93, 125, 85, 117, 96, 128, 84, 116, 92, 124, 76, 108, 70, 102)(66, 98, 73, 105, 68, 100, 81, 113, 87, 119, 80, 112, 89, 121, 86, 118, 95, 127, 77, 109, 71, 103, 79, 111, 69, 101, 83, 115, 91, 123, 75, 107)
	L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 78)(6, 77)(7, 65)(8, 89)(9, 70)(10, 95)(11, 92)(12, 66)(13, 94)(14, 87)(15, 93)(16, 90)(17, 67)(18, 71)(19, 96)(20, 91)(21, 69)(22, 88)(23, 85)(24, 75)(25, 84)(26, 83)(27, 72)(28, 86)(29, 81)(30, 73)(31, 76)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.174
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.178 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1 * Y1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2^2, Y2 * Y3^-1 * Y2 * Y1^-1, Y3^4, (R * Y1)^2, (R * Y3)^2, Y1^-3 * Y2^-1 * Y1^-1 * Y2, Y2 * Y1 * Y2 * Y3^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y1^-1, Y2^4 * Y1^2, Y1^-3 * Y3^-2 * Y1^-1, Y1^-2 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 23, 55, 16, 48, 31, 63, 19, 51, 5, 37)(3, 35, 13, 45, 24, 56, 18, 50, 30, 62, 9, 41, 28, 60, 15, 47)(4, 36, 10, 42, 25, 57, 21, 53, 7, 39, 12, 44, 27, 59, 17, 49)(6, 38, 14, 46, 26, 58, 20, 52, 32, 64, 11, 43, 29, 61, 22, 54)(65, 97, 67, 99, 76, 108, 93, 125, 83, 115, 92, 124, 85, 117, 96, 128, 80, 112, 94, 126, 74, 106, 90, 122, 72, 104, 88, 120, 81, 113, 70, 102)(66, 98, 73, 105, 91, 123, 84, 116, 69, 101, 82, 114, 71, 103, 78, 110, 95, 127, 77, 109, 89, 121, 86, 118, 87, 119, 79, 111, 68, 100, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 80)(5, 81)(6, 82)(7, 65)(8, 89)(9, 93)(10, 95)(11, 67)(12, 66)(13, 90)(14, 94)(15, 70)(16, 71)(17, 87)(18, 96)(19, 91)(20, 92)(21, 69)(22, 88)(23, 85)(24, 84)(25, 83)(26, 73)(27, 72)(28, 86)(29, 77)(30, 75)(31, 76)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.173
Graph:: bipartite
	v = 6 e = 64 f = 6
	degree seq :: [ 16^4, 32^2 ]

E27.179 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3, (Y3 * Y1^-1)^2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3^2 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y1^-2 * Y3 * Y1^2, Y1^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^2 * Y2 * Y1^2 * Y2^3, Y2^3 * Y3^-1 * Y1^-2 * Y3^-2, Y2 * Y1^-2 * Y2 * Y1^-4, (Y3^-3 * Y2)^4, (Y3 * Y2^-1)^8, Y2^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 6, 38, 16, 48, 28, 60, 25, 57, 10, 42, 19, 51, 30, 62, 23, 55, 13, 45, 22, 54, 32, 64, 26, 58, 15, 47, 5, 37)(3, 35, 9, 41, 17, 49, 8, 40, 21, 53, 29, 61, 24, 56, 14, 46, 20, 52, 7, 39, 4, 36, 12, 44, 18, 50, 31, 63, 27, 59, 11, 43)(65, 97, 67, 99, 74, 106, 88, 120, 96, 128, 82, 114, 70, 102, 81, 113, 94, 126, 84, 116, 79, 111, 91, 123, 92, 124, 85, 117, 77, 109, 68, 100)(66, 98, 71, 103, 83, 115, 75, 107, 90, 122, 93, 125, 80, 112, 76, 108, 87, 119, 73, 105, 69, 101, 78, 110, 89, 121, 95, 127, 86, 118, 72, 104)
	L = (1, 68)(2, 72)(3, 65)(4, 77)(5, 73)(6, 82)(7, 66)(8, 86)(9, 87)(10, 67)(11, 83)(12, 80)(13, 85)(14, 69)(15, 84)(16, 93)(17, 70)(18, 96)(19, 71)(20, 94)(21, 92)(22, 95)(23, 76)(24, 74)(25, 78)(26, 75)(27, 79)(28, 91)(29, 90)(30, 81)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.152
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.180 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y1^-2 * Y2^-2, Y3 * Y2^-1 * Y1^-2, R * Y2 * R * Y3^-1, Y1^-2 * Y2^-2, (R * Y1)^2, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-2 * Y2^2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y1 * Y2^11, Y1^11 * Y3^-1 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^8, (Y2^-2 * Y1^2)^4 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 23, 55, 31, 63, 19, 51, 29, 61, 20, 52, 30, 62, 24, 56, 32, 64, 22, 54, 10, 42, 5, 37)(3, 35, 9, 41, 4, 36, 12, 44, 15, 47, 28, 60, 25, 57, 13, 45, 17, 49, 7, 39, 16, 48, 8, 40, 18, 50, 27, 59, 21, 53, 11, 43)(65, 97, 67, 99, 74, 106, 85, 117, 96, 128, 82, 114, 94, 126, 80, 112, 93, 125, 81, 113, 95, 127, 89, 121, 90, 122, 79, 111, 70, 102, 68, 100)(66, 98, 71, 103, 69, 101, 77, 109, 86, 118, 92, 124, 88, 120, 76, 108, 84, 116, 73, 105, 83, 115, 75, 107, 87, 119, 91, 123, 78, 110, 72, 104)
	L = (1, 68)(2, 72)(3, 65)(4, 70)(5, 71)(6, 79)(7, 66)(8, 78)(9, 84)(10, 67)(11, 83)(12, 88)(13, 69)(14, 91)(15, 90)(16, 94)(17, 93)(18, 96)(19, 73)(20, 76)(21, 74)(22, 77)(23, 75)(24, 92)(25, 95)(26, 89)(27, 87)(28, 86)(29, 80)(30, 82)(31, 81)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.153
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.181 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y1^-1)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2^2 * Y3^2, Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y2 * Y1^-1, Y1^-2 * Y2^-1 * Y3, (R * Y3)^2, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, Y3^2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2, Y1^2 * Y3^2 * Y1^4, Y3^-6 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 29, 61, 26, 58, 13, 45, 22, 54, 14, 46, 23, 55, 17, 49, 24, 56, 32, 64, 28, 60, 16, 48, 5, 37)(3, 35, 12, 44, 4, 36, 11, 43, 20, 52, 31, 63, 25, 57, 18, 50, 7, 39, 9, 41, 6, 38, 10, 42, 21, 53, 30, 62, 27, 59, 15, 47)(65, 97, 67, 99, 77, 109, 89, 121, 96, 128, 85, 117, 72, 104, 68, 100, 78, 110, 71, 103, 80, 112, 91, 123, 93, 125, 84, 116, 81, 113, 70, 102)(66, 98, 73, 105, 86, 118, 79, 111, 92, 124, 95, 127, 83, 115, 74, 106, 87, 119, 76, 108, 69, 101, 82, 114, 90, 122, 94, 126, 88, 120, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 73)(6, 72)(7, 65)(8, 84)(9, 87)(10, 88)(11, 83)(12, 66)(13, 71)(14, 70)(15, 69)(16, 67)(17, 85)(18, 86)(19, 94)(20, 96)(21, 93)(22, 76)(23, 75)(24, 95)(25, 80)(26, 79)(27, 77)(28, 82)(29, 89)(30, 92)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.154
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.182 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 16, 16})
Quotient :: dipole
Aut^+ = C16 : C2 (small group id <32, 17>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y1^-2 * Y2^-1, Y1 * Y2 * Y1 * Y3^-1, (R * Y2)^2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3^2 * Y1^-1, (Y2^-1, Y3), (R * Y3)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2, Y1 * Y2^-1 * Y1^2 * Y2^-1 * Y1 * Y3 * Y2^-1, Y1^-3 * Y3^-1 * Y2 * Y1^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 29, 61, 28, 60, 16, 48, 23, 55, 14, 46, 22, 54, 17, 49, 24, 56, 32, 64, 26, 58, 13, 45, 5, 37)(3, 35, 12, 44, 6, 38, 10, 42, 21, 53, 30, 62, 27, 59, 18, 50, 7, 39, 9, 41, 4, 36, 11, 43, 20, 52, 31, 63, 25, 57, 15, 47)(65, 97, 67, 99, 77, 109, 89, 121, 96, 128, 84, 116, 81, 113, 68, 100, 78, 110, 71, 103, 80, 112, 91, 123, 93, 125, 85, 117, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 82, 114, 90, 122, 94, 126, 88, 120, 74, 106, 86, 118, 76, 108, 87, 119, 79, 111, 92, 124, 95, 127, 83, 115, 75, 107)
	L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 81)(7, 65)(8, 84)(9, 86)(10, 83)(11, 88)(12, 66)(13, 71)(14, 70)(15, 69)(16, 67)(17, 85)(18, 87)(19, 94)(20, 93)(21, 96)(22, 75)(23, 73)(24, 95)(25, 80)(26, 79)(27, 77)(28, 82)(29, 89)(30, 92)(31, 90)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.151
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.183 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2, (Y2^-1, Y1^-1), Y1^4, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1), (R * Y3)^2, Y2^-4 * Y1, Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 14, 46)(4, 36, 10, 42, 22, 54, 16, 48)(6, 38, 11, 43, 23, 55, 18, 50)(7, 39, 12, 44, 24, 56, 19, 51)(13, 45, 25, 57, 30, 62, 20, 52)(15, 47, 26, 58, 31, 63, 28, 60)(17, 49, 27, 59, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 75, 107, 66, 98, 73, 105, 89, 121, 87, 119, 72, 104, 85, 117, 94, 126, 82, 114, 69, 101, 78, 110, 84, 116, 70, 102)(68, 100, 71, 103, 79, 111, 91, 123, 74, 106, 76, 108, 90, 122, 96, 128, 86, 118, 88, 120, 95, 127, 93, 125, 80, 112, 83, 115, 92, 124, 81, 113)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 80)(6, 81)(7, 65)(8, 86)(9, 76)(10, 75)(11, 91)(12, 66)(13, 79)(14, 83)(15, 67)(16, 82)(17, 84)(18, 93)(19, 69)(20, 92)(21, 88)(22, 87)(23, 96)(24, 72)(25, 90)(26, 73)(27, 77)(28, 78)(29, 94)(30, 95)(31, 85)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.225
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.184 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2, (Y2, Y1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y1^4, (R * Y2)^2, Y2^-4 * Y1^-1, Y1 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 14, 46)(4, 36, 10, 42, 22, 54, 16, 48)(6, 38, 11, 43, 23, 55, 18, 50)(7, 39, 12, 44, 24, 56, 19, 51)(13, 45, 20, 52, 27, 59, 28, 60)(15, 47, 25, 57, 31, 63, 30, 62)(17, 49, 26, 58, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 82, 114, 69, 101, 78, 110, 92, 124, 87, 119, 72, 104, 85, 117, 91, 123, 75, 107, 66, 98, 73, 105, 84, 116, 70, 102)(68, 100, 71, 103, 79, 111, 93, 125, 80, 112, 83, 115, 94, 126, 96, 128, 86, 118, 88, 120, 95, 127, 90, 122, 74, 106, 76, 108, 89, 121, 81, 113)
	L = (1, 68)(2, 74)(3, 71)(4, 70)(5, 80)(6, 81)(7, 65)(8, 86)(9, 76)(10, 75)(11, 90)(12, 66)(13, 79)(14, 83)(15, 67)(16, 82)(17, 84)(18, 93)(19, 69)(20, 89)(21, 88)(22, 87)(23, 96)(24, 72)(25, 73)(26, 91)(27, 95)(28, 94)(29, 77)(30, 78)(31, 85)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.221
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.185 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2, Y1^4, (R * Y1)^2, (R * Y2)^2, (Y1, Y2^-1), (Y1, Y3), (R * Y3)^2, Y1^-1 * Y2^4, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 15, 47)(4, 36, 10, 42, 22, 54, 16, 48)(6, 38, 11, 43, 23, 55, 17, 49)(7, 39, 12, 44, 24, 56, 18, 50)(13, 45, 25, 57, 29, 61, 19, 51)(14, 46, 26, 58, 31, 63, 28, 60)(20, 52, 27, 59, 32, 64, 30, 62)(65, 97, 67, 99, 77, 109, 75, 107, 66, 98, 73, 105, 89, 121, 87, 119, 72, 104, 85, 117, 93, 125, 81, 113, 69, 101, 79, 111, 83, 115, 70, 102)(68, 100, 78, 110, 91, 123, 76, 108, 74, 106, 90, 122, 96, 128, 88, 120, 86, 118, 95, 127, 94, 126, 82, 114, 80, 112, 92, 124, 84, 116, 71, 103)
	L = (1, 68)(2, 74)(3, 78)(4, 67)(5, 80)(6, 71)(7, 65)(8, 86)(9, 90)(10, 73)(11, 76)(12, 66)(13, 91)(14, 77)(15, 92)(16, 79)(17, 82)(18, 69)(19, 84)(20, 70)(21, 95)(22, 85)(23, 88)(24, 72)(25, 96)(26, 89)(27, 75)(28, 83)(29, 94)(30, 81)(31, 93)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.223
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.186 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2, (R * Y2)^2, (Y1, Y3), (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^4, Y2^-4 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 15, 47)(4, 36, 10, 42, 22, 54, 16, 48)(6, 38, 11, 43, 23, 55, 17, 49)(7, 39, 12, 44, 24, 56, 18, 50)(13, 45, 19, 51, 26, 58, 29, 61)(14, 46, 25, 57, 31, 63, 30, 62)(20, 52, 27, 59, 32, 64, 28, 60)(65, 97, 67, 99, 77, 109, 81, 113, 69, 101, 79, 111, 93, 125, 87, 119, 72, 104, 85, 117, 90, 122, 75, 107, 66, 98, 73, 105, 83, 115, 70, 102)(68, 100, 78, 110, 92, 124, 82, 114, 80, 112, 94, 126, 96, 128, 88, 120, 86, 118, 95, 127, 91, 123, 76, 108, 74, 106, 89, 121, 84, 116, 71, 103)
	L = (1, 68)(2, 74)(3, 78)(4, 67)(5, 80)(6, 71)(7, 65)(8, 86)(9, 89)(10, 73)(11, 76)(12, 66)(13, 92)(14, 77)(15, 94)(16, 79)(17, 82)(18, 69)(19, 84)(20, 70)(21, 95)(22, 85)(23, 88)(24, 72)(25, 83)(26, 91)(27, 75)(28, 81)(29, 96)(30, 93)(31, 90)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.226
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.187 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2 * Y3 * Y1^-1, Y2 * Y3^2 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2)^2, (Y2^-1, Y3), (Y1, Y3^-1), Y1^-1 * Y2^4, (Y1^-1 * Y3^-1)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 14, 46)(4, 36, 10, 42, 22, 54, 16, 48)(6, 38, 11, 43, 23, 55, 18, 50)(7, 39, 12, 44, 24, 56, 19, 51)(13, 45, 25, 57, 30, 62, 20, 52)(15, 47, 26, 58, 31, 63, 28, 60)(17, 49, 27, 59, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 75, 107, 66, 98, 73, 105, 89, 121, 87, 119, 72, 104, 85, 117, 94, 126, 82, 114, 69, 101, 78, 110, 84, 116, 70, 102)(68, 100, 76, 108, 90, 122, 91, 123, 74, 106, 88, 120, 95, 127, 96, 128, 86, 118, 83, 115, 92, 124, 93, 125, 80, 112, 71, 103, 79, 111, 81, 113)
	L = (1, 68)(2, 74)(3, 76)(4, 75)(5, 80)(6, 81)(7, 65)(8, 86)(9, 88)(10, 87)(11, 91)(12, 66)(13, 90)(14, 71)(15, 67)(16, 70)(17, 77)(18, 93)(19, 69)(20, 79)(21, 83)(22, 82)(23, 96)(24, 72)(25, 95)(26, 73)(27, 89)(28, 78)(29, 84)(30, 92)(31, 85)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.224
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.188 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-1 * Y2^-1, (Y3, Y1^-1), Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y2^-1, Y3), (Y2, Y1^-1), (R * Y2)^2, Y1^4, (R * Y1)^2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2^12 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 21, 53, 15, 47)(4, 36, 10, 42, 22, 54, 18, 50)(6, 38, 11, 43, 23, 55, 17, 49)(7, 39, 12, 44, 24, 56, 14, 46)(13, 45, 20, 52, 27, 59, 29, 61)(16, 48, 25, 57, 31, 63, 28, 60)(19, 51, 26, 58, 32, 64, 30, 62)(65, 97, 67, 99, 77, 109, 81, 113, 69, 101, 79, 111, 93, 125, 87, 119, 72, 104, 85, 117, 91, 123, 75, 107, 66, 98, 73, 105, 84, 116, 70, 102)(68, 100, 78, 110, 92, 124, 94, 126, 82, 114, 88, 120, 95, 127, 96, 128, 86, 118, 76, 108, 89, 121, 90, 122, 74, 106, 71, 103, 80, 112, 83, 115)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 86)(9, 71)(10, 70)(11, 90)(12, 66)(13, 92)(14, 69)(15, 88)(16, 67)(17, 94)(18, 87)(19, 77)(20, 80)(21, 76)(22, 75)(23, 96)(24, 72)(25, 73)(26, 84)(27, 89)(28, 79)(29, 95)(30, 93)(31, 85)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.222
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.189 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^2, (Y1, Y2), Y3^-3 * Y1, (Y3, Y1), (R * Y1)^2, (R * Y2)^2, (Y1, Y2^-1), (R * Y3)^2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y1^-5 * Y3^-1, (Y1^3 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 19, 51, 7, 39, 12, 44, 24, 56, 31, 63, 28, 60, 15, 47, 4, 36, 10, 42, 22, 54, 17, 49, 5, 37)(3, 35, 9, 41, 21, 53, 30, 62, 27, 59, 14, 46, 16, 48, 25, 57, 32, 64, 29, 61, 18, 50, 6, 38, 11, 43, 23, 55, 26, 58, 13, 45)(65, 97, 67, 99, 71, 103, 78, 110, 79, 111, 82, 114, 69, 101, 77, 109, 83, 115, 91, 123, 92, 124, 93, 125, 81, 113, 90, 122, 84, 116, 94, 126, 95, 127, 96, 128, 86, 118, 87, 119, 72, 104, 85, 117, 88, 120, 89, 121, 74, 106, 75, 107, 66, 98, 73, 105, 76, 108, 80, 112, 68, 100, 70, 102)
	L = (1, 68)(2, 74)(3, 70)(4, 76)(5, 79)(6, 80)(7, 65)(8, 86)(9, 75)(10, 88)(11, 89)(12, 66)(13, 82)(14, 67)(15, 71)(16, 73)(17, 92)(18, 78)(19, 69)(20, 81)(21, 87)(22, 95)(23, 96)(24, 72)(25, 85)(26, 93)(27, 77)(28, 83)(29, 91)(30, 90)(31, 84)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.207
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.190 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^2, Y1^3 * Y3^-1, (R * Y3)^2, (Y2^-1, Y1), (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y1 * Y2, Y2 * Y1 * Y2 * Y1^2, Y1 * Y3^5, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^2, Y3^3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 20, 52, 15, 47, 23, 55, 30, 62, 28, 60, 19, 51, 25, 57, 18, 50, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 17, 49, 6, 38, 11, 43, 21, 53, 16, 48, 24, 56, 31, 63, 29, 61, 27, 59, 32, 64, 26, 58, 14, 46, 22, 54, 13, 45)(65, 97, 67, 99, 71, 103, 78, 110, 83, 115, 91, 123, 87, 119, 88, 120, 74, 106, 75, 107, 66, 98, 73, 105, 76, 108, 86, 118, 89, 121, 96, 128, 94, 126, 95, 127, 84, 116, 85, 117, 72, 104, 81, 113, 69, 101, 77, 109, 82, 114, 90, 122, 92, 124, 93, 125, 79, 111, 80, 112, 68, 100, 70, 102)
	L = (1, 68)(2, 74)(3, 70)(4, 79)(5, 72)(6, 80)(7, 65)(8, 84)(9, 75)(10, 87)(11, 88)(12, 66)(13, 81)(14, 67)(15, 92)(16, 93)(17, 85)(18, 69)(19, 71)(20, 94)(21, 95)(22, 73)(23, 83)(24, 91)(25, 76)(26, 77)(27, 78)(28, 82)(29, 90)(30, 89)(31, 96)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.216
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.191 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^2, Y3^-2 * Y1 * Y3^-1, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^5, Y3^-1 * Y1^3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 18, 50, 7, 39, 12, 44, 24, 56, 31, 63, 27, 59, 15, 47, 4, 36, 10, 42, 22, 54, 16, 48, 5, 37)(3, 35, 9, 41, 21, 53, 28, 60, 17, 49, 6, 38, 11, 43, 23, 55, 30, 62, 29, 61, 19, 51, 13, 45, 25, 57, 32, 64, 26, 58, 14, 46)(65, 97, 67, 99, 68, 100, 77, 109, 76, 108, 75, 107, 66, 98, 73, 105, 74, 106, 89, 121, 88, 120, 87, 119, 72, 104, 85, 117, 86, 118, 96, 128, 95, 127, 94, 126, 84, 116, 92, 124, 80, 112, 90, 122, 91, 123, 93, 125, 82, 114, 81, 113, 69, 101, 78, 110, 79, 111, 83, 115, 71, 103, 70, 102)
	L = (1, 68)(2, 74)(3, 77)(4, 76)(5, 79)(6, 67)(7, 65)(8, 86)(9, 89)(10, 88)(11, 73)(12, 66)(13, 75)(14, 83)(15, 71)(16, 91)(17, 78)(18, 69)(19, 70)(20, 80)(21, 96)(22, 95)(23, 85)(24, 72)(25, 87)(26, 93)(27, 82)(28, 90)(29, 81)(30, 92)(31, 84)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.205
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.192 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1, Y1^-3 * Y3, (Y2^-1, Y1), (Y3^-1, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-2 * Y2, Y3^5 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 21, 53, 15, 47, 23, 55, 31, 63, 27, 59, 19, 51, 25, 57, 17, 49, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 20, 52, 13, 45, 22, 54, 30, 62, 26, 58, 29, 61, 32, 64, 28, 60, 18, 50, 24, 56, 16, 48, 6, 38, 11, 43, 14, 46)(65, 97, 67, 99, 68, 100, 77, 109, 79, 111, 90, 122, 91, 123, 92, 124, 81, 113, 80, 112, 69, 101, 78, 110, 72, 104, 84, 116, 85, 117, 94, 126, 95, 127, 96, 128, 89, 121, 88, 120, 76, 108, 75, 107, 66, 98, 73, 105, 74, 106, 86, 118, 87, 119, 93, 125, 83, 115, 82, 114, 71, 103, 70, 102)
	L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 72)(6, 67)(7, 65)(8, 85)(9, 86)(10, 87)(11, 73)(12, 66)(13, 90)(14, 84)(15, 91)(16, 78)(17, 69)(18, 70)(19, 71)(20, 94)(21, 95)(22, 93)(23, 83)(24, 75)(25, 76)(26, 92)(27, 81)(28, 80)(29, 82)(30, 96)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.214
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.193 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, (Y2^-1, Y3), Y3 * Y1^-3, (Y3^-1, Y1^-1), (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-4, (Y1^-1 * Y3^3)^2, (Y2^-1 * Y3)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 9, 41, 20, 52, 15, 47, 21, 53, 30, 62, 27, 59, 19, 51, 23, 55, 17, 49, 7, 39, 11, 43, 5, 37)(3, 35, 6, 38, 10, 42, 12, 44, 16, 48, 22, 54, 24, 56, 28, 60, 31, 63, 32, 64, 26, 58, 29, 61, 25, 57, 14, 46, 18, 50, 13, 45)(65, 97, 67, 99, 69, 101, 77, 109, 75, 107, 82, 114, 71, 103, 78, 110, 81, 113, 89, 121, 87, 119, 93, 125, 83, 115, 90, 122, 91, 123, 96, 128, 94, 126, 95, 127, 85, 117, 92, 124, 79, 111, 88, 120, 84, 116, 86, 118, 73, 105, 80, 112, 68, 100, 76, 108, 72, 104, 74, 106, 66, 98, 70, 102)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 72)(6, 80)(7, 65)(8, 84)(9, 85)(10, 86)(11, 66)(12, 88)(13, 74)(14, 67)(15, 91)(16, 92)(17, 69)(18, 70)(19, 71)(20, 94)(21, 83)(22, 95)(23, 75)(24, 96)(25, 77)(26, 78)(27, 81)(28, 90)(29, 82)(30, 87)(31, 93)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.215
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.194 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1^-1), Y3^2 * Y1^-1 * Y3, (Y2, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1, Y3 * Y2^2 * Y1^-2, (Y1 * Y2^2)^2, Y1^-1 * Y3^-1 * Y1^-4 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 24, 56, 21, 53, 7, 39, 12, 44, 13, 45, 27, 59, 22, 54, 17, 49, 4, 36, 10, 42, 26, 58, 19, 51, 5, 37)(3, 35, 9, 41, 25, 57, 31, 63, 18, 50, 16, 48, 29, 61, 30, 62, 20, 52, 6, 38, 11, 43, 14, 46, 28, 60, 32, 64, 23, 55, 15, 47)(65, 97, 67, 99, 77, 109, 94, 126, 83, 115, 87, 119, 71, 103, 80, 112, 74, 106, 92, 124, 88, 120, 95, 127, 81, 113, 75, 107, 66, 98, 73, 105, 91, 123, 84, 116, 69, 101, 79, 111, 76, 108, 93, 125, 90, 122, 96, 128, 85, 117, 82, 114, 68, 100, 78, 110, 72, 104, 89, 121, 86, 118, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 76)(5, 81)(6, 82)(7, 65)(8, 90)(9, 92)(10, 77)(11, 80)(12, 66)(13, 72)(14, 93)(15, 75)(16, 67)(17, 71)(18, 79)(19, 86)(20, 95)(21, 69)(22, 85)(23, 70)(24, 83)(25, 96)(26, 91)(27, 88)(28, 94)(29, 73)(30, 89)(31, 87)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.208
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.195 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^-1, Y3^-1 * Y1^3, (Y3^-1, Y1^-1), (Y3^-1, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2, Y3^2 * Y2^-1 * Y3^-2 * Y2, Y3 * Y1 * Y3^4, (Y2^-1 * Y3)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 20, 52, 14, 46, 22, 54, 30, 62, 26, 58, 19, 51, 23, 55, 17, 49, 7, 39, 11, 43, 5, 37)(3, 35, 9, 41, 15, 47, 12, 44, 21, 53, 27, 59, 24, 56, 31, 63, 32, 64, 29, 61, 25, 57, 28, 60, 18, 50, 13, 45, 16, 48, 6, 38)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 79, 111, 68, 100, 76, 108, 74, 106, 85, 117, 84, 116, 91, 123, 78, 110, 88, 120, 86, 118, 95, 127, 94, 126, 96, 128, 90, 122, 93, 125, 83, 115, 89, 121, 87, 119, 92, 124, 81, 113, 82, 114, 71, 103, 77, 109, 75, 107, 80, 112, 69, 101, 70, 102)
	L = (1, 68)(2, 74)(3, 76)(4, 78)(5, 72)(6, 79)(7, 65)(8, 84)(9, 85)(10, 86)(11, 66)(12, 88)(13, 67)(14, 90)(15, 91)(16, 73)(17, 69)(18, 70)(19, 71)(20, 94)(21, 95)(22, 83)(23, 75)(24, 93)(25, 77)(26, 81)(27, 96)(28, 80)(29, 82)(30, 87)(31, 89)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.220
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.196 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-1 * Y3, (Y2^-1, Y1), (Y2^-1, Y3), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y3 * Y2, Y2 * Y1 * Y3^-1 * Y2 * Y1, Y1^-1 * Y3^-1 * Y1^-4, Y1^-1 * Y2 * Y1^-1 * Y2^3 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 24, 56, 21, 53, 7, 39, 12, 44, 22, 54, 28, 60, 13, 45, 17, 49, 4, 36, 10, 42, 25, 57, 19, 51, 5, 37)(3, 35, 9, 41, 18, 50, 27, 59, 32, 64, 16, 48, 20, 52, 6, 38, 11, 43, 26, 58, 30, 62, 14, 46, 23, 55, 29, 61, 31, 63, 15, 47)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 82, 114, 68, 100, 78, 110, 85, 117, 96, 128, 89, 121, 93, 125, 76, 108, 84, 116, 69, 101, 79, 111, 92, 124, 75, 107, 66, 98, 73, 105, 81, 113, 94, 126, 88, 120, 91, 123, 74, 106, 87, 119, 71, 103, 80, 112, 83, 115, 95, 127, 86, 118, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 76)(5, 81)(6, 82)(7, 65)(8, 89)(9, 87)(10, 86)(11, 91)(12, 66)(13, 85)(14, 84)(15, 94)(16, 67)(17, 71)(18, 93)(19, 77)(20, 73)(21, 69)(22, 72)(23, 70)(24, 83)(25, 92)(26, 96)(27, 95)(28, 88)(29, 75)(30, 80)(31, 90)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.211
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.197 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1, Y3^3 * Y1^-1, (Y3^-1, Y2), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y1^-4 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 18, 50, 7, 39, 11, 43, 23, 55, 30, 62, 26, 58, 14, 46, 4, 36, 10, 42, 22, 54, 16, 48, 5, 37)(3, 35, 9, 41, 21, 53, 29, 61, 19, 51, 13, 45, 25, 57, 31, 63, 32, 64, 27, 59, 15, 47, 12, 44, 24, 56, 28, 60, 17, 49, 6, 38)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 85, 117, 84, 116, 93, 125, 82, 114, 83, 115, 71, 103, 77, 109, 75, 107, 89, 121, 87, 119, 95, 127, 94, 126, 96, 128, 90, 122, 91, 123, 78, 110, 79, 111, 68, 100, 76, 108, 74, 106, 88, 120, 86, 118, 92, 124, 80, 112, 81, 113, 69, 101, 70, 102)
	L = (1, 68)(2, 74)(3, 76)(4, 75)(5, 78)(6, 79)(7, 65)(8, 86)(9, 88)(10, 87)(11, 66)(12, 89)(13, 67)(14, 71)(15, 77)(16, 90)(17, 91)(18, 69)(19, 70)(20, 80)(21, 92)(22, 94)(23, 72)(24, 95)(25, 73)(26, 82)(27, 83)(28, 96)(29, 81)(30, 84)(31, 85)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.206
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.198 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1), (Y2^-1, Y3^-1), (R * Y2)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2 * Y1 * Y2 * Y3^2, Y1^-1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3^5, Y1^-1 * Y2^4 * Y1^-1, Y1^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 25, 57, 17, 49, 21, 53, 29, 61, 13, 45, 23, 55, 31, 63, 20, 52, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 24, 56, 14, 46, 22, 54, 30, 62, 19, 51, 6, 38, 11, 43, 26, 58, 18, 50, 28, 60, 32, 64, 16, 48, 27, 59, 15, 47)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 88, 120, 95, 127, 92, 124, 74, 106, 86, 118, 71, 103, 80, 112, 81, 113, 83, 115, 69, 101, 79, 111, 93, 125, 75, 107, 66, 98, 73, 105, 87, 119, 82, 114, 68, 100, 78, 110, 84, 116, 96, 128, 89, 121, 94, 126, 76, 108, 91, 123, 85, 117, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 72)(6, 82)(7, 65)(8, 89)(9, 86)(10, 85)(11, 92)(12, 66)(13, 84)(14, 83)(15, 88)(16, 67)(17, 77)(18, 80)(19, 90)(20, 69)(21, 87)(22, 70)(23, 71)(24, 94)(25, 93)(26, 96)(27, 73)(28, 91)(29, 95)(30, 75)(31, 76)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.213
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.199 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^3 * Y1^-1, (Y3, Y1), Y1 * Y3^-3, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-4, (Y3^-1 * Y1^3)^2, (Y2^-1 * Y3)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 18, 50, 7, 39, 11, 43, 23, 55, 30, 62, 29, 61, 15, 47, 4, 36, 9, 41, 21, 53, 17, 49, 5, 37)(3, 35, 6, 38, 10, 42, 22, 54, 28, 60, 14, 46, 19, 51, 25, 57, 31, 63, 32, 64, 26, 58, 12, 44, 16, 48, 24, 56, 27, 59, 13, 45)(65, 97, 67, 99, 69, 101, 77, 109, 81, 113, 91, 123, 85, 117, 88, 120, 73, 105, 80, 112, 68, 100, 76, 108, 79, 111, 90, 122, 93, 125, 96, 128, 94, 126, 95, 127, 87, 119, 89, 121, 75, 107, 83, 115, 71, 103, 78, 110, 82, 114, 92, 124, 84, 116, 86, 118, 72, 104, 74, 106, 66, 98, 70, 102)
	L = (1, 68)(2, 73)(3, 76)(4, 75)(5, 79)(6, 80)(7, 65)(8, 85)(9, 87)(10, 88)(11, 66)(12, 83)(13, 90)(14, 67)(15, 71)(16, 89)(17, 93)(18, 69)(19, 70)(20, 81)(21, 94)(22, 91)(23, 72)(24, 95)(25, 74)(26, 78)(27, 96)(28, 77)(29, 82)(30, 84)(31, 86)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.209
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.200 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-2, (R * Y1)^2, (Y2^-1, Y3^-1), (Y3^-1, Y1), (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y1 * Y3^2, Y2 * Y3^2 * Y2 * Y3, Y3^-1 * Y1 * Y2^-4, Y1^-1 * Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 25, 57, 17, 49, 13, 45, 27, 59, 21, 53, 23, 55, 31, 63, 20, 52, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 24, 56, 14, 46, 28, 60, 32, 64, 22, 54, 30, 62, 19, 51, 6, 38, 11, 43, 26, 58, 18, 50, 16, 48, 29, 61, 15, 47)(65, 97, 67, 99, 77, 109, 94, 126, 76, 108, 93, 125, 89, 121, 96, 128, 84, 116, 82, 114, 68, 100, 78, 110, 87, 119, 75, 107, 66, 98, 73, 105, 91, 123, 83, 115, 69, 101, 79, 111, 81, 113, 86, 118, 71, 103, 80, 112, 74, 106, 92, 124, 95, 127, 90, 122, 72, 104, 88, 120, 85, 117, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 72)(6, 82)(7, 65)(8, 89)(9, 92)(10, 77)(11, 80)(12, 66)(13, 87)(14, 86)(15, 88)(16, 67)(17, 85)(18, 79)(19, 90)(20, 69)(21, 84)(22, 70)(23, 71)(24, 96)(25, 91)(26, 93)(27, 95)(28, 94)(29, 73)(30, 75)(31, 76)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.218
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.201 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^3 * Y3^-1, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, Y1^-1 * Y2 * Y3^2 * Y2, Y1 * Y3 * Y2^2 * Y1, Y1^-2 * Y3^-1 * Y2^-2, Y3^-1 * Y2 * Y3^-1 * Y2^3, Y1 * Y3^5, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 21, 53, 17, 49, 26, 58, 29, 61, 32, 64, 23, 55, 13, 45, 20, 52, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 22, 54, 14, 46, 19, 51, 6, 38, 11, 43, 24, 56, 18, 50, 27, 59, 31, 63, 28, 60, 30, 62, 16, 48, 25, 57, 15, 47)(65, 97, 67, 99, 77, 109, 92, 124, 81, 113, 75, 107, 66, 98, 73, 105, 84, 116, 94, 126, 90, 122, 88, 120, 72, 104, 86, 118, 71, 103, 80, 112, 93, 125, 82, 114, 68, 100, 78, 110, 76, 108, 89, 121, 96, 128, 91, 123, 74, 106, 83, 115, 69, 101, 79, 111, 87, 119, 95, 127, 85, 117, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 72)(6, 82)(7, 65)(8, 85)(9, 83)(10, 90)(11, 91)(12, 66)(13, 76)(14, 75)(15, 86)(16, 67)(17, 96)(18, 92)(19, 88)(20, 69)(21, 93)(22, 70)(23, 71)(24, 95)(25, 73)(26, 87)(27, 94)(28, 89)(29, 77)(30, 79)(31, 80)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.219
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.202 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2), Y3^2 * Y1^-1 * Y3, (R * Y1)^2, (Y2^-1, Y1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y2 * Y1 * Y3 * Y2 * Y1, Y3 * Y1^2 * Y2^2, Y2^-2 * Y1^3, Y2^4 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 13, 45, 21, 53, 7, 39, 12, 44, 24, 56, 28, 60, 31, 63, 17, 49, 4, 36, 10, 42, 22, 54, 19, 51, 5, 37)(3, 35, 9, 41, 23, 55, 27, 59, 30, 62, 16, 48, 25, 57, 32, 64, 18, 50, 26, 58, 29, 61, 14, 46, 20, 52, 6, 38, 11, 43, 15, 47)(65, 97, 67, 99, 77, 109, 91, 123, 76, 108, 89, 121, 95, 127, 90, 122, 74, 106, 84, 116, 69, 101, 79, 111, 72, 104, 87, 119, 71, 103, 80, 112, 92, 124, 82, 114, 68, 100, 78, 110, 83, 115, 75, 107, 66, 98, 73, 105, 85, 117, 94, 126, 88, 120, 96, 128, 81, 113, 93, 125, 86, 118, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 76)(5, 81)(6, 82)(7, 65)(8, 86)(9, 84)(10, 88)(11, 90)(12, 66)(13, 83)(14, 89)(15, 93)(16, 67)(17, 71)(18, 91)(19, 95)(20, 96)(21, 69)(22, 92)(23, 70)(24, 72)(25, 73)(26, 94)(27, 75)(28, 77)(29, 80)(30, 79)(31, 85)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.212
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.203 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-3, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y2), (R * Y1)^2, Y1^-2 * Y3^-1 * Y2^2, Y1 * Y3 * Y2^-2 * Y1, Y2 * Y1 * Y2 * Y3^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y1 * Y3^5, Y2^24 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 4, 36, 10, 42, 13, 45, 17, 49, 26, 58, 29, 61, 31, 63, 23, 55, 21, 53, 20, 52, 7, 39, 12, 44, 5, 37)(3, 35, 9, 41, 24, 56, 14, 46, 25, 57, 28, 60, 30, 62, 32, 64, 22, 54, 27, 59, 19, 51, 6, 38, 11, 43, 16, 48, 18, 50, 15, 47)(65, 97, 67, 99, 77, 109, 92, 124, 87, 119, 83, 115, 69, 101, 79, 111, 74, 106, 89, 121, 95, 127, 91, 123, 76, 108, 82, 114, 68, 100, 78, 110, 93, 125, 86, 118, 71, 103, 80, 112, 72, 104, 88, 120, 90, 122, 96, 128, 84, 116, 75, 107, 66, 98, 73, 105, 81, 113, 94, 126, 85, 117, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 72)(6, 82)(7, 65)(8, 77)(9, 89)(10, 90)(11, 79)(12, 66)(13, 93)(14, 94)(15, 88)(16, 67)(17, 95)(18, 73)(19, 80)(20, 69)(21, 76)(22, 70)(23, 71)(24, 92)(25, 96)(26, 87)(27, 75)(28, 86)(29, 85)(30, 91)(31, 84)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.217
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.204 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-3 * Y1, (Y2, Y3), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y3 * Y2^-2 * Y1, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y3, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-1, (Y3^-2 * Y1^-1)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 22, 54, 21, 53, 7, 39, 12, 44, 24, 56, 29, 61, 31, 63, 17, 49, 4, 36, 10, 42, 13, 45, 19, 51, 5, 37)(3, 35, 9, 41, 20, 52, 6, 38, 11, 43, 16, 48, 26, 58, 32, 64, 23, 55, 27, 59, 30, 62, 14, 46, 25, 57, 28, 60, 18, 50, 15, 47)(65, 97, 67, 99, 77, 109, 92, 124, 81, 113, 94, 126, 88, 120, 96, 128, 85, 117, 75, 107, 66, 98, 73, 105, 83, 115, 82, 114, 68, 100, 78, 110, 93, 125, 87, 119, 71, 103, 80, 112, 72, 104, 84, 116, 69, 101, 79, 111, 74, 106, 89, 121, 95, 127, 91, 123, 76, 108, 90, 122, 86, 118, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 76)(5, 81)(6, 82)(7, 65)(8, 77)(9, 89)(10, 88)(11, 79)(12, 66)(13, 93)(14, 90)(15, 94)(16, 67)(17, 71)(18, 91)(19, 95)(20, 92)(21, 69)(22, 83)(23, 70)(24, 72)(25, 96)(26, 73)(27, 75)(28, 87)(29, 86)(30, 80)(31, 85)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.210
Graph:: bipartite
	v = 3 e = 64 f = 9
	degree seq :: [ 32^2, 64 ]

E27.205 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y1^-1, (Y2, Y3^-1), (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^4, Y2^-1 * Y3^4, Y2^-2 * Y3^-1 * Y2^-2 * Y3, Y3^2 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 20, 52, 24, 56, 17, 49, 18, 50, 6, 38, 9, 41, 19, 51, 23, 55, 30, 62, 32, 64, 25, 57, 26, 58, 11, 43, 21, 53, 27, 59, 31, 63, 28, 60, 29, 61, 12, 44, 13, 45, 3, 35, 8, 40, 14, 46, 22, 54, 15, 47, 16, 48, 4, 36, 5, 37)(65, 97, 67, 99, 75, 107, 70, 102)(66, 98, 72, 104, 85, 117, 73, 105)(68, 100, 76, 108, 89, 121, 81, 113)(69, 101, 77, 109, 90, 122, 82, 114)(71, 103, 78, 110, 91, 123, 83, 115)(74, 106, 86, 118, 95, 127, 87, 119)(79, 111, 92, 124, 94, 126, 84, 116)(80, 112, 93, 125, 96, 128, 88, 120)
	L = (1, 68)(2, 69)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 77)(9, 82)(10, 66)(11, 89)(12, 92)(13, 93)(14, 67)(15, 78)(16, 86)(17, 84)(18, 88)(19, 70)(20, 71)(21, 90)(22, 72)(23, 73)(24, 74)(25, 94)(26, 96)(27, 75)(28, 91)(29, 95)(30, 83)(31, 85)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.191
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.206 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (Y1, Y2), (Y2, Y3), Y2^4, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-4, Y3^-1 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 15, 47, 23, 55, 14, 46, 13, 45, 3, 35, 8, 40, 12, 44, 22, 54, 28, 60, 32, 64, 27, 59, 26, 58, 11, 43, 21, 53, 25, 57, 31, 63, 30, 62, 29, 61, 19, 51, 17, 49, 6, 38, 10, 42, 16, 48, 24, 56, 20, 52, 18, 50, 7, 39, 5, 37)(65, 97, 67, 99, 75, 107, 70, 102)(66, 98, 72, 104, 85, 117, 74, 106)(68, 100, 76, 108, 89, 121, 80, 112)(69, 101, 77, 109, 90, 122, 81, 113)(71, 103, 78, 110, 91, 123, 83, 115)(73, 105, 86, 118, 95, 127, 88, 120)(79, 111, 92, 124, 94, 126, 84, 116)(82, 114, 87, 119, 96, 128, 93, 125)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 66)(6, 80)(7, 65)(8, 86)(9, 87)(10, 88)(11, 89)(12, 92)(13, 72)(14, 67)(15, 78)(16, 84)(17, 74)(18, 69)(19, 70)(20, 71)(21, 95)(22, 96)(23, 77)(24, 82)(25, 94)(26, 85)(27, 75)(28, 91)(29, 81)(30, 83)(31, 93)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.197
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.207 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3^-1), (Y3^-1, Y1^-1), Y2 * Y1 * Y3^-1 * Y1, Y3 * Y1^-2 * Y2^-1, Y1^-2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^4, Y2^-1 * Y3^4, Y2^-2 * Y1^-1 * Y2^2 * Y1, Y3 * Y2^-1 * Y1^30, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 30, 62, 32, 64, 27, 59, 15, 47, 3, 35, 9, 41, 4, 36, 10, 42, 20, 52, 26, 58, 19, 51, 25, 57, 13, 45, 23, 55, 14, 46, 24, 56, 17, 49, 18, 50, 7, 39, 12, 44, 6, 38, 11, 43, 22, 54, 31, 63, 28, 60, 29, 61, 16, 48, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 87, 119, 75, 107)(68, 100, 78, 110, 86, 118, 72, 104)(69, 101, 79, 111, 89, 121, 76, 108)(71, 103, 80, 112, 91, 123, 83, 115)(74, 106, 88, 120, 95, 127, 85, 117)(81, 113, 92, 124, 94, 126, 84, 116)(82, 114, 93, 125, 96, 128, 90, 122)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 73)(6, 72)(7, 65)(8, 84)(9, 88)(10, 82)(11, 85)(12, 66)(13, 86)(14, 92)(15, 87)(16, 67)(17, 80)(18, 69)(19, 70)(20, 71)(21, 90)(22, 94)(23, 95)(24, 93)(25, 75)(26, 76)(27, 77)(28, 91)(29, 79)(30, 83)(31, 96)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.189
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.208 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), (Y3^-1, Y1^-1), Y3 * Y1 * Y2^-1 * Y1, Y1^-1 * Y2 * Y3^-1 * Y1^-1, (Y2, Y1^-1), Y1^2 * Y2^-1 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3^-4 * Y2, (Y2 * Y3^2)^8, (Y3^-1 * Y2^-1)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 28, 60, 32, 64, 27, 59, 18, 50, 6, 38, 11, 43, 7, 39, 12, 44, 15, 47, 25, 57, 14, 46, 24, 56, 13, 45, 23, 55, 19, 51, 26, 58, 20, 52, 16, 48, 4, 36, 10, 42, 3, 35, 9, 41, 22, 54, 31, 63, 30, 62, 29, 61, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 87, 119, 75, 107)(68, 100, 78, 110, 91, 123, 81, 113)(69, 101, 74, 106, 88, 120, 82, 114)(71, 103, 72, 104, 86, 118, 83, 115)(76, 108, 85, 117, 95, 127, 90, 122)(79, 111, 92, 124, 94, 126, 84, 116)(80, 112, 89, 121, 96, 128, 93, 125)
	L = (1, 68)(2, 74)(3, 78)(4, 79)(5, 80)(6, 81)(7, 65)(8, 67)(9, 88)(10, 89)(11, 69)(12, 66)(13, 91)(14, 92)(15, 72)(16, 76)(17, 84)(18, 93)(19, 70)(20, 71)(21, 73)(22, 77)(23, 82)(24, 96)(25, 85)(26, 75)(27, 94)(28, 86)(29, 90)(30, 83)(31, 87)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.194
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.209 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y2 * Y1^2 * Y3, (Y2, Y1), (Y3^-1, Y1^-1), (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y2, Y3), (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3, Y3^-1 * Y2^-2 * Y3 * Y2^-2, Y2 * Y3^2 * Y2 * Y3^2 * Y2, Y3^-1 * Y2^-1 * Y1^30 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 30, 62, 18, 50, 4, 36, 10, 42, 6, 38, 11, 43, 22, 54, 32, 64, 17, 49, 26, 58, 19, 51, 27, 59, 13, 45, 24, 56, 16, 48, 25, 57, 20, 52, 28, 60, 29, 61, 15, 47, 3, 35, 9, 41, 7, 39, 12, 44, 23, 55, 31, 63, 14, 46, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 93, 125, 83, 115)(69, 101, 79, 111, 91, 123, 74, 106)(71, 103, 80, 112, 86, 118, 72, 104)(76, 108, 89, 121, 96, 128, 85, 117)(81, 113, 94, 126, 87, 119, 84, 116)(82, 114, 95, 127, 92, 124, 90, 122)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 70)(9, 69)(10, 90)(11, 91)(12, 66)(13, 93)(14, 94)(15, 95)(16, 67)(17, 80)(18, 96)(19, 84)(20, 71)(21, 75)(22, 77)(23, 72)(24, 79)(25, 73)(26, 89)(27, 92)(28, 76)(29, 87)(30, 86)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.199
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.210 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1^-1), Y3 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, Y2^4, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y2^-1, Y2 * Y3^-4, Y2 * Y3 * Y1 * Y2 * Y3^2 * Y1, (Y3^-1 * Y1^-2)^8, (Y3^-1 * Y1^-1)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 31, 63, 19, 51, 7, 39, 12, 44, 3, 35, 9, 41, 22, 54, 32, 64, 20, 52, 28, 60, 14, 46, 25, 57, 13, 45, 24, 56, 16, 48, 27, 59, 15, 47, 26, 58, 29, 61, 18, 50, 6, 38, 11, 43, 4, 36, 10, 42, 23, 55, 30, 62, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 72, 104, 86, 118, 80, 112)(69, 101, 76, 108, 89, 121, 82, 114)(71, 103, 78, 110, 93, 125, 81, 113)(74, 106, 85, 117, 96, 128, 91, 123)(79, 111, 87, 119, 95, 127, 84, 116)(83, 115, 92, 124, 90, 122, 94, 126)
	L = (1, 68)(2, 74)(3, 72)(4, 79)(5, 75)(6, 80)(7, 65)(8, 87)(9, 85)(10, 90)(11, 91)(12, 66)(13, 86)(14, 67)(15, 78)(16, 84)(17, 70)(18, 88)(19, 69)(20, 71)(21, 94)(22, 95)(23, 93)(24, 96)(25, 73)(26, 89)(27, 92)(28, 76)(29, 77)(30, 82)(31, 81)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.204
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.211 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3), (Y3, Y2^-1), (Y1^-1, Y2), (R * Y3)^2, Y2^4, (R * Y2)^2, (R * Y1)^2, Y3^-4 * Y2, Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2^-2 * Y1^2 * Y3^-1, Y1^-1 * Y3 * Y2^2 * Y1^-1, Y3 * Y1 * Y3^2 * Y1 * Y2, (Y3^-2 * Y2^-1)^8, Y3^2 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^2, Y1^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 25, 57, 17, 49, 28, 60, 23, 55, 15, 47, 3, 35, 9, 41, 19, 51, 29, 61, 31, 63, 22, 54, 7, 39, 12, 44, 13, 45, 18, 50, 4, 36, 10, 42, 26, 58, 32, 64, 16, 48, 21, 53, 6, 38, 11, 43, 14, 46, 27, 59, 24, 56, 30, 62, 20, 52, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 82, 114, 75, 107)(68, 100, 78, 110, 72, 104, 83, 115)(69, 101, 79, 111, 76, 108, 85, 117)(71, 103, 80, 112, 84, 116, 87, 119)(74, 106, 91, 123, 89, 121, 93, 125)(81, 113, 95, 127, 90, 122, 88, 120)(86, 118, 96, 128, 94, 126, 92, 124)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 90)(9, 91)(10, 92)(11, 93)(12, 66)(13, 72)(14, 95)(15, 75)(16, 67)(17, 80)(18, 89)(19, 88)(20, 77)(21, 73)(22, 69)(23, 70)(24, 71)(25, 96)(26, 87)(27, 86)(28, 85)(29, 94)(30, 76)(31, 84)(32, 79)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.196
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.212 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y2, Y1^-1), (Y3, Y1), (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y2^4, Y3 * Y1^2 * Y2^2, Y1^-1 * Y3^-1 * Y1^-1 * Y2^2, Y2^-2 * Y3^-1 * Y1^-2, Y3^-4 * Y2, Y1^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 25, 57, 24, 56, 30, 62, 14, 46, 21, 53, 6, 38, 11, 43, 16, 48, 27, 59, 31, 63, 18, 50, 4, 36, 10, 42, 13, 45, 22, 54, 7, 39, 12, 44, 26, 58, 32, 64, 19, 51, 15, 47, 3, 35, 9, 41, 23, 55, 29, 61, 17, 49, 28, 60, 20, 52, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 86, 118, 75, 107)(68, 100, 78, 110, 84, 116, 83, 115)(69, 101, 79, 111, 74, 106, 85, 117)(71, 103, 80, 112, 72, 104, 87, 119)(76, 108, 91, 123, 89, 121, 93, 125)(81, 113, 90, 122, 95, 127, 88, 120)(82, 114, 94, 126, 92, 124, 96, 128)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 77)(9, 85)(10, 92)(11, 79)(12, 66)(13, 84)(14, 90)(15, 94)(16, 67)(17, 80)(18, 93)(19, 88)(20, 95)(21, 96)(22, 69)(23, 70)(24, 71)(25, 86)(26, 72)(27, 73)(28, 91)(29, 75)(30, 76)(31, 87)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.202
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.213 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (Y2, Y3^-1), (Y1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, Y2^-1 * Y3^-4, Y3^-2 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1, (Y2^-1 * Y3)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 4, 36, 9, 41, 15, 47, 23, 55, 19, 51, 17, 49, 6, 38, 10, 42, 16, 48, 24, 56, 30, 62, 32, 64, 27, 59, 26, 58, 11, 43, 21, 53, 25, 57, 31, 63, 29, 61, 28, 60, 14, 46, 13, 45, 3, 35, 8, 40, 12, 44, 22, 54, 20, 52, 18, 50, 7, 39, 5, 37)(65, 97, 67, 99, 75, 107, 70, 102)(66, 98, 72, 104, 85, 117, 74, 106)(68, 100, 76, 108, 89, 121, 80, 112)(69, 101, 77, 109, 90, 122, 81, 113)(71, 103, 78, 110, 91, 123, 83, 115)(73, 105, 86, 118, 95, 127, 88, 120)(79, 111, 84, 116, 93, 125, 94, 126)(82, 114, 92, 124, 96, 128, 87, 119)
	L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 66)(6, 80)(7, 65)(8, 86)(9, 87)(10, 88)(11, 89)(12, 84)(13, 72)(14, 67)(15, 83)(16, 94)(17, 74)(18, 69)(19, 70)(20, 71)(21, 95)(22, 82)(23, 81)(24, 96)(25, 93)(26, 85)(27, 75)(28, 77)(29, 78)(30, 91)(31, 92)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.198
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.214 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2, (R * Y1)^2, (Y2, Y3^-1), (Y1^-1, Y2^-1), Y2^4, (R * Y2)^2, (R * Y3)^2, Y2 * Y3^4, Y3 * Y2 * Y1^-1 * Y3^2 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 7, 39, 10, 42, 20, 52, 24, 56, 12, 44, 13, 45, 3, 35, 8, 40, 14, 46, 22, 54, 28, 60, 32, 64, 25, 57, 26, 58, 11, 43, 21, 53, 27, 59, 31, 63, 29, 61, 30, 62, 17, 49, 18, 50, 6, 38, 9, 41, 19, 51, 23, 55, 15, 47, 16, 48, 4, 36, 5, 37)(65, 97, 67, 99, 75, 107, 70, 102)(66, 98, 72, 104, 85, 117, 73, 105)(68, 100, 76, 108, 89, 121, 81, 113)(69, 101, 77, 109, 90, 122, 82, 114)(71, 103, 78, 110, 91, 123, 83, 115)(74, 106, 86, 118, 95, 127, 87, 119)(79, 111, 84, 116, 92, 124, 93, 125)(80, 112, 88, 120, 96, 128, 94, 126)
	L = (1, 68)(2, 69)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 77)(9, 82)(10, 66)(11, 89)(12, 84)(13, 88)(14, 67)(15, 83)(16, 87)(17, 93)(18, 94)(19, 70)(20, 71)(21, 90)(22, 72)(23, 73)(24, 74)(25, 92)(26, 96)(27, 75)(28, 78)(29, 91)(30, 95)(31, 85)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.192
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.215 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2 * Y1 * Y3, (Y1^-1, Y3), Y2^-1 * Y3^-1 * Y1^-2, (R * Y3)^2, Y2^4, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^-1 * Y1 * Y3^-2 * Y1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y2^2 * Y1 * Y2 * Y1^-3, Y3^-16, Y1^24 * Y2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 30, 62, 32, 64, 27, 59, 15, 47, 3, 35, 9, 41, 7, 39, 12, 44, 17, 49, 25, 57, 19, 51, 26, 58, 13, 45, 23, 55, 16, 48, 24, 56, 20, 52, 18, 50, 4, 36, 10, 42, 6, 38, 11, 43, 22, 54, 31, 63, 29, 61, 28, 60, 14, 46, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 87, 119, 75, 107)(68, 100, 78, 110, 91, 123, 83, 115)(69, 101, 79, 111, 90, 122, 74, 106)(71, 103, 80, 112, 86, 118, 72, 104)(76, 108, 88, 120, 95, 127, 85, 117)(81, 113, 84, 116, 93, 125, 94, 126)(82, 114, 92, 124, 96, 128, 89, 121)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 70)(9, 69)(10, 89)(11, 90)(12, 66)(13, 91)(14, 84)(15, 92)(16, 67)(17, 72)(18, 76)(19, 94)(20, 71)(21, 75)(22, 77)(23, 79)(24, 73)(25, 85)(26, 96)(27, 93)(28, 88)(29, 80)(30, 86)(31, 87)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.193
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.216 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, Y2^-1 * Y1^2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y2^4, (Y3^-1, Y1^-1), Y3 * Y2 * Y3^3, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-2, (Y2 * Y3^-2)^8, (Y3 * Y2^-1)^16, (Y1^-1 * Y3^-1)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 28, 60, 32, 64, 27, 59, 18, 50, 6, 38, 11, 43, 4, 36, 10, 42, 20, 52, 26, 58, 14, 46, 24, 56, 13, 45, 23, 55, 16, 48, 25, 57, 15, 47, 19, 51, 7, 39, 12, 44, 3, 35, 9, 41, 22, 54, 31, 63, 29, 61, 30, 62, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 87, 119, 75, 107)(68, 100, 72, 104, 86, 118, 80, 112)(69, 101, 76, 108, 88, 120, 82, 114)(71, 103, 78, 110, 91, 123, 81, 113)(74, 106, 85, 117, 95, 127, 89, 121)(79, 111, 84, 116, 92, 124, 93, 125)(83, 115, 90, 122, 96, 128, 94, 126)
	L = (1, 68)(2, 74)(3, 72)(4, 79)(5, 75)(6, 80)(7, 65)(8, 84)(9, 85)(10, 83)(11, 89)(12, 66)(13, 86)(14, 67)(15, 81)(16, 93)(17, 70)(18, 87)(19, 69)(20, 71)(21, 90)(22, 92)(23, 95)(24, 73)(25, 94)(26, 76)(27, 77)(28, 78)(29, 91)(30, 82)(31, 96)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.190
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.217 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2), (Y2, Y1^-1), Y3 * Y1^-2 * Y2^-1, (R * Y2)^2, (Y3^-1, Y1^-1), Y1 * Y2 * Y3^-1 * Y1, Y1^-1 * Y3 * Y1^-1 * Y2^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, Y2 * Y3^4, Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, Y3 * Y2 * Y1 * Y3^2 * Y1 * Y2, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^2 * Y1, (Y1^-1 * Y3^-1)^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 31, 63, 18, 50, 7, 39, 12, 44, 6, 38, 11, 43, 23, 55, 32, 64, 20, 52, 28, 60, 19, 51, 27, 59, 13, 45, 24, 56, 14, 46, 25, 57, 17, 49, 26, 58, 29, 61, 15, 47, 3, 35, 9, 41, 4, 36, 10, 42, 22, 54, 30, 62, 16, 48, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 87, 119, 72, 104)(69, 101, 79, 111, 91, 123, 76, 108)(71, 103, 80, 112, 93, 125, 83, 115)(74, 106, 89, 121, 96, 128, 85, 117)(81, 113, 84, 116, 95, 127, 86, 118)(82, 114, 94, 126, 90, 122, 92, 124)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 73)(6, 72)(7, 65)(8, 86)(9, 89)(10, 90)(11, 85)(12, 66)(13, 87)(14, 84)(15, 88)(16, 67)(17, 83)(18, 69)(19, 70)(20, 71)(21, 94)(22, 93)(23, 95)(24, 96)(25, 92)(26, 91)(27, 75)(28, 76)(29, 77)(30, 79)(31, 80)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.203
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.218 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3), Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-2 * Y3^-1, Y2^4, Y3^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y3^4, Y2^2 * Y3^-1 * Y2^2 * Y3, Y1^-2 * Y2^-1 * Y3 * Y2^-1 * Y3^2, Y1^24 * Y2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 21, 53, 31, 63, 16, 48, 4, 36, 10, 42, 3, 35, 9, 41, 22, 54, 30, 62, 15, 47, 26, 58, 14, 46, 25, 57, 13, 45, 24, 56, 19, 51, 27, 59, 20, 52, 28, 60, 29, 61, 18, 50, 6, 38, 11, 43, 7, 39, 12, 44, 23, 55, 32, 64, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 88, 120, 75, 107)(68, 100, 78, 110, 93, 125, 81, 113)(69, 101, 74, 106, 89, 121, 82, 114)(71, 103, 72, 104, 86, 118, 83, 115)(76, 108, 85, 117, 94, 126, 91, 123)(79, 111, 84, 116, 87, 119, 95, 127)(80, 112, 90, 122, 92, 124, 96, 128)
	L = (1, 68)(2, 74)(3, 78)(4, 79)(5, 80)(6, 81)(7, 65)(8, 67)(9, 89)(10, 90)(11, 69)(12, 66)(13, 93)(14, 84)(15, 83)(16, 94)(17, 95)(18, 96)(19, 70)(20, 71)(21, 73)(22, 77)(23, 72)(24, 82)(25, 92)(26, 91)(27, 75)(28, 76)(29, 87)(30, 88)(31, 86)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.200
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.219 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3), (R * Y3)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, Y2^4, Y2 * Y3^4, Y3 * Y1 * Y2^2 * Y1, Y2^2 * Y3^-1 * Y1^-2, Y3 * Y1^-1 * Y3^2 * Y2^-1 * Y1^-1, Y3^2 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y1^32, (Y2^-1 * Y3)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 25, 57, 24, 56, 30, 62, 19, 51, 15, 47, 3, 35, 9, 41, 23, 55, 29, 61, 32, 64, 18, 50, 4, 36, 10, 42, 13, 45, 22, 54, 7, 39, 12, 44, 26, 58, 31, 63, 14, 46, 21, 53, 6, 38, 11, 43, 16, 48, 27, 59, 17, 49, 28, 60, 20, 52, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 86, 118, 75, 107)(68, 100, 78, 110, 84, 116, 83, 115)(69, 101, 79, 111, 74, 106, 85, 117)(71, 103, 80, 112, 72, 104, 87, 119)(76, 108, 91, 123, 89, 121, 93, 125)(81, 113, 88, 120, 96, 128, 90, 122)(82, 114, 95, 127, 92, 124, 94, 126)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 77)(9, 85)(10, 92)(11, 79)(12, 66)(13, 84)(14, 88)(15, 95)(16, 67)(17, 87)(18, 91)(19, 90)(20, 96)(21, 94)(22, 69)(23, 70)(24, 71)(25, 86)(26, 72)(27, 73)(28, 93)(29, 75)(30, 76)(31, 89)(32, 80)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.201
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.220 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3), (Y2^-1, Y3), Y2^4, (Y1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y1^2 * Y3^-1, Y2 * Y3^4, Y1 * Y2 * Y1 * Y2 * Y3^-1, Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1^32 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 25, 57, 17, 49, 28, 60, 16, 48, 21, 53, 6, 38, 11, 43, 14, 46, 27, 59, 31, 63, 22, 54, 7, 39, 12, 44, 13, 45, 18, 50, 4, 36, 10, 42, 26, 58, 32, 64, 23, 55, 15, 47, 3, 35, 9, 41, 19, 51, 29, 61, 24, 56, 30, 62, 20, 52, 5, 37)(65, 97, 67, 99, 77, 109, 70, 102)(66, 98, 73, 105, 82, 114, 75, 107)(68, 100, 78, 110, 72, 104, 83, 115)(69, 101, 79, 111, 76, 108, 85, 117)(71, 103, 80, 112, 84, 116, 87, 119)(74, 106, 91, 123, 89, 121, 93, 125)(81, 113, 88, 120, 90, 122, 95, 127)(86, 118, 92, 124, 94, 126, 96, 128)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 90)(9, 91)(10, 92)(11, 93)(12, 66)(13, 72)(14, 88)(15, 75)(16, 67)(17, 87)(18, 89)(19, 95)(20, 77)(21, 73)(22, 69)(23, 70)(24, 71)(25, 96)(26, 80)(27, 94)(28, 79)(29, 86)(30, 76)(31, 84)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 32, 64, 32, 64, 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.195
Graph:: bipartite
	v = 9 e = 64 f = 3
	degree seq :: [ 8^8, 64 ]

E27.221 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^-1 * Y2^-1, Y1^-1 * Y3 * Y2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1^2 * Y3^-1, Y2^-3 * Y1^-1, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y1), Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1^-1 * Y3^-3, (Y1^-1 * Y2^-1 * Y3^2)^8 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 30, 62, 28, 60, 19, 51, 26, 58, 14, 46, 23, 55, 13, 45, 6, 38, 11, 43, 4, 36, 10, 42, 22, 54, 31, 63, 29, 61, 18, 50, 7, 39, 12, 44, 3, 35, 9, 41, 21, 53, 16, 48, 25, 57, 15, 47, 24, 56, 32, 64, 27, 59, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 69, 101, 76, 108, 87, 119, 81, 113, 71, 103, 78, 110, 91, 123, 82, 114, 90, 122, 96, 128, 93, 125, 83, 115, 88, 120, 95, 127, 92, 124, 79, 111, 86, 118, 94, 126, 89, 121, 74, 106, 84, 116, 80, 112, 68, 100, 72, 104, 85, 117, 75, 107, 66, 98, 73, 105, 70, 102)
	L = (1, 68)(2, 74)(3, 72)(4, 79)(5, 75)(6, 80)(7, 65)(8, 86)(9, 84)(10, 88)(11, 89)(12, 66)(13, 85)(14, 67)(15, 90)(16, 92)(17, 70)(18, 69)(19, 71)(20, 95)(21, 94)(22, 96)(23, 73)(24, 78)(25, 83)(26, 76)(27, 77)(28, 82)(29, 81)(30, 93)(31, 91)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.184
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.222 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), (R * Y1)^2, (Y1, Y2^-1), Y2^2 * Y3 * Y1, Y2 * Y1 * Y2 * Y3, (R * Y3)^2, Y2^2 * Y1 * Y3, (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^3 * Y1^-1, Y2 * Y3^-2 * Y1^-3, (Y3 * Y2^-1)^4, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 22, 54, 18, 50, 4, 36, 10, 42, 24, 56, 16, 48, 27, 59, 17, 49, 28, 60, 15, 47, 3, 35, 9, 41, 23, 55, 32, 64, 31, 63, 14, 46, 6, 38, 11, 43, 25, 57, 21, 53, 30, 62, 19, 51, 29, 61, 13, 45, 7, 39, 12, 44, 26, 58, 20, 52, 5, 37)(65, 97, 67, 99, 77, 109, 88, 120, 75, 107, 66, 98, 73, 105, 71, 103, 80, 112, 89, 121, 72, 104, 87, 119, 76, 108, 91, 123, 85, 117, 86, 118, 96, 128, 90, 122, 81, 113, 94, 126, 82, 114, 95, 127, 84, 116, 92, 124, 83, 115, 68, 100, 78, 110, 69, 101, 79, 111, 93, 125, 74, 106, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 88)(9, 70)(10, 92)(11, 93)(12, 66)(13, 69)(14, 94)(15, 95)(16, 67)(17, 87)(18, 91)(19, 90)(20, 86)(21, 71)(22, 80)(23, 75)(24, 79)(25, 77)(26, 72)(27, 73)(28, 96)(29, 84)(30, 76)(31, 85)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.188
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.223 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3, (Y1, Y2^-1), Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y2^-6 * Y3^-1 * Y2^-1, Y1^-3 * Y2^4 * Y1^-1, Y2 * Y1^-2 * Y3^-1 * Y2^3 * Y1^-1, (Y3^-1 * Y1^-1)^16 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 25, 57, 32, 64, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 27, 59, 24, 56, 13, 45, 18, 50, 30, 62, 20, 52, 9, 41, 17, 49, 29, 61, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 28, 60, 19, 51, 31, 63, 22, 54, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 83, 115, 90, 122, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 92, 124, 78, 110, 91, 123, 87, 119, 75, 107, 85, 117, 94, 126, 80, 112, 70, 102, 79, 111, 93, 125, 86, 118, 96, 128, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 95, 127, 89, 121, 77, 109, 69, 101)
	L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 78)(7, 79)(8, 80)(9, 81)(10, 67)(11, 68)(12, 69)(13, 82)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 73)(21, 74)(22, 75)(23, 76)(24, 77)(25, 96)(26, 89)(27, 88)(28, 83)(29, 87)(30, 84)(31, 86)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.185
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.224 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3^-1), (Y2, Y3), (R * Y2)^2, (R * Y1)^2, Y1^-3 * Y3^-1, Y2^3 * Y1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-2, Y2^-1 * Y3 * Y1^-1 * Y2 * Y3^-1 * Y1, Y2^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1, Y1 * Y3^3 * Y2^-1 * Y3, Y3 * Y2 * Y3^2 * Y2 * Y1^-1, (Y2^-1 * Y3^-2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 7, 39, 12, 44, 24, 56, 21, 53, 30, 62, 19, 51, 28, 60, 13, 45, 6, 38, 11, 43, 23, 55, 20, 52, 29, 61, 32, 64, 31, 63, 14, 46, 25, 57, 15, 47, 3, 35, 9, 41, 22, 54, 16, 48, 26, 58, 17, 49, 27, 59, 18, 50, 4, 36, 10, 42, 5, 37)(65, 97, 67, 99, 77, 109, 69, 101, 79, 111, 92, 124, 74, 106, 89, 121, 83, 115, 68, 100, 78, 110, 94, 126, 82, 114, 95, 127, 85, 117, 91, 123, 96, 128, 88, 120, 81, 113, 93, 125, 76, 108, 90, 122, 84, 116, 71, 103, 80, 112, 87, 119, 72, 104, 86, 118, 75, 107, 66, 98, 73, 105, 70, 102)
	L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 69)(9, 89)(10, 91)(11, 92)(12, 66)(13, 94)(14, 93)(15, 95)(16, 67)(17, 86)(18, 90)(19, 88)(20, 70)(21, 71)(22, 79)(23, 77)(24, 72)(25, 96)(26, 73)(27, 80)(28, 85)(29, 75)(30, 76)(31, 84)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.187
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.225 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2 * Y2, (Y2, Y1^-1), Y1 * Y3^-1 * Y1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y3^-3, (R * Y2)^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, Y2^3 * Y1^-1 * Y2^2, Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y2 * Y1 * Y2 * Y1^5 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 20, 52, 30, 62, 27, 59, 19, 51, 26, 58, 16, 48, 25, 57, 15, 47, 7, 39, 12, 44, 3, 35, 9, 41, 21, 53, 31, 63, 29, 61, 18, 50, 6, 38, 11, 43, 4, 36, 10, 42, 22, 54, 14, 46, 24, 56, 13, 45, 23, 55, 32, 64, 28, 60, 17, 49, 5, 37)(65, 97, 67, 99, 77, 109, 90, 122, 75, 107, 66, 98, 73, 105, 87, 119, 80, 112, 68, 100, 72, 104, 85, 117, 96, 128, 89, 121, 74, 106, 84, 116, 95, 127, 92, 124, 79, 111, 86, 118, 94, 126, 93, 125, 81, 113, 71, 103, 78, 110, 91, 123, 82, 114, 69, 101, 76, 108, 88, 120, 83, 115, 70, 102)
	L = (1, 68)(2, 74)(3, 72)(4, 79)(5, 75)(6, 80)(7, 65)(8, 86)(9, 84)(10, 71)(11, 89)(12, 66)(13, 85)(14, 67)(15, 69)(16, 92)(17, 70)(18, 90)(19, 87)(20, 78)(21, 94)(22, 76)(23, 95)(24, 73)(25, 81)(26, 96)(27, 77)(28, 82)(29, 83)(30, 88)(31, 91)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.183
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.226 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 32, 32})
Quotient :: dipole
Aut^+ = C32 (small group id <32, 1>)
Aut   = D64 (small group id <64, 52>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y2^-1, (Y3^-1, Y1^-1), (Y3, Y2), (Y2, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-3 * Y2^-1 * Y3^-1 * Y2^-2, Y3^-5 * Y2^-1 * Y3^-2, (Y1^-1 * Y3^-1)^16, Y3 * Y1 * Y2^30 ]
Map:: non-degenerate
	R = (1, 33, 2, 34, 8, 40, 19, 51, 29, 61, 28, 60, 18, 50, 24, 56, 14, 46, 3, 35, 9, 41, 20, 52, 30, 62, 27, 59, 17, 49, 7, 39, 12, 44, 4, 36, 10, 42, 21, 53, 31, 63, 26, 58, 16, 48, 6, 38, 11, 43, 22, 54, 13, 45, 23, 55, 32, 64, 25, 57, 15, 47, 5, 37)(65, 97, 67, 99, 74, 106, 87, 119, 93, 125, 91, 123, 80, 112, 69, 101, 78, 110, 68, 100, 77, 109, 83, 115, 94, 126, 90, 122, 79, 111, 88, 120, 76, 108, 86, 118, 72, 104, 84, 116, 95, 127, 89, 121, 82, 114, 71, 103, 75, 107, 66, 98, 73, 105, 85, 117, 96, 128, 92, 124, 81, 113, 70, 102)
	L = (1, 68)(2, 74)(3, 77)(4, 72)(5, 76)(6, 78)(7, 65)(8, 85)(9, 87)(10, 83)(11, 67)(12, 66)(13, 84)(14, 86)(15, 71)(16, 88)(17, 69)(18, 70)(19, 95)(20, 96)(21, 93)(22, 73)(23, 94)(24, 75)(25, 81)(26, 82)(27, 79)(28, 80)(29, 90)(30, 89)(31, 92)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.186
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.227 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, Y1^3, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^6 * Y3^-5, Y3^22, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 7, 40)(4, 37, 9, 42, 6, 39)(10, 43, 15, 48, 11, 44)(12, 45, 14, 47, 13, 46)(16, 49, 18, 51, 17, 50)(19, 52, 21, 54, 20, 53)(22, 55, 24, 57, 23, 56)(25, 58, 27, 60, 26, 59)(28, 61, 30, 63, 29, 62)(31, 64, 33, 66, 32, 65)(67, 100, 69, 102, 76, 109, 82, 115, 88, 121, 94, 127, 97, 130, 93, 126, 86, 119, 78, 111, 75, 108, 71, 104, 73, 106, 77, 110, 83, 116, 89, 122, 95, 128, 98, 131, 91, 124, 87, 120, 79, 112, 70, 103, 68, 101, 74, 107, 81, 114, 84, 117, 90, 123, 96, 129, 99, 132, 92, 125, 85, 118, 80, 113, 72, 105)
	L = (1, 70)(2, 75)(3, 68)(4, 78)(5, 72)(6, 79)(7, 67)(8, 71)(9, 80)(10, 74)(11, 69)(12, 85)(13, 86)(14, 87)(15, 73)(16, 81)(17, 76)(18, 77)(19, 91)(20, 92)(21, 93)(22, 84)(23, 82)(24, 83)(25, 97)(26, 98)(27, 99)(28, 90)(29, 88)(30, 89)(31, 96)(32, 94)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.241
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.228 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2 * Y1, Y2 * Y3 * Y1, Y1^3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^6 * Y3^-5, Y3^22, (Y3 * Y2^-1)^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 7, 40, 9, 42)(4, 37, 6, 39, 8, 41)(10, 43, 11, 44, 15, 48)(12, 45, 13, 46, 14, 47)(16, 49, 17, 50, 18, 51)(19, 52, 20, 53, 21, 54)(22, 55, 23, 56, 24, 57)(25, 58, 26, 59, 27, 60)(28, 61, 29, 62, 30, 63)(31, 64, 32, 65, 33, 66)(67, 100, 69, 102, 76, 109, 82, 115, 88, 121, 94, 127, 97, 130, 93, 126, 86, 119, 78, 111, 74, 107, 68, 101, 73, 106, 77, 110, 83, 116, 89, 122, 95, 128, 98, 131, 91, 124, 87, 120, 79, 112, 70, 103, 71, 104, 75, 108, 81, 114, 84, 117, 90, 123, 96, 129, 99, 132, 92, 125, 85, 118, 80, 113, 72, 105)
	L = (1, 70)(2, 72)(3, 71)(4, 78)(5, 74)(6, 79)(7, 67)(8, 80)(9, 68)(10, 75)(11, 69)(12, 85)(13, 86)(14, 87)(15, 73)(16, 81)(17, 76)(18, 77)(19, 91)(20, 92)(21, 93)(22, 84)(23, 82)(24, 83)(25, 97)(26, 98)(27, 99)(28, 90)(29, 88)(30, 89)(31, 96)(32, 94)(33, 95)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.252
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.229 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^2 * Y1^-1 * Y3^-1, (Y3^-1, Y2^-1), (R * Y1)^2, Y1^-1 * Y2^2 * Y3^-1, (Y2, Y1^-1), (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1, (R * Y2)^2, Y3^3 * Y2 * Y3 * Y2^2, Y3^3 * Y1^-1 * Y3^3 * Y2^-1, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y1 * Y2^-1, Y3 * Y1 * Y2^31 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 13, 46)(4, 37, 9, 42, 15, 48)(6, 39, 10, 43, 16, 49)(7, 40, 11, 44, 17, 50)(12, 45, 20, 53, 25, 58)(14, 47, 21, 54, 27, 60)(18, 51, 22, 55, 28, 61)(19, 52, 23, 56, 29, 62)(24, 57, 31, 64, 33, 66)(26, 59, 30, 63, 32, 65)(67, 100, 69, 102, 75, 108, 86, 119, 93, 126, 99, 132, 92, 125, 95, 128, 84, 117, 73, 106, 76, 109, 68, 101, 74, 107, 81, 114, 91, 124, 80, 113, 90, 123, 96, 129, 85, 118, 88, 121, 77, 110, 82, 115, 71, 104, 79, 112, 70, 103, 78, 111, 87, 120, 97, 130, 98, 131, 89, 122, 94, 127, 83, 116, 72, 105)
	L = (1, 70)(2, 75)(3, 78)(4, 80)(5, 81)(6, 79)(7, 67)(8, 86)(9, 87)(10, 69)(11, 68)(12, 90)(13, 91)(14, 92)(15, 93)(16, 74)(17, 71)(18, 72)(19, 73)(20, 97)(21, 96)(22, 76)(23, 77)(24, 95)(25, 99)(26, 94)(27, 98)(28, 82)(29, 83)(30, 84)(31, 85)(32, 88)(33, 89)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.242
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.230 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3 * Y1 * Y2^2, (Y3^-1, Y1^-1), (Y2, Y1^-1), Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, Y1^-1 * Y2^-2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3 * Y2^-1 * Y3^3, Y3^-3 * Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1, (Y3 * Y2^-1)^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 13, 46)(7, 40, 11, 44, 12, 45)(15, 48, 20, 53, 24, 57)(16, 49, 21, 54, 29, 62)(18, 51, 22, 55, 26, 59)(19, 52, 23, 56, 25, 58)(27, 60, 32, 65, 28, 61)(30, 63, 31, 64, 33, 66)(67, 100, 69, 102, 78, 111, 90, 123, 89, 122, 98, 131, 97, 130, 87, 120, 84, 117, 70, 103, 79, 112, 71, 104, 80, 113, 77, 110, 86, 119, 85, 118, 93, 126, 96, 129, 82, 115, 92, 125, 83, 116, 76, 109, 68, 101, 74, 107, 73, 106, 81, 114, 91, 124, 94, 127, 99, 132, 95, 128, 88, 121, 75, 108, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 72)(9, 87)(10, 88)(11, 68)(12, 71)(13, 92)(14, 76)(15, 69)(16, 94)(17, 95)(18, 96)(19, 73)(20, 74)(21, 93)(22, 97)(23, 77)(24, 80)(25, 78)(26, 99)(27, 81)(28, 90)(29, 98)(30, 91)(31, 85)(32, 86)(33, 89)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.247
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.231 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y2, (Y2^-1, Y1^-1), Y2^-2 * Y1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3^-2 * Y2 * Y3, Y3^-2 * Y2 * Y3^-2 * Y2^2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-3 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2, (Y3 * Y2^-1)^33, (Y3^-1 * Y1^-1)^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 12, 45)(4, 37, 9, 42, 15, 48)(6, 39, 10, 43, 17, 50)(7, 40, 11, 44, 18, 51)(13, 46, 20, 53, 24, 57)(14, 47, 21, 54, 27, 60)(16, 49, 22, 55, 29, 62)(19, 52, 23, 56, 30, 63)(25, 58, 26, 59, 32, 65)(28, 61, 33, 66, 31, 64)(67, 100, 69, 102, 77, 110, 86, 119, 96, 129, 98, 131, 97, 130, 93, 126, 82, 115, 70, 103, 76, 109, 68, 101, 74, 107, 84, 117, 90, 123, 85, 118, 91, 124, 94, 127, 80, 113, 88, 121, 75, 108, 83, 116, 71, 104, 78, 111, 73, 106, 79, 112, 89, 122, 92, 125, 99, 132, 87, 120, 95, 128, 81, 114, 72, 105)
	L = (1, 70)(2, 75)(3, 76)(4, 80)(5, 81)(6, 82)(7, 67)(8, 83)(9, 87)(10, 88)(11, 68)(12, 72)(13, 69)(14, 92)(15, 93)(16, 94)(17, 95)(18, 71)(19, 73)(20, 74)(21, 98)(22, 99)(23, 77)(24, 78)(25, 79)(26, 86)(27, 91)(28, 89)(29, 97)(30, 84)(31, 85)(32, 90)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.248
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.232 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y1^-1, Y2^-1), Y3 * Y2^-3, (R * Y3)^2, (Y3^-1, Y2), (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, Y3^3 * Y2^2 * Y1^-1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^-33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 18, 51)(7, 40, 11, 44, 19, 52)(12, 45, 22, 55, 28, 61)(13, 46, 23, 56, 29, 62)(15, 48, 24, 57, 30, 63)(16, 49, 25, 58, 31, 64)(20, 53, 26, 59, 32, 65)(21, 54, 27, 60, 33, 66)(67, 100, 69, 102, 78, 111, 70, 103, 79, 112, 93, 126, 82, 115, 92, 125, 77, 110, 90, 123, 76, 109, 68, 101, 74, 107, 88, 121, 75, 108, 89, 122, 99, 132, 91, 124, 98, 131, 85, 118, 96, 129, 84, 117, 71, 104, 80, 113, 94, 127, 83, 116, 95, 128, 87, 120, 97, 130, 86, 119, 73, 106, 81, 114, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 78)(7, 67)(8, 89)(9, 91)(10, 88)(11, 68)(12, 93)(13, 92)(14, 95)(15, 69)(16, 90)(17, 97)(18, 94)(19, 71)(20, 72)(21, 73)(22, 99)(23, 98)(24, 74)(25, 96)(26, 76)(27, 77)(28, 87)(29, 86)(30, 80)(31, 81)(32, 84)(33, 85)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.250
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.233 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y3^-1, Y2), Y3 * Y2^3, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (Y3^-1, Y1), (R * Y1)^2, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-1, Y3^3 * Y1 * Y3 * Y1 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 19, 52)(7, 40, 11, 44, 20, 53)(12, 45, 22, 55, 28, 61)(13, 46, 23, 56, 30, 63)(15, 48, 24, 57, 31, 64)(16, 49, 25, 58, 29, 62)(18, 51, 26, 59, 32, 65)(21, 54, 27, 60, 33, 66)(67, 100, 69, 102, 78, 111, 73, 106, 81, 114, 95, 128, 87, 120, 98, 131, 83, 116, 96, 129, 85, 118, 71, 104, 80, 113, 94, 127, 86, 119, 97, 130, 91, 124, 99, 132, 92, 125, 75, 108, 89, 122, 76, 109, 68, 101, 74, 107, 88, 121, 77, 110, 90, 123, 82, 115, 93, 126, 84, 117, 70, 103, 79, 112, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 89)(9, 91)(10, 92)(11, 68)(12, 72)(13, 93)(14, 96)(15, 69)(16, 88)(17, 95)(18, 90)(19, 98)(20, 71)(21, 73)(22, 76)(23, 99)(24, 74)(25, 94)(26, 97)(27, 77)(28, 85)(29, 78)(30, 87)(31, 80)(32, 81)(33, 86)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.244
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.234 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y3, Y2^-1), Y2^-3 * Y3^-1, (R * Y2)^2, (Y1^-1, Y3^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^3 * Y1 * Y2^-1, Y1 * Y2 * Y3^-7, Y2^-2 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y2^-1 * Y3)^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 19, 52)(7, 40, 11, 44, 20, 53)(12, 45, 22, 55, 28, 61)(13, 46, 23, 56, 30, 63)(15, 48, 24, 57, 31, 64)(16, 49, 25, 58, 32, 65)(18, 51, 26, 59, 33, 66)(21, 54, 27, 60, 29, 62)(67, 100, 69, 102, 78, 111, 73, 106, 81, 114, 91, 124, 87, 120, 92, 125, 75, 108, 89, 122, 76, 109, 68, 101, 74, 107, 88, 121, 77, 110, 90, 123, 98, 131, 93, 126, 99, 132, 83, 116, 96, 129, 85, 118, 71, 104, 80, 113, 94, 127, 86, 119, 97, 130, 82, 115, 95, 128, 84, 117, 70, 103, 79, 112, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 89)(9, 91)(10, 92)(11, 68)(12, 72)(13, 95)(14, 96)(15, 69)(16, 94)(17, 98)(18, 97)(19, 99)(20, 71)(21, 73)(22, 76)(23, 87)(24, 74)(25, 78)(26, 81)(27, 77)(28, 85)(29, 86)(30, 93)(31, 80)(32, 88)(33, 90)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.243
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.235 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2^-1, Y1), (Y3^-1, Y1), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3^-2 * Y1, Y2^2 * Y3 * Y2 * Y3, Y2 * Y1 * Y3^-3, Y1^-1 * Y3^-1 * Y2^-1 * Y1 * Y3 * Y2, Y3^-1 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, Y2^-2 * Y1^-1 * Y3 * Y2^-2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-3, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 19, 52)(7, 40, 11, 44, 20, 53)(12, 45, 24, 57, 30, 63)(13, 46, 25, 58, 32, 65)(15, 48, 16, 49, 26, 59)(18, 51, 27, 60, 23, 56)(21, 54, 28, 61, 31, 64)(22, 55, 29, 62, 33, 66)(67, 100, 69, 102, 78, 111, 89, 122, 83, 116, 98, 131, 99, 132, 86, 119, 92, 125, 94, 127, 76, 109, 68, 101, 74, 107, 90, 123, 84, 117, 70, 103, 79, 112, 88, 121, 73, 106, 81, 114, 97, 130, 85, 118, 71, 104, 80, 113, 96, 129, 93, 126, 75, 108, 91, 124, 95, 128, 77, 110, 82, 115, 87, 120, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 91)(9, 92)(10, 93)(11, 68)(12, 88)(13, 87)(14, 98)(15, 69)(16, 74)(17, 81)(18, 77)(19, 89)(20, 71)(21, 90)(22, 72)(23, 73)(24, 95)(25, 94)(26, 80)(27, 86)(28, 96)(29, 76)(30, 99)(31, 78)(32, 97)(33, 85)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.251
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.236 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2^-1, Y3^-1), (Y1^-1, Y2^-1), (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3^-3 * Y1, Y2^2 * Y3^-1 * Y2 * Y3^-1, Y3^-2 * Y2^-1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1, Y3 * Y2^15, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 19, 52)(7, 40, 11, 44, 20, 53)(12, 45, 24, 57, 30, 63)(13, 46, 25, 58, 23, 56)(15, 48, 26, 59, 31, 64)(16, 49, 27, 60, 22, 55)(18, 51, 28, 61, 32, 65)(21, 54, 29, 62, 33, 66)(67, 100, 69, 102, 78, 111, 82, 115, 77, 110, 92, 125, 94, 127, 75, 108, 91, 124, 99, 132, 85, 118, 71, 104, 80, 113, 96, 129, 88, 121, 73, 106, 81, 114, 84, 117, 70, 103, 79, 112, 95, 128, 76, 109, 68, 101, 74, 107, 90, 123, 93, 126, 86, 119, 97, 130, 98, 131, 83, 116, 89, 122, 87, 120, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 91)(9, 93)(10, 94)(11, 68)(12, 95)(13, 77)(14, 89)(15, 69)(16, 76)(17, 88)(18, 78)(19, 98)(20, 71)(21, 81)(22, 72)(23, 73)(24, 99)(25, 86)(26, 74)(27, 85)(28, 90)(29, 92)(30, 87)(31, 80)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.246
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.237 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y3^-1, Y1^-1), (Y2^-1, Y1), (Y3^-1, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y2^3, Y3^3 * Y2 * Y1, Y3 * Y2 * Y1^-1 * Y3^2 * Y1^-1, Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 19, 52)(7, 40, 11, 44, 20, 53)(12, 45, 24, 57, 31, 64)(13, 46, 23, 56, 29, 62)(15, 48, 25, 58, 32, 65)(16, 49, 22, 55, 28, 61)(18, 51, 26, 59, 33, 66)(21, 54, 27, 60, 30, 63)(67, 100, 69, 102, 78, 111, 82, 115, 86, 119, 98, 131, 99, 132, 83, 116, 95, 128, 93, 126, 76, 109, 68, 101, 74, 107, 90, 123, 88, 121, 73, 106, 81, 114, 84, 117, 70, 103, 79, 112, 96, 129, 85, 118, 71, 104, 80, 113, 97, 130, 94, 127, 77, 110, 91, 124, 92, 125, 75, 108, 89, 122, 87, 120, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 89)(9, 88)(10, 92)(11, 68)(12, 96)(13, 86)(14, 95)(15, 69)(16, 85)(17, 94)(18, 78)(19, 99)(20, 71)(21, 81)(22, 72)(23, 73)(24, 87)(25, 74)(26, 90)(27, 91)(28, 76)(29, 77)(30, 98)(31, 93)(32, 80)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.245
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.238 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2^-1, Y1), Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^2 * Y2 * Y1, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y1 * Y3 * Y2^-1, Y2 * Y3^-1 * Y1^-1 * Y2^4, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y1^2 * Y3^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 17, 50)(6, 39, 10, 43, 16, 49)(7, 40, 11, 44, 13, 46)(12, 45, 20, 53, 26, 59)(15, 48, 21, 54, 25, 58)(18, 51, 22, 55, 28, 61)(19, 52, 23, 56, 29, 62)(24, 57, 32, 65, 30, 63)(27, 60, 33, 66, 31, 64)(67, 100, 69, 102, 78, 111, 90, 123, 88, 121, 75, 108, 73, 106, 81, 114, 93, 126, 89, 122, 76, 109, 68, 101, 74, 107, 86, 119, 98, 131, 94, 127, 83, 116, 77, 110, 87, 120, 99, 132, 95, 128, 82, 115, 71, 104, 80, 113, 92, 125, 96, 129, 84, 117, 70, 103, 79, 112, 91, 124, 97, 130, 85, 118, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 82)(5, 83)(6, 84)(7, 67)(8, 73)(9, 72)(10, 88)(11, 68)(12, 91)(13, 71)(14, 77)(15, 69)(16, 94)(17, 76)(18, 95)(19, 96)(20, 81)(21, 74)(22, 85)(23, 90)(24, 97)(25, 80)(26, 87)(27, 78)(28, 89)(29, 98)(30, 99)(31, 92)(32, 93)(33, 86)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.249
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.239 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2^-1, Y1), (Y3, Y1^-1), Y2^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (Y3, Y2^-1), Y3 * Y2^-1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y2^2 * Y3 * Y1^-1 * Y2^3, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-2 * Y1 * Y2^-1 * Y3 * Y2^-2, Y3^-33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 5, 38)(3, 36, 8, 41, 14, 47)(4, 37, 9, 42, 15, 48)(6, 39, 10, 43, 16, 49)(7, 40, 11, 44, 17, 50)(12, 45, 20, 53, 26, 59)(13, 46, 21, 54, 27, 60)(18, 51, 22, 55, 28, 61)(19, 52, 23, 56, 29, 62)(24, 57, 32, 65, 31, 64)(25, 58, 33, 66, 30, 63)(67, 100, 69, 102, 78, 111, 90, 123, 89, 122, 77, 110, 70, 103, 79, 112, 91, 124, 88, 121, 76, 109, 68, 101, 74, 107, 86, 119, 98, 131, 95, 128, 83, 116, 75, 108, 87, 120, 99, 132, 94, 127, 82, 115, 71, 104, 80, 113, 92, 125, 97, 130, 85, 118, 73, 106, 81, 114, 93, 126, 96, 129, 84, 117, 72, 105)
	L = (1, 70)(2, 75)(3, 79)(4, 74)(5, 81)(6, 77)(7, 67)(8, 87)(9, 80)(10, 83)(11, 68)(12, 91)(13, 86)(14, 93)(15, 69)(16, 73)(17, 71)(18, 89)(19, 72)(20, 99)(21, 92)(22, 95)(23, 76)(24, 88)(25, 98)(26, 96)(27, 78)(28, 85)(29, 82)(30, 90)(31, 84)(32, 94)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.240
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.240 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2 * Y3^2, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1, Y1^-1), Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3, Y1^-2 * Y2 * Y3^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2 * Y1^4 * Y3^-5, Y2^-11 * Y1^-11, Y2^33, Y1^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 16, 49, 22, 55, 28, 61, 31, 64, 27, 60, 20, 53, 13, 46, 6, 39, 11, 44, 7, 40, 12, 45, 18, 51, 24, 57, 30, 63, 32, 65, 25, 58, 21, 54, 14, 47, 4, 37, 10, 43, 3, 36, 9, 42, 17, 50, 23, 56, 29, 62, 33, 66, 26, 59, 19, 52, 15, 48, 5, 38)(67, 100, 69, 102, 78, 111, 82, 115, 89, 122, 96, 129, 97, 130, 92, 125, 87, 120, 79, 112, 71, 104, 76, 109, 73, 106, 74, 107, 83, 116, 90, 123, 94, 127, 99, 132, 91, 124, 86, 119, 81, 114, 70, 103, 77, 110, 68, 101, 75, 108, 84, 117, 88, 121, 95, 128, 98, 131, 93, 126, 85, 118, 80, 113, 72, 105)
	L = (1, 70)(2, 76)(3, 77)(4, 79)(5, 80)(6, 81)(7, 67)(8, 69)(9, 73)(10, 72)(11, 71)(12, 68)(13, 85)(14, 86)(15, 87)(16, 75)(17, 78)(18, 74)(19, 91)(20, 92)(21, 93)(22, 83)(23, 84)(24, 82)(25, 97)(26, 98)(27, 99)(28, 89)(29, 90)(30, 88)(31, 95)(32, 94)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.239
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.241 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-2, (Y3^-1, Y2), (R * Y3)^2, (Y3, Y1^-1), (R * Y2)^2, (R * Y1)^2, Y2 * Y3^4 * Y1^-1, Y3 * Y2 * Y1^-4, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 22, 55, 12, 45, 17, 50, 27, 60, 31, 64, 32, 65, 15, 48, 26, 59, 19, 52, 7, 40, 11, 44, 25, 58, 13, 46, 3, 36, 6, 39, 10, 43, 24, 57, 16, 49, 4, 37, 9, 42, 23, 56, 21, 54, 29, 62, 33, 66, 30, 63, 14, 47, 20, 53, 28, 61, 18, 51, 5, 38)(67, 100, 69, 102, 71, 104, 79, 112, 84, 117, 91, 124, 94, 127, 77, 110, 86, 119, 73, 106, 80, 113, 85, 118, 96, 129, 92, 125, 99, 132, 81, 114, 95, 128, 98, 131, 87, 120, 97, 130, 89, 122, 93, 126, 75, 108, 83, 116, 70, 103, 78, 111, 82, 115, 88, 121, 90, 123, 74, 107, 76, 109, 68, 101, 72, 105)
	L = (1, 70)(2, 75)(3, 78)(4, 81)(5, 82)(6, 83)(7, 67)(8, 89)(9, 92)(10, 93)(11, 68)(12, 95)(13, 88)(14, 69)(15, 94)(16, 98)(17, 99)(18, 90)(19, 71)(20, 72)(21, 73)(22, 87)(23, 85)(24, 97)(25, 74)(26, 84)(27, 96)(28, 76)(29, 77)(30, 79)(31, 80)(32, 86)(33, 91)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.227
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.242 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3), (Y1, Y3), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^-2 * Y1 * Y3^2, Y3 * Y1 * Y2^2 * Y1, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3, Y2 * Y1^-5, Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3, Y2^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 26, 59, 15, 48, 3, 36, 9, 42, 24, 57, 30, 63, 17, 50, 13, 46, 22, 55, 7, 40, 12, 45, 28, 61, 32, 65, 19, 52, 16, 49, 29, 62, 33, 66, 18, 51, 4, 37, 10, 43, 23, 56, 25, 58, 31, 64, 14, 47, 21, 54, 6, 39, 11, 44, 27, 60, 20, 53, 5, 38)(67, 100, 69, 102, 79, 112, 98, 131, 84, 117, 97, 130, 93, 126, 74, 107, 90, 123, 73, 106, 82, 115, 76, 109, 87, 120, 71, 104, 81, 114, 83, 116, 94, 127, 99, 132, 91, 124, 77, 110, 68, 101, 75, 108, 88, 121, 85, 118, 70, 103, 80, 113, 86, 119, 92, 125, 96, 129, 78, 111, 95, 128, 89, 122, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 85)(7, 67)(8, 89)(9, 87)(10, 79)(11, 82)(12, 68)(13, 86)(14, 94)(15, 97)(16, 69)(17, 93)(18, 96)(19, 81)(20, 99)(21, 98)(22, 71)(23, 88)(24, 72)(25, 73)(26, 91)(27, 95)(28, 74)(29, 75)(30, 77)(31, 78)(32, 92)(33, 90)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.229
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.243 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-2, (Y2, Y3^-1), (Y3, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^4 * Y1^-1, Y1^-1 * Y3^-3 * Y1^-2, (Y1^-1 * Y3^-1)^3, Y1 * Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1, Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 22, 55, 16, 49, 12, 45, 26, 59, 33, 66, 31, 64, 14, 47, 28, 61, 19, 52, 7, 40, 11, 44, 25, 58, 18, 51, 6, 39, 3, 36, 9, 42, 23, 56, 15, 48, 4, 37, 10, 43, 24, 57, 21, 54, 29, 62, 30, 63, 32, 65, 20, 53, 13, 46, 27, 60, 17, 50, 5, 38)(67, 100, 69, 102, 68, 101, 75, 108, 74, 107, 89, 122, 88, 121, 81, 114, 82, 115, 70, 103, 78, 111, 76, 109, 92, 125, 90, 123, 99, 132, 87, 120, 97, 130, 95, 128, 80, 113, 96, 129, 94, 127, 98, 131, 85, 118, 86, 119, 73, 106, 79, 112, 77, 110, 93, 126, 91, 124, 83, 116, 84, 117, 71, 104, 72, 105)
	L = (1, 70)(2, 76)(3, 78)(4, 80)(5, 81)(6, 82)(7, 67)(8, 90)(9, 92)(10, 94)(11, 68)(12, 96)(13, 69)(14, 93)(15, 97)(16, 95)(17, 89)(18, 88)(19, 71)(20, 72)(21, 73)(22, 87)(23, 99)(24, 85)(25, 74)(26, 98)(27, 75)(28, 83)(29, 77)(30, 91)(31, 79)(32, 84)(33, 86)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.234
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.244 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y2^-1, Y1^-1), (Y1^-1, Y3^-1), (R * Y2)^2, Y2^-2 * Y1 * Y3 * Y1, Y2 * Y3 * Y2 * Y1 * Y3, Y2^-1 * Y1^-5, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y1 * Y3^3 * Y1^2, Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y2^-1, Y3^29 * Y2^3, Y2^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 26, 59, 21, 54, 6, 39, 11, 44, 16, 49, 29, 62, 17, 50, 23, 56, 22, 55, 7, 40, 12, 45, 28, 61, 32, 65, 14, 47, 24, 57, 30, 63, 33, 66, 18, 51, 4, 37, 10, 43, 13, 46, 25, 58, 31, 64, 19, 52, 15, 48, 3, 36, 9, 42, 27, 60, 20, 53, 5, 38)(67, 100, 69, 102, 79, 112, 96, 129, 78, 111, 95, 128, 92, 125, 86, 119, 85, 118, 70, 103, 80, 113, 88, 121, 77, 110, 68, 101, 75, 108, 91, 124, 99, 132, 94, 127, 83, 116, 87, 120, 71, 104, 81, 114, 76, 109, 90, 123, 73, 106, 82, 115, 74, 107, 93, 126, 97, 130, 84, 117, 98, 131, 89, 122, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 85)(7, 67)(8, 79)(9, 90)(10, 89)(11, 81)(12, 68)(13, 88)(14, 87)(15, 98)(16, 69)(17, 93)(18, 95)(19, 94)(20, 99)(21, 97)(22, 71)(23, 86)(24, 72)(25, 73)(26, 91)(27, 96)(28, 74)(29, 75)(30, 77)(31, 78)(32, 92)(33, 82)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.233
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.245 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3^-1 * Y2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2, Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y1^4 * Y2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 20, 53, 6, 39, 11, 44, 25, 58, 31, 64, 16, 49, 17, 50, 29, 62, 21, 54, 7, 40, 12, 45, 26, 59, 33, 66, 22, 55, 14, 47, 28, 61, 32, 65, 18, 51, 4, 37, 10, 43, 24, 57, 23, 56, 13, 46, 27, 60, 30, 63, 15, 48, 3, 36, 9, 42, 19, 52, 5, 38)(67, 100, 69, 102, 79, 112, 70, 103, 80, 113, 78, 111, 83, 116, 77, 110, 68, 101, 75, 108, 93, 126, 76, 109, 94, 127, 92, 125, 95, 128, 91, 124, 74, 107, 85, 118, 96, 129, 90, 123, 98, 131, 99, 132, 87, 120, 97, 130, 86, 119, 71, 104, 81, 114, 89, 122, 84, 117, 88, 121, 73, 106, 82, 115, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 79)(7, 67)(8, 90)(9, 94)(10, 95)(11, 93)(12, 68)(13, 78)(14, 77)(15, 88)(16, 69)(17, 75)(18, 82)(19, 98)(20, 89)(21, 71)(22, 72)(23, 73)(24, 87)(25, 96)(26, 74)(27, 92)(28, 91)(29, 85)(30, 99)(31, 81)(32, 97)(33, 86)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.237
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.246 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^3 * Y3^-1, (Y3, Y1), (Y2^-1, Y3^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^2 * Y3^-1 * Y2^-1, Y3^3 * Y1^3, Y1^9 * Y3^-2, Y3^11, Y1^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 24, 57, 32, 65, 22, 55, 15, 48, 3, 36, 9, 42, 17, 50, 28, 61, 21, 54, 7, 40, 12, 45, 13, 46, 26, 59, 29, 62, 33, 66, 30, 63, 16, 49, 18, 51, 4, 37, 10, 43, 25, 58, 23, 56, 20, 53, 6, 39, 11, 44, 14, 47, 27, 60, 31, 64, 19, 52, 5, 38)(67, 100, 69, 102, 79, 112, 70, 103, 80, 113, 74, 107, 83, 116, 95, 128, 91, 124, 97, 130, 98, 131, 87, 120, 96, 129, 86, 119, 71, 104, 81, 114, 78, 111, 84, 117, 77, 110, 68, 101, 75, 108, 92, 125, 76, 109, 93, 126, 90, 123, 94, 127, 99, 132, 89, 122, 85, 118, 88, 121, 73, 106, 82, 115, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 79)(7, 67)(8, 91)(9, 93)(10, 94)(11, 92)(12, 68)(13, 74)(14, 95)(15, 77)(16, 69)(17, 97)(18, 75)(19, 82)(20, 78)(21, 71)(22, 72)(23, 73)(24, 89)(25, 87)(26, 90)(27, 99)(28, 85)(29, 98)(30, 81)(31, 96)(32, 86)(33, 88)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.236
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.247 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y3), (Y1, Y2^-1), Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y1^2 * Y2^-1 * Y1^2, Y3^-1 * Y2^-1 * Y1 * Y3^-2, (Y1^-1 * Y3^-1)^3 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 15, 48, 3, 36, 9, 42, 24, 57, 30, 63, 13, 46, 17, 50, 28, 61, 22, 55, 7, 40, 12, 45, 26, 59, 31, 64, 16, 49, 19, 52, 29, 62, 32, 65, 18, 51, 4, 37, 10, 43, 25, 58, 23, 56, 14, 47, 27, 60, 33, 66, 21, 54, 6, 39, 11, 44, 20, 53, 5, 38)(67, 100, 69, 102, 79, 112, 73, 106, 82, 115, 84, 117, 89, 122, 87, 120, 71, 104, 81, 114, 96, 129, 88, 121, 97, 130, 98, 131, 91, 124, 99, 132, 86, 119, 74, 107, 90, 123, 94, 127, 92, 125, 95, 128, 76, 109, 93, 126, 77, 110, 68, 101, 75, 108, 83, 116, 78, 111, 85, 118, 70, 103, 80, 113, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 85)(7, 67)(8, 91)(9, 93)(10, 94)(11, 95)(12, 68)(13, 72)(14, 78)(15, 89)(16, 69)(17, 77)(18, 79)(19, 75)(20, 98)(21, 82)(22, 71)(23, 73)(24, 99)(25, 88)(26, 74)(27, 92)(28, 86)(29, 90)(30, 87)(31, 81)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.230
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.248 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^-3 * Y3^-1, (Y3, Y1), (Y2^-1, Y3), (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3^-2, Y2 * Y1 * Y3^-1 * Y2 * Y1, Y3^3 * Y1^3, Y1^9 * Y3^-2, Y3^11, Y1^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 24, 57, 30, 63, 16, 49, 21, 54, 6, 39, 11, 44, 17, 50, 27, 60, 22, 55, 7, 40, 12, 45, 14, 47, 26, 59, 33, 66, 31, 64, 29, 62, 13, 46, 18, 51, 4, 37, 10, 43, 25, 58, 23, 56, 15, 48, 3, 36, 9, 42, 19, 52, 28, 61, 32, 65, 20, 53, 5, 38)(67, 100, 69, 102, 79, 112, 73, 106, 82, 115, 86, 119, 89, 122, 97, 130, 93, 126, 90, 123, 94, 127, 76, 109, 92, 125, 77, 110, 68, 101, 75, 108, 84, 117, 78, 111, 87, 120, 71, 104, 81, 114, 95, 128, 88, 121, 96, 129, 98, 131, 91, 124, 99, 132, 83, 116, 74, 107, 85, 118, 70, 103, 80, 113, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 83)(5, 84)(6, 85)(7, 67)(8, 91)(9, 92)(10, 93)(11, 94)(12, 68)(13, 72)(14, 74)(15, 78)(16, 69)(17, 98)(18, 77)(19, 99)(20, 79)(21, 75)(22, 71)(23, 73)(24, 89)(25, 88)(26, 90)(27, 86)(28, 97)(29, 87)(30, 81)(31, 82)(32, 95)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.231
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.249 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2^-1), Y2^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^2 * Y2^3, (Y3^-1 * Y1^-1)^3, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-3, Y1^2 * Y2^-1 * Y1 * Y3 * Y2^-2, Y1^2 * Y2^2 * Y3^-15, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 22, 55, 21, 54, 29, 62, 32, 65, 15, 48, 3, 36, 9, 42, 23, 56, 19, 52, 7, 40, 12, 45, 26, 59, 30, 63, 13, 46, 20, 53, 28, 61, 33, 66, 16, 49, 4, 37, 10, 43, 24, 57, 18, 51, 6, 39, 11, 44, 25, 58, 31, 64, 14, 47, 27, 60, 17, 50, 5, 38)(67, 100, 69, 102, 79, 112, 84, 117, 71, 104, 81, 114, 96, 129, 90, 123, 83, 116, 98, 131, 92, 125, 76, 109, 93, 126, 95, 128, 78, 111, 70, 103, 80, 113, 87, 120, 73, 106, 82, 115, 97, 130, 88, 121, 85, 118, 99, 132, 91, 124, 74, 107, 89, 122, 94, 127, 77, 110, 68, 101, 75, 108, 86, 119, 72, 105)
	L = (1, 70)(2, 76)(3, 80)(4, 75)(5, 82)(6, 78)(7, 67)(8, 90)(9, 93)(10, 89)(11, 92)(12, 68)(13, 87)(14, 86)(15, 97)(16, 69)(17, 99)(18, 73)(19, 71)(20, 95)(21, 72)(22, 84)(23, 83)(24, 85)(25, 96)(26, 74)(27, 94)(28, 98)(29, 77)(30, 88)(31, 79)(32, 91)(33, 81)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.238
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.250 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y3^-1, Y1^-1), Y3 * Y2 * Y1^-2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3^-1, (R * Y2)^2, Y2 * Y3 * Y1^-2, (Y2^-1, Y3^-1), (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2^-1 * Y3^-3 * Y1^-1, Y3 * Y2 * Y1^2 * Y2^2 * Y1, Y1^-1 * Y3^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 22, 55, 33, 66, 20, 53, 29, 62, 16, 49, 28, 61, 15, 48, 27, 60, 19, 52, 7, 40, 12, 45, 3, 36, 9, 42, 23, 56, 32, 65, 18, 51, 6, 39, 11, 44, 4, 37, 10, 43, 24, 57, 21, 54, 30, 63, 14, 47, 26, 59, 13, 46, 25, 58, 31, 64, 17, 50, 5, 38)(67, 100, 69, 102, 79, 112, 81, 114, 90, 123, 99, 132, 84, 117, 71, 104, 78, 111, 92, 125, 94, 127, 76, 109, 88, 121, 98, 131, 83, 116, 73, 106, 80, 113, 82, 115, 70, 103, 74, 107, 89, 122, 97, 130, 85, 118, 96, 129, 95, 128, 77, 110, 68, 101, 75, 108, 91, 124, 93, 126, 87, 120, 86, 119, 72, 105)
	L = (1, 70)(2, 76)(3, 74)(4, 81)(5, 77)(6, 82)(7, 67)(8, 90)(9, 88)(10, 93)(11, 94)(12, 68)(13, 89)(14, 69)(15, 97)(16, 79)(17, 72)(18, 95)(19, 71)(20, 80)(21, 73)(22, 87)(23, 99)(24, 85)(25, 98)(26, 75)(27, 83)(28, 91)(29, 92)(30, 78)(31, 84)(32, 86)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.232
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.251 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^2, (Y2^-1, Y3), (Y3^-1, Y1), (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-2, Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y1, Y2 * Y3^-1 * Y2^2 * Y3^-1 * Y1 * Y2, Y2 * Y3 * Y2^5, (Y2^-1 * Y3)^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 3, 36, 8, 41, 11, 44, 22, 55, 25, 58, 29, 62, 28, 61, 14, 47, 20, 53, 18, 51, 7, 40, 10, 43, 13, 46, 23, 56, 26, 59, 31, 64, 30, 63, 16, 49, 15, 48, 4, 37, 9, 42, 12, 45, 21, 54, 24, 57, 27, 60, 33, 66, 32, 65, 19, 52, 17, 50, 6, 39, 5, 38)(67, 100, 69, 102, 77, 110, 91, 124, 94, 127, 86, 119, 73, 106, 79, 112, 92, 125, 96, 129, 81, 114, 75, 108, 87, 120, 93, 126, 98, 131, 83, 116, 71, 104, 68, 101, 74, 107, 88, 121, 95, 128, 80, 113, 84, 117, 76, 109, 89, 122, 97, 130, 82, 115, 70, 103, 78, 111, 90, 123, 99, 132, 85, 118, 72, 105)
	L = (1, 70)(2, 75)(3, 78)(4, 80)(5, 81)(6, 82)(7, 67)(8, 87)(9, 86)(10, 68)(11, 90)(12, 84)(13, 69)(14, 83)(15, 94)(16, 95)(17, 96)(18, 71)(19, 97)(20, 72)(21, 73)(22, 93)(23, 74)(24, 76)(25, 99)(26, 77)(27, 79)(28, 85)(29, 98)(30, 91)(31, 88)(32, 92)(33, 89)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.235
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.252 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 33, 33, 33})
Quotient :: dipole
Aut^+ = C33 (small group id <33, 1>)
Aut   = D66 (small group id <66, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y2, Y1 * Y2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^3, Y1^3 * Y3^3, Y1 * Y2^-5, Y3^33 ]
Map:: non-degenerate
	R = (1, 34, 2, 35, 8, 41, 20, 53, 31, 64, 30, 63, 26, 59, 11, 44, 12, 45, 14, 47, 23, 56, 16, 49, 7, 40, 6, 39, 10, 43, 22, 55, 32, 65, 33, 66, 28, 61, 13, 46, 3, 36, 4, 37, 9, 42, 21, 54, 19, 52, 18, 51, 17, 50, 24, 57, 25, 58, 27, 60, 29, 62, 15, 48, 5, 38)(67, 100, 69, 102, 77, 110, 90, 123, 76, 109, 68, 101, 70, 103, 78, 111, 91, 124, 88, 121, 74, 107, 75, 108, 80, 113, 93, 126, 98, 131, 86, 119, 87, 120, 89, 122, 95, 128, 99, 132, 97, 130, 85, 118, 82, 115, 81, 114, 94, 127, 96, 129, 84, 117, 73, 106, 71, 104, 79, 112, 92, 125, 83, 116, 72, 105)
	L = (1, 70)(2, 75)(3, 78)(4, 80)(5, 69)(6, 68)(7, 67)(8, 87)(9, 89)(10, 74)(11, 91)(12, 93)(13, 77)(14, 95)(15, 79)(16, 71)(17, 76)(18, 72)(19, 73)(20, 85)(21, 82)(22, 86)(23, 81)(24, 88)(25, 98)(26, 90)(27, 99)(28, 92)(29, 94)(30, 83)(31, 84)(32, 97)(33, 96)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.228
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.253 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, (R * Y1)^2, (Y3^-1, Y1^-1), R * Y2 * R * Y3^-1, (Y2^-1, Y1^-1), Y1^5, Y2^7, (Y3 * Y2^-1)^7, Y3^-35 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 6, 41, 13, 48, 5, 40)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(4, 39, 8, 43, 15, 50, 23, 58, 12, 47)(9, 44, 16, 51, 24, 59, 29, 64, 19, 54)(11, 46, 17, 52, 25, 60, 31, 66, 22, 57)(18, 53, 26, 61, 32, 67, 34, 69, 28, 63)(21, 56, 27, 62, 33, 68, 35, 70, 30, 65)(71, 106, 73, 108, 79, 114, 88, 123, 91, 126, 81, 116, 74, 109)(72, 107, 77, 112, 86, 121, 96, 131, 97, 132, 87, 122, 78, 113)(75, 110, 80, 115, 89, 124, 98, 133, 100, 135, 92, 127, 82, 117)(76, 111, 84, 119, 94, 129, 102, 137, 103, 138, 95, 130, 85, 120)(83, 118, 90, 125, 99, 134, 104, 139, 105, 140, 101, 136, 93, 128)
	L = (1, 74)(2, 78)(3, 71)(4, 81)(5, 82)(6, 85)(7, 72)(8, 87)(9, 73)(10, 75)(11, 91)(12, 92)(13, 93)(14, 76)(15, 95)(16, 77)(17, 97)(18, 79)(19, 80)(20, 83)(21, 88)(22, 100)(23, 101)(24, 84)(25, 103)(26, 86)(27, 96)(28, 89)(29, 90)(30, 98)(31, 105)(32, 94)(33, 102)(34, 99)(35, 104)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.264
Graph:: bipartite
	v = 12 e = 70 f = 6
	degree seq :: [ 10^7, 14^5 ]

E27.254 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3^-1, Y2 * Y3^3, (Y1, Y3), (Y1, Y2^-1), Y2 * Y3^3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^5 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 17, 52, 5, 40)(3, 38, 9, 44, 20, 55, 27, 62, 14, 49)(4, 39, 10, 45, 21, 56, 29, 64, 16, 51)(6, 41, 11, 46, 22, 57, 30, 65, 18, 53)(7, 42, 12, 47, 23, 58, 31, 66, 19, 54)(13, 48, 24, 59, 32, 67, 34, 69, 26, 61)(15, 50, 25, 60, 33, 68, 35, 70, 28, 63)(71, 106, 73, 108, 74, 109, 83, 118, 85, 120, 77, 112, 76, 111)(72, 107, 79, 114, 80, 115, 94, 129, 95, 130, 82, 117, 81, 116)(75, 110, 84, 119, 86, 121, 96, 131, 98, 133, 89, 124, 88, 123)(78, 113, 90, 125, 91, 126, 102, 137, 103, 138, 93, 128, 92, 127)(87, 122, 97, 132, 99, 134, 104, 139, 105, 140, 101, 136, 100, 135)
	L = (1, 74)(2, 80)(3, 83)(4, 85)(5, 86)(6, 73)(7, 71)(8, 91)(9, 94)(10, 95)(11, 79)(12, 72)(13, 77)(14, 96)(15, 76)(16, 98)(17, 99)(18, 84)(19, 75)(20, 102)(21, 103)(22, 90)(23, 78)(24, 82)(25, 81)(26, 89)(27, 104)(28, 88)(29, 105)(30, 97)(31, 87)(32, 93)(33, 92)(34, 101)(35, 100)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.265
Graph:: bipartite
	v = 12 e = 70 f = 6
	degree seq :: [ 10^7, 14^5 ]

E27.255 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3, (Y2^-1, Y1), (R * Y3)^2, Y3^-1 * Y2 * Y3^-2, (R * Y2)^2, (Y3^-1, Y1), (R * Y1)^2, Y1^5, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 17, 52, 5, 40)(3, 38, 9, 44, 20, 55, 26, 61, 13, 48)(4, 39, 10, 45, 21, 56, 28, 63, 15, 50)(6, 41, 11, 46, 22, 57, 30, 65, 18, 53)(7, 42, 12, 47, 23, 58, 31, 66, 19, 54)(14, 49, 24, 59, 32, 67, 34, 69, 27, 62)(16, 51, 25, 60, 33, 68, 35, 70, 29, 64)(71, 106, 73, 108, 77, 112, 84, 119, 86, 121, 74, 109, 76, 111)(72, 107, 79, 114, 82, 117, 94, 129, 95, 130, 80, 115, 81, 116)(75, 110, 83, 118, 89, 124, 97, 132, 99, 134, 85, 120, 88, 123)(78, 113, 90, 125, 93, 128, 102, 137, 103, 138, 91, 126, 92, 127)(87, 122, 96, 131, 101, 136, 104, 139, 105, 140, 98, 133, 100, 135)
	L = (1, 74)(2, 80)(3, 76)(4, 84)(5, 85)(6, 86)(7, 71)(8, 91)(9, 81)(10, 94)(11, 95)(12, 72)(13, 88)(14, 73)(15, 97)(16, 77)(17, 98)(18, 99)(19, 75)(20, 92)(21, 102)(22, 103)(23, 78)(24, 79)(25, 82)(26, 100)(27, 83)(28, 104)(29, 89)(30, 105)(31, 87)(32, 90)(33, 93)(34, 96)(35, 101)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.263
Graph:: bipartite
	v = 12 e = 70 f = 6
	degree seq :: [ 10^7, 14^5 ]

E27.256 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1), Y2^-2 * Y3 * Y2^-1, Y1^5, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 17, 52, 5, 40)(3, 38, 9, 44, 20, 55, 27, 62, 14, 49)(4, 39, 10, 45, 21, 56, 29, 64, 16, 51)(6, 41, 11, 46, 22, 57, 30, 65, 18, 53)(7, 42, 12, 47, 23, 58, 31, 66, 19, 54)(13, 48, 24, 59, 32, 67, 34, 69, 26, 61)(15, 50, 25, 60, 33, 68, 35, 70, 28, 63)(71, 106, 73, 108, 83, 118, 74, 109, 77, 112, 85, 120, 76, 111)(72, 107, 79, 114, 94, 129, 80, 115, 82, 117, 95, 130, 81, 116)(75, 110, 84, 119, 96, 131, 86, 121, 89, 124, 98, 133, 88, 123)(78, 113, 90, 125, 102, 137, 91, 126, 93, 128, 103, 138, 92, 127)(87, 122, 97, 132, 104, 139, 99, 134, 101, 136, 105, 140, 100, 135)
	L = (1, 74)(2, 80)(3, 77)(4, 76)(5, 86)(6, 83)(7, 71)(8, 91)(9, 82)(10, 81)(11, 94)(12, 72)(13, 85)(14, 89)(15, 73)(16, 88)(17, 99)(18, 96)(19, 75)(20, 93)(21, 92)(22, 102)(23, 78)(24, 95)(25, 79)(26, 98)(27, 101)(28, 84)(29, 100)(30, 104)(31, 87)(32, 103)(33, 90)(34, 105)(35, 97)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.266
Graph:: bipartite
	v = 12 e = 70 f = 6
	degree seq :: [ 10^7, 14^5 ]

E27.257 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-2, (Y1, Y3), (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y2^-3 * Y3^-1, Y1^5, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 17, 52, 5, 40)(3, 38, 9, 44, 20, 55, 28, 63, 15, 50)(4, 39, 10, 45, 21, 56, 29, 64, 16, 51)(6, 41, 11, 46, 22, 57, 30, 65, 18, 53)(7, 42, 12, 47, 23, 58, 31, 66, 19, 54)(13, 48, 24, 59, 32, 67, 34, 69, 26, 61)(14, 49, 25, 60, 33, 68, 35, 70, 27, 62)(71, 106, 73, 108, 83, 118, 77, 112, 74, 109, 84, 119, 76, 111)(72, 107, 79, 114, 94, 129, 82, 117, 80, 115, 95, 130, 81, 116)(75, 110, 85, 120, 96, 131, 89, 124, 86, 121, 97, 132, 88, 123)(78, 113, 90, 125, 102, 137, 93, 128, 91, 126, 103, 138, 92, 127)(87, 122, 98, 133, 104, 139, 101, 136, 99, 134, 105, 140, 100, 135)
	L = (1, 74)(2, 80)(3, 84)(4, 73)(5, 86)(6, 77)(7, 71)(8, 91)(9, 95)(10, 79)(11, 82)(12, 72)(13, 76)(14, 83)(15, 97)(16, 85)(17, 99)(18, 89)(19, 75)(20, 103)(21, 90)(22, 93)(23, 78)(24, 81)(25, 94)(26, 88)(27, 96)(28, 105)(29, 98)(30, 101)(31, 87)(32, 92)(33, 102)(34, 100)(35, 104)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ), ( 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70, 14, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.262
Graph:: bipartite
	v = 12 e = 70 f = 6
	degree seq :: [ 10^7, 14^5 ]

E27.258 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^2, Y2 * Y1^-3, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y2^-1), Y3^5 * Y1 * Y2^-1, Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-2, Y1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y3^-1, (Y2^-1 * Y3)^35 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 3, 38, 6, 41, 10, 45, 5, 40)(4, 39, 9, 44, 20, 55, 12, 47, 16, 51, 23, 58, 15, 50)(7, 42, 11, 46, 21, 56, 13, 48, 18, 53, 24, 59, 17, 52)(14, 49, 22, 57, 34, 69, 26, 61, 30, 65, 33, 68, 29, 64)(19, 54, 25, 60, 28, 63, 27, 62, 32, 67, 35, 70, 31, 66)(71, 106, 73, 108, 75, 110, 78, 113, 80, 115, 72, 107, 76, 111)(74, 109, 82, 117, 85, 120, 90, 125, 93, 128, 79, 114, 86, 121)(77, 112, 83, 118, 87, 122, 91, 126, 94, 129, 81, 116, 88, 123)(84, 119, 96, 131, 99, 134, 104, 139, 103, 138, 92, 127, 100, 135)(89, 124, 97, 132, 101, 136, 98, 133, 105, 140, 95, 130, 102, 137)
	L = (1, 74)(2, 79)(3, 82)(4, 84)(5, 85)(6, 86)(7, 71)(8, 90)(9, 92)(10, 93)(11, 72)(12, 96)(13, 73)(14, 98)(15, 99)(16, 100)(17, 75)(18, 76)(19, 77)(20, 104)(21, 78)(22, 97)(23, 103)(24, 80)(25, 81)(26, 105)(27, 83)(28, 91)(29, 95)(30, 101)(31, 87)(32, 88)(33, 89)(34, 102)(35, 94)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.261
Graph:: bipartite
	v = 10 e = 70 f = 8
	degree seq :: [ 14^10 ]

E27.259 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-2, (Y3^-1, Y2), (Y3^-1, Y1^-1), (Y3, Y2), (R * Y3)^2, Y1^-2 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y1 * Y3^2 * Y1^-1, Y3 * Y2 * Y1^2 * Y3^-1 * Y1, Y3 * Y1^-2 * Y3^4, (Y1^-1 * Y3^-1)^5, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 6, 41, 3, 38, 9, 44, 5, 40)(4, 39, 10, 45, 20, 55, 16, 51, 12, 47, 22, 57, 15, 50)(7, 42, 11, 46, 21, 56, 18, 53, 13, 48, 23, 58, 17, 52)(14, 49, 24, 59, 34, 69, 30, 65, 26, 61, 33, 68, 29, 64)(19, 54, 25, 60, 28, 63, 32, 67, 27, 62, 35, 70, 31, 66)(71, 106, 73, 108, 72, 107, 79, 114, 78, 113, 75, 110, 76, 111)(74, 109, 82, 117, 80, 115, 92, 127, 90, 125, 85, 120, 86, 121)(77, 112, 83, 118, 81, 116, 93, 128, 91, 126, 87, 122, 88, 123)(84, 119, 96, 131, 94, 129, 103, 138, 104, 139, 99, 134, 100, 135)(89, 124, 97, 132, 95, 130, 105, 140, 98, 133, 101, 136, 102, 137)
	L = (1, 74)(2, 80)(3, 82)(4, 84)(5, 85)(6, 86)(7, 71)(8, 90)(9, 92)(10, 94)(11, 72)(12, 96)(13, 73)(14, 98)(15, 99)(16, 100)(17, 75)(18, 76)(19, 77)(20, 104)(21, 78)(22, 103)(23, 79)(24, 102)(25, 81)(26, 101)(27, 83)(28, 91)(29, 95)(30, 105)(31, 87)(32, 88)(33, 89)(34, 97)(35, 93)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.260
Graph:: bipartite
	v = 10 e = 70 f = 8
	degree seq :: [ 14^10 ]

E27.260 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2^-1), (Y3, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3^-4 * Y1, Y1 * Y3^-1 * Y1 * Y2^-2, Y2^5, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, Y2^-1 * Y3 * Y1^-1 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^35 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 26, 61, 35, 70, 16, 51, 31, 66, 23, 58, 18, 53, 4, 39, 10, 45, 28, 63, 24, 59, 15, 50, 3, 38, 9, 44, 27, 62, 25, 60, 17, 52, 32, 67, 21, 56, 6, 41, 11, 46, 14, 49, 30, 65, 22, 57, 7, 42, 12, 47, 13, 48, 29, 64, 19, 54, 33, 68, 34, 69, 20, 55, 5, 40)(71, 106, 73, 108, 83, 118, 93, 128, 76, 111)(72, 107, 79, 114, 99, 134, 88, 123, 81, 116)(74, 109, 84, 119, 78, 113, 97, 132, 89, 124)(75, 110, 85, 120, 82, 117, 101, 136, 91, 126)(77, 112, 86, 121, 102, 137, 90, 125, 94, 129)(80, 115, 100, 135, 96, 131, 95, 130, 103, 138)(87, 122, 104, 139, 98, 133, 92, 127, 105, 140)
	L = (1, 74)(2, 80)(3, 84)(4, 87)(5, 88)(6, 89)(7, 71)(8, 98)(9, 100)(10, 102)(11, 103)(12, 72)(13, 78)(14, 104)(15, 81)(16, 73)(17, 82)(18, 95)(19, 105)(20, 93)(21, 99)(22, 75)(23, 97)(24, 76)(25, 77)(26, 94)(27, 92)(28, 91)(29, 96)(30, 90)(31, 79)(32, 83)(33, 86)(34, 101)(35, 85)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14^10 ), ( 14^70 ) }
Outer automorphisms :: reflexible
Dual of E27.259
Graph:: bipartite
	v = 8 e = 70 f = 10
	degree seq :: [ 10^7, 70 ]

E27.261 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1 * Y2^2, (Y1, Y2^-1), Y3 * Y1^-1 * Y2^-2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y3)^2, Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y1^-1 * Y2^3, Y3^-2 * Y1^-1 * Y3^-4, Y1^4 * Y3 * Y1^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 22, 57, 31, 66, 19, 54, 7, 42, 12, 47, 14, 49, 25, 60, 34, 69, 32, 67, 21, 56, 15, 50, 3, 38, 9, 44, 23, 58, 29, 64, 33, 68, 27, 62, 16, 51, 6, 41, 11, 46, 17, 52, 26, 61, 35, 70, 28, 63, 20, 55, 13, 48, 4, 39, 10, 45, 24, 59, 30, 65, 18, 53, 5, 40)(71, 106, 73, 108, 83, 118, 82, 117, 76, 111)(72, 107, 79, 114, 74, 109, 84, 119, 81, 116)(75, 110, 85, 120, 90, 125, 77, 112, 86, 121)(78, 113, 93, 128, 80, 115, 95, 130, 87, 122)(88, 123, 91, 126, 98, 133, 89, 124, 97, 132)(92, 127, 99, 134, 94, 129, 104, 139, 96, 131)(100, 135, 102, 137, 105, 140, 101, 136, 103, 138)
	L = (1, 74)(2, 80)(3, 84)(4, 87)(5, 83)(6, 79)(7, 71)(8, 94)(9, 95)(10, 96)(11, 93)(12, 72)(13, 81)(14, 78)(15, 82)(16, 73)(17, 99)(18, 90)(19, 75)(20, 76)(21, 77)(22, 100)(23, 104)(24, 105)(25, 92)(26, 103)(27, 85)(28, 86)(29, 102)(30, 98)(31, 88)(32, 89)(33, 91)(34, 101)(35, 97)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14^10 ), ( 14^70 ) }
Outer automorphisms :: reflexible
Dual of E27.258
Graph:: bipartite
	v = 8 e = 70 f = 10
	degree seq :: [ 10^7, 70 ]

E27.262 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1, (R * Y1)^2, Y1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^2 * Y3^-1 * Y2^-2, Y2^2 * Y3 * Y2^3 * Y3, Y1^7, Y3 * Y1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^7, Y2^35 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 32, 67, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 33, 68, 23, 58, 12, 47)(9, 44, 17, 52, 25, 60, 29, 64, 35, 70, 31, 66, 20, 55)(13, 48, 18, 53, 28, 63, 34, 69, 30, 65, 19, 54, 24, 59)(71, 106, 73, 108, 79, 114, 89, 124, 93, 128, 81, 116, 91, 126, 101, 136, 104, 139, 97, 132, 84, 119, 96, 131, 99, 134, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 100, 135, 103, 138, 92, 127, 102, 137, 105, 140, 98, 133, 86, 121, 76, 111, 85, 120, 95, 130, 83, 118, 75, 110)
	L = (1, 72)(2, 76)(3, 77)(4, 71)(5, 78)(6, 84)(7, 85)(8, 86)(9, 87)(10, 73)(11, 74)(12, 75)(13, 88)(14, 92)(15, 96)(16, 97)(17, 95)(18, 98)(19, 94)(20, 79)(21, 80)(22, 81)(23, 82)(24, 83)(25, 99)(26, 102)(27, 103)(28, 104)(29, 105)(30, 89)(31, 90)(32, 91)(33, 93)(34, 100)(35, 101)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ), ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.257
Graph:: bipartite
	v = 6 e = 70 f = 12
	degree seq :: [ 14^5, 70 ]

E27.263 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y1^-2 * Y3^-1 * Y1^-1, (Y3^-1, Y2), Y2^2 * Y1 * Y2^3, Y2 * Y1^-2 * Y2^-1 * Y3^-1 * Y1^-1, (Y2^-1 * Y3)^5 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 7, 42, 4, 39, 10, 45, 5, 40)(3, 38, 9, 44, 20, 55, 15, 50, 13, 48, 23, 58, 14, 49)(6, 41, 11, 46, 21, 56, 19, 54, 16, 51, 24, 59, 17, 52)(12, 47, 22, 57, 32, 67, 29, 64, 27, 62, 34, 69, 28, 63)(18, 53, 25, 60, 33, 68, 31, 66, 30, 65, 35, 70, 26, 61)(71, 106, 73, 108, 82, 117, 96, 131, 87, 122, 75, 110, 84, 119, 98, 133, 105, 140, 94, 129, 80, 115, 93, 128, 104, 139, 100, 135, 86, 121, 74, 109, 83, 118, 97, 132, 101, 136, 89, 124, 77, 112, 85, 120, 99, 134, 103, 138, 91, 126, 78, 113, 90, 125, 102, 137, 95, 130, 81, 116, 72, 107, 79, 114, 92, 127, 88, 123, 76, 111)
	L = (1, 74)(2, 80)(3, 83)(4, 72)(5, 77)(6, 86)(7, 71)(8, 75)(9, 93)(10, 78)(11, 94)(12, 97)(13, 79)(14, 85)(15, 73)(16, 81)(17, 89)(18, 100)(19, 76)(20, 84)(21, 87)(22, 104)(23, 90)(24, 91)(25, 105)(26, 101)(27, 92)(28, 99)(29, 82)(30, 95)(31, 88)(32, 98)(33, 96)(34, 102)(35, 103)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ), ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.255
Graph:: bipartite
	v = 6 e = 70 f = 12
	degree seq :: [ 14^5, 70 ]

E27.264 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^2, Y1^-3 * Y3, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^4 * Y1^-1 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 8, 43, 4, 39, 7, 42, 11, 46, 5, 40)(3, 38, 9, 44, 20, 55, 13, 48, 15, 50, 23, 58, 14, 49)(6, 41, 10, 45, 21, 56, 16, 51, 19, 54, 25, 60, 17, 52)(12, 47, 22, 57, 32, 67, 26, 61, 28, 63, 34, 69, 27, 62)(18, 53, 24, 59, 33, 68, 29, 64, 31, 66, 35, 70, 30, 65)(71, 106, 73, 108, 82, 117, 94, 129, 80, 115, 72, 107, 79, 114, 92, 127, 103, 138, 91, 126, 78, 113, 90, 125, 102, 137, 99, 134, 86, 121, 74, 109, 83, 118, 96, 131, 101, 136, 89, 124, 77, 112, 85, 120, 98, 133, 105, 140, 95, 130, 81, 116, 93, 128, 104, 139, 100, 135, 87, 122, 75, 110, 84, 119, 97, 132, 88, 123, 76, 111)
	L = (1, 74)(2, 77)(3, 83)(4, 75)(5, 78)(6, 86)(7, 71)(8, 81)(9, 85)(10, 89)(11, 72)(12, 96)(13, 84)(14, 90)(15, 73)(16, 87)(17, 91)(18, 99)(19, 76)(20, 93)(21, 95)(22, 98)(23, 79)(24, 101)(25, 80)(26, 97)(27, 102)(28, 82)(29, 100)(30, 103)(31, 88)(32, 104)(33, 105)(34, 92)(35, 94)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ), ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.253
Graph:: bipartite
	v = 6 e = 70 f = 12
	degree seq :: [ 14^5, 70 ]

E27.265 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3 * Y1, (Y1^-1, Y2^-1), (R * Y3)^2, Y1 * Y3^-3, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, Y2^2 * Y1 * Y2^3 * Y3^-1, Y2^2 * Y3 * Y2 * Y3 * Y2^2, Y1 * Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1^-1 * Y2^2 * Y3^-2 * Y2^2 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 7, 42, 10, 45, 15, 50, 4, 39, 5, 40)(3, 38, 8, 43, 14, 49, 21, 56, 28, 63, 12, 47, 13, 48)(6, 41, 9, 44, 19, 54, 23, 58, 29, 64, 16, 51, 17, 52)(11, 46, 20, 55, 27, 62, 32, 67, 34, 69, 25, 60, 26, 61)(18, 53, 22, 57, 33, 68, 35, 70, 24, 59, 30, 65, 31, 66)(71, 106, 73, 108, 81, 116, 94, 129, 99, 134, 85, 120, 98, 133, 104, 139, 92, 127, 79, 114, 72, 107, 78, 113, 90, 125, 100, 135, 86, 121, 74, 109, 82, 117, 95, 130, 103, 138, 89, 124, 77, 112, 84, 119, 97, 132, 101, 136, 87, 122, 75, 110, 83, 118, 96, 131, 105, 140, 93, 128, 80, 115, 91, 126, 102, 137, 88, 123, 76, 111)
	L = (1, 74)(2, 75)(3, 82)(4, 80)(5, 85)(6, 86)(7, 71)(8, 83)(9, 87)(10, 72)(11, 95)(12, 91)(13, 98)(14, 73)(15, 77)(16, 93)(17, 99)(18, 100)(19, 76)(20, 96)(21, 78)(22, 101)(23, 79)(24, 103)(25, 102)(26, 104)(27, 81)(28, 84)(29, 89)(30, 105)(31, 94)(32, 90)(33, 88)(34, 97)(35, 92)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ), ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.254
Graph:: bipartite
	v = 6 e = 70 f = 12
	degree seq :: [ 14^5, 70 ]

E27.266 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 7, 7, 35})
Quotient :: dipole
Aut^+ = C35 (small group id <35, 1>)
Aut   = D70 (small group id <70, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, Y3^2 * Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (Y2, Y3), (Y2, Y1^-1), (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3^-1, Y2^-5 * Y3 * Y1, (Y2^-1 * Y3)^5 ]
Map:: non-degenerate
	R = (1, 36, 2, 37, 4, 39, 9, 44, 15, 50, 7, 42, 5, 40)(3, 38, 8, 43, 12, 47, 21, 56, 28, 63, 14, 49, 13, 48)(6, 41, 10, 45, 16, 51, 22, 57, 29, 64, 19, 54, 17, 52)(11, 46, 20, 55, 25, 60, 35, 70, 32, 67, 27, 62, 26, 61)(18, 53, 23, 58, 30, 65, 24, 59, 34, 69, 33, 68, 31, 66)(71, 106, 73, 108, 81, 116, 94, 129, 92, 127, 79, 114, 91, 126, 105, 140, 101, 136, 87, 122, 75, 110, 83, 118, 96, 131, 100, 135, 86, 121, 74, 109, 82, 117, 95, 130, 103, 138, 89, 124, 77, 112, 84, 119, 97, 132, 93, 128, 80, 115, 72, 107, 78, 113, 90, 125, 104, 139, 99, 134, 85, 120, 98, 133, 102, 137, 88, 123, 76, 111)
	L = (1, 74)(2, 79)(3, 82)(4, 85)(5, 72)(6, 86)(7, 71)(8, 91)(9, 77)(10, 92)(11, 95)(12, 98)(13, 78)(14, 73)(15, 75)(16, 99)(17, 80)(18, 100)(19, 76)(20, 105)(21, 84)(22, 89)(23, 94)(24, 103)(25, 102)(26, 90)(27, 81)(28, 83)(29, 87)(30, 104)(31, 93)(32, 96)(33, 88)(34, 101)(35, 97)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ), ( 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14, 10, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.256
Graph:: bipartite
	v = 6 e = 70 f = 12
	degree seq :: [ 14^5, 70 ]

E27.267 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {6, 6, 9, 9})
Quotient :: edge^2
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^-2, (Y2, Y1^-1), R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3^-1, Y3^-3 * Y2^-2, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y2^6, Y1^6, Y3 * Y1 * Y2^-1 * Y3^2 * Y1^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 37, 4, 40, 16, 52, 20, 56, 36, 72, 29, 65, 8, 44, 26, 62, 7, 43)(2, 38, 10, 46, 22, 58, 5, 41, 19, 55, 35, 71, 27, 63, 34, 70, 12, 48)(3, 39, 13, 49, 23, 59, 6, 42, 17, 53, 33, 69, 28, 64, 31, 67, 14, 50)(9, 45, 18, 54, 32, 68, 11, 47, 30, 66, 24, 60, 21, 57, 15, 51, 25, 61)(73, 74, 80, 99, 92, 77)(75, 81, 100, 93, 78, 83)(76, 85, 98, 103, 108, 89)(79, 96, 101, 104, 88, 97)(82, 90, 106, 87, 91, 102)(84, 95, 107, 86, 94, 105)(109, 111, 116, 136, 128, 114)(110, 117, 135, 129, 113, 119)(112, 123, 134, 138, 144, 126)(115, 120, 137, 143, 124, 130)(118, 125, 142, 121, 127, 139)(122, 133, 141, 132, 131, 140)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 36^6 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E27.270
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.268 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {6, 6, 9, 9})
Quotient :: edge^2
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1), Y2^-1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y2^6, Y1^6 ]
Map:: non-degenerate
	R = (1, 37, 4, 40, 16, 52, 8, 44, 29, 65, 36, 72, 20, 56, 26, 62, 7, 43)(2, 38, 10, 46, 30, 66, 27, 63, 35, 71, 22, 58, 5, 41, 19, 55, 12, 48)(3, 39, 13, 49, 34, 70, 28, 64, 32, 68, 23, 59, 6, 42, 17, 53, 14, 50)(9, 45, 18, 54, 24, 60, 21, 57, 15, 51, 33, 69, 11, 47, 31, 67, 25, 61)(73, 74, 80, 99, 92, 77)(75, 81, 100, 93, 78, 83)(76, 85, 101, 104, 98, 89)(79, 96, 88, 105, 108, 97)(82, 90, 107, 87, 91, 103)(84, 95, 102, 86, 94, 106)(109, 111, 116, 136, 128, 114)(110, 117, 135, 129, 113, 119)(112, 123, 137, 139, 134, 126)(115, 120, 124, 138, 144, 130)(118, 125, 143, 121, 127, 140)(122, 133, 142, 132, 131, 141)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 36^6 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E27.269
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.269 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {6, 6, 9, 9})
Quotient :: loop^2
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^-2, (Y2, Y1^-1), R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3^-1, Y3^-3 * Y2^-2, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y2^6, Y1^6, Y3 * Y1 * Y2^-1 * Y3^2 * Y1^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 37, 73, 109, 4, 40, 76, 112, 16, 52, 88, 124, 20, 56, 92, 128, 36, 72, 108, 144, 29, 65, 101, 137, 8, 44, 80, 116, 26, 62, 98, 134, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 22, 58, 94, 130, 5, 41, 77, 113, 19, 55, 91, 127, 35, 71, 107, 143, 27, 63, 99, 135, 34, 70, 106, 142, 12, 48, 84, 120)(3, 39, 75, 111, 13, 49, 85, 121, 23, 59, 95, 131, 6, 42, 78, 114, 17, 53, 89, 125, 33, 69, 105, 141, 28, 64, 100, 136, 31, 67, 103, 139, 14, 50, 86, 122)(9, 45, 81, 117, 18, 54, 90, 126, 32, 68, 104, 140, 11, 47, 83, 119, 30, 66, 102, 138, 24, 60, 96, 132, 21, 57, 93, 129, 15, 51, 87, 123, 25, 61, 97, 133)
	L = (1, 38)(2, 44)(3, 45)(4, 49)(5, 37)(6, 47)(7, 60)(8, 63)(9, 64)(10, 54)(11, 39)(12, 59)(13, 62)(14, 58)(15, 55)(16, 61)(17, 40)(18, 70)(19, 66)(20, 41)(21, 42)(22, 69)(23, 71)(24, 65)(25, 43)(26, 67)(27, 56)(28, 57)(29, 68)(30, 46)(31, 72)(32, 52)(33, 48)(34, 51)(35, 50)(36, 53)(73, 111)(74, 117)(75, 116)(76, 123)(77, 119)(78, 109)(79, 120)(80, 136)(81, 135)(82, 125)(83, 110)(84, 137)(85, 127)(86, 133)(87, 134)(88, 130)(89, 142)(90, 112)(91, 139)(92, 114)(93, 113)(94, 115)(95, 140)(96, 131)(97, 141)(98, 138)(99, 129)(100, 128)(101, 143)(102, 144)(103, 118)(104, 122)(105, 132)(106, 121)(107, 124)(108, 126)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.268
Transitivity :: VT+
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.270 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {6, 6, 9, 9})
Quotient :: loop^2
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1), Y2^-1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3 * Y2, Y2^6, Y1^6 ]
Map:: non-degenerate
	R = (1, 37, 73, 109, 4, 40, 76, 112, 16, 52, 88, 124, 8, 44, 80, 116, 29, 65, 101, 137, 36, 72, 108, 144, 20, 56, 92, 128, 26, 62, 98, 134, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 30, 66, 102, 138, 27, 63, 99, 135, 35, 71, 107, 143, 22, 58, 94, 130, 5, 41, 77, 113, 19, 55, 91, 127, 12, 48, 84, 120)(3, 39, 75, 111, 13, 49, 85, 121, 34, 70, 106, 142, 28, 64, 100, 136, 32, 68, 104, 140, 23, 59, 95, 131, 6, 42, 78, 114, 17, 53, 89, 125, 14, 50, 86, 122)(9, 45, 81, 117, 18, 54, 90, 126, 24, 60, 96, 132, 21, 57, 93, 129, 15, 51, 87, 123, 33, 69, 105, 141, 11, 47, 83, 119, 31, 67, 103, 139, 25, 61, 97, 133)
	L = (1, 38)(2, 44)(3, 45)(4, 49)(5, 37)(6, 47)(7, 60)(8, 63)(9, 64)(10, 54)(11, 39)(12, 59)(13, 65)(14, 58)(15, 55)(16, 69)(17, 40)(18, 71)(19, 67)(20, 41)(21, 42)(22, 70)(23, 66)(24, 52)(25, 43)(26, 53)(27, 56)(28, 57)(29, 68)(30, 50)(31, 46)(32, 62)(33, 72)(34, 48)(35, 51)(36, 61)(73, 111)(74, 117)(75, 116)(76, 123)(77, 119)(78, 109)(79, 120)(80, 136)(81, 135)(82, 125)(83, 110)(84, 124)(85, 127)(86, 133)(87, 137)(88, 138)(89, 143)(90, 112)(91, 140)(92, 114)(93, 113)(94, 115)(95, 141)(96, 131)(97, 142)(98, 126)(99, 129)(100, 128)(101, 139)(102, 144)(103, 134)(104, 118)(105, 122)(106, 132)(107, 121)(108, 130)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.267
Transitivity :: VT+
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.271 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 6, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1^-2 * Y2^-1, Y1^6, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^6, (R * Y2 * Y3^-1)^2, Y2^2 * Y1^-2 * Y2 * Y1^-2, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 37, 2, 38, 6, 42, 18, 54, 13, 49, 4, 40)(3, 39, 9, 45, 17, 53, 34, 70, 27, 63, 11, 47)(5, 41, 15, 51, 19, 55, 26, 62, 10, 46, 16, 52)(7, 43, 20, 56, 24, 60, 30, 66, 12, 48, 21, 57)(8, 44, 22, 58, 29, 65, 31, 67, 14, 50, 23, 59)(25, 61, 33, 69, 36, 72, 32, 68, 28, 64, 35, 71)(73, 109, 75, 111, 82, 118, 85, 121, 99, 135, 91, 127, 78, 114, 89, 125, 77, 113)(74, 110, 79, 115, 86, 122, 76, 112, 84, 120, 101, 137, 90, 126, 96, 132, 80, 116)(81, 117, 94, 130, 100, 136, 83, 119, 95, 131, 108, 144, 106, 142, 103, 139, 97, 133)(87, 123, 104, 140, 102, 138, 88, 124, 105, 141, 92, 128, 98, 134, 107, 143, 93, 129)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.272 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 6, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y1^2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2, Y1^6, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2^2 * Y1^2 * Y2 * Y1, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 37, 2, 38, 6, 42, 18, 54, 13, 49, 4, 40)(3, 39, 9, 45, 19, 55, 34, 70, 17, 53, 11, 47)(5, 41, 15, 51, 10, 46, 26, 62, 30, 66, 16, 52)(7, 43, 20, 56, 31, 67, 29, 65, 12, 48, 22, 58)(8, 44, 23, 59, 21, 57, 27, 63, 14, 50, 24, 60)(25, 61, 33, 69, 36, 72, 32, 68, 28, 64, 35, 71)(73, 109, 75, 111, 82, 118, 78, 114, 91, 127, 102, 138, 85, 121, 89, 125, 77, 113)(74, 110, 79, 115, 93, 129, 90, 126, 103, 139, 86, 122, 76, 112, 84, 120, 80, 116)(81, 117, 96, 132, 108, 144, 106, 142, 95, 131, 100, 136, 83, 119, 99, 135, 97, 133)(87, 123, 104, 140, 101, 137, 98, 134, 107, 143, 94, 130, 88, 124, 105, 141, 92, 128)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.273 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 6, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1 * Y3 * Y1, (Y2, Y3), Y2^3 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 10, 46, 4, 40, 5, 41)(3, 39, 11, 47, 15, 51, 28, 64, 13, 49, 14, 50)(6, 42, 18, 54, 20, 56, 29, 65, 12, 48, 19, 55)(8, 44, 21, 57, 23, 59, 31, 67, 16, 52, 22, 58)(9, 45, 24, 60, 26, 62, 32, 68, 17, 53, 25, 61)(27, 63, 34, 70, 36, 72, 33, 69, 30, 66, 35, 71)(73, 109, 75, 111, 84, 120, 76, 112, 85, 121, 92, 128, 79, 115, 87, 123, 78, 114)(74, 110, 80, 116, 89, 125, 77, 113, 88, 124, 98, 134, 82, 118, 95, 131, 81, 117)(83, 119, 96, 132, 102, 138, 86, 122, 97, 133, 108, 144, 100, 136, 104, 140, 99, 135)(90, 126, 105, 141, 103, 139, 91, 127, 106, 142, 93, 129, 101, 137, 107, 143, 94, 130)
	L = (1, 76)(2, 77)(3, 85)(4, 79)(5, 82)(6, 84)(7, 73)(8, 88)(9, 89)(10, 74)(11, 86)(12, 92)(13, 87)(14, 100)(15, 75)(16, 95)(17, 98)(18, 91)(19, 101)(20, 78)(21, 94)(22, 103)(23, 80)(24, 97)(25, 104)(26, 81)(27, 102)(28, 83)(29, 90)(30, 108)(31, 93)(32, 96)(33, 106)(34, 107)(35, 105)(36, 99)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.274
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.274 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 6, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1 * Y3 * Y1, (Y2, Y3), Y2^-3 * Y3^-1, (Y3 * Y1^-1)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 10, 46, 4, 40, 5, 41)(3, 39, 11, 47, 15, 51, 28, 64, 13, 49, 14, 50)(6, 42, 19, 55, 12, 48, 29, 65, 16, 52, 20, 56)(8, 44, 21, 57, 24, 60, 32, 68, 17, 53, 23, 59)(9, 45, 25, 61, 22, 58, 30, 66, 18, 54, 26, 62)(27, 63, 34, 70, 36, 72, 33, 69, 31, 67, 35, 71)(73, 109, 75, 111, 84, 120, 79, 115, 87, 123, 88, 124, 76, 112, 85, 121, 78, 114)(74, 110, 80, 116, 94, 130, 82, 118, 96, 132, 90, 126, 77, 113, 89, 125, 81, 117)(83, 119, 98, 134, 108, 144, 100, 136, 97, 133, 103, 139, 86, 122, 102, 138, 99, 135)(91, 127, 105, 141, 104, 140, 101, 137, 107, 143, 95, 131, 92, 128, 106, 142, 93, 129)
	L = (1, 76)(2, 77)(3, 85)(4, 79)(5, 82)(6, 88)(7, 73)(8, 89)(9, 90)(10, 74)(11, 86)(12, 78)(13, 87)(14, 100)(15, 75)(16, 84)(17, 96)(18, 94)(19, 92)(20, 101)(21, 95)(22, 81)(23, 104)(24, 80)(25, 98)(26, 102)(27, 103)(28, 83)(29, 91)(30, 97)(31, 108)(32, 93)(33, 106)(34, 107)(35, 105)(36, 99)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.273
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.275 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y3 * Y2^-3, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 21, 57, 15, 51)(4, 40, 10, 46, 22, 58, 17, 53)(6, 42, 11, 47, 23, 59, 18, 54)(7, 43, 12, 48, 24, 60, 19, 55)(13, 49, 25, 61, 33, 69, 29, 65)(14, 50, 26, 62, 34, 70, 30, 66)(16, 52, 27, 63, 35, 71, 31, 67)(20, 56, 28, 64, 36, 72, 32, 68)(73, 109, 75, 111, 85, 121, 76, 112, 86, 122, 92, 128, 79, 115, 88, 124, 78, 114)(74, 110, 81, 117, 97, 133, 82, 118, 98, 134, 100, 136, 84, 120, 99, 135, 83, 119)(77, 113, 87, 123, 101, 137, 89, 125, 102, 138, 104, 140, 91, 127, 103, 139, 90, 126)(80, 116, 93, 129, 105, 141, 94, 130, 106, 142, 108, 144, 96, 132, 107, 143, 95, 131)
	L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 89)(6, 85)(7, 73)(8, 94)(9, 98)(10, 84)(11, 97)(12, 74)(13, 92)(14, 88)(15, 102)(16, 75)(17, 91)(18, 101)(19, 77)(20, 78)(21, 106)(22, 96)(23, 105)(24, 80)(25, 100)(26, 99)(27, 81)(28, 83)(29, 104)(30, 103)(31, 87)(32, 90)(33, 108)(34, 107)(35, 93)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.279
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 8^9, 18^4 ]

E27.276 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y2, Y3), Y2^3 * Y3, (Y2^-1, Y1^-1), (Y3^-1, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y3, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 21, 57, 15, 51)(4, 40, 10, 46, 22, 58, 17, 53)(6, 42, 11, 47, 23, 59, 19, 55)(7, 43, 12, 48, 24, 60, 20, 56)(13, 49, 25, 61, 33, 69, 29, 65)(14, 50, 26, 62, 34, 70, 30, 66)(16, 52, 27, 63, 35, 71, 31, 67)(18, 54, 28, 64, 36, 72, 32, 68)(73, 109, 75, 111, 85, 121, 79, 115, 88, 124, 90, 126, 76, 112, 86, 122, 78, 114)(74, 110, 81, 117, 97, 133, 84, 120, 99, 135, 100, 136, 82, 118, 98, 134, 83, 119)(77, 113, 87, 123, 101, 137, 92, 128, 103, 139, 104, 140, 89, 125, 102, 138, 91, 127)(80, 116, 93, 129, 105, 141, 96, 132, 107, 143, 108, 144, 94, 130, 106, 142, 95, 131)
	L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 89)(6, 90)(7, 73)(8, 94)(9, 98)(10, 84)(11, 100)(12, 74)(13, 78)(14, 88)(15, 102)(16, 75)(17, 92)(18, 85)(19, 104)(20, 77)(21, 106)(22, 96)(23, 108)(24, 80)(25, 83)(26, 99)(27, 81)(28, 97)(29, 91)(30, 103)(31, 87)(32, 101)(33, 95)(34, 107)(35, 93)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.280
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 8^9, 18^4 ]

E27.277 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-2, (Y1^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, (Y3, Y2), (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-3, Y2 * Y3^3 * Y2 * Y3, (Y1^-1 * Y3^-1)^4 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 3, 39, 8, 44, 11, 47, 19, 55, 17, 53, 6, 42, 5, 41)(4, 40, 9, 45, 12, 48, 22, 58, 26, 62, 34, 70, 33, 69, 16, 52, 15, 51)(7, 43, 10, 46, 13, 49, 23, 59, 27, 63, 30, 66, 35, 71, 20, 56, 18, 54)(14, 50, 24, 60, 28, 64, 36, 72, 21, 57, 25, 61, 29, 65, 32, 68, 31, 67)(73, 109, 75, 111, 83, 119, 89, 125, 77, 113, 74, 110, 80, 116, 91, 127, 78, 114)(76, 112, 84, 120, 98, 134, 105, 141, 87, 123, 81, 117, 94, 130, 106, 142, 88, 124)(79, 115, 85, 121, 99, 135, 107, 143, 90, 126, 82, 118, 95, 131, 102, 138, 92, 128)(86, 122, 100, 136, 93, 129, 101, 137, 103, 139, 96, 132, 108, 144, 97, 133, 104, 140)
	L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 88)(7, 73)(8, 94)(9, 96)(10, 74)(11, 98)(12, 100)(13, 75)(14, 102)(15, 103)(16, 104)(17, 105)(18, 77)(19, 106)(20, 78)(21, 79)(22, 108)(23, 80)(24, 107)(25, 82)(26, 93)(27, 83)(28, 92)(29, 85)(30, 91)(31, 99)(32, 95)(33, 101)(34, 97)(35, 89)(36, 90)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.278
Graph:: bipartite
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.278 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1 * Y3^-2, Y2 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y2^4, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y1^-1 * Y3^-1)^9 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 3, 39, 9, 45, 21, 57, 13, 49, 24, 60, 18, 54, 6, 42, 11, 47, 5, 41)(4, 40, 10, 46, 22, 58, 14, 50, 25, 61, 33, 69, 29, 65, 35, 71, 31, 67, 17, 53, 27, 63, 16, 52)(7, 43, 12, 48, 23, 59, 15, 51, 26, 62, 34, 70, 30, 66, 36, 72, 32, 68, 20, 56, 28, 64, 19, 55)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 81, 117, 96, 132, 83, 119)(76, 112, 86, 122, 101, 137, 89, 125)(77, 113, 80, 116, 93, 129, 90, 126)(79, 115, 87, 123, 102, 138, 92, 128)(82, 118, 97, 133, 107, 143, 99, 135)(84, 120, 98, 134, 108, 144, 100, 136)(88, 124, 94, 130, 105, 141, 103, 139)(91, 127, 95, 131, 106, 142, 104, 140)
	L = (1, 76)(2, 82)(3, 86)(4, 84)(5, 88)(6, 89)(7, 73)(8, 94)(9, 97)(10, 95)(11, 99)(12, 74)(13, 101)(14, 98)(15, 75)(16, 79)(17, 100)(18, 103)(19, 77)(20, 78)(21, 105)(22, 87)(23, 80)(24, 107)(25, 106)(26, 81)(27, 91)(28, 83)(29, 108)(30, 85)(31, 92)(32, 90)(33, 102)(34, 93)(35, 104)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18^8 ), ( 18^24 ) }
Outer automorphisms :: reflexible
Dual of E27.277
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 8^9, 24^3 ]

E27.279 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^2 * Y3^-1 * Y1, (Y3^-1, Y2), (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3^-1, (Y3^-1 * Y1^-1)^9 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 4, 40, 10, 46, 19, 55, 7, 43, 12, 48, 5, 41)(3, 39, 9, 45, 22, 58, 14, 50, 25, 61, 32, 68, 16, 52, 26, 62, 15, 51)(6, 42, 11, 47, 23, 59, 17, 53, 27, 63, 34, 70, 21, 57, 29, 65, 18, 54)(13, 49, 24, 60, 35, 71, 30, 66, 36, 72, 33, 69, 20, 56, 28, 64, 31, 67)(73, 109, 75, 111, 85, 121, 89, 125, 76, 112, 86, 122, 102, 138, 93, 129, 79, 115, 88, 124, 92, 128, 78, 114)(74, 110, 81, 117, 96, 132, 99, 135, 82, 118, 97, 133, 108, 144, 101, 137, 84, 120, 98, 134, 100, 136, 83, 119)(77, 113, 87, 123, 103, 139, 95, 131, 80, 116, 94, 130, 107, 143, 106, 142, 91, 127, 104, 140, 105, 141, 90, 126)
	L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 80)(6, 89)(7, 73)(8, 91)(9, 97)(10, 84)(11, 99)(12, 74)(13, 102)(14, 88)(15, 94)(16, 75)(17, 93)(18, 95)(19, 77)(20, 85)(21, 78)(22, 104)(23, 106)(24, 108)(25, 98)(26, 81)(27, 101)(28, 96)(29, 83)(30, 92)(31, 107)(32, 87)(33, 103)(34, 90)(35, 105)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.275
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.280 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 9, 9, 12})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (Y1^-1, Y3), (Y2^-1, Y1^-1), Y3^-1 * Y1^-3, (R * Y2)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, Y2^3 * Y3^-1 * Y2, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 7, 43, 12, 48, 17, 53, 4, 40, 10, 46, 5, 41)(3, 39, 9, 45, 22, 58, 16, 52, 26, 62, 32, 68, 14, 50, 25, 61, 15, 51)(6, 42, 11, 47, 23, 59, 21, 57, 29, 65, 33, 69, 18, 54, 27, 63, 19, 55)(13, 49, 24, 60, 34, 70, 20, 56, 28, 64, 35, 71, 30, 66, 36, 72, 31, 67)(73, 109, 75, 111, 85, 121, 90, 126, 76, 112, 86, 122, 102, 138, 93, 129, 79, 115, 88, 124, 92, 128, 78, 114)(74, 110, 81, 117, 96, 132, 99, 135, 82, 118, 97, 133, 108, 144, 101, 137, 84, 120, 98, 134, 100, 136, 83, 119)(77, 113, 87, 123, 103, 139, 105, 141, 89, 125, 104, 140, 107, 143, 95, 131, 80, 116, 94, 130, 106, 142, 91, 127)
	L = (1, 76)(2, 82)(3, 86)(4, 79)(5, 89)(6, 90)(7, 73)(8, 77)(9, 97)(10, 84)(11, 99)(12, 74)(13, 102)(14, 88)(15, 104)(16, 75)(17, 80)(18, 93)(19, 105)(20, 85)(21, 78)(22, 87)(23, 91)(24, 108)(25, 98)(26, 81)(27, 101)(28, 96)(29, 83)(30, 92)(31, 107)(32, 94)(33, 95)(34, 103)(35, 106)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.276
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.281 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), Y3^-2 * Y2 * Y3^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (Y3, Y1), (R * Y3)^2, Y1^4, Y2^3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 21, 57, 15, 51)(4, 40, 10, 46, 23, 59, 17, 53)(6, 42, 11, 47, 13, 49, 19, 55)(7, 43, 12, 48, 24, 60, 20, 56)(14, 50, 25, 61, 34, 70, 31, 67)(16, 52, 26, 62, 36, 72, 32, 68)(18, 54, 27, 63, 29, 65, 33, 69)(22, 58, 28, 64, 30, 66, 35, 71)(73, 109, 75, 111, 85, 121, 80, 116, 93, 129, 78, 114)(74, 110, 81, 117, 91, 127, 77, 113, 87, 123, 83, 119)(76, 112, 86, 122, 101, 137, 95, 131, 106, 142, 90, 126)(79, 115, 88, 124, 102, 138, 96, 132, 108, 144, 94, 130)(82, 118, 97, 133, 105, 141, 89, 125, 103, 139, 99, 135)(84, 120, 98, 134, 107, 143, 92, 128, 104, 140, 100, 136)
	L = (1, 76)(2, 82)(3, 86)(4, 88)(5, 89)(6, 90)(7, 73)(8, 95)(9, 97)(10, 98)(11, 99)(12, 74)(13, 101)(14, 102)(15, 103)(16, 75)(17, 104)(18, 79)(19, 105)(20, 77)(21, 106)(22, 78)(23, 108)(24, 80)(25, 107)(26, 81)(27, 84)(28, 83)(29, 96)(30, 85)(31, 100)(32, 87)(33, 92)(34, 94)(35, 91)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.287
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 8^9, 12^6 ]

E27.282 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), Y3^2 * Y2 * Y3, (R * Y1)^2, (R * Y2)^2, (Y3, Y1), Y1^4, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-2 * Y2^-3, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-2, (Y3 * Y2^-1)^9 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 22, 58, 15, 51)(4, 40, 10, 46, 23, 59, 18, 54)(6, 42, 11, 47, 13, 49, 20, 56)(7, 43, 12, 48, 24, 60, 21, 57)(14, 50, 25, 61, 36, 72, 31, 67)(16, 52, 26, 62, 34, 70, 32, 68)(17, 53, 27, 63, 30, 66, 33, 69)(19, 55, 28, 64, 29, 65, 35, 71)(73, 109, 75, 111, 85, 121, 80, 116, 94, 130, 78, 114)(74, 110, 81, 117, 92, 128, 77, 113, 87, 123, 83, 119)(76, 112, 86, 122, 101, 137, 95, 131, 108, 144, 91, 127)(79, 115, 88, 124, 102, 138, 96, 132, 106, 142, 89, 125)(82, 118, 97, 133, 107, 143, 90, 126, 103, 139, 100, 136)(84, 120, 98, 134, 105, 141, 93, 129, 104, 140, 99, 135)
	L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 95)(9, 97)(10, 99)(11, 100)(12, 74)(13, 101)(14, 79)(15, 103)(16, 75)(17, 78)(18, 105)(19, 106)(20, 107)(21, 77)(22, 108)(23, 102)(24, 80)(25, 84)(26, 81)(27, 83)(28, 104)(29, 88)(30, 85)(31, 93)(32, 87)(33, 92)(34, 94)(35, 98)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.288
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 8^9, 12^6 ]

E27.283 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2), (Y2, Y3), (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1 * Y1^-1, Y1^2 * Y2^-3, Y1^-6, Y1^6, (Y2^-1 * Y3)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 5, 41)(3, 39, 9, 45, 23, 59, 32, 68, 20, 56, 14, 50)(4, 40, 10, 46, 24, 60, 31, 67, 19, 55, 7, 43)(6, 42, 11, 47, 12, 48, 25, 61, 30, 66, 18, 54)(13, 49, 26, 62, 35, 71, 34, 70, 29, 65, 15, 51)(16, 52, 27, 63, 28, 64, 36, 72, 33, 69, 21, 57)(73, 109, 75, 111, 84, 120, 80, 116, 95, 131, 102, 138, 89, 125, 92, 128, 78, 114)(74, 110, 81, 117, 97, 133, 94, 130, 104, 140, 90, 126, 77, 113, 86, 122, 83, 119)(76, 112, 85, 121, 100, 136, 96, 132, 107, 143, 105, 141, 91, 127, 101, 137, 88, 124)(79, 115, 87, 123, 99, 135, 82, 118, 98, 134, 108, 144, 103, 139, 106, 142, 93, 129)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 96)(9, 98)(10, 80)(11, 99)(12, 100)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 101)(21, 78)(22, 103)(23, 107)(24, 94)(25, 108)(26, 95)(27, 84)(28, 97)(29, 86)(30, 105)(31, 89)(32, 106)(33, 90)(34, 92)(35, 104)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.285
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.284 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2), Y2^-3 * Y1^-2, Y1 * Y2 * Y3 * Y2^2 * Y3, Y1^6, (Y3^-1 * Y1^-1)^4, (Y2^-1 * Y3)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 5, 41)(3, 39, 9, 45, 20, 56, 27, 63, 31, 67, 14, 50)(4, 40, 10, 46, 23, 59, 34, 70, 19, 55, 7, 43)(6, 42, 11, 47, 24, 60, 29, 65, 12, 48, 18, 54)(13, 49, 25, 61, 33, 69, 36, 72, 32, 68, 15, 51)(16, 52, 26, 62, 35, 71, 30, 66, 28, 64, 21, 57)(73, 109, 75, 111, 84, 120, 89, 125, 103, 139, 96, 132, 80, 116, 92, 128, 78, 114)(74, 110, 81, 117, 90, 126, 77, 113, 86, 122, 101, 137, 94, 130, 99, 135, 83, 119)(76, 112, 85, 121, 100, 136, 91, 127, 104, 140, 107, 143, 95, 131, 105, 141, 88, 124)(79, 115, 87, 123, 102, 138, 106, 142, 108, 144, 98, 134, 82, 118, 97, 133, 93, 129)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 95)(9, 97)(10, 80)(11, 98)(12, 100)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 105)(21, 78)(22, 106)(23, 94)(24, 107)(25, 92)(26, 96)(27, 108)(28, 90)(29, 102)(30, 84)(31, 104)(32, 86)(33, 99)(34, 89)(35, 101)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.286
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 12^6, 18^4 ]

E27.285 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), Y3^3 * Y2^-1, Y1^-2 * Y3 * Y1^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (Y3^-1, Y1), (R * Y1)^2, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y1^2 * Y2^-1 * Y1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 4, 40, 10, 46, 22, 58, 16, 52, 26, 62, 15, 51, 3, 39, 9, 45, 21, 57, 14, 50, 25, 61, 34, 70, 31, 67, 36, 72, 30, 66, 13, 49, 24, 60, 33, 69, 29, 65, 35, 71, 32, 68, 20, 56, 28, 64, 18, 54, 6, 42, 11, 47, 23, 59, 17, 53, 27, 63, 19, 55, 7, 43, 12, 48, 5, 41)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 81, 117, 96, 132, 83, 119)(76, 112, 86, 122, 101, 137, 89, 125)(77, 113, 87, 123, 102, 138, 90, 126)(79, 115, 88, 124, 103, 139, 92, 128)(80, 116, 93, 129, 105, 141, 95, 131)(82, 118, 97, 133, 107, 143, 99, 135)(84, 120, 98, 134, 108, 144, 100, 136)(91, 127, 94, 130, 106, 142, 104, 140)
	L = (1, 76)(2, 82)(3, 86)(4, 88)(5, 80)(6, 89)(7, 73)(8, 94)(9, 97)(10, 98)(11, 99)(12, 74)(13, 101)(14, 103)(15, 93)(16, 75)(17, 79)(18, 95)(19, 77)(20, 78)(21, 106)(22, 87)(23, 91)(24, 107)(25, 108)(26, 81)(27, 84)(28, 83)(29, 92)(30, 105)(31, 85)(32, 90)(33, 104)(34, 102)(35, 100)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.283
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.286 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2 * Y3^-2, (Y1, Y3^-1), (R * Y2)^2, (Y2^-1, Y1^-1), Y3^3 * Y2^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y3^2 * Y1 * Y3, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y2^2 * Y3^-1 * Y1^-2, Y2^2 * Y3^-1 * Y1 * Y2^2 * Y3^-1 * Y1 * Y2^2 * Y3^-1 * Y1 * Y2 * Y3, Y3^-1 * Y1^31 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 23, 59, 35, 71, 34, 70, 18, 54, 31, 67, 15, 51, 3, 39, 9, 45, 24, 60, 22, 58, 32, 68, 17, 53, 4, 40, 10, 46, 25, 61, 13, 49, 28, 64, 21, 57, 7, 43, 12, 48, 27, 63, 14, 50, 29, 65, 20, 56, 6, 42, 11, 47, 26, 62, 16, 52, 30, 66, 36, 72, 33, 69, 19, 55, 5, 41)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 81, 117, 100, 136, 83, 119)(76, 112, 86, 122, 105, 141, 90, 126)(77, 113, 87, 123, 97, 133, 92, 128)(79, 115, 88, 124, 95, 131, 94, 130)(80, 116, 96, 132, 93, 129, 98, 134)(82, 118, 101, 137, 91, 127, 103, 139)(84, 120, 102, 138, 107, 143, 104, 140)(89, 125, 99, 135, 108, 144, 106, 142)
	L = (1, 76)(2, 82)(3, 86)(4, 88)(5, 89)(6, 90)(7, 73)(8, 97)(9, 101)(10, 102)(11, 103)(12, 74)(13, 105)(14, 95)(15, 99)(16, 75)(17, 98)(18, 79)(19, 104)(20, 106)(21, 77)(22, 78)(23, 85)(24, 92)(25, 108)(26, 87)(27, 80)(28, 91)(29, 107)(30, 81)(31, 84)(32, 83)(33, 94)(34, 93)(35, 100)(36, 96)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 18, 12, 18, 12, 18, 12, 18 ), ( 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18, 12, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.284
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.287 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (R * Y1)^2, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y2^-2 * Y1^-3, Y1 * Y2 * Y1 * Y2 * Y1 * Y3, Y1^-1 * Y2^3 * Y1^-1 * Y2, Y2^-2 * Y1^5 * Y3, (Y2^-1 * Y3)^4, Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 34, 70, 31, 67, 30, 66, 17, 53, 5, 41)(3, 39, 9, 45, 23, 59, 21, 57, 16, 52, 28, 64, 36, 72, 32, 68, 14, 50)(4, 40, 10, 46, 24, 60, 20, 56, 29, 65, 12, 48, 26, 62, 19, 55, 7, 43)(6, 42, 11, 47, 25, 61, 35, 71, 33, 69, 15, 51, 13, 49, 27, 63, 18, 54)(73, 109, 75, 111, 84, 120, 97, 133, 80, 116, 95, 131, 91, 127, 105, 141, 106, 142, 88, 124, 76, 112, 85, 121, 102, 138, 108, 144, 96, 132, 90, 126, 77, 113, 86, 122, 101, 137, 83, 119, 74, 110, 81, 117, 98, 134, 107, 143, 94, 130, 93, 129, 79, 115, 87, 123, 103, 139, 100, 136, 82, 118, 99, 135, 89, 125, 104, 140, 92, 128, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 96)(9, 99)(10, 80)(11, 100)(12, 102)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 106)(21, 78)(22, 92)(23, 90)(24, 94)(25, 108)(26, 89)(27, 95)(28, 97)(29, 103)(30, 98)(31, 84)(32, 105)(33, 86)(34, 101)(35, 104)(36, 107)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.281
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.288 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3^-1), (Y2^-1, Y1^-1), (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y3^-4 * Y1^-1, Y2 * Y1 * Y2^3, Y2^-2 * Y1 * Y3 * Y1, Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1 * Y3^-1, Y2 * Y3^2 * Y2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 26, 62, 17, 53, 25, 61, 32, 68, 20, 56, 5, 41)(3, 39, 9, 45, 27, 63, 24, 60, 31, 67, 34, 70, 36, 72, 19, 55, 15, 51)(4, 40, 10, 46, 13, 49, 23, 59, 22, 58, 7, 43, 12, 48, 28, 64, 18, 54)(6, 42, 11, 47, 16, 52, 30, 66, 35, 71, 33, 69, 14, 50, 29, 65, 21, 57)(73, 109, 75, 111, 85, 121, 93, 129, 77, 113, 87, 123, 82, 118, 101, 137, 92, 128, 91, 127, 76, 112, 86, 122, 104, 140, 108, 144, 90, 126, 105, 141, 97, 133, 106, 142, 100, 136, 107, 143, 89, 125, 103, 139, 84, 120, 102, 138, 98, 134, 96, 132, 79, 115, 88, 124, 80, 116, 99, 135, 94, 130, 83, 119, 74, 110, 81, 117, 95, 131, 78, 114)
	L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 85)(9, 101)(10, 97)(11, 87)(12, 74)(13, 104)(14, 103)(15, 105)(16, 75)(17, 94)(18, 98)(19, 107)(20, 100)(21, 108)(22, 77)(23, 92)(24, 78)(25, 79)(26, 95)(27, 93)(28, 80)(29, 106)(30, 81)(31, 83)(32, 84)(33, 96)(34, 88)(35, 99)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.282
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.289 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2), Y1^4, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2)^2, Y2 * Y1 * Y2 * Y3 * Y1, Y3^-1 * Y1^2 * Y2^-2, Y2^-1 * Y3^4, (Y3^-2 * Y2^-1)^3, Y2^9, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 23, 59, 15, 51)(4, 40, 10, 46, 22, 58, 18, 54)(6, 42, 11, 47, 14, 50, 20, 56)(7, 43, 12, 48, 13, 49, 21, 57)(16, 52, 25, 61, 29, 65, 32, 68)(17, 53, 26, 62, 35, 71, 33, 69)(19, 55, 27, 63, 31, 67, 34, 70)(24, 60, 28, 64, 30, 66, 36, 72)(73, 109, 75, 111, 85, 121, 101, 137, 96, 132, 89, 125, 103, 139, 94, 130, 78, 114)(74, 110, 81, 117, 93, 129, 104, 140, 100, 136, 98, 134, 106, 142, 90, 126, 83, 119)(76, 112, 86, 122, 80, 116, 95, 131, 79, 115, 88, 124, 102, 138, 107, 143, 91, 127)(77, 113, 87, 123, 84, 120, 97, 133, 108, 144, 105, 141, 99, 135, 82, 118, 92, 128)
	L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 94)(9, 92)(10, 98)(11, 99)(12, 74)(13, 80)(14, 103)(15, 83)(16, 75)(17, 88)(18, 105)(19, 96)(20, 106)(21, 77)(22, 107)(23, 78)(24, 79)(25, 81)(26, 97)(27, 100)(28, 84)(29, 95)(30, 85)(31, 102)(32, 87)(33, 104)(34, 108)(35, 101)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.291
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 8^9, 18^4 ]

E27.290 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^2, (Y3^-1, Y1^-1), Y1^4, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1), Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-2 * Y1, Y2^-2 * Y1^-2 * Y3 * Y2^-2, (Y3 * Y2^-1)^6, Y2^2 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 9, 45, 21, 57, 14, 50)(4, 40, 10, 46, 22, 58, 16, 52)(6, 42, 11, 47, 23, 59, 18, 54)(7, 43, 12, 48, 24, 60, 19, 55)(13, 49, 25, 61, 34, 70, 30, 66)(15, 51, 26, 62, 36, 72, 32, 68)(17, 53, 27, 63, 29, 65, 33, 69)(20, 56, 28, 64, 31, 67, 35, 71)(73, 109, 75, 111, 85, 121, 101, 137, 94, 130, 96, 132, 108, 144, 92, 128, 78, 114)(74, 110, 81, 117, 97, 133, 105, 141, 88, 124, 91, 127, 104, 140, 100, 136, 83, 119)(76, 112, 79, 115, 87, 123, 103, 139, 95, 131, 80, 116, 93, 129, 106, 142, 89, 125)(77, 113, 86, 122, 102, 138, 99, 135, 82, 118, 84, 120, 98, 134, 107, 143, 90, 126)
	L = (1, 76)(2, 82)(3, 79)(4, 78)(5, 88)(6, 89)(7, 73)(8, 94)(9, 84)(10, 83)(11, 99)(12, 74)(13, 87)(14, 91)(15, 75)(16, 90)(17, 92)(18, 105)(19, 77)(20, 106)(21, 96)(22, 95)(23, 101)(24, 80)(25, 98)(26, 81)(27, 100)(28, 102)(29, 103)(30, 104)(31, 85)(32, 86)(33, 107)(34, 108)(35, 97)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.292
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 8^9, 18^4 ]

E27.291 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-2, Y2^-1 * Y3^-1 * Y2^-2, Y2 * Y3 * Y2^2, (R * Y2)^2, (Y3, Y2^-1), (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y1^6, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 20, 56, 17, 53, 5, 41)(3, 39, 9, 45, 21, 57, 31, 67, 27, 63, 14, 50)(4, 40, 10, 46, 22, 58, 30, 66, 19, 55, 7, 43)(6, 42, 11, 47, 23, 59, 32, 68, 29, 65, 18, 54)(12, 48, 16, 52, 25, 61, 34, 70, 35, 71, 26, 62)(13, 49, 24, 60, 33, 69, 36, 72, 28, 64, 15, 51)(73, 109, 75, 111, 84, 120, 79, 115, 87, 123, 90, 126, 77, 113, 86, 122, 98, 134, 91, 127, 100, 136, 101, 137, 89, 125, 99, 135, 107, 143, 102, 138, 108, 144, 104, 140, 92, 128, 103, 139, 106, 142, 94, 130, 105, 141, 95, 131, 80, 116, 93, 129, 97, 133, 82, 118, 96, 132, 83, 119, 74, 110, 81, 117, 88, 124, 76, 112, 85, 121, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 94)(9, 96)(10, 80)(11, 97)(12, 78)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 84)(19, 77)(20, 102)(21, 105)(22, 92)(23, 106)(24, 93)(25, 95)(26, 90)(27, 100)(28, 86)(29, 98)(30, 89)(31, 108)(32, 107)(33, 103)(34, 104)(35, 101)(36, 99)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.289
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.292 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 9, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (Y2^-1, Y1^-1), (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1 * Y2^2 * Y3, Y2^-2 * Y3^-1 * Y2^-1 * Y1^-2, Y1^6, Y2^-2 * Y1^2 * Y3 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 5, 41)(3, 39, 9, 45, 23, 59, 36, 72, 34, 70, 14, 50)(4, 40, 10, 46, 24, 60, 30, 66, 19, 55, 7, 43)(6, 42, 11, 47, 25, 61, 33, 69, 31, 67, 18, 54)(12, 48, 26, 62, 21, 57, 16, 52, 28, 64, 32, 68)(13, 49, 27, 63, 20, 56, 29, 65, 35, 71, 15, 51)(73, 109, 75, 111, 84, 120, 102, 138, 101, 137, 83, 119, 74, 110, 81, 117, 98, 134, 91, 127, 107, 143, 97, 133, 80, 116, 95, 131, 93, 129, 79, 115, 87, 123, 105, 141, 94, 130, 108, 144, 88, 124, 76, 112, 85, 121, 103, 139, 89, 125, 106, 142, 100, 136, 82, 118, 99, 135, 90, 126, 77, 113, 86, 122, 104, 140, 96, 132, 92, 128, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 96)(9, 99)(10, 80)(11, 100)(12, 103)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 108)(21, 78)(22, 102)(23, 92)(24, 94)(25, 104)(26, 90)(27, 95)(28, 97)(29, 106)(30, 89)(31, 98)(32, 105)(33, 84)(34, 107)(35, 86)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ), ( 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18, 8, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.290
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.293 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^2 * Y1^-1 * Y2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^-1 * Y3^-3 * Y2^-1 * Y3^-1, Y3^-2 * Y2 * Y3^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, (Y1^-1 * Y3 * Y2^-1 * Y3)^18 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 16, 52)(6, 42, 10, 46, 18, 54)(7, 43, 11, 47, 19, 55)(12, 48, 22, 58, 29, 65)(14, 50, 23, 59, 30, 66)(15, 51, 24, 60, 31, 67)(17, 53, 25, 61, 33, 69)(20, 56, 26, 62, 34, 70)(21, 57, 27, 63, 32, 68)(28, 64, 35, 71, 36, 72)(73, 109, 75, 111, 82, 118, 74, 110, 80, 116, 90, 126, 77, 113, 85, 121, 78, 114)(76, 112, 84, 120, 97, 133, 81, 117, 94, 130, 105, 141, 88, 124, 101, 137, 89, 125)(79, 115, 86, 122, 98, 134, 83, 119, 95, 131, 106, 142, 91, 127, 102, 138, 92, 128)(87, 123, 100, 136, 93, 129, 96, 132, 107, 143, 99, 135, 103, 139, 108, 144, 104, 140)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 88)(6, 89)(7, 73)(8, 94)(9, 96)(10, 97)(11, 74)(12, 100)(13, 101)(14, 75)(15, 102)(16, 103)(17, 104)(18, 105)(19, 77)(20, 78)(21, 79)(22, 107)(23, 80)(24, 86)(25, 93)(26, 82)(27, 83)(28, 92)(29, 108)(30, 85)(31, 95)(32, 91)(33, 99)(34, 90)(35, 98)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 24, 72, 24, 72, 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.306
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.294 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^-3 * Y1^-1, (Y2, Y3), (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, Y3^3 * Y2^-1 * Y3 * Y1^-1, Y3^-4 * Y2^-2, Y2 * Y3^2 * Y1 * Y2 * Y3^2 * Y1 * Y2 * Y3^2 * Y1 * Y2 * Y3^2, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 12, 48)(7, 43, 11, 47, 19, 55)(13, 49, 22, 58, 31, 67)(15, 51, 23, 59, 32, 68)(16, 52, 24, 60, 33, 69)(18, 54, 25, 61, 28, 64)(20, 56, 26, 62, 29, 65)(21, 57, 27, 63, 34, 70)(30, 66, 35, 71, 36, 72)(73, 109, 75, 111, 84, 120, 77, 113, 86, 122, 82, 118, 74, 110, 80, 116, 78, 114)(76, 112, 85, 121, 100, 136, 89, 125, 103, 139, 97, 133, 81, 117, 94, 130, 90, 126)(79, 115, 87, 123, 101, 137, 91, 127, 104, 140, 98, 134, 83, 119, 95, 131, 92, 128)(88, 124, 102, 138, 93, 129, 105, 141, 108, 144, 106, 142, 96, 132, 107, 143, 99, 135)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 94)(9, 96)(10, 97)(11, 74)(12, 100)(13, 102)(14, 103)(15, 75)(16, 95)(17, 105)(18, 99)(19, 77)(20, 78)(21, 79)(22, 107)(23, 80)(24, 104)(25, 106)(26, 82)(27, 83)(28, 93)(29, 84)(30, 92)(31, 108)(32, 86)(33, 87)(34, 91)(35, 98)(36, 101)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 24, 72, 24, 72, 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.308
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.295 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^3 * Y1^-1, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (Y2, Y3^-1), Y3^-3 * Y2 * Y3^-1, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y1^-1, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 13, 49)(4, 40, 9, 45, 16, 52)(6, 42, 10, 46, 18, 54)(7, 43, 11, 47, 19, 55)(12, 48, 22, 58, 29, 65)(14, 50, 23, 59, 30, 66)(15, 51, 24, 60, 31, 67)(17, 53, 25, 61, 32, 68)(20, 56, 26, 62, 33, 69)(21, 57, 27, 63, 34, 70)(28, 64, 36, 72, 35, 71)(73, 109, 75, 111, 82, 118, 74, 110, 80, 116, 90, 126, 77, 113, 85, 121, 78, 114)(76, 112, 84, 120, 97, 133, 81, 117, 94, 130, 104, 140, 88, 124, 101, 137, 89, 125)(79, 115, 86, 122, 98, 134, 83, 119, 95, 131, 105, 141, 91, 127, 102, 138, 92, 128)(87, 123, 100, 136, 99, 135, 96, 132, 108, 144, 106, 142, 103, 139, 107, 143, 93, 129)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 88)(6, 89)(7, 73)(8, 94)(9, 96)(10, 97)(11, 74)(12, 100)(13, 101)(14, 75)(15, 86)(16, 103)(17, 93)(18, 104)(19, 77)(20, 78)(21, 79)(22, 108)(23, 80)(24, 95)(25, 99)(26, 82)(27, 83)(28, 98)(29, 107)(30, 85)(31, 102)(32, 106)(33, 90)(34, 91)(35, 92)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 24, 72, 24, 72, 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.305
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.296 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1^-1 * Y2^-3, (Y1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1, Y1^-1), Y3^3 * Y2^-1 * Y3, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, Y1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 12, 48)(7, 43, 11, 47, 19, 55)(13, 49, 22, 58, 31, 67)(15, 51, 23, 59, 32, 68)(16, 52, 24, 60, 33, 69)(18, 54, 25, 61, 28, 64)(20, 56, 26, 62, 29, 65)(21, 57, 27, 63, 34, 70)(30, 66, 35, 71, 36, 72)(73, 109, 75, 111, 84, 120, 77, 113, 86, 122, 82, 118, 74, 110, 80, 116, 78, 114)(76, 112, 85, 121, 100, 136, 89, 125, 103, 139, 97, 133, 81, 117, 94, 130, 90, 126)(79, 115, 87, 123, 101, 137, 91, 127, 104, 140, 98, 134, 83, 119, 95, 131, 92, 128)(88, 124, 102, 138, 106, 142, 105, 141, 108, 144, 99, 135, 96, 132, 107, 143, 93, 129)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 94)(9, 96)(10, 97)(11, 74)(12, 100)(13, 102)(14, 103)(15, 75)(16, 87)(17, 105)(18, 93)(19, 77)(20, 78)(21, 79)(22, 107)(23, 80)(24, 95)(25, 99)(26, 82)(27, 83)(28, 106)(29, 84)(30, 101)(31, 108)(32, 86)(33, 104)(34, 91)(35, 92)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 24, 72, 24, 72, 24, 72 ), ( 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72, 24, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.307
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.297 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (Y2, Y3^-1), (Y3, Y2), (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (Y2, Y3), (R * Y1)^2, Y1^3 * Y3 * Y1, Y2^3 * Y1^-1 * Y2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1, Y2^2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 7, 43, 4, 40, 10, 46, 17, 53, 5, 41)(3, 39, 9, 45, 22, 58, 31, 67, 15, 51, 13, 49, 25, 61, 30, 66, 14, 50)(6, 42, 11, 47, 23, 59, 34, 70, 21, 57, 16, 52, 26, 62, 32, 68, 18, 54)(12, 48, 24, 60, 33, 69, 20, 56, 27, 63, 28, 64, 36, 72, 35, 71, 29, 65)(73, 109, 75, 111, 84, 120, 98, 134, 82, 118, 97, 133, 108, 144, 106, 142, 91, 127, 103, 139, 92, 128, 78, 114)(74, 110, 81, 117, 96, 132, 104, 140, 89, 125, 102, 138, 107, 143, 93, 129, 79, 115, 87, 123, 99, 135, 83, 119)(76, 112, 85, 121, 100, 136, 95, 131, 80, 116, 94, 130, 105, 141, 90, 126, 77, 113, 86, 122, 101, 137, 88, 124)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 89)(9, 97)(10, 80)(11, 98)(12, 100)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 101)(21, 78)(22, 102)(23, 104)(24, 108)(25, 94)(26, 95)(27, 84)(28, 96)(29, 99)(30, 103)(31, 86)(32, 106)(33, 107)(34, 90)(35, 92)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.302
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.298 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (Y1^-1, Y2), (Y2^-1, Y3), (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y1 * Y3^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-3, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 9, 45, 15, 51, 21, 57, 18, 54, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 23, 59, 30, 66, 32, 68, 31, 67, 14, 50, 13, 49)(6, 42, 10, 46, 16, 52, 24, 60, 33, 69, 35, 71, 26, 62, 20, 56, 17, 53)(11, 47, 22, 58, 27, 63, 19, 55, 25, 61, 34, 70, 36, 72, 29, 65, 28, 64)(73, 109, 75, 111, 83, 119, 98, 134, 90, 126, 103, 139, 108, 144, 96, 132, 81, 117, 95, 131, 91, 127, 78, 114)(74, 110, 80, 116, 94, 130, 92, 128, 79, 115, 86, 122, 101, 137, 105, 141, 87, 123, 102, 138, 97, 133, 82, 118)(76, 112, 84, 120, 99, 135, 89, 125, 77, 113, 85, 121, 100, 136, 107, 143, 93, 129, 104, 140, 106, 142, 88, 124)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 74)(6, 88)(7, 73)(8, 95)(9, 93)(10, 96)(11, 99)(12, 102)(13, 80)(14, 75)(15, 90)(16, 105)(17, 82)(18, 77)(19, 106)(20, 78)(21, 79)(22, 91)(23, 104)(24, 107)(25, 108)(26, 89)(27, 97)(28, 94)(29, 83)(30, 103)(31, 85)(32, 86)(33, 98)(34, 101)(35, 92)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.304
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.299 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y3)^2, (Y2, Y3), (R * Y1)^2, (R * Y2)^2, Y1^3 * Y3 * Y1, Y2 * Y1 * Y2^3 * Y3, (Y2^-1 * Y3)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 7, 43, 4, 40, 10, 46, 17, 53, 5, 41)(3, 39, 9, 45, 22, 58, 33, 69, 15, 51, 13, 49, 25, 61, 32, 68, 14, 50)(6, 42, 11, 47, 23, 59, 28, 64, 21, 57, 16, 52, 26, 62, 35, 71, 18, 54)(12, 48, 24, 60, 34, 70, 36, 72, 31, 67, 29, 65, 20, 56, 27, 63, 30, 66)(73, 109, 75, 111, 84, 120, 100, 136, 91, 127, 105, 141, 108, 144, 98, 134, 82, 118, 97, 133, 92, 128, 78, 114)(74, 110, 81, 117, 96, 132, 93, 129, 79, 115, 87, 123, 103, 139, 107, 143, 89, 125, 104, 140, 99, 135, 83, 119)(76, 112, 85, 121, 101, 137, 90, 126, 77, 113, 86, 122, 102, 138, 95, 131, 80, 116, 94, 130, 106, 142, 88, 124)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 89)(9, 97)(10, 80)(11, 98)(12, 101)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 106)(21, 78)(22, 104)(23, 107)(24, 92)(25, 94)(26, 95)(27, 108)(28, 90)(29, 96)(30, 103)(31, 84)(32, 105)(33, 86)(34, 99)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.301
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.300 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3), Y1 * Y3^4, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-2, Y3 * Y2^2 * Y3^2 * Y2^2, (Y2^2 * Y1)^18 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 9, 45, 15, 51, 21, 57, 18, 54, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 23, 59, 28, 64, 30, 66, 29, 65, 14, 50, 13, 49)(6, 42, 10, 46, 16, 52, 24, 60, 31, 67, 35, 71, 33, 69, 20, 56, 17, 53)(11, 47, 22, 58, 26, 62, 36, 72, 34, 70, 32, 68, 19, 55, 25, 61, 27, 63)(73, 109, 75, 111, 83, 119, 96, 132, 81, 117, 95, 131, 108, 144, 105, 141, 90, 126, 101, 137, 91, 127, 78, 114)(74, 110, 80, 116, 94, 130, 103, 139, 87, 123, 100, 136, 106, 142, 92, 128, 79, 115, 86, 122, 97, 133, 82, 118)(76, 112, 84, 120, 98, 134, 107, 143, 93, 129, 102, 138, 104, 140, 89, 125, 77, 113, 85, 121, 99, 135, 88, 124)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 74)(6, 88)(7, 73)(8, 95)(9, 93)(10, 96)(11, 98)(12, 100)(13, 80)(14, 75)(15, 90)(16, 103)(17, 82)(18, 77)(19, 99)(20, 78)(21, 79)(22, 108)(23, 102)(24, 107)(25, 83)(26, 106)(27, 94)(28, 101)(29, 85)(30, 86)(31, 105)(32, 97)(33, 89)(34, 91)(35, 92)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.303
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 18^4, 24^3 ]

E27.301 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y3^3 * Y2^-1, (R * Y3)^2, (Y3, Y2^-1), (R * Y1)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (R * Y2)^2, Y3^-1 * Y2 * Y1^-4, Y1 * Y2 * Y1^2 * Y3 * Y2 * Y1, Y3^2 * Y1^2 * Y3 * Y2^-1 * Y1^-2, (Y1^-1 * Y3^-1)^12 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 15, 51, 28, 64, 35, 71, 31, 67, 13, 49, 27, 63, 33, 69, 19, 55, 6, 42, 11, 47, 25, 61, 20, 56, 7, 43, 12, 48, 26, 62, 16, 52, 4, 40, 10, 46, 24, 60, 14, 50, 3, 39, 9, 45, 23, 59, 34, 70, 21, 57, 30, 66, 36, 72, 32, 68, 17, 53, 29, 65, 18, 54, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 89, 125)(77, 113, 86, 122, 91, 127)(79, 115, 87, 123, 93, 129)(80, 116, 95, 131, 97, 133)(82, 118, 99, 135, 101, 137)(84, 120, 100, 136, 102, 138)(88, 124, 103, 139, 104, 140)(90, 126, 96, 132, 105, 141)(92, 128, 94, 130, 106, 142)(98, 134, 107, 143, 108, 144)
	L = (1, 76)(2, 82)(3, 85)(4, 87)(5, 88)(6, 89)(7, 73)(8, 96)(9, 99)(10, 100)(11, 101)(12, 74)(13, 93)(14, 103)(15, 75)(16, 94)(17, 79)(18, 98)(19, 104)(20, 77)(21, 78)(22, 86)(23, 105)(24, 107)(25, 90)(26, 80)(27, 102)(28, 81)(29, 84)(30, 83)(31, 106)(32, 92)(33, 108)(34, 91)(35, 95)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.299
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.302 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y3^-2 * Y2 * Y3^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y3 * Y1^4, Y3^-2 * Y1^-1 * Y2 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 20, 56, 7, 43, 12, 48, 24, 60, 33, 69, 17, 53, 27, 63, 34, 70, 19, 55, 6, 42, 11, 47, 23, 59, 35, 71, 21, 57, 28, 64, 36, 72, 29, 65, 13, 49, 25, 61, 30, 66, 14, 50, 3, 39, 9, 45, 22, 58, 31, 67, 15, 51, 26, 62, 32, 68, 16, 52, 4, 40, 10, 46, 18, 54, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 89, 125)(77, 113, 86, 122, 91, 127)(79, 115, 87, 123, 93, 129)(80, 116, 94, 130, 95, 131)(82, 118, 97, 133, 99, 135)(84, 120, 98, 134, 100, 136)(88, 124, 101, 137, 105, 141)(90, 126, 102, 138, 106, 142)(92, 128, 103, 139, 107, 143)(96, 132, 104, 140, 108, 144)
	L = (1, 76)(2, 82)(3, 85)(4, 87)(5, 88)(6, 89)(7, 73)(8, 90)(9, 97)(10, 98)(11, 99)(12, 74)(13, 93)(14, 101)(15, 75)(16, 103)(17, 79)(18, 104)(19, 105)(20, 77)(21, 78)(22, 102)(23, 106)(24, 80)(25, 100)(26, 81)(27, 84)(28, 83)(29, 107)(30, 108)(31, 86)(32, 94)(33, 92)(34, 96)(35, 91)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.297
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.303 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (R * Y1)^2, Y3^-3 * Y2^-1, (Y2, Y1), (Y3^-1, Y1^-1), (R * Y2)^2, (Y2, Y3), (R * Y3)^2, Y2^-1 * Y1^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y3^2 * Y1^-3, Y3 * Y2 * Y1^2 * Y3^-1 * Y2^-1 * Y1^-2, (Y2^-1 * Y3)^9, (Y1 * Y2 * Y1 * Y3^-1)^6 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 16, 52, 29, 65, 36, 72, 34, 70, 18, 54, 30, 66, 32, 68, 14, 50, 3, 39, 9, 45, 23, 59, 21, 57, 7, 43, 12, 48, 26, 62, 17, 53, 4, 40, 10, 46, 24, 60, 20, 56, 6, 42, 11, 47, 25, 61, 33, 69, 15, 51, 28, 64, 35, 71, 31, 67, 13, 49, 27, 63, 19, 55, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 90, 126)(77, 113, 86, 122, 92, 128)(79, 115, 87, 123, 88, 124)(80, 116, 95, 131, 97, 133)(82, 118, 99, 135, 102, 138)(84, 120, 100, 136, 101, 137)(89, 125, 103, 139, 106, 142)(91, 127, 104, 140, 96, 132)(93, 129, 105, 141, 94, 130)(98, 134, 107, 143, 108, 144)
	L = (1, 76)(2, 82)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 96)(9, 99)(10, 101)(11, 102)(12, 74)(13, 79)(14, 103)(15, 75)(16, 78)(17, 94)(18, 87)(19, 98)(20, 106)(21, 77)(22, 92)(23, 91)(24, 108)(25, 104)(26, 80)(27, 84)(28, 81)(29, 83)(30, 100)(31, 93)(32, 107)(33, 86)(34, 105)(35, 95)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.300
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.304 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (Y3, Y2^-1), Y3^3 * Y2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (R * Y2)^2, Y1^4 * Y3, Y2^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1, (Y3 * Y2^-1)^9 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 21, 57, 7, 43, 12, 48, 24, 60, 29, 65, 13, 49, 25, 61, 30, 66, 14, 50, 3, 39, 9, 45, 22, 58, 31, 67, 15, 51, 26, 62, 36, 72, 34, 70, 18, 54, 28, 64, 35, 71, 20, 56, 6, 42, 11, 47, 23, 59, 32, 68, 16, 52, 27, 63, 33, 69, 17, 53, 4, 40, 10, 46, 19, 55, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 90, 126)(77, 113, 86, 122, 92, 128)(79, 115, 87, 123, 88, 124)(80, 116, 94, 130, 95, 131)(82, 118, 97, 133, 100, 136)(84, 120, 98, 134, 99, 135)(89, 125, 101, 137, 106, 142)(91, 127, 102, 138, 107, 143)(93, 129, 103, 139, 104, 140)(96, 132, 108, 144, 105, 141)
	L = (1, 76)(2, 82)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 91)(9, 97)(10, 99)(11, 100)(12, 74)(13, 79)(14, 101)(15, 75)(16, 78)(17, 104)(18, 87)(19, 105)(20, 106)(21, 77)(22, 102)(23, 107)(24, 80)(25, 84)(26, 81)(27, 83)(28, 98)(29, 93)(30, 96)(31, 86)(32, 92)(33, 95)(34, 103)(35, 108)(36, 94)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 24, 18, 24, 18, 24 ), ( 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24, 18, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.298
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.305 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1), Y2 * Y1^-1 * Y2^2, Y3^2 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y1), (Y2, Y3), (Y2^-1 * Y3)^3, Y3^-1 * Y1^-1 * Y2^-2 * Y1^-2, Y1^-1 * Y2^-2 * Y3^-1 * Y1^-2, Y3^-1 * Y1^8 * Y2, Y2^2 * Y3^-1 * Y1 * Y2^2 * Y3^-1 * Y1 * Y2^2 * Y3^-1 * Y1 * Y2^2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 15, 51, 28, 64, 35, 71, 33, 69, 17, 53, 29, 65, 18, 54, 5, 41)(3, 39, 9, 45, 23, 59, 21, 57, 30, 66, 36, 72, 32, 68, 16, 52, 4, 40, 10, 46, 24, 60, 14, 50)(6, 42, 11, 47, 25, 61, 20, 56, 7, 43, 12, 48, 26, 62, 34, 70, 31, 67, 13, 49, 27, 63, 19, 55)(73, 109, 75, 111, 83, 119, 74, 110, 81, 117, 97, 133, 80, 116, 95, 131, 92, 128, 94, 130, 93, 129, 79, 115, 87, 123, 102, 138, 84, 120, 100, 136, 108, 144, 98, 134, 107, 143, 104, 140, 106, 142, 105, 141, 88, 124, 103, 139, 89, 125, 76, 112, 85, 121, 101, 137, 82, 118, 99, 135, 90, 126, 96, 132, 91, 127, 77, 113, 86, 122, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 84)(5, 88)(6, 89)(7, 73)(8, 96)(9, 99)(10, 98)(11, 101)(12, 74)(13, 100)(14, 103)(15, 75)(16, 79)(17, 102)(18, 104)(19, 105)(20, 77)(21, 78)(22, 86)(23, 91)(24, 106)(25, 90)(26, 80)(27, 107)(28, 81)(29, 108)(30, 83)(31, 87)(32, 92)(33, 93)(34, 94)(35, 95)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.295
Graph:: bipartite
	v = 4 e = 72 f = 16
	degree seq :: [ 24^3, 72 ]

E27.306 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y1^-1 * Y3 * Y2 * Y3, Y2 * Y3^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (Y3^-1, Y1^-1), (R * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2, Y3^-1 * Y1^-2 * Y2^-2 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y2^-2 * Y3 * Y1 * Y3 * Y1^3, Y2^-1 * Y1^8 * Y3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 29, 65, 35, 71, 33, 69, 15, 51, 28, 64, 18, 54, 5, 41)(3, 39, 9, 45, 23, 59, 16, 52, 4, 40, 10, 46, 24, 60, 21, 57, 30, 66, 36, 72, 32, 68, 14, 50)(6, 42, 11, 47, 25, 61, 34, 70, 31, 67, 13, 49, 27, 63, 20, 56, 7, 43, 12, 48, 26, 62, 19, 55)(73, 109, 75, 111, 85, 121, 101, 137, 82, 118, 98, 134, 90, 126, 104, 140, 106, 142, 94, 130, 88, 124, 79, 115, 87, 123, 102, 138, 83, 119, 74, 110, 81, 117, 99, 135, 107, 143, 96, 132, 91, 127, 77, 113, 86, 122, 103, 139, 89, 125, 76, 112, 84, 120, 100, 136, 108, 144, 97, 133, 80, 116, 95, 131, 92, 128, 105, 141, 93, 129, 78, 114)
	L = (1, 76)(2, 82)(3, 84)(4, 83)(5, 88)(6, 89)(7, 73)(8, 96)(9, 98)(10, 97)(11, 101)(12, 74)(13, 100)(14, 79)(15, 75)(16, 78)(17, 102)(18, 95)(19, 94)(20, 77)(21, 103)(22, 93)(23, 91)(24, 106)(25, 107)(26, 80)(27, 90)(28, 81)(29, 108)(30, 85)(31, 87)(32, 92)(33, 86)(34, 105)(35, 104)(36, 99)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.293
Graph:: bipartite
	v = 4 e = 72 f = 16
	degree seq :: [ 24^3, 72 ]

E27.307 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1 * Y3^-1, Y2 * Y1^-1 * Y2^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (Y3, Y2), (Y1, Y2), Y2^-1 * Y3 * Y1^-4, Y2 * Y3^2 * Y2^-1 * Y1^-1 * Y3, Y3^-1 * Y1^-2 * Y3^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 17, 53, 29, 65, 35, 71, 33, 69, 15, 51, 28, 64, 18, 54, 5, 41)(3, 39, 9, 45, 23, 59, 16, 52, 4, 40, 10, 46, 24, 60, 21, 57, 30, 66, 36, 72, 32, 68, 14, 50)(6, 42, 11, 47, 25, 61, 34, 70, 31, 67, 13, 49, 27, 63, 20, 56, 7, 43, 12, 48, 26, 62, 19, 55)(73, 109, 75, 111, 83, 119, 74, 110, 81, 117, 97, 133, 80, 116, 95, 131, 106, 142, 94, 130, 88, 124, 103, 139, 89, 125, 76, 112, 85, 121, 101, 137, 82, 118, 99, 135, 107, 143, 96, 132, 92, 128, 105, 141, 93, 129, 79, 115, 87, 123, 102, 138, 84, 120, 100, 136, 108, 144, 98, 134, 90, 126, 104, 140, 91, 127, 77, 113, 86, 122, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 84)(5, 88)(6, 89)(7, 73)(8, 96)(9, 99)(10, 98)(11, 101)(12, 74)(13, 100)(14, 103)(15, 75)(16, 79)(17, 102)(18, 95)(19, 94)(20, 77)(21, 78)(22, 93)(23, 92)(24, 91)(25, 107)(26, 80)(27, 90)(28, 81)(29, 108)(30, 83)(31, 87)(32, 106)(33, 86)(34, 105)(35, 104)(36, 97)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.296
Graph:: bipartite
	v = 4 e = 72 f = 16
	degree seq :: [ 24^3, 72 ]

E27.308 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y3, Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1, (Y1, Y2), (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y2^-2 * Y3^2 * Y2^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-2, (Y3^-1 * Y1^-1)^9, Y1 * Y3 * Y1 * Y2^29 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 14, 50, 27, 63, 35, 71, 33, 69, 17, 53, 29, 65, 18, 54, 5, 41)(3, 39, 9, 45, 23, 59, 21, 57, 30, 66, 36, 72, 32, 68, 16, 52, 4, 40, 10, 46, 24, 60, 13, 49)(6, 42, 11, 47, 25, 61, 20, 56, 7, 43, 12, 48, 26, 62, 34, 70, 31, 67, 15, 51, 28, 64, 19, 55)(73, 109, 75, 111, 84, 120, 99, 135, 108, 144, 100, 136, 90, 126, 96, 132, 92, 128, 94, 130, 93, 129, 103, 139, 89, 125, 76, 112, 83, 119, 74, 110, 81, 117, 98, 134, 107, 143, 104, 140, 91, 127, 77, 113, 85, 121, 79, 115, 86, 122, 102, 138, 87, 123, 101, 137, 82, 118, 97, 133, 80, 116, 95, 131, 106, 142, 105, 141, 88, 124, 78, 114)
	L = (1, 76)(2, 82)(3, 83)(4, 87)(5, 88)(6, 89)(7, 73)(8, 96)(9, 97)(10, 100)(11, 101)(12, 74)(13, 78)(14, 75)(15, 99)(16, 103)(17, 102)(18, 104)(19, 105)(20, 77)(21, 79)(22, 85)(23, 92)(24, 91)(25, 90)(26, 80)(27, 81)(28, 107)(29, 108)(30, 84)(31, 86)(32, 106)(33, 93)(34, 94)(35, 95)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.294
Graph:: bipartite
	v = 4 e = 72 f = 16
	degree seq :: [ 24^3, 72 ]

E27.309 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3^-1 * Y2^-1 * Y3^-2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3, Y1), (R * Y2)^2, Y1^-1 * Y2^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 19, 55)(7, 43, 11, 47, 20, 56)(12, 48, 22, 58, 21, 57)(13, 49, 23, 59, 29, 65)(15, 51, 24, 60, 30, 66)(16, 52, 25, 61, 31, 67)(18, 54, 26, 62, 33, 69)(27, 63, 35, 71, 34, 70)(28, 64, 36, 72, 32, 68)(73, 109, 75, 111, 84, 120, 82, 118, 74, 110, 80, 116, 94, 130, 91, 127, 77, 113, 86, 122, 93, 129, 78, 114)(76, 112, 85, 121, 99, 135, 98, 134, 81, 117, 95, 131, 107, 143, 105, 141, 89, 125, 101, 137, 106, 142, 90, 126)(79, 115, 87, 123, 100, 136, 97, 133, 83, 119, 96, 132, 108, 144, 103, 139, 92, 128, 102, 138, 104, 140, 88, 124)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 95)(9, 97)(10, 98)(11, 74)(12, 99)(13, 79)(14, 101)(15, 75)(16, 78)(17, 103)(18, 104)(19, 105)(20, 77)(21, 106)(22, 107)(23, 83)(24, 80)(25, 82)(26, 100)(27, 87)(28, 84)(29, 92)(30, 86)(31, 91)(32, 93)(33, 108)(34, 102)(35, 96)(36, 94)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.316
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 6^12, 24^3 ]

E27.310 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-3, Y3^2 * Y2 * Y3, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y1), (Y2^-1, Y1^-1), Y2^4 * Y1, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-2, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^9 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 19, 55)(7, 43, 11, 47, 20, 56)(12, 48, 21, 57, 26, 62)(13, 49, 22, 58, 29, 65)(15, 51, 23, 59, 30, 66)(16, 52, 24, 60, 31, 67)(18, 54, 25, 61, 33, 69)(27, 63, 34, 70, 36, 72)(28, 64, 32, 68, 35, 71)(73, 109, 75, 111, 84, 120, 91, 127, 77, 113, 86, 122, 98, 134, 82, 118, 74, 110, 80, 116, 93, 129, 78, 114)(76, 112, 85, 121, 99, 135, 105, 141, 89, 125, 101, 137, 108, 144, 97, 133, 81, 117, 94, 130, 106, 142, 90, 126)(79, 115, 87, 123, 100, 136, 103, 139, 92, 128, 102, 138, 107, 143, 96, 132, 83, 119, 95, 131, 104, 140, 88, 124)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 94)(9, 96)(10, 97)(11, 74)(12, 99)(13, 79)(14, 101)(15, 75)(16, 78)(17, 103)(18, 104)(19, 105)(20, 77)(21, 106)(22, 83)(23, 80)(24, 82)(25, 107)(26, 108)(27, 87)(28, 84)(29, 92)(30, 86)(31, 91)(32, 93)(33, 100)(34, 95)(35, 98)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.315
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 6^12, 24^3 ]

E27.311 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (R * Y1)^2, (Y3^-1, Y1), (Y2^-1, Y3^-1), (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^4 * Y1^-1, Y3^3 * Y2 * Y1, Y2 * Y1 * Y3^-2 * Y2^2 * Y3^-1, Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-2, Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 19, 55)(7, 43, 11, 47, 20, 56)(12, 48, 24, 60, 21, 57)(13, 49, 23, 59, 28, 64)(15, 51, 25, 61, 31, 67)(16, 52, 22, 58, 27, 63)(18, 54, 26, 62, 34, 70)(29, 65, 32, 68, 35, 71)(30, 66, 33, 69, 36, 72)(73, 109, 75, 111, 84, 120, 82, 118, 74, 110, 80, 116, 96, 132, 91, 127, 77, 113, 86, 122, 93, 129, 78, 114)(76, 112, 85, 121, 101, 137, 98, 134, 81, 117, 95, 131, 104, 140, 106, 142, 89, 125, 100, 136, 107, 143, 90, 126)(79, 115, 87, 123, 102, 138, 99, 135, 83, 119, 97, 133, 105, 141, 88, 124, 92, 128, 103, 139, 108, 144, 94, 130)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 95)(9, 94)(10, 98)(11, 74)(12, 101)(13, 92)(14, 100)(15, 75)(16, 91)(17, 99)(18, 105)(19, 106)(20, 77)(21, 107)(22, 78)(23, 79)(24, 104)(25, 80)(26, 108)(27, 82)(28, 83)(29, 103)(30, 84)(31, 86)(32, 87)(33, 96)(34, 102)(35, 97)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.314
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 6^12, 24^3 ]

E27.312 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y3^-1, Y1), (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, Y2^-1 * Y3^-3 * Y1, Y2^4 * Y1, Y3^2 * Y1 * Y2^-1 * Y3 * Y2^-2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 14, 50)(4, 40, 9, 45, 17, 53)(6, 42, 10, 46, 19, 55)(7, 43, 11, 47, 20, 56)(12, 48, 21, 57, 28, 64)(13, 49, 24, 60, 23, 59)(15, 51, 25, 61, 31, 67)(16, 52, 26, 62, 22, 58)(18, 54, 27, 63, 34, 70)(29, 65, 35, 71, 32, 68)(30, 66, 36, 72, 33, 69)(73, 109, 75, 111, 84, 120, 91, 127, 77, 113, 86, 122, 100, 136, 82, 118, 74, 110, 80, 116, 93, 129, 78, 114)(76, 112, 85, 121, 101, 137, 106, 142, 89, 125, 95, 131, 104, 140, 99, 135, 81, 117, 96, 132, 107, 143, 90, 126)(79, 115, 87, 123, 102, 138, 98, 134, 92, 128, 103, 139, 105, 141, 88, 124, 83, 119, 97, 133, 108, 144, 94, 130)
	L = (1, 76)(2, 81)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 96)(9, 98)(10, 99)(11, 74)(12, 101)(13, 83)(14, 95)(15, 75)(16, 82)(17, 94)(18, 105)(19, 106)(20, 77)(21, 107)(22, 78)(23, 79)(24, 92)(25, 80)(26, 91)(27, 102)(28, 104)(29, 97)(30, 84)(31, 86)(32, 87)(33, 100)(34, 108)(35, 103)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 72, 18, 72, 18, 72 ), ( 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.313
Graph:: bipartite
	v = 15 e = 72 f = 5
	degree seq :: [ 6^12, 24^3 ]

E27.313 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3, (Y2^-1, Y3^-1), (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y1 * Y3^4, (Y2 * Y3 * Y2)^2, Y1 * Y2^-2 * Y3 * Y2^-2 * Y3, (Y2^-1 * Y3)^12 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 9, 45, 15, 51, 21, 57, 18, 54, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 23, 59, 30, 66, 32, 68, 31, 67, 14, 50, 13, 49)(6, 42, 10, 46, 16, 52, 24, 60, 33, 69, 26, 62, 36, 72, 20, 56, 17, 53)(11, 47, 22, 58, 27, 63, 35, 71, 19, 55, 25, 61, 34, 70, 29, 65, 28, 64)(73, 109, 75, 111, 83, 119, 98, 134, 93, 129, 104, 140, 97, 133, 82, 118, 74, 110, 80, 116, 94, 130, 108, 144, 90, 126, 103, 139, 106, 142, 88, 124, 76, 112, 84, 120, 99, 135, 92, 128, 79, 115, 86, 122, 101, 137, 96, 132, 81, 117, 95, 131, 107, 143, 89, 125, 77, 113, 85, 121, 100, 136, 105, 141, 87, 123, 102, 138, 91, 127, 78, 114)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 74)(6, 88)(7, 73)(8, 95)(9, 93)(10, 96)(11, 99)(12, 102)(13, 80)(14, 75)(15, 90)(16, 105)(17, 82)(18, 77)(19, 106)(20, 78)(21, 79)(22, 107)(23, 104)(24, 98)(25, 101)(26, 92)(27, 91)(28, 94)(29, 83)(30, 103)(31, 85)(32, 86)(33, 108)(34, 100)(35, 97)(36, 89)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.312
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.314 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1 * Y3, (Y2, Y3^-1), (Y2^-1, Y1^-1), (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-4, Y1^3 * Y3 * Y1, Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-2, (Y2^-1 * Y3)^12 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 7, 43, 4, 40, 10, 46, 17, 53, 5, 41)(3, 39, 9, 45, 22, 58, 31, 67, 15, 51, 13, 49, 24, 60, 30, 66, 14, 50)(6, 42, 11, 47, 23, 59, 34, 70, 21, 57, 16, 52, 25, 61, 33, 69, 18, 54)(12, 48, 20, 56, 26, 62, 35, 71, 29, 65, 27, 63, 32, 68, 36, 72, 28, 64)(73, 109, 75, 111, 84, 120, 90, 126, 77, 113, 86, 122, 100, 136, 105, 141, 89, 125, 102, 138, 108, 144, 97, 133, 82, 118, 96, 132, 104, 140, 88, 124, 76, 112, 85, 121, 99, 135, 93, 129, 79, 115, 87, 123, 101, 137, 106, 142, 91, 127, 103, 139, 107, 143, 95, 131, 80, 116, 94, 130, 98, 134, 83, 119, 74, 110, 81, 117, 92, 128, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 89)(9, 96)(10, 80)(11, 97)(12, 99)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 104)(21, 78)(22, 102)(23, 105)(24, 94)(25, 95)(26, 108)(27, 92)(28, 101)(29, 84)(30, 103)(31, 86)(32, 98)(33, 106)(34, 90)(35, 100)(36, 107)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.311
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.315 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-1, Y3^2 * Y1^-1, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y1)^2, Y1^4 * Y3, Y2^-1 * Y3 * Y2^-3, Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 7, 43, 4, 40, 10, 46, 17, 53, 5, 41)(3, 39, 9, 45, 22, 58, 30, 66, 15, 51, 13, 49, 25, 61, 29, 65, 14, 50)(6, 42, 11, 47, 23, 59, 33, 69, 21, 57, 16, 52, 26, 62, 31, 67, 18, 54)(12, 48, 24, 60, 34, 70, 32, 68, 20, 56, 27, 63, 35, 71, 36, 72, 28, 64)(73, 109, 75, 111, 84, 120, 88, 124, 76, 112, 85, 121, 99, 135, 83, 119, 74, 110, 81, 117, 96, 132, 98, 134, 82, 118, 97, 133, 107, 143, 95, 131, 80, 116, 94, 130, 106, 142, 103, 139, 89, 125, 101, 137, 108, 144, 105, 141, 91, 127, 102, 138, 104, 140, 90, 126, 77, 113, 86, 122, 100, 136, 93, 129, 79, 115, 87, 123, 92, 128, 78, 114)
	L = (1, 76)(2, 82)(3, 85)(4, 74)(5, 79)(6, 88)(7, 73)(8, 89)(9, 97)(10, 80)(11, 98)(12, 99)(13, 81)(14, 87)(15, 75)(16, 83)(17, 91)(18, 93)(19, 77)(20, 84)(21, 78)(22, 101)(23, 103)(24, 107)(25, 94)(26, 95)(27, 96)(28, 92)(29, 102)(30, 86)(31, 105)(32, 100)(33, 90)(34, 108)(35, 106)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.310
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.316 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 9, 12, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2, Y3 * Y1^-2, (R * Y2)^2, (Y1, Y2), (R * Y1)^2, (R * Y3)^2, (Y2, Y3), Y2^3 * Y3^-1 * Y2, Y1 * Y3^4, Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y3^2 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 9, 45, 15, 51, 21, 57, 18, 54, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 23, 59, 27, 63, 29, 65, 28, 64, 14, 50, 13, 49)(6, 42, 10, 46, 16, 52, 24, 60, 30, 66, 34, 70, 32, 68, 20, 56, 17, 53)(11, 47, 22, 58, 26, 62, 35, 71, 36, 72, 33, 69, 31, 67, 19, 55, 25, 61)(73, 109, 75, 111, 83, 119, 88, 124, 76, 112, 84, 120, 98, 134, 102, 138, 87, 123, 99, 135, 108, 144, 104, 140, 90, 126, 100, 136, 103, 139, 89, 125, 77, 113, 85, 121, 97, 133, 82, 118, 74, 110, 80, 116, 94, 130, 96, 132, 81, 117, 95, 131, 107, 143, 106, 142, 93, 129, 101, 137, 105, 141, 92, 128, 79, 115, 86, 122, 91, 127, 78, 114)
	L = (1, 76)(2, 81)(3, 84)(4, 87)(5, 74)(6, 88)(7, 73)(8, 95)(9, 93)(10, 96)(11, 98)(12, 99)(13, 80)(14, 75)(15, 90)(16, 102)(17, 82)(18, 77)(19, 83)(20, 78)(21, 79)(22, 107)(23, 101)(24, 106)(25, 94)(26, 108)(27, 100)(28, 85)(29, 86)(30, 104)(31, 97)(32, 89)(33, 91)(34, 92)(35, 105)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.309
Graph:: bipartite
	v = 5 e = 72 f = 15
	degree seq :: [ 18^4, 72 ]

E27.317 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^-9 * Y1, (Y3 * Y2^-1)^36 ]
Map::
	R = (1, 37, 2, 38, 6, 42, 4, 40)(3, 39, 7, 43, 13, 49, 10, 46)(5, 41, 8, 44, 14, 50, 11, 47)(9, 45, 15, 51, 21, 57, 18, 54)(12, 48, 16, 52, 22, 58, 19, 55)(17, 53, 23, 59, 29, 65, 26, 62)(20, 56, 24, 60, 30, 66, 27, 63)(25, 61, 31, 67, 35, 71, 33, 69)(28, 64, 32, 68, 36, 72, 34, 70)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 104, 140, 96, 132, 88, 124, 80, 116, 74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 108, 144, 102, 138, 94, 130, 86, 122, 78, 114, 85, 121, 93, 129, 101, 137, 107, 143, 106, 142, 99, 135, 91, 127, 83, 119, 76, 112, 82, 118, 90, 126, 98, 134, 105, 141, 100, 136, 92, 128, 84, 120, 77, 113)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.318 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^-9 * Y1^-1, (Y3 * Y2^-1)^36 ]
Map::
	R = (1, 37, 2, 38, 6, 42, 4, 40)(3, 39, 7, 43, 13, 49, 10, 46)(5, 41, 8, 44, 14, 50, 11, 47)(9, 45, 15, 51, 21, 57, 18, 54)(12, 48, 16, 52, 22, 58, 19, 55)(17, 53, 23, 59, 29, 65, 26, 62)(20, 56, 24, 60, 30, 66, 27, 63)(25, 61, 31, 67, 35, 71, 34, 70)(28, 64, 32, 68, 36, 72, 33, 69)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 105, 141, 99, 135, 91, 127, 83, 119, 76, 112, 82, 118, 90, 126, 98, 134, 106, 142, 108, 144, 102, 138, 94, 130, 86, 122, 78, 114, 85, 121, 93, 129, 101, 137, 107, 143, 104, 140, 96, 132, 88, 124, 80, 116, 74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 100, 136, 92, 128, 84, 120, 77, 113)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.319 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, Y2^7 * Y1^-1 * Y2^2 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 5, 41)(3, 39, 7, 43, 10, 46, 11, 47)(6, 42, 8, 44, 12, 48, 13, 49)(9, 45, 15, 51, 18, 54, 19, 55)(14, 50, 16, 52, 20, 56, 21, 57)(17, 53, 23, 59, 26, 62, 27, 63)(22, 58, 24, 60, 28, 64, 29, 65)(25, 61, 31, 67, 33, 69, 34, 70)(30, 66, 32, 68, 35, 71, 36, 72)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 104, 140, 96, 132, 88, 124, 80, 116, 74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 107, 143, 100, 136, 92, 128, 84, 120, 76, 112, 82, 118, 90, 126, 98, 134, 105, 141, 108, 144, 101, 137, 93, 129, 85, 121, 77, 113, 83, 119, 91, 127, 99, 135, 106, 142, 102, 138, 94, 130, 86, 122, 78, 114)
	L = (1, 76)(2, 77)(3, 82)(4, 73)(5, 74)(6, 84)(7, 83)(8, 85)(9, 90)(10, 75)(11, 79)(12, 78)(13, 80)(14, 92)(15, 91)(16, 93)(17, 98)(18, 81)(19, 87)(20, 86)(21, 88)(22, 100)(23, 99)(24, 101)(25, 105)(26, 89)(27, 95)(28, 94)(29, 96)(30, 107)(31, 106)(32, 108)(33, 97)(34, 103)(35, 102)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.320 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, Y2 * Y1 * Y2^-4 * Y1^-1 * Y2^3, Y2^-3 * Y1^-1 * Y2^-6 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 4, 40, 5, 41)(3, 39, 7, 43, 10, 46, 11, 47)(6, 42, 8, 44, 12, 48, 13, 49)(9, 45, 15, 51, 18, 54, 19, 55)(14, 50, 16, 52, 20, 56, 21, 57)(17, 53, 23, 59, 26, 62, 27, 63)(22, 58, 24, 60, 28, 64, 29, 65)(25, 61, 31, 67, 34, 70, 35, 71)(30, 66, 32, 68, 36, 72, 33, 69)(73, 109, 75, 111, 81, 117, 89, 125, 97, 133, 105, 141, 101, 137, 93, 129, 85, 121, 77, 113, 83, 119, 91, 127, 99, 135, 107, 143, 108, 144, 100, 136, 92, 128, 84, 120, 76, 112, 82, 118, 90, 126, 98, 134, 106, 142, 104, 140, 96, 132, 88, 124, 80, 116, 74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 102, 138, 94, 130, 86, 122, 78, 114)
	L = (1, 76)(2, 77)(3, 82)(4, 73)(5, 74)(6, 84)(7, 83)(8, 85)(9, 90)(10, 75)(11, 79)(12, 78)(13, 80)(14, 92)(15, 91)(16, 93)(17, 98)(18, 81)(19, 87)(20, 86)(21, 88)(22, 100)(23, 99)(24, 101)(25, 106)(26, 89)(27, 95)(28, 94)(29, 96)(30, 108)(31, 107)(32, 105)(33, 104)(34, 97)(35, 103)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 72, 8, 72, 8, 72, 8, 72 ), ( 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 10 e = 72 f = 10
	degree seq :: [ 8^9, 72 ]

E27.321 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2, Y1^3, (Y3, Y2), (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-2 * Y2 * Y3^-4, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 6, 42)(4, 40, 9, 45, 14, 50)(7, 43, 10, 46, 16, 52)(11, 47, 19, 55, 15, 51)(12, 48, 20, 56, 17, 53)(13, 49, 21, 57, 26, 62)(18, 54, 22, 58, 28, 64)(23, 59, 31, 67, 27, 63)(24, 60, 32, 68, 29, 65)(25, 61, 33, 69, 35, 71)(30, 66, 34, 70, 36, 72)(73, 109, 75, 111, 74, 110, 80, 116, 77, 113, 78, 114)(76, 112, 83, 119, 81, 117, 91, 127, 86, 122, 87, 123)(79, 115, 84, 120, 82, 118, 92, 128, 88, 124, 89, 125)(85, 121, 95, 131, 93, 129, 103, 139, 98, 134, 99, 135)(90, 126, 96, 132, 94, 130, 104, 140, 100, 136, 101, 137)(97, 133, 106, 142, 105, 141, 108, 144, 107, 143, 102, 138)
	L = (1, 76)(2, 81)(3, 83)(4, 85)(5, 86)(6, 87)(7, 73)(8, 91)(9, 93)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 99)(16, 77)(17, 78)(18, 79)(19, 103)(20, 80)(21, 105)(22, 82)(23, 106)(24, 84)(25, 96)(26, 107)(27, 102)(28, 88)(29, 89)(30, 90)(31, 108)(32, 92)(33, 104)(34, 94)(35, 101)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 72^6 ), ( 72^12 ) }
Outer automorphisms :: reflexible
Dual of E27.332
Graph:: bipartite
	v = 18 e = 72 f = 2
	degree seq :: [ 6^12, 12^6 ]

E27.322 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (Y2^-1, Y3^-1), (Y2 * Y1^-1)^2, Y3^-2 * Y2^-1 * Y3^2 * Y2, Y3^-4 * Y2 * Y3^-2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y2^-1 * Y3)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 6, 42, 9, 45)(4, 40, 8, 44, 14, 50)(7, 43, 10, 46, 16, 52)(11, 47, 15, 51, 20, 56)(12, 48, 17, 53, 21, 57)(13, 49, 19, 55, 26, 62)(18, 54, 22, 58, 28, 64)(23, 59, 27, 63, 32, 68)(24, 60, 29, 65, 33, 69)(25, 61, 31, 67, 36, 72)(30, 66, 34, 70, 35, 71)(73, 109, 75, 111, 77, 113, 81, 117, 74, 110, 78, 114)(76, 112, 83, 119, 86, 122, 92, 128, 80, 116, 87, 123)(79, 115, 84, 120, 88, 124, 93, 129, 82, 118, 89, 125)(85, 121, 95, 131, 98, 134, 104, 140, 91, 127, 99, 135)(90, 126, 96, 132, 100, 136, 105, 141, 94, 130, 101, 137)(97, 133, 107, 143, 108, 144, 106, 142, 103, 139, 102, 138)
	L = (1, 76)(2, 80)(3, 83)(4, 85)(5, 86)(6, 87)(7, 73)(8, 91)(9, 92)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 99)(16, 77)(17, 78)(18, 79)(19, 103)(20, 104)(21, 81)(22, 82)(23, 107)(24, 84)(25, 96)(26, 108)(27, 102)(28, 88)(29, 89)(30, 90)(31, 101)(32, 106)(33, 93)(34, 94)(35, 100)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 72^6 ), ( 72^12 ) }
Outer automorphisms :: reflexible
Dual of E27.331
Graph:: bipartite
	v = 18 e = 72 f = 2
	degree seq :: [ 6^12, 12^6 ]

E27.323 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y3 * Y1^3, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (Y1, Y2^-1), Y2^5 * Y1^-1 * Y2, Y3 * Y2^3 * Y1 * Y2^3 * Y1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 5, 41)(3, 39, 8, 44, 17, 53, 12, 48, 20, 56, 13, 49)(6, 42, 10, 46, 18, 54, 14, 50, 21, 57, 15, 51)(11, 47, 19, 55, 29, 65, 24, 60, 32, 68, 25, 61)(16, 52, 22, 58, 30, 66, 26, 62, 33, 69, 27, 63)(23, 59, 31, 67, 35, 71, 34, 70, 36, 72, 28, 64)(73, 109, 75, 111, 83, 119, 95, 131, 94, 130, 82, 118, 74, 110, 80, 116, 91, 127, 103, 139, 102, 138, 90, 126, 79, 115, 89, 125, 101, 137, 107, 143, 98, 134, 86, 122, 76, 112, 84, 120, 96, 132, 106, 142, 105, 141, 93, 129, 81, 117, 92, 128, 104, 140, 108, 144, 99, 135, 87, 123, 77, 113, 85, 121, 97, 133, 100, 136, 88, 124, 78, 114)
	L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 79)(6, 86)(7, 77)(8, 92)(9, 74)(10, 93)(11, 96)(12, 75)(13, 89)(14, 78)(15, 90)(16, 98)(17, 85)(18, 87)(19, 104)(20, 80)(21, 82)(22, 105)(23, 106)(24, 83)(25, 101)(26, 88)(27, 102)(28, 107)(29, 97)(30, 99)(31, 108)(32, 91)(33, 94)(34, 95)(35, 100)(36, 103)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.328
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.324 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y1^3, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y2, Y1^-1), Y2^2 * Y1 * Y2^4 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 4, 40, 9, 45, 5, 41)(3, 39, 8, 44, 17, 53, 12, 48, 20, 56, 13, 49)(6, 42, 10, 46, 18, 54, 14, 50, 21, 57, 15, 51)(11, 47, 19, 55, 29, 65, 24, 60, 31, 67, 25, 61)(16, 52, 22, 58, 30, 66, 26, 62, 32, 68, 27, 63)(23, 59, 28, 64, 33, 69, 34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 99, 135, 87, 123, 77, 113, 85, 121, 97, 133, 107, 143, 104, 140, 93, 129, 81, 117, 92, 128, 103, 139, 108, 144, 98, 134, 86, 122, 76, 112, 84, 120, 96, 132, 106, 142, 102, 138, 90, 126, 79, 115, 89, 125, 101, 137, 105, 141, 94, 130, 82, 118, 74, 110, 80, 116, 91, 127, 100, 136, 88, 124, 78, 114)
	L = (1, 76)(2, 81)(3, 84)(4, 73)(5, 79)(6, 86)(7, 77)(8, 92)(9, 74)(10, 93)(11, 96)(12, 75)(13, 89)(14, 78)(15, 90)(16, 98)(17, 85)(18, 87)(19, 103)(20, 80)(21, 82)(22, 104)(23, 106)(24, 83)(25, 101)(26, 88)(27, 102)(28, 108)(29, 97)(30, 99)(31, 91)(32, 94)(33, 107)(34, 95)(35, 105)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.327
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.325 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1^6, Y2^-6 * Y1, (Y3 * Y2^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 33, 69, 30, 66, 20, 56)(13, 49, 18, 54, 28, 64, 34, 70, 31, 67, 23, 59)(19, 55, 29, 65, 35, 71, 36, 72, 32, 68, 24, 60)(73, 109, 75, 111, 81, 117, 91, 127, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 101, 137, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 107, 143, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 108, 144, 103, 139, 94, 130, 83, 119, 93, 129, 102, 138, 104, 140, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 96, 132, 85, 121, 77, 113)
	L = (1, 74)(2, 78)(3, 79)(4, 73)(5, 80)(6, 86)(7, 87)(8, 88)(9, 89)(10, 75)(11, 76)(12, 77)(13, 90)(14, 83)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 81)(21, 82)(22, 84)(23, 85)(24, 91)(25, 93)(26, 94)(27, 105)(28, 106)(29, 107)(30, 92)(31, 95)(32, 96)(33, 102)(34, 103)(35, 108)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.329
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.326 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1^6, Y1 * Y2^6, (Y3 * Y2^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 6, 42, 14, 50, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 25, 61, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 26, 62, 22, 58, 12, 48)(9, 45, 17, 53, 27, 63, 33, 69, 31, 67, 20, 56)(13, 49, 18, 54, 28, 64, 34, 70, 32, 68, 23, 59)(19, 55, 24, 60, 29, 65, 35, 71, 36, 72, 30, 66)(73, 109, 75, 111, 81, 117, 91, 127, 95, 131, 84, 120, 76, 112, 82, 118, 92, 128, 102, 138, 104, 140, 94, 130, 83, 119, 93, 129, 103, 139, 108, 144, 106, 142, 98, 134, 86, 122, 97, 133, 105, 141, 107, 143, 100, 136, 88, 124, 78, 114, 87, 123, 99, 135, 101, 137, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 96, 132, 85, 121, 77, 113)
	L = (1, 74)(2, 78)(3, 79)(4, 73)(5, 80)(6, 86)(7, 87)(8, 88)(9, 89)(10, 75)(11, 76)(12, 77)(13, 90)(14, 83)(15, 97)(16, 98)(17, 99)(18, 100)(19, 96)(20, 81)(21, 82)(22, 84)(23, 85)(24, 101)(25, 93)(26, 94)(27, 105)(28, 106)(29, 107)(30, 91)(31, 92)(32, 95)(33, 103)(34, 104)(35, 108)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ), ( 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72, 6, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.330
Graph:: bipartite
	v = 7 e = 72 f = 13
	degree seq :: [ 12^6, 72 ]

E27.327 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^3, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (Y2^-1, Y1^-1), (R * Y2)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1^-3 * Y3 * Y2^-1 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 17, 53, 29, 65, 26, 62, 14, 50, 22, 58, 34, 70, 36, 72, 24, 60, 12, 48, 3, 39, 8, 44, 18, 54, 30, 66, 25, 61, 13, 49, 4, 40, 9, 45, 19, 55, 31, 67, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 32, 68, 35, 71, 23, 59, 11, 47, 21, 57, 33, 69, 27, 63, 15, 51, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 83, 119, 86, 122)(77, 113, 84, 120, 88, 124)(79, 115, 90, 126, 92, 128)(81, 117, 93, 129, 94, 130)(85, 121, 95, 131, 98, 134)(87, 123, 96, 132, 100, 136)(89, 125, 102, 138, 104, 140)(91, 127, 105, 141, 106, 142)(97, 133, 107, 143, 101, 137)(99, 135, 108, 144, 103, 139)
	L = (1, 76)(2, 81)(3, 83)(4, 73)(5, 85)(6, 86)(7, 91)(8, 93)(9, 74)(10, 94)(11, 75)(12, 95)(13, 77)(14, 78)(15, 97)(16, 98)(17, 103)(18, 105)(19, 79)(20, 106)(21, 80)(22, 82)(23, 84)(24, 107)(25, 87)(26, 88)(27, 102)(28, 101)(29, 100)(30, 99)(31, 89)(32, 108)(33, 90)(34, 92)(35, 96)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.324
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.328 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^3, (Y1^-1, Y2^-1), Y2 * Y3 * Y2^-1 * Y3, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y2)^2, Y1^-2 * Y2 * Y1^-1 * Y3 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 7, 43, 17, 53, 29, 65, 23, 59, 11, 47, 21, 57, 33, 69, 36, 72, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 32, 68, 25, 61, 13, 49, 4, 40, 9, 45, 19, 55, 31, 67, 24, 60, 12, 48, 3, 39, 8, 44, 18, 54, 30, 66, 35, 71, 26, 62, 14, 50, 22, 58, 34, 70, 27, 63, 15, 51, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 80, 116, 82, 118)(76, 112, 83, 119, 86, 122)(77, 113, 84, 120, 88, 124)(79, 115, 90, 126, 92, 128)(81, 117, 93, 129, 94, 130)(85, 121, 95, 131, 98, 134)(87, 123, 96, 132, 100, 136)(89, 125, 102, 138, 104, 140)(91, 127, 105, 141, 106, 142)(97, 133, 101, 137, 107, 143)(99, 135, 103, 139, 108, 144)
	L = (1, 76)(2, 81)(3, 83)(4, 73)(5, 85)(6, 86)(7, 91)(8, 93)(9, 74)(10, 94)(11, 75)(12, 95)(13, 77)(14, 78)(15, 97)(16, 98)(17, 103)(18, 105)(19, 79)(20, 106)(21, 80)(22, 82)(23, 84)(24, 101)(25, 87)(26, 88)(27, 104)(28, 107)(29, 96)(30, 108)(31, 89)(32, 99)(33, 90)(34, 92)(35, 100)(36, 102)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.323
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.329 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y2 * Y3^-2, (Y3, Y1), (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2 * Y3)^2, (R * Y2)^2, Y2 * Y1^-2 * Y3^-2 * Y1^2, Y1^-1 * Y3 * Y1^-5, (Y1^-1 * Y3^-1)^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 27, 63, 15, 51, 4, 40, 10, 46, 21, 57, 32, 68, 26, 62, 14, 50, 3, 39, 9, 45, 20, 56, 31, 67, 35, 71, 25, 61, 13, 49, 24, 60, 34, 70, 36, 72, 29, 65, 17, 53, 6, 42, 11, 47, 22, 58, 33, 69, 30, 66, 18, 54, 7, 43, 12, 48, 23, 59, 28, 64, 16, 52, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 79, 115)(77, 113, 86, 122, 89, 125)(80, 116, 92, 128, 94, 130)(82, 118, 96, 132, 84, 120)(87, 123, 97, 133, 90, 126)(88, 124, 98, 134, 101, 137)(91, 127, 103, 139, 105, 141)(93, 129, 106, 142, 95, 131)(99, 135, 107, 143, 102, 138)(100, 136, 104, 140, 108, 144)
	L = (1, 76)(2, 82)(3, 85)(4, 75)(5, 87)(6, 79)(7, 73)(8, 93)(9, 96)(10, 81)(11, 84)(12, 74)(13, 78)(14, 97)(15, 86)(16, 99)(17, 90)(18, 77)(19, 104)(20, 106)(21, 92)(22, 95)(23, 80)(24, 83)(25, 89)(26, 107)(27, 98)(28, 91)(29, 102)(30, 88)(31, 108)(32, 103)(33, 100)(34, 94)(35, 101)(36, 105)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.325
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.330 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y2 * Y3^-2, (Y2, Y1), (R * Y2)^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-3 * Y3^-1 * Y1^-3, Y1^-1 * Y3^-1 * Y1^-5, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 19, 55, 30, 66, 18, 54, 7, 43, 12, 48, 23, 59, 33, 69, 29, 65, 17, 53, 6, 42, 11, 47, 22, 58, 32, 68, 35, 71, 25, 61, 13, 49, 24, 60, 34, 70, 36, 72, 26, 62, 14, 50, 3, 39, 9, 45, 20, 56, 31, 67, 27, 63, 15, 51, 4, 40, 10, 46, 21, 57, 28, 64, 16, 52, 5, 41)(73, 109, 75, 111, 78, 114)(74, 110, 81, 117, 83, 119)(76, 112, 85, 121, 79, 115)(77, 113, 86, 122, 89, 125)(80, 116, 92, 128, 94, 130)(82, 118, 96, 132, 84, 120)(87, 123, 97, 133, 90, 126)(88, 124, 98, 134, 101, 137)(91, 127, 103, 139, 104, 140)(93, 129, 106, 142, 95, 131)(99, 135, 107, 143, 102, 138)(100, 136, 108, 144, 105, 141)
	L = (1, 76)(2, 82)(3, 85)(4, 75)(5, 87)(6, 79)(7, 73)(8, 93)(9, 96)(10, 81)(11, 84)(12, 74)(13, 78)(14, 97)(15, 86)(16, 99)(17, 90)(18, 77)(19, 100)(20, 106)(21, 92)(22, 95)(23, 80)(24, 83)(25, 89)(26, 107)(27, 98)(28, 103)(29, 102)(30, 88)(31, 108)(32, 105)(33, 91)(34, 94)(35, 101)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12, 72, 12, 72, 12, 72 ), ( 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72, 12, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.326
Graph:: bipartite
	v = 13 e = 72 f = 7
	degree seq :: [ 6^12, 72 ]

E27.331 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3^-1), Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y1^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1^2, Y2 * Y3^-2 * Y2 * Y3^-1 * Y2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1, Y1^-4 * Y3 * Y1^-1, Y2^5 * Y1^-1, Y1^-1 * Y3^-1 * Y2^2 * Y3^4 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 22, 58, 18, 54, 4, 40, 10, 46, 6, 42, 11, 47, 23, 59, 17, 53, 27, 63, 19, 55, 28, 64, 20, 56, 29, 65, 34, 70, 32, 68, 35, 71, 33, 69, 36, 72, 31, 67, 13, 49, 25, 61, 16, 52, 26, 62, 21, 57, 30, 66, 15, 51, 3, 39, 9, 45, 7, 43, 12, 48, 24, 60, 14, 50, 5, 41)(73, 109, 75, 111, 85, 121, 101, 137, 83, 119, 74, 110, 81, 117, 97, 133, 106, 142, 95, 131, 80, 116, 79, 115, 88, 124, 104, 140, 89, 125, 94, 130, 84, 120, 98, 134, 107, 143, 99, 135, 90, 126, 96, 132, 93, 129, 105, 141, 91, 127, 76, 112, 86, 122, 102, 138, 108, 144, 100, 136, 82, 118, 77, 113, 87, 123, 103, 139, 92, 128, 78, 114)
	L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 78)(9, 77)(10, 99)(11, 100)(12, 74)(13, 102)(14, 94)(15, 96)(16, 75)(17, 101)(18, 95)(19, 104)(20, 105)(21, 79)(22, 83)(23, 92)(24, 80)(25, 87)(26, 81)(27, 106)(28, 107)(29, 108)(30, 84)(31, 93)(32, 85)(33, 88)(34, 103)(35, 97)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.322
Graph:: bipartite
	v = 2 e = 72 f = 18
	degree seq :: [ 72^2 ]

E27.332 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 36, 36})
Quotient :: dipole
Aut^+ = C36 (small group id <36, 2>)
Aut   = D72 (small group id <72, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y1^-1 * Y2 * Y3^-3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3 * Y1^-2, Y2^-1 * Y3^-1 * Y1^-2 * Y3 * Y2^-1, Y1^-4 * Y3^-3 * Y2^-1, Y1^36, Y2^36 ]
Map:: non-degenerate
	R = (1, 37, 2, 38, 8, 44, 23, 59, 35, 71, 34, 70, 20, 56, 7, 43, 12, 48, 26, 62, 14, 50, 27, 63, 19, 55, 30, 66, 22, 58, 32, 68, 15, 51, 3, 39, 9, 45, 6, 42, 11, 47, 25, 61, 17, 53, 29, 65, 16, 52, 28, 64, 21, 57, 31, 67, 18, 54, 4, 40, 10, 46, 24, 60, 36, 72, 33, 69, 13, 49, 5, 41)(73, 109, 75, 111, 85, 121, 104, 140, 108, 144, 102, 138, 82, 118, 99, 135, 90, 126, 98, 134, 93, 129, 79, 115, 88, 124, 106, 142, 89, 125, 95, 131, 83, 119, 74, 110, 81, 117, 77, 113, 87, 123, 105, 141, 94, 130, 96, 132, 91, 127, 76, 112, 86, 122, 103, 139, 84, 120, 100, 136, 92, 128, 101, 137, 107, 143, 97, 133, 80, 116, 78, 114)
	L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 96)(9, 99)(10, 101)(11, 102)(12, 74)(13, 103)(14, 95)(15, 98)(16, 75)(17, 104)(18, 97)(19, 106)(20, 77)(21, 78)(22, 79)(23, 108)(24, 88)(25, 94)(26, 80)(27, 107)(28, 81)(29, 87)(30, 92)(31, 83)(32, 84)(33, 93)(34, 85)(35, 105)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.321
Graph:: bipartite
	v = 2 e = 72 f = 18
	degree seq :: [ 72^2 ]

E27.333 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^19, Y3^38, (Y3 * Y2^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 5, 43)(4, 42, 6, 44)(7, 45, 9, 47)(8, 46, 10, 48)(11, 49, 13, 51)(12, 50, 14, 52)(15, 53, 17, 55)(16, 54, 18, 56)(19, 57, 21, 59)(20, 58, 22, 60)(23, 61, 25, 63)(24, 62, 26, 64)(27, 65, 29, 67)(28, 66, 30, 68)(31, 69, 33, 71)(32, 70, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 83, 121, 87, 125, 91, 129, 95, 133, 99, 137, 103, 141, 107, 145, 111, 149, 112, 150, 108, 146, 104, 142, 100, 138, 96, 134, 92, 130, 88, 126, 84, 122, 80, 118)(78, 116, 81, 119, 85, 123, 89, 127, 93, 131, 97, 135, 101, 139, 105, 143, 109, 147, 113, 151, 114, 152, 110, 148, 106, 144, 102, 140, 98, 136, 94, 132, 90, 128, 86, 124, 82, 120)
	L = (1, 80)(2, 82)(3, 77)(4, 84)(5, 78)(6, 86)(7, 79)(8, 88)(9, 81)(10, 90)(11, 83)(12, 92)(13, 85)(14, 94)(15, 87)(16, 96)(17, 89)(18, 98)(19, 91)(20, 100)(21, 93)(22, 102)(23, 95)(24, 104)(25, 97)(26, 106)(27, 99)(28, 108)(29, 101)(30, 110)(31, 103)(32, 112)(33, 105)(34, 114)(35, 107)(36, 111)(37, 109)(38, 113)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.368
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.334 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-2 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y3^-4 * Y2^-1 * Y3^-5 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 15, 53)(12, 50, 16, 54)(13, 51, 17, 55)(14, 52, 18, 56)(19, 57, 23, 61)(20, 58, 24, 62)(21, 59, 25, 63)(22, 60, 26, 64)(27, 65, 31, 69)(28, 66, 32, 70)(29, 67, 33, 71)(30, 68, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 80, 118, 87, 125, 88, 126, 95, 133, 96, 134, 103, 141, 104, 142, 111, 149, 112, 150, 106, 144, 105, 143, 98, 136, 97, 135, 90, 128, 89, 127, 82, 120, 81, 119)(78, 116, 83, 121, 84, 122, 91, 129, 92, 130, 99, 137, 100, 138, 107, 145, 108, 146, 113, 151, 114, 152, 110, 148, 109, 147, 102, 140, 101, 139, 94, 132, 93, 131, 86, 124, 85, 123)
	L = (1, 80)(2, 84)(3, 87)(4, 88)(5, 79)(6, 77)(7, 91)(8, 92)(9, 83)(10, 78)(11, 95)(12, 96)(13, 81)(14, 82)(15, 99)(16, 100)(17, 85)(18, 86)(19, 103)(20, 104)(21, 89)(22, 90)(23, 107)(24, 108)(25, 93)(26, 94)(27, 111)(28, 112)(29, 97)(30, 98)(31, 113)(32, 114)(33, 101)(34, 102)(35, 106)(36, 105)(37, 110)(38, 109)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.381
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.335 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2 * Y3^-9, (Y3 * Y2^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 15, 53)(12, 50, 16, 54)(13, 51, 17, 55)(14, 52, 18, 56)(19, 57, 23, 61)(20, 58, 24, 62)(21, 59, 25, 63)(22, 60, 26, 64)(27, 65, 31, 69)(28, 66, 32, 70)(29, 67, 33, 71)(30, 68, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 82, 120, 87, 125, 90, 128, 95, 133, 98, 136, 103, 141, 106, 144, 111, 149, 112, 150, 104, 142, 105, 143, 96, 134, 97, 135, 88, 126, 89, 127, 80, 118, 81, 119)(78, 116, 83, 121, 86, 124, 91, 129, 94, 132, 99, 137, 102, 140, 107, 145, 110, 148, 113, 151, 114, 152, 108, 146, 109, 147, 100, 138, 101, 139, 92, 130, 93, 131, 84, 122, 85, 123)
	L = (1, 80)(2, 84)(3, 81)(4, 88)(5, 89)(6, 77)(7, 85)(8, 92)(9, 93)(10, 78)(11, 79)(12, 96)(13, 97)(14, 82)(15, 83)(16, 100)(17, 101)(18, 86)(19, 87)(20, 104)(21, 105)(22, 90)(23, 91)(24, 108)(25, 109)(26, 94)(27, 95)(28, 111)(29, 112)(30, 98)(31, 99)(32, 113)(33, 114)(34, 102)(35, 103)(36, 106)(37, 107)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.379
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.336 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^6 * Y2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 17, 55)(12, 50, 18, 56)(13, 51, 19, 57)(14, 52, 20, 58)(15, 53, 21, 59)(16, 54, 22, 60)(23, 61, 29, 67)(24, 62, 30, 68)(25, 63, 31, 69)(26, 64, 32, 70)(27, 65, 33, 71)(28, 66, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 80, 118, 88, 126, 99, 137, 90, 128, 100, 138, 111, 149, 102, 140, 104, 142, 112, 150, 103, 141, 92, 130, 101, 139, 91, 129, 82, 120, 89, 127, 81, 119)(78, 116, 83, 121, 93, 131, 84, 122, 94, 132, 105, 143, 96, 134, 106, 144, 113, 151, 108, 146, 110, 148, 114, 152, 109, 147, 98, 136, 107, 145, 97, 135, 86, 124, 95, 133, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 87)(6, 77)(7, 94)(8, 96)(9, 93)(10, 78)(11, 99)(12, 100)(13, 79)(14, 102)(15, 81)(16, 82)(17, 105)(18, 106)(19, 83)(20, 108)(21, 85)(22, 86)(23, 111)(24, 104)(25, 89)(26, 103)(27, 91)(28, 92)(29, 113)(30, 110)(31, 95)(32, 109)(33, 97)(34, 98)(35, 112)(36, 101)(37, 114)(38, 107)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.378
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.337 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-3, (Y2, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1, (R * Y2)^2, Y3^-6 * Y2, Y2^-1 * Y3^-3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 17, 55)(12, 50, 18, 56)(13, 51, 19, 57)(14, 52, 20, 58)(15, 53, 21, 59)(16, 54, 22, 60)(23, 61, 29, 67)(24, 62, 30, 68)(25, 63, 31, 69)(26, 64, 32, 70)(27, 65, 33, 71)(28, 66, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 82, 120, 89, 127, 99, 137, 92, 130, 101, 139, 111, 149, 104, 142, 102, 140, 112, 150, 103, 141, 90, 128, 100, 138, 91, 129, 80, 118, 88, 126, 81, 119)(78, 116, 83, 121, 93, 131, 86, 124, 95, 133, 105, 143, 98, 136, 107, 145, 113, 151, 110, 148, 108, 146, 114, 152, 109, 147, 96, 134, 106, 144, 97, 135, 84, 122, 94, 132, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 94)(8, 96)(9, 97)(10, 78)(11, 81)(12, 100)(13, 79)(14, 102)(15, 103)(16, 82)(17, 85)(18, 106)(19, 83)(20, 108)(21, 109)(22, 86)(23, 87)(24, 112)(25, 89)(26, 101)(27, 104)(28, 92)(29, 93)(30, 114)(31, 95)(32, 107)(33, 110)(34, 98)(35, 99)(36, 111)(37, 105)(38, 113)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.373
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.338 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y2^-1 * Y3 * Y2^-3, Y3^4 * Y2^-1 * Y3, Y3 * Y2 * Y3 * Y2 * Y3^2 * Y2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 91, 129, 80, 118, 88, 126, 103, 141, 106, 144, 90, 128, 104, 142, 108, 146, 94, 132, 105, 143, 107, 145, 93, 131, 82, 120, 89, 127, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 99, 137, 84, 122, 96, 134, 109, 147, 112, 150, 98, 136, 110, 148, 114, 152, 102, 140, 111, 149, 113, 151, 101, 139, 86, 124, 97, 135, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 103)(12, 104)(13, 79)(14, 105)(15, 106)(16, 87)(17, 81)(18, 82)(19, 109)(20, 110)(21, 83)(22, 111)(23, 112)(24, 95)(25, 85)(26, 86)(27, 108)(28, 107)(29, 89)(30, 94)(31, 92)(32, 93)(33, 114)(34, 113)(35, 97)(36, 102)(37, 100)(38, 101)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.371
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.339 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y2)^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3 * Y2^4, Y3^-5 * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 93, 131, 82, 120, 89, 127, 103, 141, 106, 144, 94, 132, 105, 143, 107, 145, 90, 128, 104, 142, 108, 146, 91, 129, 80, 118, 88, 126, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 101, 139, 86, 124, 97, 135, 109, 147, 112, 150, 102, 140, 111, 149, 113, 151, 98, 136, 110, 148, 114, 152, 99, 137, 84, 122, 96, 134, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 92)(12, 104)(13, 79)(14, 106)(15, 107)(16, 108)(17, 81)(18, 82)(19, 100)(20, 110)(21, 83)(22, 112)(23, 113)(24, 114)(25, 85)(26, 86)(27, 87)(28, 94)(29, 89)(30, 93)(31, 103)(32, 105)(33, 95)(34, 102)(35, 97)(36, 101)(37, 109)(38, 111)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.376
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.340 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y2 * Y3^-3, Y2^2 * Y3^-1 * Y2^3, Y3 * Y2^2 * Y3^2 * Y2^2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 103, 141, 91, 129, 80, 118, 88, 126, 104, 142, 108, 146, 94, 132, 90, 128, 106, 144, 107, 145, 93, 131, 82, 120, 89, 127, 105, 143, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 109, 147, 99, 137, 84, 122, 96, 134, 110, 148, 114, 152, 102, 140, 98, 136, 112, 150, 113, 151, 101, 139, 86, 124, 97, 135, 111, 149, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 104)(12, 106)(13, 79)(14, 89)(15, 94)(16, 103)(17, 81)(18, 82)(19, 110)(20, 112)(21, 83)(22, 97)(23, 102)(24, 109)(25, 85)(26, 86)(27, 108)(28, 107)(29, 87)(30, 105)(31, 92)(32, 93)(33, 114)(34, 113)(35, 95)(36, 111)(37, 100)(38, 101)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.369
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.341 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2 * Y3^3, Y2^-1 * Y3^-1 * Y2^-4, Y2 * Y3^-1 * Y2^2 * Y3^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 103, 141, 93, 131, 82, 120, 89, 127, 105, 143, 107, 145, 90, 128, 94, 132, 106, 144, 108, 146, 91, 129, 80, 118, 88, 126, 104, 142, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 109, 147, 101, 139, 86, 124, 97, 135, 111, 149, 113, 151, 98, 136, 102, 140, 112, 150, 114, 152, 99, 137, 84, 122, 96, 134, 110, 148, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 104)(12, 94)(13, 79)(14, 93)(15, 107)(16, 108)(17, 81)(18, 82)(19, 110)(20, 102)(21, 83)(22, 101)(23, 113)(24, 114)(25, 85)(26, 86)(27, 92)(28, 106)(29, 87)(30, 89)(31, 103)(32, 105)(33, 100)(34, 112)(35, 95)(36, 97)(37, 109)(38, 111)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.374
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.342 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-2, (Y2, Y3^-1), Y2 * Y1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y3^-1 * Y2^6, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 17, 55)(12, 50, 18, 56)(13, 51, 19, 57)(14, 52, 20, 58)(15, 53, 21, 59)(16, 54, 22, 60)(23, 61, 29, 67)(24, 62, 30, 68)(25, 63, 31, 69)(26, 64, 32, 70)(27, 65, 33, 71)(28, 66, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 99, 137, 103, 141, 91, 129, 80, 118, 88, 126, 100, 138, 111, 149, 112, 150, 102, 140, 90, 128, 82, 120, 89, 127, 101, 139, 104, 142, 92, 130, 81, 119)(78, 116, 83, 121, 93, 131, 105, 143, 109, 147, 97, 135, 84, 122, 94, 132, 106, 144, 113, 151, 114, 152, 108, 146, 96, 134, 86, 124, 95, 133, 107, 145, 110, 148, 98, 136, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 94)(8, 96)(9, 97)(10, 78)(11, 100)(12, 82)(13, 79)(14, 81)(15, 102)(16, 103)(17, 106)(18, 86)(19, 83)(20, 85)(21, 108)(22, 109)(23, 111)(24, 89)(25, 87)(26, 92)(27, 112)(28, 99)(29, 113)(30, 95)(31, 93)(32, 98)(33, 114)(34, 105)(35, 101)(36, 104)(37, 107)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.372
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.343 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-1 * Y3, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^3 * Y3 * Y2^3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 17, 55)(12, 50, 18, 56)(13, 51, 19, 57)(14, 52, 20, 58)(15, 53, 21, 59)(16, 54, 22, 60)(23, 61, 29, 67)(24, 62, 30, 68)(25, 63, 31, 69)(26, 64, 32, 70)(27, 65, 33, 71)(28, 66, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 99, 137, 104, 142, 92, 130, 82, 120, 89, 127, 101, 139, 111, 149, 112, 150, 102, 140, 90, 128, 80, 118, 88, 126, 100, 138, 103, 141, 91, 129, 81, 119)(78, 116, 83, 121, 93, 131, 105, 143, 110, 148, 98, 136, 86, 124, 95, 133, 107, 145, 113, 151, 114, 152, 108, 146, 96, 134, 84, 122, 94, 132, 106, 144, 109, 147, 97, 135, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 89)(5, 90)(6, 77)(7, 94)(8, 95)(9, 96)(10, 78)(11, 100)(12, 101)(13, 79)(14, 82)(15, 102)(16, 81)(17, 106)(18, 107)(19, 83)(20, 86)(21, 108)(22, 85)(23, 103)(24, 111)(25, 87)(26, 92)(27, 112)(28, 91)(29, 109)(30, 113)(31, 93)(32, 98)(33, 114)(34, 97)(35, 99)(36, 104)(37, 105)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.367
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.344 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y3^2 * Y2^-1, Y2^-1 * Y3^-1 * Y2^-4 * Y3^-1, Y2^-1 * Y3^-8 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 103, 141, 108, 146, 94, 132, 91, 129, 80, 118, 88, 126, 104, 142, 107, 145, 93, 131, 82, 120, 89, 127, 90, 128, 105, 143, 106, 144, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 109, 147, 114, 152, 102, 140, 99, 137, 84, 122, 96, 134, 110, 148, 113, 151, 101, 139, 86, 124, 97, 135, 98, 136, 111, 149, 112, 150, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 104)(12, 105)(13, 79)(14, 87)(15, 89)(16, 94)(17, 81)(18, 82)(19, 110)(20, 111)(21, 83)(22, 95)(23, 97)(24, 102)(25, 85)(26, 86)(27, 107)(28, 106)(29, 103)(30, 108)(31, 92)(32, 93)(33, 113)(34, 112)(35, 109)(36, 114)(37, 100)(38, 101)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.382
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.345 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y3 * Y2 * Y3^2, Y3 * Y2^-1 * Y3 * Y2^-4, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 103, 141, 106, 144, 90, 128, 93, 131, 82, 120, 89, 127, 104, 142, 107, 145, 91, 129, 80, 118, 88, 126, 94, 132, 105, 143, 108, 146, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 109, 147, 112, 150, 98, 136, 101, 139, 86, 124, 97, 135, 110, 148, 113, 151, 99, 137, 84, 122, 96, 134, 102, 140, 111, 149, 114, 152, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 94)(12, 93)(13, 79)(14, 92)(15, 106)(16, 107)(17, 81)(18, 82)(19, 102)(20, 101)(21, 83)(22, 100)(23, 112)(24, 113)(25, 85)(26, 86)(27, 105)(28, 87)(29, 89)(30, 108)(31, 103)(32, 104)(33, 111)(34, 95)(35, 97)(36, 114)(37, 109)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.377
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.346 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y2^-1 * Y3 * Y2^-1 * Y3^4, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 94, 132, 104, 142, 105, 143, 107, 145, 91, 129, 80, 118, 88, 126, 93, 131, 82, 120, 89, 127, 103, 141, 108, 146, 106, 144, 90, 128, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 102, 140, 110, 148, 111, 149, 113, 151, 99, 137, 84, 122, 96, 134, 101, 139, 86, 124, 97, 135, 109, 147, 114, 152, 112, 150, 98, 136, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 93)(12, 92)(13, 79)(14, 105)(15, 106)(16, 107)(17, 81)(18, 82)(19, 101)(20, 100)(21, 83)(22, 111)(23, 112)(24, 113)(25, 85)(26, 86)(27, 87)(28, 89)(29, 103)(30, 104)(31, 108)(32, 94)(33, 95)(34, 97)(35, 109)(36, 110)(37, 114)(38, 102)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.380
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.347 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y3 * Y2^-2, Y3^3 * Y2 * Y3 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 19, 57)(12, 50, 20, 58)(13, 51, 21, 59)(14, 52, 22, 60)(15, 53, 23, 61)(16, 54, 24, 62)(17, 55, 25, 63)(18, 56, 26, 64)(27, 65, 33, 71)(28, 66, 34, 72)(29, 67, 35, 73)(30, 68, 36, 74)(31, 69, 37, 75)(32, 70, 38, 76)(77, 115, 79, 117, 87, 125, 90, 128, 104, 142, 108, 146, 106, 144, 93, 131, 82, 120, 89, 127, 91, 129, 80, 118, 88, 126, 103, 141, 105, 143, 107, 145, 94, 132, 92, 130, 81, 119)(78, 116, 83, 121, 95, 133, 98, 136, 110, 148, 114, 152, 112, 150, 101, 139, 86, 124, 97, 135, 99, 137, 84, 122, 96, 134, 109, 147, 111, 149, 113, 151, 102, 140, 100, 138, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 90)(5, 91)(6, 77)(7, 96)(8, 98)(9, 99)(10, 78)(11, 103)(12, 104)(13, 79)(14, 105)(15, 87)(16, 89)(17, 81)(18, 82)(19, 109)(20, 110)(21, 83)(22, 111)(23, 95)(24, 97)(25, 85)(26, 86)(27, 108)(28, 107)(29, 106)(30, 92)(31, 93)(32, 94)(33, 114)(34, 113)(35, 112)(36, 100)(37, 101)(38, 102)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.375
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.348 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^-4 * Y3 * Y2^-5, (Y3 * Y2^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 15, 53)(12, 50, 16, 54)(13, 51, 17, 55)(14, 52, 18, 56)(19, 57, 23, 61)(20, 58, 24, 62)(21, 59, 25, 63)(22, 60, 26, 64)(27, 65, 31, 69)(28, 66, 32, 70)(29, 67, 33, 71)(30, 68, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 95, 133, 103, 141, 111, 149, 105, 143, 97, 135, 89, 127, 80, 118, 82, 120, 88, 126, 96, 134, 104, 142, 112, 150, 106, 144, 98, 136, 90, 128, 81, 119)(78, 116, 83, 121, 91, 129, 99, 137, 107, 145, 113, 151, 109, 147, 101, 139, 93, 131, 84, 122, 86, 124, 92, 130, 100, 138, 108, 146, 114, 152, 110, 148, 102, 140, 94, 132, 85, 123)
	L = (1, 80)(2, 84)(3, 82)(4, 81)(5, 89)(6, 77)(7, 86)(8, 85)(9, 93)(10, 78)(11, 88)(12, 79)(13, 90)(14, 97)(15, 92)(16, 83)(17, 94)(18, 101)(19, 96)(20, 87)(21, 98)(22, 105)(23, 100)(24, 91)(25, 102)(26, 109)(27, 104)(28, 95)(29, 106)(30, 111)(31, 108)(32, 99)(33, 110)(34, 113)(35, 112)(36, 103)(37, 114)(38, 107)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.370
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.349 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^-4 * Y3^-1 * Y2^-5 ]
Map:: non-degenerate
	R = (1, 39, 2, 40)(3, 41, 7, 45)(4, 42, 8, 46)(5, 43, 9, 47)(6, 44, 10, 48)(11, 49, 15, 53)(12, 50, 16, 54)(13, 51, 17, 55)(14, 52, 18, 56)(19, 57, 23, 61)(20, 58, 24, 62)(21, 59, 25, 63)(22, 60, 26, 64)(27, 65, 31, 69)(28, 66, 32, 70)(29, 67, 33, 71)(30, 68, 34, 72)(35, 73, 37, 75)(36, 74, 38, 76)(77, 115, 79, 117, 87, 125, 95, 133, 103, 141, 111, 149, 106, 144, 98, 136, 90, 128, 82, 120, 80, 118, 88, 126, 96, 134, 104, 142, 112, 150, 105, 143, 97, 135, 89, 127, 81, 119)(78, 116, 83, 121, 91, 129, 99, 137, 107, 145, 113, 151, 110, 148, 102, 140, 94, 132, 86, 124, 84, 122, 92, 130, 100, 138, 108, 146, 114, 152, 109, 147, 101, 139, 93, 131, 85, 123)
	L = (1, 80)(2, 84)(3, 88)(4, 79)(5, 82)(6, 77)(7, 92)(8, 83)(9, 86)(10, 78)(11, 96)(12, 87)(13, 90)(14, 81)(15, 100)(16, 91)(17, 94)(18, 85)(19, 104)(20, 95)(21, 98)(22, 89)(23, 108)(24, 99)(25, 102)(26, 93)(27, 112)(28, 103)(29, 106)(30, 97)(31, 114)(32, 107)(33, 110)(34, 101)(35, 105)(36, 111)(37, 109)(38, 113)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38, 76, 38, 76 ), ( 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76, 38, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.366
Graph:: bipartite
	v = 21 e = 76 f = 3
	degree seq :: [ 4^19, 38^2 ]

E27.350 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3^-1), (Y3 * Y1)^2, Y2^-3 * Y1^-1, Y3^-2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y1^-1, Y3^-3 * Y2^-1 * Y3^-3, (Y1^-1 * Y2)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 21, 59, 31, 69, 15, 53, 3, 41, 9, 47, 22, 60, 35, 73, 37, 75, 30, 68, 13, 51, 6, 44, 11, 49, 23, 61, 34, 72, 17, 55, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 24, 62, 32, 70, 14, 52, 25, 63, 16, 54, 26, 64, 36, 74, 38, 76, 29, 67, 19, 57, 27, 65, 20, 58, 28, 66, 33, 71, 18, 56)(77, 115, 79, 117, 89, 127, 81, 119, 91, 129, 106, 144, 93, 131, 107, 145, 113, 151, 110, 148, 97, 135, 111, 149, 99, 137, 84, 122, 98, 136, 87, 125, 78, 116, 85, 123, 82, 120)(80, 118, 90, 128, 105, 143, 94, 132, 108, 146, 114, 152, 109, 147, 100, 138, 112, 150, 104, 142, 88, 126, 102, 140, 96, 134, 83, 121, 92, 130, 103, 141, 86, 124, 101, 139, 95, 133)
	L = (1, 80)(2, 86)(3, 90)(4, 93)(5, 94)(6, 95)(7, 77)(8, 83)(9, 101)(10, 81)(11, 103)(12, 78)(13, 105)(14, 107)(15, 108)(16, 79)(17, 109)(18, 110)(19, 106)(20, 82)(21, 88)(22, 92)(23, 96)(24, 84)(25, 91)(26, 85)(27, 89)(28, 87)(29, 113)(30, 114)(31, 100)(32, 97)(33, 99)(34, 104)(35, 102)(36, 98)(37, 112)(38, 111)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.364
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.351 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3^-1)^2, Y3^-2 * Y1^-2, (R * Y2)^2, (Y2, Y3), Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1, Y1 * Y3^-1 * Y2 * Y1 * Y3^-3, Y1 * Y2 * Y1^5, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2, (Y2^-1 * Y3)^38 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 21, 59, 33, 71, 19, 57, 6, 44, 11, 49, 23, 61, 35, 73, 38, 76, 29, 67, 14, 52, 3, 41, 9, 47, 22, 60, 32, 70, 16, 54, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 24, 62, 34, 72, 18, 56, 27, 65, 20, 58, 28, 66, 36, 74, 37, 75, 30, 68, 13, 51, 25, 63, 15, 53, 26, 64, 31, 69, 17, 55)(77, 115, 79, 117, 87, 125, 78, 116, 85, 123, 99, 137, 84, 122, 98, 136, 111, 149, 97, 135, 108, 146, 114, 152, 109, 147, 92, 130, 105, 143, 95, 133, 81, 119, 90, 128, 82, 120)(80, 118, 89, 127, 103, 141, 86, 124, 101, 139, 96, 134, 83, 121, 91, 129, 104, 142, 88, 126, 102, 140, 112, 150, 100, 138, 107, 145, 113, 151, 110, 148, 93, 131, 106, 144, 94, 132)
	L = (1, 80)(2, 86)(3, 89)(4, 92)(5, 93)(6, 94)(7, 77)(8, 83)(9, 101)(10, 81)(11, 103)(12, 78)(13, 105)(14, 106)(15, 79)(16, 107)(17, 108)(18, 109)(19, 110)(20, 82)(21, 88)(22, 91)(23, 96)(24, 84)(25, 90)(26, 85)(27, 95)(28, 87)(29, 113)(30, 114)(31, 98)(32, 102)(33, 100)(34, 97)(35, 104)(36, 99)(37, 111)(38, 112)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.361
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.352 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^-2, (R * Y2)^2, (Y2^-1, Y3), (Y1^-1, Y2^-1), Y2^-1 * Y1^-4, Y3^4 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y1, Y2^2 * Y1 * Y2^3, Y2^-1 * Y1 * Y2^-3 * Y1^2, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y2^2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 20, 58, 6, 44, 11, 49, 23, 61, 29, 67, 21, 59, 27, 65, 31, 69, 13, 51, 24, 62, 33, 71, 15, 53, 3, 41, 9, 47, 17, 55, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 19, 57, 26, 64, 22, 60, 28, 66, 35, 73, 38, 76, 36, 74, 30, 68, 37, 75, 32, 70, 34, 72, 14, 52, 25, 63, 16, 54, 18, 56)(77, 115, 79, 117, 89, 127, 105, 143, 96, 134, 81, 119, 91, 129, 107, 145, 99, 137, 84, 122, 93, 131, 109, 147, 103, 141, 87, 125, 78, 116, 85, 123, 100, 138, 97, 135, 82, 120)(80, 118, 90, 128, 106, 144, 104, 142, 88, 126, 94, 132, 110, 148, 112, 150, 98, 136, 83, 121, 92, 130, 108, 146, 114, 152, 102, 140, 86, 124, 101, 139, 113, 151, 111, 149, 95, 133)
	L = (1, 80)(2, 86)(3, 90)(4, 93)(5, 94)(6, 95)(7, 77)(8, 83)(9, 101)(10, 81)(11, 102)(12, 78)(13, 106)(14, 109)(15, 110)(16, 79)(17, 92)(18, 85)(19, 84)(20, 88)(21, 111)(22, 82)(23, 98)(24, 113)(25, 91)(26, 96)(27, 114)(28, 87)(29, 104)(30, 103)(31, 112)(32, 89)(33, 108)(34, 100)(35, 99)(36, 97)(37, 107)(38, 105)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.359
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.353 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y1), (Y1 * Y3)^2, (R * Y1)^2, (Y1^-1, Y2), Y3^-2 * Y1^-2, (Y2^-1, Y3), (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y1^2 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3, Y2^4 * Y1^-1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 15, 53, 3, 41, 9, 47, 23, 61, 30, 68, 13, 51, 24, 62, 35, 73, 21, 59, 28, 66, 32, 70, 20, 58, 6, 44, 11, 49, 17, 55, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 14, 52, 25, 63, 16, 54, 26, 64, 29, 67, 37, 75, 31, 69, 34, 72, 38, 76, 36, 74, 33, 71, 19, 57, 27, 65, 22, 60, 18, 56)(77, 115, 79, 117, 89, 127, 104, 142, 87, 125, 78, 116, 85, 123, 100, 138, 108, 146, 93, 131, 84, 122, 99, 137, 111, 149, 96, 134, 81, 119, 91, 129, 106, 144, 97, 135, 82, 120)(80, 118, 90, 128, 105, 143, 114, 152, 103, 141, 86, 124, 101, 139, 113, 151, 112, 150, 98, 136, 83, 121, 92, 130, 107, 145, 109, 147, 94, 132, 88, 126, 102, 140, 110, 148, 95, 133)
	L = (1, 80)(2, 86)(3, 90)(4, 93)(5, 94)(6, 95)(7, 77)(8, 83)(9, 101)(10, 81)(11, 103)(12, 78)(13, 105)(14, 84)(15, 88)(16, 79)(17, 98)(18, 87)(19, 108)(20, 109)(21, 110)(22, 82)(23, 92)(24, 113)(25, 91)(26, 85)(27, 96)(28, 114)(29, 99)(30, 102)(31, 89)(32, 112)(33, 104)(34, 100)(35, 107)(36, 97)(37, 106)(38, 111)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.362
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.354 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1, Y3), Y3^-2 * Y1^-2, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-2 * Y2^-1, Y3^-2 * Y2^-5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 21, 59, 27, 65, 29, 67, 32, 70, 15, 53, 3, 41, 9, 47, 20, 58, 6, 44, 11, 49, 23, 61, 35, 73, 31, 69, 13, 51, 17, 55, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 24, 62, 36, 74, 38, 76, 33, 71, 14, 52, 25, 63, 16, 54, 19, 57, 26, 64, 22, 60, 28, 66, 37, 75, 30, 68, 34, 72, 18, 56)(77, 115, 79, 117, 89, 127, 105, 143, 99, 137, 84, 122, 96, 134, 81, 119, 91, 129, 107, 145, 103, 141, 87, 125, 78, 116, 85, 123, 93, 131, 108, 146, 111, 149, 97, 135, 82, 120)(80, 118, 90, 128, 106, 144, 112, 150, 98, 136, 83, 121, 92, 130, 94, 132, 109, 147, 113, 151, 100, 138, 102, 140, 86, 124, 101, 139, 110, 148, 114, 152, 104, 142, 88, 126, 95, 133)
	L = (1, 80)(2, 86)(3, 90)(4, 93)(5, 94)(6, 95)(7, 77)(8, 83)(9, 101)(10, 81)(11, 102)(12, 78)(13, 106)(14, 108)(15, 109)(16, 79)(17, 110)(18, 89)(19, 85)(20, 92)(21, 88)(22, 82)(23, 98)(24, 84)(25, 91)(26, 96)(27, 100)(28, 87)(29, 112)(30, 111)(31, 113)(32, 114)(33, 105)(34, 107)(35, 104)(36, 97)(37, 99)(38, 103)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.365
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.355 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (Y2^-1, Y3), (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1^-1 * Y3^2, Y2^-1 * Y3^2 * Y2^-4, Y2 * Y1 * Y2^3 * Y1 * Y2, Y2^-1 * Y3^2 * Y2^-4, Y2 * Y1^2 * Y2 * Y1 * Y2 * Y1^2, Y3^-16 * Y2^2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 13, 51, 25, 63, 36, 74, 32, 70, 20, 58, 6, 44, 11, 49, 15, 53, 3, 41, 9, 47, 23, 61, 29, 67, 35, 73, 21, 59, 17, 55, 5, 43)(4, 42, 10, 48, 7, 45, 12, 50, 24, 62, 30, 68, 38, 76, 33, 71, 19, 57, 28, 66, 22, 60, 14, 52, 26, 64, 16, 54, 27, 65, 37, 75, 34, 72, 31, 69, 18, 56)(77, 115, 79, 117, 89, 127, 105, 143, 108, 146, 93, 131, 87, 125, 78, 116, 85, 123, 101, 139, 111, 149, 96, 134, 81, 119, 91, 129, 84, 122, 99, 137, 112, 150, 97, 135, 82, 120)(80, 118, 90, 128, 88, 126, 103, 141, 114, 152, 107, 145, 104, 142, 86, 124, 102, 140, 100, 138, 113, 151, 109, 147, 94, 132, 98, 136, 83, 121, 92, 130, 106, 144, 110, 148, 95, 133)
	L = (1, 80)(2, 86)(3, 90)(4, 93)(5, 94)(6, 95)(7, 77)(8, 83)(9, 102)(10, 81)(11, 104)(12, 78)(13, 88)(14, 87)(15, 98)(16, 79)(17, 107)(18, 97)(19, 108)(20, 109)(21, 110)(22, 82)(23, 92)(24, 84)(25, 100)(26, 91)(27, 85)(28, 96)(29, 103)(30, 89)(31, 111)(32, 114)(33, 112)(34, 105)(35, 113)(36, 106)(37, 99)(38, 101)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.363
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.356 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-2, Y3^2 * Y2, (R * Y2)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^3 * Y3^-1 * Y1^-1 * Y2^-3 * Y1^-1, Y1 * Y2^9, (Y3 * Y2^-1)^38 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 3, 41, 8, 46, 11, 49, 17, 55, 19, 57, 25, 63, 27, 65, 33, 71, 35, 73, 32, 70, 31, 69, 24, 62, 23, 61, 16, 54, 15, 53, 6, 44, 5, 43)(4, 42, 9, 47, 7, 45, 10, 48, 12, 50, 18, 56, 20, 58, 26, 64, 28, 66, 34, 72, 36, 74, 38, 76, 37, 75, 30, 68, 29, 67, 22, 60, 21, 59, 14, 52, 13, 51)(77, 115, 79, 117, 87, 125, 95, 133, 103, 141, 111, 149, 107, 145, 99, 137, 91, 129, 81, 119, 78, 116, 84, 122, 93, 131, 101, 139, 109, 147, 108, 146, 100, 138, 92, 130, 82, 120)(80, 118, 83, 121, 88, 126, 96, 134, 104, 142, 112, 150, 113, 151, 105, 143, 97, 135, 89, 127, 85, 123, 86, 124, 94, 132, 102, 140, 110, 148, 114, 152, 106, 144, 98, 136, 90, 128)
	L = (1, 80)(2, 85)(3, 83)(4, 82)(5, 89)(6, 90)(7, 77)(8, 86)(9, 81)(10, 78)(11, 88)(12, 79)(13, 91)(14, 92)(15, 97)(16, 98)(17, 94)(18, 84)(19, 96)(20, 87)(21, 99)(22, 100)(23, 105)(24, 106)(25, 102)(26, 93)(27, 104)(28, 95)(29, 107)(30, 108)(31, 113)(32, 114)(33, 110)(34, 101)(35, 112)(36, 103)(37, 111)(38, 109)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.360
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.357 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y3, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y1)^2, Y1 * Y2^-9 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 6, 44, 9, 47, 15, 53, 17, 55, 23, 61, 25, 63, 31, 69, 33, 71, 36, 74, 27, 65, 29, 67, 19, 57, 21, 59, 11, 49, 13, 51, 3, 41, 5, 43)(4, 42, 8, 46, 7, 45, 10, 48, 16, 54, 18, 56, 24, 62, 26, 64, 32, 70, 34, 72, 38, 76, 35, 73, 37, 75, 28, 66, 30, 68, 20, 58, 22, 60, 12, 50, 14, 52)(77, 115, 79, 117, 87, 125, 95, 133, 103, 141, 109, 147, 101, 139, 93, 131, 85, 123, 78, 116, 81, 119, 89, 127, 97, 135, 105, 143, 112, 150, 107, 145, 99, 137, 91, 129, 82, 120)(80, 118, 88, 126, 96, 134, 104, 142, 111, 149, 110, 148, 102, 140, 94, 132, 86, 124, 84, 122, 90, 128, 98, 136, 106, 144, 113, 151, 114, 152, 108, 146, 100, 138, 92, 130, 83, 121)
	L = (1, 80)(2, 84)(3, 88)(4, 79)(5, 90)(6, 83)(7, 77)(8, 81)(9, 86)(10, 78)(11, 96)(12, 87)(13, 98)(14, 89)(15, 92)(16, 82)(17, 94)(18, 85)(19, 104)(20, 95)(21, 106)(22, 97)(23, 100)(24, 91)(25, 102)(26, 93)(27, 111)(28, 103)(29, 113)(30, 105)(31, 108)(32, 99)(33, 110)(34, 101)(35, 109)(36, 114)(37, 112)(38, 107)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.358
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.358 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-8 * Y2 * Y1^9 * Y2 * Y3^-1, Y1^-8 * Y2 * Y3^-1 * Y1^-10, (Y3^-1 * Y1^-1)^19, (Y3 * Y2)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 5, 43, 9, 47, 13, 51, 17, 55, 21, 59, 25, 63, 29, 67, 33, 71, 37, 75, 35, 73, 31, 69, 27, 65, 23, 61, 19, 57, 15, 53, 11, 49, 7, 45, 3, 41, 6, 44, 10, 48, 14, 52, 18, 56, 22, 60, 26, 64, 30, 68, 34, 72, 38, 76, 36, 74, 32, 70, 28, 66, 24, 62, 20, 58, 16, 54, 12, 50, 8, 46, 4, 42)(77, 115, 79, 117)(78, 116, 82, 120)(80, 118, 83, 121)(81, 119, 86, 124)(84, 122, 87, 125)(85, 123, 90, 128)(88, 126, 91, 129)(89, 127, 94, 132)(92, 130, 95, 133)(93, 131, 98, 136)(96, 134, 99, 137)(97, 135, 102, 140)(100, 138, 103, 141)(101, 139, 106, 144)(104, 142, 107, 145)(105, 143, 110, 148)(108, 146, 111, 149)(109, 147, 114, 152)(112, 150, 113, 151)
	L = (1, 78)(2, 81)(3, 82)(4, 77)(5, 85)(6, 86)(7, 79)(8, 80)(9, 89)(10, 90)(11, 83)(12, 84)(13, 93)(14, 94)(15, 87)(16, 88)(17, 97)(18, 98)(19, 91)(20, 92)(21, 101)(22, 102)(23, 95)(24, 96)(25, 105)(26, 106)(27, 99)(28, 100)(29, 109)(30, 110)(31, 103)(32, 104)(33, 113)(34, 114)(35, 107)(36, 108)(37, 111)(38, 112)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.357
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.359 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1 * Y3^-2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-1 * Y2 * Y3, Y2 * Y1 * Y2 * Y1^-1, Y1^-2 * Y3^-1 * Y1^-1 * Y2 * Y1^-3, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 17, 55, 29, 67, 25, 63, 13, 51, 22, 60, 34, 72, 38, 76, 36, 74, 26, 64, 14, 52, 4, 42, 9, 47, 19, 57, 31, 69, 24, 62, 12, 50, 3, 41, 8, 46, 18, 56, 30, 68, 28, 66, 16, 54, 6, 44, 10, 48, 20, 58, 32, 70, 37, 75, 35, 73, 23, 61, 11, 49, 21, 59, 33, 71, 27, 65, 15, 53, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 94, 132)(85, 123, 97, 135)(86, 124, 98, 136)(90, 128, 99, 137)(91, 129, 100, 138)(92, 130, 101, 139)(93, 131, 106, 144)(95, 133, 109, 147)(96, 134, 110, 148)(102, 140, 111, 149)(103, 141, 107, 145)(104, 142, 105, 143)(108, 146, 114, 152)(112, 150, 113, 151)
	L = (1, 80)(2, 85)(3, 87)(4, 86)(5, 90)(6, 77)(7, 95)(8, 97)(9, 96)(10, 78)(11, 98)(12, 99)(13, 79)(14, 82)(15, 102)(16, 81)(17, 107)(18, 109)(19, 108)(20, 83)(21, 110)(22, 84)(23, 89)(24, 111)(25, 88)(26, 92)(27, 112)(28, 91)(29, 100)(30, 103)(31, 113)(32, 93)(33, 114)(34, 94)(35, 101)(36, 104)(37, 105)(38, 106)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.352
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.360 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^-3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y1^-3 * Y2 * Y3 * Y1^-3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 17, 55, 29, 67, 24, 62, 11, 49, 21, 59, 33, 71, 38, 76, 36, 74, 26, 64, 14, 52, 6, 44, 10, 48, 20, 58, 32, 70, 25, 63, 12, 50, 3, 41, 8, 46, 18, 56, 30, 68, 27, 65, 15, 53, 4, 42, 9, 47, 19, 57, 31, 69, 37, 75, 35, 73, 23, 61, 13, 51, 22, 60, 34, 72, 28, 66, 16, 54, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 94, 132)(85, 123, 97, 135)(86, 124, 98, 136)(90, 128, 99, 137)(91, 129, 100, 138)(92, 130, 101, 139)(93, 131, 106, 144)(95, 133, 109, 147)(96, 134, 110, 148)(102, 140, 111, 149)(103, 141, 105, 143)(104, 142, 108, 146)(107, 145, 114, 152)(112, 150, 113, 151)
	L = (1, 80)(2, 85)(3, 87)(4, 90)(5, 91)(6, 77)(7, 95)(8, 97)(9, 82)(10, 78)(11, 99)(12, 100)(13, 79)(14, 81)(15, 102)(16, 103)(17, 107)(18, 109)(19, 86)(20, 83)(21, 89)(22, 84)(23, 88)(24, 111)(25, 105)(26, 92)(27, 112)(28, 106)(29, 113)(30, 114)(31, 96)(32, 93)(33, 98)(34, 94)(35, 101)(36, 104)(37, 108)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.356
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.361 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, Y2 * Y3^-1 * Y1^-1 * Y2 * Y3 * Y1, Y3^4 * Y1^-1 * Y3, Y2 * Y1^-2 * Y3 * Y1^-2, Y3 * Y1 * Y3^2 * Y1^2 * Y2 * Y3, (Y1^-1 * Y3^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 19, 57, 11, 49, 23, 61, 34, 72, 30, 68, 14, 52, 25, 63, 35, 73, 29, 67, 38, 76, 31, 69, 17, 55, 6, 44, 10, 48, 22, 60, 12, 50, 3, 41, 8, 46, 20, 58, 15, 53, 4, 42, 9, 47, 21, 59, 33, 71, 27, 65, 37, 75, 32, 70, 18, 56, 26, 64, 36, 74, 28, 66, 13, 51, 24, 62, 16, 54, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 96, 134)(85, 123, 99, 137)(86, 124, 100, 138)(90, 128, 103, 141)(91, 129, 95, 133)(92, 130, 98, 136)(93, 131, 104, 142)(94, 132, 105, 143)(97, 135, 110, 148)(101, 139, 113, 151)(102, 140, 114, 152)(106, 144, 109, 147)(107, 145, 112, 150)(108, 146, 111, 149)
	L = (1, 80)(2, 85)(3, 87)(4, 90)(5, 91)(6, 77)(7, 97)(8, 99)(9, 101)(10, 78)(11, 103)(12, 95)(13, 79)(14, 102)(15, 106)(16, 96)(17, 81)(18, 82)(19, 109)(20, 110)(21, 111)(22, 83)(23, 113)(24, 84)(25, 112)(26, 86)(27, 114)(28, 88)(29, 89)(30, 94)(31, 92)(32, 93)(33, 105)(34, 108)(35, 104)(36, 98)(37, 107)(38, 100)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.351
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.362 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, (Y3^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-1 * Y3^-2, Y1^-2 * Y2 * Y3^-1 * Y1^-2, Y1 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y2 * Y3^-1, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 19, 57, 13, 51, 24, 62, 34, 72, 30, 68, 18, 56, 26, 64, 36, 74, 27, 65, 37, 75, 32, 70, 15, 53, 4, 42, 9, 47, 21, 59, 12, 50, 3, 41, 8, 46, 20, 58, 17, 55, 6, 44, 10, 48, 22, 60, 33, 71, 29, 67, 38, 76, 31, 69, 14, 52, 25, 63, 35, 73, 28, 66, 11, 49, 23, 61, 16, 54, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 96, 134)(85, 123, 99, 137)(86, 124, 100, 138)(90, 128, 103, 141)(91, 129, 104, 142)(92, 130, 97, 135)(93, 131, 95, 133)(94, 132, 105, 143)(98, 136, 110, 148)(101, 139, 113, 151)(102, 140, 114, 152)(106, 144, 109, 147)(107, 145, 112, 150)(108, 146, 111, 149)
	L = (1, 80)(2, 85)(3, 87)(4, 90)(5, 91)(6, 77)(7, 97)(8, 99)(9, 101)(10, 78)(11, 103)(12, 104)(13, 79)(14, 106)(15, 107)(16, 108)(17, 81)(18, 82)(19, 88)(20, 92)(21, 111)(22, 83)(23, 113)(24, 84)(25, 94)(26, 86)(27, 109)(28, 112)(29, 89)(30, 93)(31, 110)(32, 114)(33, 95)(34, 96)(35, 102)(36, 98)(37, 105)(38, 100)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.353
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.363 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1^-1 * Y2 * Y1, (R * Y1)^2, (Y3^-1, Y1), (R * Y2)^2, (R * Y3)^2, Y1^3 * Y2 * Y3^-2, Y3^-2 * Y1^-4 * Y3^-1 * Y1^-1, Y3^5 * Y1^2 * Y2, Y3^4 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 19, 57, 33, 71, 32, 70, 38, 76, 27, 65, 13, 51, 24, 62, 15, 53, 4, 42, 9, 47, 21, 59, 34, 72, 31, 69, 18, 56, 26, 64, 12, 50, 3, 41, 8, 46, 20, 58, 14, 52, 25, 63, 36, 74, 30, 68, 17, 55, 6, 44, 10, 48, 22, 60, 11, 49, 23, 61, 35, 73, 29, 67, 37, 75, 28, 66, 16, 54, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 96, 134)(85, 123, 99, 137)(86, 124, 100, 138)(90, 128, 95, 133)(91, 129, 98, 136)(92, 130, 102, 140)(93, 131, 103, 141)(94, 132, 104, 142)(97, 135, 111, 149)(101, 139, 109, 147)(105, 143, 110, 148)(106, 144, 114, 152)(107, 145, 113, 151)(108, 146, 112, 150)
	L = (1, 80)(2, 85)(3, 87)(4, 90)(5, 91)(6, 77)(7, 97)(8, 99)(9, 101)(10, 78)(11, 95)(12, 98)(13, 79)(14, 105)(15, 96)(16, 100)(17, 81)(18, 82)(19, 110)(20, 111)(21, 112)(22, 83)(23, 109)(24, 84)(25, 113)(26, 86)(27, 88)(28, 89)(29, 114)(30, 92)(31, 93)(32, 94)(33, 107)(34, 106)(35, 108)(36, 104)(37, 103)(38, 102)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.355
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.364 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, (Y1, Y3), (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2)^2, Y3^2 * Y2 * Y1^3, Y2 * Y1^-2 * Y3^-2 * Y1^-1, Y1^5 * Y3^-3, Y3^11 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 19, 57, 33, 71, 29, 67, 37, 75, 28, 66, 11, 49, 23, 61, 17, 55, 6, 44, 10, 48, 22, 60, 34, 72, 30, 68, 14, 52, 25, 63, 12, 50, 3, 41, 8, 46, 20, 58, 18, 56, 26, 64, 36, 74, 31, 69, 15, 53, 4, 42, 9, 47, 21, 59, 13, 51, 24, 62, 35, 73, 32, 70, 38, 76, 27, 65, 16, 54, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 87, 125)(81, 119, 88, 126)(82, 120, 89, 127)(83, 121, 96, 134)(85, 123, 99, 137)(86, 124, 100, 138)(90, 128, 103, 141)(91, 129, 104, 142)(92, 130, 101, 139)(93, 131, 97, 135)(94, 132, 95, 133)(98, 136, 111, 149)(102, 140, 109, 147)(105, 143, 112, 150)(106, 144, 114, 152)(107, 145, 113, 151)(108, 146, 110, 148)
	L = (1, 80)(2, 85)(3, 87)(4, 90)(5, 91)(6, 77)(7, 97)(8, 99)(9, 101)(10, 78)(11, 103)(12, 104)(13, 79)(14, 105)(15, 106)(16, 107)(17, 81)(18, 82)(19, 89)(20, 93)(21, 88)(22, 83)(23, 92)(24, 84)(25, 113)(26, 86)(27, 112)(28, 114)(29, 111)(30, 109)(31, 110)(32, 94)(33, 100)(34, 95)(35, 96)(36, 98)(37, 108)(38, 102)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.350
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.365 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1 * Y2 * Y1, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-4 * Y1^-1 * Y3^-5, Y3^2 * Y1^34, (Y3^-1 * Y1^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 15, 53, 12, 50, 17, 55, 24, 62, 31, 69, 28, 66, 33, 71, 38, 76, 35, 73, 29, 67, 22, 60, 26, 64, 19, 57, 13, 51, 6, 44, 10, 48, 3, 41, 8, 46, 4, 42, 9, 47, 16, 54, 23, 61, 20, 58, 25, 63, 32, 70, 37, 75, 36, 74, 30, 68, 34, 72, 27, 65, 21, 59, 14, 52, 18, 56, 11, 49, 5, 43)(77, 115, 79, 117)(78, 116, 84, 122)(80, 118, 83, 121)(81, 119, 86, 124)(82, 120, 87, 125)(85, 123, 91, 129)(88, 126, 92, 130)(89, 127, 94, 132)(90, 128, 95, 133)(93, 131, 99, 137)(96, 134, 100, 138)(97, 135, 102, 140)(98, 136, 103, 141)(101, 139, 107, 145)(104, 142, 108, 146)(105, 143, 110, 148)(106, 144, 111, 149)(109, 147, 113, 151)(112, 150, 114, 152)
	L = (1, 80)(2, 85)(3, 83)(4, 88)(5, 84)(6, 77)(7, 92)(8, 91)(9, 93)(10, 78)(11, 79)(12, 96)(13, 81)(14, 82)(15, 99)(16, 100)(17, 101)(18, 86)(19, 87)(20, 104)(21, 89)(22, 90)(23, 107)(24, 108)(25, 109)(26, 94)(27, 95)(28, 112)(29, 97)(30, 98)(31, 113)(32, 114)(33, 106)(34, 102)(35, 103)(36, 105)(37, 111)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.354
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.366 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (Y2, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, Y1^2 * Y2^-2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 * Y1 * Y2^10, (Y3^-1 * Y1^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 6, 44, 11, 49, 15, 53, 19, 57, 23, 61, 27, 65, 31, 69, 35, 73, 37, 75, 33, 71, 29, 67, 25, 63, 21, 59, 17, 55, 13, 51, 9, 47, 4, 42)(3, 41, 7, 45, 12, 50, 16, 54, 20, 58, 24, 62, 28, 66, 32, 70, 36, 74, 38, 76, 34, 72, 30, 68, 26, 64, 22, 60, 18, 56, 14, 52, 10, 48, 5, 43, 8, 46)(77, 115, 79, 117, 82, 120, 88, 126, 91, 129, 96, 134, 99, 137, 104, 142, 107, 145, 112, 150, 113, 151, 110, 148, 105, 143, 102, 140, 97, 135, 94, 132, 89, 127, 86, 124, 80, 118, 84, 122, 78, 116, 83, 121, 87, 125, 92, 130, 95, 133, 100, 138, 103, 141, 108, 146, 111, 149, 114, 152, 109, 147, 106, 144, 101, 139, 98, 136, 93, 131, 90, 128, 85, 123, 81, 119)
	L = (1, 78)(2, 82)(3, 83)(4, 77)(5, 84)(6, 87)(7, 88)(8, 79)(9, 80)(10, 81)(11, 91)(12, 92)(13, 85)(14, 86)(15, 95)(16, 96)(17, 89)(18, 90)(19, 99)(20, 100)(21, 93)(22, 94)(23, 103)(24, 104)(25, 97)(26, 98)(27, 107)(28, 108)(29, 101)(30, 102)(31, 111)(32, 112)(33, 105)(34, 106)(35, 113)(36, 114)(37, 109)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.349
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.367 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-2, Y1^-1 * Y2^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y1^-4 * Y3^-1 * Y1^-5, (Y3^-1 * Y1^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 17, 55, 25, 63, 33, 71, 31, 69, 23, 61, 15, 53, 7, 45, 4, 42, 10, 48, 19, 57, 27, 65, 35, 73, 29, 67, 21, 59, 13, 51, 5, 43)(3, 41, 9, 47, 18, 56, 26, 64, 34, 72, 38, 76, 32, 70, 24, 62, 16, 54, 12, 50, 11, 49, 20, 58, 28, 66, 36, 74, 37, 75, 30, 68, 22, 60, 14, 52, 6, 44)(77, 115, 79, 117, 78, 116, 85, 123, 84, 122, 94, 132, 93, 131, 102, 140, 101, 139, 110, 148, 109, 147, 114, 152, 107, 145, 108, 146, 99, 137, 100, 138, 91, 129, 92, 130, 83, 121, 88, 126, 80, 118, 87, 125, 86, 124, 96, 134, 95, 133, 104, 142, 103, 141, 112, 150, 111, 149, 113, 151, 105, 143, 106, 144, 97, 135, 98, 136, 89, 127, 90, 128, 81, 119, 82, 120)
	L = (1, 80)(2, 86)(3, 87)(4, 78)(5, 83)(6, 88)(7, 77)(8, 95)(9, 96)(10, 84)(11, 85)(12, 79)(13, 91)(14, 92)(15, 81)(16, 82)(17, 103)(18, 104)(19, 93)(20, 94)(21, 99)(22, 100)(23, 89)(24, 90)(25, 111)(26, 112)(27, 101)(28, 102)(29, 107)(30, 108)(31, 97)(32, 98)(33, 105)(34, 113)(35, 109)(36, 110)(37, 114)(38, 106)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.343
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.368 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2, Y1 * Y2^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y1^-9 * Y3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 17, 55, 25, 63, 33, 71, 31, 69, 23, 61, 14, 52, 4, 42, 7, 45, 10, 48, 19, 57, 27, 65, 35, 73, 32, 70, 24, 62, 15, 53, 5, 43)(3, 41, 6, 44, 9, 47, 18, 56, 26, 64, 34, 72, 37, 75, 29, 67, 21, 59, 11, 49, 13, 51, 16, 54, 20, 58, 28, 66, 36, 74, 38, 76, 30, 68, 22, 60, 12, 50)(77, 115, 79, 117, 81, 119, 88, 126, 91, 129, 98, 136, 100, 138, 106, 144, 108, 146, 114, 152, 111, 149, 112, 150, 103, 141, 104, 142, 95, 133, 96, 134, 86, 124, 92, 130, 83, 121, 89, 127, 80, 118, 87, 125, 90, 128, 97, 135, 99, 137, 105, 143, 107, 145, 113, 151, 109, 147, 110, 148, 101, 139, 102, 140, 93, 131, 94, 132, 84, 122, 85, 123, 78, 116, 82, 120)
	L = (1, 80)(2, 83)(3, 87)(4, 81)(5, 90)(6, 89)(7, 77)(8, 86)(9, 92)(10, 78)(11, 88)(12, 97)(13, 79)(14, 91)(15, 99)(16, 82)(17, 95)(18, 96)(19, 84)(20, 85)(21, 98)(22, 105)(23, 100)(24, 107)(25, 103)(26, 104)(27, 93)(28, 94)(29, 106)(30, 113)(31, 108)(32, 109)(33, 111)(34, 112)(35, 101)(36, 102)(37, 114)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.333
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.369 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (Y3, Y2^-1), Y3 * Y2^2 * Y1^-1, Y3^-2 * Y1 * Y3^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1^5, Y1^2 * Y2 * Y1 * Y2 * Y1^3 * Y3^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 19, 57, 30, 68, 18, 56, 7, 45, 12, 50, 23, 61, 33, 71, 37, 75, 27, 65, 15, 53, 4, 42, 10, 48, 21, 59, 28, 66, 16, 54, 5, 43)(3, 41, 9, 47, 20, 58, 31, 69, 36, 74, 26, 64, 14, 52, 24, 62, 34, 72, 38, 76, 29, 67, 17, 55, 6, 44, 11, 49, 22, 60, 32, 70, 35, 73, 25, 63, 13, 51)(77, 115, 79, 117, 88, 126, 100, 138, 86, 124, 98, 136, 84, 122, 96, 134, 109, 147, 114, 152, 104, 142, 111, 149, 106, 144, 112, 150, 103, 141, 93, 131, 81, 119, 89, 127, 83, 121, 90, 128, 80, 118, 87, 125, 78, 116, 85, 123, 99, 137, 110, 148, 97, 135, 108, 146, 95, 133, 107, 145, 113, 151, 105, 143, 92, 130, 101, 139, 94, 132, 102, 140, 91, 129, 82, 120)
	L = (1, 80)(2, 86)(3, 87)(4, 88)(5, 91)(6, 90)(7, 77)(8, 97)(9, 98)(10, 99)(11, 100)(12, 78)(13, 82)(14, 79)(15, 83)(16, 103)(17, 102)(18, 81)(19, 104)(20, 108)(21, 109)(22, 110)(23, 84)(24, 85)(25, 93)(26, 89)(27, 94)(28, 113)(29, 112)(30, 92)(31, 111)(32, 114)(33, 95)(34, 96)(35, 105)(36, 101)(37, 106)(38, 107)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.340
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.370 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1), Y3^2 * Y2^-2, (Y3^-1 * Y2)^2, Y3^-1 * Y2^-2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1^2 * Y3^-1 * Y1^4, Y1^3 * Y2^-1 * Y1^2 * Y3^-2 * Y2^-1, Y3 * Y2^34 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 19, 57, 29, 67, 17, 55, 4, 42, 10, 48, 21, 59, 32, 70, 36, 74, 26, 64, 13, 51, 7, 45, 12, 50, 23, 61, 30, 68, 18, 56, 5, 43)(3, 41, 9, 47, 20, 58, 31, 69, 37, 75, 27, 65, 14, 52, 6, 44, 11, 49, 22, 60, 33, 71, 35, 73, 25, 63, 16, 54, 24, 62, 34, 72, 38, 76, 28, 66, 15, 53)(77, 115, 79, 117, 89, 127, 101, 139, 93, 131, 103, 141, 94, 132, 104, 142, 112, 150, 109, 147, 95, 133, 107, 145, 99, 137, 110, 148, 97, 135, 87, 125, 78, 116, 85, 123, 83, 121, 92, 130, 80, 118, 90, 128, 81, 119, 91, 129, 102, 140, 111, 149, 105, 143, 113, 151, 106, 144, 114, 152, 108, 146, 98, 136, 84, 122, 96, 134, 88, 126, 100, 138, 86, 124, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 97)(9, 82)(10, 83)(11, 100)(12, 78)(13, 81)(14, 101)(15, 103)(16, 79)(17, 102)(18, 105)(19, 108)(20, 87)(21, 88)(22, 110)(23, 84)(24, 85)(25, 91)(26, 94)(27, 111)(28, 113)(29, 112)(30, 95)(31, 98)(32, 99)(33, 114)(34, 96)(35, 104)(36, 106)(37, 109)(38, 107)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.348
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.371 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y3)^2, (R * Y1)^2, (Y1^-1, Y3), (R * Y2)^2, (Y2, Y3), (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^-1, Y3^3 * Y1^-1 * Y3, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y1^2 * Y3^-1 * Y1^3, Y1 * Y3 * Y1^2 * Y2^2 * Y1, (Y1^-1 * Y3^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 23, 61, 17, 55, 4, 42, 10, 48, 25, 63, 35, 73, 21, 59, 13, 51, 28, 66, 34, 72, 20, 58, 7, 45, 12, 50, 27, 65, 18, 56, 5, 43)(3, 41, 9, 47, 24, 62, 36, 74, 22, 60, 14, 52, 29, 67, 33, 71, 19, 57, 6, 44, 11, 49, 26, 64, 37, 75, 32, 70, 16, 54, 30, 68, 38, 76, 31, 69, 15, 53)(77, 115, 79, 117, 89, 127, 87, 125, 78, 116, 85, 123, 104, 142, 102, 140, 84, 122, 100, 138, 110, 148, 113, 151, 99, 137, 112, 150, 96, 134, 108, 146, 93, 131, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 88, 126, 106, 144, 86, 124, 105, 143, 103, 141, 114, 152, 101, 139, 109, 147, 94, 132, 107, 145, 111, 149, 95, 133, 81, 119, 91, 129, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 101)(9, 105)(10, 104)(11, 106)(12, 78)(13, 88)(14, 87)(15, 98)(16, 79)(17, 97)(18, 99)(19, 108)(20, 81)(21, 83)(22, 82)(23, 111)(24, 109)(25, 110)(26, 114)(27, 84)(28, 103)(29, 102)(30, 85)(31, 112)(32, 91)(33, 113)(34, 94)(35, 96)(36, 95)(37, 107)(38, 100)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.338
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.372 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y2^-1)^2, (Y1^-1, Y3^-1), (Y2, Y3), (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2^3, Y3^-1 * Y1^-1 * Y3^-3, Y3 * Y2 * Y3 * Y2 * Y1, Y3^-1 * Y1^-5, Y1^2 * Y3^-1 * Y1^2 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 23, 61, 20, 58, 7, 45, 12, 50, 27, 65, 31, 69, 13, 51, 21, 59, 29, 67, 35, 73, 17, 55, 4, 42, 10, 48, 25, 63, 18, 56, 5, 43)(3, 41, 9, 47, 24, 62, 37, 75, 34, 72, 16, 54, 28, 66, 38, 76, 36, 74, 19, 57, 6, 44, 11, 49, 26, 64, 32, 70, 14, 52, 22, 60, 30, 68, 33, 71, 15, 53)(77, 115, 79, 117, 89, 127, 95, 133, 81, 119, 91, 129, 107, 145, 112, 150, 94, 132, 109, 147, 103, 141, 114, 152, 101, 139, 106, 144, 88, 126, 104, 142, 86, 124, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 96, 134, 110, 148, 93, 131, 108, 146, 99, 137, 113, 151, 111, 149, 102, 140, 84, 122, 100, 138, 105, 143, 87, 125, 78, 116, 85, 123, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 101)(9, 98)(10, 97)(11, 104)(12, 78)(13, 96)(14, 95)(15, 108)(16, 79)(17, 107)(18, 111)(19, 110)(20, 81)(21, 83)(22, 82)(23, 94)(24, 106)(25, 105)(26, 114)(27, 84)(28, 85)(29, 88)(30, 87)(31, 99)(32, 112)(33, 102)(34, 91)(35, 103)(36, 113)(37, 109)(38, 100)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.342
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.373 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y3^-1 * Y2)^2, (Y2^-1, Y1), (Y3^-1, Y2^-1), (R * Y1)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-1 * Y1^3, Y3^2 * Y1^-1 * Y3 * Y2^2, Y2^4 * Y3 * Y1^-1, Y1 * Y2^-1 * Y1^2 * Y3 * Y1 * Y2^-1, Y2 * Y1^2 * Y2^3 * Y1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 17, 55, 4, 42, 10, 48, 24, 62, 31, 69, 13, 51, 26, 64, 37, 75, 21, 59, 29, 67, 36, 74, 20, 58, 7, 45, 12, 50, 18, 56, 5, 43)(3, 41, 9, 47, 23, 61, 32, 70, 14, 52, 27, 65, 38, 76, 22, 60, 30, 68, 35, 73, 19, 57, 6, 44, 11, 49, 25, 63, 34, 72, 16, 54, 28, 66, 33, 71, 15, 53)(77, 115, 79, 117, 89, 127, 106, 144, 88, 126, 104, 142, 86, 124, 103, 141, 112, 150, 101, 139, 84, 122, 99, 137, 113, 151, 95, 133, 81, 119, 91, 129, 107, 145, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 105, 143, 87, 125, 78, 116, 85, 123, 102, 140, 111, 149, 94, 132, 109, 147, 100, 138, 114, 152, 96, 134, 110, 148, 93, 131, 108, 146, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 100)(9, 103)(10, 102)(11, 104)(12, 78)(13, 105)(14, 106)(15, 108)(16, 79)(17, 107)(18, 84)(19, 110)(20, 81)(21, 83)(22, 82)(23, 114)(24, 113)(25, 109)(26, 112)(27, 111)(28, 85)(29, 88)(30, 87)(31, 97)(32, 98)(33, 99)(34, 91)(35, 101)(36, 94)(37, 96)(38, 95)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.337
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.374 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2^2, Y3^2 * Y2^-2, (Y1, Y2^-1), (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y3), Y1^4 * Y3, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-3, Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y1 * Y3^-1 * Y2^-2 * Y1^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 20, 58, 7, 45, 12, 50, 25, 63, 32, 70, 21, 59, 29, 67, 33, 71, 13, 51, 26, 64, 37, 75, 17, 55, 4, 42, 10, 48, 18, 56, 5, 43)(3, 41, 9, 47, 23, 61, 36, 74, 16, 54, 28, 66, 38, 76, 19, 57, 6, 44, 11, 49, 24, 62, 31, 69, 22, 60, 30, 68, 34, 72, 14, 52, 27, 65, 35, 73, 15, 53)(77, 115, 79, 117, 89, 127, 107, 145, 96, 134, 112, 150, 93, 131, 110, 148, 101, 139, 114, 152, 94, 132, 111, 149, 105, 143, 87, 125, 78, 116, 85, 123, 102, 140, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 108, 146, 95, 133, 81, 119, 91, 129, 109, 147, 100, 138, 84, 122, 99, 137, 113, 151, 106, 144, 88, 126, 104, 142, 86, 124, 103, 141, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 94)(9, 103)(10, 102)(11, 104)(12, 78)(13, 108)(14, 107)(15, 110)(16, 79)(17, 109)(18, 113)(19, 112)(20, 81)(21, 83)(22, 82)(23, 111)(24, 114)(25, 84)(26, 97)(27, 98)(28, 85)(29, 88)(30, 87)(31, 95)(32, 96)(33, 101)(34, 100)(35, 106)(36, 91)(37, 105)(38, 99)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.341
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.375 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3^-1), Y1^3 * Y3, (Y3, Y2^-1), Y3^-2 * Y2^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2, Y2^-1 * Y1^-2 * Y3 * Y2^-1 * Y1^-1, Y3^2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^3, Y3^-6 * Y1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 7, 45, 12, 50, 23, 61, 19, 57, 27, 65, 35, 73, 34, 72, 30, 68, 38, 76, 31, 69, 13, 51, 24, 62, 17, 55, 4, 42, 10, 48, 5, 43)(3, 41, 9, 47, 21, 59, 16, 54, 26, 64, 18, 56, 6, 44, 11, 49, 22, 60, 20, 58, 28, 66, 36, 74, 33, 71, 29, 67, 37, 75, 32, 70, 14, 52, 25, 63, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 103, 141, 87, 125, 78, 116, 85, 123, 100, 138, 113, 151, 111, 149, 98, 136, 84, 122, 97, 135, 93, 131, 108, 146, 110, 148, 96, 134, 83, 121, 92, 130, 80, 118, 90, 128, 106, 144, 104, 142, 88, 126, 102, 140, 86, 124, 101, 139, 114, 152, 112, 150, 99, 137, 94, 132, 81, 119, 91, 129, 107, 145, 109, 147, 95, 133, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 81)(9, 101)(10, 100)(11, 102)(12, 78)(13, 106)(14, 105)(15, 108)(16, 79)(17, 107)(18, 97)(19, 83)(20, 82)(21, 91)(22, 94)(23, 84)(24, 114)(25, 113)(26, 85)(27, 88)(28, 87)(29, 104)(30, 103)(31, 110)(32, 109)(33, 96)(34, 95)(35, 99)(36, 98)(37, 112)(38, 111)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.347
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.376 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-3 * Y3, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-2, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3^6, Y2^4 * Y1 * Y2^2, (Y3^-1 * Y1^-1)^19 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 4, 42, 10, 48, 22, 60, 13, 51, 24, 62, 35, 73, 30, 68, 34, 72, 38, 76, 31, 69, 19, 57, 27, 65, 18, 56, 7, 45, 12, 50, 5, 43)(3, 41, 9, 47, 21, 59, 14, 52, 25, 63, 36, 74, 29, 67, 33, 71, 37, 75, 32, 70, 20, 58, 28, 66, 17, 55, 6, 44, 11, 49, 23, 61, 16, 54, 26, 64, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 107, 145, 93, 131, 81, 119, 91, 129, 98, 136, 112, 150, 114, 152, 104, 142, 88, 126, 102, 140, 86, 124, 101, 139, 110, 148, 96, 134, 83, 121, 92, 130, 80, 118, 90, 128, 106, 144, 108, 146, 94, 132, 99, 137, 84, 122, 97, 135, 111, 149, 113, 151, 103, 141, 87, 125, 78, 116, 85, 123, 100, 138, 109, 147, 95, 133, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 84)(6, 92)(7, 77)(8, 98)(9, 101)(10, 100)(11, 102)(12, 78)(13, 106)(14, 105)(15, 97)(16, 79)(17, 99)(18, 81)(19, 83)(20, 82)(21, 112)(22, 111)(23, 91)(24, 110)(25, 109)(26, 85)(27, 88)(28, 87)(29, 108)(30, 107)(31, 94)(32, 93)(33, 96)(34, 95)(35, 114)(36, 113)(37, 104)(38, 103)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.339
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.377 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3), (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2), (Y3, Y2^-1), (R * Y2)^2, (Y3 * Y2^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^2 * Y3 * Y2^2 * Y1^2, Y2 * Y1 * Y3 * Y2^3 * Y1, Y1^3 * Y3 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 13, 51, 25, 63, 38, 76, 34, 72, 20, 58, 7, 45, 12, 50, 17, 55, 4, 42, 10, 48, 24, 62, 30, 68, 35, 73, 21, 59, 18, 56, 5, 43)(3, 41, 9, 47, 23, 61, 29, 67, 36, 74, 22, 60, 28, 66, 32, 70, 16, 54, 27, 65, 31, 69, 14, 52, 26, 64, 37, 75, 33, 71, 19, 57, 6, 44, 11, 49, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 110, 148, 104, 142, 88, 126, 103, 141, 86, 124, 102, 140, 111, 149, 95, 133, 81, 119, 91, 129, 84, 122, 99, 137, 114, 152, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 106, 144, 109, 147, 94, 132, 87, 125, 78, 116, 85, 123, 101, 139, 112, 150, 96, 134, 108, 146, 93, 131, 107, 145, 100, 138, 113, 151, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 100)(9, 102)(10, 101)(11, 103)(12, 78)(13, 106)(14, 105)(15, 107)(16, 79)(17, 84)(18, 88)(19, 108)(20, 81)(21, 83)(22, 82)(23, 113)(24, 114)(25, 111)(26, 112)(27, 85)(28, 87)(29, 109)(30, 110)(31, 99)(32, 91)(33, 104)(34, 94)(35, 96)(36, 95)(37, 98)(38, 97)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.345
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.378 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), (Y3^-1 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1, Y2), (Y3^-1, Y1^-1), Y2^-1 * Y3^2 * Y2^-1, Y1^2 * Y3 * Y1 * Y3, Y2 * Y1^2 * Y2 * Y1, Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y2^-2 * Y3^-3 * Y1^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y2^34 * Y3^-1 * Y1^2 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 21, 59, 27, 65, 30, 68, 35, 73, 17, 55, 4, 42, 10, 48, 20, 58, 7, 45, 12, 50, 24, 62, 38, 76, 31, 69, 13, 51, 18, 56, 5, 43)(3, 41, 9, 47, 19, 57, 6, 44, 11, 49, 23, 61, 37, 75, 32, 70, 14, 52, 25, 63, 34, 72, 16, 54, 26, 64, 36, 74, 22, 60, 28, 66, 29, 67, 33, 71, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 100, 138, 112, 150, 96, 134, 110, 148, 93, 131, 108, 146, 103, 141, 87, 125, 78, 116, 85, 123, 94, 132, 109, 147, 114, 152, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 106, 144, 99, 137, 84, 122, 95, 133, 81, 119, 91, 129, 107, 145, 104, 142, 88, 126, 102, 140, 86, 124, 101, 139, 111, 149, 113, 151, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 96)(9, 101)(10, 94)(11, 102)(12, 78)(13, 106)(14, 105)(15, 108)(16, 79)(17, 107)(18, 111)(19, 110)(20, 81)(21, 83)(22, 82)(23, 112)(24, 84)(25, 109)(26, 85)(27, 88)(28, 87)(29, 99)(30, 100)(31, 103)(32, 104)(33, 113)(34, 91)(35, 114)(36, 95)(37, 98)(38, 97)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.336
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.379 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2), (Y2 * Y3^-1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y1)^2, (Y1^-1, Y2), (R * Y2)^2, Y3^2 * Y1 * Y3 * Y1, Y2 * Y3 * Y1^2 * Y2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, Y1^3 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3 * Y1^-1 * Y3^7, Y3^2 * Y2^6 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 23, 61, 30, 68, 13, 51, 20, 58, 7, 45, 12, 50, 25, 63, 34, 72, 17, 55, 4, 42, 10, 48, 21, 59, 27, 65, 35, 73, 18, 56, 5, 43)(3, 41, 9, 47, 22, 60, 28, 66, 37, 75, 29, 67, 33, 71, 16, 54, 26, 64, 36, 74, 38, 76, 31, 69, 14, 52, 19, 57, 6, 44, 11, 49, 24, 62, 32, 70, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 110, 148, 114, 152, 103, 141, 87, 125, 78, 116, 85, 123, 96, 134, 109, 147, 93, 131, 107, 145, 111, 149, 100, 138, 84, 122, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 94, 132, 108, 146, 99, 137, 104, 142, 88, 126, 102, 140, 86, 124, 95, 133, 81, 119, 91, 129, 106, 144, 113, 151, 101, 139, 112, 150, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 97)(9, 95)(10, 96)(11, 102)(12, 78)(13, 94)(14, 105)(15, 107)(16, 79)(17, 106)(18, 110)(19, 109)(20, 81)(21, 83)(22, 82)(23, 103)(24, 112)(25, 84)(26, 85)(27, 88)(28, 87)(29, 108)(30, 111)(31, 113)(32, 114)(33, 91)(34, 99)(35, 101)(36, 98)(37, 100)(38, 104)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.335
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.380 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y3)^2, (Y3, Y1^-1), (Y1^-1, Y2), (Y2, Y3), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-2 * Y1^2, Y1^-4 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-6 * Y1^-1 * Y2^-2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 8, 46, 23, 61, 34, 72, 21, 59, 17, 55, 4, 42, 10, 48, 25, 63, 33, 71, 20, 58, 7, 45, 12, 50, 13, 51, 26, 64, 31, 69, 18, 56, 5, 43)(3, 41, 9, 47, 24, 62, 32, 70, 19, 57, 6, 44, 11, 49, 14, 52, 27, 65, 37, 75, 36, 74, 30, 68, 16, 54, 28, 66, 29, 67, 38, 76, 35, 73, 22, 60, 15, 53)(77, 115, 79, 117, 89, 127, 105, 143, 101, 139, 113, 151, 110, 148, 95, 133, 81, 119, 91, 129, 88, 126, 104, 142, 86, 124, 103, 141, 99, 137, 108, 146, 94, 132, 98, 136, 83, 121, 92, 130, 80, 118, 90, 128, 84, 122, 100, 138, 107, 145, 111, 149, 96, 134, 106, 144, 93, 131, 87, 125, 78, 116, 85, 123, 102, 140, 114, 152, 109, 147, 112, 150, 97, 135, 82, 120)
	L = (1, 80)(2, 86)(3, 90)(4, 89)(5, 93)(6, 92)(7, 77)(8, 101)(9, 103)(10, 102)(11, 104)(12, 78)(13, 84)(14, 105)(15, 87)(16, 79)(17, 88)(18, 97)(19, 106)(20, 81)(21, 83)(22, 82)(23, 109)(24, 113)(25, 107)(26, 99)(27, 114)(28, 85)(29, 100)(30, 91)(31, 110)(32, 112)(33, 94)(34, 96)(35, 95)(36, 98)(37, 111)(38, 108)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.346
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.381 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, (Y2, Y3^-1), (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, Y3^2 * Y2^3 * Y3 * Y2^3 * Y1^-1, Y2^28 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 7, 45, 10, 48, 17, 55, 19, 57, 26, 64, 28, 66, 33, 71, 35, 73, 37, 75, 29, 67, 32, 70, 22, 60, 23, 61, 11, 49, 15, 53, 4, 42, 5, 43)(3, 41, 8, 46, 14, 52, 16, 54, 6, 44, 9, 47, 18, 56, 20, 58, 25, 63, 27, 65, 34, 72, 36, 74, 38, 76, 30, 68, 31, 69, 21, 59, 24, 62, 12, 50, 13, 51)(77, 115, 79, 117, 87, 125, 97, 135, 105, 143, 112, 150, 104, 142, 96, 134, 86, 124, 92, 130, 81, 119, 89, 127, 99, 137, 107, 145, 113, 151, 110, 148, 102, 140, 94, 132, 83, 121, 90, 128, 80, 118, 88, 126, 98, 136, 106, 144, 111, 149, 103, 141, 95, 133, 85, 123, 78, 116, 84, 122, 91, 129, 100, 138, 108, 146, 114, 152, 109, 147, 101, 139, 93, 131, 82, 120)
	L = (1, 80)(2, 81)(3, 88)(4, 87)(5, 91)(6, 90)(7, 77)(8, 89)(9, 92)(10, 78)(11, 98)(12, 97)(13, 100)(14, 79)(15, 99)(16, 84)(17, 83)(18, 82)(19, 86)(20, 85)(21, 106)(22, 105)(23, 108)(24, 107)(25, 94)(26, 93)(27, 96)(28, 95)(29, 111)(30, 112)(31, 114)(32, 113)(33, 102)(34, 101)(35, 104)(36, 103)(37, 109)(38, 110)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.334
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.382 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 19, 19, 38})
Quotient :: dipole
Aut^+ = C38 (small group id <38, 2>)
Aut   = D76 (small group id <76, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^-1, (Y3 * Y2^-1)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y1)^2, (Y3, Y2), (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^-3 * Y1^-1 * Y3^-1 * Y2^-5, Y2^-2 * Y3^-1 * Y2^-2 * Y3^-2 * Y1^-1 * Y2^-2, Y3^-3 * Y1^-1 * Y3^-3 * Y1^-1 * Y3^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 39, 2, 40, 4, 42, 9, 47, 11, 49, 19, 57, 22, 60, 28, 66, 29, 67, 35, 73, 38, 76, 33, 71, 32, 70, 26, 64, 23, 61, 17, 55, 16, 54, 7, 45, 5, 43)(3, 41, 8, 46, 12, 50, 20, 58, 21, 59, 27, 65, 30, 68, 36, 74, 37, 75, 34, 72, 31, 69, 25, 63, 24, 62, 18, 56, 15, 53, 6, 44, 10, 48, 14, 52, 13, 51)(77, 115, 79, 117, 87, 125, 97, 135, 105, 143, 113, 151, 108, 146, 100, 138, 92, 130, 86, 124, 78, 116, 84, 122, 95, 133, 103, 141, 111, 149, 110, 148, 102, 140, 94, 132, 83, 121, 90, 128, 80, 118, 88, 126, 98, 136, 106, 144, 114, 152, 107, 145, 99, 137, 91, 129, 81, 119, 89, 127, 85, 123, 96, 134, 104, 142, 112, 150, 109, 147, 101, 139, 93, 131, 82, 120)
	L = (1, 80)(2, 85)(3, 88)(4, 87)(5, 78)(6, 90)(7, 77)(8, 96)(9, 95)(10, 89)(11, 98)(12, 97)(13, 84)(14, 79)(15, 86)(16, 81)(17, 83)(18, 82)(19, 104)(20, 103)(21, 106)(22, 105)(23, 92)(24, 91)(25, 94)(26, 93)(27, 112)(28, 111)(29, 114)(30, 113)(31, 100)(32, 99)(33, 102)(34, 101)(35, 109)(36, 110)(37, 107)(38, 108)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ), ( 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38, 4, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.344
Graph:: bipartite
	v = 3 e = 76 f = 21
	degree seq :: [ 38^2, 76 ]

E27.383 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 8, 8})
Quotient :: dipole
Aut^+ = C5 : C8 (small group id <40, 1>)
Aut   = (C5 x D8) : C2 (small group id <80, 15>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y1^-1), Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y2^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y1^-1 * Y2^-2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y3^4 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-1 * Y1 * Y2, Y1^-2 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-2 * Y1^-2 * Y2^4 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 20, 60, 5, 45)(3, 43, 13, 53, 33, 73, 24, 64, 9, 49)(4, 44, 10, 50, 25, 65, 39, 79, 18, 58)(6, 46, 16, 56, 38, 78, 26, 66, 11, 51)(7, 47, 12, 52, 27, 67, 34, 74, 14, 54)(15, 55, 35, 75, 32, 72, 22, 62, 28, 68)(17, 57, 29, 69, 40, 80, 36, 76, 23, 63)(19, 59, 37, 77, 31, 71, 21, 61, 30, 70)(81, 121, 83, 123, 94, 134, 108, 148, 120, 160, 110, 150, 90, 130, 86, 126)(82, 122, 89, 129, 87, 127, 102, 142, 116, 156, 101, 141, 105, 145, 91, 131)(84, 124, 96, 136, 85, 125, 93, 133, 114, 154, 95, 135, 109, 149, 99, 139)(88, 128, 104, 144, 92, 132, 112, 152, 103, 143, 111, 151, 119, 159, 106, 146)(97, 137, 117, 157, 98, 138, 118, 158, 100, 140, 113, 153, 107, 147, 115, 155)
	L = (1, 84)(2, 90)(3, 91)(4, 97)(5, 98)(6, 101)(7, 81)(8, 105)(9, 106)(10, 109)(11, 111)(12, 82)(13, 86)(14, 85)(15, 83)(16, 110)(17, 92)(18, 103)(19, 108)(20, 119)(21, 112)(22, 104)(23, 87)(24, 118)(25, 120)(26, 117)(27, 88)(28, 89)(29, 107)(30, 102)(31, 115)(32, 113)(33, 96)(34, 100)(35, 93)(36, 94)(37, 95)(38, 99)(39, 116)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.386
Graph:: bipartite
	v = 13 e = 80 f = 15
	degree seq :: [ 10^8, 16^5 ]

E27.384 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 8, 8})
Quotient :: dipole
Aut^+ = C5 : C8 (small group id <40, 1>)
Aut   = (C5 x D8) : C2 (small group id <80, 15>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2 * Y3^-1 * Y2, Y1^-1 * Y2^-1 * Y1^-1 * Y2, (Y3^-1, Y1), Y2^-1 * Y3 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3^-1 * Y1^-1, Y3^4 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^2 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^3, (Y1 * Y3)^4 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 5, 45)(3, 43, 13, 53, 33, 73, 24, 64, 9, 49)(4, 44, 10, 50, 25, 65, 39, 79, 18, 58)(6, 46, 15, 55, 34, 74, 26, 66, 11, 51)(7, 47, 12, 52, 27, 67, 36, 76, 20, 60)(14, 54, 29, 69, 16, 56, 38, 78, 28, 68)(17, 57, 30, 70, 40, 80, 35, 75, 23, 63)(21, 61, 37, 77, 32, 72, 22, 62, 31, 71)(81, 121, 83, 123, 90, 130, 109, 149, 120, 160, 111, 151, 100, 140, 86, 126)(82, 122, 89, 129, 105, 145, 94, 134, 115, 155, 102, 142, 87, 127, 91, 131)(84, 124, 96, 136, 110, 150, 101, 141, 116, 156, 95, 135, 85, 125, 93, 133)(88, 128, 104, 144, 119, 159, 108, 148, 103, 143, 112, 152, 92, 132, 106, 146)(97, 137, 117, 157, 107, 147, 114, 154, 99, 139, 113, 153, 98, 138, 118, 158)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 89)(7, 81)(8, 105)(9, 108)(10, 110)(11, 104)(12, 82)(13, 109)(14, 112)(15, 83)(16, 111)(17, 92)(18, 103)(19, 119)(20, 85)(21, 86)(22, 106)(23, 87)(24, 118)(25, 120)(26, 113)(27, 88)(28, 117)(29, 102)(30, 107)(31, 91)(32, 114)(33, 96)(34, 93)(35, 100)(36, 99)(37, 95)(38, 101)(39, 115)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.385
Graph:: bipartite
	v = 13 e = 80 f = 15
	degree seq :: [ 10^8, 16^5 ]

E27.385 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 8, 8})
Quotient :: dipole
Aut^+ = C5 : C8 (small group id <40, 1>)
Aut   = (C5 x D8) : C2 (small group id <80, 15>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^2, (Y2^-1, Y3), (R * Y2^-1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 6, 46, 9, 49, 11, 51, 13, 53, 3, 43, 5, 45)(4, 44, 15, 55, 18, 58, 20, 60, 27, 67, 10, 50, 12, 52, 17, 57)(7, 47, 22, 62, 21, 61, 19, 59, 26, 66, 8, 48, 14, 54, 23, 63)(16, 56, 28, 68, 33, 73, 34, 74, 40, 80, 31, 71, 29, 69, 32, 72)(24, 64, 25, 65, 36, 76, 38, 78, 39, 79, 37, 77, 30, 70, 35, 75)(81, 121, 83, 123, 91, 131, 86, 126)(82, 122, 85, 125, 93, 133, 89, 129)(84, 124, 92, 132, 107, 147, 98, 138)(87, 127, 94, 134, 106, 146, 101, 141)(88, 128, 99, 139, 102, 142, 103, 143)(90, 130, 100, 140, 95, 135, 97, 137)(96, 136, 109, 149, 120, 160, 113, 153)(104, 144, 110, 150, 119, 159, 116, 156)(105, 145, 115, 155, 117, 157, 118, 158)(108, 148, 112, 152, 111, 151, 114, 154)
	L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 99)(6, 98)(7, 81)(8, 105)(9, 103)(10, 82)(11, 107)(12, 109)(13, 102)(14, 83)(15, 93)(16, 110)(17, 89)(18, 113)(19, 115)(20, 85)(21, 86)(22, 117)(23, 118)(24, 87)(25, 112)(26, 91)(27, 120)(28, 90)(29, 119)(30, 94)(31, 95)(32, 100)(33, 104)(34, 97)(35, 111)(36, 101)(37, 114)(38, 108)(39, 106)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 10, 16, 10, 16, 10, 16, 10, 16 ), ( 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.384
Graph:: bipartite
	v = 15 e = 80 f = 13
	degree seq :: [ 8^10, 16^5 ]

E27.386 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 8, 8})
Quotient :: dipole
Aut^+ = C5 : C8 (small group id <40, 1>)
Aut   = (C5 x D8) : C2 (small group id <80, 15>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1 * Y1, (Y3^-1, Y2), Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y1 * Y3 * Y1, Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^5 * Y2^-1, Y2^-1 * Y3^-3 * Y2^-1 * Y3^-2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 3, 43, 8, 48, 11, 51, 19, 59, 6, 46, 5, 45)(4, 44, 14, 54, 12, 52, 20, 60, 27, 67, 10, 50, 17, 57, 16, 56)(7, 47, 22, 62, 13, 53, 18, 58, 26, 66, 9, 49, 21, 61, 23, 63)(15, 55, 28, 68, 29, 69, 34, 74, 40, 80, 31, 71, 33, 73, 32, 72)(24, 64, 25, 65, 30, 70, 38, 78, 39, 79, 37, 77, 36, 76, 35, 75)(81, 121, 83, 123, 91, 131, 86, 126)(82, 122, 88, 128, 99, 139, 85, 125)(84, 124, 92, 132, 107, 147, 97, 137)(87, 127, 93, 133, 106, 146, 101, 141)(89, 129, 103, 143, 102, 142, 98, 138)(90, 130, 96, 136, 94, 134, 100, 140)(95, 135, 109, 149, 120, 160, 113, 153)(104, 144, 110, 150, 119, 159, 116, 156)(105, 145, 118, 158, 117, 157, 115, 155)(108, 148, 114, 154, 111, 151, 112, 152)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 98)(6, 97)(7, 81)(8, 103)(9, 105)(10, 82)(11, 107)(12, 109)(13, 83)(14, 99)(15, 110)(16, 88)(17, 113)(18, 115)(19, 102)(20, 85)(21, 86)(22, 117)(23, 118)(24, 87)(25, 114)(26, 91)(27, 120)(28, 90)(29, 119)(30, 93)(31, 94)(32, 100)(33, 104)(34, 96)(35, 108)(36, 101)(37, 112)(38, 111)(39, 106)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 10, 16, 10, 16, 10, 16, 10, 16 ), ( 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.383
Graph:: bipartite
	v = 15 e = 80 f = 13
	degree seq :: [ 8^10, 16^5 ]

E27.387 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^2, Y1^-2 * Y2^2, (R * Y3)^2, Y1^4, Y3 * Y1^-1 * Y3 * Y1, R * Y1 * R * Y2, (Y2^-1, Y1), Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y1^-1 * Y3^-3, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 15, 55, 31, 71, 26, 66, 11, 51, 27, 67, 36, 76, 20, 60, 7, 47)(2, 42, 10, 50, 25, 65, 30, 70, 14, 54, 3, 43, 13, 53, 29, 69, 28, 68, 12, 52)(5, 45, 18, 58, 34, 74, 33, 73, 17, 57, 6, 46, 19, 59, 35, 75, 32, 72, 16, 56)(8, 48, 21, 61, 37, 77, 40, 80, 24, 64, 9, 49, 23, 63, 39, 79, 38, 78, 22, 62)(81, 82, 88, 85)(83, 89, 86, 91)(84, 92, 101, 96)(87, 90, 102, 98)(93, 104, 99, 106)(94, 103, 97, 107)(95, 108, 117, 112)(100, 105, 118, 114)(109, 120, 115, 111)(110, 119, 113, 116)(121, 123, 128, 126)(122, 129, 125, 131)(124, 134, 141, 137)(127, 133, 142, 139)(130, 144, 138, 146)(132, 143, 136, 147)(135, 150, 157, 153)(140, 149, 158, 155)(145, 160, 154, 151)(148, 159, 152, 156)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.400
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.388 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y1 * Y2^2 * Y1, Y2^4, (R * Y3)^2, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3^2 * Y1 * Y2^-1 * Y3, Y3^2 * Y1^-1 * Y3^-1 * Y2, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3^2 * Y2 * Y1^-1)^2, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 17, 57, 15, 55, 35, 75, 40, 80, 30, 70, 11, 51, 22, 62, 7, 47)(2, 42, 10, 50, 29, 69, 27, 67, 33, 73, 36, 76, 16, 56, 3, 43, 14, 54, 12, 52)(5, 45, 20, 60, 38, 78, 25, 65, 31, 71, 37, 77, 19, 59, 6, 46, 21, 61, 18, 58)(8, 48, 23, 63, 34, 74, 13, 53, 32, 72, 39, 79, 28, 68, 9, 49, 26, 66, 24, 64)(81, 82, 88, 85)(83, 93, 86, 95)(84, 92, 103, 98)(87, 90, 104, 100)(89, 105, 91, 107)(94, 114, 101, 97)(96, 112, 99, 115)(102, 109, 106, 118)(108, 111, 110, 113)(116, 119, 117, 120)(121, 123, 128, 126)(122, 129, 125, 131)(124, 136, 143, 139)(127, 134, 144, 141)(130, 148, 140, 150)(132, 146, 138, 142)(133, 151, 135, 153)(137, 156, 154, 157)(145, 155, 147, 152)(149, 159, 158, 160)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.401
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.389 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2^2, Y2^4, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y1^4, (Y1, Y2^-1), (R * Y3)^2, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-2, Y2^2 * Y3^5, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 15, 55, 31, 71, 22, 62, 8, 48, 21, 61, 36, 76, 20, 60, 7, 47)(2, 42, 10, 50, 25, 65, 32, 72, 16, 56, 5, 45, 18, 58, 34, 74, 28, 68, 12, 52)(3, 43, 13, 53, 29, 69, 33, 73, 17, 57, 6, 46, 19, 59, 35, 75, 30, 70, 14, 54)(9, 49, 23, 63, 37, 77, 39, 79, 26, 66, 11, 51, 27, 67, 40, 80, 38, 78, 24, 64)(81, 82, 88, 85)(83, 89, 86, 91)(84, 92, 101, 96)(87, 90, 102, 98)(93, 104, 99, 106)(94, 103, 97, 107)(95, 108, 116, 112)(100, 105, 111, 114)(109, 118, 115, 119)(110, 117, 113, 120)(121, 123, 128, 126)(122, 129, 125, 131)(124, 134, 141, 137)(127, 133, 142, 139)(130, 144, 138, 146)(132, 143, 136, 147)(135, 150, 156, 153)(140, 149, 151, 155)(145, 158, 154, 159)(148, 157, 152, 160)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.398
Graph:: bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.390 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-2 * Y2^-1, Y1 * Y2^-2 * Y1, Y2^4, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^2 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-2 * Y1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y3^2 * Y2^-1 * Y1, Y1^-1 * Y2^-1 * Y3^3 * Y1^-1 * Y2, Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 17, 57, 37, 77, 24, 64, 8, 48, 23, 63, 40, 80, 22, 62, 7, 47)(2, 42, 10, 50, 29, 69, 38, 78, 18, 58, 5, 45, 20, 60, 33, 73, 32, 72, 12, 52)(3, 43, 14, 54, 35, 75, 25, 65, 19, 59, 6, 46, 21, 61, 39, 79, 27, 67, 16, 56)(9, 49, 26, 66, 36, 76, 15, 55, 30, 70, 11, 51, 31, 71, 34, 74, 13, 53, 28, 68)(81, 82, 88, 85)(83, 93, 86, 95)(84, 92, 103, 98)(87, 90, 104, 100)(89, 105, 91, 107)(94, 114, 101, 116)(96, 108, 99, 110)(97, 112, 120, 118)(102, 109, 117, 113)(106, 115, 111, 119)(121, 123, 128, 126)(122, 129, 125, 131)(124, 136, 143, 139)(127, 134, 144, 141)(130, 148, 140, 150)(132, 146, 138, 151)(133, 153, 135, 149)(137, 147, 160, 145)(142, 155, 157, 159)(152, 156, 158, 154)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.399
Graph:: bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.391 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x C4 x D10 (small group id <80, 36>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 38, 78, 32, 72, 24, 64, 16, 56, 8, 48)(3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 34, 74, 26, 66, 18, 58, 10, 50)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54)(81, 82, 86, 83)(84, 88, 93, 90)(85, 87, 94, 89)(91, 96, 101, 98)(92, 95, 102, 97)(99, 104, 109, 106)(100, 103, 110, 105)(107, 112, 116, 114)(108, 111, 117, 113)(115, 118, 120, 119)(121, 123, 126, 122)(124, 130, 133, 128)(125, 129, 134, 127)(131, 138, 141, 136)(132, 137, 142, 135)(139, 146, 149, 144)(140, 145, 150, 143)(147, 154, 156, 152)(148, 153, 157, 151)(155, 159, 160, 158)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.402
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.392 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x C4 x D10 (small group id <80, 36>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y1^4, Y2^2 * Y1^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^2 * Y1^-2, R * Y1 * R * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y3 * Y1^-2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y3^26 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 17, 57, 34, 74, 13, 53, 28, 68, 9, 49, 26, 66, 22, 62, 7, 47)(2, 42, 10, 50, 29, 69, 39, 79, 25, 65, 19, 59, 6, 46, 21, 61, 32, 72, 12, 52)(3, 43, 14, 54, 35, 75, 18, 58, 5, 45, 20, 60, 33, 73, 40, 80, 27, 67, 16, 56)(8, 48, 23, 63, 37, 77, 36, 76, 15, 55, 30, 70, 11, 51, 31, 71, 38, 78, 24, 64)(81, 82, 88, 85)(83, 93, 86, 95)(84, 92, 103, 98)(87, 90, 104, 100)(89, 105, 91, 107)(94, 114, 101, 116)(96, 108, 99, 110)(97, 112, 117, 115)(102, 109, 118, 113)(106, 119, 111, 120)(121, 123, 128, 126)(122, 129, 125, 131)(124, 136, 143, 139)(127, 134, 144, 141)(130, 148, 140, 150)(132, 146, 138, 151)(133, 153, 135, 149)(137, 147, 157, 145)(142, 155, 158, 152)(154, 160, 156, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.403
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.393 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1, Y2^4, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^10, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 38, 78, 32, 72, 24, 64, 16, 56, 8, 48)(4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 39, 79, 34, 74, 26, 66, 18, 58, 10, 50)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54)(81, 82, 86, 84)(83, 88, 93, 90)(85, 87, 94, 91)(89, 96, 101, 98)(92, 95, 102, 99)(97, 104, 109, 106)(100, 103, 110, 107)(105, 112, 116, 114)(108, 111, 117, 115)(113, 118, 120, 119)(121, 122, 126, 124)(123, 128, 133, 130)(125, 127, 134, 131)(129, 136, 141, 138)(132, 135, 142, 139)(137, 144, 149, 146)(140, 143, 150, 147)(145, 152, 156, 154)(148, 151, 157, 155)(153, 158, 160, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.404
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.394 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y1^4, Y3 * Y2^-1 * Y3 * Y2, Y2^4, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^2, Y3 * Y2^2 * Y3^-1 * Y1^-2, Y3^2 * Y1 * Y3^-2 * Y2^-1, (Y2 * Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 17, 57, 35, 75, 15, 55, 30, 70, 11, 51, 31, 71, 22, 62, 7, 47)(2, 42, 10, 50, 29, 69, 40, 80, 27, 67, 16, 56, 3, 43, 14, 54, 32, 72, 12, 52)(5, 45, 20, 60, 33, 73, 39, 79, 25, 65, 19, 59, 6, 46, 21, 61, 36, 76, 18, 58)(8, 48, 23, 63, 37, 77, 34, 74, 13, 53, 28, 68, 9, 49, 26, 66, 38, 78, 24, 64)(81, 82, 88, 85)(83, 93, 86, 95)(84, 92, 103, 98)(87, 90, 104, 100)(89, 105, 91, 107)(94, 114, 101, 115)(96, 108, 99, 110)(97, 112, 117, 116)(102, 109, 118, 113)(106, 119, 111, 120)(121, 123, 128, 126)(122, 129, 125, 131)(124, 136, 143, 139)(127, 134, 144, 141)(130, 148, 140, 150)(132, 146, 138, 151)(133, 153, 135, 149)(137, 147, 157, 145)(142, 152, 158, 156)(154, 159, 155, 160)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.405
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.395 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^2, Y1^-2 * Y2^-2, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y3^-2 * Y2^-1 * Y1^-1, Y3^4, Y2^-1 * Y3^2 * Y1^-1, R * Y1 * R * Y2, (Y1, Y2^-1), Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 9, 49, 7, 47)(2, 42, 10, 50, 6, 46, 12, 52)(3, 43, 14, 54, 5, 45, 16, 56)(8, 48, 18, 58, 11, 51, 20, 60)(13, 53, 22, 62, 15, 55, 24, 64)(17, 57, 26, 66, 19, 59, 28, 68)(21, 61, 30, 70, 23, 63, 32, 72)(25, 65, 34, 74, 27, 67, 36, 76)(29, 69, 37, 77, 31, 71, 38, 78)(33, 73, 39, 79, 35, 75, 40, 80)(81, 82, 88, 97, 105, 113, 109, 103, 93, 85)(83, 89, 86, 91, 99, 107, 115, 111, 101, 95)(84, 96, 102, 112, 117, 119, 114, 106, 98, 90)(87, 94, 104, 110, 118, 120, 116, 108, 100, 92)(121, 123, 133, 141, 149, 155, 145, 139, 128, 126)(122, 129, 125, 135, 143, 151, 153, 147, 137, 131)(124, 132, 138, 148, 154, 160, 157, 150, 142, 134)(127, 130, 140, 146, 156, 159, 158, 152, 144, 136)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.406
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.396 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3 * Y2^-1, Y1^10, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 12, 52, 5, 45)(2, 42, 7, 47, 16, 56, 8, 48)(3, 43, 10, 50, 20, 60, 11, 51)(6, 46, 14, 54, 24, 64, 15, 55)(9, 49, 18, 58, 28, 68, 19, 59)(13, 53, 22, 62, 32, 72, 23, 63)(17, 57, 26, 66, 35, 75, 27, 67)(21, 61, 30, 70, 38, 78, 31, 71)(25, 65, 33, 73, 39, 79, 34, 74)(29, 69, 36, 76, 40, 80, 37, 77)(81, 82, 86, 93, 101, 109, 105, 97, 89, 83)(84, 90, 98, 106, 113, 116, 110, 102, 94, 87)(85, 91, 99, 107, 114, 117, 111, 103, 95, 88)(92, 96, 104, 112, 118, 120, 119, 115, 108, 100)(121, 123, 129, 137, 145, 149, 141, 133, 126, 122)(124, 127, 134, 142, 150, 156, 153, 146, 138, 130)(125, 128, 135, 143, 151, 157, 154, 147, 139, 131)(132, 140, 148, 155, 159, 160, 158, 152, 144, 136)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.407
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.397 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y2^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, R * Y2 * R * Y1, Y3^4, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 12, 52, 5, 45)(2, 42, 7, 47, 16, 56, 8, 48)(3, 43, 10, 50, 20, 60, 11, 51)(6, 46, 14, 54, 24, 64, 15, 55)(9, 49, 18, 58, 28, 68, 19, 59)(13, 53, 22, 62, 32, 72, 23, 63)(17, 57, 26, 66, 35, 75, 27, 67)(21, 61, 30, 70, 38, 78, 31, 71)(25, 65, 33, 73, 39, 79, 34, 74)(29, 69, 36, 76, 40, 80, 37, 77)(81, 82, 86, 93, 101, 109, 105, 97, 89, 83)(84, 91, 98, 107, 113, 117, 110, 103, 94, 88)(85, 90, 99, 106, 114, 116, 111, 102, 95, 87)(92, 96, 104, 112, 118, 120, 119, 115, 108, 100)(121, 123, 129, 137, 145, 149, 141, 133, 126, 122)(124, 128, 134, 143, 150, 157, 153, 147, 138, 131)(125, 127, 135, 142, 151, 156, 154, 146, 139, 130)(132, 140, 148, 155, 159, 160, 158, 152, 144, 136)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.408
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.398 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^2, Y1^-2 * Y2^2, (R * Y3)^2, Y1^4, Y3 * Y1^-1 * Y3 * Y1, R * Y1 * R * Y2, (Y2^-1, Y1), Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y1^-1 * Y3^-3, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 15, 55, 95, 135, 31, 71, 111, 151, 26, 66, 106, 146, 11, 51, 91, 131, 27, 67, 107, 147, 36, 76, 116, 156, 20, 60, 100, 140, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 25, 65, 105, 145, 30, 70, 110, 150, 14, 54, 94, 134, 3, 43, 83, 123, 13, 53, 93, 133, 29, 69, 109, 149, 28, 68, 108, 148, 12, 52, 92, 132)(5, 45, 85, 125, 18, 58, 98, 138, 34, 74, 114, 154, 33, 73, 113, 153, 17, 57, 97, 137, 6, 46, 86, 126, 19, 59, 99, 139, 35, 75, 115, 155, 32, 72, 112, 152, 16, 56, 96, 136)(8, 48, 88, 128, 21, 61, 101, 141, 37, 77, 117, 157, 40, 80, 120, 160, 24, 64, 104, 144, 9, 49, 89, 129, 23, 63, 103, 143, 39, 79, 119, 159, 38, 78, 118, 158, 22, 62, 102, 142)
	L = (1, 42)(2, 48)(3, 49)(4, 52)(5, 41)(6, 51)(7, 50)(8, 45)(9, 46)(10, 62)(11, 43)(12, 61)(13, 64)(14, 63)(15, 68)(16, 44)(17, 67)(18, 47)(19, 66)(20, 65)(21, 56)(22, 58)(23, 57)(24, 59)(25, 78)(26, 53)(27, 54)(28, 77)(29, 80)(30, 79)(31, 69)(32, 55)(33, 76)(34, 60)(35, 71)(36, 70)(37, 72)(38, 74)(39, 73)(40, 75)(81, 123)(82, 129)(83, 128)(84, 134)(85, 131)(86, 121)(87, 133)(88, 126)(89, 125)(90, 144)(91, 122)(92, 143)(93, 142)(94, 141)(95, 150)(96, 147)(97, 124)(98, 146)(99, 127)(100, 149)(101, 137)(102, 139)(103, 136)(104, 138)(105, 160)(106, 130)(107, 132)(108, 159)(109, 158)(110, 157)(111, 145)(112, 156)(113, 135)(114, 151)(115, 140)(116, 148)(117, 153)(118, 155)(119, 152)(120, 154)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.389
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.399 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y1 * Y2^2 * Y1, Y2^4, (R * Y3)^2, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3^2 * Y1 * Y2^-1 * Y3, Y3^2 * Y1^-1 * Y3^-1 * Y2, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3^2 * Y2 * Y1^-1)^2, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 15, 55, 95, 135, 35, 75, 115, 155, 40, 80, 120, 160, 30, 70, 110, 150, 11, 51, 91, 131, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 29, 69, 109, 149, 27, 67, 107, 147, 33, 73, 113, 153, 36, 76, 116, 156, 16, 56, 96, 136, 3, 43, 83, 123, 14, 54, 94, 134, 12, 52, 92, 132)(5, 45, 85, 125, 20, 60, 100, 140, 38, 78, 118, 158, 25, 65, 105, 145, 31, 71, 111, 151, 37, 77, 117, 157, 19, 59, 99, 139, 6, 46, 86, 126, 21, 61, 101, 141, 18, 58, 98, 138)(8, 48, 88, 128, 23, 63, 103, 143, 34, 74, 114, 154, 13, 53, 93, 133, 32, 72, 112, 152, 39, 79, 119, 159, 28, 68, 108, 148, 9, 49, 89, 129, 26, 66, 106, 146, 24, 64, 104, 144)
	L = (1, 42)(2, 48)(3, 53)(4, 52)(5, 41)(6, 55)(7, 50)(8, 45)(9, 65)(10, 64)(11, 67)(12, 63)(13, 46)(14, 74)(15, 43)(16, 72)(17, 54)(18, 44)(19, 75)(20, 47)(21, 57)(22, 69)(23, 58)(24, 60)(25, 51)(26, 78)(27, 49)(28, 71)(29, 66)(30, 73)(31, 70)(32, 59)(33, 68)(34, 61)(35, 56)(36, 79)(37, 80)(38, 62)(39, 77)(40, 76)(81, 123)(82, 129)(83, 128)(84, 136)(85, 131)(86, 121)(87, 134)(88, 126)(89, 125)(90, 148)(91, 122)(92, 146)(93, 151)(94, 144)(95, 153)(96, 143)(97, 156)(98, 142)(99, 124)(100, 150)(101, 127)(102, 132)(103, 139)(104, 141)(105, 155)(106, 138)(107, 152)(108, 140)(109, 159)(110, 130)(111, 135)(112, 145)(113, 133)(114, 157)(115, 147)(116, 154)(117, 137)(118, 160)(119, 158)(120, 149)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.390
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.400 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2^2, Y2^4, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y1^4, (Y1, Y2^-1), (R * Y3)^2, Y1 * Y3 * Y1^-1 * Y3, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-2, Y2^2 * Y3^5, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 15, 55, 95, 135, 31, 71, 111, 151, 22, 62, 102, 142, 8, 48, 88, 128, 21, 61, 101, 141, 36, 76, 116, 156, 20, 60, 100, 140, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 25, 65, 105, 145, 32, 72, 112, 152, 16, 56, 96, 136, 5, 45, 85, 125, 18, 58, 98, 138, 34, 74, 114, 154, 28, 68, 108, 148, 12, 52, 92, 132)(3, 43, 83, 123, 13, 53, 93, 133, 29, 69, 109, 149, 33, 73, 113, 153, 17, 57, 97, 137, 6, 46, 86, 126, 19, 59, 99, 139, 35, 75, 115, 155, 30, 70, 110, 150, 14, 54, 94, 134)(9, 49, 89, 129, 23, 63, 103, 143, 37, 77, 117, 157, 39, 79, 119, 159, 26, 66, 106, 146, 11, 51, 91, 131, 27, 67, 107, 147, 40, 80, 120, 160, 38, 78, 118, 158, 24, 64, 104, 144)
	L = (1, 42)(2, 48)(3, 49)(4, 52)(5, 41)(6, 51)(7, 50)(8, 45)(9, 46)(10, 62)(11, 43)(12, 61)(13, 64)(14, 63)(15, 68)(16, 44)(17, 67)(18, 47)(19, 66)(20, 65)(21, 56)(22, 58)(23, 57)(24, 59)(25, 71)(26, 53)(27, 54)(28, 76)(29, 78)(30, 77)(31, 74)(32, 55)(33, 80)(34, 60)(35, 79)(36, 72)(37, 73)(38, 75)(39, 69)(40, 70)(81, 123)(82, 129)(83, 128)(84, 134)(85, 131)(86, 121)(87, 133)(88, 126)(89, 125)(90, 144)(91, 122)(92, 143)(93, 142)(94, 141)(95, 150)(96, 147)(97, 124)(98, 146)(99, 127)(100, 149)(101, 137)(102, 139)(103, 136)(104, 138)(105, 158)(106, 130)(107, 132)(108, 157)(109, 151)(110, 156)(111, 155)(112, 160)(113, 135)(114, 159)(115, 140)(116, 153)(117, 152)(118, 154)(119, 145)(120, 148)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.387
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.401 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C20 x C2) : C2 (small group id <80, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-2 * Y2^-1, Y1 * Y2^-2 * Y1, Y2^4, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y3^2 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-2 * Y1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y3^2 * Y2^-1 * Y1, Y1^-1 * Y2^-1 * Y3^3 * Y1^-1 * Y2, Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 37, 77, 117, 157, 24, 64, 104, 144, 8, 48, 88, 128, 23, 63, 103, 143, 40, 80, 120, 160, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 29, 69, 109, 149, 38, 78, 118, 158, 18, 58, 98, 138, 5, 45, 85, 125, 20, 60, 100, 140, 33, 73, 113, 153, 32, 72, 112, 152, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 35, 75, 115, 155, 25, 65, 105, 145, 19, 59, 99, 139, 6, 46, 86, 126, 21, 61, 101, 141, 39, 79, 119, 159, 27, 67, 107, 147, 16, 56, 96, 136)(9, 49, 89, 129, 26, 66, 106, 146, 36, 76, 116, 156, 15, 55, 95, 135, 30, 70, 110, 150, 11, 51, 91, 131, 31, 71, 111, 151, 34, 74, 114, 154, 13, 53, 93, 133, 28, 68, 108, 148)
	L = (1, 42)(2, 48)(3, 53)(4, 52)(5, 41)(6, 55)(7, 50)(8, 45)(9, 65)(10, 64)(11, 67)(12, 63)(13, 46)(14, 74)(15, 43)(16, 68)(17, 72)(18, 44)(19, 70)(20, 47)(21, 76)(22, 69)(23, 58)(24, 60)(25, 51)(26, 75)(27, 49)(28, 59)(29, 77)(30, 56)(31, 79)(32, 80)(33, 62)(34, 61)(35, 71)(36, 54)(37, 73)(38, 57)(39, 66)(40, 78)(81, 123)(82, 129)(83, 128)(84, 136)(85, 131)(86, 121)(87, 134)(88, 126)(89, 125)(90, 148)(91, 122)(92, 146)(93, 153)(94, 144)(95, 149)(96, 143)(97, 147)(98, 151)(99, 124)(100, 150)(101, 127)(102, 155)(103, 139)(104, 141)(105, 137)(106, 138)(107, 160)(108, 140)(109, 133)(110, 130)(111, 132)(112, 156)(113, 135)(114, 152)(115, 157)(116, 158)(117, 159)(118, 154)(119, 142)(120, 145)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.388
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.402 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x C4 x D10 (small group id <80, 36>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 11, 51, 91, 131, 19, 59, 99, 139, 27, 67, 107, 147, 35, 75, 115, 155, 28, 68, 108, 148, 20, 60, 100, 140, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 15, 55, 95, 135, 23, 63, 103, 143, 31, 71, 111, 151, 38, 78, 118, 158, 32, 72, 112, 152, 24, 64, 104, 144, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 9, 49, 89, 129, 17, 57, 97, 137, 25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154, 26, 66, 106, 146, 18, 58, 98, 138, 10, 50, 90, 130)(6, 46, 86, 126, 13, 53, 93, 133, 21, 61, 101, 141, 29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157, 30, 70, 110, 150, 22, 62, 102, 142, 14, 54, 94, 134)
	L = (1, 42)(2, 46)(3, 41)(4, 48)(5, 47)(6, 43)(7, 54)(8, 53)(9, 45)(10, 44)(11, 56)(12, 55)(13, 50)(14, 49)(15, 62)(16, 61)(17, 52)(18, 51)(19, 64)(20, 63)(21, 58)(22, 57)(23, 70)(24, 69)(25, 60)(26, 59)(27, 72)(28, 71)(29, 66)(30, 65)(31, 77)(32, 76)(33, 68)(34, 67)(35, 78)(36, 74)(37, 73)(38, 80)(39, 75)(40, 79)(81, 123)(82, 121)(83, 126)(84, 130)(85, 129)(86, 122)(87, 125)(88, 124)(89, 134)(90, 133)(91, 138)(92, 137)(93, 128)(94, 127)(95, 132)(96, 131)(97, 142)(98, 141)(99, 146)(100, 145)(101, 136)(102, 135)(103, 140)(104, 139)(105, 150)(106, 149)(107, 154)(108, 153)(109, 144)(110, 143)(111, 148)(112, 147)(113, 157)(114, 156)(115, 159)(116, 152)(117, 151)(118, 155)(119, 160)(120, 158)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.391
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.403 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x C4 x D10 (small group id <80, 36>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y1^4, Y2^2 * Y1^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^2 * Y1^-2, R * Y1 * R * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y3 * Y1^-2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y3^26 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 34, 74, 114, 154, 13, 53, 93, 133, 28, 68, 108, 148, 9, 49, 89, 129, 26, 66, 106, 146, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 29, 69, 109, 149, 39, 79, 119, 159, 25, 65, 105, 145, 19, 59, 99, 139, 6, 46, 86, 126, 21, 61, 101, 141, 32, 72, 112, 152, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 35, 75, 115, 155, 18, 58, 98, 138, 5, 45, 85, 125, 20, 60, 100, 140, 33, 73, 113, 153, 40, 80, 120, 160, 27, 67, 107, 147, 16, 56, 96, 136)(8, 48, 88, 128, 23, 63, 103, 143, 37, 77, 117, 157, 36, 76, 116, 156, 15, 55, 95, 135, 30, 70, 110, 150, 11, 51, 91, 131, 31, 71, 111, 151, 38, 78, 118, 158, 24, 64, 104, 144)
	L = (1, 42)(2, 48)(3, 53)(4, 52)(5, 41)(6, 55)(7, 50)(8, 45)(9, 65)(10, 64)(11, 67)(12, 63)(13, 46)(14, 74)(15, 43)(16, 68)(17, 72)(18, 44)(19, 70)(20, 47)(21, 76)(22, 69)(23, 58)(24, 60)(25, 51)(26, 79)(27, 49)(28, 59)(29, 78)(30, 56)(31, 80)(32, 77)(33, 62)(34, 61)(35, 57)(36, 54)(37, 75)(38, 73)(39, 71)(40, 66)(81, 123)(82, 129)(83, 128)(84, 136)(85, 131)(86, 121)(87, 134)(88, 126)(89, 125)(90, 148)(91, 122)(92, 146)(93, 153)(94, 144)(95, 149)(96, 143)(97, 147)(98, 151)(99, 124)(100, 150)(101, 127)(102, 155)(103, 139)(104, 141)(105, 137)(106, 138)(107, 157)(108, 140)(109, 133)(110, 130)(111, 132)(112, 142)(113, 135)(114, 160)(115, 158)(116, 159)(117, 145)(118, 152)(119, 154)(120, 156)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.392
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.404 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1, Y2^4, (R * Y3)^2, R * Y2 * R * Y1, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^10, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 3, 43, 83, 123, 9, 49, 89, 129, 17, 57, 97, 137, 25, 65, 105, 145, 33, 73, 113, 153, 28, 68, 108, 148, 20, 60, 100, 140, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 15, 55, 95, 135, 23, 63, 103, 143, 31, 71, 111, 151, 38, 78, 118, 158, 32, 72, 112, 152, 24, 64, 104, 144, 16, 56, 96, 136, 8, 48, 88, 128)(4, 44, 84, 124, 11, 51, 91, 131, 19, 59, 99, 139, 27, 67, 107, 147, 35, 75, 115, 155, 39, 79, 119, 159, 34, 74, 114, 154, 26, 66, 106, 146, 18, 58, 98, 138, 10, 50, 90, 130)(6, 46, 86, 126, 13, 53, 93, 133, 21, 61, 101, 141, 29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157, 30, 70, 110, 150, 22, 62, 102, 142, 14, 54, 94, 134)
	L = (1, 42)(2, 46)(3, 48)(4, 41)(5, 47)(6, 44)(7, 54)(8, 53)(9, 56)(10, 43)(11, 45)(12, 55)(13, 50)(14, 51)(15, 62)(16, 61)(17, 64)(18, 49)(19, 52)(20, 63)(21, 58)(22, 59)(23, 70)(24, 69)(25, 72)(26, 57)(27, 60)(28, 71)(29, 66)(30, 67)(31, 77)(32, 76)(33, 78)(34, 65)(35, 68)(36, 74)(37, 75)(38, 80)(39, 73)(40, 79)(81, 122)(82, 126)(83, 128)(84, 121)(85, 127)(86, 124)(87, 134)(88, 133)(89, 136)(90, 123)(91, 125)(92, 135)(93, 130)(94, 131)(95, 142)(96, 141)(97, 144)(98, 129)(99, 132)(100, 143)(101, 138)(102, 139)(103, 150)(104, 149)(105, 152)(106, 137)(107, 140)(108, 151)(109, 146)(110, 147)(111, 157)(112, 156)(113, 158)(114, 145)(115, 148)(116, 154)(117, 155)(118, 160)(119, 153)(120, 159)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.393
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.405 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y1^4, Y3 * Y2^-1 * Y3 * Y2, Y2^4, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^2, Y3 * Y2^2 * Y3^-1 * Y1^-2, Y3^2 * Y1 * Y3^-2 * Y2^-1, (Y2 * Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 35, 75, 115, 155, 15, 55, 95, 135, 30, 70, 110, 150, 11, 51, 91, 131, 31, 71, 111, 151, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 29, 69, 109, 149, 40, 80, 120, 160, 27, 67, 107, 147, 16, 56, 96, 136, 3, 43, 83, 123, 14, 54, 94, 134, 32, 72, 112, 152, 12, 52, 92, 132)(5, 45, 85, 125, 20, 60, 100, 140, 33, 73, 113, 153, 39, 79, 119, 159, 25, 65, 105, 145, 19, 59, 99, 139, 6, 46, 86, 126, 21, 61, 101, 141, 36, 76, 116, 156, 18, 58, 98, 138)(8, 48, 88, 128, 23, 63, 103, 143, 37, 77, 117, 157, 34, 74, 114, 154, 13, 53, 93, 133, 28, 68, 108, 148, 9, 49, 89, 129, 26, 66, 106, 146, 38, 78, 118, 158, 24, 64, 104, 144)
	L = (1, 42)(2, 48)(3, 53)(4, 52)(5, 41)(6, 55)(7, 50)(8, 45)(9, 65)(10, 64)(11, 67)(12, 63)(13, 46)(14, 74)(15, 43)(16, 68)(17, 72)(18, 44)(19, 70)(20, 47)(21, 75)(22, 69)(23, 58)(24, 60)(25, 51)(26, 79)(27, 49)(28, 59)(29, 78)(30, 56)(31, 80)(32, 77)(33, 62)(34, 61)(35, 54)(36, 57)(37, 76)(38, 73)(39, 71)(40, 66)(81, 123)(82, 129)(83, 128)(84, 136)(85, 131)(86, 121)(87, 134)(88, 126)(89, 125)(90, 148)(91, 122)(92, 146)(93, 153)(94, 144)(95, 149)(96, 143)(97, 147)(98, 151)(99, 124)(100, 150)(101, 127)(102, 152)(103, 139)(104, 141)(105, 137)(106, 138)(107, 157)(108, 140)(109, 133)(110, 130)(111, 132)(112, 158)(113, 135)(114, 159)(115, 160)(116, 142)(117, 145)(118, 156)(119, 155)(120, 154)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.394
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.406 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^2, Y1^-2 * Y2^-2, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y3^-2 * Y2^-1 * Y1^-1, Y3^4, Y2^-1 * Y3^2 * Y1^-1, R * Y1 * R * Y2, (Y1, Y2^-1), Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 9, 49, 89, 129, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 6, 46, 86, 126, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 5, 45, 85, 125, 16, 56, 96, 136)(8, 48, 88, 128, 18, 58, 98, 138, 11, 51, 91, 131, 20, 60, 100, 140)(13, 53, 93, 133, 22, 62, 102, 142, 15, 55, 95, 135, 24, 64, 104, 144)(17, 57, 97, 137, 26, 66, 106, 146, 19, 59, 99, 139, 28, 68, 108, 148)(21, 61, 101, 141, 30, 70, 110, 150, 23, 63, 103, 143, 32, 72, 112, 152)(25, 65, 105, 145, 34, 74, 114, 154, 27, 67, 107, 147, 36, 76, 116, 156)(29, 69, 109, 149, 37, 77, 117, 157, 31, 71, 111, 151, 38, 78, 118, 158)(33, 73, 113, 153, 39, 79, 119, 159, 35, 75, 115, 155, 40, 80, 120, 160)
	L = (1, 42)(2, 48)(3, 49)(4, 56)(5, 41)(6, 51)(7, 54)(8, 57)(9, 46)(10, 44)(11, 59)(12, 47)(13, 45)(14, 64)(15, 43)(16, 62)(17, 65)(18, 50)(19, 67)(20, 52)(21, 55)(22, 72)(23, 53)(24, 70)(25, 73)(26, 58)(27, 75)(28, 60)(29, 63)(30, 78)(31, 61)(32, 77)(33, 69)(34, 66)(35, 71)(36, 68)(37, 79)(38, 80)(39, 74)(40, 76)(81, 123)(82, 129)(83, 133)(84, 132)(85, 135)(86, 121)(87, 130)(88, 126)(89, 125)(90, 140)(91, 122)(92, 138)(93, 141)(94, 124)(95, 143)(96, 127)(97, 131)(98, 148)(99, 128)(100, 146)(101, 149)(102, 134)(103, 151)(104, 136)(105, 139)(106, 156)(107, 137)(108, 154)(109, 155)(110, 142)(111, 153)(112, 144)(113, 147)(114, 160)(115, 145)(116, 159)(117, 150)(118, 152)(119, 158)(120, 157)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.395
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.407 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3 * Y2^-1, Y1^10, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 20, 60, 100, 140, 11, 51, 91, 131)(6, 46, 86, 126, 14, 54, 94, 134, 24, 64, 104, 144, 15, 55, 95, 135)(9, 49, 89, 129, 18, 58, 98, 138, 28, 68, 108, 148, 19, 59, 99, 139)(13, 53, 93, 133, 22, 62, 102, 142, 32, 72, 112, 152, 23, 63, 103, 143)(17, 57, 97, 137, 26, 66, 106, 146, 35, 75, 115, 155, 27, 67, 107, 147)(21, 61, 101, 141, 30, 70, 110, 150, 38, 78, 118, 158, 31, 71, 111, 151)(25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154)(29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157)
	L = (1, 42)(2, 46)(3, 41)(4, 50)(5, 51)(6, 53)(7, 44)(8, 45)(9, 43)(10, 58)(11, 59)(12, 56)(13, 61)(14, 47)(15, 48)(16, 64)(17, 49)(18, 66)(19, 67)(20, 52)(21, 69)(22, 54)(23, 55)(24, 72)(25, 57)(26, 73)(27, 74)(28, 60)(29, 65)(30, 62)(31, 63)(32, 78)(33, 76)(34, 77)(35, 68)(36, 70)(37, 71)(38, 80)(39, 75)(40, 79)(81, 123)(82, 121)(83, 129)(84, 127)(85, 128)(86, 122)(87, 134)(88, 135)(89, 137)(90, 124)(91, 125)(92, 140)(93, 126)(94, 142)(95, 143)(96, 132)(97, 145)(98, 130)(99, 131)(100, 148)(101, 133)(102, 150)(103, 151)(104, 136)(105, 149)(106, 138)(107, 139)(108, 155)(109, 141)(110, 156)(111, 157)(112, 144)(113, 146)(114, 147)(115, 159)(116, 153)(117, 154)(118, 152)(119, 160)(120, 158)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.396
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.408 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1, Y2^-1 * Y1^-1, Y2^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, R * Y2 * R * Y1, Y3^4, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 20, 60, 100, 140, 11, 51, 91, 131)(6, 46, 86, 126, 14, 54, 94, 134, 24, 64, 104, 144, 15, 55, 95, 135)(9, 49, 89, 129, 18, 58, 98, 138, 28, 68, 108, 148, 19, 59, 99, 139)(13, 53, 93, 133, 22, 62, 102, 142, 32, 72, 112, 152, 23, 63, 103, 143)(17, 57, 97, 137, 26, 66, 106, 146, 35, 75, 115, 155, 27, 67, 107, 147)(21, 61, 101, 141, 30, 70, 110, 150, 38, 78, 118, 158, 31, 71, 111, 151)(25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154)(29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157)
	L = (1, 42)(2, 46)(3, 41)(4, 51)(5, 50)(6, 53)(7, 45)(8, 44)(9, 43)(10, 59)(11, 58)(12, 56)(13, 61)(14, 48)(15, 47)(16, 64)(17, 49)(18, 67)(19, 66)(20, 52)(21, 69)(22, 55)(23, 54)(24, 72)(25, 57)(26, 74)(27, 73)(28, 60)(29, 65)(30, 63)(31, 62)(32, 78)(33, 77)(34, 76)(35, 68)(36, 71)(37, 70)(38, 80)(39, 75)(40, 79)(81, 123)(82, 121)(83, 129)(84, 128)(85, 127)(86, 122)(87, 135)(88, 134)(89, 137)(90, 125)(91, 124)(92, 140)(93, 126)(94, 143)(95, 142)(96, 132)(97, 145)(98, 131)(99, 130)(100, 148)(101, 133)(102, 151)(103, 150)(104, 136)(105, 149)(106, 139)(107, 138)(108, 155)(109, 141)(110, 157)(111, 156)(112, 144)(113, 147)(114, 146)(115, 159)(116, 154)(117, 153)(118, 152)(119, 160)(120, 158)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.397
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.409 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^10, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 8, 48, 13, 53, 10, 50)(5, 45, 7, 47, 14, 54, 11, 51)(9, 49, 16, 56, 21, 61, 18, 58)(12, 52, 15, 55, 22, 62, 19, 59)(17, 57, 24, 64, 29, 69, 26, 66)(20, 60, 23, 63, 30, 70, 27, 67)(25, 65, 32, 72, 36, 76, 34, 74)(28, 68, 31, 71, 37, 77, 35, 75)(33, 73, 38, 78, 40, 80, 39, 79)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 119, 159, 114, 154, 106, 146, 98, 138, 90, 130)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.410 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y1)^2, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 5, 45)(3, 43, 8, 48, 10, 50, 11, 51)(6, 46, 7, 47, 12, 52, 13, 53)(9, 49, 16, 56, 18, 58, 19, 59)(14, 54, 15, 55, 20, 60, 21, 61)(17, 57, 24, 64, 26, 66, 27, 67)(22, 62, 23, 63, 28, 68, 29, 69)(25, 65, 32, 72, 34, 74, 35, 75)(30, 70, 31, 71, 36, 76, 37, 77)(33, 73, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 110, 150, 102, 142, 94, 134, 86, 126)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 119, 159, 116, 156, 108, 148, 100, 140, 92, 132)(85, 125, 93, 133, 101, 141, 109, 149, 117, 157, 120, 160, 115, 155, 107, 147, 99, 139, 91, 131)
	L = (1, 84)(2, 85)(3, 90)(4, 81)(5, 82)(6, 92)(7, 93)(8, 91)(9, 98)(10, 83)(11, 88)(12, 86)(13, 87)(14, 100)(15, 101)(16, 99)(17, 106)(18, 89)(19, 96)(20, 94)(21, 95)(22, 108)(23, 109)(24, 107)(25, 114)(26, 97)(27, 104)(28, 102)(29, 103)(30, 116)(31, 117)(32, 115)(33, 119)(34, 105)(35, 112)(36, 110)(37, 111)(38, 120)(39, 113)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.411 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y1^-2 * Y3 * Y2^-5, Y2^2 * Y3 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y3 * Y2^4 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 10, 50, 18, 58, 13, 53)(4, 44, 9, 49, 19, 59, 14, 54)(6, 46, 8, 48, 20, 60, 16, 56)(11, 51, 24, 64, 33, 73, 27, 67)(12, 52, 23, 63, 34, 74, 28, 68)(15, 55, 22, 62, 35, 75, 29, 69)(17, 57, 21, 61, 36, 76, 31, 71)(25, 65, 40, 80, 30, 70, 38, 78)(26, 66, 39, 79, 32, 72, 37, 77)(81, 121, 83, 123, 91, 131, 105, 145, 115, 155, 99, 139, 114, 154, 112, 152, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 117, 157, 108, 148, 94, 134, 109, 149, 120, 160, 104, 144, 90, 130)(84, 124, 92, 132, 106, 146, 116, 156, 100, 140, 87, 127, 98, 138, 113, 153, 110, 150, 95, 135)(85, 125, 96, 136, 111, 151, 119, 159, 103, 143, 89, 129, 102, 142, 118, 158, 107, 147, 93, 133)
	L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 83)(13, 108)(14, 85)(15, 86)(16, 109)(17, 110)(18, 114)(19, 87)(20, 115)(21, 118)(22, 88)(23, 90)(24, 119)(25, 116)(26, 91)(27, 117)(28, 93)(29, 96)(30, 97)(31, 120)(32, 113)(33, 112)(34, 98)(35, 100)(36, 105)(37, 107)(38, 101)(39, 104)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.421
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.412 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y3^-1)^2, (R * Y2^-1)^2, Y3^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3^-2, Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 22, 62, 15, 55)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 9, 49, 24, 64, 20, 60)(7, 47, 10, 50, 25, 65, 21, 61)(13, 53, 29, 69, 36, 76, 31, 71)(14, 54, 27, 67, 37, 77, 32, 72)(16, 56, 30, 70, 38, 78, 33, 73)(17, 57, 26, 66, 39, 79, 34, 74)(19, 59, 28, 68, 40, 80, 35, 75)(81, 121, 83, 123, 93, 133, 99, 139, 84, 124, 94, 134, 87, 127, 96, 136, 97, 137, 86, 126)(82, 122, 89, 129, 106, 146, 110, 150, 90, 130, 107, 147, 92, 132, 108, 148, 109, 149, 91, 131)(85, 125, 100, 140, 114, 154, 113, 153, 101, 141, 112, 152, 98, 138, 115, 155, 111, 151, 95, 135)(88, 128, 102, 142, 116, 156, 120, 160, 103, 143, 117, 157, 105, 145, 118, 158, 119, 159, 104, 144)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 87)(14, 86)(15, 113)(16, 83)(17, 93)(18, 85)(19, 96)(20, 112)(21, 111)(22, 117)(23, 119)(24, 120)(25, 88)(26, 92)(27, 91)(28, 89)(29, 106)(30, 108)(31, 114)(32, 95)(33, 115)(34, 98)(35, 100)(36, 105)(37, 104)(38, 102)(39, 116)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.414
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.413 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-2, Y2^2 * Y3^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 14, 54)(4, 44, 12, 52, 22, 62, 16, 56)(6, 46, 9, 49, 23, 63, 17, 57)(7, 47, 10, 50, 24, 64, 18, 58)(13, 53, 27, 67, 34, 74, 30, 70)(15, 55, 28, 68, 35, 75, 31, 71)(19, 59, 25, 65, 36, 76, 32, 72)(20, 60, 26, 66, 37, 77, 33, 73)(29, 69, 38, 78, 40, 80, 39, 79)(81, 121, 83, 123, 84, 124, 93, 133, 95, 135, 109, 149, 100, 140, 99, 139, 87, 127, 86, 126)(82, 122, 89, 129, 90, 130, 105, 145, 106, 146, 118, 158, 108, 148, 107, 147, 92, 132, 91, 131)(85, 125, 97, 137, 98, 138, 112, 152, 113, 153, 119, 159, 111, 151, 110, 150, 96, 136, 94, 134)(88, 128, 101, 141, 102, 142, 114, 154, 115, 155, 120, 160, 117, 157, 116, 156, 104, 144, 103, 143)
	L = (1, 84)(2, 90)(3, 93)(4, 95)(5, 98)(6, 83)(7, 81)(8, 102)(9, 105)(10, 106)(11, 89)(12, 82)(13, 109)(14, 97)(15, 100)(16, 85)(17, 112)(18, 113)(19, 86)(20, 87)(21, 114)(22, 115)(23, 101)(24, 88)(25, 118)(26, 108)(27, 91)(28, 92)(29, 99)(30, 94)(31, 96)(32, 119)(33, 111)(34, 120)(35, 117)(36, 103)(37, 104)(38, 107)(39, 110)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.414 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^4, Y3^5, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, (Y3^2 * Y2^-1)^2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 13, 53)(4, 44, 12, 52, 22, 62, 16, 56)(6, 46, 9, 49, 23, 63, 18, 58)(7, 47, 10, 50, 24, 64, 19, 59)(14, 54, 27, 67, 34, 74, 29, 69)(15, 55, 28, 68, 35, 75, 31, 71)(17, 57, 25, 65, 36, 76, 32, 72)(20, 60, 26, 66, 37, 77, 33, 73)(30, 70, 38, 78, 40, 80, 39, 79)(81, 121, 83, 123, 87, 127, 94, 134, 100, 140, 110, 150, 95, 135, 97, 137, 84, 124, 86, 126)(82, 122, 89, 129, 92, 132, 105, 145, 108, 148, 118, 158, 106, 146, 107, 147, 90, 130, 91, 131)(85, 125, 98, 138, 96, 136, 112, 152, 111, 151, 119, 159, 113, 153, 109, 149, 99, 139, 93, 133)(88, 128, 101, 141, 104, 144, 114, 154, 117, 157, 120, 160, 115, 155, 116, 156, 102, 142, 103, 143)
	L = (1, 84)(2, 90)(3, 86)(4, 95)(5, 99)(6, 97)(7, 81)(8, 102)(9, 91)(10, 106)(11, 107)(12, 82)(13, 109)(14, 83)(15, 100)(16, 85)(17, 110)(18, 93)(19, 113)(20, 87)(21, 103)(22, 115)(23, 116)(24, 88)(25, 89)(26, 108)(27, 118)(28, 92)(29, 119)(30, 94)(31, 96)(32, 98)(33, 111)(34, 101)(35, 117)(36, 120)(37, 104)(38, 105)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.412
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.415 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), (Y2 * Y3)^2, (R * Y3)^2, Y3^2 * Y2^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, (R * Y2)^2, Y1^-2 * Y3 * Y1^-2 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3^-1, Y3 * Y1^2 * Y2^-4, Y1 * Y2^2 * Y3^-1 * Y1 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 22, 62, 15, 55)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 9, 49, 24, 64, 20, 60)(7, 47, 10, 50, 25, 65, 21, 61)(13, 53, 29, 69, 36, 76, 32, 72)(14, 54, 27, 67, 40, 80, 34, 74)(16, 56, 30, 70, 38, 78, 35, 75)(17, 57, 26, 66, 33, 73, 37, 77)(19, 59, 28, 68, 31, 71, 39, 79)(81, 121, 83, 123, 93, 133, 111, 151, 103, 143, 120, 160, 105, 145, 118, 158, 97, 137, 86, 126)(82, 122, 89, 129, 106, 146, 115, 155, 101, 141, 114, 154, 98, 138, 119, 159, 109, 149, 91, 131)(84, 124, 94, 134, 87, 127, 96, 136, 113, 153, 104, 144, 88, 128, 102, 142, 116, 156, 99, 139)(85, 125, 100, 140, 117, 157, 110, 150, 90, 130, 107, 147, 92, 132, 108, 148, 112, 152, 95, 135)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 87)(14, 86)(15, 115)(16, 83)(17, 116)(18, 85)(19, 118)(20, 114)(21, 112)(22, 120)(23, 113)(24, 111)(25, 88)(26, 92)(27, 91)(28, 89)(29, 117)(30, 119)(31, 96)(32, 106)(33, 93)(34, 95)(35, 108)(36, 105)(37, 98)(38, 102)(39, 100)(40, 104)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.416
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.416 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2^-1)^2, Y1^4, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y2^-2 * Y1, Y2 * Y1 * Y2^-1 * Y3^-1 * Y1, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^4 * Y2^-2, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 23, 63, 15, 55)(4, 44, 12, 52, 22, 62, 18, 58)(6, 46, 9, 49, 14, 54, 20, 60)(7, 47, 10, 50, 13, 53, 21, 61)(16, 56, 27, 67, 29, 69, 32, 72)(17, 57, 28, 68, 36, 76, 34, 74)(19, 59, 25, 65, 31, 71, 35, 75)(24, 64, 26, 66, 30, 70, 37, 77)(33, 73, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 104, 144, 113, 153, 97, 137, 111, 151, 102, 142, 86, 126)(82, 122, 89, 129, 98, 138, 115, 155, 108, 148, 118, 158, 106, 146, 112, 152, 101, 141, 91, 131)(84, 124, 94, 134, 88, 128, 103, 143, 87, 127, 96, 136, 110, 150, 119, 159, 116, 156, 99, 139)(85, 125, 100, 140, 92, 132, 105, 145, 114, 154, 120, 160, 117, 157, 107, 147, 90, 130, 95, 135)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 102)(9, 95)(10, 106)(11, 107)(12, 82)(13, 88)(14, 111)(15, 112)(16, 83)(17, 110)(18, 85)(19, 113)(20, 91)(21, 117)(22, 116)(23, 86)(24, 87)(25, 89)(26, 114)(27, 118)(28, 92)(29, 103)(30, 93)(31, 119)(32, 120)(33, 96)(34, 98)(35, 100)(36, 104)(37, 108)(38, 105)(39, 109)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.415
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.417 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3 * Y1^-1 * Y3, (Y2, Y3^-1), (R * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y1)^2, Y1^4, (R * Y2)^2, Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y1^2 * Y2, Y3^-1 * Y1 * Y2^-2 * Y1, Y2^2 * Y3^4, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 19, 59, 15, 55)(4, 44, 12, 52, 13, 53, 18, 58)(6, 46, 9, 49, 16, 56, 20, 60)(7, 47, 10, 50, 22, 62, 21, 61)(14, 54, 27, 67, 29, 69, 32, 72)(17, 57, 28, 68, 30, 70, 35, 75)(23, 63, 25, 65, 33, 73, 36, 76)(24, 64, 26, 66, 34, 74, 37, 77)(31, 71, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 97, 137, 111, 151, 104, 144, 113, 153, 102, 142, 86, 126)(82, 122, 89, 129, 101, 141, 116, 156, 106, 146, 118, 158, 108, 148, 112, 152, 98, 138, 91, 131)(84, 124, 94, 134, 110, 150, 119, 159, 114, 154, 103, 143, 87, 127, 96, 136, 88, 128, 99, 139)(85, 125, 100, 140, 90, 130, 105, 145, 117, 157, 120, 160, 115, 155, 107, 147, 92, 132, 95, 135)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 93)(9, 105)(10, 106)(11, 100)(12, 82)(13, 110)(14, 111)(15, 89)(16, 83)(17, 114)(18, 85)(19, 109)(20, 116)(21, 117)(22, 88)(23, 86)(24, 87)(25, 118)(26, 115)(27, 91)(28, 92)(29, 119)(30, 104)(31, 103)(32, 95)(33, 96)(34, 102)(35, 98)(36, 120)(37, 108)(38, 107)(39, 113)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.418 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y1^2 * Y3^-1, Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-2 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^10, Y3^6 * Y2^-4, (Y3 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 7, 47, 10, 50)(4, 44, 12, 52, 6, 46, 9, 49)(13, 53, 19, 59, 14, 54, 20, 60)(15, 55, 17, 57, 16, 56, 18, 58)(21, 61, 28, 68, 22, 62, 27, 67)(23, 63, 26, 66, 24, 64, 25, 65)(29, 69, 35, 75, 30, 70, 36, 76)(31, 71, 33, 73, 32, 72, 34, 74)(37, 77, 39, 79, 38, 78, 40, 80)(81, 121, 83, 123, 93, 133, 101, 141, 109, 149, 117, 157, 111, 151, 104, 144, 95, 135, 86, 126)(82, 122, 89, 129, 97, 137, 105, 145, 113, 153, 119, 159, 115, 155, 108, 148, 99, 139, 91, 131)(84, 124, 88, 128, 87, 127, 94, 134, 102, 142, 110, 150, 118, 158, 112, 152, 103, 143, 96, 136)(85, 125, 92, 132, 98, 138, 106, 146, 114, 154, 120, 160, 116, 156, 107, 147, 100, 140, 90, 130)
	L = (1, 84)(2, 90)(3, 88)(4, 95)(5, 91)(6, 96)(7, 81)(8, 86)(9, 85)(10, 99)(11, 100)(12, 82)(13, 87)(14, 83)(15, 103)(16, 104)(17, 92)(18, 89)(19, 107)(20, 108)(21, 94)(22, 93)(23, 111)(24, 112)(25, 98)(26, 97)(27, 115)(28, 116)(29, 102)(30, 101)(31, 118)(32, 117)(33, 106)(34, 105)(35, 120)(36, 119)(37, 110)(38, 109)(39, 114)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.423
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.419 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2^-1), Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y1 * Y3^3 * Y1 * Y2^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y3^2 * Y1^-1, Y3^-6 * Y2^-2, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 25, 65, 15, 55)(4, 44, 12, 52, 26, 66, 18, 58)(6, 46, 9, 49, 27, 67, 20, 60)(7, 47, 10, 50, 28, 68, 21, 61)(13, 53, 34, 74, 19, 59, 31, 71)(14, 54, 35, 75, 24, 64, 32, 72)(16, 56, 33, 73, 22, 62, 29, 69)(17, 57, 36, 76, 23, 63, 30, 70)(37, 77, 39, 79, 38, 78, 40, 80)(81, 121, 83, 123, 93, 133, 106, 146, 104, 144, 118, 158, 97, 137, 108, 148, 102, 142, 86, 126)(82, 122, 89, 129, 109, 149, 101, 141, 116, 156, 120, 160, 112, 152, 98, 138, 114, 154, 91, 131)(84, 124, 94, 134, 117, 157, 103, 143, 87, 127, 96, 136, 107, 147, 88, 128, 105, 145, 99, 139)(85, 125, 100, 140, 113, 153, 90, 130, 110, 150, 119, 159, 115, 155, 92, 132, 111, 151, 95, 135)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 106)(9, 110)(10, 112)(11, 113)(12, 82)(13, 117)(14, 108)(15, 109)(16, 83)(17, 107)(18, 85)(19, 118)(20, 116)(21, 115)(22, 105)(23, 86)(24, 87)(25, 104)(26, 103)(27, 93)(28, 88)(29, 119)(30, 98)(31, 89)(32, 95)(33, 120)(34, 100)(35, 91)(36, 92)(37, 102)(38, 96)(39, 114)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.422
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.420 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), (R * Y2)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y2 * Y1^-2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1^2 * Y3^3, Y2^-1 * Y3 * Y2^-3 * Y3, Y3^-1 * Y2 * Y1^-1 * Y3^2 * Y1^-1, Y3^2 * Y2^6 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 25, 65, 15, 55)(4, 44, 12, 52, 26, 66, 18, 58)(6, 46, 9, 49, 27, 67, 20, 60)(7, 47, 10, 50, 28, 68, 21, 61)(13, 53, 34, 74, 23, 63, 30, 70)(14, 54, 35, 75, 22, 62, 29, 69)(16, 56, 33, 73, 17, 57, 36, 76)(19, 59, 31, 71, 24, 64, 32, 72)(37, 77, 39, 79, 38, 78, 40, 80)(81, 121, 83, 123, 93, 133, 108, 148, 97, 137, 118, 158, 104, 144, 106, 146, 102, 142, 86, 126)(82, 122, 89, 129, 109, 149, 98, 138, 112, 152, 120, 160, 116, 156, 101, 141, 114, 154, 91, 131)(84, 124, 94, 134, 107, 147, 88, 128, 105, 145, 103, 143, 87, 127, 96, 136, 117, 157, 99, 139)(85, 125, 100, 140, 115, 155, 92, 132, 111, 151, 119, 159, 113, 153, 90, 130, 110, 150, 95, 135)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 106)(9, 110)(10, 112)(11, 113)(12, 82)(13, 107)(14, 118)(15, 116)(16, 83)(17, 105)(18, 85)(19, 108)(20, 114)(21, 111)(22, 117)(23, 86)(24, 87)(25, 102)(26, 96)(27, 104)(28, 88)(29, 95)(30, 120)(31, 89)(32, 100)(33, 98)(34, 119)(35, 91)(36, 92)(37, 93)(38, 103)(39, 109)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.424
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.421 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y1^-2 * Y2^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 10, 50, 18, 58, 13, 53)(4, 44, 9, 49, 19, 59, 14, 54)(6, 46, 8, 48, 20, 60, 16, 56)(11, 51, 24, 64, 32, 72, 27, 67)(12, 52, 23, 63, 33, 73, 28, 68)(15, 55, 22, 62, 34, 74, 29, 69)(17, 57, 21, 61, 25, 65, 31, 71)(26, 66, 36, 76, 40, 80, 38, 78)(30, 70, 35, 75, 37, 77, 39, 79)(81, 121, 83, 123, 91, 131, 105, 145, 100, 140, 87, 127, 98, 138, 112, 152, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 107, 147, 93, 133, 85, 125, 96, 136, 111, 151, 104, 144, 90, 130)(84, 124, 92, 132, 106, 146, 117, 157, 114, 154, 99, 139, 113, 153, 120, 160, 110, 150, 95, 135)(89, 129, 102, 142, 115, 155, 118, 158, 108, 148, 94, 134, 109, 149, 119, 159, 116, 156, 103, 143)
	L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 83)(13, 108)(14, 85)(15, 86)(16, 109)(17, 110)(18, 113)(19, 87)(20, 114)(21, 115)(22, 88)(23, 90)(24, 116)(25, 117)(26, 91)(27, 118)(28, 93)(29, 96)(30, 97)(31, 119)(32, 120)(33, 98)(34, 100)(35, 101)(36, 104)(37, 105)(38, 107)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.411
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.422 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^-2, (R * Y1)^2, Y1^4, (Y2, Y3^-1), (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y3^-2 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y3^2 * Y1^-1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y2^-2, Y2^10, Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y1^-1 * Y3^2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 22, 62, 15, 55)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 9, 49, 24, 64, 20, 60)(7, 47, 10, 50, 25, 65, 21, 61)(13, 53, 29, 69, 38, 78, 32, 72)(14, 54, 27, 67, 40, 80, 34, 74)(16, 56, 30, 70, 36, 76, 35, 75)(17, 57, 26, 66, 31, 71, 37, 77)(19, 59, 28, 68, 33, 73, 39, 79)(81, 121, 83, 123, 93, 133, 111, 151, 104, 144, 88, 128, 102, 142, 118, 158, 97, 137, 86, 126)(82, 122, 89, 129, 106, 146, 112, 152, 95, 135, 85, 125, 100, 140, 117, 157, 109, 149, 91, 131)(84, 124, 94, 134, 87, 127, 96, 136, 113, 153, 103, 143, 120, 160, 105, 145, 116, 156, 99, 139)(90, 130, 107, 147, 92, 132, 108, 148, 115, 155, 101, 141, 114, 154, 98, 138, 119, 159, 110, 150)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 87)(14, 86)(15, 115)(16, 83)(17, 116)(18, 85)(19, 118)(20, 114)(21, 112)(22, 120)(23, 111)(24, 113)(25, 88)(26, 92)(27, 91)(28, 89)(29, 119)(30, 117)(31, 96)(32, 108)(33, 93)(34, 95)(35, 106)(36, 102)(37, 98)(38, 105)(39, 100)(40, 104)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.419
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.423 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, (Y2^-1 * Y3)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 17, 57, 15, 55)(4, 44, 12, 52, 16, 56, 18, 58)(6, 46, 9, 49, 24, 64, 20, 60)(7, 47, 10, 50, 19, 59, 21, 61)(13, 53, 27, 67, 33, 73, 31, 71)(14, 54, 28, 68, 32, 72, 34, 74)(22, 62, 25, 65, 29, 69, 36, 76)(23, 63, 26, 66, 35, 75, 37, 77)(30, 70, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 104, 144, 88, 128, 97, 137, 113, 153, 102, 142, 86, 126)(82, 122, 89, 129, 105, 145, 111, 151, 95, 135, 85, 125, 100, 140, 116, 156, 107, 147, 91, 131)(84, 124, 94, 134, 110, 150, 103, 143, 87, 127, 96, 136, 112, 152, 119, 159, 115, 155, 99, 139)(90, 130, 106, 146, 118, 158, 108, 148, 92, 132, 101, 141, 117, 157, 120, 160, 114, 154, 98, 138)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 96)(9, 106)(10, 100)(11, 98)(12, 82)(13, 110)(14, 113)(15, 92)(16, 83)(17, 112)(18, 85)(19, 88)(20, 117)(21, 89)(22, 115)(23, 86)(24, 87)(25, 118)(26, 116)(27, 114)(28, 91)(29, 103)(30, 102)(31, 108)(32, 93)(33, 119)(34, 95)(35, 104)(36, 120)(37, 105)(38, 107)(39, 109)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.418
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.424 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C4) (small group id <40, 7>)
Aut   = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^4, Y1 * Y3 * Y1^-1 * Y3, Y2^-1 * Y1 * Y3 * Y1 * Y3^-1, Y1 * Y2 * Y3^2 * Y1, Y2^-1 * Y3 * Y2^-3 * Y3, Y2^5 * Y1^-2, Y3^-1 * Y1 * Y2^2 * Y1 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 24, 64, 15, 55)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 9, 49, 17, 57, 20, 60)(7, 47, 10, 50, 14, 54, 21, 61)(13, 53, 28, 68, 34, 74, 31, 71)(16, 56, 27, 67, 30, 70, 33, 73)(19, 59, 26, 66, 35, 75, 36, 76)(22, 62, 25, 65, 29, 69, 37, 77)(32, 72, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 97, 137, 88, 128, 104, 144, 114, 154, 102, 142, 86, 126)(82, 122, 89, 129, 105, 145, 111, 151, 95, 135, 85, 125, 100, 140, 117, 157, 108, 148, 91, 131)(84, 124, 94, 134, 110, 150, 119, 159, 115, 155, 103, 143, 87, 127, 96, 136, 112, 152, 99, 139)(90, 130, 98, 138, 116, 156, 120, 160, 113, 153, 101, 141, 92, 132, 106, 146, 118, 158, 107, 147)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 98)(10, 95)(11, 107)(12, 82)(13, 110)(14, 88)(15, 113)(16, 83)(17, 115)(18, 85)(19, 109)(20, 92)(21, 91)(22, 112)(23, 86)(24, 87)(25, 116)(26, 89)(27, 111)(28, 118)(29, 119)(30, 104)(31, 120)(32, 93)(33, 108)(34, 96)(35, 102)(36, 100)(37, 106)(38, 105)(39, 114)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.420
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.425 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3 * Y1^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 38, 78, 32, 72, 24, 64, 16, 56, 8, 48)(3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 34, 74, 26, 66, 18, 58, 10, 50)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54)(81, 82, 86, 83)(84, 89, 93, 87)(85, 90, 94, 88)(91, 95, 101, 97)(92, 96, 102, 98)(99, 105, 109, 103)(100, 106, 110, 104)(107, 111, 116, 113)(108, 112, 117, 114)(115, 119, 120, 118)(121, 123, 126, 122)(124, 127, 133, 129)(125, 128, 134, 130)(131, 137, 141, 135)(132, 138, 142, 136)(139, 143, 149, 145)(140, 144, 150, 146)(147, 153, 156, 151)(148, 154, 157, 152)(155, 158, 160, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.431
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.426 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 38, 78, 32, 72, 24, 64, 16, 56, 8, 48)(3, 43, 9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 34, 74, 26, 66, 18, 58, 10, 50)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54)(81, 82, 86, 83)(84, 90, 93, 88)(85, 89, 94, 87)(91, 96, 101, 98)(92, 95, 102, 97)(99, 106, 109, 104)(100, 105, 110, 103)(107, 112, 116, 114)(108, 111, 117, 113)(115, 119, 120, 118)(121, 123, 126, 122)(124, 128, 133, 130)(125, 127, 134, 129)(131, 138, 141, 136)(132, 137, 142, 135)(139, 144, 149, 146)(140, 143, 150, 145)(147, 154, 156, 152)(148, 153, 157, 151)(155, 158, 160, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.432
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.427 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3)^2, (Y1^-1 * Y3^-1)^2, Y2^-2 * Y1^2, Y1^4, R * Y1 * R * Y2, Y2^-1 * Y1^-2 * Y2^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y3^-1 * Y2^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-4 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^2 * Y2 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 19, 59, 34, 74, 13, 53, 28, 68, 9, 49, 26, 66, 22, 62, 7, 47)(2, 42, 10, 50, 30, 70, 39, 79, 25, 65, 18, 58, 6, 46, 21, 61, 32, 72, 12, 52)(3, 43, 14, 54, 36, 76, 17, 57, 5, 45, 20, 60, 33, 73, 40, 80, 27, 67, 16, 56)(8, 48, 23, 63, 37, 77, 35, 75, 15, 55, 29, 69, 11, 51, 31, 71, 38, 78, 24, 64)(81, 82, 88, 85)(83, 93, 86, 95)(84, 97, 103, 92)(87, 100, 104, 90)(89, 105, 91, 107)(94, 115, 101, 114)(96, 109, 98, 108)(99, 112, 117, 116)(102, 110, 118, 113)(106, 120, 111, 119)(121, 123, 128, 126)(122, 129, 125, 131)(124, 138, 143, 136)(127, 141, 144, 134)(130, 149, 140, 148)(132, 151, 137, 146)(133, 153, 135, 150)(139, 147, 157, 145)(142, 156, 158, 152)(154, 159, 155, 160)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.434
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.428 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y1 * Y3, Y1^-2 * Y2^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3^-2 * Y1^-1 * Y2^-1, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, Y2^-1 * Y1^-2 * Y2^-1, (Y1^-1 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3^8, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 9, 49, 22, 62, 29, 69, 38, 78, 33, 73, 27, 67, 13, 53, 7, 47)(2, 42, 10, 50, 6, 46, 18, 58, 26, 66, 36, 76, 37, 77, 31, 71, 21, 61, 12, 52)(3, 43, 14, 54, 25, 65, 34, 74, 39, 79, 32, 72, 23, 63, 17, 57, 5, 45, 16, 56)(8, 48, 19, 59, 11, 51, 24, 64, 30, 70, 40, 80, 35, 75, 28, 68, 15, 55, 20, 60)(81, 82, 88, 85)(83, 93, 86, 95)(84, 97, 99, 92)(87, 96, 100, 90)(89, 101, 91, 103)(94, 108, 98, 107)(102, 112, 104, 111)(105, 113, 106, 115)(109, 117, 110, 119)(114, 120, 116, 118)(121, 123, 128, 126)(122, 129, 125, 131)(124, 130, 139, 136)(127, 138, 140, 134)(132, 144, 137, 142)(133, 145, 135, 146)(141, 149, 143, 150)(147, 156, 148, 154)(151, 160, 152, 158)(153, 159, 155, 157)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.433
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.429 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y2)^2, Y1^-1 * Y2^-1 * Y3^2, (Y3^-1 * Y2^-1)^2, Y3^-1 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1, Y3^2 * Y1 * Y2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y3^2 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 13, 53, 26, 66, 33, 73, 39, 79, 29, 69, 23, 63, 9, 49, 7, 47)(2, 42, 10, 50, 21, 61, 30, 70, 37, 77, 36, 76, 27, 67, 17, 57, 6, 46, 12, 52)(3, 43, 14, 54, 5, 45, 18, 58, 22, 62, 32, 72, 38, 78, 35, 75, 25, 65, 16, 56)(8, 48, 19, 59, 15, 55, 28, 68, 34, 74, 40, 80, 31, 71, 24, 64, 11, 51, 20, 60)(81, 82, 88, 85)(83, 93, 86, 95)(84, 94, 99, 92)(87, 98, 100, 90)(89, 101, 91, 102)(96, 108, 97, 106)(103, 112, 104, 110)(105, 113, 107, 114)(109, 117, 111, 118)(115, 120, 116, 119)(121, 123, 128, 126)(122, 129, 125, 131)(124, 137, 139, 136)(127, 132, 140, 134)(130, 144, 138, 143)(133, 145, 135, 147)(141, 149, 142, 151)(146, 156, 148, 155)(150, 160, 152, 159)(153, 158, 154, 157)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.435
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.430 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y1^-2 * Y2^-2, Y3^2 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1 * Y3^-2, Y3^4, Y3^-1 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, Y3^-2 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y1, Y2^-1), Y1^10, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 9, 49, 7, 47)(2, 42, 10, 50, 6, 46, 12, 52)(3, 43, 14, 54, 5, 45, 16, 56)(8, 48, 18, 58, 11, 51, 20, 60)(13, 53, 22, 62, 15, 55, 24, 64)(17, 57, 26, 66, 19, 59, 28, 68)(21, 61, 30, 70, 23, 63, 32, 72)(25, 65, 34, 74, 27, 67, 36, 76)(29, 69, 37, 77, 31, 71, 38, 78)(33, 73, 39, 79, 35, 75, 40, 80)(81, 82, 88, 97, 105, 113, 109, 103, 93, 85)(83, 89, 86, 91, 99, 107, 115, 111, 101, 95)(84, 94, 102, 110, 117, 120, 114, 108, 98, 92)(87, 96, 104, 112, 118, 119, 116, 106, 100, 90)(121, 123, 133, 141, 149, 155, 145, 139, 128, 126)(122, 129, 125, 135, 143, 151, 153, 147, 137, 131)(124, 130, 138, 146, 154, 159, 157, 152, 142, 136)(127, 132, 140, 148, 156, 160, 158, 150, 144, 134)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.436
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.431 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3 * Y1^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 11, 51, 91, 131, 19, 59, 99, 139, 27, 67, 107, 147, 35, 75, 115, 155, 28, 68, 108, 148, 20, 60, 100, 140, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 15, 55, 95, 135, 23, 63, 103, 143, 31, 71, 111, 151, 38, 78, 118, 158, 32, 72, 112, 152, 24, 64, 104, 144, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 9, 49, 89, 129, 17, 57, 97, 137, 25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154, 26, 66, 106, 146, 18, 58, 98, 138, 10, 50, 90, 130)(6, 46, 86, 126, 13, 53, 93, 133, 21, 61, 101, 141, 29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157, 30, 70, 110, 150, 22, 62, 102, 142, 14, 54, 94, 134)
	L = (1, 42)(2, 46)(3, 41)(4, 49)(5, 50)(6, 43)(7, 44)(8, 45)(9, 53)(10, 54)(11, 55)(12, 56)(13, 47)(14, 48)(15, 61)(16, 62)(17, 51)(18, 52)(19, 65)(20, 66)(21, 57)(22, 58)(23, 59)(24, 60)(25, 69)(26, 70)(27, 71)(28, 72)(29, 63)(30, 64)(31, 76)(32, 77)(33, 67)(34, 68)(35, 79)(36, 73)(37, 74)(38, 75)(39, 80)(40, 78)(81, 123)(82, 121)(83, 126)(84, 127)(85, 128)(86, 122)(87, 133)(88, 134)(89, 124)(90, 125)(91, 137)(92, 138)(93, 129)(94, 130)(95, 131)(96, 132)(97, 141)(98, 142)(99, 143)(100, 144)(101, 135)(102, 136)(103, 149)(104, 150)(105, 139)(106, 140)(107, 153)(108, 154)(109, 145)(110, 146)(111, 147)(112, 148)(113, 156)(114, 157)(115, 158)(116, 151)(117, 152)(118, 160)(119, 155)(120, 159)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.425
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.432 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^4, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 11, 51, 91, 131, 19, 59, 99, 139, 27, 67, 107, 147, 35, 75, 115, 155, 28, 68, 108, 148, 20, 60, 100, 140, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 15, 55, 95, 135, 23, 63, 103, 143, 31, 71, 111, 151, 38, 78, 118, 158, 32, 72, 112, 152, 24, 64, 104, 144, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 9, 49, 89, 129, 17, 57, 97, 137, 25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154, 26, 66, 106, 146, 18, 58, 98, 138, 10, 50, 90, 130)(6, 46, 86, 126, 13, 53, 93, 133, 21, 61, 101, 141, 29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157, 30, 70, 110, 150, 22, 62, 102, 142, 14, 54, 94, 134)
	L = (1, 42)(2, 46)(3, 41)(4, 50)(5, 49)(6, 43)(7, 45)(8, 44)(9, 54)(10, 53)(11, 56)(12, 55)(13, 48)(14, 47)(15, 62)(16, 61)(17, 52)(18, 51)(19, 66)(20, 65)(21, 58)(22, 57)(23, 60)(24, 59)(25, 70)(26, 69)(27, 72)(28, 71)(29, 64)(30, 63)(31, 77)(32, 76)(33, 68)(34, 67)(35, 79)(36, 74)(37, 73)(38, 75)(39, 80)(40, 78)(81, 123)(82, 121)(83, 126)(84, 128)(85, 127)(86, 122)(87, 134)(88, 133)(89, 125)(90, 124)(91, 138)(92, 137)(93, 130)(94, 129)(95, 132)(96, 131)(97, 142)(98, 141)(99, 144)(100, 143)(101, 136)(102, 135)(103, 150)(104, 149)(105, 140)(106, 139)(107, 154)(108, 153)(109, 146)(110, 145)(111, 148)(112, 147)(113, 157)(114, 156)(115, 158)(116, 152)(117, 151)(118, 160)(119, 155)(120, 159)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.426
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.433 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3)^2, (Y1^-1 * Y3^-1)^2, Y2^-2 * Y1^2, Y1^4, R * Y1 * R * Y2, Y2^-1 * Y1^-2 * Y2^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y3^-1 * Y2^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-4 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^2 * Y2 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 19, 59, 99, 139, 34, 74, 114, 154, 13, 53, 93, 133, 28, 68, 108, 148, 9, 49, 89, 129, 26, 66, 106, 146, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 30, 70, 110, 150, 39, 79, 119, 159, 25, 65, 105, 145, 18, 58, 98, 138, 6, 46, 86, 126, 21, 61, 101, 141, 32, 72, 112, 152, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 36, 76, 116, 156, 17, 57, 97, 137, 5, 45, 85, 125, 20, 60, 100, 140, 33, 73, 113, 153, 40, 80, 120, 160, 27, 67, 107, 147, 16, 56, 96, 136)(8, 48, 88, 128, 23, 63, 103, 143, 37, 77, 117, 157, 35, 75, 115, 155, 15, 55, 95, 135, 29, 69, 109, 149, 11, 51, 91, 131, 31, 71, 111, 151, 38, 78, 118, 158, 24, 64, 104, 144)
	L = (1, 42)(2, 48)(3, 53)(4, 57)(5, 41)(6, 55)(7, 60)(8, 45)(9, 65)(10, 47)(11, 67)(12, 44)(13, 46)(14, 75)(15, 43)(16, 69)(17, 63)(18, 68)(19, 72)(20, 64)(21, 74)(22, 70)(23, 52)(24, 50)(25, 51)(26, 80)(27, 49)(28, 56)(29, 58)(30, 78)(31, 79)(32, 77)(33, 62)(34, 54)(35, 61)(36, 59)(37, 76)(38, 73)(39, 66)(40, 71)(81, 123)(82, 129)(83, 128)(84, 138)(85, 131)(86, 121)(87, 141)(88, 126)(89, 125)(90, 149)(91, 122)(92, 151)(93, 153)(94, 127)(95, 150)(96, 124)(97, 146)(98, 143)(99, 147)(100, 148)(101, 144)(102, 156)(103, 136)(104, 134)(105, 139)(106, 132)(107, 157)(108, 130)(109, 140)(110, 133)(111, 137)(112, 142)(113, 135)(114, 159)(115, 160)(116, 158)(117, 145)(118, 152)(119, 155)(120, 154)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.428
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.434 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y1 * Y3, Y1^-2 * Y2^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3^-2 * Y1^-1 * Y2^-1, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, Y2^-1 * Y1^-2 * Y2^-1, (Y1^-1 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3^8, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1 * Y2^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 9, 49, 89, 129, 22, 62, 102, 142, 29, 69, 109, 149, 38, 78, 118, 158, 33, 73, 113, 153, 27, 67, 107, 147, 13, 53, 93, 133, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 6, 46, 86, 126, 18, 58, 98, 138, 26, 66, 106, 146, 36, 76, 116, 156, 37, 77, 117, 157, 31, 71, 111, 151, 21, 61, 101, 141, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 25, 65, 105, 145, 34, 74, 114, 154, 39, 79, 119, 159, 32, 72, 112, 152, 23, 63, 103, 143, 17, 57, 97, 137, 5, 45, 85, 125, 16, 56, 96, 136)(8, 48, 88, 128, 19, 59, 99, 139, 11, 51, 91, 131, 24, 64, 104, 144, 30, 70, 110, 150, 40, 80, 120, 160, 35, 75, 115, 155, 28, 68, 108, 148, 15, 55, 95, 135, 20, 60, 100, 140)
	L = (1, 42)(2, 48)(3, 53)(4, 57)(5, 41)(6, 55)(7, 56)(8, 45)(9, 61)(10, 47)(11, 63)(12, 44)(13, 46)(14, 68)(15, 43)(16, 60)(17, 59)(18, 67)(19, 52)(20, 50)(21, 51)(22, 72)(23, 49)(24, 71)(25, 73)(26, 75)(27, 54)(28, 58)(29, 77)(30, 79)(31, 62)(32, 64)(33, 66)(34, 80)(35, 65)(36, 78)(37, 70)(38, 74)(39, 69)(40, 76)(81, 123)(82, 129)(83, 128)(84, 130)(85, 131)(86, 121)(87, 138)(88, 126)(89, 125)(90, 139)(91, 122)(92, 144)(93, 145)(94, 127)(95, 146)(96, 124)(97, 142)(98, 140)(99, 136)(100, 134)(101, 149)(102, 132)(103, 150)(104, 137)(105, 135)(106, 133)(107, 156)(108, 154)(109, 143)(110, 141)(111, 160)(112, 158)(113, 159)(114, 147)(115, 157)(116, 148)(117, 153)(118, 151)(119, 155)(120, 152)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.427
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.435 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y2)^2, Y1^-1 * Y2^-1 * Y3^2, (Y3^-1 * Y2^-1)^2, Y3^-1 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1, Y3^2 * Y1 * Y2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y3^2 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 13, 53, 93, 133, 26, 66, 106, 146, 33, 73, 113, 153, 39, 79, 119, 159, 29, 69, 109, 149, 23, 63, 103, 143, 9, 49, 89, 129, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 21, 61, 101, 141, 30, 70, 110, 150, 37, 77, 117, 157, 36, 76, 116, 156, 27, 67, 107, 147, 17, 57, 97, 137, 6, 46, 86, 126, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 5, 45, 85, 125, 18, 58, 98, 138, 22, 62, 102, 142, 32, 72, 112, 152, 38, 78, 118, 158, 35, 75, 115, 155, 25, 65, 105, 145, 16, 56, 96, 136)(8, 48, 88, 128, 19, 59, 99, 139, 15, 55, 95, 135, 28, 68, 108, 148, 34, 74, 114, 154, 40, 80, 120, 160, 31, 71, 111, 151, 24, 64, 104, 144, 11, 51, 91, 131, 20, 60, 100, 140)
	L = (1, 42)(2, 48)(3, 53)(4, 54)(5, 41)(6, 55)(7, 58)(8, 45)(9, 61)(10, 47)(11, 62)(12, 44)(13, 46)(14, 59)(15, 43)(16, 68)(17, 66)(18, 60)(19, 52)(20, 50)(21, 51)(22, 49)(23, 72)(24, 70)(25, 73)(26, 56)(27, 74)(28, 57)(29, 77)(30, 63)(31, 78)(32, 64)(33, 67)(34, 65)(35, 80)(36, 79)(37, 71)(38, 69)(39, 75)(40, 76)(81, 123)(82, 129)(83, 128)(84, 137)(85, 131)(86, 121)(87, 132)(88, 126)(89, 125)(90, 144)(91, 122)(92, 140)(93, 145)(94, 127)(95, 147)(96, 124)(97, 139)(98, 143)(99, 136)(100, 134)(101, 149)(102, 151)(103, 130)(104, 138)(105, 135)(106, 156)(107, 133)(108, 155)(109, 142)(110, 160)(111, 141)(112, 159)(113, 158)(114, 157)(115, 146)(116, 148)(117, 153)(118, 154)(119, 150)(120, 152)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.429
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.436 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y1^-2 * Y2^-2, Y3^2 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1 * Y3^-2, Y3^4, Y3^-1 * Y2 * Y3 * Y1^-1, R * Y1 * R * Y2, Y3^-2 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y1, Y2^-1), Y1^10, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 9, 49, 89, 129, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 6, 46, 86, 126, 12, 52, 92, 132)(3, 43, 83, 123, 14, 54, 94, 134, 5, 45, 85, 125, 16, 56, 96, 136)(8, 48, 88, 128, 18, 58, 98, 138, 11, 51, 91, 131, 20, 60, 100, 140)(13, 53, 93, 133, 22, 62, 102, 142, 15, 55, 95, 135, 24, 64, 104, 144)(17, 57, 97, 137, 26, 66, 106, 146, 19, 59, 99, 139, 28, 68, 108, 148)(21, 61, 101, 141, 30, 70, 110, 150, 23, 63, 103, 143, 32, 72, 112, 152)(25, 65, 105, 145, 34, 74, 114, 154, 27, 67, 107, 147, 36, 76, 116, 156)(29, 69, 109, 149, 37, 77, 117, 157, 31, 71, 111, 151, 38, 78, 118, 158)(33, 73, 113, 153, 39, 79, 119, 159, 35, 75, 115, 155, 40, 80, 120, 160)
	L = (1, 42)(2, 48)(3, 49)(4, 54)(5, 41)(6, 51)(7, 56)(8, 57)(9, 46)(10, 47)(11, 59)(12, 44)(13, 45)(14, 62)(15, 43)(16, 64)(17, 65)(18, 52)(19, 67)(20, 50)(21, 55)(22, 70)(23, 53)(24, 72)(25, 73)(26, 60)(27, 75)(28, 58)(29, 63)(30, 77)(31, 61)(32, 78)(33, 69)(34, 68)(35, 71)(36, 66)(37, 80)(38, 79)(39, 76)(40, 74)(81, 123)(82, 129)(83, 133)(84, 130)(85, 135)(86, 121)(87, 132)(88, 126)(89, 125)(90, 138)(91, 122)(92, 140)(93, 141)(94, 127)(95, 143)(96, 124)(97, 131)(98, 146)(99, 128)(100, 148)(101, 149)(102, 136)(103, 151)(104, 134)(105, 139)(106, 154)(107, 137)(108, 156)(109, 155)(110, 144)(111, 153)(112, 142)(113, 147)(114, 159)(115, 145)(116, 160)(117, 152)(118, 150)(119, 157)(120, 158)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.430
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.437 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^10, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 7, 47)(5, 45, 11, 51, 14, 54, 8, 48)(10, 50, 15, 55, 21, 61, 17, 57)(12, 52, 16, 56, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 23, 63)(20, 60, 27, 67, 30, 70, 24, 64)(26, 66, 31, 71, 36, 76, 33, 73)(28, 68, 32, 72, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 89, 129, 97, 137, 105, 145, 113, 153, 119, 159, 115, 155, 107, 147, 99, 139, 91, 131)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.438 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^10, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 8, 48)(5, 45, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 36, 76, 33, 73)(28, 68, 31, 71, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.439 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, (R * Y2)^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 5, 45)(3, 43, 9, 49, 11, 51, 7, 47)(6, 46, 13, 53, 12, 52, 8, 48)(10, 50, 15, 55, 19, 59, 17, 57)(14, 54, 16, 56, 20, 60, 21, 61)(18, 58, 25, 65, 27, 67, 23, 63)(22, 62, 29, 69, 28, 68, 24, 64)(26, 66, 31, 71, 35, 75, 33, 73)(30, 70, 32, 72, 36, 76, 37, 77)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 110, 150, 102, 142, 94, 134, 86, 126)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 120, 160, 116, 156, 108, 148, 100, 140, 92, 132)(85, 125, 89, 129, 97, 137, 105, 145, 113, 153, 119, 159, 117, 157, 109, 149, 101, 141, 93, 133)
	L = (1, 84)(2, 85)(3, 91)(4, 81)(5, 82)(6, 92)(7, 89)(8, 93)(9, 87)(10, 99)(11, 83)(12, 86)(13, 88)(14, 100)(15, 97)(16, 101)(17, 95)(18, 107)(19, 90)(20, 94)(21, 96)(22, 108)(23, 105)(24, 109)(25, 103)(26, 115)(27, 98)(28, 102)(29, 104)(30, 116)(31, 113)(32, 117)(33, 111)(34, 120)(35, 106)(36, 110)(37, 112)(38, 119)(39, 118)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.440 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, (R * Y2)^2, Y2 * Y3 * Y2^-1 * Y3, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (R * Y1)^2, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 5, 45)(3, 43, 9, 49, 11, 51, 8, 48)(6, 46, 13, 53, 12, 52, 7, 47)(10, 50, 16, 56, 19, 59, 17, 57)(14, 54, 15, 55, 20, 60, 21, 61)(18, 58, 25, 65, 27, 67, 24, 64)(22, 62, 29, 69, 28, 68, 23, 63)(26, 66, 32, 72, 35, 75, 33, 73)(30, 70, 31, 71, 36, 76, 37, 77)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 110, 150, 102, 142, 94, 134, 86, 126)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 120, 160, 116, 156, 108, 148, 100, 140, 92, 132)(85, 125, 93, 133, 101, 141, 109, 149, 117, 157, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129)
	L = (1, 84)(2, 85)(3, 91)(4, 81)(5, 82)(6, 92)(7, 93)(8, 89)(9, 88)(10, 99)(11, 83)(12, 86)(13, 87)(14, 100)(15, 101)(16, 97)(17, 96)(18, 107)(19, 90)(20, 94)(21, 95)(22, 108)(23, 109)(24, 105)(25, 104)(26, 115)(27, 98)(28, 102)(29, 103)(30, 116)(31, 117)(32, 113)(33, 112)(34, 120)(35, 106)(36, 110)(37, 111)(38, 119)(39, 118)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.441 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), Y3^-2 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^4, (Y2 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y2^4, Y3^5, (Y3 * Y1 * Y2)^2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 22, 62, 11, 51)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 20, 60, 24, 64, 9, 49)(7, 47, 10, 50, 25, 65, 21, 61)(14, 54, 29, 69, 36, 76, 32, 72)(15, 55, 33, 73, 37, 77, 27, 67)(16, 56, 31, 71, 38, 78, 30, 70)(17, 57, 26, 66, 39, 79, 34, 74)(19, 59, 35, 75, 40, 80, 28, 68)(81, 121, 83, 123, 94, 134, 99, 139, 84, 124, 95, 135, 87, 127, 96, 136, 97, 137, 86, 126)(82, 122, 89, 129, 106, 146, 110, 150, 90, 130, 107, 147, 92, 132, 108, 148, 109, 149, 91, 131)(85, 125, 100, 140, 114, 154, 111, 151, 101, 141, 113, 153, 98, 138, 115, 155, 112, 152, 93, 133)(88, 128, 102, 142, 116, 156, 120, 160, 103, 143, 117, 157, 105, 145, 118, 158, 119, 159, 104, 144)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 111)(14, 87)(15, 86)(16, 83)(17, 94)(18, 85)(19, 96)(20, 113)(21, 112)(22, 117)(23, 119)(24, 120)(25, 88)(26, 92)(27, 91)(28, 89)(29, 106)(30, 108)(31, 115)(32, 114)(33, 93)(34, 98)(35, 100)(36, 105)(37, 104)(38, 102)(39, 116)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.443
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.442 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-2, (Y1 * Y2)^2, (Y1^-1 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^4, Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 21, 61, 11, 51)(4, 44, 12, 52, 22, 62, 16, 56)(6, 46, 17, 57, 23, 63, 9, 49)(7, 47, 10, 50, 24, 64, 18, 58)(14, 54, 29, 69, 34, 74, 27, 67)(15, 55, 28, 68, 35, 75, 31, 71)(19, 59, 32, 72, 36, 76, 25, 65)(20, 60, 26, 66, 37, 77, 33, 73)(30, 70, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 84, 124, 94, 134, 95, 135, 110, 150, 100, 140, 99, 139, 87, 127, 86, 126)(82, 122, 89, 129, 90, 130, 105, 145, 106, 146, 118, 158, 108, 148, 107, 147, 92, 132, 91, 131)(85, 125, 97, 137, 98, 138, 112, 152, 113, 153, 119, 159, 111, 151, 109, 149, 96, 136, 93, 133)(88, 128, 101, 141, 102, 142, 114, 154, 115, 155, 120, 160, 117, 157, 116, 156, 104, 144, 103, 143)
	L = (1, 84)(2, 90)(3, 94)(4, 95)(5, 98)(6, 83)(7, 81)(8, 102)(9, 105)(10, 106)(11, 89)(12, 82)(13, 97)(14, 110)(15, 100)(16, 85)(17, 112)(18, 113)(19, 86)(20, 87)(21, 114)(22, 115)(23, 101)(24, 88)(25, 118)(26, 108)(27, 91)(28, 92)(29, 93)(30, 99)(31, 96)(32, 119)(33, 111)(34, 120)(35, 117)(36, 103)(37, 104)(38, 107)(39, 109)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.443 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y2, (Y2 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y1^4, (R * Y3)^2, Y3^5, (Y3^2 * Y2^-1)^2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 21, 61, 11, 51)(4, 44, 12, 52, 22, 62, 16, 56)(6, 46, 18, 58, 23, 63, 9, 49)(7, 47, 10, 50, 24, 64, 19, 59)(14, 54, 29, 69, 34, 74, 27, 67)(15, 55, 28, 68, 35, 75, 31, 71)(17, 57, 32, 72, 36, 76, 25, 65)(20, 60, 26, 66, 37, 77, 33, 73)(30, 70, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 87, 127, 94, 134, 100, 140, 110, 150, 95, 135, 97, 137, 84, 124, 86, 126)(82, 122, 89, 129, 92, 132, 105, 145, 108, 148, 118, 158, 106, 146, 107, 147, 90, 130, 91, 131)(85, 125, 98, 138, 96, 136, 112, 152, 111, 151, 119, 159, 113, 153, 109, 149, 99, 139, 93, 133)(88, 128, 101, 141, 104, 144, 114, 154, 117, 157, 120, 160, 115, 155, 116, 156, 102, 142, 103, 143)
	L = (1, 84)(2, 90)(3, 86)(4, 95)(5, 99)(6, 97)(7, 81)(8, 102)(9, 91)(10, 106)(11, 107)(12, 82)(13, 109)(14, 83)(15, 100)(16, 85)(17, 110)(18, 93)(19, 113)(20, 87)(21, 103)(22, 115)(23, 116)(24, 88)(25, 89)(26, 108)(27, 118)(28, 92)(29, 119)(30, 94)(31, 96)(32, 98)(33, 111)(34, 101)(35, 117)(36, 120)(37, 104)(38, 105)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.441
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.444 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y2 * Y3)^2, (Y3^-1, Y2^-1), (Y2 * Y1^-1)^2, Y3^2 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y1^-1)^2, Y1^4, Y1^-2 * Y3 * Y1^-2 * Y3^-1, (Y3^-1 * Y2 * Y1^-1)^2, (Y1^-1 * Y3^-1 * Y2^-1)^2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1^2 * Y3^-1 * Y2 * Y3^-2, Y3 * Y1^2 * Y2^-4 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 22, 62, 11, 51)(4, 44, 12, 52, 23, 63, 18, 58)(6, 46, 20, 60, 24, 64, 9, 49)(7, 47, 10, 50, 25, 65, 21, 61)(14, 54, 29, 69, 36, 76, 32, 72)(15, 55, 33, 73, 40, 80, 27, 67)(16, 56, 31, 71, 38, 78, 30, 70)(17, 57, 26, 66, 35, 75, 37, 77)(19, 59, 39, 79, 34, 74, 28, 68)(81, 121, 83, 123, 94, 134, 114, 154, 103, 143, 120, 160, 105, 145, 118, 158, 97, 137, 86, 126)(82, 122, 89, 129, 106, 146, 111, 151, 101, 141, 113, 153, 98, 138, 119, 159, 109, 149, 91, 131)(84, 124, 95, 135, 87, 127, 96, 136, 115, 155, 104, 144, 88, 128, 102, 142, 116, 156, 99, 139)(85, 125, 100, 140, 117, 157, 110, 150, 90, 130, 107, 147, 92, 132, 108, 148, 112, 152, 93, 133)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 101)(6, 99)(7, 81)(8, 103)(9, 107)(10, 109)(11, 110)(12, 82)(13, 111)(14, 87)(15, 86)(16, 83)(17, 116)(18, 85)(19, 118)(20, 113)(21, 112)(22, 120)(23, 115)(24, 114)(25, 88)(26, 92)(27, 91)(28, 89)(29, 117)(30, 119)(31, 108)(32, 106)(33, 93)(34, 96)(35, 94)(36, 105)(37, 98)(38, 102)(39, 100)(40, 104)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.445
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.445 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), Y1^-1 * Y3 * Y1 * Y3, (Y1 * Y2)^2, (Y1 * Y2^-1)^2, (R * Y2)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, Y3^-1 * Y1^-1 * Y2^2 * Y1^-1, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y2^-4 * Y3^-2, Y2^-2 * Y3^4 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 23, 63, 11, 51)(4, 44, 12, 52, 22, 62, 18, 58)(6, 46, 20, 60, 15, 55, 9, 49)(7, 47, 10, 50, 14, 54, 21, 61)(16, 56, 29, 69, 30, 70, 27, 67)(17, 57, 28, 68, 36, 76, 34, 74)(19, 59, 35, 75, 32, 72, 25, 65)(24, 64, 26, 66, 31, 71, 37, 77)(33, 73, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 94, 134, 110, 150, 104, 144, 113, 153, 97, 137, 112, 152, 102, 142, 86, 126)(82, 122, 89, 129, 98, 138, 115, 155, 108, 148, 118, 158, 106, 146, 109, 149, 101, 141, 91, 131)(84, 124, 95, 135, 88, 128, 103, 143, 87, 127, 96, 136, 111, 151, 120, 160, 116, 156, 99, 139)(85, 125, 100, 140, 92, 132, 105, 145, 114, 154, 119, 159, 117, 157, 107, 147, 90, 130, 93, 133)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 101)(6, 99)(7, 81)(8, 102)(9, 93)(10, 106)(11, 107)(12, 82)(13, 109)(14, 88)(15, 112)(16, 83)(17, 111)(18, 85)(19, 113)(20, 91)(21, 117)(22, 116)(23, 86)(24, 87)(25, 89)(26, 114)(27, 118)(28, 92)(29, 119)(30, 103)(31, 94)(32, 120)(33, 96)(34, 98)(35, 100)(36, 104)(37, 108)(38, 105)(39, 115)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.444
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.446 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y1 * Y2^-1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^4, Y3^-1 * Y1 * Y2^-2 * Y1, Y3 * Y1 * Y2 * Y1^-1 * Y2^-1, Y2^3 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3^3 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 19, 59, 11, 51)(4, 44, 12, 52, 14, 54, 18, 58)(6, 46, 20, 60, 16, 56, 9, 49)(7, 47, 10, 50, 22, 62, 21, 61)(15, 55, 29, 69, 30, 70, 27, 67)(17, 57, 28, 68, 31, 71, 35, 75)(23, 63, 36, 76, 33, 73, 25, 65)(24, 64, 26, 66, 34, 74, 37, 77)(32, 72, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 94, 134, 110, 150, 97, 137, 112, 152, 104, 144, 113, 153, 102, 142, 86, 126)(82, 122, 89, 129, 101, 141, 116, 156, 106, 146, 118, 158, 108, 148, 109, 149, 98, 138, 91, 131)(84, 124, 95, 135, 111, 151, 120, 160, 114, 154, 103, 143, 87, 127, 96, 136, 88, 128, 99, 139)(85, 125, 100, 140, 90, 130, 105, 145, 117, 157, 119, 159, 115, 155, 107, 147, 92, 132, 93, 133)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 101)(6, 99)(7, 81)(8, 94)(9, 105)(10, 106)(11, 100)(12, 82)(13, 89)(14, 111)(15, 112)(16, 83)(17, 114)(18, 85)(19, 110)(20, 116)(21, 117)(22, 88)(23, 86)(24, 87)(25, 118)(26, 115)(27, 91)(28, 92)(29, 93)(30, 120)(31, 104)(32, 103)(33, 96)(34, 102)(35, 98)(36, 119)(37, 108)(38, 107)(39, 109)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.447 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = C10 x D8 (small group id <80, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 12, 52, 5, 45)(2, 42, 7, 47, 16, 56, 8, 48)(3, 43, 10, 50, 20, 60, 11, 51)(6, 46, 14, 54, 24, 64, 15, 55)(9, 49, 18, 58, 28, 68, 19, 59)(13, 53, 22, 62, 32, 72, 23, 63)(17, 57, 26, 66, 35, 75, 27, 67)(21, 61, 30, 70, 38, 78, 31, 71)(25, 65, 33, 73, 39, 79, 34, 74)(29, 69, 36, 76, 40, 80, 37, 77)(81, 82, 86, 93, 101, 109, 105, 97, 89, 83)(84, 88, 94, 103, 110, 117, 113, 107, 98, 91)(85, 87, 95, 102, 111, 116, 114, 106, 99, 90)(92, 96, 104, 112, 118, 120, 119, 115, 108, 100)(121, 123, 129, 137, 145, 149, 141, 133, 126, 122)(124, 131, 138, 147, 153, 157, 150, 143, 134, 128)(125, 130, 139, 146, 154, 156, 151, 142, 135, 127)(132, 140, 148, 155, 159, 160, 158, 152, 144, 136)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.448
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.448 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = C10 x D8 (small group id <80, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 12, 52, 92, 132, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 16, 56, 96, 136, 8, 48, 88, 128)(3, 43, 83, 123, 10, 50, 90, 130, 20, 60, 100, 140, 11, 51, 91, 131)(6, 46, 86, 126, 14, 54, 94, 134, 24, 64, 104, 144, 15, 55, 95, 135)(9, 49, 89, 129, 18, 58, 98, 138, 28, 68, 108, 148, 19, 59, 99, 139)(13, 53, 93, 133, 22, 62, 102, 142, 32, 72, 112, 152, 23, 63, 103, 143)(17, 57, 97, 137, 26, 66, 106, 146, 35, 75, 115, 155, 27, 67, 107, 147)(21, 61, 101, 141, 30, 70, 110, 150, 38, 78, 118, 158, 31, 71, 111, 151)(25, 65, 105, 145, 33, 73, 113, 153, 39, 79, 119, 159, 34, 74, 114, 154)(29, 69, 109, 149, 36, 76, 116, 156, 40, 80, 120, 160, 37, 77, 117, 157)
	L = (1, 42)(2, 46)(3, 41)(4, 48)(5, 47)(6, 53)(7, 55)(8, 54)(9, 43)(10, 45)(11, 44)(12, 56)(13, 61)(14, 63)(15, 62)(16, 64)(17, 49)(18, 51)(19, 50)(20, 52)(21, 69)(22, 71)(23, 70)(24, 72)(25, 57)(26, 59)(27, 58)(28, 60)(29, 65)(30, 77)(31, 76)(32, 78)(33, 67)(34, 66)(35, 68)(36, 74)(37, 73)(38, 80)(39, 75)(40, 79)(81, 123)(82, 121)(83, 129)(84, 131)(85, 130)(86, 122)(87, 125)(88, 124)(89, 137)(90, 139)(91, 138)(92, 140)(93, 126)(94, 128)(95, 127)(96, 132)(97, 145)(98, 147)(99, 146)(100, 148)(101, 133)(102, 135)(103, 134)(104, 136)(105, 149)(106, 154)(107, 153)(108, 155)(109, 141)(110, 143)(111, 142)(112, 144)(113, 157)(114, 156)(115, 159)(116, 151)(117, 150)(118, 152)(119, 160)(120, 158)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.447
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.449 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^10, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 7, 47, 13, 53, 10, 50)(5, 45, 8, 48, 14, 54, 11, 51)(9, 49, 15, 55, 21, 61, 18, 58)(12, 52, 16, 56, 22, 62, 19, 59)(17, 57, 23, 63, 29, 69, 26, 66)(20, 60, 24, 64, 30, 70, 27, 67)(25, 65, 31, 71, 36, 76, 34, 74)(28, 68, 32, 72, 37, 77, 35, 75)(33, 73, 38, 78, 40, 80, 39, 79)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 119, 159, 115, 155, 107, 147, 99, 139, 91, 131)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.450 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 5, 45)(3, 43, 7, 47, 10, 50, 11, 51)(6, 46, 8, 48, 12, 52, 13, 53)(9, 49, 15, 55, 18, 58, 19, 59)(14, 54, 16, 56, 20, 60, 21, 61)(17, 57, 23, 63, 26, 66, 27, 67)(22, 62, 24, 64, 28, 68, 29, 69)(25, 65, 31, 71, 34, 74, 35, 75)(30, 70, 32, 72, 36, 76, 37, 77)(33, 73, 38, 78, 39, 79, 40, 80)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 110, 150, 102, 142, 94, 134, 86, 126)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 119, 159, 116, 156, 108, 148, 100, 140, 92, 132)(85, 125, 91, 131, 99, 139, 107, 147, 115, 155, 120, 160, 117, 157, 109, 149, 101, 141, 93, 133)
	L = (1, 84)(2, 85)(3, 90)(4, 81)(5, 82)(6, 92)(7, 91)(8, 93)(9, 98)(10, 83)(11, 87)(12, 86)(13, 88)(14, 100)(15, 99)(16, 101)(17, 106)(18, 89)(19, 95)(20, 94)(21, 96)(22, 108)(23, 107)(24, 109)(25, 114)(26, 97)(27, 103)(28, 102)(29, 104)(30, 116)(31, 115)(32, 117)(33, 119)(34, 105)(35, 111)(36, 110)(37, 112)(38, 120)(39, 113)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.451 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y3 * Y2^-1, Y1^4, Y1^-2 * Y3 * Y2^-5, Y2 * Y3 * Y2^4 * Y1^-2, Y2^2 * Y1^-1 * Y2^3 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 8, 48, 18, 58, 13, 53)(4, 44, 9, 49, 19, 59, 14, 54)(6, 46, 10, 50, 20, 60, 16, 56)(11, 51, 21, 61, 33, 73, 27, 67)(12, 52, 22, 62, 34, 74, 28, 68)(15, 55, 23, 63, 35, 75, 29, 69)(17, 57, 24, 64, 36, 76, 31, 71)(25, 65, 37, 77, 30, 70, 39, 79)(26, 66, 38, 78, 32, 72, 40, 80)(81, 121, 83, 123, 91, 131, 105, 145, 115, 155, 99, 139, 114, 154, 112, 152, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 117, 157, 109, 149, 94, 134, 108, 148, 120, 160, 104, 144, 90, 130)(84, 124, 92, 132, 106, 146, 116, 156, 100, 140, 87, 127, 98, 138, 113, 153, 110, 150, 95, 135)(85, 125, 93, 133, 107, 147, 119, 159, 103, 143, 89, 129, 102, 142, 118, 158, 111, 151, 96, 136)
	L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 83)(13, 108)(14, 85)(15, 86)(16, 109)(17, 110)(18, 114)(19, 87)(20, 115)(21, 118)(22, 88)(23, 90)(24, 119)(25, 116)(26, 91)(27, 120)(28, 93)(29, 96)(30, 97)(31, 117)(32, 113)(33, 112)(34, 98)(35, 100)(36, 105)(37, 111)(38, 101)(39, 104)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.452
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.452 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 10, 10})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (Y2^-1, Y1^-1), (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y1^4, Y2^-5 * Y1^2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 8, 48, 18, 58, 13, 53)(4, 44, 9, 49, 19, 59, 14, 54)(6, 46, 10, 50, 20, 60, 16, 56)(11, 51, 21, 61, 32, 72, 27, 67)(12, 52, 22, 62, 33, 73, 28, 68)(15, 55, 23, 63, 34, 74, 29, 69)(17, 57, 24, 64, 25, 65, 31, 71)(26, 66, 35, 75, 40, 80, 38, 78)(30, 70, 36, 76, 37, 77, 39, 79)(81, 121, 83, 123, 91, 131, 105, 145, 100, 140, 87, 127, 98, 138, 112, 152, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 111, 151, 96, 136, 85, 125, 93, 133, 107, 147, 104, 144, 90, 130)(84, 124, 92, 132, 106, 146, 117, 157, 114, 154, 99, 139, 113, 153, 120, 160, 110, 150, 95, 135)(89, 129, 102, 142, 115, 155, 119, 159, 109, 149, 94, 134, 108, 148, 118, 158, 116, 156, 103, 143)
	L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 106)(12, 83)(13, 108)(14, 85)(15, 86)(16, 109)(17, 110)(18, 113)(19, 87)(20, 114)(21, 115)(22, 88)(23, 90)(24, 116)(25, 117)(26, 91)(27, 118)(28, 93)(29, 96)(30, 97)(31, 119)(32, 120)(33, 98)(34, 100)(35, 101)(36, 104)(37, 105)(38, 107)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20, 8, 20, 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.451
Graph:: bipartite
	v = 14 e = 80 f = 14
	degree seq :: [ 8^10, 20^4 ]

E27.453 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1, Y1 * Y2, Y1^-1 * Y2^-1, Y1^-3 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y1^-1 * Y3^3 * Y1 * Y3^-1, Y3 * Y1 * Y3^3 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y1^-2)^2 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 13, 53, 20, 60, 34, 74, 40, 80, 36, 76, 23, 63, 16, 56, 5, 45)(2, 42, 7, 47, 21, 61, 14, 54, 29, 69, 37, 77, 27, 67, 11, 51, 24, 64, 8, 48)(3, 43, 9, 49, 25, 65, 12, 52, 28, 68, 38, 78, 30, 70, 15, 55, 26, 66, 10, 50)(6, 46, 17, 57, 31, 71, 22, 62, 35, 75, 39, 79, 33, 73, 19, 59, 32, 72, 18, 58)(81, 82, 86, 83)(84, 91, 98, 92)(85, 94, 97, 95)(87, 99, 90, 100)(88, 102, 89, 103)(93, 109, 112, 110)(96, 107, 111, 108)(101, 115, 106, 116)(104, 113, 105, 114)(117, 119, 118, 120)(121, 123, 126, 122)(124, 132, 138, 131)(125, 135, 137, 134)(127, 140, 130, 139)(128, 143, 129, 142)(133, 150, 152, 149)(136, 148, 151, 147)(141, 156, 146, 155)(144, 154, 145, 153)(157, 160, 158, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.460
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.454 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1 * Y2, Y2^-1 * Y1^-1 * Y3^-2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, Y2^4, Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3, Y2 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2^-2 * Y3^2 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3 * Y1 * Y3^3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 19, 59, 35, 75, 22, 62, 38, 78, 13, 53, 32, 72, 9, 49, 7, 47)(2, 42, 10, 50, 34, 74, 24, 64, 6, 46, 23, 63, 30, 70, 17, 57, 26, 66, 12, 52)(3, 43, 15, 55, 5, 45, 18, 58, 31, 71, 20, 60, 28, 68, 25, 65, 39, 79, 16, 56)(8, 48, 27, 67, 14, 54, 37, 77, 11, 51, 36, 76, 40, 80, 33, 73, 21, 61, 29, 69)(81, 82, 88, 85)(83, 93, 114, 91)(84, 97, 109, 100)(86, 101, 119, 99)(87, 104, 107, 96)(89, 110, 94, 108)(90, 113, 95, 115)(92, 117, 98, 112)(102, 106, 120, 111)(103, 116, 105, 118)(121, 123, 134, 126)(122, 129, 151, 131)(124, 138, 147, 130)(125, 141, 154, 142)(127, 145, 157, 137)(128, 146, 139, 148)(132, 158, 140, 153)(133, 159, 160, 150)(135, 156, 144, 152)(136, 149, 143, 155)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.459
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.455 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3^2, Y3 * Y2 * Y3 * Y1, Y1^4, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^2, Y3^-2 * Y2^-1 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-2 * Y1^-1 * Y3^-1, Y2 * Y3^-2 * Y2^-2 * Y1^-1, Y3^-2 * Y1 * Y2^-1 * Y1^-2, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y3^-1 * Y1^-2 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y2^2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 13, 53, 35, 75, 24, 64, 33, 73, 9, 49, 32, 72, 23, 63, 7, 47)(2, 42, 10, 50, 30, 70, 25, 65, 37, 77, 20, 60, 26, 66, 17, 57, 6, 46, 12, 52)(3, 43, 15, 55, 28, 68, 18, 58, 5, 45, 22, 62, 39, 79, 19, 59, 31, 71, 16, 56)(8, 48, 27, 67, 40, 80, 38, 78, 14, 54, 36, 76, 21, 61, 34, 74, 11, 51, 29, 69)(81, 82, 88, 85)(83, 93, 117, 91)(84, 97, 109, 99)(86, 101, 119, 104)(87, 105, 107, 95)(89, 110, 94, 108)(90, 114, 98, 115)(92, 118, 102, 112)(96, 113, 100, 116)(103, 106, 120, 111)(121, 123, 134, 126)(122, 129, 151, 131)(124, 138, 158, 140)(125, 141, 157, 143)(127, 139, 156, 130)(128, 146, 144, 148)(132, 155, 136, 147)(133, 159, 160, 150)(135, 154, 137, 152)(142, 149, 145, 153)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.458
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.456 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 10, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y1^-1, (Y1 * Y2^-1)^2, Y1^4, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y2^-1 * Y1 * Y3 * Y1^-1, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-2 * Y3 * Y2^2, Y2^-1 * Y3^-1 * Y2 * Y1 * Y3 * Y1^-1, Y2^-2 * Y1^2 * Y3^-2, Y3^-1 * Y2^2 * Y3 * Y1^-2, Y2^-1 * Y3^2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 9, 49, 32, 72, 13, 53, 34, 74, 21, 61, 38, 78, 23, 63, 7, 47)(2, 42, 10, 50, 26, 66, 19, 59, 30, 70, 24, 64, 6, 46, 17, 57, 36, 76, 12, 52)(3, 43, 15, 55, 39, 79, 18, 58, 28, 68, 25, 65, 31, 71, 22, 62, 5, 45, 16, 56)(8, 48, 27, 67, 20, 60, 35, 75, 40, 80, 37, 77, 11, 51, 33, 73, 14, 54, 29, 69)(81, 82, 88, 85)(83, 93, 116, 91)(84, 97, 109, 95)(86, 100, 119, 103)(87, 99, 107, 105)(89, 110, 94, 108)(90, 113, 102, 112)(92, 115, 96, 118)(98, 114, 104, 117)(101, 106, 120, 111)(121, 123, 134, 126)(122, 129, 151, 131)(124, 138, 153, 139)(125, 140, 156, 141)(127, 142, 149, 132)(128, 146, 143, 148)(130, 154, 145, 155)(133, 159, 160, 150)(135, 147, 144, 158)(136, 157, 137, 152)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.457
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.457 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1, Y1 * Y2, Y1^-1 * Y2^-1, Y1^-3 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y1^-1 * Y3^3 * Y1 * Y3^-1, Y3 * Y1 * Y3^3 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y1^-2)^2 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 13, 53, 93, 133, 20, 60, 100, 140, 34, 74, 114, 154, 40, 80, 120, 160, 36, 76, 116, 156, 23, 63, 103, 143, 16, 56, 96, 136, 5, 45, 85, 125)(2, 42, 82, 122, 7, 47, 87, 127, 21, 61, 101, 141, 14, 54, 94, 134, 29, 69, 109, 149, 37, 77, 117, 157, 27, 67, 107, 147, 11, 51, 91, 131, 24, 64, 104, 144, 8, 48, 88, 128)(3, 43, 83, 123, 9, 49, 89, 129, 25, 65, 105, 145, 12, 52, 92, 132, 28, 68, 108, 148, 38, 78, 118, 158, 30, 70, 110, 150, 15, 55, 95, 135, 26, 66, 106, 146, 10, 50, 90, 130)(6, 46, 86, 126, 17, 57, 97, 137, 31, 71, 111, 151, 22, 62, 102, 142, 35, 75, 115, 155, 39, 79, 119, 159, 33, 73, 113, 153, 19, 59, 99, 139, 32, 72, 112, 152, 18, 58, 98, 138)
	L = (1, 42)(2, 46)(3, 41)(4, 51)(5, 54)(6, 43)(7, 59)(8, 62)(9, 63)(10, 60)(11, 58)(12, 44)(13, 69)(14, 57)(15, 45)(16, 67)(17, 55)(18, 52)(19, 50)(20, 47)(21, 75)(22, 49)(23, 48)(24, 73)(25, 74)(26, 76)(27, 71)(28, 56)(29, 72)(30, 53)(31, 68)(32, 70)(33, 65)(34, 64)(35, 66)(36, 61)(37, 79)(38, 80)(39, 78)(40, 77)(81, 123)(82, 121)(83, 126)(84, 132)(85, 135)(86, 122)(87, 140)(88, 143)(89, 142)(90, 139)(91, 124)(92, 138)(93, 150)(94, 125)(95, 137)(96, 148)(97, 134)(98, 131)(99, 127)(100, 130)(101, 156)(102, 128)(103, 129)(104, 154)(105, 153)(106, 155)(107, 136)(108, 151)(109, 133)(110, 152)(111, 147)(112, 149)(113, 144)(114, 145)(115, 141)(116, 146)(117, 160)(118, 159)(119, 157)(120, 158)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.456
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.458 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1 * Y2, Y2^-1 * Y1^-1 * Y3^-2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1^-1)^2, Y2^4, Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3, Y2 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2^-2 * Y3^2 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1, Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3 * Y1 * Y3^3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 19, 59, 99, 139, 35, 75, 115, 155, 22, 62, 102, 142, 38, 78, 118, 158, 13, 53, 93, 133, 32, 72, 112, 152, 9, 49, 89, 129, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 34, 74, 114, 154, 24, 64, 104, 144, 6, 46, 86, 126, 23, 63, 103, 143, 30, 70, 110, 150, 17, 57, 97, 137, 26, 66, 106, 146, 12, 52, 92, 132)(3, 43, 83, 123, 15, 55, 95, 135, 5, 45, 85, 125, 18, 58, 98, 138, 31, 71, 111, 151, 20, 60, 100, 140, 28, 68, 108, 148, 25, 65, 105, 145, 39, 79, 119, 159, 16, 56, 96, 136)(8, 48, 88, 128, 27, 67, 107, 147, 14, 54, 94, 134, 37, 77, 117, 157, 11, 51, 91, 131, 36, 76, 116, 156, 40, 80, 120, 160, 33, 73, 113, 153, 21, 61, 101, 141, 29, 69, 109, 149)
	L = (1, 42)(2, 48)(3, 53)(4, 57)(5, 41)(6, 61)(7, 64)(8, 45)(9, 70)(10, 73)(11, 43)(12, 77)(13, 74)(14, 68)(15, 75)(16, 47)(17, 69)(18, 72)(19, 46)(20, 44)(21, 79)(22, 66)(23, 76)(24, 67)(25, 78)(26, 80)(27, 56)(28, 49)(29, 60)(30, 54)(31, 62)(32, 52)(33, 55)(34, 51)(35, 50)(36, 65)(37, 58)(38, 63)(39, 59)(40, 71)(81, 123)(82, 129)(83, 134)(84, 138)(85, 141)(86, 121)(87, 145)(88, 146)(89, 151)(90, 124)(91, 122)(92, 158)(93, 159)(94, 126)(95, 156)(96, 149)(97, 127)(98, 147)(99, 148)(100, 153)(101, 154)(102, 125)(103, 155)(104, 152)(105, 157)(106, 139)(107, 130)(108, 128)(109, 143)(110, 133)(111, 131)(112, 135)(113, 132)(114, 142)(115, 136)(116, 144)(117, 137)(118, 140)(119, 160)(120, 150)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.455
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.459 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3^2, Y3 * Y2 * Y3 * Y1, Y1^4, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^2, Y3^-2 * Y2^-1 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-2 * Y1^-1 * Y3^-1, Y2 * Y3^-2 * Y2^-2 * Y1^-1, Y3^-2 * Y1 * Y2^-1 * Y1^-2, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y3^-1 * Y1^-2 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y2^2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 13, 53, 93, 133, 35, 75, 115, 155, 24, 64, 104, 144, 33, 73, 113, 153, 9, 49, 89, 129, 32, 72, 112, 152, 23, 63, 103, 143, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 30, 70, 110, 150, 25, 65, 105, 145, 37, 77, 117, 157, 20, 60, 100, 140, 26, 66, 106, 146, 17, 57, 97, 137, 6, 46, 86, 126, 12, 52, 92, 132)(3, 43, 83, 123, 15, 55, 95, 135, 28, 68, 108, 148, 18, 58, 98, 138, 5, 45, 85, 125, 22, 62, 102, 142, 39, 79, 119, 159, 19, 59, 99, 139, 31, 71, 111, 151, 16, 56, 96, 136)(8, 48, 88, 128, 27, 67, 107, 147, 40, 80, 120, 160, 38, 78, 118, 158, 14, 54, 94, 134, 36, 76, 116, 156, 21, 61, 101, 141, 34, 74, 114, 154, 11, 51, 91, 131, 29, 69, 109, 149)
	L = (1, 42)(2, 48)(3, 53)(4, 57)(5, 41)(6, 61)(7, 65)(8, 45)(9, 70)(10, 74)(11, 43)(12, 78)(13, 77)(14, 68)(15, 47)(16, 73)(17, 69)(18, 75)(19, 44)(20, 76)(21, 79)(22, 72)(23, 66)(24, 46)(25, 67)(26, 80)(27, 55)(28, 49)(29, 59)(30, 54)(31, 63)(32, 52)(33, 60)(34, 58)(35, 50)(36, 56)(37, 51)(38, 62)(39, 64)(40, 71)(81, 123)(82, 129)(83, 134)(84, 138)(85, 141)(86, 121)(87, 139)(88, 146)(89, 151)(90, 127)(91, 122)(92, 155)(93, 159)(94, 126)(95, 154)(96, 147)(97, 152)(98, 158)(99, 156)(100, 124)(101, 157)(102, 149)(103, 125)(104, 148)(105, 153)(106, 144)(107, 132)(108, 128)(109, 145)(110, 133)(111, 131)(112, 135)(113, 142)(114, 137)(115, 136)(116, 130)(117, 143)(118, 140)(119, 160)(120, 150)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.454
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.460 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 10, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C4) (small group id <40, 12>)
Aut   = C2 x C2 x (C5 : C4) (small group id <80, 50>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y1^-1, (Y1 * Y2^-1)^2, Y1^4, Y2^4, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y2^-1 * Y1 * Y3 * Y1^-1, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-2 * Y3 * Y2^2, Y2^-1 * Y3^-1 * Y2 * Y1 * Y3 * Y1^-1, Y2^-2 * Y1^2 * Y3^-2, Y3^-1 * Y2^2 * Y3 * Y1^-2, Y2^-1 * Y3^2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 9, 49, 89, 129, 32, 72, 112, 152, 13, 53, 93, 133, 34, 74, 114, 154, 21, 61, 101, 141, 38, 78, 118, 158, 23, 63, 103, 143, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 26, 66, 106, 146, 19, 59, 99, 139, 30, 70, 110, 150, 24, 64, 104, 144, 6, 46, 86, 126, 17, 57, 97, 137, 36, 76, 116, 156, 12, 52, 92, 132)(3, 43, 83, 123, 15, 55, 95, 135, 39, 79, 119, 159, 18, 58, 98, 138, 28, 68, 108, 148, 25, 65, 105, 145, 31, 71, 111, 151, 22, 62, 102, 142, 5, 45, 85, 125, 16, 56, 96, 136)(8, 48, 88, 128, 27, 67, 107, 147, 20, 60, 100, 140, 35, 75, 115, 155, 40, 80, 120, 160, 37, 77, 117, 157, 11, 51, 91, 131, 33, 73, 113, 153, 14, 54, 94, 134, 29, 69, 109, 149)
	L = (1, 42)(2, 48)(3, 53)(4, 57)(5, 41)(6, 60)(7, 59)(8, 45)(9, 70)(10, 73)(11, 43)(12, 75)(13, 76)(14, 68)(15, 44)(16, 78)(17, 69)(18, 74)(19, 67)(20, 79)(21, 66)(22, 72)(23, 46)(24, 77)(25, 47)(26, 80)(27, 65)(28, 49)(29, 55)(30, 54)(31, 61)(32, 50)(33, 62)(34, 64)(35, 56)(36, 51)(37, 58)(38, 52)(39, 63)(40, 71)(81, 123)(82, 129)(83, 134)(84, 138)(85, 140)(86, 121)(87, 142)(88, 146)(89, 151)(90, 154)(91, 122)(92, 127)(93, 159)(94, 126)(95, 147)(96, 157)(97, 152)(98, 153)(99, 124)(100, 156)(101, 125)(102, 149)(103, 148)(104, 158)(105, 155)(106, 143)(107, 144)(108, 128)(109, 132)(110, 133)(111, 131)(112, 136)(113, 139)(114, 145)(115, 130)(116, 141)(117, 137)(118, 135)(119, 160)(120, 150)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.453
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.461 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, Y2^-5 * Y1, Y3^-4 * Y2 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-2, Y3^-2 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 104, 144, 89, 129, 82, 122, 87, 127, 99, 139, 96, 136, 85, 125)(84, 124, 92, 132, 107, 147, 116, 156, 103, 143, 88, 128, 100, 140, 113, 153, 110, 150, 95, 135)(86, 126, 93, 133, 108, 148, 117, 157, 105, 145, 90, 130, 101, 141, 114, 154, 111, 151, 97, 137)(94, 134, 109, 149, 119, 159, 112, 152, 98, 138, 102, 142, 115, 155, 120, 160, 118, 158, 106, 146)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 109)(13, 83)(14, 101)(15, 106)(16, 110)(17, 85)(18, 86)(19, 113)(20, 115)(21, 87)(22, 93)(23, 98)(24, 116)(25, 89)(26, 90)(27, 119)(28, 91)(29, 114)(30, 118)(31, 96)(32, 97)(33, 120)(34, 99)(35, 108)(36, 112)(37, 104)(38, 105)(39, 111)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.490
Graph:: bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.462 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^2 * Y1 * Y3^2, Y3 * Y1 * Y2 * Y3 * Y2, Y2^-2 * Y3^8, Y2^10, Y1 * Y2 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-1 * Y2^3 * Y3^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 18, 58)(12, 52, 17, 57)(13, 53, 19, 59)(14, 54, 16, 56)(15, 55, 20, 60)(21, 61, 23, 63)(22, 62, 28, 68)(24, 64, 26, 66)(25, 65, 27, 67)(29, 69, 31, 71)(30, 70, 32, 72)(33, 73, 35, 75)(34, 74, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123, 91, 131, 101, 141, 109, 149, 117, 157, 113, 153, 107, 147, 96, 136, 85, 125)(82, 122, 87, 127, 98, 138, 103, 143, 111, 151, 119, 159, 115, 155, 105, 145, 94, 134, 89, 129)(84, 124, 92, 132, 90, 130, 99, 139, 108, 148, 112, 152, 120, 160, 116, 156, 106, 146, 95, 135)(86, 126, 93, 133, 102, 142, 110, 150, 118, 158, 114, 154, 104, 144, 100, 140, 88, 128, 97, 137)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 97)(8, 96)(9, 100)(10, 82)(11, 90)(12, 89)(13, 83)(14, 104)(15, 105)(16, 106)(17, 85)(18, 86)(19, 87)(20, 107)(21, 99)(22, 91)(23, 93)(24, 113)(25, 114)(26, 115)(27, 116)(28, 98)(29, 108)(30, 101)(31, 102)(32, 103)(33, 120)(34, 117)(35, 118)(36, 119)(37, 112)(38, 109)(39, 110)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.489
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.463 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y1 * Y3^-1 * Y1, (Y3, Y2^-1), Y2 * Y1 * Y2^-1 * Y1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^2 * Y3^-1 * Y1, Y3^5 * Y2 * Y3 * Y1, Y2^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 102, 142, 114, 154, 120, 160, 117, 157, 106, 146, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 94, 134, 108, 148, 119, 159, 111, 151, 98, 138, 104, 144, 89, 129)(84, 124, 92, 132, 107, 147, 115, 155, 112, 152, 116, 156, 105, 145, 90, 130, 101, 141, 95, 135)(86, 126, 93, 133, 103, 143, 88, 128, 100, 140, 113, 153, 109, 149, 118, 158, 110, 150, 97, 137)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 108)(13, 83)(14, 109)(15, 99)(16, 101)(17, 85)(18, 86)(19, 113)(20, 114)(21, 87)(22, 115)(23, 91)(24, 93)(25, 89)(26, 90)(27, 119)(28, 118)(29, 117)(30, 96)(31, 97)(32, 98)(33, 120)(34, 112)(35, 111)(36, 104)(37, 105)(38, 106)(39, 110)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.491
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.464 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y2^10, (Y3 * Y2^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 15, 55)(12, 52, 16, 56)(13, 53, 17, 57)(14, 54, 18, 58)(19, 59, 23, 63)(20, 60, 24, 64)(21, 61, 25, 65)(22, 62, 26, 66)(27, 67, 31, 71)(28, 68, 32, 72)(29, 69, 33, 73)(30, 70, 34, 74)(35, 75, 38, 78)(36, 76, 39, 79)(37, 77, 40, 80)(81, 121, 83, 123, 91, 131, 99, 139, 107, 147, 115, 155, 110, 150, 102, 142, 94, 134, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 114, 154, 106, 146, 98, 138, 89, 129)(84, 124, 86, 126, 92, 132, 100, 140, 108, 148, 116, 156, 117, 157, 109, 149, 101, 141, 93, 133)(88, 128, 90, 130, 96, 136, 104, 144, 112, 152, 119, 159, 120, 160, 113, 153, 105, 145, 97, 137)
	L = (1, 84)(2, 88)(3, 86)(4, 85)(5, 93)(6, 81)(7, 90)(8, 89)(9, 97)(10, 82)(11, 92)(12, 83)(13, 94)(14, 101)(15, 96)(16, 87)(17, 98)(18, 105)(19, 100)(20, 91)(21, 102)(22, 109)(23, 104)(24, 95)(25, 106)(26, 113)(27, 108)(28, 99)(29, 110)(30, 117)(31, 112)(32, 103)(33, 114)(34, 120)(35, 116)(36, 107)(37, 115)(38, 119)(39, 111)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.492
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.465 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1), (Y3 * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y1^-2, (Y2, Y3^-1), Y1^-2 * Y3^3, Y2^2 * Y3^-1 * Y2^2, Y2 * Y3 * Y2 * Y3 * Y2^2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 18, 58, 4, 44, 10, 50, 7, 47, 12, 52, 17, 57, 5, 45)(3, 43, 9, 49, 23, 63, 34, 74, 14, 54, 26, 66, 16, 56, 27, 67, 33, 73, 15, 55)(6, 46, 11, 51, 24, 64, 36, 76, 19, 59, 28, 68, 22, 62, 30, 70, 35, 75, 20, 60)(13, 53, 25, 65, 38, 78, 40, 80, 31, 71, 37, 77, 21, 61, 29, 69, 39, 79, 32, 72)(81, 121, 83, 123, 93, 133, 99, 139, 84, 124, 94, 134, 111, 151, 115, 155, 97, 137, 113, 153, 119, 159, 104, 144, 88, 128, 103, 143, 118, 158, 102, 142, 87, 127, 96, 136, 101, 141, 86, 126)(82, 122, 89, 129, 105, 145, 108, 148, 90, 130, 106, 146, 117, 157, 100, 140, 85, 125, 95, 135, 112, 152, 116, 156, 98, 138, 114, 154, 120, 160, 110, 150, 92, 132, 107, 147, 109, 149, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 106)(10, 85)(11, 108)(12, 82)(13, 111)(14, 113)(15, 114)(16, 83)(17, 88)(18, 92)(19, 115)(20, 116)(21, 93)(22, 86)(23, 96)(24, 102)(25, 117)(26, 95)(27, 89)(28, 100)(29, 105)(30, 91)(31, 119)(32, 120)(33, 103)(34, 107)(35, 104)(36, 110)(37, 112)(38, 101)(39, 118)(40, 109)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.478
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.466 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3^-1), (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y3^-2 * Y1^-2, (R * Y2)^2, Y3^-2 * Y1^2 * Y3^-1, Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y3^-2 * Y2^-2 * Y3^-1 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 18, 58, 4, 44, 10, 50, 7, 47, 12, 52, 17, 57, 5, 45)(3, 43, 9, 49, 23, 63, 36, 76, 14, 54, 26, 66, 16, 56, 27, 67, 35, 75, 15, 55)(6, 46, 11, 51, 24, 64, 37, 77, 19, 59, 28, 68, 22, 62, 30, 70, 31, 71, 20, 60)(13, 53, 25, 65, 21, 61, 29, 69, 32, 72, 39, 79, 34, 74, 40, 80, 38, 78, 33, 73)(81, 121, 83, 123, 93, 133, 111, 151, 97, 137, 115, 155, 118, 158, 102, 142, 87, 127, 96, 136, 114, 154, 99, 139, 84, 124, 94, 134, 112, 152, 104, 144, 88, 128, 103, 143, 101, 141, 86, 126)(82, 122, 89, 129, 105, 145, 100, 140, 85, 125, 95, 135, 113, 153, 110, 150, 92, 132, 107, 147, 120, 160, 108, 148, 90, 130, 106, 146, 119, 159, 117, 157, 98, 138, 116, 156, 109, 149, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 106)(10, 85)(11, 108)(12, 82)(13, 112)(14, 115)(15, 116)(16, 83)(17, 88)(18, 92)(19, 111)(20, 117)(21, 114)(22, 86)(23, 96)(24, 102)(25, 119)(26, 95)(27, 89)(28, 100)(29, 120)(30, 91)(31, 104)(32, 118)(33, 109)(34, 93)(35, 103)(36, 107)(37, 110)(38, 101)(39, 113)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.479
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.467 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y1)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y3^-2 * Y1^-2, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y1^2 * Y3^-1, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1^2, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y3^-1, (Y2^-1 * Y3)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 18, 58, 4, 44, 10, 50, 7, 47, 12, 52, 17, 57, 5, 45)(3, 43, 9, 49, 23, 63, 34, 74, 14, 54, 26, 66, 16, 56, 27, 67, 33, 73, 15, 55)(6, 46, 11, 51, 24, 64, 36, 76, 19, 59, 28, 68, 22, 62, 30, 70, 35, 75, 20, 60)(13, 53, 25, 65, 37, 77, 40, 80, 31, 71, 39, 79, 32, 72, 38, 78, 21, 61, 29, 69)(81, 121, 83, 123, 93, 133, 104, 144, 88, 128, 103, 143, 117, 157, 99, 139, 84, 124, 94, 134, 111, 151, 102, 142, 87, 127, 96, 136, 112, 152, 115, 155, 97, 137, 113, 153, 101, 141, 86, 126)(82, 122, 89, 129, 105, 145, 116, 156, 98, 138, 114, 154, 120, 160, 108, 148, 90, 130, 106, 146, 119, 159, 110, 150, 92, 132, 107, 147, 118, 158, 100, 140, 85, 125, 95, 135, 109, 149, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 106)(10, 85)(11, 108)(12, 82)(13, 111)(14, 113)(15, 114)(16, 83)(17, 88)(18, 92)(19, 115)(20, 116)(21, 117)(22, 86)(23, 96)(24, 102)(25, 119)(26, 95)(27, 89)(28, 100)(29, 120)(30, 91)(31, 101)(32, 93)(33, 103)(34, 107)(35, 104)(36, 110)(37, 112)(38, 105)(39, 109)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.477
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.468 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3^-1)^2, (Y2^-1, Y1^-1), (Y2^-1, Y3), (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y2^2 * Y3^-2, Y2^-6 * Y1, Y2 * Y3 * Y2^2 * Y3 * Y2 * Y1^-2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 21, 61, 27, 67, 37, 77, 31, 71, 13, 53, 17, 57, 5, 45)(3, 43, 9, 49, 20, 60, 6, 46, 11, 51, 23, 63, 35, 75, 29, 69, 32, 72, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52, 24, 64, 36, 76, 39, 79, 30, 70, 34, 74, 18, 58)(14, 54, 25, 65, 16, 56, 19, 59, 26, 66, 22, 62, 28, 68, 38, 78, 40, 80, 33, 73)(81, 121, 83, 123, 93, 133, 109, 149, 107, 147, 91, 131, 82, 122, 89, 129, 97, 137, 112, 152, 117, 157, 103, 143, 88, 128, 100, 140, 85, 125, 95, 135, 111, 151, 115, 155, 101, 141, 86, 126)(84, 124, 94, 134, 110, 150, 118, 158, 104, 144, 106, 146, 90, 130, 105, 145, 114, 154, 120, 160, 116, 156, 102, 142, 87, 127, 96, 136, 98, 138, 113, 153, 119, 159, 108, 148, 92, 132, 99, 139)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 105)(10, 85)(11, 106)(12, 82)(13, 110)(14, 112)(15, 113)(16, 83)(17, 114)(18, 93)(19, 89)(20, 96)(21, 92)(22, 86)(23, 102)(24, 88)(25, 95)(26, 100)(27, 104)(28, 91)(29, 118)(30, 117)(31, 119)(32, 120)(33, 109)(34, 111)(35, 108)(36, 101)(37, 116)(38, 103)(39, 107)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.484
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.469 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y3, Y2^2 * Y3 * Y1^-1, (R * Y2)^2, (Y1, Y2^-1), (R * Y3)^2, Y1^-2 * Y3^-2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-3, Y3^-2 * Y1^8, (Y1 * Y3^-1)^10, (Y3 * Y2^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 29, 69, 37, 77, 33, 73, 26, 66, 15, 55, 5, 45)(3, 43, 9, 49, 20, 60, 30, 70, 38, 78, 35, 75, 28, 68, 17, 57, 24, 64, 13, 53)(4, 44, 10, 50, 7, 47, 12, 52, 22, 62, 31, 71, 39, 79, 34, 74, 25, 65, 16, 56)(6, 46, 11, 51, 21, 61, 14, 54, 23, 63, 32, 72, 40, 80, 36, 76, 27, 67, 18, 58)(81, 121, 83, 123, 92, 132, 103, 143, 109, 149, 118, 158, 114, 154, 107, 147, 95, 135, 104, 144, 90, 130, 101, 141, 88, 128, 100, 140, 111, 151, 120, 160, 113, 153, 108, 148, 96, 136, 86, 126)(82, 122, 89, 129, 102, 142, 112, 152, 117, 157, 115, 155, 105, 145, 98, 138, 85, 125, 93, 133, 87, 127, 94, 134, 99, 139, 110, 150, 119, 159, 116, 156, 106, 146, 97, 137, 84, 124, 91, 131)
	L = (1, 84)(2, 90)(3, 91)(4, 95)(5, 96)(6, 97)(7, 81)(8, 87)(9, 101)(10, 85)(11, 104)(12, 82)(13, 86)(14, 83)(15, 105)(16, 106)(17, 107)(18, 108)(19, 92)(20, 94)(21, 93)(22, 88)(23, 89)(24, 98)(25, 113)(26, 114)(27, 115)(28, 116)(29, 102)(30, 103)(31, 99)(32, 100)(33, 119)(34, 117)(35, 120)(36, 118)(37, 111)(38, 112)(39, 109)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.487
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.470 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1 * Y2, (Y3 * Y1)^2, Y1^-1 * Y3^-2 * Y1^-1, (Y3, Y1^-1), (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2 * Y1, Y1^-2 * Y3^4 * Y1^-4, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 27, 67, 35, 75, 31, 71, 24, 64, 14, 54, 5, 45)(3, 43, 9, 49, 20, 60, 28, 68, 36, 76, 39, 79, 34, 74, 25, 65, 17, 57, 6, 46)(4, 44, 10, 50, 7, 47, 11, 51, 21, 61, 29, 69, 37, 77, 32, 72, 23, 63, 15, 55)(12, 52, 18, 58, 13, 53, 22, 62, 30, 70, 38, 78, 40, 80, 33, 73, 26, 66, 16, 56)(81, 121, 83, 123, 82, 122, 89, 129, 88, 128, 100, 140, 99, 139, 108, 148, 107, 147, 116, 156, 115, 155, 119, 159, 111, 151, 114, 154, 104, 144, 105, 145, 94, 134, 97, 137, 85, 125, 86, 126)(84, 124, 92, 132, 90, 130, 98, 138, 87, 127, 93, 133, 91, 131, 102, 142, 101, 141, 110, 150, 109, 149, 118, 158, 117, 157, 120, 160, 112, 152, 113, 153, 103, 143, 106, 146, 95, 135, 96, 136)
	L = (1, 84)(2, 90)(3, 92)(4, 94)(5, 95)(6, 96)(7, 81)(8, 87)(9, 98)(10, 85)(11, 82)(12, 97)(13, 83)(14, 103)(15, 104)(16, 105)(17, 106)(18, 86)(19, 91)(20, 93)(21, 88)(22, 89)(23, 111)(24, 112)(25, 113)(26, 114)(27, 101)(28, 102)(29, 99)(30, 100)(31, 117)(32, 115)(33, 119)(34, 120)(35, 109)(36, 110)(37, 107)(38, 108)(39, 118)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.483
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.471 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y2)^2, (Y2, Y1), (Y3^-1, Y1^-1), (Y1^-1 * Y3^-1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y1)^2, Y3^3 * Y2^-2 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1 * Y3^-1 * Y2^-1, Y2^3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2^-2 * Y1^7, (Y1 * Y3^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 37, 77, 33, 73, 40, 80, 34, 74, 17, 57, 5, 45)(3, 43, 9, 49, 24, 64, 19, 59, 30, 70, 22, 62, 32, 72, 39, 79, 35, 75, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52, 26, 66, 21, 61, 31, 71, 13, 53, 27, 67, 18, 58)(6, 46, 11, 51, 25, 65, 38, 78, 36, 76, 14, 54, 28, 68, 16, 56, 29, 69, 20, 60)(81, 121, 83, 123, 93, 133, 105, 145, 88, 128, 104, 144, 98, 138, 116, 156, 117, 157, 110, 150, 90, 130, 108, 148, 120, 160, 112, 152, 92, 132, 109, 149, 97, 137, 115, 155, 101, 141, 86, 126)(82, 122, 89, 129, 107, 147, 118, 158, 103, 143, 99, 139, 84, 124, 94, 134, 113, 153, 102, 142, 87, 127, 96, 136, 114, 154, 119, 159, 106, 146, 100, 140, 85, 125, 95, 135, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 108)(10, 85)(11, 110)(12, 82)(13, 113)(14, 115)(15, 116)(16, 83)(17, 107)(18, 114)(19, 109)(20, 104)(21, 103)(22, 86)(23, 92)(24, 96)(25, 102)(26, 88)(27, 120)(28, 95)(29, 89)(30, 100)(31, 117)(32, 91)(33, 101)(34, 93)(35, 118)(36, 119)(37, 106)(38, 112)(39, 105)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.486
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.472 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, (Y3^-1, Y1), Y3^-2 * Y1^-2, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^4 * Y1^-6, Y3^10, Y3^-2 * Y1^2 * Y2^-1 * Y3^-1 * Y1 * Y3^-3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 27, 67, 35, 75, 33, 73, 26, 66, 15, 55, 5, 45)(3, 43, 6, 46, 10, 50, 20, 60, 28, 68, 36, 76, 39, 79, 32, 72, 23, 63, 13, 53)(4, 44, 9, 49, 7, 47, 11, 51, 21, 61, 29, 69, 37, 77, 34, 74, 25, 65, 16, 56)(12, 52, 17, 57, 14, 54, 18, 58, 22, 62, 30, 70, 38, 78, 40, 80, 31, 71, 24, 64)(81, 121, 83, 123, 85, 125, 93, 133, 95, 135, 103, 143, 106, 146, 112, 152, 113, 153, 119, 159, 115, 155, 116, 156, 107, 147, 108, 148, 99, 139, 100, 140, 88, 128, 90, 130, 82, 122, 86, 126)(84, 124, 92, 132, 96, 136, 104, 144, 105, 145, 111, 151, 114, 154, 120, 160, 117, 157, 118, 158, 109, 149, 110, 150, 101, 141, 102, 142, 91, 131, 98, 138, 87, 127, 94, 134, 89, 129, 97, 137)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 97)(7, 81)(8, 87)(9, 85)(10, 94)(11, 82)(12, 103)(13, 104)(14, 83)(15, 105)(16, 106)(17, 93)(18, 86)(19, 91)(20, 98)(21, 88)(22, 90)(23, 111)(24, 112)(25, 113)(26, 114)(27, 101)(28, 102)(29, 99)(30, 100)(31, 119)(32, 120)(33, 117)(34, 115)(35, 109)(36, 110)(37, 107)(38, 108)(39, 118)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.485
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.473 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^-1 * Y2^-2 * Y1 * Y3^-2, Y1^-1 * Y3^3 * Y2^2, Y1^-2 * Y2 * Y3 * Y2 * Y1^-1, Y1^-2 * Y2^-4, (Y2^-2 * Y3)^2, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 37, 77, 34, 74, 40, 80, 35, 75, 17, 57, 5, 45)(3, 43, 9, 49, 24, 64, 38, 78, 36, 76, 19, 59, 30, 70, 22, 62, 32, 72, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52, 26, 66, 13, 53, 27, 67, 21, 61, 31, 71, 18, 58)(6, 46, 11, 51, 25, 65, 14, 54, 28, 68, 16, 56, 29, 69, 39, 79, 33, 73, 20, 60)(81, 121, 83, 123, 93, 133, 113, 153, 97, 137, 112, 152, 92, 132, 109, 149, 120, 160, 110, 150, 90, 130, 108, 148, 117, 157, 116, 156, 98, 138, 105, 145, 88, 128, 104, 144, 101, 141, 86, 126)(82, 122, 89, 129, 107, 147, 100, 140, 85, 125, 95, 135, 106, 146, 119, 159, 115, 155, 102, 142, 87, 127, 96, 136, 114, 154, 99, 139, 84, 124, 94, 134, 103, 143, 118, 158, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 108)(10, 85)(11, 110)(12, 82)(13, 103)(14, 112)(15, 105)(16, 83)(17, 111)(18, 115)(19, 113)(20, 116)(21, 114)(22, 86)(23, 92)(24, 96)(25, 102)(26, 88)(27, 117)(28, 95)(29, 89)(30, 100)(31, 120)(32, 91)(33, 118)(34, 93)(35, 101)(36, 119)(37, 106)(38, 109)(39, 104)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.488
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.474 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3^-1, Y3^-2 * Y1^-2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3^10, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 27, 67, 35, 75, 33, 73, 26, 66, 15, 55, 5, 45)(3, 43, 9, 49, 18, 58, 22, 62, 30, 70, 38, 78, 39, 79, 32, 72, 23, 63, 14, 54)(4, 44, 10, 50, 7, 47, 12, 52, 21, 61, 29, 69, 37, 77, 34, 74, 25, 65, 16, 56)(6, 46, 11, 51, 20, 60, 28, 68, 36, 76, 40, 80, 31, 71, 24, 64, 13, 53, 17, 57)(81, 121, 83, 123, 84, 124, 93, 133, 95, 135, 103, 143, 105, 145, 111, 151, 113, 153, 119, 159, 117, 157, 116, 156, 107, 147, 110, 150, 101, 141, 100, 140, 88, 128, 98, 138, 87, 127, 86, 126)(82, 122, 89, 129, 90, 130, 97, 137, 85, 125, 94, 134, 96, 136, 104, 144, 106, 146, 112, 152, 114, 154, 120, 160, 115, 155, 118, 158, 109, 149, 108, 148, 99, 139, 102, 142, 92, 132, 91, 131)
	L = (1, 84)(2, 90)(3, 93)(4, 95)(5, 96)(6, 83)(7, 81)(8, 87)(9, 97)(10, 85)(11, 89)(12, 82)(13, 103)(14, 104)(15, 105)(16, 106)(17, 94)(18, 86)(19, 92)(20, 98)(21, 88)(22, 91)(23, 111)(24, 112)(25, 113)(26, 114)(27, 101)(28, 102)(29, 99)(30, 100)(31, 119)(32, 120)(33, 117)(34, 115)(35, 109)(36, 110)(37, 107)(38, 108)(39, 116)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.481
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.475 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3, Y3^-2 * Y1^-2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, (Y2^-1, Y1), Y3^4 * Y1^4, Y3^-6 * Y1^4, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 27, 67, 35, 75, 31, 71, 24, 64, 15, 55, 5, 45)(3, 43, 9, 49, 20, 60, 28, 68, 36, 76, 40, 80, 33, 73, 26, 66, 17, 57, 13, 53)(4, 44, 10, 50, 7, 47, 12, 52, 21, 61, 29, 69, 37, 77, 32, 72, 23, 63, 16, 56)(6, 46, 11, 51, 14, 54, 22, 62, 30, 70, 38, 78, 39, 79, 34, 74, 25, 65, 18, 58)(81, 121, 83, 123, 87, 127, 94, 134, 88, 128, 100, 140, 101, 141, 110, 150, 107, 147, 116, 156, 117, 157, 119, 159, 111, 151, 113, 153, 103, 143, 105, 145, 95, 135, 97, 137, 84, 124, 86, 126)(82, 122, 89, 129, 92, 132, 102, 142, 99, 139, 108, 148, 109, 149, 118, 158, 115, 155, 120, 160, 112, 152, 114, 154, 104, 144, 106, 146, 96, 136, 98, 138, 85, 125, 93, 133, 90, 130, 91, 131)
	L = (1, 84)(2, 90)(3, 86)(4, 95)(5, 96)(6, 97)(7, 81)(8, 87)(9, 91)(10, 85)(11, 93)(12, 82)(13, 98)(14, 83)(15, 103)(16, 104)(17, 105)(18, 106)(19, 92)(20, 94)(21, 88)(22, 89)(23, 111)(24, 112)(25, 113)(26, 114)(27, 101)(28, 102)(29, 99)(30, 100)(31, 117)(32, 115)(33, 119)(34, 120)(35, 109)(36, 110)(37, 107)(38, 108)(39, 116)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.482
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.476 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (R * Y1)^2, (Y2^-1, Y3), (Y1^-1, Y3), (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y2^2 * Y3^-3, Y3 * Y2^6, Y1^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 36, 76, 40, 80, 30, 70, 34, 74, 17, 57, 5, 45)(3, 43, 9, 49, 19, 59, 26, 66, 22, 62, 28, 68, 35, 75, 39, 79, 32, 72, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52, 21, 61, 27, 67, 38, 78, 31, 71, 13, 53, 18, 58)(6, 46, 11, 51, 24, 64, 37, 77, 29, 69, 33, 73, 14, 54, 25, 65, 16, 56, 20, 60)(81, 121, 83, 123, 93, 133, 109, 149, 116, 156, 102, 142, 87, 127, 96, 136, 97, 137, 112, 152, 118, 158, 104, 144, 88, 128, 99, 139, 84, 124, 94, 134, 110, 150, 115, 155, 101, 141, 86, 126)(82, 122, 89, 129, 98, 138, 113, 153, 120, 160, 108, 148, 92, 132, 100, 140, 85, 125, 95, 135, 111, 151, 117, 157, 103, 143, 106, 146, 90, 130, 105, 145, 114, 154, 119, 159, 107, 147, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 105)(10, 85)(11, 106)(12, 82)(13, 110)(14, 112)(15, 113)(16, 83)(17, 93)(18, 114)(19, 96)(20, 89)(21, 88)(22, 86)(23, 92)(24, 102)(25, 95)(26, 100)(27, 103)(28, 91)(29, 115)(30, 118)(31, 120)(32, 109)(33, 119)(34, 111)(35, 104)(36, 101)(37, 108)(38, 116)(39, 117)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.480
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.477 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1^4, Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 17, 57, 6, 46, 10, 50, 20, 60, 32, 72, 18, 58, 24, 64, 34, 74, 30, 70, 14, 54, 23, 63, 31, 71, 15, 55, 4, 44, 9, 49, 16, 56, 5, 45)(3, 43, 8, 48, 19, 59, 28, 68, 13, 53, 22, 62, 33, 73, 39, 79, 29, 69, 36, 76, 40, 80, 37, 77, 25, 65, 35, 75, 38, 78, 26, 66, 11, 51, 21, 61, 27, 67, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 99, 139)(89, 129, 101, 141)(90, 130, 102, 142)(94, 134, 105, 145)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 108, 148)(98, 138, 109, 149)(100, 140, 113, 153)(103, 143, 115, 155)(104, 144, 116, 156)(110, 150, 117, 157)(111, 151, 118, 158)(112, 152, 119, 159)(114, 154, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 96)(8, 101)(9, 103)(10, 82)(11, 105)(12, 106)(13, 83)(14, 98)(15, 110)(16, 111)(17, 85)(18, 86)(19, 107)(20, 87)(21, 115)(22, 88)(23, 104)(24, 90)(25, 109)(26, 117)(27, 118)(28, 92)(29, 93)(30, 112)(31, 114)(32, 97)(33, 99)(34, 100)(35, 116)(36, 102)(37, 119)(38, 120)(39, 108)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.467
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.478 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^5, Y3^-1 * Y1^2 * Y3 * Y1^-2, Y3^-2 * Y1^4, Y1 * Y3 * Y1^2 * Y3^2 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 14, 54, 25, 65, 32, 72, 17, 57, 6, 46, 10, 50, 22, 62, 15, 55, 4, 44, 9, 49, 21, 61, 33, 73, 18, 58, 26, 66, 16, 56, 5, 45)(3, 43, 8, 48, 20, 60, 34, 74, 27, 67, 37, 77, 39, 79, 30, 70, 13, 53, 24, 64, 36, 76, 28, 68, 11, 51, 23, 63, 35, 75, 40, 80, 31, 71, 38, 78, 29, 69, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 109, 149)(97, 137, 110, 150)(98, 138, 111, 151)(99, 139, 114, 154)(101, 141, 115, 155)(102, 142, 116, 156)(105, 145, 117, 157)(106, 146, 118, 158)(112, 152, 119, 159)(113, 153, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 107)(12, 108)(13, 83)(14, 98)(15, 99)(16, 102)(17, 85)(18, 86)(19, 113)(20, 115)(21, 112)(22, 87)(23, 117)(24, 88)(25, 106)(26, 90)(27, 111)(28, 114)(29, 116)(30, 92)(31, 93)(32, 96)(33, 97)(34, 120)(35, 119)(36, 100)(37, 118)(38, 104)(39, 109)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.465
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.479 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-1 * Y2 * Y1 * Y2, (Y3, Y1), (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, Y3^-5, Y3^-2 * Y1^-4 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 18, 58, 26, 66, 33, 73, 15, 55, 4, 44, 9, 49, 21, 61, 17, 57, 6, 46, 10, 50, 22, 62, 32, 72, 14, 54, 25, 65, 16, 56, 5, 45)(3, 43, 8, 48, 20, 60, 34, 74, 31, 71, 38, 78, 40, 80, 28, 68, 11, 51, 23, 63, 35, 75, 30, 70, 13, 53, 24, 64, 36, 76, 39, 79, 27, 67, 37, 77, 29, 69, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 109, 149)(97, 137, 110, 150)(98, 138, 111, 151)(99, 139, 114, 154)(101, 141, 115, 155)(102, 142, 116, 156)(105, 145, 117, 157)(106, 146, 118, 158)(112, 152, 119, 159)(113, 153, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 107)(12, 108)(13, 83)(14, 98)(15, 112)(16, 113)(17, 85)(18, 86)(19, 97)(20, 115)(21, 96)(22, 87)(23, 117)(24, 88)(25, 106)(26, 90)(27, 111)(28, 119)(29, 120)(30, 92)(31, 93)(32, 99)(33, 102)(34, 110)(35, 109)(36, 100)(37, 118)(38, 104)(39, 114)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.466
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.480 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3, Y1 * Y2 * Y1^-1 * Y2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^10, (Y3^-1 * Y1^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 8, 48, 12, 52, 16, 56, 20, 60, 24, 64, 28, 68, 32, 72, 36, 76, 37, 77, 30, 70, 29, 69, 22, 62, 21, 61, 14, 54, 13, 53, 6, 46, 5, 45)(3, 43, 7, 47, 9, 49, 15, 55, 17, 57, 23, 63, 25, 65, 31, 71, 33, 73, 38, 78, 39, 79, 40, 80, 35, 75, 34, 74, 27, 67, 26, 66, 19, 59, 18, 58, 11, 51, 10, 50)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 89, 129)(85, 125, 90, 130)(86, 126, 91, 131)(88, 128, 95, 135)(92, 132, 97, 137)(93, 133, 98, 138)(94, 134, 99, 139)(96, 136, 103, 143)(100, 140, 105, 145)(101, 141, 106, 146)(102, 142, 107, 147)(104, 144, 111, 151)(108, 148, 113, 153)(109, 149, 114, 154)(110, 150, 115, 155)(112, 152, 118, 158)(116, 156, 119, 159)(117, 157, 120, 160)
	L = (1, 84)(2, 88)(3, 89)(4, 92)(5, 82)(6, 81)(7, 95)(8, 96)(9, 97)(10, 87)(11, 83)(12, 100)(13, 85)(14, 86)(15, 103)(16, 104)(17, 105)(18, 90)(19, 91)(20, 108)(21, 93)(22, 94)(23, 111)(24, 112)(25, 113)(26, 98)(27, 99)(28, 116)(29, 101)(30, 102)(31, 118)(32, 117)(33, 119)(34, 106)(35, 107)(36, 110)(37, 109)(38, 120)(39, 115)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.476
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.481 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y1 * Y2 * Y1^-1 * Y2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 6, 46, 8, 48, 14, 54, 16, 56, 22, 62, 24, 64, 30, 70, 32, 72, 36, 76, 37, 77, 28, 68, 29, 69, 20, 60, 21, 61, 12, 52, 13, 53, 4, 44, 5, 45)(3, 43, 7, 47, 11, 51, 15, 55, 19, 59, 23, 63, 27, 67, 31, 71, 35, 75, 38, 78, 39, 79, 40, 80, 33, 73, 34, 74, 25, 65, 26, 66, 17, 57, 18, 58, 9, 49, 10, 50)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 89, 129)(85, 125, 90, 130)(86, 126, 91, 131)(88, 128, 95, 135)(92, 132, 97, 137)(93, 133, 98, 138)(94, 134, 99, 139)(96, 136, 103, 143)(100, 140, 105, 145)(101, 141, 106, 146)(102, 142, 107, 147)(104, 144, 111, 151)(108, 148, 113, 153)(109, 149, 114, 154)(110, 150, 115, 155)(112, 152, 118, 158)(116, 156, 119, 159)(117, 157, 120, 160)
	L = (1, 84)(2, 85)(3, 89)(4, 92)(5, 93)(6, 81)(7, 90)(8, 82)(9, 97)(10, 98)(11, 83)(12, 100)(13, 101)(14, 86)(15, 87)(16, 88)(17, 105)(18, 106)(19, 91)(20, 108)(21, 109)(22, 94)(23, 95)(24, 96)(25, 113)(26, 114)(27, 99)(28, 116)(29, 117)(30, 102)(31, 103)(32, 104)(33, 119)(34, 120)(35, 107)(36, 110)(37, 112)(38, 111)(39, 115)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.474
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.482 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y1^2 * Y3^3, Y3 * Y1^-6 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 31, 71, 15, 55, 4, 44, 9, 49, 18, 58, 24, 64, 35, 75, 30, 70, 14, 54, 17, 57, 6, 46, 10, 50, 21, 61, 32, 72, 16, 56, 5, 45)(3, 43, 8, 48, 20, 60, 33, 73, 38, 78, 26, 66, 11, 51, 22, 62, 29, 69, 36, 76, 40, 80, 37, 77, 25, 65, 28, 68, 13, 53, 23, 63, 34, 74, 39, 79, 27, 67, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 102, 142)(90, 130, 103, 143)(94, 134, 105, 145)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 108, 148)(98, 138, 109, 149)(99, 139, 113, 153)(101, 141, 114, 154)(104, 144, 116, 156)(110, 150, 117, 157)(111, 151, 118, 158)(112, 152, 119, 159)(115, 155, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 98)(8, 102)(9, 97)(10, 82)(11, 105)(12, 106)(13, 83)(14, 96)(15, 110)(16, 111)(17, 85)(18, 86)(19, 104)(20, 109)(21, 87)(22, 108)(23, 88)(24, 90)(25, 107)(26, 117)(27, 118)(28, 92)(29, 93)(30, 112)(31, 115)(32, 99)(33, 116)(34, 100)(35, 101)(36, 103)(37, 119)(38, 120)(39, 113)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.475
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.483 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, (Y3, Y1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y3^-3 * Y2, Y1^-2 * Y2 * Y3^-3, Y1 * Y3 * Y1 * Y3 * Y2 * Y3, Y3^4 * Y1^-4, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 33, 73, 28, 68, 11, 51, 23, 63, 18, 58, 26, 66, 38, 78, 30, 70, 14, 54, 25, 65, 13, 53, 24, 64, 37, 77, 32, 72, 16, 56, 5, 45)(3, 43, 8, 48, 20, 60, 34, 74, 31, 71, 15, 55, 4, 44, 9, 49, 21, 61, 35, 75, 40, 80, 39, 79, 27, 67, 17, 57, 6, 46, 10, 50, 22, 62, 36, 76, 29, 69, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 109, 149)(97, 137, 105, 145)(98, 138, 101, 141)(99, 139, 114, 154)(102, 142, 117, 157)(106, 146, 115, 155)(110, 150, 119, 159)(111, 151, 113, 153)(112, 152, 116, 156)(118, 158, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 107)(12, 108)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 115)(20, 98)(21, 93)(22, 87)(23, 97)(24, 88)(25, 92)(26, 90)(27, 96)(28, 119)(29, 113)(30, 116)(31, 118)(32, 114)(33, 120)(34, 106)(35, 104)(36, 99)(37, 100)(38, 102)(39, 112)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.470
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.484 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y1^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-1 * Y3^3 * Y1, Y3^10, (Y2 * Y3)^10, (Y3^-1 * Y1^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 15, 55, 12, 52, 17, 57, 24, 64, 31, 71, 28, 68, 33, 73, 39, 79, 37, 77, 30, 70, 34, 74, 27, 67, 21, 61, 14, 54, 18, 58, 11, 51, 5, 45)(3, 43, 8, 48, 4, 44, 9, 49, 16, 56, 23, 63, 20, 60, 25, 65, 32, 72, 38, 78, 36, 76, 40, 80, 35, 75, 29, 69, 22, 62, 26, 66, 19, 59, 13, 53, 6, 46, 10, 50)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 87, 127)(85, 125, 90, 130)(86, 126, 91, 131)(89, 129, 95, 135)(92, 132, 96, 136)(93, 133, 98, 138)(94, 134, 99, 139)(97, 137, 103, 143)(100, 140, 104, 144)(101, 141, 106, 146)(102, 142, 107, 147)(105, 145, 111, 151)(108, 148, 112, 152)(109, 149, 114, 154)(110, 150, 115, 155)(113, 153, 118, 158)(116, 156, 119, 159)(117, 157, 120, 160)
	L = (1, 84)(2, 89)(3, 87)(4, 92)(5, 88)(6, 81)(7, 96)(8, 95)(9, 97)(10, 82)(11, 83)(12, 100)(13, 85)(14, 86)(15, 103)(16, 104)(17, 105)(18, 90)(19, 91)(20, 108)(21, 93)(22, 94)(23, 111)(24, 112)(25, 113)(26, 98)(27, 99)(28, 116)(29, 101)(30, 102)(31, 118)(32, 119)(33, 120)(34, 106)(35, 107)(36, 110)(37, 109)(38, 117)(39, 115)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.468
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.485 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y2 * Y1, Y3 * Y2 * Y3^-1 * Y2, Y1^-2 * Y3^-1 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y3^10, Y3^-1 * Y1^16 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 15, 55, 14, 54, 18, 58, 24, 64, 31, 71, 30, 70, 34, 74, 39, 79, 37, 77, 28, 68, 33, 73, 27, 67, 21, 61, 12, 52, 17, 57, 11, 51, 5, 45)(3, 43, 8, 48, 6, 46, 10, 50, 16, 56, 23, 63, 22, 62, 26, 66, 32, 72, 38, 78, 36, 76, 40, 80, 35, 75, 29, 69, 20, 60, 25, 65, 19, 59, 13, 53, 4, 44, 9, 49)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 89, 129)(86, 126, 87, 127)(90, 130, 95, 135)(92, 132, 99, 139)(93, 133, 97, 137)(94, 134, 96, 136)(98, 138, 103, 143)(100, 140, 107, 147)(101, 141, 105, 145)(102, 142, 104, 144)(106, 146, 111, 151)(108, 148, 115, 155)(109, 149, 113, 153)(110, 150, 112, 152)(114, 154, 118, 158)(116, 156, 119, 159)(117, 157, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 92)(5, 93)(6, 81)(7, 83)(8, 85)(9, 97)(10, 82)(11, 99)(12, 100)(13, 101)(14, 86)(15, 88)(16, 87)(17, 105)(18, 90)(19, 107)(20, 108)(21, 109)(22, 94)(23, 95)(24, 96)(25, 113)(26, 98)(27, 115)(28, 116)(29, 117)(30, 102)(31, 103)(32, 104)(33, 120)(34, 106)(35, 119)(36, 110)(37, 118)(38, 111)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.472
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.486 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1, Y2 * Y1^2 * Y3^-2, Y3 * Y1^2 * Y3 * Y1^2 * Y3^4, Y1^-4 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y3 * Y1^3 * Y2 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 29, 69, 37, 77, 35, 75, 27, 67, 18, 58, 12, 52, 3, 43, 8, 48, 14, 54, 22, 62, 31, 71, 39, 79, 33, 73, 25, 65, 16, 56, 5, 45)(4, 44, 9, 49, 20, 60, 30, 70, 38, 78, 34, 74, 26, 66, 17, 57, 6, 46, 10, 50, 11, 51, 21, 61, 24, 64, 32, 72, 40, 80, 36, 76, 28, 68, 23, 63, 13, 53, 15, 55)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 94, 134)(89, 129, 101, 141)(90, 130, 95, 135)(96, 136, 98, 138)(97, 137, 103, 143)(99, 139, 102, 142)(100, 140, 104, 144)(105, 145, 107, 147)(106, 146, 108, 148)(109, 149, 111, 151)(110, 150, 112, 152)(113, 153, 115, 155)(114, 154, 116, 156)(117, 157, 119, 159)(118, 158, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 100)(8, 101)(9, 102)(10, 82)(11, 87)(12, 90)(13, 83)(14, 104)(15, 88)(16, 93)(17, 85)(18, 86)(19, 110)(20, 111)(21, 99)(22, 112)(23, 92)(24, 109)(25, 103)(26, 96)(27, 97)(28, 98)(29, 118)(30, 119)(31, 120)(32, 117)(33, 108)(34, 105)(35, 106)(36, 107)(37, 114)(38, 113)(39, 116)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.471
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.487 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y3^2 * Y1^-3, Y3 * Y1 * Y3 * Y2 * Y3^2 * Y1, Y3 * Y1 * Y3^3 * Y1 * Y2, Y1^-1 * Y3^-2 * Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y2 * Y3^2 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 14, 54, 25, 65, 31, 71, 39, 79, 29, 69, 12, 52, 3, 43, 8, 48, 20, 60, 36, 76, 27, 67, 34, 74, 18, 58, 26, 66, 16, 56, 5, 45)(4, 44, 9, 49, 21, 61, 37, 77, 32, 72, 30, 70, 13, 53, 24, 64, 38, 78, 28, 68, 11, 51, 23, 63, 35, 75, 40, 80, 33, 73, 17, 57, 6, 46, 10, 50, 22, 62, 15, 55)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 109, 149)(97, 137, 110, 150)(98, 138, 111, 151)(99, 139, 116, 156)(101, 141, 115, 155)(102, 142, 118, 158)(105, 145, 114, 154)(106, 146, 119, 159)(112, 152, 113, 153)(117, 157, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 107)(12, 108)(13, 83)(14, 112)(15, 99)(16, 102)(17, 85)(18, 86)(19, 117)(20, 115)(21, 111)(22, 87)(23, 114)(24, 88)(25, 110)(26, 90)(27, 113)(28, 116)(29, 118)(30, 92)(31, 93)(32, 109)(33, 96)(34, 97)(35, 98)(36, 120)(37, 119)(38, 100)(39, 104)(40, 106)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.469
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.488 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2 * Y3, Y2 * Y1 * Y2 * Y1^-1, Y3^-2 * Y1^-4, Y3^-1 * Y1^2 * Y2 * Y3^-3, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 18, 58, 26, 66, 27, 67, 39, 79, 29, 69, 12, 52, 3, 43, 8, 48, 20, 60, 36, 76, 31, 71, 33, 73, 14, 54, 25, 65, 16, 56, 5, 45)(4, 44, 9, 49, 21, 61, 17, 57, 6, 46, 10, 50, 22, 62, 37, 77, 35, 75, 28, 68, 11, 51, 23, 63, 38, 78, 30, 70, 13, 53, 24, 64, 32, 72, 40, 80, 34, 74, 15, 55)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 107, 147)(95, 135, 108, 148)(96, 136, 109, 149)(97, 137, 110, 150)(98, 138, 111, 151)(99, 139, 116, 156)(101, 141, 118, 158)(102, 142, 112, 152)(105, 145, 119, 159)(106, 146, 113, 153)(114, 154, 115, 155)(117, 157, 120, 160)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 107)(12, 108)(13, 83)(14, 112)(15, 113)(16, 114)(17, 85)(18, 86)(19, 97)(20, 118)(21, 96)(22, 87)(23, 119)(24, 88)(25, 120)(26, 90)(27, 102)(28, 106)(29, 115)(30, 92)(31, 93)(32, 100)(33, 104)(34, 111)(35, 98)(36, 110)(37, 99)(38, 109)(39, 117)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.473
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.489 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^2, (Y2, Y1^-1), (R * Y2)^2, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-2, Y2^5 * Y3^5, (Y1^-1 * Y3^-1)^10, Y2^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 14, 54, 29, 69, 21, 61, 31, 71, 40, 80, 36, 76, 16, 56, 30, 70, 39, 79, 35, 75, 13, 53, 28, 68, 22, 62, 32, 72, 18, 58, 5, 45)(3, 43, 9, 49, 24, 64, 37, 77, 34, 74, 19, 59, 6, 46, 11, 51, 26, 66, 17, 57, 4, 44, 10, 50, 25, 65, 38, 78, 33, 73, 20, 60, 7, 47, 12, 52, 27, 67, 15, 55)(81, 121, 83, 123, 93, 133, 113, 153, 120, 160, 106, 146, 88, 128, 104, 144, 102, 142, 87, 127, 96, 136, 84, 124, 94, 134, 114, 154, 98, 138, 107, 147, 119, 159, 105, 145, 101, 141, 86, 126)(82, 122, 89, 129, 108, 148, 100, 140, 116, 156, 97, 137, 103, 143, 117, 157, 112, 152, 92, 132, 110, 150, 90, 130, 109, 149, 99, 139, 85, 125, 95, 135, 115, 155, 118, 158, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 105)(9, 109)(10, 108)(11, 110)(12, 82)(13, 114)(14, 113)(15, 103)(16, 83)(17, 115)(18, 106)(19, 116)(20, 85)(21, 87)(22, 86)(23, 118)(24, 101)(25, 102)(26, 119)(27, 88)(28, 99)(29, 100)(30, 89)(31, 92)(32, 91)(33, 98)(34, 120)(35, 117)(36, 95)(37, 111)(38, 112)(39, 104)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.462
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.490 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2^2, Y2^3 * Y1^-1, (Y3, Y2^-1), Y3^-1 * Y2^-1 * Y1 * Y3^-1, (R * Y1)^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1^6, (Y1^-1 * Y3^-1)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 31, 71, 25, 65, 13, 53, 3, 43, 9, 49, 20, 60, 32, 72, 29, 69, 17, 57, 6, 46, 11, 51, 22, 62, 34, 74, 28, 68, 16, 56, 5, 45)(4, 44, 10, 50, 21, 61, 33, 73, 30, 70, 18, 58, 7, 47, 12, 52, 23, 63, 35, 75, 39, 79, 37, 77, 26, 66, 14, 54, 24, 64, 36, 76, 40, 80, 38, 78, 27, 67, 15, 55)(81, 121, 83, 123, 91, 131, 82, 122, 89, 129, 102, 142, 88, 128, 100, 140, 114, 154, 99, 139, 112, 152, 108, 148, 111, 151, 109, 149, 96, 136, 105, 145, 97, 137, 85, 125, 93, 133, 86, 126)(84, 124, 92, 132, 104, 144, 90, 130, 103, 143, 116, 156, 101, 141, 115, 155, 120, 160, 113, 153, 119, 159, 118, 158, 110, 150, 117, 157, 107, 147, 98, 138, 106, 146, 95, 135, 87, 127, 94, 134)
	L = (1, 84)(2, 90)(3, 92)(4, 91)(5, 95)(6, 94)(7, 81)(8, 101)(9, 103)(10, 102)(11, 104)(12, 82)(13, 87)(14, 83)(15, 86)(16, 107)(17, 106)(18, 85)(19, 113)(20, 115)(21, 114)(22, 116)(23, 88)(24, 89)(25, 98)(26, 93)(27, 97)(28, 118)(29, 117)(30, 96)(31, 110)(32, 119)(33, 108)(34, 120)(35, 99)(36, 100)(37, 105)(38, 109)(39, 111)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.461
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.491 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-2, Y1^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y3^2 * Y2^-2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3 * Y1^-3)^2, Y3 * Y1^3 * Y3^-1 * Y1^-3, (Y2 * Y1^-1)^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 31, 71, 26, 66, 13, 53, 6, 46, 11, 51, 22, 62, 34, 74, 28, 68, 15, 55, 3, 43, 9, 49, 20, 60, 32, 72, 30, 70, 18, 58, 5, 45)(4, 44, 10, 50, 21, 61, 33, 73, 39, 79, 37, 77, 25, 65, 16, 56, 24, 64, 36, 76, 40, 80, 38, 78, 27, 67, 14, 54, 7, 47, 12, 52, 23, 63, 35, 75, 29, 69, 17, 57)(81, 121, 83, 123, 93, 133, 85, 125, 95, 135, 106, 146, 98, 138, 108, 148, 111, 151, 110, 150, 114, 154, 99, 139, 112, 152, 102, 142, 88, 128, 100, 140, 91, 131, 82, 122, 89, 129, 86, 126)(84, 124, 94, 134, 105, 145, 97, 137, 107, 147, 117, 157, 109, 149, 118, 158, 119, 159, 115, 155, 120, 160, 113, 153, 103, 143, 116, 156, 101, 141, 92, 132, 104, 144, 90, 130, 87, 127, 96, 136)
	L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 101)(9, 87)(10, 86)(11, 104)(12, 82)(13, 105)(14, 85)(15, 107)(16, 83)(17, 106)(18, 109)(19, 113)(20, 92)(21, 91)(22, 116)(23, 88)(24, 89)(25, 95)(26, 117)(27, 98)(28, 118)(29, 111)(30, 115)(31, 119)(32, 103)(33, 102)(34, 120)(35, 99)(36, 100)(37, 108)(38, 110)(39, 114)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.463
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.492 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C2 (small group id <40, 9>)
Aut   = C2 x D40 (small group id <80, 37>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y3^3, (Y3^-1, Y1^-1), Y2^-2 * Y3^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2 * Y3^-2 * Y1, Y1^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3, Y1^6 * Y3^-2, Y2^14 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 31, 71, 26, 66, 13, 53, 7, 47, 12, 52, 23, 63, 35, 75, 29, 69, 17, 57, 4, 44, 10, 50, 21, 61, 33, 73, 30, 70, 18, 58, 5, 45)(3, 43, 9, 49, 20, 60, 32, 72, 39, 79, 37, 77, 25, 65, 16, 56, 24, 64, 36, 76, 40, 80, 38, 78, 27, 67, 14, 54, 6, 46, 11, 51, 22, 62, 34, 74, 28, 68, 15, 55)(81, 121, 83, 123, 93, 133, 105, 145, 97, 137, 107, 147, 98, 138, 108, 148, 111, 151, 119, 159, 115, 155, 120, 160, 113, 153, 102, 142, 88, 128, 100, 140, 92, 132, 104, 144, 90, 130, 86, 126)(82, 122, 89, 129, 87, 127, 96, 136, 84, 124, 94, 134, 85, 125, 95, 135, 106, 146, 117, 157, 109, 149, 118, 158, 110, 150, 114, 154, 99, 139, 112, 152, 103, 143, 116, 156, 101, 141, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 101)(9, 86)(10, 87)(11, 104)(12, 82)(13, 85)(14, 105)(15, 107)(16, 83)(17, 106)(18, 109)(19, 113)(20, 91)(21, 92)(22, 116)(23, 88)(24, 89)(25, 95)(26, 98)(27, 117)(28, 118)(29, 111)(30, 115)(31, 110)(32, 102)(33, 103)(34, 120)(35, 99)(36, 100)(37, 108)(38, 119)(39, 114)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.464
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.493 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 10, 20, 20})
Quotient :: edge^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^2, (Y2, Y1), R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3, Y2^-9 * Y1^-1, Y1^20, Y1^-2 * Y2^-2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 4, 44)(2, 42, 9, 49)(3, 43, 11, 51)(5, 45, 13, 53)(6, 46, 12, 52)(7, 47, 18, 58)(8, 48, 19, 59)(10, 50, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(16, 56, 27, 67)(17, 57, 28, 68)(23, 63, 30, 70)(24, 64, 29, 69)(25, 65, 35, 75)(26, 66, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(33, 73, 39, 79)(34, 74, 40, 80)(81, 82, 87, 96, 105, 113, 112, 104, 95, 86, 90, 83, 88, 97, 106, 114, 111, 103, 94, 85)(84, 91, 98, 108, 115, 120, 118, 110, 102, 93, 100, 89, 99, 107, 116, 119, 117, 109, 101, 92)(121, 123, 127, 137, 145, 154, 152, 143, 135, 125, 130, 122, 128, 136, 146, 153, 151, 144, 134, 126)(124, 129, 138, 147, 155, 159, 158, 149, 142, 132, 140, 131, 139, 148, 156, 160, 157, 150, 141, 133)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.496
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.494 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 10, 20, 20})
Quotient :: edge^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1), Y3 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3^3 * Y1^-1 * Y3 * Y1^-1, (Y1^-2 * Y3^-1)^2, Y1^20 ]
Map:: non-degenerate
	R = (1, 41, 4, 44, 15, 55, 28, 68, 9, 49, 27, 67, 19, 59, 36, 76, 22, 62, 7, 47)(2, 42, 10, 50, 29, 69, 39, 79, 24, 64, 21, 61, 6, 46, 16, 56, 32, 72, 12, 52)(3, 43, 13, 53, 33, 73, 38, 78, 23, 63, 20, 60, 5, 45, 17, 57, 34, 74, 14, 54)(8, 48, 25, 65, 18, 58, 35, 75, 37, 77, 31, 71, 11, 51, 30, 70, 40, 80, 26, 66)(81, 82, 88, 103, 102, 112, 120, 113, 99, 86, 91, 83, 89, 104, 117, 114, 95, 109, 98, 85)(84, 93, 105, 101, 87, 94, 106, 119, 116, 97, 110, 90, 107, 100, 111, 92, 108, 118, 115, 96)(121, 123, 128, 144, 142, 154, 160, 149, 139, 125, 131, 122, 129, 143, 157, 152, 135, 153, 138, 126)(124, 130, 145, 140, 127, 132, 146, 158, 156, 136, 150, 133, 147, 141, 151, 134, 148, 159, 155, 137)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.495
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.495 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 10, 20, 20})
Quotient :: loop^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^2, (Y2, Y1), R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3, Y2^-9 * Y1^-1, Y1^20, Y1^-2 * Y2^-2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124)(2, 42, 82, 122, 9, 49, 89, 129)(3, 43, 83, 123, 11, 51, 91, 131)(5, 45, 85, 125, 13, 53, 93, 133)(6, 46, 86, 126, 12, 52, 92, 132)(7, 47, 87, 127, 18, 58, 98, 138)(8, 48, 88, 128, 19, 59, 99, 139)(10, 50, 90, 130, 20, 60, 100, 140)(14, 54, 94, 134, 21, 61, 101, 141)(15, 55, 95, 135, 22, 62, 102, 142)(16, 56, 96, 136, 27, 67, 107, 147)(17, 57, 97, 137, 28, 68, 108, 148)(23, 63, 103, 143, 30, 70, 110, 150)(24, 64, 104, 144, 29, 69, 109, 149)(25, 65, 105, 145, 35, 75, 115, 155)(26, 66, 106, 146, 36, 76, 116, 156)(31, 71, 111, 151, 37, 77, 117, 157)(32, 72, 112, 152, 38, 78, 118, 158)(33, 73, 113, 153, 39, 79, 119, 159)(34, 74, 114, 154, 40, 80, 120, 160)
	L = (1, 42)(2, 47)(3, 48)(4, 51)(5, 41)(6, 50)(7, 56)(8, 57)(9, 59)(10, 43)(11, 58)(12, 44)(13, 60)(14, 45)(15, 46)(16, 65)(17, 66)(18, 68)(19, 67)(20, 49)(21, 52)(22, 53)(23, 54)(24, 55)(25, 73)(26, 74)(27, 76)(28, 75)(29, 61)(30, 62)(31, 63)(32, 64)(33, 72)(34, 71)(35, 80)(36, 79)(37, 69)(38, 70)(39, 77)(40, 78)(81, 123)(82, 128)(83, 127)(84, 129)(85, 130)(86, 121)(87, 137)(88, 136)(89, 138)(90, 122)(91, 139)(92, 140)(93, 124)(94, 126)(95, 125)(96, 146)(97, 145)(98, 147)(99, 148)(100, 131)(101, 133)(102, 132)(103, 135)(104, 134)(105, 154)(106, 153)(107, 155)(108, 156)(109, 142)(110, 141)(111, 144)(112, 143)(113, 151)(114, 152)(115, 159)(116, 160)(117, 150)(118, 149)(119, 158)(120, 157)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.494
Transitivity :: VT+
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.496 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 10, 20, 20})
Quotient :: loop^2
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1), Y3 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3^3 * Y1^-1 * Y3 * Y1^-1, (Y1^-2 * Y3^-1)^2, Y1^20 ]
Map:: non-degenerate
	R = (1, 41, 81, 121, 4, 44, 84, 124, 15, 55, 95, 135, 28, 68, 108, 148, 9, 49, 89, 129, 27, 67, 107, 147, 19, 59, 99, 139, 36, 76, 116, 156, 22, 62, 102, 142, 7, 47, 87, 127)(2, 42, 82, 122, 10, 50, 90, 130, 29, 69, 109, 149, 39, 79, 119, 159, 24, 64, 104, 144, 21, 61, 101, 141, 6, 46, 86, 126, 16, 56, 96, 136, 32, 72, 112, 152, 12, 52, 92, 132)(3, 43, 83, 123, 13, 53, 93, 133, 33, 73, 113, 153, 38, 78, 118, 158, 23, 63, 103, 143, 20, 60, 100, 140, 5, 45, 85, 125, 17, 57, 97, 137, 34, 74, 114, 154, 14, 54, 94, 134)(8, 48, 88, 128, 25, 65, 105, 145, 18, 58, 98, 138, 35, 75, 115, 155, 37, 77, 117, 157, 31, 71, 111, 151, 11, 51, 91, 131, 30, 70, 110, 150, 40, 80, 120, 160, 26, 66, 106, 146)
	L = (1, 42)(2, 48)(3, 49)(4, 53)(5, 41)(6, 51)(7, 54)(8, 63)(9, 64)(10, 67)(11, 43)(12, 68)(13, 65)(14, 66)(15, 69)(16, 44)(17, 70)(18, 45)(19, 46)(20, 71)(21, 47)(22, 72)(23, 62)(24, 77)(25, 61)(26, 79)(27, 60)(28, 78)(29, 58)(30, 50)(31, 52)(32, 80)(33, 59)(34, 55)(35, 56)(36, 57)(37, 74)(38, 75)(39, 76)(40, 73)(81, 123)(82, 129)(83, 128)(84, 130)(85, 131)(86, 121)(87, 132)(88, 144)(89, 143)(90, 145)(91, 122)(92, 146)(93, 147)(94, 148)(95, 153)(96, 150)(97, 124)(98, 126)(99, 125)(100, 127)(101, 151)(102, 154)(103, 157)(104, 142)(105, 140)(106, 158)(107, 141)(108, 159)(109, 139)(110, 133)(111, 134)(112, 135)(113, 138)(114, 160)(115, 137)(116, 136)(117, 152)(118, 156)(119, 155)(120, 149)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.493
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.497 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y3), (R * Y3)^2, Y1^-2 * Y3^-2, (Y2^-1, Y3), (Y1^-1 * Y3^-1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, (R * Y1)^2, Y2^2 * Y3^-1 * Y2^2, Y1 * Y2 * Y3^-1 * Y1 * Y2, Y3^-2 * Y1^2 * Y3^-1, Y2 * Y3^-2 * Y2^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 18, 58, 4, 44, 10, 50, 7, 47, 12, 52, 17, 57, 5, 45)(3, 43, 13, 53, 25, 65, 29, 69, 15, 55, 32, 72, 16, 56, 21, 61, 30, 70, 11, 51)(6, 46, 20, 60, 26, 66, 9, 49, 19, 59, 36, 76, 24, 64, 28, 68, 35, 75, 22, 62)(14, 54, 27, 67, 38, 78, 40, 80, 34, 74, 37, 77, 23, 63, 31, 71, 39, 79, 33, 73)(81, 121, 83, 123, 94, 134, 99, 139, 84, 124, 95, 135, 114, 154, 115, 155, 97, 137, 110, 150, 119, 159, 106, 146, 88, 128, 105, 145, 118, 158, 104, 144, 87, 127, 96, 136, 103, 143, 86, 126)(82, 122, 89, 129, 107, 147, 109, 149, 90, 130, 108, 148, 117, 157, 101, 141, 85, 125, 100, 140, 113, 153, 93, 133, 98, 138, 116, 156, 120, 160, 112, 152, 92, 132, 102, 142, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 108)(10, 85)(11, 109)(12, 82)(13, 112)(14, 114)(15, 110)(16, 83)(17, 88)(18, 92)(19, 115)(20, 116)(21, 93)(22, 89)(23, 94)(24, 86)(25, 96)(26, 104)(27, 117)(28, 100)(29, 101)(30, 105)(31, 107)(32, 91)(33, 120)(34, 119)(35, 106)(36, 102)(37, 113)(38, 103)(39, 118)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.504
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.498 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, (Y3^-1, Y1^-1), (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^5, Y3^-1 * Y1^4, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y1 * Y2^2 * Y1^-1 * Y2^-2, Y2^-4 * Y3^2, (Y2^-1 * Y3^-1 * Y1)^2, Y3^-2 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 4, 44, 10, 50, 7, 47, 12, 52, 18, 58, 5, 45)(3, 43, 13, 53, 27, 67, 32, 72, 15, 55, 22, 62, 17, 57, 11, 51, 30, 70, 16, 56)(6, 46, 23, 63, 28, 68, 21, 61, 20, 60, 9, 49, 26, 66, 39, 79, 34, 74, 24, 64)(14, 54, 29, 69, 25, 65, 31, 71, 35, 75, 38, 78, 37, 77, 33, 73, 40, 80, 36, 76)(81, 121, 83, 123, 94, 134, 114, 154, 98, 138, 110, 150, 120, 160, 106, 146, 87, 127, 97, 137, 117, 157, 100, 140, 84, 124, 95, 135, 115, 155, 108, 148, 88, 128, 107, 147, 105, 145, 86, 126)(82, 122, 89, 129, 109, 149, 102, 142, 85, 125, 101, 141, 116, 156, 112, 152, 92, 132, 103, 143, 113, 153, 93, 133, 90, 130, 104, 144, 118, 158, 96, 136, 99, 139, 119, 159, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 95)(4, 98)(5, 99)(6, 100)(7, 81)(8, 87)(9, 104)(10, 85)(11, 93)(12, 82)(13, 102)(14, 115)(15, 110)(16, 112)(17, 83)(18, 88)(19, 92)(20, 114)(21, 119)(22, 96)(23, 89)(24, 101)(25, 117)(26, 86)(27, 97)(28, 106)(29, 118)(30, 107)(31, 113)(32, 91)(33, 109)(34, 108)(35, 120)(36, 111)(37, 94)(38, 116)(39, 103)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.505
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.499 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y3), (Y3 * Y1)^2, (R * Y1)^2, Y3^-2 * Y1^-2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, Y3^-2 * Y1^2 * Y3^-1, Y2^4 * Y3^2, Y1 * Y2^2 * Y1^-1 * Y2^-2, (Y2^-1 * Y3)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 19, 59, 4, 44, 10, 50, 7, 47, 12, 52, 18, 58, 5, 45)(3, 43, 13, 53, 27, 67, 22, 62, 15, 55, 11, 51, 17, 57, 34, 74, 37, 77, 16, 56)(6, 46, 23, 63, 28, 68, 31, 71, 20, 60, 21, 61, 26, 66, 9, 49, 29, 69, 24, 64)(14, 54, 30, 70, 39, 79, 38, 78, 35, 75, 33, 73, 36, 76, 40, 80, 25, 65, 32, 72)(81, 121, 83, 123, 94, 134, 108, 148, 88, 128, 107, 147, 119, 159, 100, 140, 84, 124, 95, 135, 115, 155, 106, 146, 87, 127, 97, 137, 116, 156, 109, 149, 98, 138, 117, 157, 105, 145, 86, 126)(82, 122, 89, 129, 110, 150, 114, 154, 99, 139, 104, 144, 118, 158, 96, 136, 90, 130, 103, 143, 113, 153, 93, 133, 92, 132, 111, 151, 120, 160, 102, 142, 85, 125, 101, 141, 112, 152, 91, 131)
	L = (1, 84)(2, 90)(3, 95)(4, 98)(5, 99)(6, 100)(7, 81)(8, 87)(9, 103)(10, 85)(11, 96)(12, 82)(13, 91)(14, 115)(15, 117)(16, 102)(17, 83)(18, 88)(19, 92)(20, 109)(21, 104)(22, 114)(23, 101)(24, 111)(25, 119)(26, 86)(27, 97)(28, 106)(29, 108)(30, 113)(31, 89)(32, 118)(33, 112)(34, 93)(35, 105)(36, 94)(37, 107)(38, 120)(39, 116)(40, 110)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.503
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.500 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, (Y3, Y1^-1), (R * Y3)^2, (Y2^-1, Y3^-1), Y2^2 * Y3^-3, Y3^-1 * Y1 * Y2^2 * Y1, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, Y3^-2 * Y1^8, Y2^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 25, 65, 38, 78, 40, 80, 34, 74, 35, 75, 17, 57, 5, 45)(3, 43, 13, 53, 19, 59, 36, 76, 24, 64, 28, 68, 37, 77, 21, 61, 30, 70, 11, 51)(4, 44, 10, 50, 7, 47, 12, 52, 23, 63, 31, 71, 39, 79, 33, 73, 14, 54, 18, 58)(6, 46, 20, 60, 26, 66, 9, 49, 27, 67, 29, 69, 15, 55, 32, 72, 16, 56, 22, 62)(81, 121, 83, 123, 94, 134, 107, 147, 118, 158, 104, 144, 87, 127, 96, 136, 97, 137, 110, 150, 119, 159, 106, 146, 88, 128, 99, 139, 84, 124, 95, 135, 114, 154, 117, 157, 103, 143, 86, 126)(82, 122, 89, 129, 98, 138, 116, 156, 120, 160, 112, 152, 92, 132, 101, 141, 85, 125, 100, 140, 113, 153, 93, 133, 105, 145, 109, 149, 90, 130, 108, 148, 115, 155, 102, 142, 111, 151, 91, 131)
	L = (1, 84)(2, 90)(3, 95)(4, 97)(5, 98)(6, 99)(7, 81)(8, 87)(9, 108)(10, 85)(11, 109)(12, 82)(13, 112)(14, 114)(15, 110)(16, 83)(17, 94)(18, 115)(19, 96)(20, 116)(21, 89)(22, 93)(23, 88)(24, 86)(25, 92)(26, 104)(27, 117)(28, 100)(29, 101)(30, 107)(31, 105)(32, 91)(33, 120)(34, 119)(35, 113)(36, 102)(37, 106)(38, 103)(39, 118)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.507
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.501 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y2, Y3^-1 * Y1^-2 * Y3^-1, (Y3 * Y1)^2, (Y1^-1, Y3^-1), (R * Y2)^2, Y3^-2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y1^-1 * Y3 * Y1^3 * Y3, Y2 * Y1 * Y2 * Y1 * Y3^-2, Y1 * Y2 * Y1 * Y2 * Y1^2, Y3^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^2, (Y1^-2 * Y3)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 38, 78, 34, 74, 39, 79, 31, 71, 16, 56, 5, 45)(3, 43, 13, 53, 24, 64, 20, 60, 30, 70, 11, 51, 29, 69, 28, 68, 18, 58, 14, 54)(4, 44, 10, 50, 7, 47, 12, 52, 25, 65, 35, 75, 40, 80, 32, 72, 36, 76, 17, 57)(6, 46, 21, 61, 15, 55, 33, 73, 37, 77, 19, 59, 27, 67, 9, 49, 26, 66, 22, 62)(81, 121, 83, 123, 87, 127, 95, 135, 88, 128, 104, 144, 105, 145, 117, 157, 118, 158, 110, 150, 120, 160, 107, 147, 119, 159, 109, 149, 116, 156, 106, 146, 96, 136, 98, 138, 84, 124, 86, 126)(82, 122, 89, 129, 92, 132, 108, 148, 103, 143, 102, 142, 115, 155, 94, 134, 114, 154, 101, 141, 112, 152, 93, 133, 111, 151, 113, 153, 97, 137, 100, 140, 85, 125, 99, 139, 90, 130, 91, 131)
	L = (1, 84)(2, 90)(3, 86)(4, 96)(5, 97)(6, 98)(7, 81)(8, 87)(9, 91)(10, 85)(11, 99)(12, 82)(13, 101)(14, 102)(15, 83)(16, 116)(17, 111)(18, 106)(19, 100)(20, 113)(21, 94)(22, 108)(23, 92)(24, 95)(25, 88)(26, 109)(27, 110)(28, 89)(29, 107)(30, 117)(31, 112)(32, 114)(33, 93)(34, 115)(35, 103)(36, 119)(37, 104)(38, 105)(39, 120)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.506
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.502 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^-2 * Y1^-2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y1 * Y2^-1 * Y1 * Y2^-1, (Y1 * Y3^-1 * Y2^-1)^2, (Y2^-1, Y1^-1)^2, Y1^-1 * Y2^-1 * Y1 * Y2 * Y3^5 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 23, 63, 38, 78, 31, 71, 39, 79, 35, 75, 16, 56, 5, 45)(3, 43, 13, 53, 22, 62, 36, 76, 37, 77, 19, 59, 29, 69, 11, 51, 28, 68, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52, 25, 65, 33, 73, 40, 80, 32, 72, 34, 74, 17, 57)(6, 46, 20, 60, 24, 64, 18, 58, 27, 67, 9, 49, 26, 66, 30, 70, 14, 54, 21, 61)(81, 121, 83, 123, 84, 124, 94, 134, 96, 136, 108, 148, 114, 154, 106, 146, 119, 159, 109, 149, 120, 160, 107, 147, 118, 158, 117, 157, 105, 145, 104, 144, 88, 128, 102, 142, 87, 127, 86, 126)(82, 122, 89, 129, 90, 130, 99, 139, 85, 125, 98, 138, 97, 137, 116, 156, 115, 155, 100, 140, 112, 152, 93, 133, 111, 151, 101, 141, 113, 153, 95, 135, 103, 143, 110, 150, 92, 132, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 96)(5, 97)(6, 83)(7, 81)(8, 87)(9, 99)(10, 85)(11, 89)(12, 82)(13, 101)(14, 108)(15, 110)(16, 114)(17, 115)(18, 116)(19, 98)(20, 93)(21, 95)(22, 86)(23, 92)(24, 102)(25, 88)(26, 109)(27, 117)(28, 106)(29, 107)(30, 91)(31, 113)(32, 111)(33, 103)(34, 119)(35, 112)(36, 100)(37, 104)(38, 105)(39, 120)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.508
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 20^4, 40^2 ]

E27.503 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (R * Y2)^2, Y3 * Y1^4, Y3^5, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y2, Y1 * Y3 * Y2 * Y1 * Y3^2 * Y2, Y2 * Y3 * Y1 * Y2 * Y3^2 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 6, 46, 10, 50, 22, 62, 37, 77, 20, 60, 28, 68, 39, 79, 29, 69, 15, 55, 27, 67, 35, 75, 16, 56, 4, 44, 9, 49, 18, 58, 5, 45)(3, 43, 11, 51, 21, 61, 33, 73, 14, 54, 31, 71, 38, 78, 24, 64, 34, 74, 17, 57, 25, 65, 8, 48, 23, 63, 36, 76, 40, 80, 26, 66, 12, 52, 30, 70, 32, 72, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 92, 132)(85, 125, 97, 137)(86, 126, 94, 134)(87, 127, 101, 141)(89, 129, 104, 144)(90, 130, 106, 146)(91, 131, 109, 149)(93, 133, 108, 148)(95, 135, 103, 143)(96, 136, 111, 151)(98, 138, 112, 152)(99, 139, 116, 156)(100, 140, 114, 154)(102, 142, 118, 158)(105, 145, 119, 159)(107, 147, 113, 153)(110, 150, 117, 157)(115, 155, 120, 160)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 98)(8, 104)(9, 107)(10, 82)(11, 110)(12, 103)(13, 106)(14, 83)(15, 100)(16, 109)(17, 111)(18, 115)(19, 85)(20, 86)(21, 112)(22, 87)(23, 114)(24, 113)(25, 118)(26, 88)(27, 108)(28, 90)(29, 117)(30, 116)(31, 91)(32, 120)(33, 93)(34, 94)(35, 119)(36, 97)(37, 99)(38, 101)(39, 102)(40, 105)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.499
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.504 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1, Y3^-1), Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y2, Y3^5, Y3 * Y1^-2 * Y3^-1 * Y1^2, Y1^-4 * Y3^2, Y1^-2 * Y2 * Y1^2 * Y2, Y1 * Y3 * Y1^2 * Y3^2 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 21, 61, 15, 55, 27, 67, 35, 75, 19, 59, 6, 46, 10, 50, 24, 64, 16, 56, 4, 44, 9, 49, 23, 63, 36, 76, 20, 60, 28, 68, 18, 58, 5, 45)(3, 43, 11, 51, 22, 62, 25, 65, 30, 70, 39, 79, 40, 80, 32, 72, 14, 54, 17, 57, 26, 66, 8, 48, 12, 52, 29, 69, 37, 77, 38, 78, 33, 73, 34, 74, 31, 71, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 92, 132)(85, 125, 97, 137)(86, 126, 94, 134)(87, 127, 102, 142)(89, 129, 105, 145)(90, 130, 93, 133)(91, 131, 96, 136)(95, 135, 110, 150)(98, 138, 111, 151)(99, 139, 114, 154)(100, 140, 113, 153)(101, 141, 109, 149)(103, 143, 117, 157)(104, 144, 106, 146)(107, 147, 118, 158)(108, 148, 112, 152)(115, 155, 120, 160)(116, 156, 119, 159)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 103)(8, 105)(9, 107)(10, 82)(11, 109)(12, 110)(13, 88)(14, 83)(15, 100)(16, 101)(17, 91)(18, 104)(19, 85)(20, 86)(21, 116)(22, 117)(23, 115)(24, 87)(25, 118)(26, 102)(27, 108)(28, 90)(29, 119)(30, 113)(31, 106)(32, 93)(33, 94)(34, 97)(35, 98)(36, 99)(37, 120)(38, 112)(39, 114)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.497
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.505 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y3^-5, Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y3^-2 * Y1^-4, Y2 * Y1^2 * Y2 * Y1^-2, Y1^2 * Y3^-1 * Y1^2 * Y3^-2, Y1^-1 * Y3^2 * Y2 * Y3 * Y1^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 21, 61, 20, 60, 28, 68, 36, 76, 16, 56, 4, 44, 9, 49, 23, 63, 19, 59, 6, 46, 10, 50, 24, 64, 34, 74, 15, 55, 27, 67, 18, 58, 5, 45)(3, 43, 11, 51, 22, 62, 26, 66, 33, 73, 39, 79, 40, 80, 31, 71, 12, 52, 17, 57, 25, 65, 8, 48, 14, 54, 29, 69, 37, 77, 38, 78, 30, 70, 35, 75, 32, 72, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 92, 132)(85, 125, 97, 137)(86, 126, 94, 134)(87, 127, 102, 142)(89, 129, 93, 133)(90, 130, 106, 146)(91, 131, 99, 139)(95, 135, 110, 150)(96, 136, 115, 155)(98, 138, 112, 152)(100, 140, 113, 153)(101, 141, 109, 149)(103, 143, 105, 145)(104, 144, 117, 157)(107, 147, 111, 151)(108, 148, 118, 158)(114, 154, 119, 159)(116, 156, 120, 160)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 103)(8, 93)(9, 107)(10, 82)(11, 97)(12, 110)(13, 111)(14, 83)(15, 100)(16, 114)(17, 115)(18, 116)(19, 85)(20, 86)(21, 99)(22, 105)(23, 98)(24, 87)(25, 112)(26, 88)(27, 108)(28, 90)(29, 91)(30, 113)(31, 118)(32, 120)(33, 94)(34, 101)(35, 119)(36, 104)(37, 102)(38, 106)(39, 109)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.498
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.506 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1 * Y3^2 * Y1, Y1 * Y3^-2 * Y2 * Y1 * Y2, (Y1^-1 * Y3 * Y2)^2, Y2 * Y1^2 * Y2 * Y1^-2, Y1^-6 * Y3 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 21, 61, 35, 75, 16, 56, 4, 44, 9, 49, 20, 60, 28, 68, 39, 79, 29, 69, 15, 55, 19, 59, 6, 46, 10, 50, 23, 63, 37, 77, 18, 58, 5, 45)(3, 43, 11, 51, 22, 62, 36, 76, 40, 80, 27, 67, 12, 52, 30, 70, 34, 74, 17, 57, 26, 66, 8, 48, 24, 64, 33, 73, 14, 54, 31, 71, 38, 78, 25, 65, 32, 72, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 92, 132)(85, 125, 97, 137)(86, 126, 94, 134)(87, 127, 102, 142)(89, 129, 105, 145)(90, 130, 107, 147)(91, 131, 109, 149)(93, 133, 108, 148)(95, 135, 104, 144)(96, 136, 111, 151)(98, 138, 112, 152)(99, 139, 116, 156)(100, 140, 114, 154)(101, 141, 113, 153)(103, 143, 118, 158)(106, 146, 119, 159)(110, 150, 117, 157)(115, 155, 120, 160)
	L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 100)(8, 105)(9, 99)(10, 82)(11, 110)(12, 104)(13, 107)(14, 83)(15, 98)(16, 109)(17, 111)(18, 115)(19, 85)(20, 86)(21, 108)(22, 114)(23, 87)(24, 112)(25, 116)(26, 118)(27, 88)(28, 90)(29, 117)(30, 113)(31, 91)(32, 120)(33, 93)(34, 94)(35, 119)(36, 97)(37, 101)(38, 102)(39, 103)(40, 106)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.501
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.507 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^2 * Y3^-1, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3^-4 * Y1^-1 * Y2, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-3 * Y2, Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2 * Y3^5 * Y1, (Y3^-1 * Y1^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 4, 44, 8, 48, 13, 53, 20, 60, 27, 67, 36, 76, 40, 80, 24, 64, 35, 75, 21, 61, 32, 72, 37, 77, 31, 71, 30, 70, 16, 56, 15, 55, 6, 46, 5, 45)(3, 43, 9, 49, 10, 50, 22, 62, 23, 63, 38, 78, 39, 79, 29, 69, 28, 68, 14, 54, 19, 59, 7, 47, 17, 57, 18, 58, 33, 73, 34, 74, 26, 66, 25, 65, 12, 52, 11, 51)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 90, 130)(85, 125, 94, 134)(86, 126, 92, 132)(88, 128, 98, 138)(89, 129, 101, 141)(91, 131, 104, 144)(93, 133, 103, 143)(95, 135, 109, 149)(96, 136, 106, 146)(97, 137, 112, 152)(99, 139, 115, 155)(100, 140, 114, 154)(102, 142, 117, 157)(105, 145, 116, 156)(107, 147, 119, 159)(108, 148, 120, 160)(110, 150, 118, 158)(111, 151, 113, 153)
	L = (1, 84)(2, 88)(3, 90)(4, 93)(5, 82)(6, 81)(7, 98)(8, 100)(9, 102)(10, 103)(11, 89)(12, 83)(13, 107)(14, 87)(15, 85)(16, 86)(17, 113)(18, 114)(19, 97)(20, 116)(21, 117)(22, 118)(23, 119)(24, 101)(25, 91)(26, 92)(27, 120)(28, 99)(29, 94)(30, 95)(31, 96)(32, 111)(33, 106)(34, 105)(35, 112)(36, 104)(37, 110)(38, 109)(39, 108)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.500
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.508 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 20, 20})
Quotient :: dipole
Aut^+ = C5 x D8 (small group id <40, 10>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2 * Y3^2, Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y3^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 6, 46, 8, 48, 16, 56, 20, 60, 31, 71, 36, 76, 39, 79, 25, 65, 34, 74, 21, 61, 32, 72, 37, 77, 27, 67, 28, 68, 13, 53, 14, 54, 4, 44, 5, 45)(3, 43, 9, 49, 12, 52, 22, 62, 26, 66, 38, 78, 40, 80, 29, 69, 30, 70, 15, 55, 18, 58, 7, 47, 17, 57, 19, 59, 33, 73, 35, 75, 23, 63, 24, 64, 10, 50, 11, 51)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 90, 130)(85, 125, 95, 135)(86, 126, 92, 132)(88, 128, 99, 139)(89, 129, 101, 141)(91, 131, 105, 145)(93, 133, 103, 143)(94, 134, 109, 149)(96, 136, 106, 146)(97, 137, 112, 152)(98, 138, 114, 154)(100, 140, 115, 155)(102, 142, 117, 157)(104, 144, 116, 156)(107, 147, 113, 153)(108, 148, 118, 158)(110, 150, 119, 159)(111, 151, 120, 160)
	L = (1, 84)(2, 85)(3, 90)(4, 93)(5, 94)(6, 81)(7, 95)(8, 82)(9, 91)(10, 103)(11, 104)(12, 83)(13, 107)(14, 108)(15, 109)(16, 86)(17, 98)(18, 110)(19, 87)(20, 88)(21, 105)(22, 89)(23, 113)(24, 115)(25, 116)(26, 92)(27, 112)(28, 117)(29, 118)(30, 120)(31, 96)(32, 114)(33, 97)(34, 119)(35, 99)(36, 100)(37, 101)(38, 102)(39, 111)(40, 106)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40, 20, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.502
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.509 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y2^-1, Y2^4 * Y1, Y3^2 * Y1 * Y2 * Y3^3, (Y2 * Y3^-3)^10 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 16, 56)(12, 52, 19, 59)(13, 53, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(17, 57, 23, 63)(18, 58, 24, 64)(25, 65, 31, 71)(26, 66, 32, 72)(27, 67, 34, 74)(28, 68, 35, 75)(29, 69, 33, 73)(30, 70, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123, 91, 131, 89, 129, 82, 122, 87, 127, 96, 136, 85, 125)(84, 124, 92, 132, 105, 145, 102, 142, 88, 128, 99, 139, 111, 151, 95, 135)(86, 126, 93, 133, 106, 146, 103, 143, 90, 130, 100, 140, 112, 152, 97, 137)(94, 134, 107, 147, 117, 157, 116, 156, 101, 141, 114, 154, 119, 159, 110, 150)(98, 138, 108, 148, 118, 158, 109, 149, 104, 144, 115, 155, 120, 160, 113, 153)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 114)(20, 87)(21, 113)(22, 116)(23, 89)(24, 90)(25, 117)(26, 91)(27, 104)(28, 93)(29, 103)(30, 118)(31, 119)(32, 96)(33, 97)(34, 98)(35, 100)(36, 120)(37, 115)(38, 106)(39, 108)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40, 80, 40, 80 ), ( 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.516
Graph:: bipartite
	v = 25 e = 80 f = 3
	degree seq :: [ 4^20, 16^5 ]

E27.510 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y1 * Y2 * Y1, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y1 * Y2^4, Y3^-5 * Y2^-1, (Y2^-1 * Y3)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 16, 56)(12, 52, 19, 59)(13, 53, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(17, 57, 23, 63)(18, 58, 24, 64)(25, 65, 31, 71)(26, 66, 32, 72)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 89, 129, 82, 122, 87, 127, 96, 136, 85, 125)(84, 124, 92, 132, 105, 145, 102, 142, 88, 128, 99, 139, 111, 151, 95, 135)(86, 126, 93, 133, 106, 146, 103, 143, 90, 130, 100, 140, 112, 152, 97, 137)(94, 134, 107, 147, 117, 157, 116, 156, 101, 141, 113, 153, 120, 160, 110, 150)(98, 138, 108, 148, 118, 158, 115, 155, 104, 144, 114, 154, 119, 159, 109, 149)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 113)(20, 87)(21, 115)(22, 116)(23, 89)(24, 90)(25, 117)(26, 91)(27, 98)(28, 93)(29, 97)(30, 119)(31, 120)(32, 96)(33, 104)(34, 100)(35, 103)(36, 118)(37, 108)(38, 106)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40, 80, 40, 80 ), ( 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80, 40, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.515
Graph:: bipartite
	v = 25 e = 80 f = 3
	degree seq :: [ 4^20, 16^5 ]

E27.511 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y1)^2, Y1^-2 * Y3 * Y1^-1, Y1^-1 * Y3^3, (Y2^-1, Y1^-1), Y1^-2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2), Y1^-1 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y2^3 * Y3^-1 * Y2, Y2^-2 * Y1 * Y3^-1 * Y2^-3, Y2 * Y1 * Y2^3 * Y1 * Y2, Y1 * Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 4, 44, 10, 50, 7, 47, 12, 52, 5, 45)(3, 43, 9, 49, 21, 61, 14, 54, 24, 64, 16, 56, 25, 65, 15, 55)(6, 46, 11, 51, 22, 62, 17, 57, 26, 66, 20, 60, 28, 68, 18, 58)(13, 53, 23, 63, 35, 75, 30, 70, 38, 78, 32, 72, 39, 79, 31, 71)(19, 59, 27, 67, 37, 77, 33, 73, 40, 80, 36, 76, 29, 69, 34, 74)(81, 121, 83, 123, 93, 133, 109, 149, 108, 148, 92, 132, 105, 145, 119, 159, 120, 160, 106, 146, 90, 130, 104, 144, 118, 158, 117, 157, 102, 142, 88, 128, 101, 141, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 113, 153, 97, 137, 84, 124, 94, 134, 110, 150, 107, 147, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 92)(5, 88)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 105)(15, 101)(16, 83)(17, 108)(18, 102)(19, 113)(20, 86)(21, 96)(22, 100)(23, 118)(24, 95)(25, 89)(26, 98)(27, 120)(28, 91)(29, 107)(30, 119)(31, 115)(32, 93)(33, 109)(34, 117)(35, 112)(36, 99)(37, 116)(38, 111)(39, 103)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.513
Graph:: bipartite
	v = 7 e = 80 f = 21
	degree seq :: [ 16^5, 40^2 ]

E27.512 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-2, Y3^-3 * Y1, Y3^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (Y2^-1, Y3^-1), (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-2 * Y1 * Y2^-3 * Y1, Y2 * Y3 * Y2 * Y3 * Y2^3, Y2^2 * Y3^-1 * Y2^3 * Y1, (Y2^-1 * Y3)^40 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 4, 44, 10, 50, 7, 47, 12, 52, 5, 45)(3, 43, 9, 49, 21, 61, 14, 54, 24, 64, 16, 56, 25, 65, 15, 55)(6, 46, 11, 51, 22, 62, 17, 57, 26, 66, 20, 60, 28, 68, 18, 58)(13, 53, 23, 63, 37, 77, 30, 70, 38, 78, 32, 72, 35, 75, 31, 71)(19, 59, 27, 67, 29, 69, 33, 73, 39, 79, 36, 76, 40, 80, 34, 74)(81, 121, 83, 123, 93, 133, 109, 149, 102, 142, 88, 128, 101, 141, 117, 157, 119, 159, 106, 146, 90, 130, 104, 144, 118, 158, 120, 160, 108, 148, 92, 132, 105, 145, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 113, 153, 97, 137, 84, 124, 94, 134, 110, 150, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 107, 147, 91, 131)
	L = (1, 84)(2, 90)(3, 94)(4, 92)(5, 88)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 105)(15, 101)(16, 83)(17, 108)(18, 102)(19, 113)(20, 86)(21, 96)(22, 100)(23, 118)(24, 95)(25, 89)(26, 98)(27, 119)(28, 91)(29, 116)(30, 115)(31, 117)(32, 93)(33, 120)(34, 109)(35, 103)(36, 99)(37, 112)(38, 111)(39, 114)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ), ( 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80, 4, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.514
Graph:: bipartite
	v = 7 e = 80 f = 21
	degree seq :: [ 16^5, 40^2 ]

E27.513 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y2 * Y3^4, Y2 * Y1^-2 * Y3 * Y1^-3, (Y1^-1 * Y3^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 27, 67, 11, 51, 23, 63, 36, 76, 40, 80, 30, 70, 14, 54, 25, 65, 37, 77, 33, 73, 17, 57, 6, 46, 10, 50, 22, 62, 28, 68, 12, 52, 3, 43, 8, 48, 20, 60, 31, 71, 15, 55, 4, 44, 9, 49, 21, 61, 35, 75, 34, 74, 18, 58, 26, 66, 38, 78, 39, 79, 29, 69, 13, 53, 24, 64, 32, 72, 16, 56, 5, 45)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 98, 138)(95, 135, 107, 147)(96, 136, 108, 148)(97, 137, 109, 149)(99, 139, 111, 151)(101, 141, 116, 156)(102, 142, 112, 152)(105, 145, 106, 146)(110, 150, 114, 154)(113, 153, 119, 159)(115, 155, 120, 160)(117, 157, 118, 158)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 98)(12, 107)(13, 83)(14, 93)(15, 110)(16, 111)(17, 85)(18, 86)(19, 115)(20, 116)(21, 117)(22, 87)(23, 106)(24, 88)(25, 104)(26, 90)(27, 114)(28, 99)(29, 92)(30, 109)(31, 120)(32, 100)(33, 96)(34, 97)(35, 113)(36, 118)(37, 112)(38, 102)(39, 108)(40, 119)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16, 40, 16, 40 ), ( 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.511
Graph:: bipartite
	v = 21 e = 80 f = 7
	degree seq :: [ 4^20, 80 ]

E27.514 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y3^4, Y1^-1 * Y3 * Y1^-4, (Y1^-1 * Y3^-1)^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 7, 47, 19, 59, 15, 55, 4, 44, 9, 49, 21, 61, 34, 74, 30, 70, 14, 54, 25, 65, 37, 77, 39, 79, 29, 69, 13, 53, 24, 64, 36, 76, 28, 68, 12, 52, 3, 43, 8, 48, 20, 60, 33, 73, 27, 67, 11, 51, 23, 63, 35, 75, 40, 80, 32, 72, 18, 58, 26, 66, 38, 78, 31, 71, 17, 57, 6, 46, 10, 50, 22, 62, 16, 56, 5, 45)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 100, 140)(89, 129, 103, 143)(90, 130, 104, 144)(94, 134, 98, 138)(95, 135, 107, 147)(96, 136, 108, 148)(97, 137, 109, 149)(99, 139, 113, 153)(101, 141, 115, 155)(102, 142, 116, 156)(105, 145, 106, 146)(110, 150, 112, 152)(111, 151, 119, 159)(114, 154, 120, 160)(117, 157, 118, 158)
	L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 101)(8, 103)(9, 105)(10, 82)(11, 98)(12, 107)(13, 83)(14, 93)(15, 110)(16, 99)(17, 85)(18, 86)(19, 114)(20, 115)(21, 117)(22, 87)(23, 106)(24, 88)(25, 104)(26, 90)(27, 112)(28, 113)(29, 92)(30, 109)(31, 96)(32, 97)(33, 120)(34, 119)(35, 118)(36, 100)(37, 116)(38, 102)(39, 108)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16, 40, 16, 40 ), ( 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40, 16, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.512
Graph:: bipartite
	v = 21 e = 80 f = 7
	degree seq :: [ 4^20, 80 ]

E27.515 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^2, (Y1^-1, Y3^-1), (Y2^-1, Y1^-1), (R * Y1)^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y1^3 * Y2^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-3 * Y3^-1, Y1^-1 * Y2^-2 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y2^40 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 14, 54, 26, 66, 40, 80, 35, 75, 21, 61, 28, 68, 32, 72, 16, 56, 27, 67, 31, 71, 13, 53, 25, 65, 39, 79, 36, 76, 22, 62, 18, 58, 5, 45)(3, 43, 9, 49, 23, 63, 30, 70, 38, 78, 33, 73, 19, 59, 6, 46, 11, 51, 17, 57, 4, 44, 10, 50, 24, 64, 29, 69, 37, 77, 34, 74, 20, 60, 7, 47, 12, 52, 15, 55)(81, 121, 83, 123, 93, 133, 109, 149, 115, 155, 99, 139, 85, 125, 95, 135, 111, 151, 104, 144, 120, 160, 113, 153, 98, 138, 92, 132, 107, 147, 90, 130, 106, 146, 118, 158, 102, 142, 87, 127, 96, 136, 84, 124, 94, 134, 110, 150, 116, 156, 100, 140, 112, 152, 97, 137, 88, 128, 103, 143, 119, 159, 114, 154, 108, 148, 91, 131, 82, 122, 89, 129, 105, 145, 117, 157, 101, 141, 86, 126)
	L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 104)(9, 106)(10, 105)(11, 107)(12, 82)(13, 110)(14, 109)(15, 88)(16, 83)(17, 111)(18, 91)(19, 112)(20, 85)(21, 87)(22, 86)(23, 120)(24, 119)(25, 118)(26, 117)(27, 89)(28, 92)(29, 116)(30, 115)(31, 103)(32, 95)(33, 108)(34, 98)(35, 100)(36, 99)(37, 102)(38, 101)(39, 113)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.510
Graph:: bipartite
	v = 3 e = 80 f = 25
	degree seq :: [ 40^2, 80 ]

E27.516 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y1^-1, Y3), (Y1, Y2), (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2^-1 * Y1^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-2 * Y1^-1 * Y3^-3 * Y2^-1, (Y2 * Y3 * Y1^-1)^5, (Y1^-1 * Y3^-1)^8 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 13, 53, 25, 65, 39, 79, 36, 76, 22, 62, 28, 68, 32, 72, 16, 56, 27, 67, 31, 71, 14, 54, 26, 66, 40, 80, 35, 75, 21, 61, 18, 58, 5, 45)(3, 43, 9, 49, 23, 63, 29, 69, 38, 78, 34, 74, 20, 60, 7, 47, 12, 52, 17, 57, 4, 44, 10, 50, 24, 64, 30, 70, 37, 77, 33, 73, 19, 59, 6, 46, 11, 51, 15, 55)(81, 121, 83, 123, 93, 133, 109, 149, 116, 156, 100, 140, 112, 152, 97, 137, 111, 151, 104, 144, 120, 160, 113, 153, 98, 138, 91, 131, 82, 122, 89, 129, 105, 145, 118, 158, 102, 142, 87, 127, 96, 136, 84, 124, 94, 134, 110, 150, 115, 155, 99, 139, 85, 125, 95, 135, 88, 128, 103, 143, 119, 159, 114, 154, 108, 148, 92, 132, 107, 147, 90, 130, 106, 146, 117, 157, 101, 141, 86, 126)
	L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 104)(9, 106)(10, 105)(11, 107)(12, 82)(13, 110)(14, 109)(15, 111)(16, 83)(17, 88)(18, 92)(19, 112)(20, 85)(21, 87)(22, 86)(23, 120)(24, 119)(25, 117)(26, 118)(27, 89)(28, 91)(29, 115)(30, 116)(31, 103)(32, 95)(33, 108)(34, 98)(35, 100)(36, 99)(37, 102)(38, 101)(39, 113)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.509
Graph:: bipartite
	v = 3 e = 80 f = 25
	degree seq :: [ 40^2, 80 ]

E27.517 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (Y3, Y2^-1), (R * Y2)^2, Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y2^-1 * Y3^5 * Y1, (Y2^-1 * Y3)^8 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 98, 138, 108, 148, 119, 159, 116, 156, 102, 142, 104, 144, 89, 129, 82, 122, 87, 127, 99, 139, 106, 146, 114, 154, 120, 160, 110, 150, 94, 134, 96, 136, 85, 125)(84, 124, 92, 132, 97, 137, 86, 126, 93, 133, 107, 147, 112, 152, 115, 155, 117, 157, 103, 143, 88, 128, 100, 140, 105, 145, 90, 130, 101, 141, 113, 153, 118, 158, 109, 149, 111, 151, 95, 135)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 97)(12, 96)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 105)(20, 104)(21, 87)(22, 115)(23, 116)(24, 117)(25, 89)(26, 90)(27, 91)(28, 93)(29, 114)(30, 118)(31, 120)(32, 98)(33, 99)(34, 101)(35, 108)(36, 112)(37, 119)(38, 106)(39, 107)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16, 80, 16, 80 ), ( 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.519
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.518 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, Y2^-1 * Y3^-2 * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y3^2 * Y2, Y3 * Y2^2 * Y3 * Y2 * Y1, Y3^6 * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, Y2^20 ]
Map:: non-degenerate
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 106, 146, 114, 154, 120, 160, 110, 150, 94, 134, 104, 144, 89, 129, 82, 122, 87, 127, 99, 139, 98, 138, 108, 148, 119, 159, 116, 156, 102, 142, 96, 136, 85, 125)(84, 124, 92, 132, 105, 145, 90, 130, 101, 141, 113, 153, 112, 152, 109, 149, 117, 157, 103, 143, 88, 128, 100, 140, 97, 137, 86, 126, 93, 133, 107, 147, 118, 158, 115, 155, 111, 151, 95, 135)
	L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 105)(12, 104)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 97)(20, 96)(21, 87)(22, 115)(23, 116)(24, 117)(25, 89)(26, 90)(27, 91)(28, 93)(29, 108)(30, 112)(31, 120)(32, 98)(33, 99)(34, 101)(35, 114)(36, 118)(37, 119)(38, 106)(39, 107)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16, 80, 16, 80 ), ( 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80, 16, 80 ) }
Outer automorphisms :: reflexible
Dual of E27.520
Graph:: bipartite
	v = 22 e = 80 f = 6
	degree seq :: [ 4^20, 40^2 ]

E27.519 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^-1 * Y1, Y3^3 * Y1^-1, (Y1, Y3^-1), Y3^2 * Y1^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3, Y2), (R * Y1)^2, Y2^-4 * Y1 * Y2^-1, Y3^-1 * Y1 * Y2^-2 * Y3 * Y2^-3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 4, 44, 10, 50, 7, 47, 12, 52, 5, 45)(3, 43, 9, 49, 21, 61, 14, 54, 24, 64, 16, 56, 25, 65, 15, 55)(6, 46, 11, 51, 22, 62, 17, 57, 26, 66, 20, 60, 28, 68, 18, 58)(13, 53, 23, 63, 35, 75, 29, 69, 37, 77, 31, 71, 38, 78, 30, 70)(19, 59, 27, 67, 36, 76, 32, 72, 39, 79, 34, 74, 40, 80, 33, 73)(81, 121, 83, 123, 93, 133, 107, 147, 91, 131, 82, 122, 89, 129, 103, 143, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 112, 152, 97, 137, 84, 124, 94, 134, 109, 149, 119, 159, 106, 146, 90, 130, 104, 144, 117, 157, 114, 154, 100, 140, 87, 127, 96, 136, 111, 151, 120, 160, 108, 148, 92, 132, 105, 145, 118, 158, 113, 153, 98, 138, 85, 125, 95, 135, 110, 150, 99, 139, 86, 126)
	L = (1, 84)(2, 90)(3, 94)(4, 92)(5, 88)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 109)(14, 105)(15, 101)(16, 83)(17, 108)(18, 102)(19, 112)(20, 86)(21, 96)(22, 100)(23, 117)(24, 95)(25, 89)(26, 98)(27, 119)(28, 91)(29, 118)(30, 115)(31, 93)(32, 120)(33, 116)(34, 99)(35, 111)(36, 114)(37, 110)(38, 103)(39, 113)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.517
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 16^5, 80 ]

E27.520 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20, 40})
Quotient :: dipole
Aut^+ = C40 (small group id <40, 2>)
Aut   = D80 (small group id <80, 7>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, Y1^-2 * Y3 * Y1^-1, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^-2 * Y1 * Y3^-1, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y3, Y2), Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2^-2 * Y3^-1 * Y2^-3, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 41, 2, 42, 8, 48, 4, 44, 10, 50, 7, 47, 12, 52, 5, 45)(3, 43, 9, 49, 21, 61, 14, 54, 24, 64, 16, 56, 25, 65, 15, 55)(6, 46, 11, 51, 22, 62, 17, 57, 26, 66, 20, 60, 28, 68, 18, 58)(13, 53, 23, 63, 35, 75, 30, 70, 38, 78, 32, 72, 39, 79, 31, 71)(19, 59, 27, 67, 36, 76, 33, 73, 40, 80, 29, 69, 37, 77, 34, 74)(81, 121, 83, 123, 93, 133, 109, 149, 100, 140, 87, 127, 96, 136, 112, 152, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 120, 160, 106, 146, 90, 130, 104, 144, 118, 158, 107, 147, 91, 131, 82, 122, 89, 129, 103, 143, 117, 157, 108, 148, 92, 132, 105, 145, 119, 159, 113, 153, 97, 137, 84, 124, 94, 134, 110, 150, 99, 139, 86, 126)
	L = (1, 84)(2, 90)(3, 94)(4, 92)(5, 88)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 105)(15, 101)(16, 83)(17, 108)(18, 102)(19, 113)(20, 86)(21, 96)(22, 100)(23, 118)(24, 95)(25, 89)(26, 98)(27, 120)(28, 91)(29, 99)(30, 119)(31, 115)(32, 93)(33, 117)(34, 116)(35, 112)(36, 109)(37, 107)(38, 111)(39, 103)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.518
Graph:: bipartite
	v = 6 e = 80 f = 22
	degree seq :: [ 16^5, 80 ]

E27.521 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, Y2^-2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^-2 * Y1 * Y3^-2 * Y1, Y3^-2 * Y2^5, Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y2, Y3^-2 * Y2 * Y3^-4, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^3 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1, (Y3 * Y2^-1)^14 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 14, 56)(5, 47, 9, 51)(6, 48, 17, 59)(8, 50, 21, 63)(10, 52, 24, 66)(11, 53, 18, 60)(12, 54, 27, 69)(13, 55, 28, 70)(15, 57, 22, 64)(16, 58, 30, 72)(19, 61, 31, 73)(20, 62, 34, 76)(23, 65, 29, 71)(25, 67, 35, 77)(26, 68, 39, 81)(32, 74, 41, 83)(33, 75, 38, 80)(36, 78, 40, 82)(37, 79, 42, 84)(85, 127, 87, 129, 95, 137, 109, 151, 117, 159, 99, 141, 89, 131)(86, 128, 91, 133, 102, 144, 119, 161, 122, 164, 106, 148, 93, 135)(88, 130, 96, 138, 90, 132, 97, 139, 110, 152, 116, 158, 100, 142)(92, 134, 103, 145, 94, 136, 104, 146, 120, 162, 121, 163, 107, 149)(98, 140, 111, 153, 101, 143, 112, 154, 123, 165, 125, 167, 114, 156)(105, 147, 115, 157, 108, 150, 118, 160, 124, 166, 126, 168, 113, 155)
	L = (1, 88)(2, 92)(3, 96)(4, 99)(5, 100)(6, 85)(7, 103)(8, 106)(9, 107)(10, 86)(11, 90)(12, 89)(13, 87)(14, 113)(15, 116)(16, 117)(17, 115)(18, 94)(19, 93)(20, 91)(21, 114)(22, 121)(23, 122)(24, 111)(25, 97)(26, 95)(27, 105)(28, 108)(29, 125)(30, 126)(31, 98)(32, 109)(33, 110)(34, 101)(35, 104)(36, 102)(37, 119)(38, 120)(39, 118)(40, 112)(41, 124)(42, 123)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.539
Graph:: simple bipartite
	v = 27 e = 84 f = 5
	degree seq :: [ 4^21, 14^6 ]

E27.522 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, Y2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^7, Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3 * Y2^-1)^14 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 13, 55)(5, 47, 9, 51)(6, 48, 16, 58)(8, 50, 19, 61)(10, 52, 22, 64)(11, 53, 17, 59)(12, 54, 25, 67)(14, 56, 27, 69)(15, 57, 21, 63)(18, 60, 34, 76)(20, 62, 36, 78)(23, 65, 32, 74)(24, 66, 35, 77)(26, 68, 33, 75)(28, 70, 42, 84)(29, 71, 40, 82)(30, 72, 39, 81)(31, 73, 38, 80)(37, 79, 41, 83)(85, 127, 87, 129, 95, 137, 107, 149, 114, 156, 99, 141, 89, 131)(86, 128, 91, 133, 101, 143, 116, 158, 123, 165, 105, 147, 93, 135)(88, 130, 90, 132, 96, 138, 108, 150, 125, 167, 113, 155, 98, 140)(92, 134, 94, 136, 102, 144, 117, 159, 126, 168, 122, 164, 104, 146)(97, 139, 100, 142, 109, 151, 119, 161, 121, 163, 124, 166, 111, 153)(103, 145, 106, 148, 118, 160, 110, 152, 112, 154, 115, 157, 120, 162)
	L = (1, 88)(2, 92)(3, 90)(4, 89)(5, 98)(6, 85)(7, 94)(8, 93)(9, 104)(10, 86)(11, 96)(12, 87)(13, 110)(14, 99)(15, 113)(16, 112)(17, 102)(18, 91)(19, 119)(20, 105)(21, 122)(22, 121)(23, 108)(24, 95)(25, 115)(26, 111)(27, 118)(28, 97)(29, 114)(30, 125)(31, 100)(32, 117)(33, 101)(34, 124)(35, 120)(36, 109)(37, 103)(38, 123)(39, 126)(40, 106)(41, 107)(42, 116)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.538
Graph:: simple bipartite
	v = 27 e = 84 f = 5
	degree seq :: [ 4^21, 14^6 ]

E27.523 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^7, Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 13, 55)(5, 47, 9, 51)(6, 48, 16, 58)(8, 50, 19, 61)(10, 52, 22, 64)(11, 53, 17, 59)(12, 54, 25, 67)(14, 56, 20, 62)(15, 57, 30, 72)(18, 60, 34, 76)(21, 63, 39, 81)(23, 65, 32, 74)(24, 66, 40, 82)(26, 68, 38, 80)(27, 69, 42, 84)(28, 70, 37, 79)(29, 71, 35, 77)(31, 73, 33, 75)(36, 78, 41, 83)(85, 127, 87, 129, 95, 137, 107, 149, 112, 154, 98, 140, 89, 131)(86, 128, 91, 133, 101, 143, 116, 158, 121, 163, 104, 146, 93, 135)(88, 130, 96, 138, 108, 150, 125, 167, 113, 155, 99, 141, 90, 132)(92, 134, 102, 144, 117, 159, 126, 168, 122, 164, 105, 147, 94, 136)(97, 139, 109, 151, 124, 166, 120, 162, 119, 161, 114, 156, 100, 142)(103, 145, 118, 160, 115, 157, 111, 153, 110, 152, 123, 165, 106, 148)
	L = (1, 88)(2, 92)(3, 96)(4, 87)(5, 90)(6, 85)(7, 102)(8, 91)(9, 94)(10, 86)(11, 108)(12, 95)(13, 110)(14, 99)(15, 89)(16, 111)(17, 117)(18, 101)(19, 119)(20, 105)(21, 93)(22, 120)(23, 125)(24, 107)(25, 123)(26, 109)(27, 97)(28, 113)(29, 98)(30, 115)(31, 100)(32, 126)(33, 116)(34, 114)(35, 118)(36, 103)(37, 122)(38, 104)(39, 124)(40, 106)(41, 112)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.536
Graph:: simple bipartite
	v = 27 e = 84 f = 5
	degree seq :: [ 4^21, 14^6 ]

E27.524 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y1 * Y2 * Y1 * Y2^-1, (Y2, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^4, Y3^-1 * Y2^2 * Y3^-1 * Y2, Y1 * Y3^-2 * Y1 * Y3^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y3, Y2^7 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 14, 56)(5, 47, 9, 51)(6, 48, 19, 61)(8, 50, 24, 66)(10, 52, 29, 71)(11, 53, 21, 63)(12, 54, 32, 74)(13, 55, 33, 75)(15, 57, 25, 67)(16, 58, 35, 77)(17, 59, 27, 69)(18, 60, 37, 79)(20, 62, 30, 72)(22, 64, 40, 82)(23, 65, 34, 76)(26, 68, 38, 80)(28, 70, 42, 84)(31, 73, 41, 83)(36, 78, 39, 81)(85, 127, 87, 129, 95, 137, 99, 141, 104, 146, 101, 143, 89, 131)(86, 128, 91, 133, 105, 147, 109, 151, 114, 156, 111, 153, 93, 135)(88, 130, 96, 138, 115, 157, 102, 144, 90, 132, 97, 139, 100, 142)(92, 134, 106, 148, 123, 165, 112, 154, 94, 136, 107, 149, 110, 152)(98, 140, 116, 158, 125, 167, 121, 163, 103, 145, 117, 159, 119, 161)(108, 150, 124, 166, 120, 162, 126, 168, 113, 155, 118, 160, 122, 164)
	L = (1, 88)(2, 92)(3, 96)(4, 99)(5, 100)(6, 85)(7, 106)(8, 109)(9, 110)(10, 86)(11, 115)(12, 104)(13, 87)(14, 118)(15, 102)(16, 95)(17, 97)(18, 89)(19, 120)(20, 90)(21, 123)(22, 114)(23, 91)(24, 117)(25, 112)(26, 105)(27, 107)(28, 93)(29, 125)(30, 94)(31, 101)(32, 122)(33, 126)(34, 121)(35, 113)(36, 98)(37, 124)(38, 103)(39, 111)(40, 119)(41, 108)(42, 116)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.540
Graph:: simple bipartite
	v = 27 e = 84 f = 5
	degree seq :: [ 4^21, 14^6 ]

E27.525 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y3, Y2^-1), (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y2 * Y3^-3, Y3 * Y2 * Y3 * Y2^2, Y1 * Y3^-2 * Y1 * Y3^2, Y1 * Y3^-2 * Y1 * Y3^2, Y2 * Y1 * Y3 * Y2^2 * Y3 * Y1, Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 14, 56)(5, 47, 9, 51)(6, 48, 19, 61)(8, 50, 24, 66)(10, 52, 29, 71)(11, 53, 21, 63)(12, 54, 32, 74)(13, 55, 33, 75)(15, 57, 25, 67)(16, 58, 35, 77)(17, 59, 27, 69)(18, 60, 37, 79)(20, 62, 30, 72)(22, 64, 38, 80)(23, 65, 40, 82)(26, 68, 41, 83)(28, 70, 34, 76)(31, 73, 42, 84)(36, 78, 39, 81)(85, 127, 87, 129, 95, 137, 104, 146, 99, 141, 101, 143, 89, 131)(86, 128, 91, 133, 105, 147, 114, 156, 109, 151, 111, 153, 93, 135)(88, 130, 96, 138, 102, 144, 90, 132, 97, 139, 115, 157, 100, 142)(92, 134, 106, 148, 112, 154, 94, 136, 107, 149, 123, 165, 110, 152)(98, 140, 116, 158, 121, 163, 103, 145, 117, 159, 126, 168, 119, 161)(108, 150, 122, 164, 118, 160, 113, 155, 124, 166, 120, 162, 125, 167)
	L = (1, 88)(2, 92)(3, 96)(4, 99)(5, 100)(6, 85)(7, 106)(8, 109)(9, 110)(10, 86)(11, 102)(12, 101)(13, 87)(14, 118)(15, 97)(16, 104)(17, 115)(18, 89)(19, 120)(20, 90)(21, 112)(22, 111)(23, 91)(24, 121)(25, 107)(26, 114)(27, 123)(28, 93)(29, 126)(30, 94)(31, 95)(32, 113)(33, 125)(34, 117)(35, 122)(36, 98)(37, 124)(38, 103)(39, 105)(40, 119)(41, 116)(42, 108)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42, 28, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.537
Graph:: simple bipartite
	v = 27 e = 84 f = 5
	degree seq :: [ 4^21, 14^6 ]

E27.526 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y1)^2, Y1^-2 * Y2^2, Y1^-2 * Y3^-2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y3^-1 * Y2^-2 * Y3^-1, (R * Y3)^2, Y2^2 * Y3 * Y2^-2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3, Y2^2 * Y1 * Y2^2 * Y3^-2, Y1 * Y3^-1 * Y2^4 * Y3^-1, Y2^2 * Y1^5, (Y3 * Y2^-1)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 22, 64, 35, 77, 16, 58, 5, 47)(3, 45, 9, 51, 23, 65, 36, 78, 19, 61, 6, 48, 11, 53)(4, 46, 10, 52, 7, 49, 12, 54, 24, 66, 34, 76, 17, 59)(13, 55, 25, 67, 14, 56, 26, 68, 39, 81, 20, 62, 29, 71)(15, 57, 27, 69, 21, 63, 30, 72, 37, 79, 18, 60, 28, 70)(31, 73, 40, 82, 33, 75, 38, 80, 42, 84, 32, 74, 41, 83)(85, 127, 87, 129, 92, 134, 107, 149, 119, 161, 103, 145, 89, 131, 95, 137, 86, 128, 93, 135, 106, 148, 120, 162, 100, 142, 90, 132)(88, 130, 99, 141, 91, 133, 105, 147, 108, 150, 121, 163, 101, 143, 112, 154, 94, 136, 111, 153, 96, 138, 114, 156, 118, 160, 102, 144)(97, 139, 115, 157, 98, 140, 117, 159, 123, 165, 126, 168, 113, 155, 125, 167, 109, 151, 124, 166, 110, 152, 122, 164, 104, 146, 116, 158)
	L = (1, 88)(2, 94)(3, 97)(4, 100)(5, 101)(6, 104)(7, 85)(8, 91)(9, 109)(10, 89)(11, 113)(12, 86)(13, 90)(14, 87)(15, 116)(16, 118)(17, 119)(18, 122)(19, 123)(20, 120)(21, 115)(22, 96)(23, 98)(24, 92)(25, 95)(26, 93)(27, 125)(28, 126)(29, 103)(30, 124)(31, 99)(32, 102)(33, 105)(34, 106)(35, 108)(36, 110)(37, 117)(38, 114)(39, 107)(40, 111)(41, 112)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.533
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 14^6, 28^3 ]

E27.527 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (Y1, Y3), Y1^-2 * Y3^-2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^2 * Y2^-2, Y2^3 * Y1^-1 * Y2, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y3^-2)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 23, 65, 13, 55, 18, 60, 5, 47)(3, 45, 9, 51, 21, 63, 6, 48, 11, 53, 27, 69, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 28, 70, 41, 83, 19, 61)(14, 56, 29, 71, 16, 58, 22, 64, 32, 74, 24, 66, 33, 75)(17, 59, 30, 72, 25, 67, 20, 62, 31, 73, 26, 68, 34, 76)(35, 77, 42, 84, 37, 79, 36, 78, 39, 81, 38, 80, 40, 82)(85, 127, 87, 129, 97, 139, 95, 137, 86, 128, 93, 135, 102, 144, 111, 153, 92, 134, 105, 147, 89, 131, 99, 141, 107, 149, 90, 132)(88, 130, 101, 143, 112, 154, 115, 157, 94, 136, 114, 156, 125, 167, 110, 152, 91, 133, 109, 151, 103, 145, 118, 160, 96, 138, 104, 146)(98, 140, 119, 161, 116, 158, 123, 165, 113, 155, 126, 168, 108, 150, 122, 164, 100, 142, 121, 163, 117, 159, 124, 166, 106, 148, 120, 162)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 106)(7, 85)(8, 91)(9, 113)(10, 89)(11, 116)(12, 86)(13, 112)(14, 111)(15, 117)(16, 87)(17, 123)(18, 125)(19, 97)(20, 119)(21, 100)(22, 93)(23, 96)(24, 90)(25, 124)(26, 121)(27, 108)(28, 92)(29, 99)(30, 122)(31, 126)(32, 105)(33, 95)(34, 120)(35, 114)(36, 115)(37, 104)(38, 118)(39, 110)(40, 101)(41, 107)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.534
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 14^6, 28^3 ]

E27.528 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3 * Y1^2 * Y3, (Y2, Y1^-1), (R * Y3)^2, Y3^-2 * Y2^-2 * Y1, Y2 * Y1^-2 * Y2 * Y1^-1, Y1^-1 * Y2^-4, Y2 * Y1^-1 * Y3^2 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1^2 * Y2 * Y3^-1, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 13, 55, 23, 65, 18, 60, 5, 47)(3, 45, 9, 51, 27, 69, 21, 63, 6, 48, 11, 53, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 28, 70, 35, 77, 19, 61)(14, 56, 29, 71, 16, 58, 30, 72, 22, 64, 33, 75, 24, 66)(17, 59, 31, 73, 25, 67, 34, 76, 20, 62, 32, 74, 26, 68)(36, 78, 40, 82, 38, 80, 41, 83, 37, 79, 42, 84, 39, 81)(85, 127, 87, 129, 97, 139, 105, 147, 89, 131, 99, 141, 92, 134, 111, 153, 102, 144, 95, 137, 86, 128, 93, 135, 107, 149, 90, 132)(88, 130, 101, 143, 96, 138, 118, 160, 103, 145, 110, 152, 91, 133, 109, 151, 119, 161, 116, 158, 94, 136, 115, 157, 112, 154, 104, 146)(98, 140, 120, 162, 114, 156, 125, 167, 108, 150, 123, 165, 100, 142, 122, 164, 117, 159, 126, 168, 113, 155, 124, 166, 106, 148, 121, 163)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 106)(7, 85)(8, 91)(9, 113)(10, 89)(11, 117)(12, 86)(13, 96)(14, 95)(15, 108)(16, 87)(17, 124)(18, 119)(19, 107)(20, 126)(21, 114)(22, 111)(23, 112)(24, 90)(25, 125)(26, 120)(27, 100)(28, 92)(29, 99)(30, 93)(31, 122)(32, 123)(33, 105)(34, 121)(35, 97)(36, 104)(37, 115)(38, 110)(39, 118)(40, 116)(41, 101)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.531
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 14^6, 28^3 ]

E27.529 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1, (Y3 * Y1)^2, (R * Y1^-1)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-6 * Y1, Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3^-3 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 23, 65, 34, 76, 15, 57, 5, 47)(3, 45, 9, 51, 24, 66, 40, 82, 35, 77, 18, 60, 6, 48)(4, 46, 10, 52, 7, 49, 11, 53, 25, 67, 33, 75, 16, 58)(12, 54, 20, 62, 13, 55, 26, 68, 41, 83, 38, 80, 19, 61)(14, 56, 22, 64, 21, 63, 27, 69, 42, 84, 36, 78, 17, 59)(28, 70, 31, 73, 30, 72, 37, 79, 32, 74, 39, 81, 29, 71)(85, 127, 87, 129, 86, 128, 93, 135, 92, 134, 108, 150, 107, 149, 124, 166, 118, 160, 119, 161, 99, 141, 102, 144, 89, 131, 90, 132)(88, 130, 98, 140, 94, 136, 106, 148, 91, 133, 105, 147, 95, 137, 111, 153, 109, 151, 126, 168, 117, 159, 120, 162, 100, 142, 101, 143)(96, 138, 112, 154, 104, 146, 115, 157, 97, 139, 114, 156, 110, 152, 121, 163, 125, 167, 116, 158, 122, 164, 123, 165, 103, 145, 113, 155)
	L = (1, 88)(2, 94)(3, 96)(4, 99)(5, 100)(6, 103)(7, 85)(8, 91)(9, 104)(10, 89)(11, 86)(12, 102)(13, 87)(14, 114)(15, 117)(16, 118)(17, 115)(18, 122)(19, 119)(20, 90)(21, 116)(22, 121)(23, 95)(24, 97)(25, 92)(26, 93)(27, 123)(28, 111)(29, 105)(30, 120)(31, 126)(32, 98)(33, 107)(34, 109)(35, 125)(36, 112)(37, 101)(38, 124)(39, 106)(40, 110)(41, 108)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.532
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 14^6, 28^3 ]

E27.530 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1, Y1^2 * Y3^2, Y1^2 * Y3^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y1 * Y3^-6, Y1^7, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 23, 65, 37, 79, 16, 58, 5, 47)(3, 45, 6, 48, 10, 52, 24, 66, 40, 82, 29, 71, 13, 55)(4, 46, 9, 51, 7, 49, 11, 53, 25, 67, 36, 78, 17, 59)(12, 54, 19, 61, 14, 56, 20, 62, 26, 68, 41, 83, 30, 72)(15, 57, 18, 60, 21, 63, 22, 64, 27, 69, 42, 84, 34, 76)(28, 70, 31, 73, 32, 74, 33, 75, 38, 80, 35, 77, 39, 81)(85, 127, 87, 129, 89, 131, 97, 139, 100, 142, 113, 155, 121, 163, 124, 166, 107, 149, 108, 150, 92, 134, 94, 136, 86, 128, 90, 132)(88, 130, 99, 141, 101, 143, 118, 160, 120, 162, 126, 168, 109, 151, 111, 153, 95, 137, 106, 148, 91, 133, 105, 147, 93, 135, 102, 144)(96, 138, 112, 154, 114, 156, 123, 165, 125, 167, 119, 161, 110, 152, 122, 164, 104, 146, 117, 159, 98, 140, 116, 158, 103, 145, 115, 157)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 101)(6, 103)(7, 85)(8, 91)(9, 89)(10, 98)(11, 86)(12, 113)(13, 114)(14, 87)(15, 117)(16, 120)(17, 121)(18, 122)(19, 97)(20, 90)(21, 119)(22, 123)(23, 95)(24, 104)(25, 92)(26, 94)(27, 112)(28, 105)(29, 125)(30, 124)(31, 106)(32, 111)(33, 126)(34, 116)(35, 99)(36, 107)(37, 109)(38, 118)(39, 102)(40, 110)(41, 108)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.535
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 14^6, 28^3 ]

E27.531 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * R)^2, Y1 * Y3 * Y1^-2 * Y2, Y3 * Y1 * Y2 * Y1^-2, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1 * Y2, Y3^2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3^2 * Y1^3 * Y3^2, Y1 * Y3^2 * Y1 * Y3^2 * Y1, Y1 * Y3 * Y1^4 * Y3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 23, 65, 42, 84, 33, 75, 14, 56, 27, 69, 31, 73, 16, 58, 29, 71, 40, 82, 22, 64, 30, 72, 32, 74, 12, 54, 26, 68, 36, 78, 37, 79, 19, 61, 5, 47)(3, 45, 11, 53, 9, 51, 28, 70, 41, 83, 21, 63, 6, 48, 18, 60, 8, 50, 25, 67, 24, 66, 38, 80, 34, 76, 17, 59, 10, 52, 4, 46, 15, 57, 35, 77, 39, 81, 20, 62, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 101, 143)(90, 132, 98, 140)(91, 133, 99, 141)(93, 135, 110, 152)(94, 136, 111, 153)(95, 137, 115, 157)(97, 139, 114, 156)(100, 142, 109, 151)(102, 144, 116, 158)(103, 145, 105, 147)(104, 146, 117, 159)(106, 148, 118, 160)(107, 149, 112, 154)(108, 150, 120, 162)(113, 155, 119, 161)(121, 163, 123, 165)(122, 164, 126, 168)(124, 166, 125, 167)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 102)(6, 85)(7, 108)(8, 110)(9, 113)(10, 86)(11, 91)(12, 109)(13, 111)(14, 87)(15, 120)(16, 112)(17, 116)(18, 115)(19, 97)(20, 89)(21, 114)(22, 90)(23, 123)(24, 124)(25, 107)(26, 119)(27, 92)(28, 121)(29, 122)(30, 94)(31, 99)(32, 95)(33, 101)(34, 98)(35, 126)(36, 125)(37, 118)(38, 103)(39, 106)(40, 104)(41, 117)(42, 105)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 28, 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.528
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.532 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (Y2 * R)^2, (R * Y3)^2, Y1 * Y2 * Y3 * Y1^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3^3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1 * Y3^-2 * Y1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y3^2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 14, 56, 27, 69, 33, 75, 24, 66, 31, 73, 32, 74, 41, 83, 38, 80, 34, 76, 42, 84, 37, 79, 39, 81, 16, 58, 29, 71, 36, 78, 12, 54, 20, 62, 5, 47)(3, 45, 11, 53, 23, 65, 6, 48, 22, 64, 9, 51, 28, 70, 26, 68, 8, 50, 25, 67, 19, 61, 10, 52, 30, 72, 18, 60, 40, 82, 35, 77, 21, 63, 17, 59, 4, 46, 15, 57, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 102, 144)(90, 132, 98, 140)(91, 133, 105, 147)(93, 135, 104, 146)(94, 136, 111, 153)(95, 137, 116, 158)(97, 139, 121, 163)(99, 141, 117, 159)(100, 142, 119, 161)(101, 143, 122, 164)(103, 145, 120, 162)(106, 148, 118, 160)(107, 149, 113, 155)(108, 150, 112, 154)(109, 151, 125, 167)(110, 152, 123, 165)(114, 156, 126, 168)(115, 157, 124, 166)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 103)(6, 85)(7, 102)(8, 104)(9, 113)(10, 86)(11, 117)(12, 119)(13, 122)(14, 87)(15, 91)(16, 114)(17, 115)(18, 120)(19, 123)(20, 107)(21, 89)(22, 116)(23, 121)(24, 90)(25, 108)(26, 118)(27, 92)(28, 98)(29, 97)(30, 125)(31, 94)(32, 99)(33, 105)(34, 95)(35, 126)(36, 110)(37, 101)(38, 124)(39, 106)(40, 111)(41, 112)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 28, 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.529
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.533 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^3 * Y2, Y1 * Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 12, 54, 26, 68, 34, 76, 16, 58, 29, 71, 32, 74, 41, 83, 36, 78, 33, 75, 42, 84, 35, 77, 39, 81, 24, 66, 31, 73, 37, 79, 14, 56, 20, 62, 5, 47)(3, 45, 11, 53, 17, 59, 4, 46, 15, 57, 10, 52, 30, 72, 27, 69, 8, 50, 25, 67, 21, 63, 9, 51, 28, 70, 18, 60, 40, 82, 38, 80, 19, 61, 23, 65, 6, 48, 22, 64, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 102, 144)(90, 132, 98, 140)(91, 133, 103, 145)(93, 135, 110, 152)(94, 136, 104, 146)(95, 137, 116, 158)(97, 139, 119, 161)(99, 141, 117, 159)(100, 142, 114, 156)(101, 143, 115, 157)(105, 147, 121, 163)(106, 148, 118, 160)(107, 149, 120, 162)(108, 150, 122, 164)(109, 151, 125, 167)(111, 153, 123, 165)(112, 154, 126, 168)(113, 155, 124, 166)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 103)(6, 85)(7, 106)(8, 110)(9, 113)(10, 86)(11, 117)(12, 114)(13, 115)(14, 87)(15, 123)(16, 109)(17, 104)(18, 91)(19, 118)(20, 92)(21, 89)(22, 116)(23, 119)(24, 90)(25, 126)(26, 124)(27, 121)(28, 108)(29, 107)(30, 125)(31, 94)(32, 99)(33, 111)(34, 95)(35, 101)(36, 97)(37, 102)(38, 98)(39, 105)(40, 120)(41, 112)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 28, 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.526
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.534 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^3 * Y3^2, Y2 * Y1 * Y3 * Y1 * Y3^-2, Y3^2 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-21 * Y2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 20, 62, 27, 69, 33, 75, 40, 82, 41, 83, 29, 71, 12, 54, 23, 65, 31, 73, 13, 55, 24, 66, 39, 81, 42, 84, 37, 79, 30, 72, 15, 57, 17, 59, 5, 47)(3, 45, 11, 53, 28, 70, 32, 74, 18, 60, 36, 78, 34, 76, 22, 64, 8, 50, 4, 46, 14, 56, 19, 61, 6, 48, 16, 58, 35, 77, 38, 80, 21, 63, 9, 51, 25, 67, 26, 68, 10, 52)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 100, 142)(90, 132, 97, 139)(91, 133, 105, 147)(93, 135, 107, 149)(94, 136, 108, 150)(95, 137, 113, 155)(98, 140, 114, 156)(99, 141, 109, 151)(101, 143, 120, 162)(102, 144, 115, 157)(103, 145, 111, 153)(104, 146, 116, 158)(106, 148, 123, 165)(110, 152, 117, 159)(112, 154, 121, 163)(118, 160, 124, 166)(119, 161, 125, 167)(122, 164, 126, 168)
	L = (1, 88)(2, 93)(3, 96)(4, 99)(5, 95)(6, 85)(7, 102)(8, 107)(9, 101)(10, 86)(11, 114)(12, 109)(13, 87)(14, 117)(15, 118)(16, 113)(17, 119)(18, 89)(19, 108)(20, 90)(21, 115)(22, 91)(23, 120)(24, 92)(25, 124)(26, 123)(27, 94)(28, 111)(29, 98)(30, 110)(31, 100)(32, 97)(33, 106)(34, 126)(35, 121)(36, 125)(37, 103)(38, 104)(39, 105)(40, 122)(41, 112)(42, 116)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 28, 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.527
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.535 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y1^3 * Y3^-2, Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 15, 57, 25, 67, 37, 79, 40, 82, 41, 83, 29, 71, 13, 55, 24, 66, 32, 74, 12, 54, 23, 65, 39, 81, 42, 84, 35, 77, 30, 72, 20, 62, 18, 60, 5, 47)(3, 45, 11, 53, 28, 70, 31, 73, 17, 59, 36, 78, 38, 80, 22, 64, 8, 50, 6, 48, 19, 61, 16, 58, 4, 46, 14, 56, 33, 75, 34, 76, 21, 63, 10, 52, 27, 69, 26, 68, 9, 51)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 98, 140)(90, 132, 97, 139)(91, 133, 105, 147)(93, 135, 107, 149)(94, 136, 108, 150)(95, 137, 113, 155)(99, 141, 115, 157)(100, 142, 109, 151)(101, 143, 116, 158)(102, 144, 120, 162)(103, 145, 114, 156)(104, 146, 111, 153)(106, 148, 123, 165)(110, 152, 121, 163)(112, 154, 119, 161)(117, 159, 125, 167)(118, 160, 126, 168)(122, 164, 124, 166)
	L = (1, 88)(2, 93)(3, 96)(4, 99)(5, 101)(6, 85)(7, 106)(8, 107)(9, 109)(10, 86)(11, 89)(12, 115)(13, 87)(14, 116)(15, 118)(16, 119)(17, 91)(18, 94)(19, 113)(20, 90)(21, 123)(22, 121)(23, 100)(24, 92)(25, 112)(26, 114)(27, 97)(28, 125)(29, 98)(30, 95)(31, 126)(32, 105)(33, 102)(34, 124)(35, 117)(36, 108)(37, 103)(38, 104)(39, 110)(40, 111)(41, 120)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 28, 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.530
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.536 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2^-1)^2, (Y3 * Y2^-1)^2, Y1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1, Y1 * Y3 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, R * Y2^-1 * R * Y3^-1 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2^3 * Y1 * Y3 * Y1^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^14 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 6, 48, 16, 58, 33, 75, 38, 80, 41, 83, 39, 81, 42, 84, 40, 82, 25, 67, 27, 69, 12, 54, 4, 46)(3, 45, 9, 51, 17, 59, 32, 74, 15, 57, 31, 73, 34, 76, 26, 68, 35, 77, 20, 62, 29, 71, 13, 55, 21, 63, 8, 50)(5, 47, 11, 53, 18, 60, 7, 49, 19, 61, 30, 72, 37, 79, 22, 64, 36, 78, 23, 65, 10, 52, 24, 66, 28, 70, 14, 56)(85, 127, 87, 129, 94, 136, 109, 151, 113, 155, 121, 163, 125, 167, 118, 160, 102, 144, 90, 132, 101, 143, 112, 154, 96, 138, 105, 147, 120, 162, 126, 168, 119, 161, 103, 145, 117, 159, 99, 141, 89, 131)(86, 128, 91, 133, 104, 146, 111, 153, 98, 140, 115, 157, 123, 165, 107, 149, 93, 135, 100, 142, 114, 156, 97, 139, 88, 130, 95, 137, 110, 152, 124, 166, 108, 150, 116, 158, 122, 164, 106, 148, 92, 134)
	L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 95)(6, 100)(7, 103)(8, 87)(9, 101)(10, 108)(11, 102)(12, 88)(13, 105)(14, 89)(15, 115)(16, 117)(17, 116)(18, 91)(19, 114)(20, 113)(21, 92)(22, 120)(23, 94)(24, 112)(25, 111)(26, 119)(27, 96)(28, 98)(29, 97)(30, 121)(31, 118)(32, 99)(33, 122)(34, 110)(35, 104)(36, 107)(37, 106)(38, 125)(39, 126)(40, 109)(41, 123)(42, 124)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.523
Graph:: bipartite
	v = 5 e = 84 f = 27
	degree seq :: [ 28^3, 42^2 ]

E27.537 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^3, Y1^-1 * Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y2^-1 * Y1 * Y2^-1 * Y3^-1, (Y3 * Y2^-1)^2, Y2 * Y1^-1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1 * Y2 * Y1^3 * Y2, Y3^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y3^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, (Y2^-1 * Y1^-1 * R)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 26, 68, 18, 60, 4, 46, 10, 52, 28, 70, 22, 64, 7, 49, 12, 54, 30, 72, 20, 62, 5, 47)(3, 45, 13, 55, 27, 69, 21, 63, 35, 77, 11, 53, 25, 67, 42, 84, 39, 81, 16, 58, 34, 76, 41, 83, 38, 80, 15, 57)(6, 48, 17, 59, 29, 71, 36, 78, 40, 82, 23, 65, 33, 75, 37, 79, 14, 56, 19, 61, 32, 74, 9, 51, 31, 73, 24, 66)(85, 127, 87, 129, 98, 140, 106, 148, 123, 165, 113, 155, 92, 134, 111, 153, 116, 158, 96, 138, 118, 160, 124, 166, 102, 144, 119, 161, 115, 157, 104, 146, 122, 164, 117, 159, 94, 136, 109, 151, 90, 132)(86, 128, 93, 135, 99, 141, 91, 133, 107, 149, 126, 168, 110, 152, 108, 150, 97, 139, 114, 156, 121, 163, 100, 142, 88, 130, 101, 143, 105, 147, 89, 131, 103, 145, 125, 167, 112, 154, 120, 162, 95, 137)
	L = (1, 88)(2, 94)(3, 95)(4, 96)(5, 102)(6, 107)(7, 85)(8, 112)(9, 113)(10, 114)(11, 118)(12, 86)(13, 109)(14, 108)(15, 119)(16, 87)(17, 117)(18, 91)(19, 90)(20, 110)(21, 123)(22, 89)(23, 116)(24, 124)(25, 125)(26, 106)(27, 126)(28, 104)(29, 121)(30, 92)(31, 120)(32, 101)(33, 93)(34, 97)(35, 100)(36, 98)(37, 115)(38, 105)(39, 99)(40, 103)(41, 111)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.525
Graph:: bipartite
	v = 5 e = 84 f = 27
	degree seq :: [ 28^3, 42^2 ]

E27.538 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^3, (Y3^-1, Y1^-1), (Y3 * Y2^-1)^2, Y2 * Y1 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2, (Y1^-1 * Y3 * Y1^-1)^2, Y1^-5 * Y3^-1, Y2 * Y3 * Y1^2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 26, 68, 19, 61, 7, 49, 12, 54, 30, 72, 20, 62, 4, 46, 10, 52, 28, 70, 22, 64, 5, 47)(3, 45, 13, 55, 27, 69, 31, 73, 39, 81, 17, 59, 36, 78, 42, 84, 25, 67, 15, 57, 34, 76, 11, 53, 35, 77, 16, 58)(6, 48, 23, 65, 29, 71, 21, 63, 32, 74, 9, 51, 14, 56, 37, 79, 40, 82, 24, 66, 33, 75, 38, 80, 41, 83, 18, 60)(85, 127, 87, 129, 98, 140, 96, 138, 120, 162, 125, 167, 106, 148, 119, 161, 116, 158, 103, 145, 123, 165, 117, 159, 94, 136, 118, 160, 113, 155, 92, 134, 111, 153, 124, 166, 104, 146, 109, 151, 90, 132)(86, 128, 93, 135, 115, 157, 114, 156, 122, 164, 99, 141, 89, 131, 105, 147, 97, 139, 91, 133, 108, 150, 126, 168, 112, 154, 107, 149, 100, 142, 110, 152, 121, 163, 101, 143, 88, 130, 102, 144, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 103)(5, 104)(6, 108)(7, 85)(8, 112)(9, 90)(10, 91)(11, 120)(12, 86)(13, 118)(14, 107)(15, 123)(16, 109)(17, 87)(18, 124)(19, 89)(20, 110)(21, 125)(22, 114)(23, 117)(24, 116)(25, 115)(26, 106)(27, 95)(28, 96)(29, 122)(30, 92)(31, 119)(32, 102)(33, 93)(34, 101)(35, 126)(36, 97)(37, 113)(38, 98)(39, 100)(40, 105)(41, 121)(42, 111)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.522
Graph:: bipartite
	v = 5 e = 84 f = 27
	degree seq :: [ 28^3, 42^2 ]

E27.539 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y3^-1), Y1^3 * Y3^-1, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y2^-3, Y3 * Y1^-1 * Y3^4, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 4, 46, 10, 52, 31, 73, 19, 61, 37, 79, 29, 71, 42, 84, 22, 64, 7, 49, 12, 54, 5, 47)(3, 45, 13, 55, 30, 72, 15, 57, 36, 78, 28, 70, 40, 82, 21, 63, 39, 81, 11, 53, 38, 80, 17, 59, 26, 68, 16, 58)(6, 48, 23, 65, 14, 56, 24, 66, 35, 77, 20, 62, 34, 76, 9, 51, 32, 74, 18, 60, 33, 75, 27, 69, 41, 83, 25, 67)(85, 127, 87, 129, 98, 140, 92, 134, 114, 156, 119, 161, 94, 136, 120, 162, 118, 160, 103, 145, 124, 166, 116, 158, 113, 155, 123, 165, 117, 159, 106, 148, 122, 164, 125, 167, 96, 138, 110, 152, 90, 132)(86, 128, 93, 135, 101, 143, 88, 130, 102, 144, 100, 142, 115, 157, 111, 153, 97, 139, 121, 163, 109, 151, 99, 141, 126, 168, 107, 149, 112, 154, 91, 133, 108, 150, 105, 147, 89, 131, 104, 146, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 103)(5, 92)(6, 108)(7, 85)(8, 115)(9, 117)(10, 121)(11, 110)(12, 86)(13, 120)(14, 104)(15, 124)(16, 114)(17, 87)(18, 125)(19, 126)(20, 116)(21, 122)(22, 89)(23, 119)(24, 118)(25, 98)(26, 97)(27, 90)(28, 123)(29, 91)(30, 112)(31, 113)(32, 111)(33, 109)(34, 102)(35, 93)(36, 105)(37, 106)(38, 100)(39, 101)(40, 95)(41, 107)(42, 96)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.521
Graph:: bipartite
	v = 5 e = 84 f = 27
	degree seq :: [ 28^3, 42^2 ]

E27.540 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y1), (Y3 * Y2^-1)^2, Y3^-1 * Y1^-3, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-3 * Y3, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^4, (Y2^-1 * Y1^-1 * R)^2, Y2 * Y1^-2 * Y2^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2 * Y3^-2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 7, 49, 12, 54, 31, 73, 29, 71, 42, 84, 19, 61, 36, 78, 20, 62, 4, 46, 10, 52, 5, 47)(3, 45, 13, 55, 26, 68, 17, 59, 38, 80, 22, 64, 39, 81, 11, 53, 37, 79, 28, 70, 40, 82, 15, 57, 35, 77, 16, 58)(6, 48, 23, 65, 30, 72, 27, 69, 41, 83, 18, 60, 33, 75, 21, 63, 34, 76, 9, 51, 32, 74, 24, 66, 14, 56, 25, 67)(85, 127, 87, 129, 98, 140, 94, 136, 119, 161, 116, 158, 104, 146, 124, 166, 118, 160, 103, 145, 121, 163, 117, 159, 113, 155, 123, 165, 125, 167, 96, 138, 122, 164, 114, 156, 92, 134, 110, 152, 90, 132)(86, 128, 93, 135, 106, 148, 89, 131, 105, 147, 101, 143, 88, 130, 102, 144, 97, 139, 120, 162, 111, 153, 100, 142, 126, 168, 107, 149, 99, 141, 115, 157, 109, 151, 112, 154, 91, 133, 108, 150, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 103)(5, 104)(6, 108)(7, 85)(8, 89)(9, 117)(10, 120)(11, 122)(12, 86)(13, 119)(14, 93)(15, 121)(16, 124)(17, 87)(18, 114)(19, 115)(20, 126)(21, 125)(22, 110)(23, 98)(24, 118)(25, 116)(26, 100)(27, 90)(28, 123)(29, 91)(30, 109)(31, 92)(32, 105)(33, 111)(34, 102)(35, 112)(36, 113)(37, 106)(38, 97)(39, 101)(40, 95)(41, 107)(42, 96)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.524
Graph:: bipartite
	v = 5 e = 84 f = 27
	degree seq :: [ 28^3, 42^2 ]

E27.541 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1, Y3^2 * Y1 * Y3^-2 * Y1, Y2^2 * Y1 * Y2^-2 * Y1, Y3^3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^3 * Y1 * Y2 * Y3^-2 * Y1 * Y3^-1 * Y1, Y2^3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^14, (Y3 * Y2^-1)^7 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 9, 51)(5, 47, 11, 53)(6, 48, 13, 55)(8, 50, 12, 54)(10, 52, 14, 56)(15, 57, 25, 67)(16, 58, 27, 69)(17, 59, 26, 68)(18, 60, 29, 71)(19, 61, 30, 72)(20, 62, 32, 74)(21, 63, 34, 76)(22, 64, 33, 75)(23, 65, 36, 78)(24, 66, 37, 79)(28, 70, 35, 77)(31, 73, 38, 80)(39, 81, 41, 83)(40, 82, 42, 84)(85, 127, 87, 129, 92, 134, 101, 143, 112, 154, 120, 162, 126, 168, 118, 160, 125, 167, 116, 158, 115, 157, 103, 145, 94, 136, 88, 130)(86, 128, 89, 131, 96, 138, 106, 148, 119, 161, 113, 155, 124, 166, 111, 153, 123, 165, 109, 151, 122, 164, 108, 150, 98, 140, 90, 132)(91, 133, 99, 141, 110, 152, 121, 163, 107, 149, 97, 139, 105, 147, 95, 137, 104, 146, 117, 159, 114, 156, 102, 144, 93, 135, 100, 142)
	L = (1, 88)(2, 90)(3, 85)(4, 94)(5, 86)(6, 98)(7, 100)(8, 87)(9, 102)(10, 103)(11, 105)(12, 89)(13, 107)(14, 108)(15, 91)(16, 93)(17, 92)(18, 114)(19, 115)(20, 95)(21, 97)(22, 96)(23, 121)(24, 122)(25, 123)(26, 99)(27, 124)(28, 101)(29, 119)(30, 117)(31, 116)(32, 125)(33, 104)(34, 126)(35, 106)(36, 112)(37, 110)(38, 109)(39, 111)(40, 113)(41, 118)(42, 120)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.550
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.542 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2^-1, Y2^-2 * Y1 * Y3 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2^-1, Y3^4 * Y2^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 15, 57)(5, 47, 17, 59)(6, 48, 19, 61)(7, 49, 21, 63)(8, 50, 25, 67)(9, 51, 27, 69)(10, 52, 29, 71)(12, 54, 22, 64)(13, 55, 23, 65)(14, 56, 24, 66)(16, 58, 26, 68)(18, 60, 28, 70)(20, 62, 30, 72)(31, 73, 42, 84)(32, 74, 41, 83)(33, 75, 40, 82)(34, 76, 39, 81)(35, 77, 38, 80)(36, 78, 37, 79)(85, 127, 87, 129, 96, 138, 88, 130, 97, 139, 118, 160, 100, 142, 119, 161, 104, 146, 120, 162, 102, 144, 90, 132, 98, 140, 89, 131)(86, 128, 91, 133, 106, 148, 92, 134, 107, 149, 124, 166, 110, 152, 125, 167, 114, 156, 126, 168, 112, 154, 94, 136, 108, 150, 93, 135)(95, 137, 115, 157, 99, 141, 113, 155, 123, 165, 111, 153, 122, 164, 105, 147, 121, 163, 109, 151, 103, 145, 117, 159, 101, 143, 116, 158)
	L = (1, 88)(2, 92)(3, 97)(4, 100)(5, 96)(6, 85)(7, 107)(8, 110)(9, 106)(10, 86)(11, 113)(12, 118)(13, 119)(14, 87)(15, 111)(16, 120)(17, 115)(18, 89)(19, 116)(20, 90)(21, 103)(22, 124)(23, 125)(24, 91)(25, 101)(26, 126)(27, 121)(28, 93)(29, 122)(30, 94)(31, 123)(32, 99)(33, 95)(34, 104)(35, 102)(36, 98)(37, 117)(38, 109)(39, 105)(40, 114)(41, 112)(42, 108)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.547
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.543 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, Y3 * Y2^3, (R * Y2)^2, Y3^-5 * Y2^-1, Y3^-1 * Y1 * Y2^-2 * Y1 * Y2^-1, (Y3^2 * Y2^-1)^2, Y3 * Y1 * Y2^-1 * Y1 * Y3 * Y1, Y3^2 * Y1 * Y3^-2 * Y1, Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1, Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 15, 57)(5, 47, 18, 60)(6, 48, 19, 61)(7, 49, 21, 63)(8, 50, 25, 67)(9, 51, 28, 70)(10, 52, 29, 71)(12, 54, 22, 64)(13, 55, 23, 65)(14, 56, 24, 66)(16, 58, 26, 68)(17, 59, 27, 69)(20, 62, 30, 72)(31, 73, 41, 83)(32, 74, 40, 82)(33, 75, 42, 84)(34, 76, 38, 80)(35, 77, 37, 79)(36, 78, 39, 81)(85, 127, 87, 129, 96, 138, 90, 132, 98, 140, 118, 160, 104, 146, 120, 162, 100, 142, 119, 161, 101, 143, 88, 130, 97, 139, 89, 131)(86, 128, 91, 133, 106, 148, 94, 136, 108, 150, 124, 166, 114, 156, 126, 168, 110, 152, 125, 167, 111, 153, 92, 134, 107, 149, 93, 135)(95, 137, 115, 157, 103, 145, 109, 151, 122, 164, 112, 154, 123, 165, 105, 147, 121, 163, 113, 155, 99, 141, 116, 158, 102, 144, 117, 159)
	L = (1, 88)(2, 92)(3, 97)(4, 100)(5, 101)(6, 85)(7, 107)(8, 110)(9, 111)(10, 86)(11, 116)(12, 89)(13, 119)(14, 87)(15, 105)(16, 118)(17, 120)(18, 113)(19, 117)(20, 90)(21, 122)(22, 93)(23, 125)(24, 91)(25, 95)(26, 124)(27, 126)(28, 103)(29, 123)(30, 94)(31, 102)(32, 121)(33, 99)(34, 96)(35, 104)(36, 98)(37, 112)(38, 115)(39, 109)(40, 106)(41, 114)(42, 108)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.546
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.544 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), Y3^3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3^2 * Y1, Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y3^-2 * Y2^-4, Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 15, 57)(5, 47, 17, 59)(6, 48, 20, 62)(7, 49, 21, 63)(8, 50, 25, 67)(9, 51, 27, 69)(10, 52, 30, 72)(12, 54, 22, 64)(13, 55, 23, 65)(14, 56, 24, 66)(16, 58, 26, 68)(18, 60, 28, 70)(19, 61, 29, 71)(31, 73, 40, 82)(32, 74, 39, 81)(33, 75, 38, 80)(34, 76, 37, 79)(35, 77, 42, 84)(36, 78, 41, 83)(85, 127, 87, 129, 96, 138, 117, 159, 100, 142, 88, 130, 97, 139, 118, 160, 103, 145, 90, 132, 98, 140, 119, 161, 102, 144, 89, 131)(86, 128, 91, 133, 106, 148, 123, 165, 110, 152, 92, 134, 107, 149, 124, 166, 113, 155, 94, 136, 108, 150, 125, 167, 112, 154, 93, 135)(95, 137, 114, 156, 122, 164, 120, 162, 99, 141, 111, 153, 121, 163, 105, 147, 104, 146, 116, 158, 126, 168, 109, 151, 101, 143, 115, 157)
	L = (1, 88)(2, 92)(3, 97)(4, 98)(5, 100)(6, 85)(7, 107)(8, 108)(9, 110)(10, 86)(11, 111)(12, 118)(13, 119)(14, 87)(15, 116)(16, 90)(17, 120)(18, 117)(19, 89)(20, 115)(21, 101)(22, 124)(23, 125)(24, 91)(25, 122)(26, 94)(27, 126)(28, 123)(29, 93)(30, 121)(31, 99)(32, 95)(33, 103)(34, 102)(35, 96)(36, 104)(37, 109)(38, 105)(39, 113)(40, 112)(41, 106)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.549
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.545 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2^-1, Y3), Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^5 * Y3, Y2 * Y1 * Y2^-1 * Y3 * Y1 * Y3^-1, (Y2^-2 * Y3)^2, Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 11, 53)(4, 46, 15, 57)(5, 47, 18, 60)(6, 48, 20, 62)(7, 49, 21, 63)(8, 50, 25, 67)(9, 51, 28, 70)(10, 52, 30, 72)(12, 54, 22, 64)(13, 55, 23, 65)(14, 56, 24, 66)(16, 58, 26, 68)(17, 59, 27, 69)(19, 61, 29, 71)(31, 73, 39, 81)(32, 74, 41, 83)(33, 75, 37, 79)(34, 76, 42, 84)(35, 77, 38, 80)(36, 78, 40, 82)(85, 127, 87, 129, 96, 138, 117, 159, 100, 142, 90, 132, 98, 140, 119, 161, 101, 143, 88, 130, 97, 139, 118, 160, 103, 145, 89, 131)(86, 128, 91, 133, 106, 148, 123, 165, 110, 152, 94, 136, 108, 150, 125, 167, 111, 153, 92, 134, 107, 149, 124, 166, 113, 155, 93, 135)(95, 137, 109, 151, 121, 163, 120, 162, 104, 146, 112, 154, 122, 164, 105, 147, 99, 141, 115, 157, 126, 168, 114, 156, 102, 144, 116, 158)
	L = (1, 88)(2, 92)(3, 97)(4, 100)(5, 101)(6, 85)(7, 107)(8, 110)(9, 111)(10, 86)(11, 115)(12, 118)(13, 90)(14, 87)(15, 120)(16, 89)(17, 117)(18, 105)(19, 119)(20, 116)(21, 121)(22, 124)(23, 94)(24, 91)(25, 126)(26, 93)(27, 123)(28, 95)(29, 125)(30, 122)(31, 104)(32, 99)(33, 103)(34, 98)(35, 96)(36, 102)(37, 114)(38, 109)(39, 113)(40, 108)(41, 106)(42, 112)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 14, 42, 14, 42 ), ( 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.548
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.546 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, (Y2^-1 * Y3^-1)^2, (Y3, Y1), (R * Y3)^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (Y2^-1, Y1), Y2^-1 * Y1^-1 * Y3 * Y2^2 * Y3^-1, Y2^3 * Y3^2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y3^2 * R * Y2^-1 * R * Y2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^6, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y1^7, Y2 * Y1 * Y2^5, Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 25, 67, 38, 80, 18, 60, 5, 47)(3, 45, 9, 51, 26, 68, 41, 83, 23, 65, 35, 77, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 28, 70, 37, 79, 19, 61)(6, 48, 11, 53, 27, 69, 13, 55, 29, 71, 39, 81, 21, 63)(14, 56, 30, 72, 16, 58, 31, 73, 40, 82, 20, 62, 33, 75)(17, 59, 32, 74, 24, 66, 36, 78, 42, 84, 22, 64, 34, 76)(85, 127, 87, 129, 97, 139, 109, 151, 125, 167, 105, 147, 89, 131, 99, 141, 111, 153, 92, 134, 110, 152, 123, 165, 102, 144, 119, 161, 95, 137, 86, 128, 93, 135, 113, 155, 122, 164, 107, 149, 90, 132)(88, 130, 101, 143, 114, 156, 96, 138, 120, 162, 124, 166, 103, 145, 118, 160, 98, 140, 91, 133, 108, 150, 115, 157, 121, 163, 106, 148, 117, 159, 94, 136, 116, 158, 100, 142, 112, 154, 126, 168, 104, 146)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 106)(7, 85)(8, 91)(9, 114)(10, 89)(11, 118)(12, 86)(13, 116)(14, 119)(15, 117)(16, 87)(17, 90)(18, 121)(19, 122)(20, 125)(21, 126)(22, 123)(23, 124)(24, 111)(25, 96)(26, 100)(27, 101)(28, 92)(29, 108)(30, 99)(31, 93)(32, 95)(33, 107)(34, 105)(35, 104)(36, 97)(37, 109)(38, 112)(39, 120)(40, 110)(41, 115)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.543
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 14^6, 42^2 ]

E27.547 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2^3, (Y2, Y1), Y3^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y3^-2, (Y2 * Y3 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^2, (Y3 * Y2 * Y1^-1)^2, Y3^-2 * Y1 * Y3^-1 * Y1^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 25, 67, 39, 81, 18, 60, 5, 47)(3, 45, 9, 51, 26, 68, 40, 82, 42, 84, 36, 78, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 28, 70, 38, 80, 19, 61)(6, 48, 11, 53, 27, 69, 41, 83, 37, 79, 35, 77, 13, 55)(14, 56, 29, 71, 16, 58, 20, 62, 31, 73, 24, 66, 34, 76)(17, 59, 30, 72, 23, 65, 21, 63, 32, 74, 22, 64, 33, 75)(85, 127, 87, 129, 97, 139, 89, 131, 99, 141, 119, 161, 102, 144, 120, 162, 121, 163, 123, 165, 126, 168, 125, 167, 109, 151, 124, 166, 111, 153, 92, 134, 110, 152, 95, 137, 86, 128, 93, 135, 90, 132)(88, 130, 101, 143, 100, 142, 103, 145, 117, 159, 113, 155, 122, 164, 106, 148, 98, 140, 112, 154, 116, 158, 118, 160, 96, 138, 105, 147, 108, 150, 91, 133, 107, 149, 115, 157, 94, 136, 114, 156, 104, 146)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 105)(7, 85)(8, 91)(9, 113)(10, 89)(11, 116)(12, 86)(13, 107)(14, 120)(15, 118)(16, 87)(17, 111)(18, 122)(19, 123)(20, 93)(21, 119)(22, 90)(23, 121)(24, 124)(25, 96)(26, 100)(27, 106)(28, 92)(29, 99)(30, 125)(31, 110)(32, 97)(33, 95)(34, 126)(35, 114)(36, 108)(37, 101)(38, 109)(39, 112)(40, 104)(41, 117)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.542
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 14^6, 42^2 ]

E27.548 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^-2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1), Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y1^2 * Y2 * Y3, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y2^-1, Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-1, (Y3 * Y1^-1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-4 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 25, 67, 38, 80, 17, 59, 5, 47)(3, 45, 9, 51, 26, 68, 41, 83, 40, 82, 35, 77, 14, 56)(4, 46, 10, 52, 7, 49, 12, 54, 28, 70, 36, 78, 18, 60)(6, 48, 11, 53, 27, 69, 37, 79, 42, 84, 39, 81, 20, 62)(13, 55, 29, 71, 15, 57, 30, 72, 19, 61, 32, 74, 24, 66)(16, 58, 31, 73, 23, 65, 34, 76, 21, 63, 33, 75, 22, 64)(85, 127, 87, 129, 95, 137, 86, 128, 93, 135, 111, 153, 92, 134, 110, 152, 121, 163, 109, 151, 125, 167, 126, 168, 122, 164, 124, 166, 123, 165, 101, 143, 119, 161, 104, 146, 89, 131, 98, 140, 90, 132)(88, 130, 100, 142, 116, 158, 94, 136, 115, 157, 108, 150, 91, 133, 107, 149, 97, 139, 96, 138, 118, 160, 113, 155, 112, 154, 105, 147, 99, 141, 120, 162, 117, 159, 114, 156, 102, 144, 106, 148, 103, 145)
	L = (1, 88)(2, 94)(3, 97)(4, 101)(5, 102)(6, 105)(7, 85)(8, 91)(9, 113)(10, 89)(11, 117)(12, 86)(13, 119)(14, 108)(15, 87)(16, 95)(17, 120)(18, 122)(19, 110)(20, 118)(21, 123)(22, 90)(23, 121)(24, 124)(25, 96)(26, 99)(27, 106)(28, 92)(29, 98)(30, 93)(31, 111)(32, 125)(33, 104)(34, 126)(35, 116)(36, 109)(37, 100)(38, 112)(39, 107)(40, 103)(41, 114)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.545
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 14^6, 42^2 ]

E27.549 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), (Y3 * Y1)^2, Y3 * Y1^2 * Y3, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1^2 * Y2, Y2 * Y1^-1 * R * Y2^-1 * R, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2^-2 * Y3 * Y2, Y3^-2 * Y1 * Y3^-4, Y3^-2 * Y2^-2 * Y3^-1 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 27, 69, 39, 81, 18, 60, 5, 47)(3, 45, 9, 51, 23, 65, 31, 73, 41, 83, 35, 77, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 29, 71, 38, 80, 19, 61)(6, 48, 11, 53, 28, 70, 42, 84, 34, 76, 13, 55, 21, 63)(14, 56, 26, 68, 16, 58, 30, 72, 37, 79, 40, 82, 20, 62)(17, 59, 24, 66, 25, 67, 32, 74, 33, 75, 36, 78, 22, 64)(85, 127, 87, 129, 97, 139, 102, 144, 119, 161, 126, 168, 111, 153, 115, 157, 95, 137, 86, 128, 93, 135, 105, 147, 89, 131, 99, 141, 118, 160, 123, 165, 125, 167, 112, 154, 92, 134, 107, 149, 90, 132)(88, 130, 101, 143, 121, 163, 122, 164, 120, 162, 100, 142, 96, 138, 116, 158, 98, 140, 94, 136, 108, 150, 124, 166, 103, 145, 106, 148, 114, 156, 113, 155, 117, 159, 110, 152, 91, 133, 109, 151, 104, 146)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 106)(7, 85)(8, 91)(9, 110)(10, 89)(11, 101)(12, 86)(13, 117)(14, 119)(15, 104)(16, 87)(17, 105)(18, 122)(19, 123)(20, 125)(21, 120)(22, 97)(23, 100)(24, 90)(25, 95)(26, 99)(27, 96)(28, 108)(29, 92)(30, 93)(31, 114)(32, 112)(33, 126)(34, 116)(35, 124)(36, 118)(37, 107)(38, 111)(39, 113)(40, 115)(41, 121)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.544
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 14^6, 42^2 ]

E27.550 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 7, 14, 21})
Quotient :: dipole
Aut^+ = C7 x S3 (small group id <42, 3>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, (R * Y3)^2, (Y2, Y1^-1), (R * Y1)^2, (Y3^-1, Y1^-1), Y2 * Y1 * Y3 * Y2 * Y3^-1, Y3^-2 * Y2^-3, Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, R * Y2 * R * Y1^-1 * Y2^-1, Y1^-1 * Y3^6, Y1^7 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 27, 69, 38, 80, 18, 60, 5, 47)(3, 45, 9, 51, 28, 70, 42, 84, 40, 82, 23, 65, 15, 57)(4, 46, 10, 52, 7, 49, 12, 54, 29, 71, 37, 79, 19, 61)(6, 48, 11, 53, 13, 55, 30, 72, 36, 78, 39, 81, 21, 63)(14, 56, 20, 62, 16, 58, 26, 68, 32, 74, 41, 83, 34, 76)(17, 59, 22, 64, 25, 67, 24, 66, 31, 73, 33, 75, 35, 77)(85, 127, 87, 129, 97, 139, 92, 134, 112, 154, 120, 162, 122, 164, 124, 166, 105, 147, 89, 131, 99, 141, 95, 137, 86, 128, 93, 135, 114, 156, 111, 153, 126, 168, 123, 165, 102, 144, 107, 149, 90, 132)(88, 130, 101, 143, 110, 152, 91, 133, 109, 151, 125, 167, 113, 155, 115, 157, 98, 140, 103, 145, 119, 161, 100, 142, 94, 136, 106, 148, 116, 158, 96, 138, 108, 150, 118, 160, 121, 163, 117, 159, 104, 146)
	L = (1, 88)(2, 94)(3, 98)(4, 102)(5, 103)(6, 106)(7, 85)(8, 91)(9, 104)(10, 89)(11, 109)(12, 86)(13, 108)(14, 107)(15, 118)(16, 87)(17, 120)(18, 121)(19, 122)(20, 99)(21, 101)(22, 123)(23, 125)(24, 90)(25, 105)(26, 93)(27, 96)(28, 100)(29, 92)(30, 115)(31, 95)(32, 112)(33, 97)(34, 124)(35, 114)(36, 117)(37, 111)(38, 113)(39, 119)(40, 116)(41, 126)(42, 110)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.541
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 14^6, 42^2 ]

E27.551 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 21, 21})
Quotient :: edge^2
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y2^-3 * Y1^-3, Y2^-2 * Y1^5, Y1 * Y3 * Y2 * Y1^-1 * Y2^3 * Y3 * Y2^-1, Y2^-9 * Y3 * Y2^-1 * Y1 * Y3, Y2^21 ]
Map:: non-degenerate
	R = (1, 43, 4, 46)(2, 44, 9, 51)(3, 45, 12, 54)(5, 47, 15, 57)(6, 48, 14, 56)(7, 49, 21, 63)(8, 50, 24, 66)(10, 52, 25, 67)(11, 53, 28, 70)(13, 55, 30, 72)(16, 58, 34, 76)(17, 59, 33, 75)(18, 60, 32, 74)(19, 61, 35, 77)(20, 62, 36, 78)(22, 64, 37, 79)(23, 65, 38, 80)(26, 68, 39, 81)(27, 69, 40, 82)(29, 71, 41, 83)(31, 73, 42, 84)(85, 86, 91, 103, 113, 95, 107, 101, 90, 94, 106, 115, 97, 87, 92, 104, 102, 110, 111, 100, 89)(88, 96, 112, 124, 121, 105, 120, 117, 99, 114, 125, 123, 109, 93, 108, 122, 118, 126, 119, 116, 98)(127, 129, 137, 153, 148, 133, 146, 143, 131, 139, 155, 152, 136, 128, 134, 149, 142, 157, 145, 144, 132)(130, 135, 147, 161, 167, 154, 164, 159, 140, 151, 163, 168, 156, 138, 150, 162, 158, 165, 166, 160, 141)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 24^4 ), ( 24^21 ) }
Outer automorphisms :: reflexible
Dual of E27.554
Graph:: simple bipartite
	v = 25 e = 84 f = 7
	degree seq :: [ 4^21, 21^4 ]

E27.552 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 21, 21})
Quotient :: edge^2
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, Y1^-1 * Y3^2 * Y2^-1, R * Y1 * R * Y2, Y3^2 * Y2 * Y3 * Y2 * Y3, (Y1 * Y2)^3, Y1^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1, Y1^5 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 43, 4, 46, 9, 51, 28, 70, 18, 60, 7, 49)(2, 44, 10, 52, 23, 65, 21, 63, 6, 48, 12, 54)(3, 45, 14, 56, 27, 69, 19, 61, 5, 47, 16, 58)(8, 50, 24, 66, 20, 62, 30, 72, 11, 53, 26, 68)(13, 55, 32, 74, 17, 59, 36, 78, 15, 57, 34, 76)(22, 64, 37, 79, 29, 71, 39, 81, 25, 67, 38, 80)(31, 73, 40, 82, 35, 77, 42, 84, 33, 75, 41, 83)(85, 86, 92, 106, 117, 97, 111, 102, 90, 95, 109, 119, 99, 87, 93, 107, 104, 113, 115, 101, 89)(88, 98, 116, 124, 122, 108, 105, 91, 100, 118, 125, 123, 110, 94, 112, 103, 120, 126, 121, 114, 96)(127, 129, 139, 157, 151, 134, 149, 144, 131, 141, 159, 155, 137, 128, 135, 153, 143, 161, 148, 146, 132)(130, 136, 150, 163, 167, 158, 145, 133, 138, 152, 164, 168, 160, 140, 154, 147, 156, 165, 166, 162, 142)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 8^12 ), ( 8^21 ) }
Outer automorphisms :: reflexible
Dual of E27.553
Graph:: bipartite
	v = 11 e = 84 f = 21
	degree seq :: [ 12^7, 21^4 ]

E27.553 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 21, 21})
Quotient :: loop^2
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y2^-3 * Y1^-3, Y2^-2 * Y1^5, Y1 * Y3 * Y2 * Y1^-1 * Y2^3 * Y3 * Y2^-1, Y2^-9 * Y3 * Y2^-1 * Y1 * Y3, Y2^21 ]
Map:: non-degenerate
	R = (1, 43, 85, 127, 4, 46, 88, 130)(2, 44, 86, 128, 9, 51, 93, 135)(3, 45, 87, 129, 12, 54, 96, 138)(5, 47, 89, 131, 15, 57, 99, 141)(6, 48, 90, 132, 14, 56, 98, 140)(7, 49, 91, 133, 21, 63, 105, 147)(8, 50, 92, 134, 24, 66, 108, 150)(10, 52, 94, 136, 25, 67, 109, 151)(11, 53, 95, 137, 28, 70, 112, 154)(13, 55, 97, 139, 30, 72, 114, 156)(16, 58, 100, 142, 34, 76, 118, 160)(17, 59, 101, 143, 33, 75, 117, 159)(18, 60, 102, 144, 32, 74, 116, 158)(19, 61, 103, 145, 35, 77, 119, 161)(20, 62, 104, 146, 36, 78, 120, 162)(22, 64, 106, 148, 37, 79, 121, 163)(23, 65, 107, 149, 38, 80, 122, 164)(26, 68, 110, 152, 39, 81, 123, 165)(27, 69, 111, 153, 40, 82, 124, 166)(29, 71, 113, 155, 41, 83, 125, 167)(31, 73, 115, 157, 42, 84, 126, 168)
	L = (1, 44)(2, 49)(3, 50)(4, 54)(5, 43)(6, 52)(7, 61)(8, 62)(9, 66)(10, 64)(11, 65)(12, 70)(13, 45)(14, 46)(15, 72)(16, 47)(17, 48)(18, 68)(19, 71)(20, 60)(21, 78)(22, 73)(23, 59)(24, 80)(25, 51)(26, 69)(27, 58)(28, 82)(29, 53)(30, 83)(31, 55)(32, 56)(33, 57)(34, 84)(35, 74)(36, 75)(37, 63)(38, 76)(39, 67)(40, 79)(41, 81)(42, 77)(85, 129)(86, 134)(87, 137)(88, 135)(89, 139)(90, 127)(91, 146)(92, 149)(93, 147)(94, 128)(95, 153)(96, 150)(97, 155)(98, 151)(99, 130)(100, 157)(101, 131)(102, 132)(103, 144)(104, 143)(105, 161)(106, 133)(107, 142)(108, 162)(109, 163)(110, 136)(111, 148)(112, 164)(113, 152)(114, 138)(115, 145)(116, 165)(117, 140)(118, 141)(119, 167)(120, 158)(121, 168)(122, 159)(123, 166)(124, 160)(125, 154)(126, 156)
	local type(s) :: { ( 12, 21, 12, 21, 12, 21, 12, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.552
Transitivity :: VT+
Graph::
	v = 21 e = 84 f = 11
	degree seq :: [ 8^21 ]

E27.554 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 21, 21})
Quotient :: loop^2
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, Y1^-1 * Y3^2 * Y2^-1, R * Y1 * R * Y2, Y3^2 * Y2 * Y3 * Y2 * Y3, (Y1 * Y2)^3, Y1^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1, Y1^5 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 43, 85, 127, 4, 46, 88, 130, 9, 51, 93, 135, 28, 70, 112, 154, 18, 60, 102, 144, 7, 49, 91, 133)(2, 44, 86, 128, 10, 52, 94, 136, 23, 65, 107, 149, 21, 63, 105, 147, 6, 48, 90, 132, 12, 54, 96, 138)(3, 45, 87, 129, 14, 56, 98, 140, 27, 69, 111, 153, 19, 61, 103, 145, 5, 47, 89, 131, 16, 58, 100, 142)(8, 50, 92, 134, 24, 66, 108, 150, 20, 62, 104, 146, 30, 72, 114, 156, 11, 53, 95, 137, 26, 68, 110, 152)(13, 55, 97, 139, 32, 74, 116, 158, 17, 59, 101, 143, 36, 78, 120, 162, 15, 57, 99, 141, 34, 76, 118, 160)(22, 64, 106, 148, 37, 79, 121, 163, 29, 71, 113, 155, 39, 81, 123, 165, 25, 67, 109, 151, 38, 80, 122, 164)(31, 73, 115, 157, 40, 82, 124, 166, 35, 77, 119, 161, 42, 84, 126, 168, 33, 75, 117, 159, 41, 83, 125, 167)
	L = (1, 44)(2, 50)(3, 51)(4, 56)(5, 43)(6, 53)(7, 58)(8, 64)(9, 65)(10, 70)(11, 67)(12, 46)(13, 69)(14, 74)(15, 45)(16, 76)(17, 47)(18, 48)(19, 78)(20, 71)(21, 49)(22, 75)(23, 62)(24, 63)(25, 77)(26, 52)(27, 60)(28, 61)(29, 73)(30, 54)(31, 59)(32, 82)(33, 55)(34, 83)(35, 57)(36, 84)(37, 72)(38, 66)(39, 68)(40, 80)(41, 81)(42, 79)(85, 129)(86, 135)(87, 139)(88, 136)(89, 141)(90, 127)(91, 138)(92, 149)(93, 153)(94, 150)(95, 128)(96, 152)(97, 157)(98, 154)(99, 159)(100, 130)(101, 161)(102, 131)(103, 133)(104, 132)(105, 156)(106, 146)(107, 144)(108, 163)(109, 134)(110, 164)(111, 143)(112, 147)(113, 137)(114, 165)(115, 151)(116, 145)(117, 155)(118, 140)(119, 148)(120, 142)(121, 167)(122, 168)(123, 166)(124, 162)(125, 158)(126, 160)
	local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.551
Transitivity :: VT+
Graph::
	v = 7 e = 84 f = 25
	degree seq :: [ 24^7 ]

E27.555 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2, Y3^3, (Y2, Y3), (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1^-1 * Y2 * Y1 * Y2, Y2^-7 * Y3^-1, (Y2^-1 * Y3)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 4, 46, 9, 51, 7, 49, 5, 47)(3, 45, 11, 53, 13, 55, 17, 59, 14, 56, 10, 52)(6, 48, 16, 58, 15, 57, 8, 50, 20, 62, 18, 60)(12, 54, 24, 66, 26, 68, 22, 64, 27, 69, 23, 65)(19, 61, 30, 72, 28, 70, 29, 71, 32, 74, 21, 63)(25, 67, 34, 76, 38, 80, 35, 77, 39, 81, 36, 78)(31, 73, 33, 75, 40, 82, 42, 84, 37, 79, 41, 83)(85, 127, 87, 129, 96, 138, 109, 151, 121, 163, 116, 158, 104, 146, 91, 133, 98, 140, 111, 153, 123, 165, 124, 166, 112, 154, 99, 141, 88, 130, 97, 139, 110, 152, 122, 164, 115, 157, 103, 145, 90, 132)(86, 128, 92, 134, 105, 147, 117, 159, 120, 162, 108, 150, 101, 143, 89, 131, 100, 142, 113, 155, 125, 167, 119, 161, 107, 149, 95, 137, 93, 135, 102, 144, 114, 156, 126, 168, 118, 160, 106, 148, 94, 136)
	L = (1, 88)(2, 93)(3, 97)(4, 91)(5, 86)(6, 99)(7, 85)(8, 102)(9, 89)(10, 95)(11, 101)(12, 110)(13, 98)(14, 87)(15, 104)(16, 92)(17, 94)(18, 100)(19, 112)(20, 90)(21, 114)(22, 107)(23, 108)(24, 106)(25, 122)(26, 111)(27, 96)(28, 116)(29, 105)(30, 113)(31, 124)(32, 103)(33, 126)(34, 119)(35, 120)(36, 118)(37, 115)(38, 123)(39, 109)(40, 121)(41, 117)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.561
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.556 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3, (R * Y1)^2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y1^-3 * Y3 * Y1^-1 * Y3, Y1^2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^6, Y1 * Y3^-1 * Y1^-3 * Y3^-1, Y3 * Y1^-1 * Y2^2 * Y3^-4 * Y1^-1, Y1 * Y2^4 * Y1 * Y2^-3, Y2^21, (Y3 * Y2^-1)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 6, 48, 16, 58, 15, 57, 5, 47)(3, 45, 9, 51, 17, 59, 14, 56, 22, 64, 8, 50)(4, 46, 11, 53, 18, 60, 7, 49, 19, 61, 13, 55)(10, 52, 24, 66, 29, 71, 21, 63, 33, 75, 23, 65)(12, 54, 27, 69, 30, 72, 26, 68, 31, 73, 20, 62)(25, 67, 34, 76, 40, 82, 35, 77, 42, 84, 36, 78)(28, 70, 32, 74, 41, 83, 39, 81, 37, 79, 38, 80)(85, 127, 87, 129, 94, 136, 109, 151, 121, 163, 115, 157, 103, 145, 99, 141, 106, 148, 117, 159, 126, 168, 125, 167, 114, 156, 102, 144, 90, 132, 101, 143, 113, 155, 124, 166, 112, 154, 96, 138, 88, 130)(86, 128, 91, 133, 104, 146, 116, 158, 120, 162, 108, 150, 98, 140, 89, 131, 95, 137, 110, 152, 122, 164, 119, 161, 107, 149, 93, 135, 100, 142, 97, 139, 111, 153, 123, 165, 118, 160, 105, 147, 92, 134)
	L = (1, 88)(2, 92)(3, 85)(4, 96)(5, 98)(6, 102)(7, 86)(8, 105)(9, 107)(10, 87)(11, 89)(12, 112)(13, 100)(14, 108)(15, 103)(16, 93)(17, 90)(18, 114)(19, 115)(20, 91)(21, 118)(22, 99)(23, 119)(24, 120)(25, 94)(26, 95)(27, 97)(28, 124)(29, 101)(30, 125)(31, 121)(32, 104)(33, 106)(34, 123)(35, 122)(36, 116)(37, 109)(38, 110)(39, 111)(40, 113)(41, 126)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.564
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.557 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y3 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^2 * Y1 * Y3^-1 * Y1^-1 * Y2, (Y3^2 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^3, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y3^2 * Y2 * Y1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 26, 68, 20, 62, 5, 47)(3, 45, 13, 55, 27, 69, 21, 63, 35, 77, 11, 53)(4, 46, 15, 57, 28, 70, 12, 54, 37, 79, 17, 59)(6, 48, 18, 60, 29, 71, 9, 51, 31, 73, 22, 64)(7, 49, 24, 66, 30, 72, 19, 61, 34, 76, 10, 52)(14, 56, 36, 78, 25, 67, 39, 81, 42, 84, 33, 75)(16, 58, 40, 82, 23, 65, 32, 74, 41, 83, 38, 80)(85, 127, 87, 129, 88, 130, 98, 140, 100, 142, 118, 160, 115, 157, 104, 146, 119, 161, 121, 163, 126, 168, 125, 167, 114, 156, 113, 155, 92, 134, 111, 153, 112, 154, 109, 151, 107, 149, 91, 133, 90, 132)(86, 128, 93, 135, 94, 136, 116, 158, 117, 159, 99, 141, 105, 147, 89, 131, 102, 144, 103, 145, 124, 166, 123, 165, 101, 143, 97, 139, 110, 152, 106, 148, 108, 150, 122, 164, 120, 162, 96, 138, 95, 137)
	L = (1, 88)(2, 94)(3, 98)(4, 100)(5, 103)(6, 87)(7, 85)(8, 112)(9, 116)(10, 117)(11, 93)(12, 86)(13, 106)(14, 118)(15, 89)(16, 115)(17, 110)(18, 124)(19, 123)(20, 121)(21, 102)(22, 122)(23, 90)(24, 120)(25, 91)(26, 108)(27, 109)(28, 107)(29, 111)(30, 92)(31, 119)(32, 99)(33, 105)(34, 104)(35, 126)(36, 95)(37, 125)(38, 96)(39, 97)(40, 101)(41, 113)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.566
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.558 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2^-1), (Y3 * Y1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, (R * Y3)^2, Y1^-2 * Y3^-1 * Y2^-2, Y3^4 * Y2, Y1 * Y3^-1 * Y1^-1 * Y2^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y3, Y2^-1 * Y1^-2 * Y2^-1 * Y3^-1, Y2 * Y3^-2 * Y1^-1 * Y3 * Y1^-1, Y1^6, Y2^-5 * Y3, Y3^2 * Y1 * Y2 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 30, 72, 23, 65, 5, 47)(3, 45, 13, 55, 27, 69, 24, 66, 36, 78, 11, 53)(4, 46, 17, 59, 26, 68, 12, 54, 37, 79, 19, 61)(6, 48, 21, 63, 31, 73, 9, 51, 15, 57, 25, 67)(7, 49, 28, 70, 32, 74, 22, 64, 14, 56, 10, 52)(16, 58, 38, 80, 18, 60, 35, 77, 40, 82, 39, 81)(20, 62, 34, 76, 41, 83, 42, 84, 29, 71, 33, 75)(85, 127, 87, 129, 98, 140, 124, 166, 104, 146, 88, 130, 99, 141, 107, 149, 120, 162, 116, 158, 102, 144, 113, 155, 121, 163, 115, 157, 92, 134, 111, 153, 91, 133, 100, 142, 125, 167, 110, 152, 90, 132)(86, 128, 93, 135, 101, 143, 126, 168, 119, 161, 94, 136, 108, 150, 89, 131, 105, 147, 103, 145, 118, 160, 122, 164, 106, 148, 97, 139, 114, 156, 109, 151, 96, 138, 117, 159, 123, 165, 112, 154, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 102)(5, 106)(6, 104)(7, 85)(8, 110)(9, 108)(10, 118)(11, 119)(12, 86)(13, 123)(14, 107)(15, 113)(16, 87)(17, 89)(18, 111)(19, 114)(20, 116)(21, 97)(22, 117)(23, 121)(24, 122)(25, 95)(26, 124)(27, 90)(28, 126)(29, 91)(30, 112)(31, 125)(32, 92)(33, 93)(34, 109)(35, 103)(36, 115)(37, 100)(38, 96)(39, 101)(40, 120)(41, 98)(42, 105)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.563
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.559 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-2, (Y1^-1 * Y2)^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1^-1, Y1^2 * Y3^-1 * Y2^-3, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^6, Y3 * Y1^-3 * Y3 * Y1^-1, Y1^2 * Y3 * Y2^17 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 26, 68, 20, 62, 5, 47)(3, 45, 13, 55, 27, 69, 21, 63, 35, 77, 11, 53)(4, 46, 16, 58, 28, 70, 12, 54, 38, 80, 17, 59)(6, 48, 18, 60, 29, 71, 9, 51, 31, 73, 22, 64)(7, 49, 25, 67, 30, 72, 19, 61, 34, 76, 10, 52)(14, 56, 39, 81, 41, 83, 36, 78, 24, 66, 33, 75)(15, 57, 37, 79, 42, 84, 32, 74, 23, 65, 40, 82)(85, 127, 87, 129, 98, 140, 114, 156, 112, 154, 126, 168, 115, 157, 104, 146, 119, 161, 108, 150, 91, 133, 88, 130, 99, 141, 113, 155, 92, 134, 111, 153, 125, 167, 118, 160, 122, 164, 107, 149, 90, 132)(86, 128, 93, 135, 116, 158, 101, 143, 109, 151, 123, 165, 105, 147, 89, 131, 102, 144, 121, 163, 96, 138, 94, 136, 117, 159, 97, 139, 110, 152, 106, 148, 124, 166, 100, 142, 103, 145, 120, 162, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 87)(5, 103)(6, 91)(7, 85)(8, 112)(9, 117)(10, 93)(11, 96)(12, 86)(13, 101)(14, 113)(15, 98)(16, 89)(17, 110)(18, 120)(19, 102)(20, 122)(21, 100)(22, 123)(23, 108)(24, 90)(25, 106)(26, 109)(27, 126)(28, 111)(29, 114)(30, 92)(31, 118)(32, 97)(33, 116)(34, 104)(35, 107)(36, 121)(37, 95)(38, 119)(39, 124)(40, 105)(41, 115)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.562
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.560 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, Y1 * Y2 * Y1^-1 * Y3^-2, Y2 * Y3 * Y2^3, Y1 * Y3 * Y2 * Y1 * Y3^-1, Y1^2 * Y3^-1 * Y2^-1 * Y3^-1, Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^5 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 30, 72, 23, 65, 5, 47)(3, 45, 13, 55, 31, 73, 24, 66, 29, 71, 11, 53)(4, 46, 17, 59, 32, 74, 12, 54, 27, 69, 19, 61)(6, 48, 21, 63, 18, 60, 9, 51, 33, 75, 25, 67)(7, 49, 28, 70, 15, 57, 22, 64, 36, 78, 10, 52)(14, 56, 35, 77, 20, 62, 38, 80, 41, 83, 40, 82)(16, 58, 34, 76, 26, 68, 37, 79, 42, 84, 39, 81)(85, 127, 87, 129, 98, 140, 111, 153, 91, 133, 100, 142, 117, 159, 107, 149, 113, 155, 125, 167, 116, 158, 120, 162, 126, 168, 102, 144, 92, 134, 115, 157, 104, 146, 88, 130, 99, 141, 110, 152, 90, 132)(86, 128, 93, 135, 118, 160, 106, 148, 96, 138, 119, 161, 108, 150, 89, 131, 105, 147, 123, 165, 112, 154, 101, 143, 124, 166, 97, 139, 114, 156, 109, 151, 121, 163, 94, 136, 103, 145, 122, 164, 95, 137)
	L = (1, 88)(2, 94)(3, 99)(4, 102)(5, 106)(6, 104)(7, 85)(8, 116)(9, 103)(10, 97)(11, 121)(12, 86)(13, 123)(14, 110)(15, 92)(16, 87)(17, 89)(18, 125)(19, 114)(20, 126)(21, 96)(22, 95)(23, 111)(24, 118)(25, 101)(26, 115)(27, 90)(28, 108)(29, 91)(30, 112)(31, 120)(32, 117)(33, 98)(34, 122)(35, 93)(36, 107)(37, 124)(38, 109)(39, 119)(40, 105)(41, 100)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.565
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.561 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, Y1 * Y3 * Y2 * Y1 * Y2, (Y1^-1 * Y3 * Y2)^2, Y3^-1 * Y1^7, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 19, 61, 33, 75, 28, 70, 15, 57, 4, 46, 9, 51, 21, 63, 35, 77, 42, 84, 32, 74, 18, 60, 6, 48, 10, 52, 22, 64, 36, 78, 31, 73, 17, 59, 5, 47)(3, 45, 11, 53, 25, 67, 39, 81, 37, 79, 20, 62, 24, 66, 12, 54, 16, 58, 29, 71, 40, 82, 38, 80, 23, 65, 8, 50, 14, 56, 26, 68, 30, 72, 41, 83, 34, 76, 27, 69, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 96, 138)(89, 131, 100, 142)(90, 132, 98, 140)(91, 133, 104, 146)(93, 135, 97, 139)(94, 136, 108, 150)(95, 137, 102, 144)(99, 141, 110, 152)(101, 143, 114, 156)(103, 145, 118, 160)(105, 147, 107, 149)(106, 148, 111, 153)(109, 151, 112, 154)(113, 155, 116, 158)(115, 157, 123, 165)(117, 159, 124, 166)(119, 161, 121, 163)(120, 162, 122, 164)(125, 167, 126, 168)
	L = (1, 88)(2, 93)(3, 96)(4, 90)(5, 99)(6, 85)(7, 105)(8, 97)(9, 94)(10, 86)(11, 100)(12, 98)(13, 108)(14, 87)(15, 102)(16, 110)(17, 112)(18, 89)(19, 119)(20, 107)(21, 106)(22, 91)(23, 111)(24, 92)(25, 113)(26, 95)(27, 104)(28, 116)(29, 114)(30, 109)(31, 117)(32, 101)(33, 126)(34, 121)(35, 120)(36, 103)(37, 122)(38, 118)(39, 124)(40, 125)(41, 123)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.555
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.562 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2, (Y1^-1 * Y2 * Y1^-2)^2, Y2 * Y1^-5 * Y2 * Y1^2, (Y3 * Y2)^6, (Y3^-1 * Y1^-1)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 5, 47, 11, 53, 23, 65, 32, 74, 41, 83, 34, 76, 17, 59, 29, 71, 40, 82, 42, 84, 33, 75, 16, 58, 28, 70, 39, 81, 35, 77, 38, 80, 22, 64, 10, 52, 4, 46)(3, 45, 7, 49, 15, 57, 31, 73, 26, 68, 12, 54, 25, 67, 20, 62, 9, 51, 19, 61, 36, 78, 30, 72, 14, 56, 6, 48, 13, 55, 27, 69, 21, 63, 37, 79, 24, 66, 18, 60, 8, 50)(85, 127, 87, 129)(86, 128, 90, 132)(88, 130, 93, 135)(89, 131, 96, 138)(91, 133, 100, 142)(92, 134, 101, 143)(94, 136, 105, 147)(95, 137, 108, 150)(97, 139, 112, 154)(98, 140, 113, 155)(99, 141, 116, 158)(102, 144, 119, 161)(103, 145, 117, 159)(104, 146, 118, 160)(106, 148, 115, 157)(107, 149, 120, 162)(109, 151, 123, 165)(110, 152, 124, 166)(111, 153, 125, 167)(114, 156, 122, 164)(121, 163, 126, 168)
	L = (1, 86)(2, 89)(3, 91)(4, 85)(5, 95)(6, 97)(7, 99)(8, 87)(9, 103)(10, 88)(11, 107)(12, 109)(13, 111)(14, 90)(15, 115)(16, 112)(17, 113)(18, 92)(19, 120)(20, 93)(21, 121)(22, 94)(23, 116)(24, 102)(25, 104)(26, 96)(27, 105)(28, 123)(29, 124)(30, 98)(31, 110)(32, 125)(33, 100)(34, 101)(35, 122)(36, 114)(37, 108)(38, 106)(39, 119)(40, 126)(41, 118)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.559
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.563 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1), (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y3, Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^4, Y1 * Y2 * Y1^-2 * Y2 * Y3, (Y3^-1 * Y1 * Y2)^2, Y2 * R * Y2 * Y3 * Y1 * R * Y1^-1, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 17, 59, 4, 46, 9, 51, 24, 66, 39, 81, 16, 58, 29, 71, 33, 75, 36, 78, 38, 80, 22, 64, 31, 73, 41, 83, 20, 62, 6, 48, 10, 52, 19, 61, 5, 47)(3, 45, 11, 53, 28, 70, 30, 72, 12, 54, 23, 65, 37, 79, 40, 82, 18, 60, 27, 69, 15, 57, 21, 63, 26, 68, 8, 50, 25, 67, 42, 84, 35, 77, 14, 56, 32, 74, 34, 76, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 99, 141)(89, 131, 102, 144)(90, 132, 105, 147)(91, 133, 107, 149)(93, 135, 112, 154)(94, 136, 114, 156)(95, 137, 106, 148)(96, 138, 117, 159)(97, 139, 100, 142)(98, 140, 120, 162)(101, 143, 116, 158)(103, 145, 119, 161)(104, 146, 118, 160)(108, 150, 126, 168)(109, 151, 115, 157)(110, 152, 113, 155)(111, 153, 122, 164)(121, 163, 125, 167)(123, 165, 124, 166)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 101)(6, 85)(7, 108)(8, 98)(9, 113)(10, 86)(11, 107)(12, 102)(13, 114)(14, 87)(15, 109)(16, 122)(17, 123)(18, 110)(19, 91)(20, 89)(21, 126)(22, 90)(23, 111)(24, 117)(25, 116)(26, 119)(27, 92)(28, 121)(29, 106)(30, 124)(31, 94)(32, 95)(33, 115)(34, 112)(35, 97)(36, 125)(37, 99)(38, 104)(39, 120)(40, 105)(41, 103)(42, 118)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.558
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.564 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3 * Y1^-1)^2, Y1^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * R * Y1^-2 * Y3 * R * Y2 * Y1^-1, (Y3 * Y2)^6 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 19, 61, 27, 69, 38, 80, 42, 84, 40, 82, 28, 70, 15, 57, 4, 46, 6, 48, 9, 51, 21, 63, 37, 79, 39, 81, 41, 83, 30, 72, 35, 77, 17, 59, 5, 47)(3, 45, 10, 52, 23, 65, 25, 67, 14, 56, 20, 62, 36, 78, 33, 75, 16, 58, 26, 68, 11, 53, 13, 55, 24, 66, 8, 50, 22, 64, 31, 73, 34, 76, 18, 60, 32, 74, 29, 71, 12, 54)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 98, 140)(89, 131, 100, 142)(90, 132, 102, 144)(91, 133, 104, 146)(93, 135, 110, 152)(94, 136, 105, 147)(95, 137, 111, 153)(96, 138, 112, 154)(97, 139, 114, 156)(99, 141, 108, 150)(101, 143, 118, 160)(103, 145, 116, 158)(106, 148, 121, 163)(107, 149, 122, 164)(109, 151, 119, 161)(113, 155, 125, 167)(115, 157, 126, 168)(117, 159, 124, 166)(120, 162, 123, 165)
	L = (1, 88)(2, 90)(3, 95)(4, 89)(5, 99)(6, 85)(7, 93)(8, 107)(9, 86)(10, 97)(11, 96)(12, 110)(13, 87)(14, 106)(15, 101)(16, 116)(17, 112)(18, 120)(19, 105)(20, 115)(21, 91)(22, 109)(23, 108)(24, 94)(25, 92)(26, 113)(27, 121)(28, 119)(29, 100)(30, 126)(31, 98)(32, 117)(33, 102)(34, 104)(35, 124)(36, 118)(37, 103)(38, 123)(39, 111)(40, 114)(41, 122)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.556
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.565 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-3, Y2 * Y1^-2 * Y2 * Y3^-1, Y1 * Y2 * Y3 * Y2 * Y1, Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^2, (Y3 * Y1^-1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y2, Y3 * Y1 * Y2 * Y3^-2 * Y2, Y3^-1 * Y1^-5, Y2 * Y1^-1 * R * Y2 * Y3^2 * R, (Y1^-2 * Y3)^3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 23, 65, 20, 62, 6, 48, 10, 52, 25, 67, 35, 77, 42, 84, 22, 64, 16, 58, 30, 72, 32, 74, 39, 81, 17, 59, 4, 46, 9, 51, 24, 66, 19, 61, 5, 47)(3, 45, 11, 53, 21, 63, 38, 80, 36, 78, 14, 56, 34, 76, 41, 83, 18, 60, 40, 82, 37, 79, 29, 71, 27, 69, 8, 50, 26, 68, 31, 73, 12, 54, 33, 75, 28, 70, 15, 57, 13, 55)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 99, 141)(89, 131, 102, 144)(90, 132, 105, 147)(91, 133, 98, 140)(93, 135, 113, 155)(94, 136, 115, 157)(95, 137, 116, 158)(96, 138, 103, 145)(97, 139, 119, 161)(100, 142, 117, 159)(101, 143, 118, 160)(104, 146, 121, 163)(106, 148, 120, 162)(107, 149, 112, 154)(108, 150, 122, 164)(109, 151, 125, 167)(110, 152, 123, 165)(111, 153, 126, 168)(114, 156, 124, 166)
	L = (1, 88)(2, 93)(3, 96)(4, 100)(5, 101)(6, 85)(7, 108)(8, 102)(9, 114)(10, 86)(11, 117)(12, 113)(13, 115)(14, 87)(15, 110)(16, 94)(17, 106)(18, 122)(19, 123)(20, 89)(21, 112)(22, 90)(23, 103)(24, 116)(25, 91)(26, 124)(27, 125)(28, 92)(29, 118)(30, 109)(31, 121)(32, 119)(33, 111)(34, 95)(35, 107)(36, 97)(37, 98)(38, 99)(39, 126)(40, 120)(41, 105)(42, 104)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.560
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.566 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C3 x D14 (small group id <42, 4>)
Aut   = S3 x D14 (small group id <84, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3^-1, (R * Y3^-1)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^2, R * Y3 * Y2 * Y3^-1 * R * Y2, (Y1 * Y3^-1 * Y2)^2, Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2, (Y3 * Y1^-1 * Y3^2)^3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 6, 48, 8, 50, 18, 60, 24, 66, 36, 78, 39, 81, 29, 71, 38, 80, 42, 84, 40, 82, 41, 83, 25, 67, 37, 79, 31, 73, 27, 69, 14, 56, 15, 57, 4, 46, 5, 47)(3, 45, 9, 51, 12, 54, 26, 68, 30, 72, 17, 59, 33, 75, 34, 76, 16, 58, 32, 74, 35, 77, 20, 62, 21, 63, 7, 49, 19, 61, 22, 64, 13, 55, 28, 70, 23, 65, 10, 52, 11, 53)(85, 127, 87, 129)(86, 128, 91, 133)(88, 130, 97, 139)(89, 131, 100, 142)(90, 132, 101, 143)(92, 134, 107, 149)(93, 135, 109, 151)(94, 136, 111, 153)(95, 137, 113, 155)(96, 138, 108, 150)(98, 140, 104, 146)(99, 141, 110, 152)(102, 144, 119, 161)(103, 145, 121, 163)(105, 147, 122, 164)(106, 148, 120, 162)(112, 154, 124, 166)(114, 156, 126, 168)(115, 157, 117, 159)(116, 158, 125, 167)(118, 160, 123, 165)
	L = (1, 88)(2, 89)(3, 94)(4, 98)(5, 99)(6, 85)(7, 104)(8, 86)(9, 95)(10, 112)(11, 107)(12, 87)(13, 103)(14, 115)(15, 111)(16, 117)(17, 110)(18, 90)(19, 105)(20, 116)(21, 119)(22, 91)(23, 97)(24, 92)(25, 124)(26, 93)(27, 121)(28, 106)(29, 120)(30, 96)(31, 109)(32, 118)(33, 114)(34, 101)(35, 100)(36, 102)(37, 125)(38, 123)(39, 108)(40, 122)(41, 126)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.557
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.567 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y1, Y3^3, (Y2, Y3), (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2^7 * Y3, (Y2^-1 * Y3)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 4, 46, 9, 51, 7, 49, 5, 47)(3, 45, 8, 50, 12, 54, 20, 62, 14, 56, 13, 55)(6, 48, 10, 52, 15, 57, 21, 63, 18, 60, 16, 58)(11, 53, 19, 61, 24, 66, 32, 74, 26, 68, 25, 67)(17, 59, 22, 64, 27, 69, 33, 75, 30, 72, 28, 70)(23, 65, 31, 73, 36, 78, 41, 83, 38, 80, 37, 79)(29, 71, 34, 76, 39, 81, 42, 84, 35, 77, 40, 82)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 114, 156, 102, 144, 91, 133, 98, 140, 110, 152, 122, 164, 123, 165, 111, 153, 99, 141, 88, 130, 96, 138, 108, 150, 120, 162, 113, 155, 101, 143, 90, 132)(86, 128, 92, 134, 103, 145, 115, 157, 124, 166, 112, 154, 100, 142, 89, 131, 97, 139, 109, 151, 121, 163, 126, 168, 117, 159, 105, 147, 93, 135, 104, 146, 116, 158, 125, 167, 118, 160, 106, 148, 94, 136)
	L = (1, 88)(2, 93)(3, 96)(4, 91)(5, 86)(6, 99)(7, 85)(8, 104)(9, 89)(10, 105)(11, 108)(12, 98)(13, 92)(14, 87)(15, 102)(16, 94)(17, 111)(18, 90)(19, 116)(20, 97)(21, 100)(22, 117)(23, 120)(24, 110)(25, 103)(26, 95)(27, 114)(28, 106)(29, 123)(30, 101)(31, 125)(32, 109)(33, 112)(34, 126)(35, 113)(36, 122)(37, 115)(38, 107)(39, 119)(40, 118)(41, 121)(42, 124)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.568
Graph:: bipartite
	v = 9 e = 84 f = 23
	degree seq :: [ 12^7, 42^2 ]

E27.568 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 21, 21})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, Y3^-1 * Y1^7, (Y1^-1 * Y3^-1)^21 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 17, 59, 29, 71, 26, 68, 14, 56, 4, 46, 9, 51, 19, 61, 31, 73, 38, 80, 28, 70, 16, 58, 6, 48, 10, 52, 20, 62, 32, 74, 27, 69, 15, 57, 5, 47)(3, 45, 8, 50, 18, 60, 30, 72, 39, 81, 35, 77, 23, 65, 11, 53, 21, 63, 33, 75, 40, 82, 42, 84, 37, 79, 25, 67, 13, 55, 22, 64, 34, 76, 41, 83, 36, 78, 24, 66, 12, 54)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 95, 137)(89, 131, 96, 138)(90, 132, 97, 139)(91, 133, 102, 144)(93, 135, 105, 147)(94, 136, 106, 148)(98, 140, 107, 149)(99, 141, 108, 150)(100, 142, 109, 151)(101, 143, 114, 156)(103, 145, 117, 159)(104, 146, 118, 160)(110, 152, 119, 161)(111, 153, 120, 162)(112, 154, 121, 163)(113, 155, 123, 165)(115, 157, 124, 166)(116, 158, 125, 167)(122, 164, 126, 168)
	L = (1, 88)(2, 93)(3, 95)(4, 90)(5, 98)(6, 85)(7, 103)(8, 105)(9, 94)(10, 86)(11, 97)(12, 107)(13, 87)(14, 100)(15, 110)(16, 89)(17, 115)(18, 117)(19, 104)(20, 91)(21, 106)(22, 92)(23, 109)(24, 119)(25, 96)(26, 112)(27, 113)(28, 99)(29, 122)(30, 124)(31, 116)(32, 101)(33, 118)(34, 102)(35, 121)(36, 123)(37, 108)(38, 111)(39, 126)(40, 125)(41, 114)(42, 120)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 42, 12, 42 ), ( 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42, 12, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.567
Graph:: bipartite
	v = 23 e = 84 f = 9
	degree seq :: [ 4^21, 42^2 ]

E27.569 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^14, (Y3 * Y2^-1)^42 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 4, 46)(3, 45, 6, 48, 9, 51)(5, 47, 7, 49, 10, 52)(8, 50, 12, 54, 15, 57)(11, 53, 13, 55, 16, 58)(14, 56, 18, 60, 21, 63)(17, 59, 19, 61, 22, 64)(20, 62, 24, 66, 27, 69)(23, 65, 25, 67, 28, 70)(26, 68, 30, 72, 33, 75)(29, 71, 31, 73, 34, 76)(32, 74, 36, 78, 39, 81)(35, 77, 37, 79, 40, 82)(38, 80, 41, 83, 42, 84)(85, 127, 87, 129, 92, 134, 98, 140, 104, 146, 110, 152, 116, 158, 122, 164, 119, 161, 113, 155, 107, 149, 101, 143, 95, 137, 89, 131)(86, 128, 90, 132, 96, 138, 102, 144, 108, 150, 114, 156, 120, 162, 125, 167, 121, 163, 115, 157, 109, 151, 103, 145, 97, 139, 91, 133)(88, 130, 93, 135, 99, 141, 105, 147, 111, 153, 117, 159, 123, 165, 126, 168, 124, 166, 118, 160, 112, 154, 106, 148, 100, 142, 94, 136)
	L = (1, 86)(2, 88)(3, 90)(4, 85)(5, 91)(6, 93)(7, 94)(8, 96)(9, 87)(10, 89)(11, 97)(12, 99)(13, 100)(14, 102)(15, 92)(16, 95)(17, 103)(18, 105)(19, 106)(20, 108)(21, 98)(22, 101)(23, 109)(24, 111)(25, 112)(26, 114)(27, 104)(28, 107)(29, 115)(30, 117)(31, 118)(32, 120)(33, 110)(34, 113)(35, 121)(36, 123)(37, 124)(38, 125)(39, 116)(40, 119)(41, 126)(42, 122)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 6, 84, 6, 84, 6, 84 ), ( 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84, 6, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.570
Graph:: bipartite
	v = 17 e = 84 f = 15
	degree seq :: [ 6^14, 28^3 ]

E27.570 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y2^3, R * Y2 * R * Y3^-1, (R * Y1)^2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), (Y3 * Y2^-1)^3, Y2 * Y1^14, (Y1^-1 * Y3^-1)^14 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 6, 48, 12, 54, 18, 60, 24, 66, 30, 72, 36, 78, 40, 82, 34, 76, 28, 70, 22, 64, 16, 58, 10, 52, 4, 46, 8, 50, 14, 56, 20, 62, 26, 68, 32, 74, 38, 80, 42, 84, 39, 81, 33, 75, 27, 69, 21, 63, 15, 57, 9, 51, 3, 45, 7, 49, 13, 55, 19, 61, 25, 67, 31, 73, 37, 79, 41, 83, 35, 77, 29, 71, 23, 65, 17, 59, 11, 53, 5, 47)(85, 127, 87, 129, 88, 130)(86, 128, 91, 133, 92, 134)(89, 131, 93, 135, 94, 136)(90, 132, 97, 139, 98, 140)(95, 137, 99, 141, 100, 142)(96, 138, 103, 145, 104, 146)(101, 143, 105, 147, 106, 148)(102, 144, 109, 151, 110, 152)(107, 149, 111, 153, 112, 154)(108, 150, 115, 157, 116, 158)(113, 155, 117, 159, 118, 160)(114, 156, 121, 163, 122, 164)(119, 161, 123, 165, 124, 166)(120, 162, 125, 167, 126, 168)
	L = (1, 88)(2, 92)(3, 85)(4, 87)(5, 94)(6, 98)(7, 86)(8, 91)(9, 89)(10, 93)(11, 100)(12, 104)(13, 90)(14, 97)(15, 95)(16, 99)(17, 106)(18, 110)(19, 96)(20, 103)(21, 101)(22, 105)(23, 112)(24, 116)(25, 102)(26, 109)(27, 107)(28, 111)(29, 118)(30, 122)(31, 108)(32, 115)(33, 113)(34, 117)(35, 124)(36, 126)(37, 114)(38, 121)(39, 119)(40, 123)(41, 120)(42, 125)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 6, 28, 6, 28, 6, 28 ), ( 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.569
Graph:: bipartite
	v = 15 e = 84 f = 17
	degree seq :: [ 6^14, 84 ]

E27.571 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2^-1, Y3), Y2^-3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^-1 * Y1 * Y3, Y3^-3 * Y2 * Y1 * Y3^-4, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 8, 50)(5, 47, 9, 51)(6, 48, 10, 52)(11, 53, 17, 59)(12, 54, 18, 60)(13, 55, 19, 61)(14, 56, 20, 62)(15, 57, 21, 63)(16, 58, 22, 64)(23, 65, 29, 71)(24, 66, 30, 72)(25, 67, 31, 73)(26, 68, 32, 74)(27, 69, 33, 75)(28, 70, 34, 76)(35, 77, 41, 83)(36, 78, 37, 79)(38, 80, 40, 82)(39, 81, 42, 84)(85, 127, 87, 129, 93, 135, 86, 128, 91, 133, 89, 131)(88, 130, 95, 137, 104, 146, 92, 134, 101, 143, 98, 140)(90, 132, 96, 138, 105, 147, 94, 136, 102, 144, 99, 141)(97, 139, 107, 149, 116, 158, 103, 145, 113, 155, 110, 152)(100, 142, 108, 150, 117, 159, 106, 148, 114, 156, 111, 153)(109, 151, 119, 161, 124, 166, 115, 157, 125, 167, 122, 164)(112, 154, 120, 162, 126, 168, 118, 160, 121, 163, 123, 165)
	L = (1, 88)(2, 92)(3, 95)(4, 97)(5, 98)(6, 85)(7, 101)(8, 103)(9, 104)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 89)(16, 90)(17, 113)(18, 91)(19, 115)(20, 116)(21, 93)(22, 94)(23, 119)(24, 96)(25, 121)(26, 122)(27, 99)(28, 100)(29, 125)(30, 102)(31, 120)(32, 124)(33, 105)(34, 106)(35, 123)(36, 108)(37, 114)(38, 118)(39, 111)(40, 112)(41, 126)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 28, 84, 28, 84 ), ( 28, 84, 28, 84, 28, 84, 28, 84, 28, 84, 28, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.574
Graph:: bipartite
	v = 28 e = 84 f = 4
	degree seq :: [ 4^21, 12^7 ]

E27.572 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, (Y2, Y1^-1), (Y2, Y3), (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-4, Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 4, 46, 9, 51, 7, 49, 5, 47)(3, 45, 8, 50, 12, 54, 20, 62, 14, 56, 13, 55)(6, 48, 10, 52, 15, 57, 21, 63, 18, 60, 16, 58)(11, 53, 19, 61, 24, 66, 32, 74, 26, 68, 25, 67)(17, 59, 22, 64, 27, 69, 33, 75, 30, 72, 28, 70)(23, 65, 31, 73, 36, 78, 41, 83, 38, 80, 37, 79)(29, 71, 34, 76, 39, 81, 35, 77, 42, 84, 40, 82)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 117, 159, 105, 147, 93, 135, 104, 146, 116, 158, 125, 167, 113, 155, 101, 143, 90, 132)(86, 128, 92, 134, 103, 145, 115, 157, 126, 168, 114, 156, 102, 144, 91, 133, 98, 140, 110, 152, 122, 164, 118, 160, 106, 148, 94, 136)(88, 130, 96, 138, 108, 150, 120, 162, 124, 166, 112, 154, 100, 142, 89, 131, 97, 139, 109, 151, 121, 163, 123, 165, 111, 153, 99, 141)
	L = (1, 88)(2, 93)(3, 96)(4, 91)(5, 86)(6, 99)(7, 85)(8, 104)(9, 89)(10, 105)(11, 108)(12, 98)(13, 92)(14, 87)(15, 102)(16, 94)(17, 111)(18, 90)(19, 116)(20, 97)(21, 100)(22, 117)(23, 120)(24, 110)(25, 103)(26, 95)(27, 114)(28, 106)(29, 123)(30, 101)(31, 125)(32, 109)(33, 112)(34, 119)(35, 124)(36, 122)(37, 115)(38, 107)(39, 126)(40, 118)(41, 121)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84 ), ( 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84, 4, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.573
Graph:: bipartite
	v = 10 e = 84 f = 22
	degree seq :: [ 12^7, 28^3 ]

E27.573 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y1^-1 * Y2, Y1^-7 * Y2 * Y3^-1, Y1 * Y2 * Y1^3 * Y3 * Y1^3, Y1^-4 * Y3 * Y1^-3 * Y2 * Y3, Y3 * Y2 * Y1^-3 * Y3 * Y1^-4 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 7, 49, 17, 59, 29, 71, 37, 79, 25, 67, 13, 55, 22, 64, 34, 76, 42, 84, 38, 80, 26, 68, 14, 56, 4, 46, 9, 51, 19, 61, 31, 73, 36, 78, 24, 66, 12, 54, 3, 45, 8, 50, 18, 60, 30, 72, 40, 82, 28, 70, 16, 58, 6, 48, 10, 52, 20, 62, 32, 74, 41, 83, 35, 77, 23, 65, 11, 53, 21, 63, 33, 75, 39, 81, 27, 69, 15, 57, 5, 47)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 95, 137)(89, 131, 96, 138)(90, 132, 97, 139)(91, 133, 102, 144)(93, 135, 105, 147)(94, 136, 106, 148)(98, 140, 107, 149)(99, 141, 108, 150)(100, 142, 109, 151)(101, 143, 114, 156)(103, 145, 117, 159)(104, 146, 118, 160)(110, 152, 119, 161)(111, 153, 120, 162)(112, 154, 121, 163)(113, 155, 124, 166)(115, 157, 123, 165)(116, 158, 126, 168)(122, 164, 125, 167)
	L = (1, 88)(2, 93)(3, 95)(4, 90)(5, 98)(6, 85)(7, 103)(8, 105)(9, 94)(10, 86)(11, 97)(12, 107)(13, 87)(14, 100)(15, 110)(16, 89)(17, 115)(18, 117)(19, 104)(20, 91)(21, 106)(22, 92)(23, 109)(24, 119)(25, 96)(26, 112)(27, 122)(28, 99)(29, 120)(30, 123)(31, 116)(32, 101)(33, 118)(34, 102)(35, 121)(36, 125)(37, 108)(38, 124)(39, 126)(40, 111)(41, 113)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 28, 12, 28 ), ( 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28, 12, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.572
Graph:: bipartite
	v = 22 e = 84 f = 10
	degree seq :: [ 4^21, 84 ]

E27.574 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y2), (Y3^-1 * Y2)^2, Y2^-2 * Y3^2, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y3^-1), (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^2, Y3^2 * Y2 * Y1^-1 * Y3 * Y2^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-3, Y3^-1 * Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 8, 50, 23, 65, 34, 76, 42, 84, 38, 80, 16, 58, 30, 72, 41, 83, 40, 82, 33, 75, 18, 60, 5, 47)(3, 45, 9, 51, 24, 66, 21, 63, 31, 73, 39, 81, 17, 59, 4, 46, 10, 52, 25, 67, 22, 64, 32, 74, 37, 79, 15, 57)(6, 48, 11, 53, 26, 68, 36, 78, 14, 56, 29, 71, 20, 62, 7, 49, 12, 54, 27, 69, 35, 77, 13, 55, 28, 70, 19, 61)(85, 127, 87, 129, 97, 139, 117, 159, 116, 158, 96, 138, 114, 156, 94, 136, 113, 155, 126, 168, 123, 165, 110, 152, 92, 134, 108, 150, 103, 145, 89, 131, 99, 141, 119, 161, 124, 166, 106, 148, 91, 133, 100, 142, 88, 130, 98, 140, 118, 160, 115, 157, 95, 137, 86, 128, 93, 135, 112, 154, 102, 144, 121, 163, 111, 153, 125, 167, 109, 151, 104, 146, 122, 164, 101, 143, 120, 162, 107, 149, 105, 147, 90, 132)
	L = (1, 88)(2, 94)(3, 98)(4, 97)(5, 101)(6, 100)(7, 85)(8, 109)(9, 113)(10, 112)(11, 114)(12, 86)(13, 118)(14, 117)(15, 120)(16, 87)(17, 119)(18, 123)(19, 122)(20, 89)(21, 91)(22, 90)(23, 106)(24, 104)(25, 103)(26, 125)(27, 92)(28, 126)(29, 102)(30, 93)(31, 96)(32, 95)(33, 115)(34, 116)(35, 107)(36, 124)(37, 110)(38, 99)(39, 111)(40, 105)(41, 108)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.571
Graph:: bipartite
	v = 4 e = 84 f = 28
	degree seq :: [ 28^3, 84 ]

E27.575 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^2, Y2^4 * Y3^3, Y2^-2 * Y1 * Y3^3 * Y2^-1, Y2^2 * Y1 * Y3^-1 * Y2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 8, 50)(5, 47, 9, 51)(6, 48, 10, 52)(11, 53, 19, 61)(12, 54, 20, 62)(13, 55, 21, 63)(14, 56, 22, 64)(15, 57, 23, 65)(16, 58, 24, 66)(17, 59, 25, 67)(18, 60, 26, 68)(27, 69, 32, 74)(28, 70, 39, 81)(29, 71, 33, 75)(30, 72, 40, 82)(31, 73, 34, 76)(35, 77, 38, 80)(36, 78, 41, 83)(37, 79, 42, 84)(85, 127, 87, 129, 95, 137, 111, 153, 122, 164, 108, 150, 93, 135, 86, 128, 91, 133, 103, 145, 116, 158, 119, 161, 100, 142, 89, 131)(88, 130, 96, 138, 112, 154, 121, 163, 102, 144, 115, 157, 107, 149, 92, 134, 104, 146, 123, 165, 126, 168, 110, 152, 118, 160, 99, 141)(90, 132, 97, 139, 113, 155, 106, 148, 124, 166, 125, 167, 109, 151, 94, 136, 105, 147, 117, 159, 98, 140, 114, 156, 120, 162, 101, 143)
	L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 112)(12, 114)(13, 87)(14, 116)(15, 117)(16, 118)(17, 89)(18, 90)(19, 123)(20, 124)(21, 91)(22, 111)(23, 113)(24, 115)(25, 93)(26, 94)(27, 121)(28, 120)(29, 95)(30, 119)(31, 97)(32, 126)(33, 103)(34, 105)(35, 110)(36, 100)(37, 101)(38, 102)(39, 125)(40, 122)(41, 108)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 12, 84, 12, 84 ), ( 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84, 12, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.576
Graph:: bipartite
	v = 24 e = 84 f = 8
	degree seq :: [ 4^21, 28^3 ]

E27.576 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 14, 42})
Quotient :: dipole
Aut^+ = C42 (small group id <42, 6>)
Aut   = D84 (small group id <84, 14>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^2, Y3^3, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2^3 * Y1 * Y2^4 ]
Map:: non-degenerate
	R = (1, 43, 2, 44, 4, 46, 9, 51, 7, 49, 5, 47)(3, 45, 8, 50, 12, 54, 20, 62, 14, 56, 13, 55)(6, 48, 10, 52, 15, 57, 21, 63, 18, 60, 16, 58)(11, 53, 19, 61, 24, 66, 32, 74, 26, 68, 25, 67)(17, 59, 22, 64, 27, 69, 33, 75, 30, 72, 28, 70)(23, 65, 31, 73, 36, 78, 41, 83, 38, 80, 37, 79)(29, 71, 34, 76, 39, 81, 42, 84, 40, 82, 35, 77)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 112, 154, 100, 142, 89, 131, 97, 139, 109, 151, 121, 163, 124, 166, 114, 156, 102, 144, 91, 133, 98, 140, 110, 152, 122, 164, 126, 168, 117, 159, 105, 147, 93, 135, 104, 146, 116, 158, 125, 167, 123, 165, 111, 153, 99, 141, 88, 130, 96, 138, 108, 150, 120, 162, 118, 160, 106, 148, 94, 136, 86, 128, 92, 134, 103, 145, 115, 157, 113, 155, 101, 143, 90, 132)
	L = (1, 88)(2, 93)(3, 96)(4, 91)(5, 86)(6, 99)(7, 85)(8, 104)(9, 89)(10, 105)(11, 108)(12, 98)(13, 92)(14, 87)(15, 102)(16, 94)(17, 111)(18, 90)(19, 116)(20, 97)(21, 100)(22, 117)(23, 120)(24, 110)(25, 103)(26, 95)(27, 114)(28, 106)(29, 123)(30, 101)(31, 125)(32, 109)(33, 112)(34, 126)(35, 118)(36, 122)(37, 115)(38, 107)(39, 124)(40, 113)(41, 121)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.575
Graph:: bipartite
	v = 8 e = 84 f = 24
	degree seq :: [ 12^7, 84 ]

E27.577 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, (Y2^-1, Y3^-1), Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^9 * Y2^-1 * Y3^2, (Y2^-1 * Y3)^22 ]
Map:: non-degenerate
	R = (1, 45, 2, 46)(3, 47, 5, 49)(4, 48, 7, 51)(6, 50, 8, 52)(9, 53, 12, 56)(10, 54, 13, 57)(11, 55, 15, 59)(14, 58, 16, 60)(17, 61, 20, 64)(18, 62, 21, 65)(19, 63, 23, 67)(22, 66, 24, 68)(25, 69, 28, 72)(26, 70, 29, 73)(27, 71, 31, 75)(30, 74, 32, 76)(33, 77, 36, 80)(34, 78, 37, 81)(35, 79, 39, 83)(38, 82, 40, 84)(41, 85, 43, 87)(42, 86, 44, 88)(89, 133, 91, 135, 90, 134, 93, 137)(92, 136, 97, 141, 95, 139, 100, 144)(94, 138, 98, 142, 96, 140, 101, 145)(99, 143, 105, 149, 103, 147, 108, 152)(102, 146, 106, 150, 104, 148, 109, 153)(107, 151, 113, 157, 111, 155, 116, 160)(110, 154, 114, 158, 112, 156, 117, 161)(115, 159, 121, 165, 119, 163, 124, 168)(118, 162, 122, 166, 120, 164, 125, 169)(123, 167, 129, 173, 127, 171, 131, 175)(126, 170, 130, 174, 128, 172, 132, 176)
	L = (1, 92)(2, 95)(3, 97)(4, 99)(5, 100)(6, 89)(7, 103)(8, 90)(9, 105)(10, 91)(11, 107)(12, 108)(13, 93)(14, 94)(15, 111)(16, 96)(17, 113)(18, 98)(19, 115)(20, 116)(21, 101)(22, 102)(23, 119)(24, 104)(25, 121)(26, 106)(27, 123)(28, 124)(29, 109)(30, 110)(31, 127)(32, 112)(33, 129)(34, 114)(35, 130)(36, 131)(37, 117)(38, 118)(39, 132)(40, 120)(41, 128)(42, 122)(43, 126)(44, 125)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 44, 88, 44, 88 ), ( 44, 88, 44, 88, 44, 88, 44, 88 ) }
Outer automorphisms :: reflexible
Dual of E27.580
Graph:: bipartite
	v = 33 e = 88 f = 3
	degree seq :: [ 4^22, 8^11 ]

E27.578 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^-11 * Y1^2, (Y3 * Y2^-1)^44 ]
Map:: non-degenerate
	R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 44, 88, 42, 86)(36, 80, 40, 84, 41, 85, 43, 87)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 129, 173, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 132, 176, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)(90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 131, 175, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 130, 174, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140)
	L = (1, 90)(2, 94)(3, 95)(4, 89)(5, 96)(6, 92)(7, 101)(8, 102)(9, 103)(10, 91)(11, 93)(12, 104)(13, 98)(14, 99)(15, 109)(16, 110)(17, 111)(18, 97)(19, 100)(20, 112)(21, 106)(22, 107)(23, 117)(24, 118)(25, 119)(26, 105)(27, 108)(28, 120)(29, 114)(30, 115)(31, 125)(32, 126)(33, 127)(34, 113)(35, 116)(36, 128)(37, 122)(38, 123)(39, 132)(40, 129)(41, 131)(42, 121)(43, 124)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 4, 88, 4, 88, 4, 88, 4, 88 ), ( 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88, 4, 88 ) }
Outer automorphisms :: reflexible
Dual of E27.579
Graph:: bipartite
	v = 13 e = 88 f = 23
	degree seq :: [ 8^11, 44^2 ]

E27.579 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-2 * Y2, Y2 * Y3^-2, (Y3^-1, Y1), (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, (R * Y1)^2, Y1^-3 * Y3^-1 * Y1^-8, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 45, 2, 46, 7, 51, 15, 59, 23, 67, 31, 75, 39, 83, 38, 82, 30, 74, 22, 66, 14, 58, 6, 50, 10, 54, 18, 62, 26, 70, 34, 78, 42, 86, 43, 87, 35, 79, 27, 71, 19, 63, 11, 55, 3, 47, 8, 52, 16, 60, 24, 68, 32, 76, 40, 84, 44, 88, 36, 80, 28, 72, 20, 64, 12, 56, 4, 48, 9, 53, 17, 61, 25, 69, 33, 77, 41, 85, 37, 81, 29, 73, 21, 65, 13, 57, 5, 49)(89, 133, 91, 135)(90, 134, 96, 140)(92, 136, 94, 138)(93, 137, 99, 143)(95, 139, 104, 148)(97, 141, 98, 142)(100, 144, 102, 146)(101, 145, 107, 151)(103, 147, 112, 156)(105, 149, 106, 150)(108, 152, 110, 154)(109, 153, 115, 159)(111, 155, 120, 164)(113, 157, 114, 158)(116, 160, 118, 162)(117, 161, 123, 167)(119, 163, 128, 172)(121, 165, 122, 166)(124, 168, 126, 170)(125, 169, 131, 175)(127, 171, 132, 176)(129, 173, 130, 174)
	L = (1, 92)(2, 97)(3, 94)(4, 91)(5, 100)(6, 89)(7, 105)(8, 98)(9, 96)(10, 90)(11, 102)(12, 99)(13, 108)(14, 93)(15, 113)(16, 106)(17, 104)(18, 95)(19, 110)(20, 107)(21, 116)(22, 101)(23, 121)(24, 114)(25, 112)(26, 103)(27, 118)(28, 115)(29, 124)(30, 109)(31, 129)(32, 122)(33, 120)(34, 111)(35, 126)(36, 123)(37, 132)(38, 117)(39, 125)(40, 130)(41, 128)(42, 119)(43, 127)(44, 131)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 8, 44, 8, 44 ), ( 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44, 8, 44 ) }
Outer automorphisms :: reflexible
Dual of E27.578
Graph:: bipartite
	v = 23 e = 88 f = 13
	degree seq :: [ 4^22, 88 ]

E27.580 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2), Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-2 * Y3^-1 * Y2^-1, (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3^-2 * Y2^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^3 * Y2^-6, Y1 * Y3^-1 * Y1^8 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3 * Y1^4 ]
Map:: non-degenerate
	R = (1, 45, 2, 46, 8, 52, 19, 63, 29, 73, 37, 81, 44, 88, 34, 78, 27, 71, 13, 57, 22, 66, 16, 60, 23, 67, 18, 62, 24, 68, 32, 76, 40, 84, 43, 87, 33, 77, 28, 72, 14, 58, 5, 49)(3, 47, 9, 53, 7, 51, 12, 56, 21, 65, 31, 75, 39, 83, 42, 86, 35, 79, 25, 69, 17, 61, 4, 48, 10, 54, 6, 50, 11, 55, 20, 64, 30, 74, 38, 82, 41, 85, 36, 80, 26, 70, 15, 59)(89, 133, 91, 135, 101, 145, 113, 157, 121, 165, 129, 173, 125, 169, 119, 163, 112, 156, 99, 143, 90, 134, 97, 141, 110, 154, 105, 149, 116, 160, 124, 168, 132, 176, 127, 171, 120, 164, 108, 152, 96, 140, 95, 139, 104, 148, 92, 136, 102, 146, 114, 158, 122, 166, 130, 174, 128, 172, 118, 162, 107, 151, 100, 144, 111, 155, 98, 142, 93, 137, 103, 147, 115, 159, 123, 167, 131, 175, 126, 170, 117, 161, 109, 153, 106, 150, 94, 138)
	L = (1, 92)(2, 98)(3, 102)(4, 101)(5, 105)(6, 104)(7, 89)(8, 94)(9, 93)(10, 110)(11, 111)(12, 90)(13, 114)(14, 113)(15, 116)(16, 91)(17, 115)(18, 95)(19, 99)(20, 106)(21, 96)(22, 103)(23, 97)(24, 100)(25, 122)(26, 121)(27, 124)(28, 123)(29, 108)(30, 112)(31, 107)(32, 109)(33, 130)(34, 129)(35, 132)(36, 131)(37, 118)(38, 120)(39, 117)(40, 119)(41, 128)(42, 125)(43, 127)(44, 126)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.577
Graph:: bipartite
	v = 3 e = 88 f = 33
	degree seq :: [ 44^2, 88 ]

E27.581 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3^2 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^2 * Y2^9, Y3^44 ]
Map:: non-degenerate
	R = (1, 45, 2, 46)(3, 47, 7, 51)(4, 48, 8, 52)(5, 49, 9, 53)(6, 50, 10, 54)(11, 55, 14, 58)(12, 56, 19, 63)(13, 57, 15, 59)(16, 60, 18, 62)(17, 61, 20, 64)(21, 65, 23, 67)(22, 66, 24, 68)(25, 69, 27, 71)(26, 70, 28, 72)(29, 73, 31, 75)(30, 74, 32, 76)(33, 77, 35, 79)(34, 78, 36, 80)(37, 81, 39, 83)(38, 82, 40, 84)(41, 85, 43, 87)(42, 86, 44, 88)(89, 133, 91, 135, 99, 143, 109, 153, 117, 161, 125, 169, 131, 175, 123, 167, 115, 159, 106, 150, 97, 141, 90, 134, 95, 139, 102, 146, 111, 155, 119, 163, 127, 171, 129, 173, 121, 165, 113, 157, 104, 148, 93, 137)(92, 136, 100, 144, 110, 154, 118, 162, 126, 170, 130, 174, 122, 166, 114, 158, 105, 149, 94, 138, 101, 145, 96, 140, 107, 151, 112, 156, 120, 164, 128, 172, 132, 176, 124, 168, 116, 160, 108, 152, 98, 142, 103, 147)
	L = (1, 92)(2, 96)(3, 100)(4, 102)(5, 103)(6, 89)(7, 107)(8, 99)(9, 101)(10, 90)(11, 110)(12, 111)(13, 91)(14, 112)(15, 95)(16, 98)(17, 93)(18, 94)(19, 109)(20, 97)(21, 118)(22, 119)(23, 120)(24, 117)(25, 108)(26, 104)(27, 105)(28, 106)(29, 126)(30, 127)(31, 128)(32, 125)(33, 116)(34, 113)(35, 114)(36, 115)(37, 130)(38, 129)(39, 132)(40, 131)(41, 124)(42, 121)(43, 122)(44, 123)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 8, 88, 8, 88 ), ( 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88, 8, 88 ) }
Outer automorphisms :: reflexible
Dual of E27.582
Graph:: bipartite
	v = 24 e = 88 f = 12
	degree seq :: [ 4^22, 44^2 ]

E27.582 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 22, 44})
Quotient :: dipole
Aut^+ = C44 (small group id <44, 2>)
Aut   = D88 (small group id <88, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^10 * Y3^-1 * Y2, (Y2^-1 * Y1)^22 ]
Map:: non-degenerate
	R = (1, 45, 2, 46, 6, 50, 4, 48)(3, 47, 7, 51, 13, 57, 10, 54)(5, 49, 8, 52, 14, 58, 11, 55)(9, 53, 15, 59, 21, 65, 18, 62)(12, 56, 16, 60, 22, 66, 19, 63)(17, 61, 23, 67, 29, 73, 26, 70)(20, 64, 24, 68, 30, 74, 27, 71)(25, 69, 31, 75, 37, 81, 34, 78)(28, 72, 32, 76, 38, 82, 35, 79)(33, 77, 39, 83, 43, 87, 41, 85)(36, 80, 40, 84, 44, 88, 42, 86)(89, 133, 91, 135, 97, 141, 105, 149, 113, 157, 121, 165, 128, 172, 120, 164, 112, 156, 104, 148, 96, 140, 90, 134, 95, 139, 103, 147, 111, 155, 119, 163, 127, 171, 132, 176, 126, 170, 118, 162, 110, 154, 102, 146, 94, 138, 101, 145, 109, 153, 117, 161, 125, 169, 131, 175, 130, 174, 123, 167, 115, 159, 107, 151, 99, 143, 92, 136, 98, 142, 106, 150, 114, 158, 122, 166, 129, 173, 124, 168, 116, 160, 108, 152, 100, 144, 93, 137)
	L = (1, 90)(2, 94)(3, 95)(4, 89)(5, 96)(6, 92)(7, 101)(8, 102)(9, 103)(10, 91)(11, 93)(12, 104)(13, 98)(14, 99)(15, 109)(16, 110)(17, 111)(18, 97)(19, 100)(20, 112)(21, 106)(22, 107)(23, 117)(24, 118)(25, 119)(26, 105)(27, 108)(28, 120)(29, 114)(30, 115)(31, 125)(32, 126)(33, 127)(34, 113)(35, 116)(36, 128)(37, 122)(38, 123)(39, 131)(40, 132)(41, 121)(42, 124)(43, 129)(44, 130)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176)
	local type(s) :: { ( 4, 44, 4, 44, 4, 44, 4, 44 ), ( 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44, 4, 44 ) }
Outer automorphisms :: reflexible
Dual of E27.581
Graph:: bipartite
	v = 12 e = 88 f = 24
	degree seq :: [ 8^11, 88 ]

E27.583 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y3^2 * Y1^-2, (Y2, Y3^-1), Y2^4, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-2 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 11, 59, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 28, 76)(13, 61, 24, 72, 38, 86, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(19, 67, 36, 84, 21, 69, 37, 85)(25, 73, 41, 89, 26, 74, 42, 90)(29, 77, 43, 91, 30, 78, 44, 92)(31, 79, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 110, 158, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 116, 164)(103, 151, 112, 160, 129, 177, 117, 165)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 121, 169, 135, 183, 125, 173)(108, 156, 122, 170, 136, 184, 126, 174)(113, 161, 130, 178, 141, 189, 132, 180)(114, 162, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(124, 172, 138, 186, 144, 192, 140, 188)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 127)(14, 118)(15, 122)(16, 99)(17, 123)(18, 124)(19, 119)(20, 126)(21, 102)(22, 112)(23, 117)(24, 135)(25, 111)(26, 105)(27, 114)(28, 113)(29, 116)(30, 107)(31, 134)(32, 136)(33, 109)(34, 137)(35, 138)(36, 139)(37, 140)(38, 129)(39, 128)(40, 120)(41, 131)(42, 130)(43, 133)(44, 132)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.590
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.584 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y1^-1 * Y3^-2 * Y1^-1, Y2^4, (Y2^-1, Y1^-1), Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1, Y3^-1 * Y2^2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 11, 59, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 28, 76)(13, 61, 24, 72, 40, 88, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(19, 67, 37, 85, 21, 69, 39, 87)(25, 73, 43, 91, 26, 74, 44, 92)(29, 77, 46, 94, 30, 78, 48, 96)(31, 79, 47, 95, 33, 81, 45, 93)(36, 84, 42, 90, 38, 86, 41, 89)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 110, 158, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 116, 164)(103, 151, 112, 160, 129, 177, 117, 165)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 121, 169, 137, 185, 125, 173)(108, 156, 122, 170, 138, 186, 126, 174)(113, 161, 130, 178, 143, 191, 133, 181)(114, 162, 131, 179, 141, 189, 135, 183)(123, 171, 139, 187, 132, 180, 142, 190)(124, 172, 140, 188, 134, 182, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 127)(14, 118)(15, 122)(16, 99)(17, 132)(18, 134)(19, 119)(20, 126)(21, 102)(22, 112)(23, 117)(24, 137)(25, 111)(26, 105)(27, 141)(28, 143)(29, 116)(30, 107)(31, 136)(32, 138)(33, 109)(34, 142)(35, 144)(36, 114)(37, 139)(38, 113)(39, 140)(40, 129)(41, 128)(42, 120)(43, 135)(44, 133)(45, 124)(46, 131)(47, 123)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.589
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.585 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y1^4, Y3^2 * Y1^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, Y2^4, Y3 * Y2^-2 * Y3^-1 * Y1^-1 * Y2^-2 * Y1, Y2^-1 * Y3 * Y2^-1 * Y1^-2 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2^2 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2 * Y2^-2 * Y3^-1, Y3 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 11, 59, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 28, 76)(13, 61, 24, 72, 40, 88, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(19, 67, 37, 85, 21, 69, 39, 87)(25, 73, 43, 91, 26, 74, 44, 92)(29, 77, 46, 94, 30, 78, 48, 96)(31, 79, 45, 93, 33, 81, 47, 95)(36, 84, 41, 89, 38, 86, 42, 90)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 110, 158, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 116, 164)(103, 151, 112, 160, 129, 177, 117, 165)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 121, 169, 137, 185, 125, 173)(108, 156, 122, 170, 138, 186, 126, 174)(113, 161, 130, 178, 141, 189, 133, 181)(114, 162, 131, 179, 143, 191, 135, 183)(123, 171, 139, 187, 134, 182, 142, 190)(124, 172, 140, 188, 132, 180, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 127)(14, 118)(15, 122)(16, 99)(17, 132)(18, 134)(19, 119)(20, 126)(21, 102)(22, 112)(23, 117)(24, 137)(25, 111)(26, 105)(27, 141)(28, 143)(29, 116)(30, 107)(31, 136)(32, 138)(33, 109)(34, 144)(35, 142)(36, 114)(37, 140)(38, 113)(39, 139)(40, 129)(41, 128)(42, 120)(43, 133)(44, 135)(45, 124)(46, 130)(47, 123)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.588
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.586 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, Y1^4, Y3^4, Y1 * Y3^-2 * Y1, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^4, Y3 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1, Y2 * Y3^2 * Y2^-1 * Y1^-2, (Y3^-1 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 7, 55, 19, 67)(6, 54, 23, 71, 27, 75, 24, 72)(9, 57, 28, 76, 21, 69, 31, 79)(10, 58, 33, 81, 12, 60, 34, 82)(11, 59, 36, 84, 22, 70, 37, 85)(14, 62, 29, 77, 44, 92, 41, 89)(15, 63, 30, 78, 17, 65, 32, 80)(20, 68, 35, 83, 25, 73, 38, 86)(39, 87, 46, 94, 43, 91, 47, 95)(40, 88, 45, 93, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 111, 159, 136, 184, 116, 164)(101, 149, 117, 165, 137, 185, 118, 166)(103, 151, 113, 161, 138, 186, 121, 169)(104, 152, 122, 170, 140, 188, 123, 171)(106, 154, 126, 174, 142, 190, 131, 179)(108, 156, 128, 176, 143, 191, 134, 182)(109, 157, 135, 183, 119, 167, 130, 178)(112, 160, 139, 187, 120, 168, 129, 177)(114, 162, 124, 172, 141, 189, 132, 180)(115, 163, 127, 175, 144, 192, 133, 181)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 126)(10, 101)(11, 131)(12, 98)(13, 124)(14, 136)(15, 122)(16, 127)(17, 99)(18, 129)(19, 130)(20, 123)(21, 128)(22, 134)(23, 132)(24, 133)(25, 102)(26, 113)(27, 121)(28, 112)(29, 142)(30, 117)(31, 109)(32, 105)(33, 115)(34, 114)(35, 118)(36, 120)(37, 119)(38, 107)(39, 141)(40, 140)(41, 143)(42, 110)(43, 144)(44, 138)(45, 139)(46, 137)(47, 125)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.587
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.587 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, Y3^4, (R * Y2)^2, Y1 * Y3 * Y1 * Y3^-1, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^4, (Y3, Y2), Y3 * Y1^-1 * Y3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 18, 66, 20, 68, 5, 53)(3, 51, 9, 57, 24, 72, 35, 83, 36, 84, 15, 63)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(6, 54, 11, 59, 25, 73, 39, 87, 40, 88, 21, 69)(13, 61, 26, 74, 42, 90, 46, 94, 47, 95, 32, 80)(14, 62, 34, 82, 28, 76, 16, 64, 37, 85, 27, 75)(19, 67, 38, 86, 30, 78, 23, 71, 41, 89, 29, 77)(31, 79, 45, 93, 44, 92, 33, 81, 48, 96, 43, 91)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 110, 158, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 117, 165)(103, 151, 112, 160, 129, 177, 119, 167)(104, 152, 120, 168, 138, 186, 121, 169)(106, 154, 123, 171, 139, 187, 125, 173)(108, 156, 124, 172, 140, 188, 126, 174)(113, 161, 130, 178, 141, 189, 134, 182)(114, 162, 131, 179, 142, 190, 135, 183)(116, 164, 132, 180, 143, 191, 136, 184)(118, 166, 133, 181, 144, 192, 137, 185)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 113)(6, 115)(7, 97)(8, 118)(9, 123)(10, 116)(11, 125)(12, 98)(13, 127)(14, 131)(15, 130)(16, 99)(17, 104)(18, 103)(19, 135)(20, 108)(21, 134)(22, 101)(23, 102)(24, 133)(25, 137)(26, 139)(27, 132)(28, 105)(29, 136)(30, 107)(31, 142)(32, 141)(33, 109)(34, 120)(35, 112)(36, 124)(37, 111)(38, 121)(39, 119)(40, 126)(41, 117)(42, 144)(43, 143)(44, 122)(45, 138)(46, 129)(47, 140)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.586
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.588 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, Y3^4, (Y3, Y2^-1), (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^4, Y1^6, Y1^2 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y1 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 24, 72, 20, 68, 5, 53)(3, 51, 13, 61, 35, 83, 45, 93, 25, 73, 9, 57)(4, 52, 17, 65, 42, 90, 40, 88, 26, 74, 10, 58)(6, 54, 21, 69, 46, 94, 41, 89, 27, 75, 11, 59)(7, 55, 22, 70, 47, 95, 39, 87, 28, 76, 12, 60)(14, 62, 29, 77, 43, 91, 18, 66, 32, 80, 36, 84)(15, 63, 30, 78, 48, 96, 23, 71, 34, 82, 37, 85)(16, 64, 31, 79, 44, 92, 19, 67, 33, 81, 38, 86)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 111, 159, 135, 183, 115, 163)(101, 149, 109, 157, 132, 180, 117, 165)(103, 151, 112, 160, 136, 184, 119, 167)(104, 152, 121, 169, 139, 187, 123, 171)(106, 154, 126, 174, 143, 191, 129, 177)(108, 156, 127, 175, 138, 186, 130, 178)(113, 161, 133, 181, 124, 172, 140, 188)(114, 162, 137, 185, 120, 168, 141, 189)(116, 164, 131, 179, 128, 176, 142, 190)(118, 166, 134, 182, 122, 170, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 133)(14, 135)(15, 137)(16, 99)(17, 139)(18, 103)(19, 141)(20, 138)(21, 140)(22, 101)(23, 102)(24, 136)(25, 144)(26, 132)(27, 134)(28, 104)(29, 143)(30, 142)(31, 105)(32, 108)(33, 131)(34, 107)(35, 130)(36, 124)(37, 123)(38, 109)(39, 120)(40, 110)(41, 112)(42, 125)(43, 118)(44, 121)(45, 119)(46, 127)(47, 116)(48, 117)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.585
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.589 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, (R * Y2)^2, Y2^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y3^4, (Y3, Y2), Y2 * Y1^-3 * Y2, Y2 * Y1^-1 * Y2 * Y1^2, Y3 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 20, 68, 5, 53)(3, 51, 13, 61, 11, 59, 6, 54, 21, 69, 9, 57)(4, 52, 17, 65, 36, 84, 33, 81, 24, 72, 10, 58)(7, 55, 22, 70, 40, 88, 34, 82, 25, 73, 12, 60)(15, 63, 26, 74, 38, 86, 19, 67, 29, 77, 31, 79)(16, 64, 27, 75, 41, 89, 23, 71, 30, 78, 32, 80)(18, 66, 28, 76, 42, 90, 46, 94, 47, 95, 37, 85)(35, 83, 45, 93, 44, 92, 39, 87, 48, 96, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 111, 159, 129, 177, 115, 163)(101, 149, 109, 157, 104, 152, 117, 165)(103, 151, 112, 160, 130, 178, 119, 167)(106, 154, 122, 170, 132, 180, 125, 173)(108, 156, 123, 171, 136, 184, 126, 174)(113, 161, 127, 175, 120, 168, 134, 182)(114, 162, 131, 179, 142, 190, 135, 183)(118, 166, 128, 176, 121, 169, 137, 185)(124, 172, 139, 187, 143, 191, 140, 188)(133, 181, 141, 189, 138, 186, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 115)(7, 97)(8, 120)(9, 122)(10, 124)(11, 125)(12, 98)(13, 127)(14, 129)(15, 131)(16, 99)(17, 133)(18, 103)(19, 135)(20, 132)(21, 134)(22, 101)(23, 102)(24, 138)(25, 104)(26, 139)(27, 105)(28, 108)(29, 140)(30, 107)(31, 141)(32, 109)(33, 142)(34, 110)(35, 112)(36, 143)(37, 118)(38, 144)(39, 119)(40, 116)(41, 117)(42, 121)(43, 123)(44, 126)(45, 128)(46, 130)(47, 136)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.584
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.590 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, (R * Y2)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y3, Y2), Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4, Y1^-1 * Y3^2 * Y1^-2, Y1 * Y3 * Y1^-1 * Y3 * Y1, Y2 * Y1 * Y3^2 * Y2^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 18, 66, 20, 68, 5, 53)(3, 51, 13, 61, 31, 79, 37, 85, 24, 72, 9, 57)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(6, 54, 21, 69, 40, 88, 39, 87, 25, 73, 11, 59)(14, 62, 26, 74, 42, 90, 48, 96, 45, 93, 32, 80)(15, 63, 27, 75, 34, 82, 16, 64, 28, 76, 33, 81)(19, 67, 29, 77, 41, 89, 23, 71, 30, 78, 38, 86)(35, 83, 46, 94, 44, 92, 36, 84, 47, 95, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 111, 159, 131, 179, 115, 163)(101, 149, 109, 157, 128, 176, 117, 165)(103, 151, 112, 160, 132, 180, 119, 167)(104, 152, 120, 168, 138, 186, 121, 169)(106, 154, 123, 171, 139, 187, 125, 173)(108, 156, 124, 172, 140, 188, 126, 174)(113, 161, 129, 177, 142, 190, 134, 182)(114, 162, 133, 181, 144, 192, 135, 183)(116, 164, 127, 175, 141, 189, 136, 184)(118, 166, 130, 178, 143, 191, 137, 185)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 115)(7, 97)(8, 118)(9, 123)(10, 116)(11, 125)(12, 98)(13, 129)(14, 131)(15, 133)(16, 99)(17, 104)(18, 103)(19, 135)(20, 108)(21, 134)(22, 101)(23, 102)(24, 130)(25, 137)(26, 139)(27, 127)(28, 105)(29, 136)(30, 107)(31, 124)(32, 142)(33, 120)(34, 109)(35, 144)(36, 110)(37, 112)(38, 121)(39, 119)(40, 126)(41, 117)(42, 143)(43, 141)(44, 122)(45, 140)(46, 138)(47, 128)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.583
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.591 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-2, Y3^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y3^2 * Y1^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 9, 57)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 20, 68, 23, 71, 11, 59)(10, 58, 27, 75, 12, 60, 28, 76)(14, 62, 24, 72, 38, 86, 31, 79)(15, 63, 34, 82, 16, 64, 35, 83)(19, 67, 37, 85, 21, 69, 36, 84)(25, 73, 41, 89, 26, 74, 42, 90)(29, 77, 44, 92, 30, 78, 43, 91)(32, 80, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 112, 160, 128, 176, 115, 163)(101, 149, 109, 157, 127, 175, 116, 164)(103, 151, 111, 159, 129, 177, 117, 165)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 122, 170, 135, 183, 125, 173)(108, 156, 121, 169, 136, 184, 126, 174)(113, 161, 130, 178, 141, 189, 132, 180)(114, 162, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(124, 172, 138, 186, 144, 192, 140, 188)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 117)(7, 97)(8, 103)(9, 121)(10, 101)(11, 126)(12, 98)(13, 122)(14, 128)(15, 118)(16, 99)(17, 123)(18, 124)(19, 102)(20, 125)(21, 119)(22, 112)(23, 115)(24, 135)(25, 109)(26, 105)(27, 114)(28, 113)(29, 107)(30, 116)(31, 136)(32, 134)(33, 110)(34, 138)(35, 137)(36, 140)(37, 139)(38, 129)(39, 127)(40, 120)(41, 130)(42, 131)(43, 132)(44, 133)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.603
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.592 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^2 * Y1, Y1^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, Y2 * Y1 * Y2^2 * Y1^-1 * Y2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1^-1 * Y3 * Y2 * Y1 * Y3^-1 * Y1, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 9, 57)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 20, 68, 23, 71, 11, 59)(10, 58, 27, 75, 12, 60, 28, 76)(14, 62, 24, 72, 40, 88, 31, 79)(15, 63, 34, 82, 16, 64, 35, 83)(19, 67, 39, 87, 21, 69, 37, 85)(25, 73, 43, 91, 26, 74, 44, 92)(29, 77, 48, 96, 30, 78, 46, 94)(32, 80, 45, 93, 33, 81, 47, 95)(36, 84, 41, 89, 38, 86, 42, 90)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 112, 160, 128, 176, 115, 163)(101, 149, 109, 157, 127, 175, 116, 164)(103, 151, 111, 159, 129, 177, 117, 165)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 122, 170, 137, 185, 125, 173)(108, 156, 121, 169, 138, 186, 126, 174)(113, 161, 130, 178, 141, 189, 133, 181)(114, 162, 131, 179, 143, 191, 135, 183)(123, 171, 139, 187, 134, 182, 142, 190)(124, 172, 140, 188, 132, 180, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 117)(7, 97)(8, 103)(9, 121)(10, 101)(11, 126)(12, 98)(13, 122)(14, 128)(15, 118)(16, 99)(17, 132)(18, 134)(19, 102)(20, 125)(21, 119)(22, 112)(23, 115)(24, 137)(25, 109)(26, 105)(27, 141)(28, 143)(29, 107)(30, 116)(31, 138)(32, 136)(33, 110)(34, 142)(35, 144)(36, 114)(37, 139)(38, 113)(39, 140)(40, 129)(41, 127)(42, 120)(43, 135)(44, 133)(45, 124)(46, 131)(47, 123)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.605
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.593 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, Y1 * Y3^-2 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 9, 57)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 20, 68, 23, 71, 11, 59)(10, 58, 27, 75, 12, 60, 28, 76)(14, 62, 24, 72, 40, 88, 31, 79)(15, 63, 34, 82, 16, 64, 35, 83)(19, 67, 39, 87, 21, 69, 37, 85)(25, 73, 43, 91, 26, 74, 44, 92)(29, 77, 48, 96, 30, 78, 46, 94)(32, 80, 47, 95, 33, 81, 45, 93)(36, 84, 42, 90, 38, 86, 41, 89)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 112, 160, 128, 176, 115, 163)(101, 149, 109, 157, 127, 175, 116, 164)(103, 151, 111, 159, 129, 177, 117, 165)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 122, 170, 137, 185, 125, 173)(108, 156, 121, 169, 138, 186, 126, 174)(113, 161, 130, 178, 143, 191, 133, 181)(114, 162, 131, 179, 141, 189, 135, 183)(123, 171, 139, 187, 132, 180, 142, 190)(124, 172, 140, 188, 134, 182, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 117)(7, 97)(8, 103)(9, 121)(10, 101)(11, 126)(12, 98)(13, 122)(14, 128)(15, 118)(16, 99)(17, 132)(18, 134)(19, 102)(20, 125)(21, 119)(22, 112)(23, 115)(24, 137)(25, 109)(26, 105)(27, 141)(28, 143)(29, 107)(30, 116)(31, 138)(32, 136)(33, 110)(34, 144)(35, 142)(36, 114)(37, 140)(38, 113)(39, 139)(40, 129)(41, 127)(42, 120)(43, 133)(44, 135)(45, 124)(46, 130)(47, 123)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.604
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.594 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y2^-1 * Y1^-2 * Y2^-1, Y3 * Y1^-2 * Y3, Y1^4, Y1^-1 * Y2^2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2^-2 * Y3^-1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(9, 57, 21, 69, 11, 59, 23, 71)(10, 58, 25, 73, 12, 60, 27, 75)(14, 62, 31, 79, 16, 64, 33, 81)(18, 66, 35, 83, 20, 68, 36, 84)(22, 70, 39, 87, 24, 72, 41, 89)(26, 74, 43, 91, 28, 76, 44, 92)(29, 77, 37, 85, 30, 78, 38, 86)(32, 80, 45, 93, 34, 82, 46, 94)(40, 88, 47, 95, 42, 90, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 116, 164)(106, 154, 122, 170, 108, 156, 124, 172)(109, 157, 125, 173, 111, 159, 126, 174)(110, 158, 128, 176, 112, 160, 130, 178)(113, 161, 127, 175, 115, 163, 129, 177)(117, 165, 133, 181, 119, 167, 134, 182)(118, 166, 136, 184, 120, 168, 138, 186)(121, 169, 135, 183, 123, 171, 137, 185)(131, 179, 141, 189, 132, 180, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 118)(10, 101)(11, 120)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 121)(18, 117)(19, 123)(20, 119)(21, 116)(22, 107)(23, 114)(24, 105)(25, 115)(26, 111)(27, 113)(28, 109)(29, 136)(30, 138)(31, 139)(32, 133)(33, 140)(34, 134)(35, 135)(36, 137)(37, 130)(38, 128)(39, 132)(40, 126)(41, 131)(42, 125)(43, 129)(44, 127)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.602
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.595 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y1 * Y2^-2 * Y1, Y2^-1 * Y3^-2 * Y2^-1, Y1^-1 * Y2^-2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y3)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(9, 57, 21, 69, 11, 59, 23, 71)(10, 58, 25, 73, 12, 60, 27, 75)(14, 62, 31, 79, 16, 64, 33, 81)(18, 66, 37, 85, 20, 68, 38, 86)(22, 70, 41, 89, 24, 72, 43, 91)(26, 74, 47, 95, 28, 76, 48, 96)(29, 77, 39, 87, 30, 78, 40, 88)(32, 80, 46, 94, 34, 82, 45, 93)(35, 83, 44, 92, 36, 84, 42, 90)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 116, 164)(106, 154, 122, 170, 108, 156, 124, 172)(109, 157, 125, 173, 111, 159, 126, 174)(110, 158, 128, 176, 112, 160, 130, 178)(113, 161, 127, 175, 115, 163, 129, 177)(117, 165, 135, 183, 119, 167, 136, 184)(118, 166, 138, 186, 120, 168, 140, 188)(121, 169, 137, 185, 123, 171, 139, 187)(131, 179, 144, 192, 132, 180, 143, 191)(133, 181, 142, 190, 134, 182, 141, 189)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 118)(10, 101)(11, 120)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 131)(18, 117)(19, 132)(20, 119)(21, 116)(22, 107)(23, 114)(24, 105)(25, 141)(26, 111)(27, 142)(28, 109)(29, 138)(30, 140)(31, 139)(32, 135)(33, 137)(34, 136)(35, 115)(36, 113)(37, 144)(38, 143)(39, 130)(40, 128)(41, 127)(42, 126)(43, 129)(44, 125)(45, 123)(46, 121)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.600
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.596 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, Y2^-2 * Y1^2, Y1 * Y3^-2 * Y1, Y2^-1 * Y1^-2 * Y2^-1, Y3 * Y2^-2 * Y3, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y3 * Y1^-1, (Y3 * Y2^-1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(9, 57, 21, 69, 11, 59, 23, 71)(10, 58, 25, 73, 12, 60, 27, 75)(14, 62, 31, 79, 16, 64, 33, 81)(18, 66, 37, 85, 20, 68, 38, 86)(22, 70, 41, 89, 24, 72, 43, 91)(26, 74, 47, 95, 28, 76, 48, 96)(29, 77, 39, 87, 30, 78, 40, 88)(32, 80, 45, 93, 34, 82, 46, 94)(35, 83, 42, 90, 36, 84, 44, 92)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 116, 164)(106, 154, 122, 170, 108, 156, 124, 172)(109, 157, 125, 173, 111, 159, 126, 174)(110, 158, 128, 176, 112, 160, 130, 178)(113, 161, 127, 175, 115, 163, 129, 177)(117, 165, 135, 183, 119, 167, 136, 184)(118, 166, 138, 186, 120, 168, 140, 188)(121, 169, 137, 185, 123, 171, 139, 187)(131, 179, 143, 191, 132, 180, 144, 192)(133, 181, 141, 189, 134, 182, 142, 190)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 118)(10, 101)(11, 120)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 131)(18, 117)(19, 132)(20, 119)(21, 116)(22, 107)(23, 114)(24, 105)(25, 141)(26, 111)(27, 142)(28, 109)(29, 138)(30, 140)(31, 137)(32, 135)(33, 139)(34, 136)(35, 115)(36, 113)(37, 143)(38, 144)(39, 130)(40, 128)(41, 129)(42, 126)(43, 127)(44, 125)(45, 123)(46, 121)(47, 134)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.601
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.597 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-2, Y3^-2 * Y1^-2, R * Y2 * R * Y2^-1, Y3^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, Y1 * Y2^-1 * Y3^2 * Y2 * Y1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3, Y2 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 7, 55, 20, 68)(6, 54, 23, 71, 27, 75, 24, 72)(9, 57, 28, 76, 21, 69, 31, 79)(10, 58, 33, 81, 12, 60, 35, 83)(11, 59, 36, 84, 22, 70, 37, 85)(14, 62, 29, 77, 44, 92, 41, 89)(15, 63, 34, 82, 17, 65, 38, 86)(19, 67, 30, 78, 25, 73, 32, 80)(39, 87, 46, 94, 43, 91, 47, 95)(40, 88, 45, 93, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 115, 163, 136, 184, 111, 159)(101, 149, 117, 165, 137, 185, 118, 166)(103, 151, 121, 169, 138, 186, 113, 161)(104, 152, 122, 170, 140, 188, 123, 171)(106, 154, 130, 178, 142, 190, 126, 174)(108, 156, 134, 182, 143, 191, 128, 176)(109, 157, 131, 179, 119, 167, 135, 183)(112, 160, 129, 177, 120, 168, 139, 187)(114, 162, 132, 180, 141, 189, 124, 172)(116, 164, 133, 181, 144, 192, 127, 175)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 126)(10, 101)(11, 130)(12, 98)(13, 132)(14, 136)(15, 122)(16, 133)(17, 99)(18, 129)(19, 123)(20, 131)(21, 128)(22, 134)(23, 124)(24, 127)(25, 102)(26, 113)(27, 121)(28, 120)(29, 142)(30, 117)(31, 119)(32, 105)(33, 116)(34, 118)(35, 114)(36, 112)(37, 109)(38, 107)(39, 141)(40, 140)(41, 143)(42, 110)(43, 144)(44, 138)(45, 139)(46, 137)(47, 125)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.607
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.598 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, Y2^4, Y3^-1 * Y1^-2 * Y3^-1, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^4, (R * Y1)^2, R * Y2 * R * Y2^-1, Y2 * Y1 * Y2^-1 * Y1 * Y3 * Y1^-1, Y3 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 7, 55, 20, 68)(6, 54, 23, 71, 27, 75, 24, 72)(9, 57, 28, 76, 21, 69, 31, 79)(10, 58, 33, 81, 12, 60, 35, 83)(11, 59, 36, 84, 22, 70, 37, 85)(14, 62, 29, 77, 44, 92, 41, 89)(15, 63, 34, 82, 17, 65, 38, 86)(19, 67, 30, 78, 25, 73, 32, 80)(39, 87, 47, 95, 43, 91, 46, 94)(40, 88, 48, 96, 42, 90, 45, 93)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 115, 163, 136, 184, 111, 159)(101, 149, 117, 165, 137, 185, 118, 166)(103, 151, 121, 169, 138, 186, 113, 161)(104, 152, 122, 170, 140, 188, 123, 171)(106, 154, 130, 178, 142, 190, 126, 174)(108, 156, 134, 182, 143, 191, 128, 176)(109, 157, 135, 183, 119, 167, 129, 177)(112, 160, 139, 187, 120, 168, 131, 179)(114, 162, 127, 175, 144, 192, 133, 181)(116, 164, 124, 172, 141, 189, 132, 180)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 126)(10, 101)(11, 130)(12, 98)(13, 127)(14, 136)(15, 122)(16, 124)(17, 99)(18, 139)(19, 123)(20, 135)(21, 128)(22, 134)(23, 133)(24, 132)(25, 102)(26, 113)(27, 121)(28, 109)(29, 142)(30, 117)(31, 112)(32, 105)(33, 144)(34, 118)(35, 141)(36, 119)(37, 120)(38, 107)(39, 114)(40, 140)(41, 143)(42, 110)(43, 116)(44, 138)(45, 129)(46, 137)(47, 125)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.606
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.599 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-2 * Y1^-2, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^2, Y3^4, R * Y2 * R * Y2^-1, Y2^4, Y2 * Y1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y3^-1 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 7, 55, 20, 68)(6, 54, 23, 71, 27, 75, 24, 72)(9, 57, 28, 76, 21, 69, 31, 79)(10, 58, 33, 81, 12, 60, 35, 83)(11, 59, 36, 84, 22, 70, 37, 85)(14, 62, 29, 77, 44, 92, 41, 89)(15, 63, 34, 82, 17, 65, 38, 86)(19, 67, 30, 78, 25, 73, 32, 80)(39, 87, 46, 94, 43, 91, 47, 95)(40, 88, 45, 93, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 115, 163, 136, 184, 111, 159)(101, 149, 117, 165, 137, 185, 118, 166)(103, 151, 121, 169, 138, 186, 113, 161)(104, 152, 122, 170, 140, 188, 123, 171)(106, 154, 130, 178, 142, 190, 126, 174)(108, 156, 134, 182, 143, 191, 128, 176)(109, 157, 135, 183, 119, 167, 131, 179)(112, 160, 139, 187, 120, 168, 129, 177)(114, 162, 124, 172, 141, 189, 132, 180)(116, 164, 127, 175, 144, 192, 133, 181)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 126)(10, 101)(11, 130)(12, 98)(13, 124)(14, 136)(15, 122)(16, 127)(17, 99)(18, 139)(19, 123)(20, 135)(21, 128)(22, 134)(23, 132)(24, 133)(25, 102)(26, 113)(27, 121)(28, 112)(29, 142)(30, 117)(31, 109)(32, 105)(33, 144)(34, 118)(35, 141)(36, 120)(37, 119)(38, 107)(39, 114)(40, 140)(41, 143)(42, 110)(43, 116)(44, 138)(45, 129)(46, 137)(47, 125)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.608
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.600 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2^4, Y3^4, Y3^-1 * Y1 * Y3 * Y1, Y1^2 * Y2^-1 * Y1^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 20, 68, 5, 53)(3, 51, 13, 61, 11, 59, 6, 54, 21, 69, 9, 57)(4, 52, 17, 65, 36, 84, 33, 81, 24, 72, 10, 58)(7, 55, 22, 70, 40, 88, 34, 82, 25, 73, 12, 60)(15, 63, 26, 74, 37, 85, 18, 66, 28, 76, 31, 79)(16, 64, 27, 75, 41, 89, 23, 71, 30, 78, 32, 80)(19, 67, 29, 77, 42, 90, 46, 94, 47, 95, 38, 86)(35, 83, 45, 93, 44, 92, 39, 87, 48, 96, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 114, 162, 129, 177, 111, 159)(101, 149, 109, 157, 104, 152, 117, 165)(103, 151, 119, 167, 130, 178, 112, 160)(106, 154, 124, 172, 132, 180, 122, 170)(108, 156, 126, 174, 136, 184, 123, 171)(113, 161, 133, 181, 120, 168, 127, 175)(115, 163, 131, 179, 142, 190, 135, 183)(118, 166, 137, 185, 121, 169, 128, 176)(125, 173, 139, 187, 143, 191, 140, 188)(134, 182, 141, 189, 138, 186, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 113)(6, 114)(7, 97)(8, 120)(9, 122)(10, 125)(11, 124)(12, 98)(13, 127)(14, 129)(15, 131)(16, 99)(17, 134)(18, 135)(19, 103)(20, 132)(21, 133)(22, 101)(23, 102)(24, 138)(25, 104)(26, 139)(27, 105)(28, 140)(29, 108)(30, 107)(31, 141)(32, 109)(33, 142)(34, 110)(35, 112)(36, 143)(37, 144)(38, 118)(39, 119)(40, 116)(41, 117)(42, 121)(43, 123)(44, 126)(45, 128)(46, 130)(47, 136)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.595
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.601 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, R * Y2 * R * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^6, Y3 * Y1^3 * Y3 * Y2^-2, Y1^2 * Y3 * Y2 * Y3 * Y1^-1 * Y2^-1, Y1^2 * Y2 * Y1^-1 * Y2 * Y3^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 2, 50, 8, 56, 24, 72, 20, 68, 5, 53)(3, 51, 13, 61, 35, 83, 45, 93, 25, 73, 9, 57)(4, 52, 17, 65, 42, 90, 40, 88, 26, 74, 10, 58)(6, 54, 21, 69, 46, 94, 41, 89, 27, 75, 11, 59)(7, 55, 22, 70, 47, 95, 39, 87, 28, 76, 12, 60)(14, 62, 29, 77, 44, 92, 19, 67, 33, 81, 36, 84)(15, 63, 30, 78, 48, 96, 23, 71, 34, 82, 37, 85)(16, 64, 31, 79, 43, 91, 18, 66, 32, 80, 38, 86)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 114, 162, 135, 183, 111, 159)(101, 149, 109, 157, 132, 180, 117, 165)(103, 151, 119, 167, 136, 184, 112, 160)(104, 152, 121, 169, 140, 188, 123, 171)(106, 154, 128, 176, 143, 191, 126, 174)(108, 156, 130, 178, 138, 186, 127, 175)(113, 161, 139, 187, 124, 172, 133, 181)(115, 163, 137, 185, 120, 168, 141, 189)(116, 164, 131, 179, 129, 177, 142, 190)(118, 166, 144, 192, 122, 170, 134, 182)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 113)(6, 114)(7, 97)(8, 122)(9, 126)(10, 129)(11, 128)(12, 98)(13, 133)(14, 135)(15, 137)(16, 99)(17, 140)(18, 141)(19, 103)(20, 138)(21, 139)(22, 101)(23, 102)(24, 136)(25, 144)(26, 132)(27, 134)(28, 104)(29, 143)(30, 142)(31, 105)(32, 131)(33, 108)(34, 107)(35, 130)(36, 124)(37, 123)(38, 109)(39, 120)(40, 110)(41, 112)(42, 125)(43, 121)(44, 118)(45, 119)(46, 127)(47, 116)(48, 117)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.596
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.602 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, R * Y2 * R * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y1 * Y3^-1 * Y1^-2 * Y3^-1, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 19, 67, 20, 68, 5, 53)(3, 51, 13, 61, 31, 79, 37, 85, 24, 72, 9, 57)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(6, 54, 21, 69, 40, 88, 39, 87, 25, 73, 11, 59)(14, 62, 26, 74, 42, 90, 48, 96, 45, 93, 32, 80)(15, 63, 27, 75, 34, 82, 16, 64, 28, 76, 33, 81)(18, 66, 29, 77, 41, 89, 23, 71, 30, 78, 38, 86)(35, 83, 46, 94, 44, 92, 36, 84, 47, 95, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 114, 162, 131, 179, 111, 159)(101, 149, 109, 157, 128, 176, 117, 165)(103, 151, 119, 167, 132, 180, 112, 160)(104, 152, 120, 168, 138, 186, 121, 169)(106, 154, 125, 173, 139, 187, 123, 171)(108, 156, 126, 174, 140, 188, 124, 172)(113, 161, 134, 182, 142, 190, 129, 177)(115, 163, 133, 181, 144, 192, 135, 183)(116, 164, 127, 175, 141, 189, 136, 184)(118, 166, 137, 185, 143, 191, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 113)(6, 114)(7, 97)(8, 118)(9, 123)(10, 116)(11, 125)(12, 98)(13, 129)(14, 131)(15, 133)(16, 99)(17, 104)(18, 135)(19, 103)(20, 108)(21, 134)(22, 101)(23, 102)(24, 130)(25, 137)(26, 139)(27, 127)(28, 105)(29, 136)(30, 107)(31, 124)(32, 142)(33, 120)(34, 109)(35, 144)(36, 110)(37, 112)(38, 121)(39, 119)(40, 126)(41, 117)(42, 143)(43, 141)(44, 122)(45, 140)(46, 138)(47, 128)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.594
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.603 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4, Y3^4, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y1 * Y3^-1 * Y1^-2 * Y3^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 18, 66, 20, 68, 5, 53)(3, 51, 13, 61, 31, 79, 37, 85, 24, 72, 9, 57)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(6, 54, 21, 69, 40, 88, 39, 87, 25, 73, 11, 59)(14, 62, 26, 74, 42, 90, 48, 96, 45, 93, 32, 80)(15, 63, 27, 75, 34, 82, 16, 64, 28, 76, 33, 81)(19, 67, 29, 77, 41, 89, 23, 71, 30, 78, 38, 86)(35, 83, 46, 94, 44, 92, 36, 84, 47, 95, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 112, 160, 131, 179, 115, 163)(101, 149, 109, 157, 128, 176, 117, 165)(103, 151, 111, 159, 132, 180, 119, 167)(104, 152, 120, 168, 138, 186, 121, 169)(106, 154, 124, 172, 139, 187, 125, 173)(108, 156, 123, 171, 140, 188, 126, 174)(113, 161, 130, 178, 142, 190, 134, 182)(114, 162, 133, 181, 144, 192, 135, 183)(116, 164, 127, 175, 141, 189, 136, 184)(118, 166, 129, 177, 143, 191, 137, 185)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 119)(7, 97)(8, 118)(9, 123)(10, 116)(11, 126)(12, 98)(13, 129)(14, 131)(15, 133)(16, 99)(17, 104)(18, 103)(19, 102)(20, 108)(21, 137)(22, 101)(23, 135)(24, 130)(25, 134)(26, 139)(27, 127)(28, 105)(29, 107)(30, 136)(31, 124)(32, 142)(33, 120)(34, 109)(35, 144)(36, 110)(37, 112)(38, 117)(39, 115)(40, 125)(41, 121)(42, 143)(43, 141)(44, 122)(45, 140)(46, 138)(47, 128)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.591
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.604 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1, Y2^4, Y3^4, (R * Y2 * Y3^-1)^2, Y1^6, Y1^2 * Y3^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y1 * Y2 * Y1^-1 * Y3^-2 * Y2 * Y1, Y3 * Y1^3 * Y3 * Y2^-2, Y1 * Y2^2 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 24, 72, 20, 68, 5, 53)(3, 51, 13, 61, 35, 83, 45, 93, 25, 73, 9, 57)(4, 52, 17, 65, 42, 90, 40, 88, 26, 74, 10, 58)(6, 54, 21, 69, 46, 94, 41, 89, 27, 75, 11, 59)(7, 55, 22, 70, 47, 95, 39, 87, 28, 76, 12, 60)(14, 62, 29, 77, 43, 91, 18, 66, 32, 80, 36, 84)(15, 63, 30, 78, 44, 92, 19, 67, 33, 81, 37, 85)(16, 64, 31, 79, 48, 96, 23, 71, 34, 82, 38, 86)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 112, 160, 135, 183, 115, 163)(101, 149, 109, 157, 132, 180, 117, 165)(103, 151, 111, 159, 136, 184, 119, 167)(104, 152, 121, 169, 139, 187, 123, 171)(106, 154, 127, 175, 143, 191, 129, 177)(108, 156, 126, 174, 138, 186, 130, 178)(113, 161, 134, 182, 124, 172, 140, 188)(114, 162, 137, 185, 120, 168, 141, 189)(116, 164, 131, 179, 128, 176, 142, 190)(118, 166, 133, 181, 122, 170, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 119)(7, 97)(8, 122)(9, 126)(10, 128)(11, 130)(12, 98)(13, 133)(14, 135)(15, 137)(16, 99)(17, 139)(18, 103)(19, 102)(20, 138)(21, 144)(22, 101)(23, 141)(24, 136)(25, 140)(26, 132)(27, 134)(28, 104)(29, 143)(30, 142)(31, 105)(32, 108)(33, 107)(34, 131)(35, 129)(36, 124)(37, 123)(38, 109)(39, 120)(40, 110)(41, 112)(42, 125)(43, 118)(44, 117)(45, 115)(46, 127)(47, 116)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.593
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.605 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, Y3^4, Y3^-1 * Y1 * Y3 * Y1, Y2 * Y1^-2 * Y2 * Y1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 20, 68, 5, 53)(3, 51, 13, 61, 11, 59, 6, 54, 21, 69, 9, 57)(4, 52, 17, 65, 36, 84, 33, 81, 24, 72, 10, 58)(7, 55, 22, 70, 40, 88, 34, 82, 25, 73, 12, 60)(15, 63, 26, 74, 41, 89, 23, 71, 30, 78, 31, 79)(16, 64, 27, 75, 38, 86, 19, 67, 29, 77, 32, 80)(18, 66, 28, 76, 42, 90, 46, 94, 47, 95, 37, 85)(35, 83, 45, 93, 44, 92, 39, 87, 48, 96, 43, 91)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 112, 160, 129, 177, 115, 163)(101, 149, 109, 157, 104, 152, 117, 165)(103, 151, 111, 159, 130, 178, 119, 167)(106, 154, 123, 171, 132, 180, 125, 173)(108, 156, 122, 170, 136, 184, 126, 174)(113, 161, 128, 176, 120, 168, 134, 182)(114, 162, 131, 179, 142, 190, 135, 183)(118, 166, 127, 175, 121, 169, 137, 185)(124, 172, 139, 187, 143, 191, 140, 188)(133, 181, 141, 189, 138, 186, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 119)(7, 97)(8, 120)(9, 122)(10, 124)(11, 126)(12, 98)(13, 127)(14, 129)(15, 131)(16, 99)(17, 133)(18, 103)(19, 102)(20, 132)(21, 137)(22, 101)(23, 135)(24, 138)(25, 104)(26, 139)(27, 105)(28, 108)(29, 107)(30, 140)(31, 141)(32, 109)(33, 142)(34, 110)(35, 112)(36, 143)(37, 118)(38, 117)(39, 115)(40, 116)(41, 144)(42, 121)(43, 123)(44, 125)(45, 128)(46, 130)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.592
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.606 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3^4, Y2^4, Y1 * Y3^-1 * Y1^-2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 18, 66, 20, 68, 5, 53)(3, 51, 9, 57, 24, 72, 35, 83, 36, 84, 15, 63)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(6, 54, 11, 59, 25, 73, 39, 87, 40, 88, 21, 69)(13, 61, 26, 74, 42, 90, 46, 94, 47, 95, 32, 80)(14, 62, 34, 82, 28, 76, 16, 64, 37, 85, 27, 75)(19, 67, 38, 86, 30, 78, 23, 71, 41, 89, 29, 77)(31, 79, 45, 93, 44, 92, 33, 81, 48, 96, 43, 91)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 112, 160, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 117, 165)(103, 151, 110, 158, 129, 177, 119, 167)(104, 152, 120, 168, 138, 186, 121, 169)(106, 154, 124, 172, 139, 187, 125, 173)(108, 156, 123, 171, 140, 188, 126, 174)(113, 161, 133, 181, 141, 189, 134, 182)(114, 162, 131, 179, 142, 190, 135, 183)(116, 164, 132, 180, 143, 191, 136, 184)(118, 166, 130, 178, 144, 192, 137, 185)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 113)(6, 119)(7, 97)(8, 118)(9, 123)(10, 116)(11, 126)(12, 98)(13, 127)(14, 131)(15, 130)(16, 99)(17, 104)(18, 103)(19, 102)(20, 108)(21, 137)(22, 101)(23, 135)(24, 133)(25, 134)(26, 139)(27, 132)(28, 105)(29, 107)(30, 136)(31, 142)(32, 141)(33, 109)(34, 120)(35, 112)(36, 124)(37, 111)(38, 117)(39, 115)(40, 125)(41, 121)(42, 144)(43, 143)(44, 122)(45, 138)(46, 129)(47, 140)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.598
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.607 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^4, Y3^4, Y3^-1 * Y1 * Y3 * Y1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^2 * Y1^3, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 13, 61, 20, 68, 5, 53)(3, 51, 9, 57, 21, 69, 6, 54, 11, 59, 15, 63)(4, 52, 17, 65, 36, 84, 31, 79, 24, 72, 10, 58)(7, 55, 22, 70, 40, 88, 32, 80, 25, 73, 12, 60)(14, 62, 33, 81, 30, 78, 23, 71, 41, 89, 26, 74)(16, 64, 35, 83, 29, 77, 19, 67, 38, 86, 27, 75)(18, 66, 28, 76, 42, 90, 45, 93, 47, 95, 37, 85)(34, 82, 43, 91, 48, 96, 39, 87, 44, 92, 46, 94)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 112, 160, 127, 175, 115, 163)(101, 149, 111, 159, 104, 152, 117, 165)(103, 151, 110, 158, 128, 176, 119, 167)(106, 154, 123, 171, 132, 180, 125, 173)(108, 156, 122, 170, 136, 184, 126, 174)(113, 161, 131, 179, 120, 168, 134, 182)(114, 162, 130, 178, 141, 189, 135, 183)(118, 166, 129, 177, 121, 169, 137, 185)(124, 172, 139, 187, 143, 191, 140, 188)(133, 181, 142, 190, 138, 186, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 113)(6, 119)(7, 97)(8, 120)(9, 122)(10, 124)(11, 126)(12, 98)(13, 127)(14, 130)(15, 129)(16, 99)(17, 133)(18, 103)(19, 102)(20, 132)(21, 137)(22, 101)(23, 135)(24, 138)(25, 104)(26, 139)(27, 105)(28, 108)(29, 107)(30, 140)(31, 141)(32, 109)(33, 142)(34, 112)(35, 111)(36, 143)(37, 118)(38, 117)(39, 115)(40, 116)(41, 144)(42, 121)(43, 123)(44, 125)(45, 128)(46, 131)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.597
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.608 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1 * Y3^-1, Y2 * Y3 * Y2^-1 * Y3, Y3^4, Y2^4, Y1^6, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y3 * Y1^3 * Y3 * Y2^-2, Y3 * Y1^-2 * Y2 * Y3^-1 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 24, 72, 20, 68, 5, 53)(3, 51, 9, 57, 25, 73, 45, 93, 40, 88, 15, 63)(4, 52, 17, 65, 42, 90, 37, 85, 26, 74, 10, 58)(6, 54, 11, 59, 27, 75, 39, 87, 46, 94, 21, 69)(7, 55, 22, 70, 47, 95, 35, 83, 28, 76, 12, 60)(13, 61, 29, 77, 43, 91, 18, 66, 32, 80, 36, 84)(14, 62, 38, 86, 33, 81, 19, 67, 44, 92, 30, 78)(16, 64, 41, 89, 34, 82, 23, 71, 48, 96, 31, 79)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 112, 160, 131, 179, 115, 163)(101, 149, 111, 159, 132, 180, 117, 165)(103, 151, 110, 158, 133, 181, 119, 167)(104, 152, 121, 169, 139, 187, 123, 171)(106, 154, 127, 175, 143, 191, 129, 177)(108, 156, 126, 174, 138, 186, 130, 178)(113, 161, 137, 185, 124, 172, 140, 188)(114, 162, 135, 183, 120, 168, 141, 189)(116, 164, 136, 184, 128, 176, 142, 190)(118, 166, 134, 182, 122, 170, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 113)(6, 119)(7, 97)(8, 122)(9, 126)(10, 128)(11, 130)(12, 98)(13, 131)(14, 135)(15, 134)(16, 99)(17, 139)(18, 103)(19, 102)(20, 138)(21, 144)(22, 101)(23, 141)(24, 133)(25, 140)(26, 132)(27, 137)(28, 104)(29, 143)(30, 142)(31, 105)(32, 108)(33, 107)(34, 136)(35, 120)(36, 124)(37, 109)(38, 123)(39, 112)(40, 129)(41, 111)(42, 125)(43, 118)(44, 117)(45, 115)(46, 127)(47, 116)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.599
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.609 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-2, Y3^4, R * Y2 * R * Y2^-1, Y1^4, (R * Y3)^2, Y1 * Y3^2 * Y1, Y2^4, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(6, 54, 9, 57, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 29, 77)(13, 61, 24, 72, 38, 86, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(18, 66, 36, 84, 21, 69, 37, 85)(25, 73, 41, 89, 26, 74, 42, 90)(28, 76, 43, 91, 30, 78, 44, 92)(31, 79, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 114, 162, 127, 175, 110, 158)(101, 149, 116, 164, 128, 176, 111, 159)(103, 151, 117, 165, 129, 177, 112, 160)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 124, 172, 135, 183, 121, 169)(108, 156, 126, 174, 136, 184, 122, 170)(113, 161, 130, 178, 141, 189, 132, 180)(115, 163, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(125, 173, 138, 186, 144, 192, 140, 188)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 121)(10, 101)(11, 124)(12, 98)(13, 127)(14, 118)(15, 126)(16, 99)(17, 123)(18, 119)(19, 125)(20, 122)(21, 102)(22, 112)(23, 117)(24, 135)(25, 116)(26, 105)(27, 115)(28, 111)(29, 113)(30, 107)(31, 134)(32, 136)(33, 109)(34, 139)(35, 140)(36, 137)(37, 138)(38, 129)(39, 128)(40, 120)(41, 133)(42, 132)(43, 131)(44, 130)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.613
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.610 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, Y1^-1 * Y3^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, R * Y2 * R * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2^4, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2^-2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y2^-2 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-2 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(6, 54, 9, 57, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 29, 77)(13, 61, 24, 72, 40, 88, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(18, 66, 37, 85, 21, 69, 39, 87)(25, 73, 43, 91, 26, 74, 44, 92)(28, 76, 46, 94, 30, 78, 48, 96)(31, 79, 47, 95, 33, 81, 45, 93)(36, 84, 42, 90, 38, 86, 41, 89)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 114, 162, 127, 175, 110, 158)(101, 149, 116, 164, 128, 176, 111, 159)(103, 151, 117, 165, 129, 177, 112, 160)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 124, 172, 137, 185, 121, 169)(108, 156, 126, 174, 138, 186, 122, 170)(113, 161, 130, 178, 143, 191, 133, 181)(115, 163, 131, 179, 141, 189, 135, 183)(123, 171, 139, 187, 132, 180, 142, 190)(125, 173, 140, 188, 134, 182, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 121)(10, 101)(11, 124)(12, 98)(13, 127)(14, 118)(15, 126)(16, 99)(17, 132)(18, 119)(19, 134)(20, 122)(21, 102)(22, 112)(23, 117)(24, 137)(25, 116)(26, 105)(27, 141)(28, 111)(29, 143)(30, 107)(31, 136)(32, 138)(33, 109)(34, 139)(35, 140)(36, 115)(37, 142)(38, 113)(39, 144)(40, 129)(41, 128)(42, 120)(43, 131)(44, 130)(45, 125)(46, 135)(47, 123)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.614
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.611 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y3^-2 * Y1^2, Y1^-1 * Y3^-2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2 * R * Y2^-1, Y3^4, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2^4, Y2^-2 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, Y3^-1 * Y1^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(6, 54, 9, 57, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 29, 77)(13, 61, 24, 72, 40, 88, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(18, 66, 37, 85, 21, 69, 39, 87)(25, 73, 43, 91, 26, 74, 44, 92)(28, 76, 46, 94, 30, 78, 48, 96)(31, 79, 45, 93, 33, 81, 47, 95)(36, 84, 41, 89, 38, 86, 42, 90)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 114, 162, 127, 175, 110, 158)(101, 149, 116, 164, 128, 176, 111, 159)(103, 151, 117, 165, 129, 177, 112, 160)(104, 152, 118, 166, 136, 184, 119, 167)(106, 154, 124, 172, 137, 185, 121, 169)(108, 156, 126, 174, 138, 186, 122, 170)(113, 161, 130, 178, 141, 189, 133, 181)(115, 163, 131, 179, 143, 191, 135, 183)(123, 171, 139, 187, 134, 182, 142, 190)(125, 173, 140, 188, 132, 180, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 121)(10, 101)(11, 124)(12, 98)(13, 127)(14, 118)(15, 126)(16, 99)(17, 132)(18, 119)(19, 134)(20, 122)(21, 102)(22, 112)(23, 117)(24, 137)(25, 116)(26, 105)(27, 141)(28, 111)(29, 143)(30, 107)(31, 136)(32, 138)(33, 109)(34, 140)(35, 139)(36, 115)(37, 144)(38, 113)(39, 142)(40, 129)(41, 128)(42, 120)(43, 130)(44, 131)(45, 125)(46, 133)(47, 123)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.612
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.612 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y2^4, Y2^2 * Y3^-2, Y3^4, Y1^-1 * Y3^-1 * Y1^-1 * Y3, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y2 * Y3^2 * Y2, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y3 * Y2, Y2 * Y1^-1 * Y3^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y1^2 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 20, 68, 5, 53)(3, 51, 13, 61, 33, 81, 43, 91, 24, 72, 9, 57)(4, 52, 17, 65, 39, 87, 38, 86, 25, 73, 10, 58)(6, 54, 21, 69, 44, 92, 42, 90, 26, 74, 11, 59)(7, 55, 22, 70, 45, 93, 37, 85, 27, 75, 12, 60)(14, 62, 28, 76, 46, 94, 48, 96, 47, 95, 34, 82)(15, 63, 29, 77, 40, 88, 18, 66, 31, 79, 35, 83)(16, 64, 30, 78, 41, 89, 19, 67, 32, 80, 36, 84)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 124, 172, 107, 155)(100, 148, 114, 162, 103, 151, 115, 163)(101, 149, 109, 157, 130, 178, 117, 165)(104, 152, 120, 168, 142, 190, 122, 170)(106, 154, 127, 175, 108, 156, 128, 176)(111, 159, 133, 181, 112, 160, 134, 182)(113, 161, 136, 184, 118, 166, 137, 185)(116, 164, 129, 177, 143, 191, 140, 188)(119, 167, 139, 187, 144, 192, 138, 186)(121, 169, 131, 179, 123, 171, 132, 180)(125, 173, 141, 189, 126, 174, 135, 183)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 113)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 131)(14, 103)(15, 102)(16, 99)(17, 130)(18, 138)(19, 139)(20, 135)(21, 132)(22, 101)(23, 134)(24, 136)(25, 142)(26, 137)(27, 104)(28, 108)(29, 107)(30, 105)(31, 140)(32, 129)(33, 127)(34, 118)(35, 117)(36, 109)(37, 119)(38, 144)(39, 143)(40, 122)(41, 120)(42, 115)(43, 114)(44, 128)(45, 116)(46, 123)(47, 141)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.611
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.613 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3^-2, Y3^-2 * Y2^-2, Y2^4, (R * Y1)^2, Y3^4, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3^2 * Y1^-2, Y2 * Y1^-1 * Y2 * Y1^2, (R * Y2 * Y3^-1)^2, R * Y1 * Y2^2 * R * Y1^-2, (Y3 * Y2^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 20, 68, 5, 53)(3, 51, 13, 61, 11, 59, 6, 54, 21, 69, 9, 57)(4, 52, 17, 65, 12, 60, 7, 55, 22, 70, 10, 58)(15, 63, 23, 71, 28, 76, 16, 64, 24, 72, 27, 75)(18, 66, 25, 73, 32, 80, 19, 67, 26, 74, 31, 79)(29, 77, 39, 87, 36, 84, 30, 78, 40, 88, 35, 83)(33, 81, 43, 91, 38, 86, 34, 82, 44, 92, 37, 85)(41, 89, 45, 93, 48, 96, 42, 90, 46, 94, 47, 95)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 114, 162, 103, 151, 115, 163)(101, 149, 109, 157, 104, 152, 117, 165)(106, 154, 121, 169, 108, 156, 122, 170)(111, 159, 125, 173, 112, 160, 126, 174)(113, 161, 127, 175, 118, 166, 128, 176)(119, 167, 131, 179, 120, 168, 132, 180)(123, 171, 135, 183, 124, 172, 136, 184)(129, 177, 137, 185, 130, 178, 138, 186)(133, 181, 141, 189, 134, 182, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 113)(6, 112)(7, 97)(8, 118)(9, 119)(10, 116)(11, 120)(12, 98)(13, 123)(14, 103)(15, 102)(16, 99)(17, 104)(18, 129)(19, 130)(20, 108)(21, 124)(22, 101)(23, 107)(24, 105)(25, 133)(26, 134)(27, 117)(28, 109)(29, 137)(30, 138)(31, 139)(32, 140)(33, 115)(34, 114)(35, 141)(36, 142)(37, 122)(38, 121)(39, 143)(40, 144)(41, 126)(42, 125)(43, 128)(44, 127)(45, 132)(46, 131)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.609
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.614 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y3^4, Y2^2 * Y3^-2, Y2^4, Y3 * Y2^2 * Y3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3, (R * Y3)^2, Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1^6, Y1 * Y3^-1 * Y1^-2 * Y2 * Y3^-1 * Y2^-1, Y1^2 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 20, 68, 5, 53)(3, 51, 13, 61, 33, 81, 42, 90, 24, 72, 9, 57)(4, 52, 17, 65, 39, 87, 37, 85, 25, 73, 10, 58)(6, 54, 21, 69, 44, 92, 43, 91, 26, 74, 11, 59)(7, 55, 22, 70, 45, 93, 38, 86, 27, 75, 12, 60)(14, 62, 28, 76, 46, 94, 48, 96, 47, 95, 34, 82)(15, 63, 29, 77, 41, 89, 19, 67, 32, 80, 35, 83)(16, 64, 30, 78, 40, 88, 18, 66, 31, 79, 36, 84)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 124, 172, 107, 155)(100, 148, 114, 162, 103, 151, 115, 163)(101, 149, 109, 157, 130, 178, 117, 165)(104, 152, 120, 168, 142, 190, 122, 170)(106, 154, 127, 175, 108, 156, 128, 176)(111, 159, 133, 181, 112, 160, 134, 182)(113, 161, 136, 184, 118, 166, 137, 185)(116, 164, 129, 177, 143, 191, 140, 188)(119, 167, 138, 186, 144, 192, 139, 187)(121, 169, 132, 180, 123, 171, 131, 179)(125, 173, 135, 183, 126, 174, 141, 189)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 113)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 131)(14, 103)(15, 102)(16, 99)(17, 130)(18, 138)(19, 139)(20, 135)(21, 132)(22, 101)(23, 133)(24, 137)(25, 142)(26, 136)(27, 104)(28, 108)(29, 107)(30, 105)(31, 129)(32, 140)(33, 128)(34, 118)(35, 117)(36, 109)(37, 144)(38, 119)(39, 143)(40, 120)(41, 122)(42, 115)(43, 114)(44, 127)(45, 116)(46, 123)(47, 141)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.610
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.615 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^2 * Y2, Y2 * Y1^-2 * Y2, Y2^-1 * Y3^2 * Y2^-1, Y1^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^2 * Y1^-2, Y3^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, R * Y2 * R * Y2^-1, Y3^-1 * Y2^-1 * Y1^-2 * Y3^-1 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(9, 57, 19, 67, 11, 59, 21, 69)(10, 58, 23, 71, 12, 60, 24, 72)(14, 62, 29, 77, 16, 64, 30, 78)(20, 68, 37, 85, 22, 70, 38, 86)(25, 73, 35, 83, 27, 75, 33, 81)(26, 74, 43, 91, 28, 76, 44, 92)(31, 79, 47, 95, 32, 80, 48, 96)(34, 82, 46, 94, 36, 84, 45, 93)(39, 87, 42, 90, 40, 88, 41, 89)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 103, 151, 110, 158)(106, 154, 118, 166, 108, 156, 116, 164)(109, 157, 121, 169, 111, 159, 123, 171)(113, 161, 127, 175, 114, 162, 128, 176)(115, 163, 129, 177, 117, 165, 131, 179)(119, 167, 135, 183, 120, 168, 136, 184)(122, 170, 138, 186, 124, 172, 137, 185)(125, 173, 141, 189, 126, 174, 142, 190)(130, 178, 144, 192, 132, 180, 143, 191)(133, 181, 139, 187, 134, 182, 140, 188)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 116)(10, 101)(11, 118)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 119)(18, 120)(19, 130)(20, 107)(21, 132)(22, 105)(23, 114)(24, 113)(25, 137)(26, 111)(27, 138)(28, 109)(29, 139)(30, 140)(31, 136)(32, 135)(33, 143)(34, 117)(35, 144)(36, 115)(37, 142)(38, 141)(39, 127)(40, 128)(41, 123)(42, 121)(43, 126)(44, 125)(45, 133)(46, 134)(47, 131)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.618
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.616 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y3^-1 * Y2^2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^4, Y1^4, Y2 * Y3^2 * Y2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y1 * Y2 * Y3 * Y1 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(9, 57, 19, 67, 11, 59, 21, 69)(10, 58, 23, 71, 12, 60, 24, 72)(14, 62, 29, 77, 16, 64, 30, 78)(20, 68, 37, 85, 22, 70, 38, 86)(25, 73, 35, 83, 27, 75, 33, 81)(26, 74, 43, 91, 28, 76, 44, 92)(31, 79, 47, 95, 32, 80, 48, 96)(34, 82, 45, 93, 36, 84, 46, 94)(39, 87, 41, 89, 40, 88, 42, 90)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 103, 151, 110, 158)(106, 154, 118, 166, 108, 156, 116, 164)(109, 157, 121, 169, 111, 159, 123, 171)(113, 161, 127, 175, 114, 162, 128, 176)(115, 163, 129, 177, 117, 165, 131, 179)(119, 167, 135, 183, 120, 168, 136, 184)(122, 170, 138, 186, 124, 172, 137, 185)(125, 173, 141, 189, 126, 174, 142, 190)(130, 178, 143, 191, 132, 180, 144, 192)(133, 181, 140, 188, 134, 182, 139, 187)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 116)(10, 101)(11, 118)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 119)(18, 120)(19, 130)(20, 107)(21, 132)(22, 105)(23, 114)(24, 113)(25, 137)(26, 111)(27, 138)(28, 109)(29, 139)(30, 140)(31, 136)(32, 135)(33, 144)(34, 117)(35, 143)(36, 115)(37, 141)(38, 142)(39, 127)(40, 128)(41, 123)(42, 121)(43, 126)(44, 125)(45, 134)(46, 133)(47, 129)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.617
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.617 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y3 * Y2 * Y3 * Y2^-1, Y2^4, (R * Y1)^2, (R * Y3)^2, Y1^3 * Y2^2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1^-2, Y1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1)^3, Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 23, 71, 5, 53)(3, 51, 13, 61, 28, 76, 6, 54, 26, 74, 16, 64)(4, 52, 18, 66, 43, 91, 41, 89, 25, 73, 19, 67)(7, 55, 29, 77, 10, 58, 35, 83, 46, 94, 30, 78)(9, 57, 32, 80, 38, 86, 11, 59, 37, 85, 33, 81)(12, 60, 39, 87, 31, 79, 40, 88, 48, 96, 22, 70)(15, 63, 42, 90, 21, 69, 27, 75, 44, 92, 24, 72)(17, 65, 45, 93, 36, 84, 20, 68, 47, 95, 34, 82)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 119, 167, 107, 155)(100, 148, 113, 161, 137, 185, 116, 164)(101, 149, 117, 165, 104, 152, 120, 168)(103, 151, 111, 159, 131, 179, 123, 171)(106, 154, 130, 178, 126, 174, 132, 180)(108, 156, 122, 170, 136, 184, 109, 157)(112, 160, 115, 163, 124, 172, 139, 187)(114, 162, 133, 181, 121, 169, 128, 176)(118, 166, 141, 189, 127, 175, 143, 191)(125, 173, 134, 182, 142, 190, 129, 177)(135, 183, 138, 186, 144, 192, 140, 188)
	L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 118)(6, 123)(7, 97)(8, 127)(9, 122)(10, 108)(11, 109)(12, 98)(13, 132)(14, 137)(15, 113)(16, 134)(17, 99)(18, 104)(19, 135)(20, 102)(21, 128)(22, 121)(23, 126)(24, 133)(25, 101)(26, 130)(27, 116)(28, 129)(29, 139)(30, 136)(31, 114)(32, 141)(33, 138)(34, 105)(35, 110)(36, 107)(37, 143)(38, 140)(39, 142)(40, 119)(41, 131)(42, 124)(43, 144)(44, 112)(45, 117)(46, 115)(47, 120)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.616
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.618 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2^2, Y3 * Y2 * Y3 * Y2^-1, R * Y2 * R * Y2^-1, Y3^-1 * Y2^-2 * Y3^-1, Y3^4, Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 14, 62, 20, 68, 5, 53)(3, 51, 13, 61, 24, 72, 6, 54, 23, 71, 16, 64)(4, 52, 18, 66, 12, 60, 7, 55, 22, 70, 10, 58)(9, 57, 25, 73, 30, 78, 11, 59, 29, 77, 27, 75)(15, 63, 35, 83, 34, 82, 17, 65, 38, 86, 32, 80)(19, 67, 41, 89, 44, 92, 21, 69, 43, 91, 42, 90)(26, 74, 33, 81, 48, 96, 28, 76, 31, 79, 46, 94)(36, 84, 40, 88, 45, 93, 37, 85, 39, 87, 47, 95)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 116, 164, 107, 155)(100, 148, 113, 161, 103, 151, 111, 159)(101, 149, 115, 163, 104, 152, 117, 165)(106, 154, 124, 172, 108, 156, 122, 170)(109, 157, 127, 175, 119, 167, 129, 177)(112, 160, 132, 180, 120, 168, 133, 181)(114, 162, 135, 183, 118, 166, 136, 184)(121, 169, 141, 189, 125, 173, 143, 191)(123, 171, 128, 176, 126, 174, 130, 178)(131, 179, 137, 185, 134, 182, 139, 187)(138, 186, 144, 192, 140, 188, 142, 190)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 114)(6, 113)(7, 97)(8, 118)(9, 122)(10, 116)(11, 124)(12, 98)(13, 128)(14, 103)(15, 102)(16, 131)(17, 99)(18, 104)(19, 136)(20, 108)(21, 135)(22, 101)(23, 130)(24, 134)(25, 142)(26, 107)(27, 129)(28, 105)(29, 144)(30, 127)(31, 123)(32, 119)(33, 126)(34, 109)(35, 120)(36, 139)(37, 137)(38, 112)(39, 115)(40, 117)(41, 132)(42, 141)(43, 133)(44, 143)(45, 140)(46, 125)(47, 138)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.615
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.619 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 x (C3 : Q8) (small group id <48, 34>)
Aut   = C2 x ((C12 x C2) : C2) (small group id <96, 208>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^-2, Y3^2 * Y1^2, Y1^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3^-2 * Y2^-2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, R * Y2 * R * Y2^-1, (R * Y1)^2, Y1^-1 * Y3^2 * Y1^-1, Y2^4, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 6, 54, 9, 57)(4, 52, 15, 63, 7, 55, 16, 64)(10, 58, 19, 67, 12, 60, 20, 68)(13, 61, 21, 69, 14, 62, 22, 70)(17, 65, 25, 73, 18, 66, 26, 74)(23, 71, 31, 79, 24, 72, 32, 80)(27, 75, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 30, 78, 38, 86)(33, 81, 41, 89, 34, 82, 42, 90)(39, 87, 43, 91, 40, 88, 44, 92)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 110, 158, 103, 151, 109, 157)(106, 154, 114, 162, 108, 156, 113, 161)(111, 159, 117, 165, 112, 160, 118, 166)(115, 163, 121, 169, 116, 164, 122, 170)(119, 167, 126, 174, 120, 168, 125, 173)(123, 171, 130, 178, 124, 172, 129, 177)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191)
	L = (1, 100)(2, 106)(3, 109)(4, 104)(5, 108)(6, 110)(7, 97)(8, 103)(9, 113)(10, 101)(11, 114)(12, 98)(13, 102)(14, 99)(15, 119)(16, 120)(17, 107)(18, 105)(19, 123)(20, 124)(21, 125)(22, 126)(23, 112)(24, 111)(25, 129)(26, 130)(27, 116)(28, 115)(29, 118)(30, 117)(31, 135)(32, 136)(33, 122)(34, 121)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.620
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.620 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = C2 x (C3 : Q8) (small group id <48, 34>)
Aut   = C2 x ((C12 x C2) : C2) (small group id <96, 208>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^2 * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2, Y2 * Y3^-2 * Y2, Y3^4, (R * Y1)^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 21, 69, 18, 66, 5, 53)(3, 51, 13, 61, 29, 77, 36, 84, 22, 70, 9, 57)(4, 52, 17, 65, 33, 81, 37, 85, 23, 71, 10, 58)(6, 54, 19, 67, 34, 82, 38, 86, 24, 72, 11, 59)(7, 55, 20, 68, 35, 83, 39, 87, 25, 73, 12, 60)(14, 62, 26, 74, 40, 88, 46, 94, 43, 91, 30, 78)(15, 63, 27, 75, 41, 89, 47, 95, 44, 92, 31, 79)(16, 64, 28, 76, 42, 90, 48, 96, 45, 93, 32, 80)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 112, 160, 103, 151, 111, 159)(101, 149, 109, 157, 126, 174, 115, 163)(104, 152, 118, 166, 136, 184, 120, 168)(106, 154, 124, 172, 108, 156, 123, 171)(113, 161, 128, 176, 116, 164, 127, 175)(114, 162, 125, 173, 139, 187, 130, 178)(117, 165, 132, 180, 142, 190, 134, 182)(119, 167, 138, 186, 121, 169, 137, 185)(129, 177, 141, 189, 131, 179, 140, 188)(133, 181, 144, 192, 135, 183, 143, 191)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 113)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 127)(14, 103)(15, 102)(16, 99)(17, 126)(18, 129)(19, 128)(20, 101)(21, 133)(22, 137)(23, 136)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 140)(30, 116)(31, 115)(32, 109)(33, 139)(34, 141)(35, 114)(36, 143)(37, 142)(38, 144)(39, 117)(40, 121)(41, 120)(42, 118)(43, 131)(44, 130)(45, 125)(46, 135)(47, 134)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.619
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.621 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^4, Y2^-2 * Y1^2, Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 10, 58, 6, 54, 8, 56)(4, 52, 12, 60, 16, 64, 13, 61)(9, 57, 18, 66, 15, 63, 19, 67)(11, 59, 21, 69, 14, 62, 22, 70)(17, 65, 25, 73, 20, 68, 26, 74)(23, 71, 31, 79, 24, 72, 32, 80)(27, 75, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 30, 78, 38, 86)(33, 81, 41, 89, 34, 82, 42, 90)(39, 87, 44, 92, 40, 88, 43, 91)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 103, 151, 102, 150)(98, 146, 104, 152, 101, 149, 106, 154)(100, 148, 107, 155, 112, 160, 110, 158)(105, 153, 113, 161, 111, 159, 116, 164)(108, 156, 118, 166, 109, 157, 117, 165)(114, 162, 122, 170, 115, 163, 121, 169)(119, 167, 126, 174, 120, 168, 125, 173)(123, 171, 130, 178, 124, 172, 129, 177)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 141, 189, 136, 184, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 97)(5, 111)(6, 110)(7, 112)(8, 113)(9, 98)(10, 116)(11, 99)(12, 119)(13, 120)(14, 102)(15, 101)(16, 103)(17, 104)(18, 123)(19, 124)(20, 106)(21, 125)(22, 126)(23, 108)(24, 109)(25, 129)(26, 130)(27, 114)(28, 115)(29, 117)(30, 118)(31, 135)(32, 136)(33, 121)(34, 122)(35, 139)(36, 140)(37, 141)(38, 142)(39, 127)(40, 128)(41, 143)(42, 144)(43, 131)(44, 132)(45, 133)(46, 134)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.626
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.622 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^4, Y2^-1 * Y3^2 * Y2^-1, Y1^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y1)^2, Y2^2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y1 * Y2)^2, (Y3^-1 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59)(4, 52, 15, 63, 7, 55, 16, 64)(10, 58, 19, 67, 12, 60, 20, 68)(13, 61, 21, 69, 14, 62, 22, 70)(17, 65, 25, 73, 18, 66, 26, 74)(23, 71, 31, 79, 24, 72, 32, 80)(27, 75, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 30, 78, 38, 86)(33, 81, 41, 89, 34, 82, 42, 90)(39, 87, 43, 91, 40, 88, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 110, 158, 103, 151, 109, 157)(106, 154, 114, 162, 108, 156, 113, 161)(111, 159, 118, 166, 112, 160, 117, 165)(115, 163, 122, 170, 116, 164, 121, 169)(119, 167, 125, 173, 120, 168, 126, 174)(123, 171, 129, 177, 124, 172, 130, 178)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191)
	L = (1, 100)(2, 106)(3, 109)(4, 104)(5, 108)(6, 110)(7, 97)(8, 103)(9, 113)(10, 101)(11, 114)(12, 98)(13, 102)(14, 99)(15, 119)(16, 120)(17, 107)(18, 105)(19, 123)(20, 124)(21, 125)(22, 126)(23, 112)(24, 111)(25, 129)(26, 130)(27, 116)(28, 115)(29, 118)(30, 117)(31, 135)(32, 136)(33, 122)(34, 121)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.627
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.623 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^-1 * Y1^-2 * Y2^-1, Y1^4, Y2^-2 * Y1^2, Y2^-1 * Y1^-2 * Y2^-1, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, (Y3 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 6, 54, 13, 61)(4, 52, 14, 62, 18, 66, 15, 63)(8, 56, 19, 67, 10, 58, 21, 69)(9, 57, 22, 70, 17, 65, 23, 71)(12, 60, 24, 72, 16, 64, 20, 68)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 48, 96, 44, 92, 46, 94)(97, 145, 99, 147, 103, 151, 102, 150)(98, 146, 104, 152, 101, 149, 106, 154)(100, 148, 108, 156, 114, 162, 112, 160)(105, 153, 116, 164, 113, 161, 120, 168)(107, 155, 121, 169, 109, 157, 123, 171)(110, 158, 124, 172, 111, 159, 122, 170)(115, 163, 125, 173, 117, 165, 127, 175)(118, 166, 128, 176, 119, 167, 126, 174)(129, 177, 137, 185, 130, 178, 139, 187)(131, 179, 140, 188, 132, 180, 138, 186)(133, 181, 141, 189, 134, 182, 143, 191)(135, 183, 144, 192, 136, 184, 142, 190)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 113)(6, 112)(7, 114)(8, 116)(9, 98)(10, 120)(11, 122)(12, 99)(13, 124)(14, 121)(15, 123)(16, 102)(17, 101)(18, 103)(19, 126)(20, 104)(21, 128)(22, 125)(23, 127)(24, 106)(25, 110)(26, 107)(27, 111)(28, 109)(29, 118)(30, 115)(31, 119)(32, 117)(33, 138)(34, 140)(35, 137)(36, 139)(37, 142)(38, 144)(39, 141)(40, 143)(41, 131)(42, 129)(43, 132)(44, 130)(45, 135)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.625
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.624 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y3^2, R^2, (Y2 * Y1^-1)^2, Y1^4, Y2^2 * Y1^2, (R * Y2)^2, Y1^-1 * Y2^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 6, 54, 10, 58)(4, 52, 12, 60, 16, 64, 13, 61)(9, 57, 18, 66, 15, 63, 19, 67)(11, 59, 21, 69, 14, 62, 22, 70)(17, 65, 25, 73, 20, 68, 26, 74)(23, 71, 31, 79, 24, 72, 32, 80)(27, 75, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 30, 78, 38, 86)(33, 81, 41, 89, 34, 82, 42, 90)(39, 87, 44, 92, 40, 88, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 103, 151, 102, 150)(98, 146, 104, 152, 101, 149, 106, 154)(100, 148, 107, 155, 112, 160, 110, 158)(105, 153, 113, 161, 111, 159, 116, 164)(108, 156, 117, 165, 109, 157, 118, 166)(114, 162, 121, 169, 115, 163, 122, 170)(119, 167, 125, 173, 120, 168, 126, 174)(123, 171, 129, 177, 124, 172, 130, 178)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 141, 189, 136, 184, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 97)(5, 111)(6, 110)(7, 112)(8, 113)(9, 98)(10, 116)(11, 99)(12, 119)(13, 120)(14, 102)(15, 101)(16, 103)(17, 104)(18, 123)(19, 124)(20, 106)(21, 125)(22, 126)(23, 108)(24, 109)(25, 129)(26, 130)(27, 114)(28, 115)(29, 117)(30, 118)(31, 135)(32, 136)(33, 121)(34, 122)(35, 139)(36, 140)(37, 141)(38, 142)(39, 127)(40, 128)(41, 143)(42, 144)(43, 131)(44, 132)(45, 133)(46, 134)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.628
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.625 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, Y2^4, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 19, 67, 5, 53)(3, 51, 10, 58, 21, 69, 38, 86, 32, 80, 13, 61)(4, 52, 14, 62, 33, 81, 41, 89, 22, 70, 15, 63)(6, 54, 8, 56, 23, 71, 36, 84, 34, 82, 17, 65)(9, 57, 26, 74, 18, 66, 35, 83, 37, 85, 27, 75)(11, 59, 24, 72, 39, 87, 46, 94, 43, 91, 29, 77)(12, 60, 30, 78, 44, 92, 47, 95, 40, 88, 25, 73)(16, 64, 31, 79, 45, 93, 48, 96, 42, 90, 28, 76)(97, 145, 99, 147, 107, 155, 102, 150)(98, 146, 104, 152, 120, 168, 106, 154)(100, 148, 108, 156, 122, 170, 112, 160)(101, 149, 113, 161, 125, 173, 109, 157)(103, 151, 117, 165, 135, 183, 119, 167)(105, 153, 121, 169, 111, 159, 124, 172)(110, 158, 127, 175, 114, 162, 126, 174)(115, 163, 128, 176, 139, 187, 130, 178)(116, 164, 132, 180, 142, 190, 134, 182)(118, 166, 136, 184, 123, 171, 138, 186)(129, 177, 140, 188, 131, 179, 141, 189)(133, 181, 143, 191, 137, 185, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 114)(6, 112)(7, 118)(8, 121)(9, 98)(10, 124)(11, 122)(12, 99)(13, 127)(14, 125)(15, 120)(16, 102)(17, 126)(18, 101)(19, 129)(20, 133)(21, 136)(22, 103)(23, 138)(24, 111)(25, 104)(26, 107)(27, 135)(28, 106)(29, 110)(30, 113)(31, 109)(32, 140)(33, 115)(34, 141)(35, 139)(36, 143)(37, 116)(38, 144)(39, 123)(40, 117)(41, 142)(42, 119)(43, 131)(44, 128)(45, 130)(46, 137)(47, 132)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.623
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.626 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, Y1^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y2)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 36, 84, 21, 69, 8, 56)(4, 52, 14, 62, 33, 81, 41, 89, 22, 70, 15, 63)(6, 54, 19, 67, 35, 83, 38, 86, 23, 71, 10, 58)(9, 57, 26, 74, 17, 65, 34, 82, 37, 85, 27, 75)(12, 60, 24, 72, 39, 87, 46, 94, 43, 91, 30, 78)(13, 61, 28, 76, 40, 88, 48, 96, 44, 92, 32, 80)(16, 64, 25, 73, 42, 90, 47, 95, 45, 93, 31, 79)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 120, 168, 106, 154)(100, 148, 109, 157, 122, 170, 112, 160)(101, 149, 107, 155, 126, 174, 115, 163)(103, 151, 117, 165, 135, 183, 119, 167)(105, 153, 121, 169, 111, 159, 124, 172)(110, 158, 128, 176, 113, 161, 127, 175)(114, 162, 125, 173, 139, 187, 131, 179)(116, 164, 132, 180, 142, 190, 134, 182)(118, 166, 136, 184, 123, 171, 138, 186)(129, 177, 140, 188, 130, 178, 141, 189)(133, 181, 143, 191, 137, 185, 144, 192)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 113)(6, 112)(7, 118)(8, 121)(9, 98)(10, 124)(11, 127)(12, 122)(13, 99)(14, 126)(15, 120)(16, 102)(17, 101)(18, 129)(19, 128)(20, 133)(21, 136)(22, 103)(23, 138)(24, 111)(25, 104)(26, 108)(27, 135)(28, 106)(29, 140)(30, 110)(31, 107)(32, 115)(33, 114)(34, 139)(35, 141)(36, 143)(37, 116)(38, 144)(39, 123)(40, 117)(41, 142)(42, 119)(43, 130)(44, 125)(45, 131)(46, 137)(47, 132)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.621
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.627 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>)
Aut   = (C6 x D8) : C2 (small group id <96, 211>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^-2, (R * Y1)^2, Y3 * Y2^-2 * Y3, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, (Y1^-1 * Y2^-1)^2, (Y2^-1 * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1^6, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 21, 69, 19, 67, 5, 53)(3, 51, 13, 61, 29, 77, 38, 86, 22, 70, 11, 59)(4, 52, 17, 65, 33, 81, 37, 85, 23, 71, 10, 58)(6, 54, 18, 66, 34, 82, 36, 84, 24, 72, 9, 57)(7, 55, 20, 68, 35, 83, 39, 87, 25, 73, 12, 60)(14, 62, 26, 74, 40, 88, 46, 94, 43, 91, 31, 79)(15, 63, 28, 76, 41, 89, 48, 96, 44, 92, 30, 78)(16, 64, 27, 75, 42, 90, 47, 95, 45, 93, 32, 80)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 112, 160, 103, 151, 111, 159)(101, 149, 114, 162, 127, 175, 109, 157)(104, 152, 118, 166, 136, 184, 120, 168)(106, 154, 124, 172, 108, 156, 123, 171)(113, 161, 126, 174, 116, 164, 128, 176)(115, 163, 125, 173, 139, 187, 130, 178)(117, 165, 132, 180, 142, 190, 134, 182)(119, 167, 138, 186, 121, 169, 137, 185)(129, 177, 141, 189, 131, 179, 140, 188)(133, 181, 144, 192, 135, 183, 143, 191)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 113)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 126)(14, 103)(15, 102)(16, 99)(17, 127)(18, 128)(19, 129)(20, 101)(21, 133)(22, 137)(23, 136)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 140)(30, 114)(31, 116)(32, 109)(33, 139)(34, 141)(35, 115)(36, 143)(37, 142)(38, 144)(39, 117)(40, 121)(41, 120)(42, 118)(43, 131)(44, 130)(45, 125)(46, 135)(47, 134)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.622
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.628 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 4, 6})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^4, (Y1^-1 * Y2^-1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3 * Y1 * Y3 * Y2, Y3 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, (Y3 * Y1^-2)^2, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 19, 67, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 21, 69, 10, 58)(4, 52, 14, 62, 33, 81, 41, 89, 22, 70, 15, 63)(6, 54, 17, 65, 34, 82, 36, 84, 23, 71, 8, 56)(9, 57, 26, 74, 18, 66, 35, 83, 37, 85, 27, 75)(12, 60, 24, 72, 39, 87, 46, 94, 43, 91, 31, 79)(13, 61, 25, 73, 40, 88, 47, 95, 44, 92, 32, 80)(16, 64, 28, 76, 42, 90, 48, 96, 45, 93, 30, 78)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 120, 168, 106, 154)(100, 148, 109, 157, 122, 170, 112, 160)(101, 149, 113, 161, 127, 175, 107, 155)(103, 151, 117, 165, 135, 183, 119, 167)(105, 153, 121, 169, 111, 159, 124, 172)(110, 158, 126, 174, 114, 162, 128, 176)(115, 163, 125, 173, 139, 187, 130, 178)(116, 164, 132, 180, 142, 190, 134, 182)(118, 166, 136, 184, 123, 171, 138, 186)(129, 177, 140, 188, 131, 179, 141, 189)(133, 181, 143, 191, 137, 185, 144, 192)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 114)(6, 112)(7, 118)(8, 121)(9, 98)(10, 124)(11, 126)(12, 122)(13, 99)(14, 127)(15, 120)(16, 102)(17, 128)(18, 101)(19, 129)(20, 133)(21, 136)(22, 103)(23, 138)(24, 111)(25, 104)(26, 108)(27, 135)(28, 106)(29, 140)(30, 107)(31, 110)(32, 113)(33, 115)(34, 141)(35, 139)(36, 143)(37, 116)(38, 144)(39, 123)(40, 117)(41, 142)(42, 119)(43, 131)(44, 125)(45, 130)(46, 137)(47, 132)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.624
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.629 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 6, 6})
Quotient :: edge^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3^-1, Y3^-1 * Y2^2 * Y1 * Y2, Y3 * Y2^2 * Y1^-1 * Y2, Y1^2 * Y2 * Y3 * Y2^-1, Y2^6, Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y3, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, Y1^6 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 10, 58, 12, 60)(3, 51, 15, 63, 17, 65)(5, 53, 22, 70, 25, 73)(6, 54, 19, 67, 29, 77)(8, 56, 16, 64, 27, 75)(9, 57, 21, 69, 28, 76)(11, 59, 36, 84, 39, 87)(13, 61, 35, 83, 24, 72)(14, 62, 42, 90, 43, 91)(18, 66, 30, 78, 41, 89)(20, 68, 31, 79, 45, 93)(23, 71, 46, 94, 47, 95)(26, 74, 37, 85, 40, 88)(32, 80, 34, 82, 38, 86)(33, 81, 44, 92, 48, 96)(97, 98, 104, 128, 119, 101)(99, 109, 118, 124, 140, 112)(100, 111, 138, 130, 105, 115)(102, 122, 121, 110, 116, 123)(103, 126, 133, 134, 107, 127)(106, 117, 137, 142, 113, 132)(108, 120, 141, 143, 129, 136)(114, 131, 125, 135, 144, 139)(145, 147, 158, 176, 172, 150)(146, 153, 174, 167, 159, 155)(148, 162, 170, 178, 183, 164)(149, 165, 177, 152, 161, 168)(151, 156, 171, 182, 191, 169)(154, 179, 175, 190, 192, 181)(157, 163, 180, 188, 186, 185)(160, 173, 184, 166, 187, 189)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^6 ) }
Outer automorphisms :: reflexible
Dual of E27.635
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 6^32 ]

E27.630 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 6, 6})
Quotient :: edge^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y3, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y3 * Y1 * Y2^2, Y1 * Y2^2 * Y1^-1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-2, Y1^2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y2^6, Y1^6, (Y2^-1 * Y1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 6, 54, 11, 59)(3, 51, 13, 61, 15, 63)(5, 53, 20, 68, 22, 70)(8, 56, 10, 58, 30, 78)(9, 57, 19, 67, 32, 80)(12, 60, 38, 86, 39, 87)(14, 62, 24, 72, 43, 91)(16, 64, 18, 66, 33, 81)(17, 65, 41, 89, 45, 93)(21, 69, 46, 94, 40, 88)(23, 71, 25, 73, 44, 92)(26, 74, 27, 75, 47, 95)(28, 76, 29, 77, 42, 90)(31, 79, 34, 82, 37, 85)(35, 83, 36, 84, 48, 96)(97, 98, 104, 124, 117, 101)(99, 103, 122, 128, 138, 110)(100, 112, 134, 125, 140, 113)(102, 119, 123, 142, 114, 120)(105, 107, 131, 109, 136, 127)(106, 129, 132, 116, 121, 130)(108, 111, 126, 141, 115, 118)(133, 135, 143, 144, 137, 139)(145, 147, 156, 181, 169, 150)(146, 153, 170, 183, 160, 154)(148, 149, 163, 175, 187, 162)(151, 161, 174, 178, 184, 171)(152, 159, 179, 191, 167, 173)(155, 168, 186, 182, 166, 180)(157, 158, 185, 188, 164, 165)(172, 176, 189, 192, 177, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^6 ) }
Outer automorphisms :: reflexible
Dual of E27.636
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 6^32 ]

E27.631 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 6, 6})
Quotient :: edge^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, (R * Y3)^2, Y3^4, R * Y2 * R * Y1, Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-2 * Y1 * Y3^-1, Y3^-2 * Y2 * Y3^-2 * Y1^-1, Y1^6, Y2^6, Y1^2 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3, Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y3, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1 * Y3^-1, (Y1^-1 * Y3^-1 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 28, 76, 14, 62)(6, 54, 18, 66, 43, 91, 19, 67)(9, 57, 26, 74, 15, 63, 27, 75)(11, 59, 29, 77, 16, 64, 31, 79)(13, 61, 34, 82, 47, 95, 35, 83)(17, 65, 40, 88, 48, 96, 41, 89)(20, 68, 25, 73, 23, 71, 38, 86)(22, 70, 36, 84, 24, 72, 32, 80)(30, 78, 33, 81, 39, 87, 37, 85)(42, 90, 45, 93, 44, 92, 46, 94)(97, 98, 102, 113, 109, 100)(99, 105, 121, 136, 126, 107)(101, 111, 134, 137, 135, 112)(103, 116, 141, 130, 127, 118)(104, 119, 142, 131, 125, 120)(106, 117, 139, 144, 143, 124)(108, 128, 122, 114, 138, 129)(110, 132, 123, 115, 140, 133)(145, 146, 150, 161, 157, 148)(147, 153, 169, 184, 174, 155)(149, 159, 182, 185, 183, 160)(151, 164, 189, 178, 175, 166)(152, 167, 190, 179, 173, 168)(154, 165, 187, 192, 191, 172)(156, 176, 170, 162, 186, 177)(158, 180, 171, 163, 188, 181)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.633
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.632 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 6, 6})
Quotient :: edge^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2^-2, Y3^2 * Y2 * Y1^-1, (Y1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3^2 * Y1, Y1^6, Y1 * Y3 * Y2^-2 * Y3^-1 * Y1 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3^-1, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^2 * Y3 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y2^-2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 11, 59, 7, 55)(2, 50, 10, 58, 3, 51, 12, 60)(5, 53, 17, 65, 6, 54, 20, 68)(8, 56, 23, 71, 9, 57, 24, 72)(13, 61, 31, 79, 14, 62, 32, 80)(15, 63, 33, 81, 16, 64, 36, 84)(18, 66, 41, 89, 19, 67, 42, 90)(21, 69, 43, 91, 22, 70, 44, 92)(25, 73, 30, 78, 26, 74, 29, 77)(27, 75, 37, 85, 28, 76, 38, 86)(34, 82, 40, 88, 35, 83, 39, 87)(45, 93, 48, 96, 46, 94, 47, 95)(97, 98, 104, 117, 114, 101)(99, 105, 118, 115, 102, 107)(100, 109, 125, 139, 130, 111)(103, 110, 126, 140, 131, 112)(106, 121, 143, 137, 129, 123)(108, 122, 144, 138, 132, 124)(113, 133, 128, 119, 141, 135)(116, 134, 127, 120, 142, 136)(145, 147, 152, 166, 162, 150)(146, 153, 165, 163, 149, 155)(148, 158, 173, 188, 178, 160)(151, 157, 174, 187, 179, 159)(154, 170, 191, 186, 177, 172)(156, 169, 192, 185, 180, 171)(161, 182, 176, 168, 189, 184)(164, 181, 175, 167, 190, 183)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.634
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.633 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 6, 6})
Quotient :: loop^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3^-1, Y3^-1 * Y2^2 * Y1 * Y2, Y3 * Y2^2 * Y1^-1 * Y2, Y1^2 * Y2 * Y3 * Y2^-1, Y2^6, Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y3, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, Y1^6 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 17, 65, 113, 161)(5, 53, 101, 149, 22, 70, 118, 166, 25, 73, 121, 169)(6, 54, 102, 150, 19, 67, 115, 163, 29, 77, 125, 173)(8, 56, 104, 152, 16, 64, 112, 160, 27, 75, 123, 171)(9, 57, 105, 153, 21, 69, 117, 165, 28, 76, 124, 172)(11, 59, 107, 155, 36, 84, 132, 180, 39, 87, 135, 183)(13, 61, 109, 157, 35, 83, 131, 179, 24, 72, 120, 168)(14, 62, 110, 158, 42, 90, 138, 186, 43, 91, 139, 187)(18, 66, 114, 162, 30, 78, 126, 174, 41, 89, 137, 185)(20, 68, 116, 164, 31, 79, 127, 175, 45, 93, 141, 189)(23, 71, 119, 167, 46, 94, 142, 190, 47, 95, 143, 191)(26, 74, 122, 170, 37, 85, 133, 181, 40, 88, 136, 184)(32, 80, 128, 176, 34, 82, 130, 178, 38, 86, 134, 182)(33, 81, 129, 177, 44, 92, 140, 188, 48, 96, 144, 192)
	L = (1, 50)(2, 56)(3, 61)(4, 63)(5, 49)(6, 74)(7, 78)(8, 80)(9, 67)(10, 69)(11, 79)(12, 72)(13, 70)(14, 68)(15, 90)(16, 51)(17, 84)(18, 83)(19, 52)(20, 75)(21, 89)(22, 76)(23, 53)(24, 93)(25, 62)(26, 73)(27, 54)(28, 92)(29, 87)(30, 85)(31, 55)(32, 71)(33, 88)(34, 57)(35, 77)(36, 58)(37, 86)(38, 59)(39, 96)(40, 60)(41, 94)(42, 82)(43, 66)(44, 64)(45, 95)(46, 65)(47, 81)(48, 91)(97, 147)(98, 153)(99, 158)(100, 162)(101, 165)(102, 145)(103, 156)(104, 161)(105, 174)(106, 179)(107, 146)(108, 171)(109, 163)(110, 176)(111, 155)(112, 173)(113, 168)(114, 170)(115, 180)(116, 148)(117, 177)(118, 187)(119, 159)(120, 149)(121, 151)(122, 178)(123, 182)(124, 150)(125, 184)(126, 167)(127, 190)(128, 172)(129, 152)(130, 183)(131, 175)(132, 188)(133, 154)(134, 191)(135, 164)(136, 166)(137, 157)(138, 185)(139, 189)(140, 186)(141, 160)(142, 192)(143, 169)(144, 181)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.631
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.634 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 6, 6})
Quotient :: loop^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y3, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y3 * Y1 * Y2^2, Y1 * Y2^2 * Y1^-1 * Y3, Y2 * Y3^-1 * Y2^-1 * Y1^-2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-2, Y1^2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y2^6, Y1^6, (Y2^-1 * Y1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 6, 54, 102, 150, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 15, 63, 111, 159)(5, 53, 101, 149, 20, 68, 116, 164, 22, 70, 118, 166)(8, 56, 104, 152, 10, 58, 106, 154, 30, 78, 126, 174)(9, 57, 105, 153, 19, 67, 115, 163, 32, 80, 128, 176)(12, 60, 108, 156, 38, 86, 134, 182, 39, 87, 135, 183)(14, 62, 110, 158, 24, 72, 120, 168, 43, 91, 139, 187)(16, 64, 112, 160, 18, 66, 114, 162, 33, 81, 129, 177)(17, 65, 113, 161, 41, 89, 137, 185, 45, 93, 141, 189)(21, 69, 117, 165, 46, 94, 142, 190, 40, 88, 136, 184)(23, 71, 119, 167, 25, 73, 121, 169, 44, 92, 140, 188)(26, 74, 122, 170, 27, 75, 123, 171, 47, 95, 143, 191)(28, 76, 124, 172, 29, 77, 125, 173, 42, 90, 138, 186)(31, 79, 127, 175, 34, 82, 130, 178, 37, 85, 133, 181)(35, 83, 131, 179, 36, 84, 132, 180, 48, 96, 144, 192)
	L = (1, 50)(2, 56)(3, 55)(4, 64)(5, 49)(6, 71)(7, 74)(8, 76)(9, 59)(10, 81)(11, 83)(12, 63)(13, 88)(14, 51)(15, 78)(16, 86)(17, 52)(18, 72)(19, 70)(20, 73)(21, 53)(22, 60)(23, 75)(24, 54)(25, 82)(26, 80)(27, 94)(28, 69)(29, 92)(30, 93)(31, 57)(32, 90)(33, 84)(34, 58)(35, 61)(36, 68)(37, 87)(38, 77)(39, 95)(40, 79)(41, 91)(42, 62)(43, 85)(44, 65)(45, 67)(46, 66)(47, 96)(48, 89)(97, 147)(98, 153)(99, 156)(100, 149)(101, 163)(102, 145)(103, 161)(104, 159)(105, 170)(106, 146)(107, 168)(108, 181)(109, 158)(110, 185)(111, 179)(112, 154)(113, 174)(114, 148)(115, 175)(116, 165)(117, 157)(118, 180)(119, 173)(120, 186)(121, 150)(122, 183)(123, 151)(124, 176)(125, 152)(126, 178)(127, 187)(128, 189)(129, 190)(130, 184)(131, 191)(132, 155)(133, 169)(134, 166)(135, 160)(136, 171)(137, 188)(138, 182)(139, 162)(140, 164)(141, 192)(142, 172)(143, 167)(144, 177)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.632
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.635 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 6, 6})
Quotient :: loop^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, (R * Y3)^2, Y3^4, R * Y2 * R * Y1, Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-2 * Y1 * Y3^-1, Y3^-2 * Y2 * Y3^-2 * Y1^-1, Y1^6, Y2^6, Y1^2 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3, Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y3, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1 * Y3^-1, (Y1^-1 * Y3^-1 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 3, 51, 99, 147, 10, 58, 106, 154, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 21, 69, 117, 165, 8, 56, 104, 152)(4, 52, 100, 148, 12, 60, 108, 156, 28, 76, 124, 172, 14, 62, 110, 158)(6, 54, 102, 150, 18, 66, 114, 162, 43, 91, 139, 187, 19, 67, 115, 163)(9, 57, 105, 153, 26, 74, 122, 170, 15, 63, 111, 159, 27, 75, 123, 171)(11, 59, 107, 155, 29, 77, 125, 173, 16, 64, 112, 160, 31, 79, 127, 175)(13, 61, 109, 157, 34, 82, 130, 178, 47, 95, 143, 191, 35, 83, 131, 179)(17, 65, 113, 161, 40, 88, 136, 184, 48, 96, 144, 192, 41, 89, 137, 185)(20, 68, 116, 164, 25, 73, 121, 169, 23, 71, 119, 167, 38, 86, 134, 182)(22, 70, 118, 166, 36, 84, 132, 180, 24, 72, 120, 168, 32, 80, 128, 176)(30, 78, 126, 174, 33, 81, 129, 177, 39, 87, 135, 183, 37, 85, 133, 181)(42, 90, 138, 186, 45, 93, 141, 189, 44, 92, 140, 188, 46, 94, 142, 190)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 73)(10, 69)(11, 51)(12, 80)(13, 52)(14, 84)(15, 86)(16, 53)(17, 61)(18, 90)(19, 92)(20, 93)(21, 91)(22, 55)(23, 94)(24, 56)(25, 88)(26, 66)(27, 67)(28, 58)(29, 72)(30, 59)(31, 70)(32, 74)(33, 60)(34, 79)(35, 77)(36, 75)(37, 62)(38, 89)(39, 64)(40, 78)(41, 87)(42, 81)(43, 96)(44, 85)(45, 82)(46, 83)(47, 76)(48, 95)(97, 146)(98, 150)(99, 153)(100, 145)(101, 159)(102, 161)(103, 164)(104, 167)(105, 169)(106, 165)(107, 147)(108, 176)(109, 148)(110, 180)(111, 182)(112, 149)(113, 157)(114, 186)(115, 188)(116, 189)(117, 187)(118, 151)(119, 190)(120, 152)(121, 184)(122, 162)(123, 163)(124, 154)(125, 168)(126, 155)(127, 166)(128, 170)(129, 156)(130, 175)(131, 173)(132, 171)(133, 158)(134, 185)(135, 160)(136, 174)(137, 183)(138, 177)(139, 192)(140, 181)(141, 178)(142, 179)(143, 172)(144, 191)
	local type(s) :: { ( 6^16 ) }
Outer automorphisms :: reflexible
Dual of E27.629
Transitivity :: VT+
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.636 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 6, 6})
Quotient :: loop^2
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2^-2, Y3^2 * Y2 * Y1^-1, (Y1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3^2 * Y1, Y1^6, Y1 * Y3 * Y2^-2 * Y3^-1 * Y1 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y3^-1, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2^2 * Y3 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y2^-2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 11, 59, 107, 155, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 17, 65, 113, 161, 6, 54, 102, 150, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167, 9, 57, 105, 153, 24, 72, 120, 168)(13, 61, 109, 157, 31, 79, 127, 175, 14, 62, 110, 158, 32, 80, 128, 176)(15, 63, 111, 159, 33, 81, 129, 177, 16, 64, 112, 160, 36, 84, 132, 180)(18, 66, 114, 162, 41, 89, 137, 185, 19, 67, 115, 163, 42, 90, 138, 186)(21, 69, 117, 165, 43, 91, 139, 187, 22, 70, 118, 166, 44, 92, 140, 188)(25, 73, 121, 169, 30, 78, 126, 174, 26, 74, 122, 170, 29, 77, 125, 173)(27, 75, 123, 171, 37, 85, 133, 181, 28, 76, 124, 172, 38, 86, 134, 182)(34, 82, 130, 178, 40, 88, 136, 184, 35, 83, 131, 179, 39, 87, 135, 183)(45, 93, 141, 189, 48, 96, 144, 192, 46, 94, 142, 190, 47, 95, 143, 191)
	L = (1, 50)(2, 56)(3, 57)(4, 61)(5, 49)(6, 59)(7, 62)(8, 69)(9, 70)(10, 73)(11, 51)(12, 74)(13, 77)(14, 78)(15, 52)(16, 55)(17, 85)(18, 53)(19, 54)(20, 86)(21, 66)(22, 67)(23, 93)(24, 94)(25, 95)(26, 96)(27, 58)(28, 60)(29, 91)(30, 92)(31, 72)(32, 71)(33, 75)(34, 63)(35, 64)(36, 76)(37, 80)(38, 79)(39, 65)(40, 68)(41, 81)(42, 84)(43, 82)(44, 83)(45, 87)(46, 88)(47, 89)(48, 90)(97, 147)(98, 153)(99, 152)(100, 158)(101, 155)(102, 145)(103, 157)(104, 166)(105, 165)(106, 170)(107, 146)(108, 169)(109, 174)(110, 173)(111, 151)(112, 148)(113, 182)(114, 150)(115, 149)(116, 181)(117, 163)(118, 162)(119, 190)(120, 189)(121, 192)(122, 191)(123, 156)(124, 154)(125, 188)(126, 187)(127, 167)(128, 168)(129, 172)(130, 160)(131, 159)(132, 171)(133, 175)(134, 176)(135, 164)(136, 161)(137, 180)(138, 177)(139, 179)(140, 178)(141, 184)(142, 183)(143, 186)(144, 185)
	local type(s) :: { ( 6^16 ) }
Outer automorphisms :: reflexible
Dual of E27.630
Transitivity :: VT+
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.637 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1 * Y3, Y1^3, Y2^4, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^2 * Y3 * Y2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, R * Y3^-1 * Y2 * Y3 * Y2 * R * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 14, 62)(4, 52, 7, 55, 10, 58)(6, 54, 20, 68, 22, 70)(8, 56, 26, 74, 29, 77)(9, 57, 31, 79, 33, 81)(12, 60, 27, 75, 40, 88)(13, 61, 15, 63, 35, 83)(16, 64, 28, 76, 30, 78)(17, 65, 32, 80, 34, 82)(18, 66, 44, 92, 38, 86)(19, 67, 46, 94, 37, 85)(21, 69, 23, 71, 36, 84)(24, 72, 45, 93, 43, 91)(25, 73, 47, 95, 42, 90)(39, 87, 41, 89, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 123, 171, 105, 153)(100, 148, 112, 160, 135, 183, 113, 161)(101, 149, 114, 162, 136, 184, 115, 163)(103, 151, 120, 168, 137, 185, 121, 169)(106, 154, 131, 179, 144, 192, 132, 180)(107, 155, 133, 181, 116, 164, 134, 182)(109, 157, 138, 186, 117, 165, 139, 187)(110, 158, 122, 170, 118, 166, 127, 175)(111, 159, 124, 172, 119, 167, 128, 176)(125, 173, 140, 188, 129, 177, 142, 190)(126, 174, 141, 189, 130, 178, 143, 191)
	L = (1, 100)(2, 103)(3, 109)(4, 101)(5, 106)(6, 117)(7, 97)(8, 124)(9, 128)(10, 98)(11, 111)(12, 135)(13, 110)(14, 131)(15, 99)(16, 122)(17, 127)(18, 141)(19, 143)(20, 119)(21, 118)(22, 132)(23, 102)(24, 140)(25, 142)(26, 126)(27, 137)(28, 125)(29, 112)(30, 104)(31, 130)(32, 129)(33, 113)(34, 105)(35, 107)(36, 116)(37, 121)(38, 120)(39, 136)(40, 144)(41, 108)(42, 115)(43, 114)(44, 139)(45, 134)(46, 138)(47, 133)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.659
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.638 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3^-2 * Y2 * Y1^-1, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3, Y3^-1 * Y1 * Y3 * Y1 * Y2 * Y1, Y3 * Y2^-2 * Y1^-1 * Y3 * Y1^-1, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2^-1 * Y3^-1 * Y1 * Y3, Y3^6, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y1^-1 * R * Y2^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 19, 67)(6, 54, 25, 73, 26, 74)(7, 55, 28, 76, 29, 77)(8, 56, 31, 79, 34, 82)(9, 57, 36, 84, 14, 62)(10, 58, 37, 85, 38, 86)(11, 59, 40, 88, 30, 78)(13, 61, 32, 80, 44, 92)(16, 64, 35, 83, 20, 68)(18, 66, 27, 75, 39, 87)(21, 69, 48, 96, 42, 90)(22, 70, 45, 93, 33, 81)(23, 71, 47, 95, 43, 91)(24, 72, 46, 94, 41, 89)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 128, 176, 106, 154)(100, 148, 114, 162, 136, 184, 116, 164)(101, 149, 117, 165, 140, 188, 119, 167)(103, 151, 113, 161, 129, 177, 126, 174)(105, 153, 123, 171, 142, 190, 112, 160)(107, 155, 132, 180, 115, 163, 137, 185)(108, 156, 138, 186, 121, 169, 139, 187)(110, 158, 125, 173, 120, 168, 141, 189)(111, 159, 133, 181, 122, 170, 127, 175)(118, 166, 135, 183, 124, 172, 131, 179)(130, 178, 143, 191, 134, 182, 144, 192)
	L = (1, 100)(2, 105)(3, 110)(4, 111)(5, 118)(6, 120)(7, 97)(8, 129)(9, 130)(10, 103)(11, 98)(12, 126)(13, 136)(14, 140)(15, 135)(16, 99)(17, 143)(18, 119)(19, 128)(20, 117)(21, 115)(22, 138)(23, 107)(24, 101)(25, 113)(26, 131)(27, 102)(28, 139)(29, 127)(30, 144)(31, 137)(32, 142)(33, 109)(34, 114)(35, 104)(36, 121)(37, 132)(38, 116)(39, 106)(40, 122)(41, 108)(42, 123)(43, 112)(44, 124)(45, 133)(46, 134)(47, 141)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.657
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.639 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3^3, (R * Y1)^2, Y2^4, (R * Y3)^2, Y2 * Y1 * Y2 * Y3 * Y1, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y1 * Y3, (R * Y2 * Y3^-1)^2, (Y1^-1 * R * Y2^-1)^2, Y2^-2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1, Y1 * Y3^-1 * Y1 * Y2^-2 * Y3^-1, (Y3 * Y2 * Y1^-1)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 19, 67)(6, 54, 25, 73, 27, 75)(7, 55, 29, 77, 31, 79)(8, 56, 32, 80, 34, 82)(9, 57, 36, 84, 37, 85)(10, 58, 30, 78, 38, 86)(11, 59, 40, 88, 42, 90)(13, 61, 33, 81, 44, 92)(14, 62, 23, 71, 41, 89)(16, 64, 35, 83, 20, 68)(18, 66, 28, 76, 39, 87)(21, 69, 43, 91, 26, 74)(22, 70, 46, 94, 45, 93)(24, 72, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 129, 177, 106, 154)(100, 148, 114, 162, 136, 184, 116, 164)(101, 149, 117, 165, 140, 188, 119, 167)(103, 151, 126, 174, 141, 189, 128, 176)(105, 153, 124, 172, 143, 191, 112, 160)(107, 155, 137, 185, 115, 163, 139, 187)(108, 156, 120, 168, 121, 169, 133, 181)(110, 158, 127, 175, 122, 170, 142, 190)(111, 159, 113, 161, 123, 171, 138, 186)(118, 166, 135, 183, 125, 173, 131, 179)(130, 178, 132, 180, 134, 182, 144, 192)
	L = (1, 100)(2, 105)(3, 110)(4, 103)(5, 118)(6, 122)(7, 97)(8, 123)(9, 107)(10, 111)(11, 98)(12, 128)(13, 136)(14, 112)(15, 135)(16, 99)(17, 132)(18, 119)(19, 129)(20, 117)(21, 134)(22, 120)(23, 130)(24, 101)(25, 126)(26, 124)(27, 131)(28, 102)(29, 133)(30, 137)(31, 138)(32, 139)(33, 143)(34, 114)(35, 104)(36, 142)(37, 140)(38, 116)(39, 106)(40, 141)(41, 121)(42, 144)(43, 108)(44, 125)(45, 109)(46, 113)(47, 115)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.658
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.640 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2 * Y1^-1, Y1^3, (R * Y3^-1)^2, Y3^-1 * Y1^-2 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1, Y3^-1 * Y2^2 * Y1 * Y2, Y3 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y2, Y3^6, Y3^2 * Y1 * Y3^3 * Y2^-1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 7, 55)(4, 52, 15, 63, 17, 65)(6, 54, 21, 69, 23, 71)(8, 56, 27, 75, 10, 58)(9, 57, 29, 77, 31, 79)(12, 60, 18, 66, 14, 62)(13, 61, 34, 82, 32, 80)(16, 64, 37, 85, 39, 87)(19, 67, 41, 89, 20, 68)(22, 70, 40, 88, 33, 81)(24, 72, 42, 90, 26, 74)(25, 73, 30, 78, 45, 93)(28, 76, 43, 91, 36, 84)(35, 83, 48, 96, 47, 95)(38, 86, 46, 94, 44, 92)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 114, 162, 100, 148)(101, 149, 115, 163, 110, 158, 105, 153)(103, 151, 120, 168, 119, 167, 121, 169)(106, 154, 128, 176, 113, 161, 129, 177)(107, 155, 118, 166, 117, 165, 109, 157)(111, 159, 124, 172, 123, 171, 112, 160)(116, 164, 132, 180, 127, 175, 135, 183)(122, 170, 142, 190, 141, 189, 143, 191)(125, 173, 138, 186, 137, 185, 126, 174)(130, 178, 140, 188, 136, 184, 131, 179)(133, 181, 144, 192, 139, 187, 134, 182)
	L = (1, 100)(2, 105)(3, 109)(4, 112)(5, 102)(6, 118)(7, 97)(8, 124)(9, 126)(10, 98)(11, 121)(12, 104)(13, 131)(14, 99)(15, 128)(16, 134)(17, 114)(18, 115)(19, 138)(20, 101)(21, 120)(22, 140)(23, 108)(24, 125)(25, 137)(26, 103)(27, 129)(28, 144)(29, 132)(30, 142)(31, 110)(32, 117)(33, 107)(34, 106)(35, 133)(36, 111)(37, 127)(38, 122)(39, 123)(40, 113)(41, 135)(42, 143)(43, 116)(44, 139)(45, 119)(46, 130)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.660
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.641 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y3^3, (Y2^-1 * Y3^-1)^2, Y1^4, (Y2 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 15, 63)(4, 52, 16, 64, 27, 75, 17, 65)(6, 54, 22, 70, 28, 76, 23, 71)(7, 55, 24, 72, 29, 77, 25, 73)(9, 57, 30, 78, 18, 66, 32, 80)(10, 58, 33, 81, 19, 67, 34, 82)(11, 59, 35, 83, 20, 68, 36, 84)(12, 60, 37, 85, 21, 69, 38, 86)(14, 62, 31, 79, 48, 96, 41, 89)(39, 87, 46, 94, 42, 90, 44, 92)(40, 88, 47, 95, 43, 91, 45, 93)(97, 145, 99, 147, 100, 148, 110, 158, 103, 151, 102, 150)(98, 146, 105, 153, 106, 154, 127, 175, 108, 156, 107, 155)(101, 149, 114, 162, 115, 163, 137, 185, 117, 165, 116, 164)(104, 152, 122, 170, 123, 171, 144, 192, 125, 173, 124, 172)(109, 157, 130, 178, 135, 183, 120, 168, 132, 180, 136, 184)(111, 159, 129, 177, 138, 186, 121, 169, 131, 179, 139, 187)(112, 160, 140, 188, 133, 181, 118, 166, 141, 189, 126, 174)(113, 161, 142, 190, 134, 182, 119, 167, 143, 191, 128, 176)
	L = (1, 100)(2, 106)(3, 110)(4, 103)(5, 115)(6, 99)(7, 97)(8, 123)(9, 127)(10, 108)(11, 105)(12, 98)(13, 135)(14, 102)(15, 138)(16, 133)(17, 134)(18, 137)(19, 117)(20, 114)(21, 101)(22, 126)(23, 128)(24, 136)(25, 139)(26, 144)(27, 125)(28, 122)(29, 104)(30, 140)(31, 107)(32, 142)(33, 121)(34, 120)(35, 111)(36, 109)(37, 141)(38, 143)(39, 132)(40, 130)(41, 116)(42, 131)(43, 129)(44, 118)(45, 112)(46, 119)(47, 113)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.649
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.642 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^2 * Y3^-1 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y2, Y3 * Y2^-1 * Y1^2 * Y2^-1 * Y1^-1, (Y1^-1 * Y2^-1 * Y3^-1)^2, (Y1 * Y3)^3, (Y3 * Y2 * Y1^-1)^2, Y3 * Y2 * Y1 * Y2^-3, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y1^-1 * R * Y2^-1)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 31, 79, 15, 63)(4, 52, 17, 65, 32, 80, 19, 67)(6, 54, 16, 64, 33, 81, 25, 73)(7, 55, 28, 76, 34, 82, 26, 74)(9, 57, 24, 72, 20, 68, 36, 84)(10, 58, 37, 85, 21, 69, 39, 87)(11, 59, 29, 77, 22, 70, 40, 88)(12, 60, 43, 91, 23, 71, 41, 89)(14, 62, 44, 92, 30, 78, 35, 83)(18, 66, 38, 86, 27, 75, 42, 90)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 106, 154, 134, 182, 122, 170, 102, 150)(98, 146, 105, 153, 128, 176, 123, 171, 137, 185, 107, 155)(100, 148, 114, 162, 139, 187, 118, 166, 101, 149, 116, 164)(103, 151, 125, 173, 141, 189, 109, 157, 115, 163, 126, 174)(104, 152, 127, 175, 117, 165, 138, 186, 124, 172, 129, 177)(108, 156, 121, 169, 144, 192, 120, 168, 135, 183, 140, 188)(110, 158, 130, 178, 136, 184, 142, 190, 111, 159, 113, 161)(112, 160, 143, 191, 132, 180, 133, 181, 131, 179, 119, 167)
	L = (1, 100)(2, 106)(3, 110)(4, 103)(5, 117)(6, 120)(7, 97)(8, 128)(9, 131)(10, 108)(11, 111)(12, 98)(13, 134)(14, 112)(15, 138)(16, 99)(17, 139)(18, 129)(19, 137)(20, 140)(21, 119)(22, 109)(23, 101)(24, 123)(25, 127)(26, 142)(27, 102)(28, 141)(29, 105)(30, 121)(31, 126)(32, 130)(33, 132)(34, 104)(35, 125)(36, 114)(37, 122)(38, 118)(39, 124)(40, 116)(41, 143)(42, 107)(43, 144)(44, 136)(45, 135)(46, 133)(47, 115)(48, 113)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.650
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.643 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1 * Y3 * Y2^-1, Y3^2 * Y1^-1 * Y2^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1 * Y3 * Y2^4, Y3^2 * Y2 * Y3 * Y2^-1 * Y1^-1, (Y1^-1 * R * Y2^-1)^2, Y2 * Y3 * Y2 * Y3 * Y1^2, Y3 * Y2^-1 * Y1^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2^2 * Y1^-1, (Y3 * Y1)^3, Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, Y1^-2 * Y3^2 * Y1 * Y2^-1, (Y3 * Y2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 15, 63)(4, 52, 17, 65, 30, 78, 19, 67)(6, 54, 16, 64, 31, 79, 24, 72)(7, 55, 27, 75, 32, 80, 25, 73)(9, 57, 33, 81, 20, 68, 35, 83)(10, 58, 37, 85, 21, 69, 39, 87)(11, 59, 36, 84, 22, 70, 40, 88)(12, 60, 43, 91, 23, 71, 41, 89)(14, 62, 44, 92, 28, 76, 34, 82)(18, 66, 38, 86, 26, 74, 42, 90)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 134, 182, 121, 169, 102, 150)(98, 146, 105, 153, 126, 174, 122, 170, 137, 185, 107, 155)(100, 148, 114, 162, 139, 187, 118, 166, 101, 149, 116, 164)(103, 151, 115, 163, 141, 189, 109, 157, 132, 180, 124, 172)(104, 152, 125, 173, 117, 165, 138, 186, 123, 171, 127, 175)(108, 156, 135, 183, 143, 191, 129, 177, 120, 168, 140, 188)(110, 158, 128, 176, 113, 161, 142, 190, 111, 159, 136, 184)(112, 160, 130, 178, 119, 167, 133, 181, 144, 192, 131, 179)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 117)(6, 108)(7, 97)(8, 126)(9, 130)(10, 129)(11, 128)(12, 98)(13, 134)(14, 133)(15, 138)(16, 99)(17, 139)(18, 127)(19, 137)(20, 140)(21, 131)(22, 103)(23, 101)(24, 125)(25, 142)(26, 102)(27, 141)(28, 135)(29, 124)(30, 111)(31, 119)(32, 104)(33, 122)(34, 115)(35, 114)(36, 105)(37, 121)(38, 118)(39, 123)(40, 116)(41, 144)(42, 107)(43, 143)(44, 113)(45, 120)(46, 112)(47, 136)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.652
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.644 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, Y1^4, Y1^-2 * Y3^-1 * Y2^2, Y1 * Y3 * Y2^-2 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y3^-1, Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 16, 64)(4, 52, 18, 66, 14, 62, 20, 68)(6, 54, 26, 74, 17, 65, 27, 75)(7, 55, 28, 76, 19, 67, 29, 77)(9, 57, 30, 78, 22, 70, 32, 80)(10, 58, 33, 81, 23, 71, 34, 82)(11, 59, 35, 83, 24, 72, 36, 84)(12, 60, 37, 85, 25, 73, 38, 86)(15, 63, 31, 79, 41, 89, 42, 90)(39, 87, 45, 93, 43, 91, 47, 95)(40, 88, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 110, 158, 137, 185, 115, 163, 102, 150)(98, 146, 105, 153, 119, 167, 138, 186, 121, 169, 107, 155)(100, 148, 111, 159, 103, 151, 113, 161, 104, 152, 117, 165)(101, 149, 118, 166, 106, 154, 127, 175, 108, 156, 120, 168)(109, 157, 130, 178, 139, 187, 125, 173, 131, 179, 136, 184)(112, 160, 129, 177, 135, 183, 124, 172, 132, 180, 140, 188)(114, 162, 141, 189, 134, 182, 123, 171, 144, 192, 126, 174)(116, 164, 143, 191, 133, 181, 122, 170, 142, 190, 128, 176)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 119)(6, 117)(7, 97)(8, 110)(9, 127)(10, 121)(11, 118)(12, 98)(13, 135)(14, 103)(15, 102)(16, 139)(17, 99)(18, 133)(19, 104)(20, 134)(21, 137)(22, 138)(23, 108)(24, 105)(25, 101)(26, 126)(27, 128)(28, 136)(29, 140)(30, 143)(31, 107)(32, 141)(33, 125)(34, 124)(35, 112)(36, 109)(37, 144)(38, 142)(39, 131)(40, 129)(41, 113)(42, 120)(43, 132)(44, 130)(45, 122)(46, 114)(47, 123)(48, 116)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.656
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.645 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y1^4, Y2^2 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3 * Y2^-1 * Y1 * Y3^-1, Y2^2 * Y3^2 * Y1, Y1 * Y2 * Y1^-1 * Y3^-1 * Y2, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, (Y3 * Y2 * Y1^-1)^2, (Y1^-1 * Y2)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 33, 81, 15, 63)(4, 52, 17, 65, 32, 80, 20, 68)(6, 54, 16, 64, 34, 82, 26, 74)(7, 55, 29, 77, 19, 67, 27, 75)(9, 57, 35, 83, 21, 69, 25, 73)(10, 58, 38, 86, 22, 70, 40, 88)(11, 59, 37, 85, 23, 71, 30, 78)(12, 60, 43, 91, 24, 72, 41, 89)(14, 62, 44, 92, 31, 79, 36, 84)(18, 66, 39, 87, 28, 76, 42, 90)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 135, 183, 123, 171, 102, 150)(98, 146, 105, 153, 128, 176, 124, 172, 137, 185, 107, 155)(100, 148, 114, 162, 139, 187, 119, 167, 101, 149, 117, 165)(103, 151, 126, 174, 141, 189, 109, 157, 113, 161, 127, 175)(104, 152, 129, 177, 118, 166, 138, 186, 125, 173, 130, 178)(108, 156, 112, 160, 143, 191, 131, 179, 134, 182, 140, 188)(110, 158, 115, 163, 133, 181, 142, 190, 111, 159, 116, 164)(120, 168, 122, 170, 144, 192, 121, 169, 136, 184, 132, 180)
	L = (1, 100)(2, 106)(3, 110)(4, 115)(5, 118)(6, 121)(7, 97)(8, 128)(9, 132)(10, 120)(11, 109)(12, 98)(13, 135)(14, 122)(15, 138)(16, 99)(17, 139)(18, 130)(19, 104)(20, 137)(21, 140)(22, 108)(23, 111)(24, 101)(25, 114)(26, 129)(27, 142)(28, 102)(29, 141)(30, 117)(31, 112)(32, 103)(33, 127)(34, 131)(35, 124)(36, 126)(37, 105)(38, 123)(39, 119)(40, 125)(41, 144)(42, 107)(43, 143)(44, 133)(45, 134)(46, 136)(47, 116)(48, 113)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.655
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.646 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1 * Y3^-1 * Y1, Y1^4, Y2^-2 * Y3^-2, (R * Y3)^2, Y2^-1 * Y1^-2 * Y3^-1, Y1 * Y3 * Y2 * Y1, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y2^-1 * Y1 * Y3, Y3^-2 * Y2^4, (Y2 * Y1)^3, Y2^-3 * Y1 * Y2^-3 * Y1^-1, Y3^-2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y2, Y3^-2 * Y1 * Y3 * Y1^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 7, 55, 15, 63)(4, 52, 17, 65, 6, 54, 19, 67)(9, 57, 21, 69, 12, 60, 23, 71)(10, 58, 25, 73, 11, 59, 27, 75)(14, 62, 31, 79, 16, 64, 33, 81)(18, 66, 37, 85, 20, 68, 38, 86)(22, 70, 41, 89, 24, 72, 43, 91)(26, 74, 47, 95, 28, 76, 48, 96)(29, 77, 40, 88, 30, 78, 39, 87)(32, 80, 42, 90, 34, 82, 44, 92)(35, 83, 46, 94, 36, 84, 45, 93)(97, 145, 99, 147, 110, 158, 128, 176, 114, 162, 102, 150)(98, 146, 105, 153, 118, 166, 138, 186, 122, 170, 107, 155)(100, 148, 104, 152, 103, 151, 112, 160, 130, 178, 116, 164)(101, 149, 108, 156, 120, 168, 140, 188, 124, 172, 106, 154)(109, 157, 123, 171, 142, 190, 133, 181, 137, 185, 126, 174)(111, 159, 121, 169, 141, 189, 134, 182, 139, 187, 125, 173)(113, 161, 131, 179, 143, 191, 129, 177, 136, 184, 117, 165)(115, 163, 132, 180, 144, 192, 127, 175, 135, 183, 119, 167)
	L = (1, 100)(2, 106)(3, 104)(4, 114)(5, 107)(6, 116)(7, 97)(8, 102)(9, 101)(10, 122)(11, 124)(12, 98)(13, 125)(14, 103)(15, 126)(16, 99)(17, 119)(18, 130)(19, 117)(20, 128)(21, 135)(22, 108)(23, 136)(24, 105)(25, 109)(26, 140)(27, 111)(28, 138)(29, 137)(30, 139)(31, 143)(32, 112)(33, 144)(34, 110)(35, 115)(36, 113)(37, 141)(38, 142)(39, 129)(40, 127)(41, 134)(42, 120)(43, 133)(44, 118)(45, 123)(46, 121)(47, 132)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.653
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.647 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-2 * Y3^-1, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y2^-1)^2, Y1 * Y2^-3 * Y1, Y1 * Y3^-2 * Y2 * Y1, Y3^-1 * Y1^-1 * Y3 * Y2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3, (Y3^-1 * Y1^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 19, 67, 16, 64)(4, 52, 18, 66, 17, 65, 20, 68)(6, 54, 26, 74, 14, 62, 27, 75)(7, 55, 28, 76, 21, 69, 29, 77)(9, 57, 30, 78, 22, 70, 32, 80)(10, 58, 33, 81, 23, 71, 34, 82)(11, 59, 35, 83, 24, 72, 36, 84)(12, 60, 37, 85, 25, 73, 38, 86)(15, 63, 31, 79, 41, 89, 42, 90)(39, 87, 46, 94, 43, 91, 48, 96)(40, 88, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 110, 158, 104, 152, 115, 163, 102, 150)(98, 146, 105, 153, 120, 168, 101, 149, 118, 166, 107, 155)(100, 148, 111, 159, 103, 151, 113, 161, 137, 185, 117, 165)(106, 154, 127, 175, 108, 156, 119, 167, 138, 186, 121, 169)(109, 157, 130, 178, 140, 188, 112, 160, 129, 177, 136, 184)(114, 162, 141, 189, 128, 176, 116, 164, 143, 191, 126, 174)(122, 170, 142, 190, 134, 182, 123, 171, 144, 192, 133, 181)(124, 172, 132, 180, 139, 187, 125, 173, 131, 179, 135, 183)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 119)(6, 117)(7, 97)(8, 113)(9, 127)(10, 118)(11, 121)(12, 98)(13, 135)(14, 103)(15, 102)(16, 139)(17, 99)(18, 133)(19, 137)(20, 134)(21, 104)(22, 138)(23, 105)(24, 108)(25, 101)(26, 126)(27, 128)(28, 136)(29, 140)(30, 144)(31, 107)(32, 142)(33, 125)(34, 124)(35, 112)(36, 109)(37, 143)(38, 141)(39, 129)(40, 131)(41, 110)(42, 120)(43, 130)(44, 132)(45, 122)(46, 114)(47, 123)(48, 116)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.654
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.648 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1 * Y2^-1, (R * Y3^-1)^2, Y2^2 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y2 * Y3^-1 * Y1^-1 * Y2, Y2^-1 * Y1^2 * Y3^-1 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1, (Y1 * Y3)^3, Y3^6, Y1 * Y3^3 * Y2^-1 * Y3^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 12, 60, 23, 71, 7, 55)(4, 52, 15, 63, 19, 67, 17, 65)(6, 54, 14, 62, 10, 58, 22, 70)(9, 57, 20, 68, 18, 66, 11, 59)(13, 61, 30, 78, 25, 73, 27, 75)(16, 64, 38, 86, 42, 90, 40, 88)(21, 69, 44, 92, 28, 76, 46, 94)(24, 72, 33, 81, 32, 80, 26, 74)(29, 77, 43, 91, 34, 82, 31, 79)(35, 83, 41, 89, 37, 85, 36, 84)(39, 87, 47, 95, 48, 96, 45, 93)(97, 145, 99, 147, 106, 154, 104, 152, 119, 167, 102, 150)(98, 146, 105, 153, 115, 163, 101, 149, 114, 162, 100, 148)(103, 151, 120, 168, 109, 157, 108, 156, 128, 176, 121, 169)(107, 155, 125, 173, 123, 171, 116, 164, 130, 178, 126, 174)(110, 158, 131, 179, 124, 172, 118, 166, 133, 181, 117, 165)(111, 159, 132, 180, 138, 186, 113, 161, 137, 185, 112, 160)(122, 170, 143, 191, 142, 190, 129, 177, 141, 189, 140, 188)(127, 175, 144, 192, 136, 184, 139, 187, 135, 183, 134, 182)
	L = (1, 100)(2, 106)(3, 109)(4, 112)(5, 102)(6, 117)(7, 97)(8, 115)(9, 123)(10, 124)(11, 98)(12, 104)(13, 130)(14, 99)(15, 105)(16, 135)(17, 114)(18, 126)(19, 138)(20, 101)(21, 141)(22, 119)(23, 121)(24, 142)(25, 125)(26, 103)(27, 120)(28, 143)(29, 136)(30, 128)(31, 107)(32, 140)(33, 108)(34, 134)(35, 113)(36, 110)(37, 111)(38, 132)(39, 122)(40, 137)(41, 118)(42, 144)(43, 116)(44, 131)(45, 139)(46, 133)(47, 127)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.651
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.649 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^2, Y2^3, Y3^3, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2, (Y2 * Y1^-1)^4, (Y3 * Y2^-1)^4, (Y2 * Y3^-1 * Y2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 10, 58, 4, 52, 5, 53)(3, 51, 11, 59, 14, 62, 33, 81, 12, 60, 13, 61)(6, 54, 19, 67, 22, 70, 34, 82, 20, 68, 21, 69)(8, 56, 25, 73, 28, 76, 15, 63, 26, 74, 27, 75)(9, 57, 29, 77, 32, 80, 16, 64, 30, 78, 31, 79)(17, 65, 36, 84, 42, 90, 23, 71, 35, 83, 41, 89)(18, 66, 40, 88, 44, 92, 24, 72, 38, 86, 43, 91)(37, 85, 46, 94, 48, 96, 39, 87, 45, 93, 47, 95)(97, 145, 99, 147, 102, 150)(98, 146, 104, 152, 105, 153)(100, 148, 111, 159, 112, 160)(101, 149, 113, 161, 114, 162)(103, 151, 119, 167, 120, 168)(106, 154, 129, 177, 130, 178)(107, 155, 122, 170, 131, 179)(108, 156, 121, 169, 132, 180)(109, 157, 133, 181, 134, 182)(110, 158, 135, 183, 136, 184)(115, 163, 124, 172, 141, 189)(116, 164, 123, 171, 142, 190)(117, 165, 128, 176, 140, 188)(118, 166, 127, 175, 139, 187)(125, 173, 137, 185, 143, 191)(126, 174, 138, 186, 144, 192)
	L = (1, 100)(2, 101)(3, 108)(4, 103)(5, 106)(6, 116)(7, 97)(8, 122)(9, 126)(10, 98)(11, 109)(12, 110)(13, 129)(14, 99)(15, 121)(16, 125)(17, 131)(18, 134)(19, 117)(20, 118)(21, 130)(22, 102)(23, 132)(24, 136)(25, 123)(26, 124)(27, 111)(28, 104)(29, 127)(30, 128)(31, 112)(32, 105)(33, 107)(34, 115)(35, 138)(36, 137)(37, 141)(38, 140)(39, 142)(40, 139)(41, 119)(42, 113)(43, 120)(44, 114)(45, 144)(46, 143)(47, 135)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.641
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.650 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^3, (R * Y3)^2, Y2 * Y1^-1 * Y3^-1 * Y1, (R * Y1)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1, Y3 * Y1^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1, (Y3 * Y2^-1)^4, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 30, 78, 21, 69, 5, 53)(3, 51, 13, 61, 31, 79, 33, 81, 44, 92, 15, 63)(4, 52, 9, 57, 25, 73, 42, 90, 14, 62, 18, 66)(6, 54, 24, 72, 29, 77, 46, 94, 19, 67, 23, 71)(7, 55, 11, 59, 36, 84, 40, 88, 41, 89, 28, 76)(10, 58, 16, 64, 37, 85, 47, 95, 20, 68, 35, 83)(12, 60, 32, 80, 45, 93, 27, 75, 22, 70, 39, 87)(17, 65, 34, 82, 26, 74, 38, 86, 48, 96, 43, 91)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 115, 163)(101, 149, 116, 164, 118, 166)(103, 151, 123, 171, 125, 173)(104, 152, 112, 160, 128, 176)(106, 154, 130, 178, 124, 172)(108, 156, 119, 167, 136, 184)(109, 157, 114, 162, 133, 181)(110, 158, 137, 185, 117, 165)(111, 159, 139, 187, 141, 189)(120, 168, 138, 186, 134, 182)(121, 169, 131, 179, 140, 188)(122, 170, 135, 183, 127, 175)(126, 174, 129, 177, 142, 190)(132, 180, 143, 191, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 103)(5, 111)(6, 121)(7, 97)(8, 127)(9, 116)(10, 108)(11, 133)(12, 98)(13, 130)(14, 112)(15, 119)(16, 99)(17, 137)(18, 139)(19, 132)(20, 129)(21, 143)(22, 109)(23, 101)(24, 124)(25, 122)(26, 102)(27, 117)(28, 141)(29, 104)(30, 138)(31, 125)(32, 140)(33, 105)(34, 118)(35, 113)(36, 135)(37, 134)(38, 107)(39, 115)(40, 126)(41, 131)(42, 136)(43, 142)(44, 144)(45, 120)(46, 114)(47, 123)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.642
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.651 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3 * Y1^-1 * Y3, Y1 * Y2^-1 * Y1^2 * Y3, Y1^2 * Y3^-1 * Y2 * Y3, Y3^-1 * Y2 * Y1^-1 * R * Y2^-1 * R, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1, Y1^6, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 32, 80, 22, 70, 5, 53)(3, 51, 13, 61, 21, 69, 42, 90, 41, 89, 14, 62)(4, 52, 16, 64, 25, 73, 31, 79, 9, 57, 19, 67)(6, 54, 20, 68, 24, 72, 45, 93, 47, 95, 26, 74)(7, 55, 28, 76, 44, 92, 18, 66, 11, 59, 30, 78)(10, 58, 15, 63, 37, 85, 40, 88, 33, 81, 36, 84)(12, 60, 23, 71, 46, 94, 29, 77, 34, 82, 39, 87)(17, 65, 35, 83, 27, 75, 38, 86, 48, 96, 43, 91)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 116, 164)(101, 149, 111, 159, 119, 167)(103, 151, 125, 173, 122, 170)(104, 152, 129, 177, 130, 178)(106, 154, 131, 179, 126, 174)(108, 156, 120, 168, 114, 162)(109, 157, 121, 169, 132, 180)(110, 158, 123, 171, 135, 183)(112, 160, 124, 172, 118, 166)(115, 163, 133, 181, 137, 185)(117, 165, 139, 187, 142, 190)(127, 175, 134, 182, 143, 191)(128, 176, 138, 186, 141, 189)(136, 184, 144, 192, 140, 188)
	L = (1, 100)(2, 106)(3, 105)(4, 114)(5, 117)(6, 121)(7, 97)(8, 110)(9, 129)(10, 125)(11, 133)(12, 98)(13, 131)(14, 120)(15, 99)(16, 111)(17, 124)(18, 128)(19, 123)(20, 126)(21, 122)(22, 136)(23, 137)(24, 101)(25, 139)(26, 104)(27, 102)(28, 132)(29, 118)(30, 135)(31, 103)(32, 127)(33, 138)(34, 109)(35, 119)(36, 134)(37, 113)(38, 107)(39, 143)(40, 108)(41, 144)(42, 112)(43, 141)(44, 142)(45, 115)(46, 116)(47, 140)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.648
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.652 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y3^2 * Y1^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^2 * Y1 * Y2, Y1 * Y2 * R * Y2^-1 * R, Y1^2 * Y3^-1 * Y2 * Y3, Y1 * Y3 * Y1 * Y3 * Y2^-1, Y1 * Y2 * Y3 * Y2 * Y3^-1, Y1^2 * Y2 * Y3^-2 * Y2^-1, Y2^-1 * Y3^-4 * Y1^-1, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 32, 80, 23, 71, 5, 53)(3, 51, 13, 61, 11, 59, 37, 85, 44, 92, 15, 63)(4, 52, 17, 65, 12, 60, 39, 87, 14, 62, 19, 67)(6, 54, 26, 74, 42, 90, 46, 94, 21, 69, 27, 75)(7, 55, 29, 77, 35, 83, 40, 88, 22, 70, 30, 78)(9, 57, 34, 82, 33, 81, 45, 93, 41, 89, 24, 72)(10, 58, 16, 64, 31, 79, 47, 95, 20, 68, 25, 73)(18, 66, 36, 84, 28, 76, 38, 86, 48, 96, 43, 91)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 114, 162, 116, 164)(101, 149, 117, 165, 120, 168)(103, 151, 115, 163, 127, 175)(104, 152, 122, 170, 129, 177)(106, 154, 132, 180, 126, 174)(108, 156, 121, 169, 136, 184)(109, 157, 137, 185, 138, 186)(110, 158, 118, 166, 139, 187)(111, 159, 119, 167, 141, 189)(112, 160, 135, 183, 134, 182)(113, 161, 125, 173, 124, 172)(123, 171, 140, 188, 130, 178)(128, 176, 133, 181, 142, 190)(131, 179, 143, 191, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 118)(6, 108)(7, 97)(8, 125)(9, 116)(10, 130)(11, 127)(12, 98)(13, 132)(14, 122)(15, 121)(16, 99)(17, 117)(18, 111)(19, 119)(20, 133)(21, 131)(22, 123)(23, 143)(24, 103)(25, 101)(26, 126)(27, 114)(28, 102)(29, 138)(30, 141)(31, 104)(32, 135)(33, 136)(34, 124)(35, 105)(36, 120)(37, 113)(38, 107)(39, 140)(40, 128)(41, 139)(42, 134)(43, 142)(44, 144)(45, 112)(46, 115)(47, 137)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.643
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.653 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (Y3^-1, Y1), Y3^-2 * Y1^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y2, Y2^-1 * R * Y2 * R * Y1^-1, Y1^2 * Y2 * Y1^-1 * Y2, Y3^2 * Y1^4, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^6, Y3^2 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 29, 77, 20, 68, 5, 53)(3, 51, 13, 61, 11, 59, 35, 83, 43, 91, 15, 63)(4, 52, 10, 58, 30, 78, 22, 70, 7, 55, 12, 60)(6, 54, 23, 71, 40, 88, 47, 95, 19, 67, 25, 73)(9, 57, 32, 80, 31, 79, 44, 92, 39, 87, 21, 69)(14, 62, 18, 66, 36, 84, 45, 93, 16, 64, 37, 85)(17, 65, 33, 81, 34, 82, 46, 94, 41, 89, 28, 76)(24, 72, 42, 90, 48, 96, 27, 75, 26, 74, 38, 86)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 114, 162)(101, 149, 115, 163, 117, 165)(103, 151, 123, 171, 124, 172)(104, 152, 119, 167, 127, 175)(106, 154, 120, 168, 130, 178)(108, 156, 133, 181, 134, 182)(109, 157, 135, 183, 136, 184)(110, 158, 137, 185, 138, 186)(111, 159, 116, 164, 140, 188)(112, 160, 118, 166, 142, 190)(121, 169, 139, 187, 128, 176)(122, 170, 141, 189, 129, 177)(125, 173, 131, 179, 143, 191)(126, 174, 132, 180, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 120)(7, 97)(8, 126)(9, 129)(10, 125)(11, 132)(12, 98)(13, 114)(14, 107)(15, 133)(16, 99)(17, 128)(18, 131)(19, 122)(20, 103)(21, 113)(22, 101)(23, 138)(24, 136)(25, 134)(26, 102)(27, 121)(28, 105)(29, 118)(30, 116)(31, 142)(32, 130)(33, 127)(34, 140)(35, 141)(36, 139)(37, 109)(38, 119)(39, 124)(40, 144)(41, 117)(42, 143)(43, 112)(44, 137)(45, 111)(46, 135)(47, 123)(48, 115)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.646
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.654 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^-2 * Y3^2, (R * Y3)^2, Y1 * Y2^-1 * Y3 * Y2^-1, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y1^-6, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, Y3^6, Y3 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 18, 66, 5, 53)(3, 51, 13, 61, 37, 85, 45, 93, 35, 83, 15, 63)(4, 52, 10, 58, 27, 75, 20, 68, 7, 55, 12, 60)(6, 54, 21, 69, 42, 90, 46, 94, 32, 80, 22, 70)(9, 57, 29, 77, 24, 72, 43, 91, 38, 86, 31, 79)(11, 59, 33, 81, 14, 62, 39, 87, 48, 96, 34, 82)(16, 64, 30, 78, 19, 67, 44, 92, 40, 88, 28, 76)(17, 65, 41, 89, 47, 95, 26, 74, 23, 71, 36, 84)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 112, 160, 111, 159)(101, 149, 113, 161, 115, 163)(103, 151, 117, 165, 120, 168)(104, 152, 122, 170, 124, 172)(106, 154, 128, 176, 127, 175)(108, 156, 129, 177, 132, 180)(109, 157, 134, 182, 119, 167)(110, 158, 136, 184, 118, 166)(114, 162, 139, 187, 135, 183)(116, 164, 140, 188, 133, 181)(121, 169, 141, 189, 142, 190)(123, 171, 144, 192, 143, 191)(125, 173, 137, 185, 131, 179)(126, 174, 138, 186, 130, 178)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 113)(7, 97)(8, 123)(9, 126)(10, 121)(11, 99)(12, 98)(13, 135)(14, 133)(15, 129)(16, 125)(17, 138)(18, 103)(19, 139)(20, 101)(21, 137)(22, 132)(23, 102)(24, 140)(25, 116)(26, 118)(27, 114)(28, 105)(29, 115)(30, 120)(31, 112)(32, 119)(33, 109)(34, 111)(35, 107)(36, 117)(37, 144)(38, 124)(39, 141)(40, 127)(41, 142)(42, 143)(43, 136)(44, 134)(45, 130)(46, 122)(47, 128)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.647
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.655 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (R * Y3)^2, Y3^-1 * Y1^2 * Y2^-1, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^2, Y3 * Y1^2 * Y3^-1 * Y2, R * Y2 * Y3 * R * Y2^-1, Y1 * Y3 * Y1 * Y3 * Y2^-1, Y1 * Y2 * Y3 * Y1^-1 * Y2, (Y3 * Y2)^3, Y3^6, (Y2 * R * Y2^-1 * Y1^-1)^2, (Y2 * Y3 * Y2^-1 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 32, 80, 22, 70, 5, 53)(3, 51, 13, 61, 39, 87, 29, 77, 7, 55, 15, 63)(4, 52, 17, 65, 26, 74, 23, 71, 14, 62, 19, 67)(6, 54, 25, 73, 35, 83, 10, 58, 16, 64, 27, 75)(9, 57, 28, 76, 40, 88, 37, 85, 12, 60, 31, 79)(11, 59, 36, 84, 46, 94, 33, 81, 34, 82, 18, 66)(20, 68, 24, 72, 47, 95, 21, 69, 30, 78, 38, 86)(41, 89, 43, 91, 45, 93, 42, 90, 44, 92, 48, 96)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 104, 152, 116, 164)(101, 149, 117, 165, 119, 167)(103, 151, 124, 172, 126, 174)(106, 154, 128, 176, 125, 173)(108, 156, 120, 168, 109, 157)(110, 158, 135, 183, 137, 185)(111, 159, 138, 186, 113, 161)(112, 160, 127, 175, 140, 188)(114, 162, 122, 170, 131, 179)(115, 163, 123, 171, 142, 190)(118, 166, 133, 181, 129, 177)(121, 169, 136, 184, 139, 187)(130, 178, 134, 182, 144, 192)(132, 180, 143, 191, 141, 189)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 107)(6, 122)(7, 97)(8, 129)(9, 121)(10, 115)(11, 123)(12, 98)(13, 128)(14, 116)(15, 120)(16, 99)(17, 117)(18, 141)(19, 138)(20, 132)(21, 130)(22, 102)(23, 142)(24, 101)(25, 125)(26, 137)(27, 139)(28, 118)(29, 113)(30, 104)(31, 103)(32, 119)(33, 131)(34, 105)(35, 140)(36, 133)(37, 112)(38, 108)(39, 126)(40, 109)(41, 143)(42, 134)(43, 111)(44, 135)(45, 127)(46, 144)(47, 124)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.645
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.656 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y3^2 * Y1^-2, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1^-1 * Y2, Y2^-1 * R * Y2 * R * Y3^-1, Y1^2 * Y2 * Y3^-1 * Y2, Y3^-4 * Y1^-2, Y1^6, Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y2^-1, (Y3^-1 * Y2^-1)^3, Y1^2 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 29, 77, 20, 68, 5, 53)(3, 51, 13, 61, 18, 66, 36, 84, 43, 91, 15, 63)(4, 52, 10, 58, 30, 78, 22, 70, 7, 55, 12, 60)(6, 54, 23, 71, 42, 90, 48, 96, 27, 75, 25, 73)(9, 57, 32, 80, 34, 82, 46, 94, 39, 87, 28, 76)(11, 59, 35, 83, 45, 93, 16, 64, 37, 85, 14, 62)(17, 65, 33, 81, 31, 79, 44, 92, 41, 89, 21, 69)(19, 67, 26, 74, 38, 86, 24, 72, 40, 88, 47, 95)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 114, 162)(101, 149, 115, 163, 117, 165)(103, 151, 123, 171, 124, 172)(104, 152, 120, 168, 127, 175)(106, 154, 119, 167, 130, 178)(108, 156, 133, 181, 134, 182)(109, 157, 135, 183, 136, 184)(110, 158, 137, 185, 138, 186)(111, 159, 118, 166, 140, 188)(112, 160, 116, 164, 142, 190)(121, 169, 141, 189, 129, 177)(122, 170, 139, 187, 128, 176)(125, 173, 132, 180, 144, 192)(126, 174, 131, 179, 143, 191)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 120)(7, 97)(8, 126)(9, 129)(10, 125)(11, 132)(12, 98)(13, 107)(14, 114)(15, 133)(16, 99)(17, 128)(18, 131)(19, 121)(20, 103)(21, 105)(22, 101)(23, 136)(24, 138)(25, 134)(26, 102)(27, 122)(28, 113)(29, 118)(30, 116)(31, 142)(32, 127)(33, 130)(34, 140)(35, 139)(36, 141)(37, 109)(38, 119)(39, 117)(40, 144)(41, 124)(42, 143)(43, 112)(44, 135)(45, 111)(46, 137)(47, 123)(48, 115)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.644
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 6^16, 12^8 ]

E27.657 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6, Y2 * Y3^-2 * Y1^3, Y3 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-3 * Y2 * Y3^-1, Y2 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y3 * Y1^2 * Y3^-2 * Y1, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 18, 66, 17, 65, 5, 53)(3, 51, 9, 57, 27, 75, 13, 61, 33, 81, 11, 59)(4, 52, 12, 60, 30, 78, 10, 58, 29, 77, 14, 62)(7, 55, 21, 69, 41, 89, 25, 73, 45, 93, 23, 71)(8, 56, 24, 72, 43, 91, 22, 70, 42, 90, 26, 74)(15, 63, 28, 76, 38, 86, 19, 67, 37, 85, 36, 84)(16, 64, 32, 80, 40, 88, 20, 68, 39, 87, 35, 83)(31, 79, 44, 92, 48, 96, 47, 95, 34, 82, 46, 94)(97, 145, 99, 147, 106, 154, 114, 162, 109, 157, 100, 148)(98, 146, 103, 151, 118, 166, 113, 161, 121, 169, 104, 152)(101, 149, 111, 159, 116, 164, 102, 150, 115, 163, 112, 160)(105, 153, 117, 165, 133, 181, 129, 177, 141, 189, 124, 172)(107, 155, 127, 175, 135, 183, 123, 171, 143, 191, 128, 176)(108, 156, 119, 167, 140, 188, 125, 173, 137, 185, 130, 178)(110, 158, 122, 170, 136, 184, 126, 174, 139, 187, 131, 179)(120, 168, 134, 182, 144, 192, 138, 186, 132, 180, 142, 190)
	L = (1, 100)(2, 104)(3, 97)(4, 109)(5, 112)(6, 116)(7, 98)(8, 121)(9, 124)(10, 99)(11, 128)(12, 130)(13, 114)(14, 131)(15, 101)(16, 115)(17, 118)(18, 106)(19, 102)(20, 111)(21, 105)(22, 103)(23, 108)(24, 142)(25, 113)(26, 110)(27, 135)(28, 141)(29, 140)(30, 136)(31, 107)(32, 143)(33, 133)(34, 137)(35, 139)(36, 138)(37, 117)(38, 120)(39, 127)(40, 122)(41, 125)(42, 144)(43, 126)(44, 119)(45, 129)(46, 132)(47, 123)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.638
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.658 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-2, (Y3 * Y2^-1)^3, Y1^6, Y2^6, Y2^-2 * Y1^-1 * Y2^-2 * Y1^2, Y2 * Y1 * Y2^2 * Y1^-2 * Y3^-1, Y1 * Y3^2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y1^2 * Y3 * Y2^-1 * Y1^-1 * Y2^-2, Y3^2 * Y1^-1 * Y2 * Y3^-2 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 18, 66, 17, 65, 5, 53)(3, 51, 9, 57, 8, 56, 22, 70, 30, 78, 11, 59)(4, 52, 12, 60, 31, 79, 38, 86, 15, 63, 14, 62)(7, 55, 20, 68, 19, 67, 41, 89, 40, 88, 16, 64)(10, 58, 26, 74, 25, 73, 44, 92, 39, 87, 28, 76)(13, 61, 33, 81, 21, 69, 42, 90, 35, 83, 34, 82)(23, 71, 36, 84, 32, 80, 29, 77, 24, 72, 37, 85)(27, 75, 43, 91, 45, 93, 48, 96, 47, 95, 46, 94)(97, 145, 99, 147, 106, 154, 123, 171, 109, 157, 100, 148)(98, 146, 103, 151, 117, 165, 139, 187, 119, 167, 104, 152)(101, 149, 111, 159, 133, 181, 142, 190, 135, 183, 112, 160)(102, 150, 108, 156, 128, 176, 141, 189, 122, 170, 115, 163)(105, 153, 120, 168, 127, 175, 129, 177, 136, 184, 121, 169)(107, 155, 113, 161, 137, 185, 130, 178, 143, 191, 125, 173)(110, 158, 131, 179, 116, 164, 124, 172, 126, 174, 132, 180)(114, 162, 118, 166, 140, 188, 144, 192, 138, 186, 134, 182)
	L = (1, 100)(2, 104)(3, 97)(4, 109)(5, 112)(6, 115)(7, 98)(8, 119)(9, 121)(10, 99)(11, 125)(12, 102)(13, 123)(14, 132)(15, 101)(16, 135)(17, 107)(18, 134)(19, 122)(20, 131)(21, 103)(22, 114)(23, 139)(24, 105)(25, 136)(26, 141)(27, 106)(28, 116)(29, 143)(30, 124)(31, 120)(32, 108)(33, 127)(34, 137)(35, 110)(36, 126)(37, 111)(38, 138)(39, 142)(40, 129)(41, 113)(42, 144)(43, 117)(44, 118)(45, 128)(46, 133)(47, 130)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.639
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.659 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y2 * Y3, Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6, Y1^6, Y3 * Y1^-1 * Y2 * Y1^2 * Y2^-1, Y3 * Y1 * Y3^-2 * Y1^-2, Y1^-2 * Y2 * Y3^-1 * Y1 * Y2^-1, (Y3 * Y2^-1)^3, Y3 * Y1^2 * Y3^-1 * Y1^-1 * Y2^-1, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 18, 66, 17, 65, 5, 53)(3, 51, 9, 57, 22, 70, 38, 86, 33, 81, 11, 59)(4, 52, 12, 60, 28, 76, 39, 87, 36, 84, 14, 62)(7, 55, 21, 69, 41, 89, 32, 80, 47, 95, 23, 71)(8, 56, 24, 72, 44, 92, 35, 83, 13, 61, 26, 74)(10, 58, 19, 67, 40, 88, 37, 85, 15, 63, 30, 78)(16, 64, 25, 73, 43, 91, 20, 68, 42, 90, 27, 75)(29, 77, 45, 93, 34, 82, 48, 96, 31, 79, 46, 94)(97, 145, 99, 147, 106, 154, 125, 173, 109, 157, 100, 148)(98, 146, 103, 151, 118, 166, 141, 189, 121, 169, 104, 152)(101, 149, 111, 159, 119, 167, 142, 190, 132, 180, 112, 160)(102, 150, 115, 163, 137, 185, 130, 178, 108, 156, 116, 164)(105, 153, 123, 171, 136, 184, 122, 170, 143, 191, 124, 172)(107, 155, 127, 175, 138, 186, 131, 179, 113, 161, 128, 176)(110, 158, 129, 177, 139, 187, 126, 174, 140, 188, 117, 165)(114, 162, 134, 182, 133, 181, 144, 192, 120, 168, 135, 183)
	L = (1, 100)(2, 104)(3, 97)(4, 109)(5, 112)(6, 116)(7, 98)(8, 121)(9, 124)(10, 99)(11, 128)(12, 130)(13, 125)(14, 117)(15, 101)(16, 132)(17, 131)(18, 135)(19, 102)(20, 108)(21, 140)(22, 103)(23, 111)(24, 144)(25, 141)(26, 136)(27, 105)(28, 143)(29, 106)(30, 139)(31, 107)(32, 113)(33, 110)(34, 137)(35, 138)(36, 142)(37, 134)(38, 114)(39, 120)(40, 123)(41, 115)(42, 127)(43, 129)(44, 126)(45, 118)(46, 119)(47, 122)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.637
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.660 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6, 6})
Quotient :: dipole
Aut^+ = C2 x SL(2,3) (small group id <48, 32>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, Y3^-1 * Y1^-2 * Y2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-2 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2^2 * Y3 * Y2, Y1 * Y3^-1 * Y2^-1 * Y3^-2, Y1 * Y2^-2 * Y3^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * R * Y2^-1)^2, Y3^6, Y2^6, Y2 * Y1 * Y3^-2 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 34, 82, 21, 69, 5, 53)(3, 51, 13, 61, 11, 59, 22, 70, 12, 60, 16, 64)(4, 52, 17, 65, 23, 71, 9, 57, 24, 72, 20, 68)(6, 54, 25, 73, 7, 55, 30, 78, 10, 58, 27, 75)(14, 62, 37, 85, 35, 83, 41, 89, 38, 86, 19, 67)(15, 63, 36, 84, 42, 90, 32, 80, 26, 74, 33, 81)(18, 66, 28, 76, 31, 79, 29, 77, 43, 91, 45, 93)(39, 87, 48, 96, 47, 95, 46, 94, 44, 92, 40, 88)(97, 145, 99, 147, 110, 158, 135, 183, 124, 172, 102, 150)(98, 146, 105, 153, 125, 173, 144, 192, 129, 177, 107, 155)(100, 148, 114, 162, 140, 188, 138, 186, 112, 160, 117, 165)(101, 149, 106, 154, 122, 170, 136, 184, 134, 182, 119, 167)(103, 151, 127, 175, 113, 161, 131, 179, 109, 157, 128, 176)(104, 152, 121, 169, 132, 180, 143, 191, 133, 181, 116, 164)(108, 156, 111, 159, 123, 171, 141, 189, 120, 168, 115, 163)(118, 166, 137, 185, 142, 190, 139, 187, 126, 174, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 122)(7, 97)(8, 99)(9, 131)(10, 127)(11, 110)(12, 98)(13, 117)(14, 119)(15, 136)(16, 137)(17, 104)(18, 126)(19, 142)(20, 125)(21, 121)(22, 128)(23, 114)(24, 101)(25, 141)(26, 112)(27, 130)(28, 120)(29, 102)(30, 132)(31, 140)(32, 143)(33, 103)(34, 105)(35, 135)(36, 107)(37, 108)(38, 109)(39, 138)(40, 139)(41, 116)(42, 123)(43, 113)(44, 133)(45, 144)(46, 129)(47, 124)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.640
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.661 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^2 * Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y3^4 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 17, 65, 43, 91, 48, 96, 28, 76, 8, 56, 7, 55)(2, 50, 9, 57, 30, 78, 18, 66, 44, 92, 38, 86, 20, 68, 11, 59)(3, 51, 13, 61, 5, 53, 19, 67, 45, 93, 31, 79, 36, 84, 15, 63)(6, 54, 23, 71, 14, 62, 40, 88, 26, 74, 25, 73, 46, 94, 24, 72)(10, 58, 33, 81, 27, 75, 16, 64, 42, 90, 35, 83, 22, 70, 34, 82)(12, 60, 37, 85, 32, 80, 39, 87, 21, 69, 47, 95, 41, 89, 29, 77)(97, 98, 101)(99, 108, 110)(100, 112, 114)(102, 118, 113)(103, 111, 120)(104, 122, 123)(105, 125, 127)(106, 128, 126)(107, 124, 130)(109, 134, 135)(115, 136, 139)(116, 138, 137)(117, 142, 141)(119, 143, 129)(121, 133, 131)(132, 144, 140)(145, 147, 150)(146, 152, 154)(148, 153, 163)(149, 164, 165)(151, 169, 160)(155, 179, 173)(156, 180, 174)(157, 181, 184)(158, 185, 171)(159, 172, 182)(161, 186, 188)(162, 177, 183)(166, 190, 176)(167, 178, 187)(168, 175, 191)(170, 192, 189)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 32^3 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.665
Graph:: simple bipartite
	v = 38 e = 96 f = 6
	degree seq :: [ 3^32, 16^6 ]

E27.662 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, Y3 * Y1^-1 * Y3^-1 * Y2, Y3^2 * Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2, (Y1 * Y2)^4, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 8, 56, 27, 75, 48, 96, 46, 94, 23, 71, 7, 55)(2, 50, 9, 57, 19, 67, 38, 86, 47, 95, 25, 73, 33, 81, 11, 59)(3, 51, 13, 61, 36, 84, 35, 83, 45, 93, 21, 69, 5, 53, 15, 63)(6, 54, 17, 65, 42, 90, 16, 64, 26, 74, 40, 88, 14, 62, 24, 72)(10, 58, 30, 78, 22, 70, 29, 77, 44, 92, 18, 66, 28, 76, 34, 82)(12, 60, 31, 79, 39, 87, 43, 91, 20, 68, 41, 89, 32, 80, 37, 85)(97, 98, 101)(99, 108, 110)(100, 109, 113)(102, 118, 119)(103, 114, 121)(104, 122, 124)(105, 123, 126)(106, 128, 129)(107, 127, 131)(111, 134, 137)(112, 133, 125)(115, 140, 135)(116, 138, 141)(117, 136, 142)(120, 139, 130)(132, 144, 143)(145, 147, 150)(146, 152, 154)(148, 160, 162)(149, 163, 164)(151, 155, 165)(153, 173, 175)(156, 180, 177)(157, 171, 182)(158, 183, 172)(159, 181, 184)(161, 179, 187)(166, 186, 176)(167, 188, 191)(168, 174, 190)(169, 178, 185)(170, 192, 189)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 32^3 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.666
Graph:: simple bipartite
	v = 38 e = 96 f = 6
	degree seq :: [ 3^32, 16^6 ]

E27.663 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^-1 * Y1^2 * Y2^-1, (Y2^-1, Y1), Y1 * Y2^3, Y2^-1 * Y1^-3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y3)^2, Y2^2 * Y1^-2, (Y2^-1 * Y1)^2, R * Y2 * R * Y1, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 10, 58, 12, 60)(3, 51, 13, 61, 14, 62)(5, 53, 19, 67, 16, 64)(6, 54, 20, 68, 15, 63)(8, 56, 23, 71, 24, 72)(9, 57, 25, 73, 26, 74)(11, 59, 30, 78, 27, 75)(17, 65, 35, 83, 22, 70)(18, 66, 36, 84, 21, 69)(28, 76, 43, 91, 32, 80)(29, 77, 44, 92, 31, 79)(33, 81, 37, 85, 45, 93)(34, 82, 38, 86, 46, 94)(39, 87, 47, 95, 42, 90)(40, 88, 48, 96, 41, 89)(97, 98, 104, 102, 107, 99, 105, 101)(100, 111, 129, 114, 126, 112, 130, 113)(103, 117, 124, 106, 123, 118, 125, 109)(108, 127, 135, 119, 110, 128, 136, 121)(115, 120, 137, 134, 116, 122, 138, 133)(131, 141, 144, 140, 132, 142, 143, 139)(145, 147, 152, 149, 155, 146, 153, 150)(148, 160, 177, 161, 174, 159, 178, 162)(151, 166, 172, 157, 171, 165, 173, 154)(156, 176, 183, 169, 158, 175, 184, 167)(163, 170, 185, 181, 164, 168, 186, 182)(179, 190, 192, 187, 180, 189, 191, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.667
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.664 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1, Y3^3, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y2 * Y1^-1 * Y3^-1, Y3 * Y1 * Y2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^2 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-1, Y2^8 ]
Map:: polytopal non-degenerate
	R = (1, 49, 3, 51, 5, 53)(2, 50, 7, 55, 8, 56)(4, 52, 11, 59, 13, 61)(6, 54, 17, 65, 18, 66)(9, 57, 23, 71, 24, 72)(10, 58, 25, 73, 27, 75)(12, 60, 30, 78, 20, 68)(14, 62, 33, 81, 16, 64)(15, 63, 34, 82, 35, 83)(19, 67, 39, 87, 26, 74)(21, 69, 29, 77, 36, 84)(22, 70, 41, 89, 42, 90)(28, 76, 43, 91, 44, 92)(31, 79, 32, 80, 46, 94)(37, 85, 47, 95, 40, 88)(38, 86, 45, 93, 48, 96)(97, 98, 102, 112, 132, 121, 108, 100)(99, 105, 118, 104, 117, 130, 122, 106)(101, 110, 128, 120, 125, 107, 124, 111)(103, 115, 134, 114, 123, 137, 136, 116)(109, 113, 133, 140, 129, 126, 141, 127)(119, 139, 144, 138, 131, 142, 143, 135)(145, 146, 150, 160, 180, 169, 156, 148)(147, 153, 166, 152, 165, 178, 170, 154)(149, 158, 176, 168, 173, 155, 172, 159)(151, 163, 182, 162, 171, 185, 184, 164)(157, 161, 181, 188, 177, 174, 189, 175)(167, 187, 192, 186, 179, 190, 191, 183)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.668
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.665 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^2 * Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y3^4 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 17, 65, 113, 161, 43, 91, 139, 187, 48, 96, 144, 192, 28, 76, 124, 172, 8, 56, 104, 152, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 30, 78, 126, 174, 18, 66, 114, 162, 44, 92, 140, 188, 38, 86, 134, 182, 20, 68, 116, 164, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 5, 53, 101, 149, 19, 67, 115, 163, 45, 93, 141, 189, 31, 79, 127, 175, 36, 84, 132, 180, 15, 63, 111, 159)(6, 54, 102, 150, 23, 71, 119, 167, 14, 62, 110, 158, 40, 88, 136, 184, 26, 74, 122, 170, 25, 73, 121, 169, 46, 94, 142, 190, 24, 72, 120, 168)(10, 58, 106, 154, 33, 81, 129, 177, 27, 75, 123, 171, 16, 64, 112, 160, 42, 90, 138, 186, 35, 83, 131, 179, 22, 70, 118, 166, 34, 82, 130, 178)(12, 60, 108, 156, 37, 85, 133, 181, 32, 80, 128, 176, 39, 87, 135, 183, 21, 69, 117, 165, 47, 95, 143, 191, 41, 89, 137, 185, 29, 77, 125, 173)
	L = (1, 50)(2, 53)(3, 60)(4, 64)(5, 49)(6, 70)(7, 63)(8, 74)(9, 77)(10, 80)(11, 76)(12, 62)(13, 86)(14, 51)(15, 72)(16, 66)(17, 54)(18, 52)(19, 88)(20, 90)(21, 94)(22, 65)(23, 95)(24, 55)(25, 85)(26, 75)(27, 56)(28, 82)(29, 79)(30, 58)(31, 57)(32, 78)(33, 71)(34, 59)(35, 73)(36, 96)(37, 83)(38, 87)(39, 61)(40, 91)(41, 68)(42, 89)(43, 67)(44, 84)(45, 69)(46, 93)(47, 81)(48, 92)(97, 147)(98, 152)(99, 150)(100, 153)(101, 164)(102, 145)(103, 169)(104, 154)(105, 163)(106, 146)(107, 179)(108, 180)(109, 181)(110, 185)(111, 172)(112, 151)(113, 186)(114, 177)(115, 148)(116, 165)(117, 149)(118, 190)(119, 178)(120, 175)(121, 160)(122, 192)(123, 158)(124, 182)(125, 155)(126, 156)(127, 191)(128, 166)(129, 183)(130, 187)(131, 173)(132, 174)(133, 184)(134, 159)(135, 162)(136, 157)(137, 171)(138, 188)(139, 167)(140, 161)(141, 170)(142, 176)(143, 168)(144, 189)
	local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.661
Transitivity :: VT+
Graph::
	v = 6 e = 96 f = 38
	degree seq :: [ 32^6 ]

E27.666 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, Y3 * Y1^-1 * Y3^-1 * Y2, Y3^2 * Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2, (Y1 * Y2)^4, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 8, 56, 104, 152, 27, 75, 123, 171, 48, 96, 144, 192, 46, 94, 142, 190, 23, 71, 119, 167, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 19, 67, 115, 163, 38, 86, 134, 182, 47, 95, 143, 191, 25, 73, 121, 169, 33, 81, 129, 177, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 36, 84, 132, 180, 35, 83, 131, 179, 45, 93, 141, 189, 21, 69, 117, 165, 5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 17, 65, 113, 161, 42, 90, 138, 186, 16, 64, 112, 160, 26, 74, 122, 170, 40, 88, 136, 184, 14, 62, 110, 158, 24, 72, 120, 168)(10, 58, 106, 154, 30, 78, 126, 174, 22, 70, 118, 166, 29, 77, 125, 173, 44, 92, 140, 188, 18, 66, 114, 162, 28, 76, 124, 172, 34, 82, 130, 178)(12, 60, 108, 156, 31, 79, 127, 175, 39, 87, 135, 183, 43, 91, 139, 187, 20, 68, 116, 164, 41, 89, 137, 185, 32, 80, 128, 176, 37, 85, 133, 181)
	L = (1, 50)(2, 53)(3, 60)(4, 61)(5, 49)(6, 70)(7, 66)(8, 74)(9, 75)(10, 80)(11, 79)(12, 62)(13, 65)(14, 51)(15, 86)(16, 85)(17, 52)(18, 73)(19, 92)(20, 90)(21, 88)(22, 71)(23, 54)(24, 91)(25, 55)(26, 76)(27, 78)(28, 56)(29, 64)(30, 57)(31, 83)(32, 81)(33, 58)(34, 72)(35, 59)(36, 96)(37, 77)(38, 89)(39, 67)(40, 94)(41, 63)(42, 93)(43, 82)(44, 87)(45, 68)(46, 69)(47, 84)(48, 95)(97, 147)(98, 152)(99, 150)(100, 160)(101, 163)(102, 145)(103, 155)(104, 154)(105, 173)(106, 146)(107, 165)(108, 180)(109, 171)(110, 183)(111, 181)(112, 162)(113, 179)(114, 148)(115, 164)(116, 149)(117, 151)(118, 186)(119, 188)(120, 174)(121, 178)(122, 192)(123, 182)(124, 158)(125, 175)(126, 190)(127, 153)(128, 166)(129, 156)(130, 185)(131, 187)(132, 177)(133, 184)(134, 157)(135, 172)(136, 159)(137, 169)(138, 176)(139, 161)(140, 191)(141, 170)(142, 168)(143, 167)(144, 189)
	local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.662
Transitivity :: VT+
Graph::
	v = 6 e = 96 f = 38
	degree seq :: [ 32^6 ]

E27.667 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^-1 * Y1^2 * Y2^-1, (Y2^-1, Y1), Y1 * Y2^3, Y2^-1 * Y1^-3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y3)^2, Y2^2 * Y1^-2, (Y2^-1 * Y1)^2, R * Y2 * R * Y1, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 12, 60, 108, 156)(3, 51, 99, 147, 13, 61, 109, 157, 14, 62, 110, 158)(5, 53, 101, 149, 19, 67, 115, 163, 16, 64, 112, 160)(6, 54, 102, 150, 20, 68, 116, 164, 15, 63, 111, 159)(8, 56, 104, 152, 23, 71, 119, 167, 24, 72, 120, 168)(9, 57, 105, 153, 25, 73, 121, 169, 26, 74, 122, 170)(11, 59, 107, 155, 30, 78, 126, 174, 27, 75, 123, 171)(17, 65, 113, 161, 35, 83, 131, 179, 22, 70, 118, 166)(18, 66, 114, 162, 36, 84, 132, 180, 21, 69, 117, 165)(28, 76, 124, 172, 43, 91, 139, 187, 32, 80, 128, 176)(29, 77, 125, 173, 44, 92, 140, 188, 31, 79, 127, 175)(33, 81, 129, 177, 37, 85, 133, 181, 45, 93, 141, 189)(34, 82, 130, 178, 38, 86, 134, 182, 46, 94, 142, 190)(39, 87, 135, 183, 47, 95, 143, 191, 42, 90, 138, 186)(40, 88, 136, 184, 48, 96, 144, 192, 41, 89, 137, 185)
	L = (1, 50)(2, 56)(3, 57)(4, 63)(5, 49)(6, 59)(7, 69)(8, 54)(9, 53)(10, 75)(11, 51)(12, 79)(13, 55)(14, 80)(15, 81)(16, 82)(17, 52)(18, 78)(19, 72)(20, 74)(21, 76)(22, 77)(23, 62)(24, 89)(25, 60)(26, 90)(27, 70)(28, 58)(29, 61)(30, 64)(31, 87)(32, 88)(33, 66)(34, 65)(35, 93)(36, 94)(37, 67)(38, 68)(39, 71)(40, 73)(41, 86)(42, 85)(43, 83)(44, 84)(45, 96)(46, 95)(47, 91)(48, 92)(97, 147)(98, 153)(99, 152)(100, 160)(101, 155)(102, 145)(103, 166)(104, 149)(105, 150)(106, 151)(107, 146)(108, 176)(109, 171)(110, 175)(111, 178)(112, 177)(113, 174)(114, 148)(115, 170)(116, 168)(117, 173)(118, 172)(119, 156)(120, 186)(121, 158)(122, 185)(123, 165)(124, 157)(125, 154)(126, 159)(127, 184)(128, 183)(129, 161)(130, 162)(131, 190)(132, 189)(133, 164)(134, 163)(135, 169)(136, 167)(137, 181)(138, 182)(139, 180)(140, 179)(141, 191)(142, 192)(143, 188)(144, 187)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.663
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.668 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1, Y3^3, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y2 * Y1^-1 * Y3^-1, Y3 * Y1 * Y2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^2 * Y3^-1 * Y2 * Y3 * Y1 * Y3^-1, Y2^8 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 3, 51, 99, 147, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 8, 56, 104, 152)(4, 52, 100, 148, 11, 59, 107, 155, 13, 61, 109, 157)(6, 54, 102, 150, 17, 65, 113, 161, 18, 66, 114, 162)(9, 57, 105, 153, 23, 71, 119, 167, 24, 72, 120, 168)(10, 58, 106, 154, 25, 73, 121, 169, 27, 75, 123, 171)(12, 60, 108, 156, 30, 78, 126, 174, 20, 68, 116, 164)(14, 62, 110, 158, 33, 81, 129, 177, 16, 64, 112, 160)(15, 63, 111, 159, 34, 82, 130, 178, 35, 83, 131, 179)(19, 67, 115, 163, 39, 87, 135, 183, 26, 74, 122, 170)(21, 69, 117, 165, 29, 77, 125, 173, 36, 84, 132, 180)(22, 70, 118, 166, 41, 89, 137, 185, 42, 90, 138, 186)(28, 76, 124, 172, 43, 91, 139, 187, 44, 92, 140, 188)(31, 79, 127, 175, 32, 80, 128, 176, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191, 40, 88, 136, 184)(38, 86, 134, 182, 45, 93, 141, 189, 48, 96, 144, 192)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 64)(7, 67)(8, 69)(9, 70)(10, 51)(11, 76)(12, 52)(13, 65)(14, 80)(15, 53)(16, 84)(17, 85)(18, 75)(19, 86)(20, 55)(21, 82)(22, 56)(23, 91)(24, 77)(25, 60)(26, 58)(27, 89)(28, 63)(29, 59)(30, 93)(31, 61)(32, 72)(33, 78)(34, 74)(35, 94)(36, 73)(37, 92)(38, 66)(39, 71)(40, 68)(41, 88)(42, 83)(43, 96)(44, 81)(45, 79)(46, 95)(47, 87)(48, 90)(97, 146)(98, 150)(99, 153)(100, 145)(101, 158)(102, 160)(103, 163)(104, 165)(105, 166)(106, 147)(107, 172)(108, 148)(109, 161)(110, 176)(111, 149)(112, 180)(113, 181)(114, 171)(115, 182)(116, 151)(117, 178)(118, 152)(119, 187)(120, 173)(121, 156)(122, 154)(123, 185)(124, 159)(125, 155)(126, 189)(127, 157)(128, 168)(129, 174)(130, 170)(131, 190)(132, 169)(133, 188)(134, 162)(135, 167)(136, 164)(137, 184)(138, 179)(139, 192)(140, 177)(141, 175)(142, 191)(143, 183)(144, 186)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.664
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.669 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^2, Y2 * Y1^-1 * Y2 * Y1 * Y2^2 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 16, 64, 18, 66)(7, 55, 19, 67, 20, 68)(9, 57, 24, 72, 25, 73)(11, 59, 28, 76, 29, 77)(12, 60, 30, 78, 31, 79)(15, 63, 27, 75, 35, 83)(17, 65, 33, 81, 37, 85)(21, 69, 38, 86, 40, 88)(22, 70, 36, 84, 34, 82)(23, 71, 39, 87, 41, 89)(26, 74, 32, 80, 44, 92)(42, 90, 48, 96, 46, 94)(43, 91, 45, 93, 47, 95)(97, 145, 99, 147, 105, 153, 112, 160, 132, 180, 127, 175, 111, 159, 101, 149)(98, 146, 102, 150, 113, 161, 124, 172, 130, 178, 110, 158, 117, 165, 103, 151)(100, 148, 107, 155, 119, 167, 104, 152, 118, 166, 116, 164, 128, 176, 108, 156)(106, 154, 122, 170, 138, 186, 120, 168, 126, 174, 137, 185, 141, 189, 123, 171)(109, 157, 121, 169, 139, 187, 134, 182, 114, 162, 131, 179, 142, 190, 129, 177)(115, 163, 133, 181, 143, 191, 140, 188, 125, 173, 136, 184, 144, 192, 135, 183)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.670 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^3 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 16, 64, 18, 66)(7, 55, 19, 67, 20, 68)(9, 57, 24, 72, 26, 74)(11, 59, 28, 76, 25, 73)(12, 60, 30, 78, 31, 79)(15, 63, 35, 83, 23, 71)(17, 65, 38, 86, 39, 87)(21, 69, 22, 70, 37, 85)(27, 75, 33, 81, 40, 88)(29, 77, 45, 93, 34, 82)(32, 80, 36, 84, 44, 92)(41, 89, 46, 94, 47, 95)(42, 90, 43, 91, 48, 96)(97, 145, 99, 147, 105, 153, 121, 169, 136, 184, 115, 163, 111, 159, 101, 149)(98, 146, 102, 150, 113, 161, 106, 154, 123, 171, 126, 174, 117, 165, 103, 151)(100, 148, 107, 155, 125, 173, 114, 162, 129, 177, 109, 157, 128, 176, 108, 156)(104, 152, 118, 166, 137, 185, 122, 170, 116, 164, 134, 182, 138, 186, 119, 167)(110, 158, 120, 168, 139, 187, 140, 188, 124, 172, 131, 179, 142, 190, 130, 178)(112, 160, 132, 180, 143, 191, 135, 183, 127, 175, 141, 189, 144, 192, 133, 181)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.671 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3, Y1^3, (R * Y1)^2, (R * Y3)^2, R * Y3 * Y2 * Y1^-1 * R * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2 * Y1 * Y2^-2, (Y3^-1 * Y1^-1)^3, Y3 * Y1 * Y2^-1 * Y1^-1 * Y2^3, Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2, Y2 * Y3^-1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 16, 64, 18, 66)(7, 55, 19, 67, 20, 68)(9, 57, 24, 72, 25, 73)(11, 59, 28, 76, 29, 77)(12, 60, 30, 78, 31, 79)(15, 63, 27, 75, 35, 83)(17, 65, 33, 81, 37, 85)(21, 69, 38, 86, 40, 88)(22, 70, 36, 84, 34, 82)(23, 71, 39, 87, 41, 89)(26, 74, 32, 80, 44, 92)(42, 90, 48, 96, 46, 94)(43, 91, 45, 93, 47, 95)(97, 145, 99, 147, 105, 153, 112, 160, 132, 180, 127, 175, 111, 159, 101, 149)(98, 146, 102, 150, 113, 161, 124, 172, 130, 178, 110, 158, 117, 165, 103, 151)(100, 148, 107, 155, 119, 167, 104, 152, 118, 166, 116, 164, 128, 176, 108, 156)(106, 154, 122, 170, 138, 186, 120, 168, 126, 174, 137, 185, 141, 189, 123, 171)(109, 157, 121, 169, 139, 187, 134, 182, 114, 162, 131, 179, 142, 190, 129, 177)(115, 163, 133, 181, 143, 191, 140, 188, 125, 173, 136, 184, 144, 192, 135, 183)
	L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 109)(6, 112)(7, 115)(8, 106)(9, 120)(10, 99)(11, 124)(12, 126)(13, 110)(14, 101)(15, 123)(16, 114)(17, 129)(18, 102)(19, 116)(20, 103)(21, 134)(22, 132)(23, 135)(24, 121)(25, 105)(26, 128)(27, 131)(28, 125)(29, 107)(30, 127)(31, 108)(32, 140)(33, 133)(34, 118)(35, 111)(36, 130)(37, 113)(38, 136)(39, 137)(40, 117)(41, 119)(42, 144)(43, 141)(44, 122)(45, 143)(46, 138)(47, 139)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.672 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y3^-1, Y1^3, Y3^4, (Y2 * R)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2, Y1 * Y3 * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 14, 62)(4, 52, 15, 63, 17, 65)(6, 54, 22, 70, 23, 71)(7, 55, 25, 73, 26, 74)(8, 56, 27, 75, 28, 76)(9, 57, 29, 77, 31, 79)(10, 58, 24, 72, 32, 80)(11, 59, 34, 82, 35, 83)(13, 61, 18, 66, 38, 86)(16, 64, 30, 78, 42, 90)(19, 67, 43, 91, 41, 89)(20, 68, 33, 81, 44, 92)(21, 69, 45, 93, 40, 88)(36, 84, 46, 94, 47, 95)(37, 85, 39, 87, 48, 96)(97, 145, 99, 147, 100, 148, 109, 157, 112, 160, 120, 168, 103, 151, 102, 150)(98, 146, 104, 152, 105, 153, 110, 158, 126, 174, 129, 177, 107, 155, 106, 154)(101, 149, 114, 162, 115, 163, 124, 172, 138, 186, 118, 166, 117, 165, 116, 164)(108, 156, 130, 178, 132, 180, 113, 161, 128, 176, 125, 173, 133, 181, 122, 170)(111, 159, 135, 183, 136, 184, 134, 182, 121, 169, 142, 190, 137, 185, 119, 167)(123, 171, 141, 189, 143, 191, 127, 175, 140, 188, 139, 187, 144, 192, 131, 179)
	L = (1, 100)(2, 105)(3, 109)(4, 112)(5, 115)(6, 99)(7, 97)(8, 110)(9, 126)(10, 104)(11, 98)(12, 132)(13, 120)(14, 129)(15, 136)(16, 103)(17, 125)(18, 124)(19, 138)(20, 114)(21, 101)(22, 116)(23, 135)(24, 102)(25, 137)(26, 130)(27, 143)(28, 118)(29, 122)(30, 107)(31, 139)(32, 133)(33, 106)(34, 113)(35, 141)(36, 128)(37, 108)(38, 142)(39, 134)(40, 121)(41, 111)(42, 117)(43, 131)(44, 144)(45, 127)(46, 119)(47, 140)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.673 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^2, Y1^3, (R * Y3)^2, Y3^4, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y2 * Y1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, (Y3^-1 * Y1^-1)^3, Y3 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 13, 61)(4, 52, 15, 63, 17, 65)(6, 54, 23, 71, 24, 72)(7, 55, 25, 73, 26, 74)(8, 56, 14, 62, 27, 75)(9, 57, 29, 77, 31, 79)(10, 58, 32, 80, 33, 81)(11, 59, 34, 82, 35, 83)(16, 64, 30, 78, 36, 84)(18, 66, 21, 69, 42, 90)(19, 67, 28, 76, 43, 91)(20, 68, 44, 92, 37, 85)(22, 70, 45, 93, 40, 88)(38, 86, 48, 96, 46, 94)(39, 87, 47, 95, 41, 89)(97, 145, 99, 147, 103, 151, 110, 158, 112, 160, 114, 162, 100, 148, 102, 150)(98, 146, 104, 152, 107, 155, 124, 172, 126, 174, 120, 168, 105, 153, 106, 154)(101, 149, 115, 163, 118, 166, 108, 156, 132, 180, 129, 177, 116, 164, 117, 165)(109, 157, 133, 181, 135, 183, 121, 169, 138, 186, 136, 184, 134, 182, 111, 159)(113, 161, 137, 185, 130, 178, 119, 167, 122, 170, 142, 190, 125, 173, 123, 171)(127, 175, 143, 191, 141, 189, 128, 176, 131, 179, 144, 192, 140, 188, 139, 187)
	L = (1, 100)(2, 105)(3, 102)(4, 112)(5, 116)(6, 114)(7, 97)(8, 106)(9, 126)(10, 120)(11, 98)(12, 115)(13, 134)(14, 99)(15, 136)(16, 103)(17, 125)(18, 110)(19, 117)(20, 132)(21, 129)(22, 101)(23, 137)(24, 124)(25, 133)(26, 130)(27, 142)(28, 104)(29, 122)(30, 107)(31, 140)(32, 143)(33, 108)(34, 113)(35, 141)(36, 118)(37, 111)(38, 138)(39, 109)(40, 121)(41, 123)(42, 135)(43, 144)(44, 131)(45, 127)(46, 119)(47, 139)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.674 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1^3, (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y1, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y2 * Y1^-1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1 * Y3^2 * Y1, Y3 * Y2^-1 * Y1^-1 * Y2 * Y1, Y3^6, (R * Y2 * Y3^-1)^2, Y3^6, (Y3^-1 * Y1^-1)^3, Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 19, 67)(6, 54, 25, 73, 27, 75)(7, 55, 13, 61, 29, 77)(8, 56, 32, 80, 26, 74)(9, 57, 34, 82, 35, 83)(10, 58, 36, 84, 28, 76)(11, 59, 31, 79, 39, 87)(14, 62, 43, 91, 33, 81)(16, 64, 37, 85, 21, 69)(18, 66, 22, 70, 45, 93)(20, 68, 38, 86, 23, 71)(24, 72, 41, 89, 46, 94)(30, 78, 48, 96, 40, 88)(42, 90, 47, 95, 44, 92)(97, 145, 99, 147, 109, 157, 133, 181, 143, 191, 132, 180, 118, 166, 102, 150)(98, 146, 104, 152, 127, 175, 111, 159, 140, 188, 116, 164, 100, 148, 106, 154)(101, 149, 117, 165, 137, 185, 122, 170, 138, 186, 121, 169, 105, 153, 119, 167)(103, 151, 124, 172, 135, 183, 110, 158, 114, 162, 108, 156, 113, 161, 126, 174)(107, 155, 134, 182, 142, 190, 129, 177, 115, 163, 128, 176, 130, 178, 136, 184)(112, 160, 141, 189, 144, 192, 120, 168, 123, 171, 125, 173, 139, 187, 131, 179)
	L = (1, 100)(2, 105)(3, 110)(4, 114)(5, 118)(6, 122)(7, 97)(8, 129)(9, 115)(10, 133)(11, 98)(12, 104)(13, 120)(14, 123)(15, 102)(16, 99)(17, 142)(18, 143)(19, 140)(20, 136)(21, 139)(22, 131)(23, 111)(24, 101)(25, 144)(26, 106)(27, 132)(28, 116)(29, 113)(30, 112)(31, 103)(32, 117)(33, 124)(34, 125)(35, 138)(36, 126)(37, 119)(38, 121)(39, 130)(40, 108)(41, 107)(42, 109)(43, 134)(44, 137)(45, 135)(46, 141)(47, 127)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.675 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, (Y3^-1 * Y1)^2, (Y3^-1 * Y1)^2, (Y3 * Y2^-1)^2, Y1 * Y3 * Y2^-1 * Y3^-1, R * Y1 * R * Y2, Y3^2 * Y2^-1 * Y1^-1, (R * Y3)^2, Y3^2 * Y1^-1 * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1^-1, Y2 * Y3^2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-22 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 8, 56, 26, 74, 46, 94, 45, 93, 22, 70, 7, 55)(2, 50, 9, 57, 17, 65, 39, 87, 44, 92, 35, 83, 31, 79, 11, 59)(3, 51, 13, 61, 33, 81, 47, 95, 42, 90, 19, 67, 5, 53, 15, 63)(6, 54, 21, 69, 40, 88, 43, 91, 25, 73, 37, 85, 14, 62, 23, 71)(10, 58, 30, 78, 20, 68, 24, 72, 38, 86, 48, 96, 27, 75, 16, 64)(12, 60, 34, 82, 36, 84, 28, 76, 18, 66, 41, 89, 29, 77, 32, 80)(97, 98, 101)(99, 108, 110)(100, 112, 107)(102, 116, 118)(103, 111, 119)(104, 121, 123)(105, 124, 115)(106, 125, 127)(109, 131, 128)(113, 134, 132)(114, 136, 138)(117, 137, 126)(120, 135, 141)(122, 143, 139)(129, 142, 140)(130, 144, 133)(145, 147, 150)(146, 152, 154)(148, 153, 159)(149, 161, 162)(151, 165, 168)(155, 174, 176)(156, 177, 175)(157, 178, 167)(158, 180, 171)(160, 170, 181)(163, 185, 187)(164, 184, 173)(166, 182, 188)(169, 190, 186)(172, 183, 192)(179, 191, 189)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 32^3 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.679
Graph:: simple bipartite
	v = 38 e = 96 f = 6
	degree seq :: [ 3^32, 16^6 ]

E27.676 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^3, (Y3^-1 * Y2^-1)^2, Y1^-1 * Y3^-2 * Y2^-1, Y3 * Y1^-1 * Y3^-1 * Y2, (Y3 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1 * Y3)^2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1, Y3^2 * Y2^-1 * Y3^4 * Y1^-1, Y2 * Y3^-2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 17, 65, 41, 89, 46, 94, 27, 75, 8, 56, 7, 55)(2, 50, 9, 57, 29, 77, 37, 85, 42, 90, 43, 91, 20, 68, 11, 59)(3, 51, 13, 61, 5, 53, 21, 69, 44, 92, 48, 96, 33, 81, 15, 63)(6, 54, 18, 66, 14, 62, 36, 84, 25, 73, 45, 93, 39, 87, 16, 64)(10, 58, 24, 72, 26, 74, 47, 95, 40, 88, 19, 67, 23, 71, 28, 76)(12, 60, 30, 78, 31, 79, 38, 86, 22, 70, 32, 80, 35, 83, 34, 82)(97, 98, 101)(99, 108, 110)(100, 109, 114)(102, 119, 113)(103, 120, 105)(104, 121, 122)(106, 127, 125)(107, 128, 117)(111, 133, 126)(112, 134, 124)(115, 139, 137)(116, 136, 131)(118, 135, 140)(123, 144, 141)(129, 142, 138)(130, 143, 132)(145, 147, 150)(146, 152, 154)(148, 160, 163)(149, 164, 166)(151, 155, 157)(153, 172, 174)(156, 177, 173)(158, 179, 170)(159, 178, 162)(161, 184, 186)(165, 182, 189)(167, 183, 175)(168, 171, 180)(169, 190, 188)(176, 187, 191)(181, 192, 185)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 32^3 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.680
Graph:: simple bipartite
	v = 38 e = 96 f = 6
	degree seq :: [ 3^32, 16^6 ]

E27.677 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^-1 * Y2^2 * Y1^-1, (Y2^-1 * Y1)^2, (Y1 * Y3^-1)^2, Y2^-3 * Y1^-1, Y2^2 * Y1^-2, Y1^-2 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y2 * Y3^-1)^2, R * Y2 * R * Y1, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 10, 58, 12, 60)(3, 51, 13, 61, 14, 62)(5, 53, 17, 65, 18, 66)(6, 54, 19, 67, 20, 68)(8, 56, 23, 71, 24, 72)(9, 57, 25, 73, 26, 74)(11, 59, 29, 77, 30, 78)(15, 63, 33, 81, 21, 69)(16, 64, 34, 82, 22, 70)(27, 75, 43, 91, 31, 79)(28, 76, 44, 92, 32, 80)(35, 83, 46, 94, 37, 85)(36, 84, 45, 93, 38, 86)(39, 87, 47, 95, 41, 89)(40, 88, 48, 96, 42, 90)(97, 98, 104, 102, 107, 99, 105, 101)(100, 111, 128, 110, 125, 112, 127, 108)(103, 113, 131, 118, 126, 115, 132, 117)(106, 123, 138, 122, 109, 124, 137, 120)(114, 121, 136, 134, 116, 119, 135, 133)(129, 141, 144, 139, 130, 142, 143, 140)(145, 147, 152, 149, 155, 146, 153, 150)(148, 160, 176, 156, 173, 159, 175, 158)(151, 163, 179, 165, 174, 161, 180, 166)(154, 172, 186, 168, 157, 171, 185, 170)(162, 167, 184, 181, 164, 169, 183, 182)(177, 190, 192, 188, 178, 189, 191, 187)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.681
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.678 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 8, 8})
Quotient :: edge^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1, Y3^3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^8, Y2^8, (Y3 * Y1^-3)^2, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y1^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 3, 51, 5, 53)(2, 50, 7, 55, 8, 56)(4, 52, 11, 59, 9, 57)(6, 54, 15, 63, 16, 64)(10, 58, 20, 68, 13, 61)(12, 60, 24, 72, 22, 70)(14, 62, 28, 76, 29, 77)(17, 65, 32, 80, 18, 66)(19, 67, 23, 71, 36, 84)(21, 69, 39, 87, 37, 85)(25, 73, 42, 90, 41, 89)(26, 74, 38, 86, 43, 91)(27, 75, 44, 92, 45, 93)(30, 78, 46, 94, 31, 79)(33, 81, 35, 83, 47, 95)(34, 82, 48, 96, 40, 88)(97, 98, 102, 110, 123, 121, 108, 100)(99, 105, 115, 131, 140, 125, 117, 106)(101, 109, 122, 138, 141, 129, 113, 103)(104, 114, 130, 120, 137, 139, 126, 111)(107, 118, 136, 135, 124, 112, 127, 119)(116, 133, 144, 128, 143, 132, 142, 134)(145, 146, 150, 158, 171, 169, 156, 148)(147, 153, 163, 179, 188, 173, 165, 154)(149, 157, 170, 186, 189, 177, 161, 151)(152, 162, 178, 168, 185, 187, 174, 159)(155, 166, 184, 183, 172, 160, 175, 167)(164, 181, 192, 176, 191, 180, 190, 182)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^6 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E27.682
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.679 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^3, (Y3^-1 * Y1)^2, (Y3^-1 * Y1)^2, (Y3 * Y2^-1)^2, Y1 * Y3 * Y2^-1 * Y3^-1, R * Y1 * R * Y2, Y3^2 * Y2^-1 * Y1^-1, (R * Y3)^2, Y3^2 * Y1^-1 * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1^-1, Y2 * Y3^2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^-22 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 8, 56, 104, 152, 26, 74, 122, 170, 46, 94, 142, 190, 45, 93, 141, 189, 22, 70, 118, 166, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 17, 65, 113, 161, 39, 87, 135, 183, 44, 92, 140, 188, 35, 83, 131, 179, 31, 79, 127, 175, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 33, 81, 129, 177, 47, 95, 143, 191, 42, 90, 138, 186, 19, 67, 115, 163, 5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 21, 69, 117, 165, 40, 88, 136, 184, 43, 91, 139, 187, 25, 73, 121, 169, 37, 85, 133, 181, 14, 62, 110, 158, 23, 71, 119, 167)(10, 58, 106, 154, 30, 78, 126, 174, 20, 68, 116, 164, 24, 72, 120, 168, 38, 86, 134, 182, 48, 96, 144, 192, 27, 75, 123, 171, 16, 64, 112, 160)(12, 60, 108, 156, 34, 82, 130, 178, 36, 84, 132, 180, 28, 76, 124, 172, 18, 66, 114, 162, 41, 89, 137, 185, 29, 77, 125, 173, 32, 80, 128, 176)
	L = (1, 50)(2, 53)(3, 60)(4, 64)(5, 49)(6, 68)(7, 63)(8, 73)(9, 76)(10, 77)(11, 52)(12, 62)(13, 83)(14, 51)(15, 71)(16, 59)(17, 86)(18, 88)(19, 57)(20, 70)(21, 89)(22, 54)(23, 55)(24, 87)(25, 75)(26, 95)(27, 56)(28, 67)(29, 79)(30, 69)(31, 58)(32, 61)(33, 94)(34, 96)(35, 80)(36, 65)(37, 82)(38, 84)(39, 93)(40, 90)(41, 78)(42, 66)(43, 74)(44, 81)(45, 72)(46, 92)(47, 91)(48, 85)(97, 147)(98, 152)(99, 150)(100, 153)(101, 161)(102, 145)(103, 165)(104, 154)(105, 159)(106, 146)(107, 174)(108, 177)(109, 178)(110, 180)(111, 148)(112, 170)(113, 162)(114, 149)(115, 185)(116, 184)(117, 168)(118, 182)(119, 157)(120, 151)(121, 190)(122, 181)(123, 158)(124, 183)(125, 164)(126, 176)(127, 156)(128, 155)(129, 175)(130, 167)(131, 191)(132, 171)(133, 160)(134, 188)(135, 192)(136, 173)(137, 187)(138, 169)(139, 163)(140, 166)(141, 179)(142, 186)(143, 189)(144, 172)
	local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.675
Transitivity :: VT+
Graph::
	v = 6 e = 96 f = 38
	degree seq :: [ 32^6 ]

E27.680 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^3, (Y3^-1 * Y2^-1)^2, Y1^-1 * Y3^-2 * Y2^-1, Y3 * Y1^-1 * Y3^-1 * Y2, (Y3 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y1 * Y3)^2, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1, Y3^2 * Y2^-1 * Y3^4 * Y1^-1, Y2 * Y3^-2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 17, 65, 113, 161, 41, 89, 137, 185, 46, 94, 142, 190, 27, 75, 123, 171, 8, 56, 104, 152, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 29, 77, 125, 173, 37, 85, 133, 181, 42, 90, 138, 186, 43, 91, 139, 187, 20, 68, 116, 164, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 5, 53, 101, 149, 21, 69, 117, 165, 44, 92, 140, 188, 48, 96, 144, 192, 33, 81, 129, 177, 15, 63, 111, 159)(6, 54, 102, 150, 18, 66, 114, 162, 14, 62, 110, 158, 36, 84, 132, 180, 25, 73, 121, 169, 45, 93, 141, 189, 39, 87, 135, 183, 16, 64, 112, 160)(10, 58, 106, 154, 24, 72, 120, 168, 26, 74, 122, 170, 47, 95, 143, 191, 40, 88, 136, 184, 19, 67, 115, 163, 23, 71, 119, 167, 28, 76, 124, 172)(12, 60, 108, 156, 30, 78, 126, 174, 31, 79, 127, 175, 38, 86, 134, 182, 22, 70, 118, 166, 32, 80, 128, 176, 35, 83, 131, 179, 34, 82, 130, 178)
	L = (1, 50)(2, 53)(3, 60)(4, 61)(5, 49)(6, 71)(7, 72)(8, 73)(9, 55)(10, 79)(11, 80)(12, 62)(13, 66)(14, 51)(15, 85)(16, 86)(17, 54)(18, 52)(19, 91)(20, 88)(21, 59)(22, 87)(23, 65)(24, 57)(25, 74)(26, 56)(27, 96)(28, 64)(29, 58)(30, 63)(31, 77)(32, 69)(33, 94)(34, 95)(35, 68)(36, 82)(37, 78)(38, 76)(39, 92)(40, 83)(41, 67)(42, 81)(43, 89)(44, 70)(45, 75)(46, 90)(47, 84)(48, 93)(97, 147)(98, 152)(99, 150)(100, 160)(101, 164)(102, 145)(103, 155)(104, 154)(105, 172)(106, 146)(107, 157)(108, 177)(109, 151)(110, 179)(111, 178)(112, 163)(113, 184)(114, 159)(115, 148)(116, 166)(117, 182)(118, 149)(119, 183)(120, 171)(121, 190)(122, 158)(123, 180)(124, 174)(125, 156)(126, 153)(127, 167)(128, 187)(129, 173)(130, 162)(131, 170)(132, 168)(133, 192)(134, 189)(135, 175)(136, 186)(137, 181)(138, 161)(139, 191)(140, 169)(141, 165)(142, 188)(143, 176)(144, 185)
	local type(s) :: { ( 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16, 3, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.676
Transitivity :: VT+
Graph::
	v = 6 e = 96 f = 38
	degree seq :: [ 32^6 ]

E27.681 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = C2 x GL(2,3) (small group id <96, 189>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^-1 * Y2^2 * Y1^-1, (Y2^-1 * Y1)^2, (Y1 * Y3^-1)^2, Y2^-3 * Y1^-1, Y2^2 * Y1^-2, Y1^-2 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y2 * Y3^-1)^2, R * Y2 * R * Y1, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 12, 60, 108, 156)(3, 51, 99, 147, 13, 61, 109, 157, 14, 62, 110, 158)(5, 53, 101, 149, 17, 65, 113, 161, 18, 66, 114, 162)(6, 54, 102, 150, 19, 67, 115, 163, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167, 24, 72, 120, 168)(9, 57, 105, 153, 25, 73, 121, 169, 26, 74, 122, 170)(11, 59, 107, 155, 29, 77, 125, 173, 30, 78, 126, 174)(15, 63, 111, 159, 33, 81, 129, 177, 21, 69, 117, 165)(16, 64, 112, 160, 34, 82, 130, 178, 22, 70, 118, 166)(27, 75, 123, 171, 43, 91, 139, 187, 31, 79, 127, 175)(28, 76, 124, 172, 44, 92, 140, 188, 32, 80, 128, 176)(35, 83, 131, 179, 46, 94, 142, 190, 37, 85, 133, 181)(36, 84, 132, 180, 45, 93, 141, 189, 38, 86, 134, 182)(39, 87, 135, 183, 47, 95, 143, 191, 41, 89, 137, 185)(40, 88, 136, 184, 48, 96, 144, 192, 42, 90, 138, 186)
	L = (1, 50)(2, 56)(3, 57)(4, 63)(5, 49)(6, 59)(7, 65)(8, 54)(9, 53)(10, 75)(11, 51)(12, 52)(13, 76)(14, 77)(15, 80)(16, 79)(17, 83)(18, 73)(19, 84)(20, 71)(21, 55)(22, 78)(23, 87)(24, 58)(25, 88)(26, 61)(27, 90)(28, 89)(29, 64)(30, 67)(31, 60)(32, 62)(33, 93)(34, 94)(35, 70)(36, 69)(37, 66)(38, 68)(39, 85)(40, 86)(41, 72)(42, 74)(43, 82)(44, 81)(45, 96)(46, 95)(47, 92)(48, 91)(97, 147)(98, 153)(99, 152)(100, 160)(101, 155)(102, 145)(103, 163)(104, 149)(105, 150)(106, 172)(107, 146)(108, 173)(109, 171)(110, 148)(111, 175)(112, 176)(113, 180)(114, 167)(115, 179)(116, 169)(117, 174)(118, 151)(119, 184)(120, 157)(121, 183)(122, 154)(123, 185)(124, 186)(125, 159)(126, 161)(127, 158)(128, 156)(129, 190)(130, 189)(131, 165)(132, 166)(133, 164)(134, 162)(135, 182)(136, 181)(137, 170)(138, 168)(139, 177)(140, 178)(141, 191)(142, 192)(143, 187)(144, 188)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.677
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.682 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 8, 8})
Quotient :: loop^2
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y2^-1, Y3^3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^8, Y2^8, (Y3 * Y1^-3)^2, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y1^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 3, 51, 99, 147, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 8, 56, 104, 152)(4, 52, 100, 148, 11, 59, 107, 155, 9, 57, 105, 153)(6, 54, 102, 150, 15, 63, 111, 159, 16, 64, 112, 160)(10, 58, 106, 154, 20, 68, 116, 164, 13, 61, 109, 157)(12, 60, 108, 156, 24, 72, 120, 168, 22, 70, 118, 166)(14, 62, 110, 158, 28, 76, 124, 172, 29, 77, 125, 173)(17, 65, 113, 161, 32, 80, 128, 176, 18, 66, 114, 162)(19, 67, 115, 163, 23, 71, 119, 167, 36, 84, 132, 180)(21, 69, 117, 165, 39, 87, 135, 183, 37, 85, 133, 181)(25, 73, 121, 169, 42, 90, 138, 186, 41, 89, 137, 185)(26, 74, 122, 170, 38, 86, 134, 182, 43, 91, 139, 187)(27, 75, 123, 171, 44, 92, 140, 188, 45, 93, 141, 189)(30, 78, 126, 174, 46, 94, 142, 190, 31, 79, 127, 175)(33, 81, 129, 177, 35, 83, 131, 179, 47, 95, 143, 191)(34, 82, 130, 178, 48, 96, 144, 192, 40, 88, 136, 184)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 61)(6, 62)(7, 53)(8, 66)(9, 67)(10, 51)(11, 70)(12, 52)(13, 74)(14, 75)(15, 56)(16, 79)(17, 55)(18, 82)(19, 83)(20, 85)(21, 58)(22, 88)(23, 59)(24, 89)(25, 60)(26, 90)(27, 73)(28, 64)(29, 69)(30, 63)(31, 71)(32, 95)(33, 65)(34, 72)(35, 92)(36, 94)(37, 96)(38, 68)(39, 76)(40, 87)(41, 91)(42, 93)(43, 78)(44, 77)(45, 81)(46, 86)(47, 84)(48, 80)(97, 146)(98, 150)(99, 153)(100, 145)(101, 157)(102, 158)(103, 149)(104, 162)(105, 163)(106, 147)(107, 166)(108, 148)(109, 170)(110, 171)(111, 152)(112, 175)(113, 151)(114, 178)(115, 179)(116, 181)(117, 154)(118, 184)(119, 155)(120, 185)(121, 156)(122, 186)(123, 169)(124, 160)(125, 165)(126, 159)(127, 167)(128, 191)(129, 161)(130, 168)(131, 188)(132, 190)(133, 192)(134, 164)(135, 172)(136, 183)(137, 187)(138, 189)(139, 174)(140, 173)(141, 177)(142, 182)(143, 180)(144, 176)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.678
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.683 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-3 * Y1)^2, Y2^-2 * Y1 * Y2 * Y1^-1 * Y2^-3 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 12, 60, 6, 54)(7, 55, 15, 63, 11, 59)(9, 57, 18, 66, 20, 68)(13, 61, 25, 73, 23, 71)(14, 62, 24, 72, 28, 76)(16, 64, 31, 79, 29, 77)(17, 65, 33, 81, 21, 69)(19, 67, 36, 84, 32, 80)(22, 70, 30, 78, 41, 89)(26, 74, 40, 88, 43, 91)(27, 75, 44, 92, 34, 82)(35, 83, 46, 94, 38, 86)(37, 85, 45, 93, 48, 96)(39, 87, 47, 95, 42, 90)(97, 145, 99, 147, 105, 153, 115, 163, 133, 181, 122, 170, 109, 157, 101, 149)(98, 146, 102, 150, 110, 158, 123, 171, 141, 189, 128, 176, 112, 160, 103, 151)(100, 148, 107, 155, 118, 166, 136, 184, 144, 192, 130, 178, 113, 161, 104, 152)(106, 154, 117, 165, 135, 183, 121, 169, 139, 187, 137, 185, 131, 179, 114, 162)(108, 156, 119, 167, 138, 186, 127, 175, 132, 180, 116, 164, 134, 182, 120, 168)(111, 159, 125, 173, 143, 191, 129, 177, 140, 188, 124, 172, 142, 190, 126, 174)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.684 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2^8, (Y2^-3 * Y1^-1)^2, (Y2^2 * Y1^-1 * Y2^-1 * Y1^-1)^2, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 7, 55)(5, 53, 10, 58, 12, 60)(6, 54, 14, 62, 11, 59)(9, 57, 19, 67, 18, 66)(13, 61, 23, 71, 25, 73)(15, 63, 29, 77, 28, 76)(16, 64, 17, 65, 31, 79)(20, 68, 37, 85, 36, 84)(21, 69, 39, 87, 24, 72)(22, 70, 27, 75, 41, 89)(26, 74, 43, 91, 30, 78)(32, 80, 47, 95, 40, 88)(33, 81, 42, 90, 44, 92)(34, 82, 35, 83, 45, 93)(38, 86, 46, 94, 48, 96)(97, 145, 99, 147, 105, 153, 116, 164, 134, 182, 122, 170, 109, 157, 101, 149)(98, 146, 102, 150, 111, 159, 126, 174, 142, 190, 128, 176, 112, 160, 103, 151)(100, 148, 106, 154, 117, 165, 136, 184, 144, 192, 133, 181, 118, 166, 107, 155)(104, 152, 113, 161, 129, 177, 121, 169, 139, 187, 125, 173, 130, 178, 114, 162)(108, 156, 119, 167, 138, 186, 137, 185, 132, 180, 115, 163, 131, 179, 120, 168)(110, 158, 123, 171, 140, 188, 127, 175, 143, 191, 135, 183, 141, 189, 124, 172)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.685 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1, Y1^3, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-1 * Y1 * Y2^-2)^2, Y2 * Y3^-2 * Y2^2 * Y1^-2 * Y2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y1^-1 * Y2^-1, Y3^-1 * Y2^-1 * R * Y2^-3 * R * Y2^2, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 12, 60, 6, 54)(7, 55, 15, 63, 11, 59)(9, 57, 18, 66, 20, 68)(13, 61, 25, 73, 23, 71)(14, 62, 24, 72, 28, 76)(16, 64, 31, 79, 29, 77)(17, 65, 33, 81, 21, 69)(19, 67, 36, 84, 32, 80)(22, 70, 30, 78, 41, 89)(26, 74, 40, 88, 43, 91)(27, 75, 44, 92, 34, 82)(35, 83, 46, 94, 38, 86)(37, 85, 45, 93, 48, 96)(39, 87, 47, 95, 42, 90)(97, 145, 99, 147, 105, 153, 115, 163, 133, 181, 122, 170, 109, 157, 101, 149)(98, 146, 102, 150, 110, 158, 123, 171, 141, 189, 128, 176, 112, 160, 103, 151)(100, 148, 107, 155, 118, 166, 136, 184, 144, 192, 130, 178, 113, 161, 104, 152)(106, 154, 117, 165, 135, 183, 121, 169, 139, 187, 137, 185, 131, 179, 114, 162)(108, 156, 119, 167, 138, 186, 127, 175, 132, 180, 116, 164, 134, 182, 120, 168)(111, 159, 125, 173, 143, 191, 129, 177, 140, 188, 124, 172, 142, 190, 126, 174)
	L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 108)(6, 101)(7, 111)(8, 106)(9, 114)(10, 99)(11, 103)(12, 102)(13, 121)(14, 120)(15, 107)(16, 127)(17, 129)(18, 116)(19, 132)(20, 105)(21, 113)(22, 126)(23, 109)(24, 124)(25, 119)(26, 136)(27, 140)(28, 110)(29, 112)(30, 137)(31, 125)(32, 115)(33, 117)(34, 123)(35, 142)(36, 128)(37, 141)(38, 131)(39, 143)(40, 139)(41, 118)(42, 135)(43, 122)(44, 130)(45, 144)(46, 134)(47, 138)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.686 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y2, Y1^3, (Y2^-1 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^3, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, (Y1^-1 * Y2^-1 * Y3)^2, (Y3 * Y2^-1 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 10, 58)(4, 52, 14, 62, 16, 64)(6, 54, 18, 66, 22, 70)(7, 55, 23, 71, 24, 72)(8, 56, 25, 73, 20, 68)(9, 57, 27, 75, 29, 77)(11, 59, 31, 79, 32, 80)(13, 61, 35, 83, 36, 84)(15, 63, 28, 76, 40, 88)(17, 65, 41, 89, 26, 74)(19, 67, 43, 91, 39, 87)(21, 69, 44, 92, 38, 86)(30, 78, 48, 96, 42, 90)(33, 81, 45, 93, 46, 94)(34, 82, 37, 85, 47, 95)(97, 145, 99, 147, 103, 151, 109, 157, 111, 159, 113, 161, 100, 148, 102, 150)(98, 146, 104, 152, 107, 155, 122, 170, 124, 172, 126, 174, 105, 153, 106, 154)(101, 149, 114, 162, 117, 165, 138, 186, 136, 184, 131, 179, 115, 163, 116, 164)(108, 156, 123, 171, 130, 178, 112, 160, 137, 185, 127, 175, 129, 177, 120, 168)(110, 158, 133, 181, 135, 183, 132, 180, 119, 167, 141, 189, 134, 182, 118, 166)(121, 169, 139, 187, 143, 191, 125, 173, 144, 192, 140, 188, 142, 190, 128, 176)
	L = (1, 100)(2, 105)(3, 102)(4, 111)(5, 115)(6, 113)(7, 97)(8, 106)(9, 124)(10, 126)(11, 98)(12, 129)(13, 99)(14, 134)(15, 103)(16, 123)(17, 109)(18, 116)(19, 136)(20, 131)(21, 101)(22, 141)(23, 135)(24, 127)(25, 142)(26, 104)(27, 120)(28, 107)(29, 139)(30, 122)(31, 112)(32, 140)(33, 137)(34, 108)(35, 138)(36, 133)(37, 118)(38, 119)(39, 110)(40, 117)(41, 130)(42, 114)(43, 128)(44, 125)(45, 132)(46, 144)(47, 121)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.687 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y1^3, (Y2^-1 * Y1^-1)^2, Y3^4, (R * Y3)^2, (Y2 * R)^2, (Y1 * Y2)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y1 * Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1 * Y2^-1)^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 14, 62)(4, 52, 15, 63, 17, 65)(6, 54, 21, 69, 8, 56)(7, 55, 23, 71, 24, 72)(9, 57, 26, 74, 28, 76)(10, 58, 29, 77, 18, 66)(11, 59, 31, 79, 32, 80)(13, 61, 34, 82, 30, 78)(16, 64, 27, 75, 39, 87)(19, 67, 42, 90, 38, 86)(20, 68, 43, 91, 35, 83)(22, 70, 41, 89, 45, 93)(25, 73, 46, 94, 33, 81)(36, 84, 48, 96, 44, 92)(37, 85, 47, 95, 40, 88)(97, 145, 99, 147, 100, 148, 109, 157, 112, 160, 118, 166, 103, 151, 102, 150)(98, 146, 104, 152, 105, 153, 121, 169, 123, 171, 126, 174, 107, 155, 106, 154)(101, 149, 114, 162, 115, 163, 137, 185, 135, 183, 129, 177, 116, 164, 108, 156)(110, 158, 131, 179, 132, 180, 119, 167, 141, 189, 134, 182, 133, 181, 111, 159)(113, 161, 136, 184, 122, 170, 117, 165, 120, 168, 140, 188, 127, 175, 130, 178)(124, 172, 143, 191, 138, 186, 125, 173, 128, 176, 144, 192, 139, 187, 142, 190)
	L = (1, 100)(2, 105)(3, 109)(4, 112)(5, 115)(6, 99)(7, 97)(8, 121)(9, 123)(10, 104)(11, 98)(12, 114)(13, 118)(14, 132)(15, 131)(16, 103)(17, 122)(18, 137)(19, 135)(20, 101)(21, 140)(22, 102)(23, 134)(24, 127)(25, 126)(26, 120)(27, 107)(28, 138)(29, 144)(30, 106)(31, 113)(32, 139)(33, 108)(34, 136)(35, 119)(36, 141)(37, 110)(38, 111)(39, 116)(40, 117)(41, 129)(42, 128)(43, 124)(44, 130)(45, 133)(46, 143)(47, 125)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.688 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2 * Y1^-1)^2, Y3 * Y2^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y3 * Y2 * Y3^-1 * Y2 * Y1, Y2^-2 * Y3^2 * Y1, (Y3^-1 * Y1^-1)^3, Y3^6, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y1 * Y3 * Y1^-1, Y3 * Y2^4 * Y3^2, (Y1 * Y2)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 10, 58)(4, 52, 16, 64, 19, 67)(6, 54, 20, 68, 15, 63)(7, 55, 24, 72, 26, 74)(8, 56, 28, 76, 21, 69)(9, 57, 30, 78, 31, 79)(11, 59, 27, 75, 34, 82)(13, 61, 37, 85, 18, 66)(14, 62, 38, 86, 29, 77)(17, 65, 42, 90, 25, 73)(22, 70, 35, 83, 41, 89)(23, 71, 45, 93, 33, 81)(32, 80, 48, 96, 39, 87)(36, 84, 40, 88, 47, 95)(43, 91, 46, 94, 44, 92)(97, 145, 99, 147, 109, 157, 128, 176, 140, 188, 138, 186, 120, 168, 102, 150)(98, 146, 104, 152, 100, 148, 113, 161, 139, 187, 141, 189, 123, 171, 106, 154)(101, 149, 116, 164, 105, 153, 119, 167, 142, 190, 144, 192, 131, 179, 117, 165)(103, 151, 121, 169, 112, 160, 136, 184, 114, 162, 108, 156, 130, 178, 110, 158)(107, 155, 129, 177, 126, 174, 132, 180, 115, 163, 124, 172, 137, 185, 125, 173)(111, 159, 122, 170, 134, 182, 118, 166, 135, 183, 133, 181, 143, 191, 127, 175)
	L = (1, 100)(2, 105)(3, 110)(4, 114)(5, 109)(6, 119)(7, 97)(8, 125)(9, 115)(10, 128)(11, 98)(12, 104)(13, 127)(14, 135)(15, 99)(16, 137)(17, 102)(18, 140)(19, 139)(20, 134)(21, 113)(22, 101)(23, 106)(24, 118)(25, 141)(26, 112)(27, 103)(28, 116)(29, 121)(30, 122)(31, 142)(32, 117)(33, 144)(34, 126)(35, 107)(36, 108)(37, 130)(38, 129)(39, 138)(40, 111)(41, 133)(42, 136)(43, 131)(44, 123)(45, 132)(46, 120)(47, 124)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 16, 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 22 e = 96 f = 22
	degree seq :: [ 6^16, 16^6 ]

E27.689 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C8 : C2) x S3 (small group id <96, 113>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-2 * Y3 * Y1^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y2^-1 * Y3 * Y2^5 ]
Map:: non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 20, 68)(6, 54, 22, 70)(7, 55, 24, 72)(8, 56, 27, 75)(10, 58, 34, 82)(11, 59, 35, 83)(12, 60, 29, 77)(14, 62, 41, 89)(15, 63, 37, 85)(16, 64, 25, 73)(17, 65, 23, 71)(18, 66, 36, 84)(19, 67, 32, 80)(21, 69, 39, 87)(26, 74, 45, 93)(28, 76, 48, 96)(30, 78, 43, 91)(31, 79, 42, 90)(33, 81, 47, 95)(38, 86, 44, 92)(40, 88, 46, 94)(97, 98, 103, 119, 138, 133, 108, 101)(99, 107, 102, 117, 121, 140, 132, 110)(100, 111, 120, 116, 127, 105, 125, 113)(104, 122, 106, 129, 139, 136, 115, 124)(109, 134, 118, 137, 112, 131, 114, 135)(123, 142, 130, 144, 126, 141, 128, 143)(145, 147, 156, 180, 186, 169, 151, 150)(146, 152, 149, 163, 181, 187, 167, 154)(148, 160, 173, 166, 175, 157, 168, 162)(153, 174, 164, 178, 159, 171, 161, 176)(155, 172, 158, 184, 188, 177, 165, 170)(179, 191, 185, 189, 182, 192, 183, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.698
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.690 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1 * Y2^2 * Y1, (R * Y3)^2, (Y3 * Y1^-1)^2, R * Y2 * R * Y1, (Y2^-1 * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1, Y1^8, Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 15, 63)(6, 54, 16, 64)(7, 55, 20, 68)(8, 56, 23, 71)(10, 58, 25, 73)(11, 59, 27, 75)(12, 60, 29, 77)(14, 62, 31, 79)(17, 65, 33, 81)(18, 66, 34, 82)(19, 67, 36, 84)(21, 69, 38, 86)(22, 70, 40, 88)(24, 72, 41, 89)(26, 74, 42, 90)(28, 76, 43, 91)(30, 78, 44, 92)(32, 80, 45, 93)(35, 83, 46, 94)(37, 85, 47, 95)(39, 87, 48, 96)(97, 98, 103, 115, 131, 126, 108, 101)(99, 107, 102, 114, 117, 135, 124, 110)(100, 111, 125, 140, 142, 132, 116, 105)(104, 118, 106, 122, 133, 128, 113, 120)(109, 127, 139, 144, 134, 130, 112, 123)(119, 137, 129, 141, 143, 138, 121, 136)(145, 147, 156, 172, 179, 165, 151, 150)(146, 152, 149, 161, 174, 181, 163, 154)(148, 160, 164, 182, 190, 187, 173, 157)(153, 169, 180, 191, 188, 177, 159, 167)(155, 168, 158, 176, 183, 170, 162, 166)(171, 184, 178, 186, 192, 189, 175, 185)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.699
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.691 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-2 * Y2^-2, (R * Y3)^2, R * Y1 * R * Y2, (Y2^-1 * Y3 * Y2^-1)^2, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-3 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 20, 68)(6, 54, 22, 70)(7, 55, 24, 72)(8, 56, 27, 75)(10, 58, 34, 82)(11, 59, 35, 83)(12, 60, 31, 79)(14, 62, 41, 89)(15, 63, 23, 71)(16, 64, 36, 84)(17, 65, 37, 85)(18, 66, 25, 73)(19, 67, 30, 78)(21, 69, 38, 86)(26, 74, 45, 93)(28, 76, 48, 96)(29, 77, 42, 90)(32, 80, 43, 91)(33, 81, 46, 94)(39, 87, 44, 92)(40, 88, 47, 95)(97, 98, 103, 119, 138, 133, 108, 101)(99, 107, 102, 117, 121, 140, 132, 110)(100, 111, 127, 105, 125, 116, 120, 113)(104, 122, 106, 129, 139, 136, 115, 124)(109, 134, 112, 131, 114, 137, 118, 135)(123, 142, 126, 141, 128, 144, 130, 143)(145, 147, 156, 180, 186, 169, 151, 150)(146, 152, 149, 163, 181, 187, 167, 154)(148, 160, 168, 157, 173, 166, 175, 162)(153, 174, 159, 171, 161, 178, 164, 176)(155, 172, 158, 184, 188, 177, 165, 170)(179, 191, 182, 192, 183, 189, 185, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.700
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.692 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C8 : C2) x S3 (small group id <96, 113>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, Y3 * Y2 * Y1 * Y3, Y1^-2 * Y2^-2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3 * Y1^-1, Y3^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 9, 57, 33, 81, 13, 61, 7, 55)(2, 50, 10, 58, 6, 54, 25, 73, 32, 80, 12, 60)(3, 51, 15, 63, 34, 82, 23, 71, 5, 53, 17, 65)(8, 56, 29, 77, 11, 59, 40, 88, 24, 72, 31, 79)(14, 62, 38, 86, 22, 70, 42, 90, 16, 64, 35, 83)(18, 66, 44, 92, 21, 69, 43, 91, 27, 75, 45, 93)(19, 67, 30, 78, 26, 74, 39, 87, 20, 68, 28, 76)(36, 84, 47, 95, 41, 89, 48, 96, 37, 85, 46, 94)(97, 98, 104, 124, 142, 140, 110, 101)(99, 109, 102, 120, 126, 144, 139, 112)(100, 114, 125, 119, 132, 108, 134, 116)(103, 117, 127, 113, 133, 106, 131, 115)(105, 128, 107, 135, 143, 141, 118, 130)(111, 137, 121, 138, 122, 129, 123, 136)(145, 147, 158, 187, 190, 174, 152, 150)(146, 153, 149, 166, 188, 191, 172, 155)(148, 163, 182, 154, 180, 161, 173, 165)(151, 170, 179, 169, 181, 159, 175, 171)(156, 185, 167, 184, 162, 177, 164, 186)(157, 178, 160, 189, 192, 183, 168, 176)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.695
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.693 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1)^2, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^2 * Y2^-1 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y2 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, (Y1 * Y2)^3, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^8, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 9, 57, 27, 75, 13, 61, 7, 55)(2, 50, 10, 58, 6, 54, 21, 69, 26, 74, 12, 60)(3, 51, 15, 63, 28, 76, 18, 66, 5, 53, 17, 65)(8, 56, 23, 71, 11, 59, 30, 78, 20, 68, 25, 73)(14, 62, 32, 80, 19, 67, 35, 83, 16, 64, 34, 82)(22, 70, 38, 86, 24, 72, 42, 90, 29, 77, 40, 88)(31, 79, 43, 91, 36, 84, 45, 93, 33, 81, 44, 92)(37, 85, 46, 94, 39, 87, 48, 96, 41, 89, 47, 95)(97, 98, 104, 118, 133, 129, 110, 101)(99, 109, 102, 116, 120, 137, 127, 112)(100, 114, 128, 141, 142, 136, 119, 108)(103, 113, 130, 140, 143, 134, 121, 106)(105, 122, 107, 125, 135, 132, 115, 124)(111, 131, 139, 144, 138, 126, 117, 123)(145, 147, 158, 175, 181, 168, 152, 150)(146, 153, 149, 163, 177, 183, 166, 155)(148, 154, 167, 182, 190, 188, 176, 161)(151, 165, 169, 186, 191, 187, 178, 159)(156, 174, 184, 192, 189, 179, 162, 171)(157, 172, 160, 180, 185, 173, 164, 170)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.696
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.694 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y2^-2, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3 * Y2^2 * Y3^-1 * Y1^-1, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y1 * Y2)^3, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^-3 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y3^-1 * Y2^2 * Y3 * Y1^-2, (Y3^-1 * Y2^-1 * Y1^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, (Y2^-1 * Y3 * Y1)^2, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 9, 57, 33, 81, 13, 61, 7, 55)(2, 50, 10, 58, 6, 54, 25, 73, 32, 80, 12, 60)(3, 51, 15, 63, 34, 82, 23, 71, 5, 53, 17, 65)(8, 56, 29, 77, 11, 59, 40, 88, 24, 72, 31, 79)(14, 62, 36, 84, 22, 70, 41, 89, 16, 64, 37, 85)(18, 66, 28, 76, 21, 69, 30, 78, 27, 75, 39, 87)(19, 67, 43, 91, 26, 74, 45, 93, 20, 68, 44, 92)(35, 83, 46, 94, 38, 86, 47, 95, 42, 90, 48, 96)(97, 98, 104, 124, 142, 140, 110, 101)(99, 109, 102, 120, 126, 144, 139, 112)(100, 114, 132, 108, 134, 119, 125, 116)(103, 117, 133, 106, 131, 113, 127, 115)(105, 128, 107, 135, 143, 141, 118, 130)(111, 136, 122, 129, 123, 137, 121, 138)(145, 147, 158, 187, 190, 174, 152, 150)(146, 153, 149, 166, 188, 191, 172, 155)(148, 163, 173, 161, 182, 154, 180, 165)(151, 170, 175, 159, 179, 169, 181, 171)(156, 185, 162, 177, 164, 184, 167, 186)(157, 178, 160, 189, 192, 183, 168, 176)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.697
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.695 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C8 : C2) x S3 (small group id <96, 113>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-2 * Y3 * Y1^2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1, Y3 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y2^-1 * Y3 * Y2^5 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 20, 68, 116, 164)(6, 54, 102, 150, 22, 70, 118, 166)(7, 55, 103, 151, 24, 72, 120, 168)(8, 56, 104, 152, 27, 75, 123, 171)(10, 58, 106, 154, 34, 82, 130, 178)(11, 59, 107, 155, 35, 83, 131, 179)(12, 60, 108, 156, 29, 77, 125, 173)(14, 62, 110, 158, 41, 89, 137, 185)(15, 63, 111, 159, 37, 85, 133, 181)(16, 64, 112, 160, 25, 73, 121, 169)(17, 65, 113, 161, 23, 71, 119, 167)(18, 66, 114, 162, 36, 84, 132, 180)(19, 67, 115, 163, 32, 80, 128, 176)(21, 69, 117, 165, 39, 87, 135, 183)(26, 74, 122, 170, 45, 93, 141, 189)(28, 76, 124, 172, 48, 96, 144, 192)(30, 78, 126, 174, 43, 91, 139, 187)(31, 79, 127, 175, 42, 90, 138, 186)(33, 81, 129, 177, 47, 95, 143, 191)(38, 86, 134, 182, 44, 92, 140, 188)(40, 88, 136, 184, 46, 94, 142, 190)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 69)(7, 71)(8, 74)(9, 77)(10, 81)(11, 54)(12, 53)(13, 86)(14, 51)(15, 72)(16, 83)(17, 52)(18, 87)(19, 76)(20, 79)(21, 73)(22, 89)(23, 90)(24, 68)(25, 92)(26, 58)(27, 94)(28, 56)(29, 65)(30, 93)(31, 57)(32, 95)(33, 91)(34, 96)(35, 66)(36, 62)(37, 60)(38, 70)(39, 61)(40, 67)(41, 64)(42, 85)(43, 88)(44, 84)(45, 80)(46, 82)(47, 75)(48, 78)(97, 147)(98, 152)(99, 156)(100, 160)(101, 163)(102, 145)(103, 150)(104, 149)(105, 174)(106, 146)(107, 172)(108, 180)(109, 168)(110, 184)(111, 171)(112, 173)(113, 176)(114, 148)(115, 181)(116, 178)(117, 170)(118, 175)(119, 154)(120, 162)(121, 151)(122, 155)(123, 161)(124, 158)(125, 166)(126, 164)(127, 157)(128, 153)(129, 165)(130, 159)(131, 191)(132, 186)(133, 187)(134, 192)(135, 190)(136, 188)(137, 189)(138, 169)(139, 167)(140, 177)(141, 182)(142, 179)(143, 185)(144, 183)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.692
Transitivity :: VT+
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.696 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1 * Y2^2 * Y1, (R * Y3)^2, (Y3 * Y1^-1)^2, R * Y2 * R * Y1, (Y2^-1 * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1, Y1^8, Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 16, 64, 112, 160)(7, 55, 103, 151, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 27, 75, 123, 171)(12, 60, 108, 156, 29, 77, 125, 173)(14, 62, 110, 158, 31, 79, 127, 175)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 36, 84, 132, 180)(21, 69, 117, 165, 38, 86, 134, 182)(22, 70, 118, 166, 40, 88, 136, 184)(24, 72, 120, 168, 41, 89, 137, 185)(26, 74, 122, 170, 42, 90, 138, 186)(28, 76, 124, 172, 43, 91, 139, 187)(30, 78, 126, 174, 44, 92, 140, 188)(32, 80, 128, 176, 45, 93, 141, 189)(35, 83, 131, 179, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191)(39, 87, 135, 183, 48, 96, 144, 192)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 66)(7, 67)(8, 70)(9, 52)(10, 74)(11, 54)(12, 53)(13, 79)(14, 51)(15, 77)(16, 75)(17, 72)(18, 69)(19, 83)(20, 57)(21, 87)(22, 58)(23, 89)(24, 56)(25, 88)(26, 85)(27, 61)(28, 62)(29, 92)(30, 60)(31, 91)(32, 65)(33, 93)(34, 64)(35, 78)(36, 68)(37, 80)(38, 82)(39, 76)(40, 71)(41, 81)(42, 73)(43, 96)(44, 94)(45, 95)(46, 84)(47, 90)(48, 86)(97, 147)(98, 152)(99, 156)(100, 160)(101, 161)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 168)(108, 172)(109, 148)(110, 176)(111, 167)(112, 164)(113, 174)(114, 166)(115, 154)(116, 182)(117, 151)(118, 155)(119, 153)(120, 158)(121, 180)(122, 162)(123, 184)(124, 179)(125, 157)(126, 181)(127, 185)(128, 183)(129, 159)(130, 186)(131, 165)(132, 191)(133, 163)(134, 190)(135, 170)(136, 178)(137, 171)(138, 192)(139, 173)(140, 177)(141, 175)(142, 187)(143, 188)(144, 189)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.693
Transitivity :: VT+
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.697 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-2 * Y2^-2, (R * Y3)^2, R * Y1 * R * Y2, (Y2^-1 * Y3 * Y2^-1)^2, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^-3 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 20, 68, 116, 164)(6, 54, 102, 150, 22, 70, 118, 166)(7, 55, 103, 151, 24, 72, 120, 168)(8, 56, 104, 152, 27, 75, 123, 171)(10, 58, 106, 154, 34, 82, 130, 178)(11, 59, 107, 155, 35, 83, 131, 179)(12, 60, 108, 156, 31, 79, 127, 175)(14, 62, 110, 158, 41, 89, 137, 185)(15, 63, 111, 159, 23, 71, 119, 167)(16, 64, 112, 160, 36, 84, 132, 180)(17, 65, 113, 161, 37, 85, 133, 181)(18, 66, 114, 162, 25, 73, 121, 169)(19, 67, 115, 163, 30, 78, 126, 174)(21, 69, 117, 165, 38, 86, 134, 182)(26, 74, 122, 170, 45, 93, 141, 189)(28, 76, 124, 172, 48, 96, 144, 192)(29, 77, 125, 173, 42, 90, 138, 186)(32, 80, 128, 176, 43, 91, 139, 187)(33, 81, 129, 177, 46, 94, 142, 190)(39, 87, 135, 183, 44, 92, 140, 188)(40, 88, 136, 184, 47, 95, 143, 191)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 69)(7, 71)(8, 74)(9, 77)(10, 81)(11, 54)(12, 53)(13, 86)(14, 51)(15, 79)(16, 83)(17, 52)(18, 89)(19, 76)(20, 72)(21, 73)(22, 87)(23, 90)(24, 65)(25, 92)(26, 58)(27, 94)(28, 56)(29, 68)(30, 93)(31, 57)(32, 96)(33, 91)(34, 95)(35, 66)(36, 62)(37, 60)(38, 64)(39, 61)(40, 67)(41, 70)(42, 85)(43, 88)(44, 84)(45, 80)(46, 78)(47, 75)(48, 82)(97, 147)(98, 152)(99, 156)(100, 160)(101, 163)(102, 145)(103, 150)(104, 149)(105, 174)(106, 146)(107, 172)(108, 180)(109, 173)(110, 184)(111, 171)(112, 168)(113, 178)(114, 148)(115, 181)(116, 176)(117, 170)(118, 175)(119, 154)(120, 157)(121, 151)(122, 155)(123, 161)(124, 158)(125, 166)(126, 159)(127, 162)(128, 153)(129, 165)(130, 164)(131, 191)(132, 186)(133, 187)(134, 192)(135, 189)(136, 188)(137, 190)(138, 169)(139, 167)(140, 177)(141, 185)(142, 179)(143, 182)(144, 183)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.694
Transitivity :: VT+
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.698 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C8 : C2) x S3 (small group id <96, 113>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, Y3 * Y2 * Y1 * Y3, Y1^-2 * Y2^-2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3 * Y1^-1, Y3^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 9, 57, 105, 153, 33, 81, 129, 177, 13, 61, 109, 157, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 6, 54, 102, 150, 25, 73, 121, 169, 32, 80, 128, 176, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 34, 82, 130, 178, 23, 71, 119, 167, 5, 53, 101, 149, 17, 65, 113, 161)(8, 56, 104, 152, 29, 77, 125, 173, 11, 59, 107, 155, 40, 88, 136, 184, 24, 72, 120, 168, 31, 79, 127, 175)(14, 62, 110, 158, 38, 86, 134, 182, 22, 70, 118, 166, 42, 90, 138, 186, 16, 64, 112, 160, 35, 83, 131, 179)(18, 66, 114, 162, 44, 92, 140, 188, 21, 69, 117, 165, 43, 91, 139, 187, 27, 75, 123, 171, 45, 93, 141, 189)(19, 67, 115, 163, 30, 78, 126, 174, 26, 74, 122, 170, 39, 87, 135, 183, 20, 68, 116, 164, 28, 76, 124, 172)(36, 84, 132, 180, 47, 95, 143, 191, 41, 89, 137, 185, 48, 96, 144, 192, 37, 85, 133, 181, 46, 94, 142, 190)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 72)(7, 69)(8, 76)(9, 80)(10, 83)(11, 87)(12, 86)(13, 54)(14, 53)(15, 89)(16, 51)(17, 85)(18, 77)(19, 55)(20, 52)(21, 79)(22, 82)(23, 84)(24, 78)(25, 90)(26, 81)(27, 88)(28, 94)(29, 71)(30, 96)(31, 65)(32, 59)(33, 75)(34, 57)(35, 67)(36, 60)(37, 58)(38, 68)(39, 95)(40, 63)(41, 73)(42, 74)(43, 64)(44, 62)(45, 70)(46, 92)(47, 93)(48, 91)(97, 147)(98, 153)(99, 158)(100, 163)(101, 166)(102, 145)(103, 170)(104, 150)(105, 149)(106, 180)(107, 146)(108, 185)(109, 178)(110, 187)(111, 175)(112, 189)(113, 173)(114, 177)(115, 182)(116, 186)(117, 148)(118, 188)(119, 184)(120, 176)(121, 181)(122, 179)(123, 151)(124, 155)(125, 165)(126, 152)(127, 171)(128, 157)(129, 164)(130, 160)(131, 169)(132, 161)(133, 159)(134, 154)(135, 168)(136, 162)(137, 167)(138, 156)(139, 190)(140, 191)(141, 192)(142, 174)(143, 172)(144, 183)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.689
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.699 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1)^2, Y1^-1 * Y3 * Y2 * Y3^-1, Y3^2 * Y2^-1 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, R * Y2 * R * Y1, Y1^-1 * Y2 * Y3 * Y1^-1 * Y3^-1 * Y2^-1, (Y1 * Y2)^3, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^8, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 9, 57, 105, 153, 27, 75, 123, 171, 13, 61, 109, 157, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 6, 54, 102, 150, 21, 69, 117, 165, 26, 74, 122, 170, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 28, 76, 124, 172, 18, 66, 114, 162, 5, 53, 101, 149, 17, 65, 113, 161)(8, 56, 104, 152, 23, 71, 119, 167, 11, 59, 107, 155, 30, 78, 126, 174, 20, 68, 116, 164, 25, 73, 121, 169)(14, 62, 110, 158, 32, 80, 128, 176, 19, 67, 115, 163, 35, 83, 131, 179, 16, 64, 112, 160, 34, 82, 130, 178)(22, 70, 118, 166, 38, 86, 134, 182, 24, 72, 120, 168, 42, 90, 138, 186, 29, 77, 125, 173, 40, 88, 136, 184)(31, 79, 127, 175, 43, 91, 139, 187, 36, 84, 132, 180, 45, 93, 141, 189, 33, 81, 129, 177, 44, 92, 140, 188)(37, 85, 133, 181, 46, 94, 142, 190, 39, 87, 135, 183, 48, 96, 144, 192, 41, 89, 137, 185, 47, 95, 143, 191)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 68)(7, 65)(8, 70)(9, 74)(10, 55)(11, 77)(12, 52)(13, 54)(14, 53)(15, 83)(16, 51)(17, 82)(18, 80)(19, 76)(20, 72)(21, 75)(22, 85)(23, 60)(24, 89)(25, 58)(26, 59)(27, 63)(28, 57)(29, 87)(30, 69)(31, 64)(32, 93)(33, 62)(34, 92)(35, 91)(36, 67)(37, 81)(38, 73)(39, 84)(40, 71)(41, 79)(42, 78)(43, 96)(44, 95)(45, 94)(46, 88)(47, 86)(48, 90)(97, 147)(98, 153)(99, 158)(100, 154)(101, 163)(102, 145)(103, 165)(104, 150)(105, 149)(106, 167)(107, 146)(108, 174)(109, 172)(110, 175)(111, 151)(112, 180)(113, 148)(114, 171)(115, 177)(116, 170)(117, 169)(118, 155)(119, 182)(120, 152)(121, 186)(122, 157)(123, 156)(124, 160)(125, 164)(126, 184)(127, 181)(128, 161)(129, 183)(130, 159)(131, 162)(132, 185)(133, 168)(134, 190)(135, 166)(136, 192)(137, 173)(138, 191)(139, 178)(140, 176)(141, 179)(142, 188)(143, 187)(144, 189)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.690
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.700 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y2^-2, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3 * Y2^2 * Y3^-1 * Y1^-1, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y1 * Y2)^3, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^-3 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y3^-1 * Y2^2 * Y3 * Y1^-2, (Y3^-1 * Y2^-1 * Y1^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, (Y2^-1 * Y3 * Y1)^2, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 9, 57, 105, 153, 33, 81, 129, 177, 13, 61, 109, 157, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 6, 54, 102, 150, 25, 73, 121, 169, 32, 80, 128, 176, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 34, 82, 130, 178, 23, 71, 119, 167, 5, 53, 101, 149, 17, 65, 113, 161)(8, 56, 104, 152, 29, 77, 125, 173, 11, 59, 107, 155, 40, 88, 136, 184, 24, 72, 120, 168, 31, 79, 127, 175)(14, 62, 110, 158, 36, 84, 132, 180, 22, 70, 118, 166, 41, 89, 137, 185, 16, 64, 112, 160, 37, 85, 133, 181)(18, 66, 114, 162, 28, 76, 124, 172, 21, 69, 117, 165, 30, 78, 126, 174, 27, 75, 123, 171, 39, 87, 135, 183)(19, 67, 115, 163, 43, 91, 139, 187, 26, 74, 122, 170, 45, 93, 141, 189, 20, 68, 116, 164, 44, 92, 140, 188)(35, 83, 131, 179, 46, 94, 142, 190, 38, 86, 134, 182, 47, 95, 143, 191, 42, 90, 138, 186, 48, 96, 144, 192)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 72)(7, 69)(8, 76)(9, 80)(10, 83)(11, 87)(12, 86)(13, 54)(14, 53)(15, 88)(16, 51)(17, 79)(18, 84)(19, 55)(20, 52)(21, 85)(22, 82)(23, 77)(24, 78)(25, 90)(26, 81)(27, 89)(28, 94)(29, 68)(30, 96)(31, 67)(32, 59)(33, 75)(34, 57)(35, 65)(36, 60)(37, 58)(38, 71)(39, 95)(40, 74)(41, 73)(42, 63)(43, 64)(44, 62)(45, 70)(46, 92)(47, 93)(48, 91)(97, 147)(98, 153)(99, 158)(100, 163)(101, 166)(102, 145)(103, 170)(104, 150)(105, 149)(106, 180)(107, 146)(108, 185)(109, 178)(110, 187)(111, 179)(112, 189)(113, 182)(114, 177)(115, 173)(116, 184)(117, 148)(118, 188)(119, 186)(120, 176)(121, 181)(122, 175)(123, 151)(124, 155)(125, 161)(126, 152)(127, 159)(128, 157)(129, 164)(130, 160)(131, 169)(132, 165)(133, 171)(134, 154)(135, 168)(136, 167)(137, 162)(138, 156)(139, 190)(140, 191)(141, 192)(142, 174)(143, 172)(144, 183)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.691
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.701 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y2^6, Y3 * Y2^-1 * Y3 * Y2 * Y3^2 * Y2, Y3^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 8, 56)(5, 53, 7, 55)(6, 54, 10, 58)(11, 59, 24, 72)(12, 60, 22, 70)(13, 61, 25, 73)(14, 62, 20, 68)(15, 63, 23, 71)(16, 64, 19, 67)(17, 65, 21, 69)(18, 66, 26, 74)(27, 75, 38, 86)(28, 76, 43, 91)(29, 77, 46, 94)(30, 78, 44, 92)(31, 79, 47, 95)(32, 80, 39, 87)(33, 81, 41, 89)(34, 82, 45, 93)(35, 83, 40, 88)(36, 84, 42, 90)(37, 85, 48, 96)(97, 145, 99, 147, 107, 155, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 134, 182, 120, 168, 105, 153)(100, 148, 110, 158, 128, 176, 133, 181, 124, 172, 108, 156)(102, 150, 113, 161, 131, 179, 130, 178, 125, 173, 109, 157)(104, 152, 118, 166, 139, 187, 144, 192, 135, 183, 116, 164)(106, 154, 121, 169, 142, 190, 141, 189, 136, 184, 117, 165)(111, 159, 126, 174, 132, 180, 114, 162, 127, 175, 129, 177)(119, 167, 137, 185, 143, 191, 122, 170, 138, 186, 140, 188)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 110)(6, 97)(7, 116)(8, 119)(9, 118)(10, 98)(11, 124)(12, 126)(13, 99)(14, 129)(15, 130)(16, 128)(17, 101)(18, 102)(19, 135)(20, 137)(21, 103)(22, 140)(23, 141)(24, 139)(25, 105)(26, 106)(27, 133)(28, 132)(29, 107)(30, 131)(31, 109)(32, 127)(33, 125)(34, 123)(35, 112)(36, 113)(37, 114)(38, 144)(39, 143)(40, 115)(41, 142)(42, 117)(43, 138)(44, 136)(45, 134)(46, 120)(47, 121)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.714
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.702 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y2^-1, Y1^-1), Y1^6, Y2^-4 * Y1^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 16, 64, 5, 53)(3, 51, 8, 56, 20, 68, 37, 85, 31, 79, 13, 61)(4, 52, 14, 62, 32, 80, 38, 86, 21, 69, 9, 57)(6, 54, 10, 58, 22, 70, 27, 75, 35, 83, 17, 65)(11, 59, 23, 71, 36, 84, 18, 66, 26, 74, 29, 77)(12, 60, 30, 78, 45, 93, 48, 96, 39, 87, 24, 72)(15, 63, 33, 81, 46, 94, 43, 91, 40, 88, 25, 73)(28, 76, 44, 92, 42, 90, 34, 82, 47, 95, 41, 89)(97, 145, 99, 147, 107, 155, 123, 171, 115, 163, 133, 181, 114, 162, 102, 150)(98, 146, 104, 152, 119, 167, 131, 179, 112, 160, 127, 175, 122, 170, 106, 154)(100, 148, 108, 156, 124, 172, 139, 187, 134, 182, 144, 192, 130, 178, 111, 159)(101, 149, 109, 157, 125, 173, 118, 166, 103, 151, 116, 164, 132, 180, 113, 161)(105, 153, 120, 168, 137, 185, 142, 190, 128, 176, 141, 189, 138, 186, 121, 169)(110, 158, 126, 174, 140, 188, 136, 184, 117, 165, 135, 183, 143, 191, 129, 177)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 111)(7, 117)(8, 120)(9, 98)(10, 121)(11, 124)(12, 99)(13, 126)(14, 101)(15, 102)(16, 128)(17, 129)(18, 130)(19, 134)(20, 135)(21, 103)(22, 136)(23, 137)(24, 104)(25, 106)(26, 138)(27, 139)(28, 107)(29, 140)(30, 109)(31, 141)(32, 112)(33, 113)(34, 114)(35, 142)(36, 143)(37, 144)(38, 115)(39, 116)(40, 118)(41, 119)(42, 122)(43, 123)(44, 125)(45, 127)(46, 131)(47, 132)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.709
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.703 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y1^6, Y2 * Y1^-1 * Y2^3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 16, 64, 5, 53)(3, 51, 11, 59, 27, 75, 37, 85, 20, 68, 8, 56)(4, 52, 14, 62, 32, 80, 38, 86, 21, 69, 9, 57)(6, 54, 17, 65, 35, 83, 30, 78, 22, 70, 10, 58)(12, 60, 23, 71, 36, 84, 18, 66, 26, 74, 28, 76)(13, 61, 24, 72, 39, 87, 48, 96, 43, 91, 29, 77)(15, 63, 25, 73, 40, 88, 45, 93, 46, 94, 33, 81)(31, 79, 44, 92, 42, 90, 34, 82, 47, 95, 41, 89)(97, 145, 99, 147, 108, 156, 126, 174, 115, 163, 133, 181, 114, 162, 102, 150)(98, 146, 104, 152, 119, 167, 131, 179, 112, 160, 123, 171, 122, 170, 106, 154)(100, 148, 109, 157, 127, 175, 141, 189, 134, 182, 144, 192, 130, 178, 111, 159)(101, 149, 107, 155, 124, 172, 118, 166, 103, 151, 116, 164, 132, 180, 113, 161)(105, 153, 120, 168, 137, 185, 142, 190, 128, 176, 139, 187, 138, 186, 121, 169)(110, 158, 125, 173, 140, 188, 136, 184, 117, 165, 135, 183, 143, 191, 129, 177)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 111)(7, 117)(8, 120)(9, 98)(10, 121)(11, 125)(12, 127)(13, 99)(14, 101)(15, 102)(16, 128)(17, 129)(18, 130)(19, 134)(20, 135)(21, 103)(22, 136)(23, 137)(24, 104)(25, 106)(26, 138)(27, 139)(28, 140)(29, 107)(30, 141)(31, 108)(32, 112)(33, 113)(34, 114)(35, 142)(36, 143)(37, 144)(38, 115)(39, 116)(40, 118)(41, 119)(42, 122)(43, 123)(44, 124)(45, 126)(46, 131)(47, 132)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.708
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.704 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2, Y3^3, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, (Y1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 13, 61, 21, 69, 14, 62, 10, 58)(6, 54, 16, 64, 17, 65, 20, 68, 15, 63, 8, 56)(12, 60, 22, 70, 25, 73, 33, 81, 26, 74, 23, 71)(18, 66, 19, 67, 27, 75, 32, 80, 29, 77, 28, 76)(24, 72, 35, 83, 37, 85, 44, 92, 38, 86, 34, 82)(30, 78, 40, 88, 41, 89, 43, 91, 39, 87, 31, 79)(36, 84, 42, 90, 46, 94, 48, 96, 47, 95, 45, 93)(97, 145, 99, 147, 108, 156, 120, 168, 132, 180, 126, 174, 114, 162, 102, 150)(98, 146, 104, 152, 115, 163, 127, 175, 138, 186, 130, 178, 118, 166, 106, 154)(100, 148, 110, 158, 121, 169, 134, 182, 142, 190, 135, 183, 123, 171, 111, 159)(101, 149, 112, 160, 124, 172, 136, 184, 141, 189, 131, 179, 119, 167, 107, 155)(103, 151, 109, 157, 122, 170, 133, 181, 143, 191, 137, 185, 125, 173, 113, 161)(105, 153, 116, 164, 128, 176, 139, 187, 144, 192, 140, 188, 129, 177, 117, 165)
	L = (1, 100)(2, 105)(3, 109)(4, 103)(5, 98)(6, 113)(7, 97)(8, 112)(9, 101)(10, 107)(11, 117)(12, 121)(13, 110)(14, 99)(15, 102)(16, 116)(17, 111)(18, 123)(19, 128)(20, 104)(21, 106)(22, 129)(23, 118)(24, 133)(25, 122)(26, 108)(27, 125)(28, 115)(29, 114)(30, 137)(31, 136)(32, 124)(33, 119)(34, 131)(35, 140)(36, 142)(37, 134)(38, 120)(39, 126)(40, 139)(41, 135)(42, 144)(43, 127)(44, 130)(45, 138)(46, 143)(47, 132)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.710
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.705 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y1)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y2 * Y1^-1)^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y1)^2, Y3^-2 * Y1^4, (Y3^-1 * Y1^2)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3 * Y1, Y1^-1 * Y2^-3 * Y3^-1 * Y1 * Y2, Y3^-1 * Y1^2 * Y2^4, Y2^-1 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 17, 65, 5, 53)(3, 51, 13, 61, 33, 81, 46, 94, 24, 72, 11, 59)(4, 52, 10, 58, 7, 55, 12, 60, 26, 74, 18, 66)(6, 54, 20, 68, 39, 87, 45, 93, 25, 73, 9, 57)(14, 62, 32, 80, 41, 89, 47, 95, 43, 91, 34, 82)(15, 63, 30, 78, 16, 64, 35, 83, 44, 92, 31, 79)(19, 67, 40, 88, 36, 84, 28, 76, 21, 69, 29, 77)(22, 70, 27, 75, 37, 85, 48, 96, 38, 86, 42, 90)(97, 145, 99, 147, 110, 158, 132, 180, 122, 170, 140, 188, 118, 166, 102, 150)(98, 146, 105, 153, 123, 171, 131, 179, 114, 162, 136, 184, 128, 176, 107, 155)(100, 148, 112, 160, 133, 181, 121, 169, 104, 152, 120, 168, 137, 185, 115, 163)(101, 149, 116, 164, 138, 186, 127, 175, 108, 156, 124, 172, 130, 178, 109, 157)(103, 151, 111, 159, 134, 182, 135, 183, 113, 161, 129, 177, 139, 187, 117, 165)(106, 154, 125, 173, 143, 191, 142, 190, 119, 167, 141, 189, 144, 192, 126, 174)
	L = (1, 100)(2, 106)(3, 111)(4, 113)(5, 114)(6, 117)(7, 97)(8, 103)(9, 124)(10, 101)(11, 127)(12, 98)(13, 126)(14, 133)(15, 120)(16, 99)(17, 122)(18, 119)(19, 102)(20, 125)(21, 121)(22, 137)(23, 108)(24, 140)(25, 132)(26, 104)(27, 143)(28, 141)(29, 105)(30, 107)(31, 142)(32, 144)(33, 112)(34, 123)(35, 109)(36, 135)(37, 139)(38, 110)(39, 115)(40, 116)(41, 134)(42, 128)(43, 118)(44, 129)(45, 136)(46, 131)(47, 138)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.711
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.706 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1 * Y3^-1, R * Y2 * Y3 * R * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2, Y2 * Y3^-1 * Y2 * Y3^2, Y2^2 * Y3^-3, (Y3^2 * Y1^-1)^2, (Y2 * Y3^-1 * Y1^-1)^2, Y1^6, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 32, 80, 24, 72, 5, 53)(3, 51, 13, 61, 30, 78, 35, 83, 27, 75, 11, 59)(4, 52, 17, 65, 33, 81, 12, 60, 26, 74, 20, 68)(6, 54, 22, 70, 15, 63, 40, 88, 18, 66, 9, 57)(7, 55, 28, 76, 14, 62, 23, 71, 37, 85, 10, 58)(16, 64, 44, 92, 43, 91, 39, 87, 29, 77, 38, 86)(19, 67, 36, 84, 48, 96, 45, 93, 31, 79, 42, 90)(21, 69, 47, 95, 46, 94, 41, 89, 25, 73, 34, 82)(97, 145, 99, 147, 110, 158, 139, 187, 144, 192, 142, 190, 122, 170, 102, 150)(98, 146, 105, 153, 116, 164, 143, 191, 141, 189, 140, 188, 119, 167, 107, 155)(100, 148, 114, 162, 104, 152, 123, 171, 133, 181, 112, 160, 127, 175, 117, 165)(101, 149, 118, 166, 108, 156, 137, 185, 132, 180, 135, 183, 124, 172, 109, 157)(103, 151, 125, 173, 115, 163, 121, 169, 129, 177, 111, 159, 120, 168, 126, 174)(106, 154, 131, 179, 128, 176, 136, 184, 113, 161, 130, 178, 138, 186, 134, 182)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 119)(6, 121)(7, 97)(8, 129)(9, 109)(10, 132)(11, 135)(12, 98)(13, 134)(14, 104)(15, 117)(16, 99)(17, 101)(18, 142)(19, 110)(20, 128)(21, 139)(22, 131)(23, 138)(24, 122)(25, 112)(26, 127)(27, 102)(28, 141)(29, 123)(30, 114)(31, 103)(32, 124)(33, 144)(34, 105)(35, 140)(36, 116)(37, 120)(38, 143)(39, 130)(40, 107)(41, 136)(42, 108)(43, 126)(44, 137)(45, 113)(46, 125)(47, 118)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.713
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.707 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2 * Y1^-1 * Y3 * Y2^-1, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3 * Y2 * Y3^-2, Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y3^3 * Y2, Y1^6, (Y3^-1 * Y2^-1 * Y1^-1)^2, (Y3^2 * Y1^-1)^2, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 32, 80, 24, 72, 5, 53)(3, 51, 13, 61, 25, 73, 35, 83, 21, 69, 11, 59)(4, 52, 17, 65, 33, 81, 12, 60, 14, 62, 20, 68)(6, 54, 22, 70, 29, 77, 39, 87, 16, 64, 9, 57)(7, 55, 28, 76, 26, 74, 23, 71, 38, 86, 10, 58)(15, 63, 40, 88, 18, 66, 43, 91, 44, 92, 41, 89)(19, 67, 37, 85, 48, 96, 45, 93, 31, 79, 42, 90)(27, 75, 47, 95, 46, 94, 34, 82, 30, 78, 36, 84)(97, 145, 99, 147, 110, 158, 140, 188, 144, 192, 142, 190, 122, 170, 102, 150)(98, 146, 105, 153, 119, 167, 143, 191, 141, 189, 139, 187, 116, 164, 107, 155)(100, 148, 114, 162, 127, 175, 123, 171, 134, 182, 112, 160, 104, 152, 117, 165)(101, 149, 118, 166, 124, 172, 130, 178, 133, 181, 137, 185, 108, 156, 109, 157)(103, 151, 125, 173, 120, 168, 121, 169, 129, 177, 111, 159, 115, 163, 126, 174)(106, 154, 132, 180, 138, 186, 136, 184, 113, 161, 131, 179, 128, 176, 135, 183)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 119)(6, 121)(7, 97)(8, 129)(9, 130)(10, 133)(11, 118)(12, 98)(13, 135)(14, 127)(15, 123)(16, 99)(17, 101)(18, 142)(19, 122)(20, 128)(21, 140)(22, 132)(23, 138)(24, 110)(25, 114)(26, 104)(27, 102)(28, 141)(29, 117)(30, 112)(31, 103)(32, 124)(33, 144)(34, 136)(35, 105)(36, 139)(37, 116)(38, 120)(39, 143)(40, 107)(41, 131)(42, 108)(43, 109)(44, 126)(45, 113)(46, 125)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.712
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.708 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, R * Y2 * R * Y3 * Y2 * Y3, (R * Y2 * Y3)^2, Y1^8, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-3 * Y3, (Y3 * Y2)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 25, 73, 13, 61, 5, 53)(3, 51, 7, 55, 15, 63, 27, 75, 41, 89, 36, 84, 21, 69, 10, 58)(4, 52, 8, 56, 16, 64, 28, 76, 42, 90, 40, 88, 24, 72, 12, 60)(9, 57, 17, 65, 29, 77, 43, 91, 37, 85, 48, 96, 35, 83, 20, 68)(11, 59, 18, 66, 30, 78, 44, 92, 33, 81, 47, 95, 39, 87, 23, 71)(19, 67, 31, 79, 45, 93, 38, 86, 22, 70, 32, 80, 46, 94, 34, 82)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 106, 154)(102, 150, 111, 159)(104, 152, 114, 162)(105, 153, 115, 163)(108, 156, 119, 167)(109, 157, 117, 165)(110, 158, 123, 171)(112, 160, 126, 174)(113, 161, 127, 175)(116, 164, 130, 178)(118, 166, 133, 181)(120, 168, 135, 183)(121, 169, 132, 180)(122, 170, 137, 185)(124, 172, 140, 188)(125, 173, 141, 189)(128, 176, 144, 192)(129, 177, 138, 186)(131, 179, 142, 190)(134, 182, 139, 187)(136, 184, 143, 191)
	L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 99)(10, 116)(11, 118)(12, 101)(13, 120)(14, 124)(15, 125)(16, 102)(17, 103)(18, 128)(19, 129)(20, 106)(21, 131)(22, 107)(23, 134)(24, 109)(25, 136)(26, 138)(27, 139)(28, 110)(29, 111)(30, 142)(31, 143)(32, 114)(33, 115)(34, 140)(35, 117)(36, 144)(37, 137)(38, 119)(39, 141)(40, 121)(41, 133)(42, 122)(43, 123)(44, 130)(45, 135)(46, 126)(47, 127)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.703
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.709 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-3, Y1^8, (Y3 * Y2)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 16, 64, 32, 80, 31, 79, 15, 63, 5, 53)(3, 51, 9, 57, 17, 65, 35, 83, 45, 93, 39, 87, 27, 75, 11, 59)(4, 52, 8, 56, 18, 66, 34, 82, 46, 94, 44, 92, 29, 77, 13, 61)(7, 55, 19, 67, 33, 81, 24, 72, 42, 90, 30, 78, 14, 62, 21, 69)(10, 58, 22, 70, 36, 84, 47, 95, 40, 88, 48, 96, 38, 86, 25, 73)(12, 60, 20, 68, 37, 85, 26, 74, 43, 91, 23, 71, 41, 89, 28, 76)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(107, 155, 122, 170)(109, 157, 121, 169)(111, 159, 123, 171)(112, 160, 129, 177)(114, 162, 133, 181)(115, 163, 134, 182)(116, 164, 135, 183)(117, 165, 136, 184)(124, 172, 131, 179)(125, 173, 137, 185)(126, 174, 132, 180)(127, 175, 138, 186)(128, 176, 141, 189)(130, 178, 143, 191)(139, 187, 142, 190)(140, 188, 144, 192)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 118)(10, 99)(11, 121)(12, 117)(13, 101)(14, 124)(15, 125)(16, 130)(17, 132)(18, 102)(19, 133)(20, 103)(21, 108)(22, 105)(23, 138)(24, 139)(25, 107)(26, 129)(27, 134)(28, 110)(29, 111)(30, 137)(31, 140)(32, 142)(33, 122)(34, 112)(35, 143)(36, 113)(37, 115)(38, 123)(39, 144)(40, 141)(41, 126)(42, 119)(43, 120)(44, 127)(45, 136)(46, 128)(47, 131)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.702
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.710 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, Y3 * Y1^-1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1^-1 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 17, 65, 29, 77, 28, 76, 16, 64, 5, 53)(3, 51, 11, 59, 23, 71, 35, 83, 40, 88, 30, 78, 18, 66, 8, 56)(4, 52, 10, 58, 19, 67, 32, 80, 41, 89, 38, 86, 26, 74, 14, 62)(6, 54, 9, 57, 20, 68, 31, 79, 42, 90, 39, 87, 27, 75, 15, 63)(12, 60, 25, 73, 36, 84, 46, 94, 47, 95, 44, 92, 33, 81, 22, 70)(13, 61, 24, 72, 37, 85, 45, 93, 48, 96, 43, 91, 34, 82, 21, 69)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 107, 155)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 121, 169)(111, 159, 120, 168)(112, 160, 119, 167)(113, 161, 126, 174)(115, 163, 129, 177)(116, 164, 130, 178)(122, 170, 132, 180)(123, 171, 133, 181)(124, 172, 131, 179)(125, 173, 136, 184)(127, 175, 139, 187)(128, 176, 140, 188)(134, 182, 142, 190)(135, 183, 141, 189)(137, 185, 143, 191)(138, 186, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 102)(5, 111)(6, 97)(7, 115)(8, 117)(9, 106)(10, 98)(11, 120)(12, 109)(13, 99)(14, 101)(15, 110)(16, 122)(17, 127)(18, 129)(19, 116)(20, 103)(21, 118)(22, 104)(23, 132)(24, 121)(25, 107)(26, 123)(27, 112)(28, 135)(29, 137)(30, 139)(31, 128)(32, 113)(33, 130)(34, 114)(35, 141)(36, 133)(37, 119)(38, 124)(39, 134)(40, 143)(41, 138)(42, 125)(43, 140)(44, 126)(45, 142)(46, 131)(47, 144)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.704
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.711 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1 * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (Y1^-1 * Y3^-1 * Y2)^2, Y3^6, Y1^2 * Y3 * Y1 * Y3^-2 * Y1, Y1^2 * Y2 * Y1 * Y3 * Y1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 32, 80, 37, 85, 17, 65, 5, 53)(3, 51, 11, 59, 27, 75, 43, 91, 48, 96, 38, 86, 20, 68, 8, 56)(4, 52, 10, 58, 21, 69, 35, 83, 18, 66, 25, 73, 34, 82, 15, 63)(6, 54, 9, 57, 22, 70, 33, 81, 14, 62, 26, 74, 36, 84, 16, 64)(12, 60, 29, 77, 44, 92, 41, 89, 31, 79, 46, 94, 39, 87, 24, 72)(13, 61, 28, 76, 45, 93, 42, 90, 30, 78, 47, 95, 40, 88, 23, 71)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 107, 155)(102, 150, 109, 157)(103, 151, 116, 164)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 126, 174)(111, 159, 125, 173)(112, 160, 124, 172)(113, 161, 123, 171)(114, 162, 127, 175)(115, 163, 134, 182)(117, 165, 135, 183)(118, 166, 136, 184)(121, 169, 137, 185)(122, 170, 138, 186)(128, 176, 144, 192)(129, 177, 143, 191)(130, 178, 140, 188)(131, 179, 142, 190)(132, 180, 141, 189)(133, 181, 139, 187)
	L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 112)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 101)(16, 131)(17, 130)(18, 102)(19, 129)(20, 135)(21, 132)(22, 103)(23, 137)(24, 104)(25, 133)(26, 106)(27, 140)(28, 142)(29, 107)(30, 144)(31, 109)(32, 114)(33, 111)(34, 118)(35, 115)(36, 113)(37, 122)(38, 143)(39, 141)(40, 116)(41, 139)(42, 120)(43, 138)(44, 136)(45, 123)(46, 134)(47, 125)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.705
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.712 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-3, Y1 * Y3^-1 * Y1 * Y3^2, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3, (R * Y2 * Y3^-1)^2, (Y2 * Y1^-1 * Y3)^2, Y2 * Y3^-2 * Y2 * Y3^2, Y3 * Y1^3 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 25, 73, 46, 94, 42, 90, 19, 67, 5, 53)(3, 51, 11, 59, 35, 83, 48, 96, 44, 92, 47, 95, 26, 74, 8, 56)(4, 52, 14, 62, 27, 75, 20, 68, 34, 82, 10, 58, 24, 72, 17, 65)(6, 54, 21, 69, 16, 64, 18, 66, 32, 80, 9, 57, 30, 78, 23, 71)(12, 60, 38, 86, 45, 93, 29, 77, 15, 63, 37, 85, 41, 89, 33, 81)(13, 61, 40, 88, 39, 87, 28, 76, 22, 70, 36, 84, 43, 91, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 107, 155)(102, 150, 118, 166)(103, 151, 122, 170)(105, 153, 127, 175)(106, 154, 129, 177)(108, 156, 130, 178)(109, 157, 128, 176)(110, 158, 125, 173)(112, 160, 135, 183)(113, 161, 133, 181)(114, 162, 136, 184)(115, 163, 131, 179)(116, 164, 134, 182)(117, 165, 124, 172)(119, 167, 132, 180)(120, 168, 137, 185)(121, 169, 143, 191)(123, 171, 141, 189)(126, 174, 139, 187)(138, 186, 144, 192)(140, 188, 142, 190)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 123)(8, 124)(9, 113)(10, 98)(11, 132)(12, 135)(13, 99)(14, 138)(15, 139)(16, 103)(17, 121)(18, 106)(19, 120)(20, 101)(21, 116)(22, 140)(23, 110)(24, 102)(25, 119)(26, 137)(27, 128)(28, 133)(29, 104)(30, 115)(31, 134)(32, 142)(33, 144)(34, 126)(35, 141)(36, 129)(37, 107)(38, 143)(39, 131)(40, 125)(41, 109)(42, 117)(43, 122)(44, 111)(45, 118)(46, 130)(47, 136)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.707
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.713 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1 * Y3^-2, Y3 * Y1^2 * Y3^2, Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1, Y3^-1 * Y1^3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 25, 73, 46, 94, 42, 90, 19, 67, 5, 53)(3, 51, 11, 59, 35, 83, 48, 96, 44, 92, 47, 95, 26, 74, 8, 56)(4, 52, 14, 62, 24, 72, 20, 68, 34, 82, 10, 58, 32, 80, 17, 65)(6, 54, 21, 69, 27, 75, 18, 66, 31, 79, 9, 57, 16, 64, 23, 71)(12, 60, 38, 86, 41, 89, 29, 77, 15, 63, 37, 85, 45, 93, 33, 81)(13, 61, 40, 88, 43, 91, 28, 76, 22, 70, 36, 84, 39, 87, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 107, 155)(102, 150, 118, 166)(103, 151, 122, 170)(105, 153, 126, 174)(106, 154, 129, 177)(108, 156, 130, 178)(109, 157, 127, 175)(110, 158, 125, 173)(112, 160, 135, 183)(113, 161, 133, 181)(114, 162, 136, 184)(115, 163, 131, 179)(116, 164, 134, 182)(117, 165, 124, 172)(119, 167, 132, 180)(120, 168, 137, 185)(121, 169, 143, 191)(123, 171, 139, 187)(128, 176, 141, 189)(138, 186, 144, 192)(140, 188, 142, 190)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 120)(8, 124)(9, 116)(10, 98)(11, 132)(12, 135)(13, 99)(14, 138)(15, 139)(16, 115)(17, 121)(18, 110)(19, 128)(20, 101)(21, 113)(22, 140)(23, 106)(24, 102)(25, 119)(26, 141)(27, 103)(28, 134)(29, 104)(30, 133)(31, 142)(32, 127)(33, 144)(34, 123)(35, 137)(36, 125)(37, 107)(38, 143)(39, 122)(40, 129)(41, 109)(42, 117)(43, 131)(44, 111)(45, 118)(46, 130)(47, 136)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.706
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.714 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y1, Y2), Y3^2 * Y2^-2, (R * Y1)^2, Y2^-2 * Y1^-2, (Y3, Y2^-1), (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1^2 * Y3, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3, Y3 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3^2 * Y2^6, Y3^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 22, 70, 40, 88, 33, 81, 13, 61, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59, 23, 71, 41, 89, 31, 79, 15, 63)(4, 52, 17, 65, 7, 55, 21, 69, 24, 72, 44, 92, 32, 80, 18, 66)(10, 58, 27, 75, 12, 60, 30, 78, 42, 90, 38, 86, 19, 67, 28, 76)(14, 62, 34, 82, 16, 64, 37, 85, 20, 68, 39, 87, 43, 91, 35, 83)(25, 73, 45, 93, 26, 74, 47, 95, 29, 77, 48, 96, 36, 84, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 136, 184, 119, 167, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 111, 159, 129, 177, 137, 185, 118, 166, 107, 155)(100, 148, 110, 158, 128, 176, 139, 187, 120, 168, 116, 164, 103, 151, 112, 160)(106, 154, 121, 169, 115, 163, 132, 180, 138, 186, 125, 173, 108, 156, 122, 170)(113, 161, 130, 178, 114, 162, 131, 179, 140, 188, 135, 183, 117, 165, 133, 181)(123, 171, 141, 189, 124, 172, 142, 190, 134, 182, 144, 192, 126, 174, 143, 191)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 103)(9, 121)(10, 101)(11, 122)(12, 98)(13, 128)(14, 127)(15, 132)(16, 99)(17, 126)(18, 123)(19, 129)(20, 102)(21, 134)(22, 108)(23, 116)(24, 104)(25, 111)(26, 105)(27, 140)(28, 117)(29, 107)(30, 114)(31, 139)(32, 136)(33, 138)(34, 143)(35, 141)(36, 137)(37, 144)(38, 113)(39, 142)(40, 120)(41, 125)(42, 118)(43, 119)(44, 124)(45, 135)(46, 133)(47, 131)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.701
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.715 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1 * Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^2 * Y2^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^5, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 20, 68)(6, 54, 22, 70)(7, 55, 24, 72)(8, 56, 27, 75)(10, 58, 34, 82)(11, 59, 35, 83)(12, 60, 31, 79)(14, 62, 41, 89)(15, 63, 23, 71)(16, 64, 37, 85)(17, 65, 38, 86)(18, 66, 25, 73)(19, 67, 30, 78)(21, 69, 39, 87)(26, 74, 45, 93)(28, 76, 48, 96)(29, 77, 42, 90)(32, 80, 43, 91)(33, 81, 46, 94)(36, 84, 47, 95)(40, 88, 44, 92)(97, 98, 103, 119, 138, 134, 108, 101)(99, 107, 102, 117, 121, 140, 133, 110)(100, 111, 127, 105, 125, 116, 120, 113)(104, 122, 106, 129, 139, 132, 115, 124)(109, 135, 112, 131, 114, 137, 118, 136)(123, 142, 126, 141, 128, 144, 130, 143)(145, 147, 156, 181, 186, 169, 151, 150)(146, 152, 149, 163, 182, 187, 167, 154)(148, 160, 168, 157, 173, 166, 175, 162)(153, 174, 159, 171, 161, 178, 164, 176)(155, 177, 158, 170, 188, 172, 165, 180)(179, 189, 183, 190, 184, 191, 185, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.721
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.716 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1^2 * Y2, (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y1^8, Y2^8 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 15, 63)(6, 54, 16, 64)(7, 55, 20, 68)(8, 56, 23, 71)(10, 58, 25, 73)(11, 59, 27, 75)(12, 60, 30, 78)(14, 62, 32, 80)(17, 65, 33, 81)(18, 66, 34, 82)(19, 67, 36, 84)(21, 69, 38, 86)(22, 70, 40, 88)(24, 72, 41, 89)(26, 74, 42, 90)(28, 76, 43, 91)(29, 77, 44, 92)(31, 79, 45, 93)(35, 83, 46, 94)(37, 85, 47, 95)(39, 87, 48, 96)(97, 98, 103, 115, 131, 127, 108, 101)(99, 107, 102, 114, 117, 135, 125, 110)(100, 111, 126, 141, 142, 132, 116, 105)(104, 118, 106, 122, 133, 124, 113, 120)(109, 128, 140, 144, 134, 130, 112, 123)(119, 137, 129, 139, 143, 138, 121, 136)(145, 147, 156, 173, 179, 165, 151, 150)(146, 152, 149, 161, 175, 181, 163, 154)(148, 160, 164, 182, 190, 188, 174, 157)(153, 169, 180, 191, 189, 177, 159, 167)(155, 170, 158, 166, 183, 168, 162, 172)(171, 187, 178, 185, 192, 184, 176, 186)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.722
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.717 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y2, (R * Y3)^2, Y1^-1 * Y2^-2 * Y1^-1, R * Y1 * R * Y2, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-2 * Y1^3 * Y2^-1, Y2^3 * Y3^-2 * Y1^-1, Y3^-3 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y3^6, Y3 * Y2^-1 * Y1 * Y3 * Y2^2, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 19, 67, 45, 93, 29, 77, 7, 55)(2, 50, 10, 58, 39, 87, 27, 75, 46, 94, 12, 60)(3, 51, 15, 63, 36, 84, 18, 66, 30, 78, 17, 65)(5, 53, 21, 69, 32, 80, 28, 76, 41, 89, 23, 71)(6, 54, 25, 73, 34, 82, 20, 68, 47, 95, 26, 74)(8, 56, 31, 79, 22, 70, 44, 92, 16, 64, 33, 81)(9, 57, 35, 83, 13, 61, 38, 86, 48, 96, 37, 85)(11, 59, 42, 90, 24, 72, 40, 88, 14, 62, 43, 91)(97, 98, 104, 126, 144, 143, 110, 101)(99, 109, 102, 120, 128, 125, 135, 112)(100, 114, 139, 108, 133, 119, 127, 116)(103, 113, 136, 106, 134, 117, 129, 122)(105, 130, 107, 137, 115, 142, 118, 132)(111, 138, 123, 131, 124, 140, 121, 141)(145, 147, 158, 183, 192, 176, 152, 150)(146, 153, 149, 166, 191, 163, 174, 155)(148, 154, 175, 161, 181, 170, 187, 165)(151, 171, 177, 159, 182, 169, 184, 172)(156, 188, 162, 179, 164, 186, 167, 189)(157, 185, 160, 178, 173, 180, 168, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.719
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.718 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 8, 8})
Quotient :: edge^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^-2, (Y3 * Y1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (Y2 * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, Y3^2 * Y2^-1 * Y1^3, Y1 * Y2^-1 * Y3^-2 * Y2^-2, Y3^6, Y3 * Y2^-1 * Y1 * Y3 * Y1^-2, Y2^-1 * Y1^-1 * Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 20, 68, 43, 91, 25, 73, 7, 55)(2, 50, 10, 58, 35, 83, 48, 96, 38, 86, 12, 60)(3, 51, 15, 63, 32, 80, 45, 93, 26, 74, 17, 65)(5, 53, 22, 70, 28, 76, 46, 94, 36, 84, 18, 66)(6, 54, 24, 72, 30, 78, 47, 95, 40, 88, 19, 67)(8, 56, 27, 75, 21, 69, 42, 90, 16, 64, 29, 77)(9, 57, 31, 79, 13, 61, 39, 87, 44, 92, 33, 81)(11, 59, 37, 85, 23, 71, 41, 89, 14, 62, 34, 82)(97, 98, 104, 122, 140, 136, 110, 101)(99, 109, 102, 119, 124, 121, 131, 112)(100, 114, 130, 143, 129, 141, 123, 108)(103, 118, 137, 115, 135, 113, 125, 106)(105, 126, 107, 132, 116, 134, 117, 128)(111, 138, 144, 139, 142, 133, 120, 127)(145, 147, 158, 179, 188, 172, 152, 150)(146, 153, 149, 165, 184, 164, 170, 155)(148, 163, 171, 166, 177, 154, 178, 161)(151, 168, 173, 190, 183, 192, 185, 159)(156, 181, 189, 187, 191, 186, 162, 175)(157, 180, 160, 174, 169, 176, 167, 182)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.720
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.719 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, (Y2^-1 * Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^2 * Y2^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^5, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 20, 68, 116, 164)(6, 54, 102, 150, 22, 70, 118, 166)(7, 55, 103, 151, 24, 72, 120, 168)(8, 56, 104, 152, 27, 75, 123, 171)(10, 58, 106, 154, 34, 82, 130, 178)(11, 59, 107, 155, 35, 83, 131, 179)(12, 60, 108, 156, 31, 79, 127, 175)(14, 62, 110, 158, 41, 89, 137, 185)(15, 63, 111, 159, 23, 71, 119, 167)(16, 64, 112, 160, 37, 85, 133, 181)(17, 65, 113, 161, 38, 86, 134, 182)(18, 66, 114, 162, 25, 73, 121, 169)(19, 67, 115, 163, 30, 78, 126, 174)(21, 69, 117, 165, 39, 87, 135, 183)(26, 74, 122, 170, 45, 93, 141, 189)(28, 76, 124, 172, 48, 96, 144, 192)(29, 77, 125, 173, 42, 90, 138, 186)(32, 80, 128, 176, 43, 91, 139, 187)(33, 81, 129, 177, 46, 94, 142, 190)(36, 84, 132, 180, 47, 95, 143, 191)(40, 88, 136, 184, 44, 92, 140, 188)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 69)(7, 71)(8, 74)(9, 77)(10, 81)(11, 54)(12, 53)(13, 87)(14, 51)(15, 79)(16, 83)(17, 52)(18, 89)(19, 76)(20, 72)(21, 73)(22, 88)(23, 90)(24, 65)(25, 92)(26, 58)(27, 94)(28, 56)(29, 68)(30, 93)(31, 57)(32, 96)(33, 91)(34, 95)(35, 66)(36, 67)(37, 62)(38, 60)(39, 64)(40, 61)(41, 70)(42, 86)(43, 84)(44, 85)(45, 80)(46, 78)(47, 75)(48, 82)(97, 147)(98, 152)(99, 156)(100, 160)(101, 163)(102, 145)(103, 150)(104, 149)(105, 174)(106, 146)(107, 177)(108, 181)(109, 173)(110, 170)(111, 171)(112, 168)(113, 178)(114, 148)(115, 182)(116, 176)(117, 180)(118, 175)(119, 154)(120, 157)(121, 151)(122, 188)(123, 161)(124, 165)(125, 166)(126, 159)(127, 162)(128, 153)(129, 158)(130, 164)(131, 189)(132, 155)(133, 186)(134, 187)(135, 190)(136, 191)(137, 192)(138, 169)(139, 167)(140, 172)(141, 183)(142, 184)(143, 185)(144, 179)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.717
Transitivity :: VT+
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.720 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1^2 * Y2, (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y1^8, Y2^8 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 16, 64, 112, 160)(7, 55, 103, 151, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 27, 75, 123, 171)(12, 60, 108, 156, 30, 78, 126, 174)(14, 62, 110, 158, 32, 80, 128, 176)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 36, 84, 132, 180)(21, 69, 117, 165, 38, 86, 134, 182)(22, 70, 118, 166, 40, 88, 136, 184)(24, 72, 120, 168, 41, 89, 137, 185)(26, 74, 122, 170, 42, 90, 138, 186)(28, 76, 124, 172, 43, 91, 139, 187)(29, 77, 125, 173, 44, 92, 140, 188)(31, 79, 127, 175, 45, 93, 141, 189)(35, 83, 131, 179, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191)(39, 87, 135, 183, 48, 96, 144, 192)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 66)(7, 67)(8, 70)(9, 52)(10, 74)(11, 54)(12, 53)(13, 80)(14, 51)(15, 78)(16, 75)(17, 72)(18, 69)(19, 83)(20, 57)(21, 87)(22, 58)(23, 89)(24, 56)(25, 88)(26, 85)(27, 61)(28, 65)(29, 62)(30, 93)(31, 60)(32, 92)(33, 91)(34, 64)(35, 79)(36, 68)(37, 76)(38, 82)(39, 77)(40, 71)(41, 81)(42, 73)(43, 95)(44, 96)(45, 94)(46, 84)(47, 90)(48, 86)(97, 147)(98, 152)(99, 156)(100, 160)(101, 161)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 170)(108, 173)(109, 148)(110, 166)(111, 167)(112, 164)(113, 175)(114, 172)(115, 154)(116, 182)(117, 151)(118, 183)(119, 153)(120, 162)(121, 180)(122, 158)(123, 187)(124, 155)(125, 179)(126, 157)(127, 181)(128, 186)(129, 159)(130, 185)(131, 165)(132, 191)(133, 163)(134, 190)(135, 168)(136, 176)(137, 192)(138, 171)(139, 178)(140, 174)(141, 177)(142, 188)(143, 189)(144, 184)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.718
Transitivity :: VT+
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.721 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y2, (R * Y3)^2, Y1^-1 * Y2^-2 * Y1^-1, R * Y1 * R * Y2, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-2 * Y1^3 * Y2^-1, Y2^3 * Y3^-2 * Y1^-1, Y3^-3 * Y2 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y3^6, Y3 * Y2^-1 * Y1 * Y3 * Y2^2, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 19, 67, 115, 163, 45, 93, 141, 189, 29, 77, 125, 173, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 39, 87, 135, 183, 27, 75, 123, 171, 46, 94, 142, 190, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 36, 84, 132, 180, 18, 66, 114, 162, 30, 78, 126, 174, 17, 65, 113, 161)(5, 53, 101, 149, 21, 69, 117, 165, 32, 80, 128, 176, 28, 76, 124, 172, 41, 89, 137, 185, 23, 71, 119, 167)(6, 54, 102, 150, 25, 73, 121, 169, 34, 82, 130, 178, 20, 68, 116, 164, 47, 95, 143, 191, 26, 74, 122, 170)(8, 56, 104, 152, 31, 79, 127, 175, 22, 70, 118, 166, 44, 92, 140, 188, 16, 64, 112, 160, 33, 81, 129, 177)(9, 57, 105, 153, 35, 83, 131, 179, 13, 61, 109, 157, 38, 86, 134, 182, 48, 96, 144, 192, 37, 85, 133, 181)(11, 59, 107, 155, 42, 90, 138, 186, 24, 72, 120, 168, 40, 88, 136, 184, 14, 62, 110, 158, 43, 91, 139, 187)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 72)(7, 65)(8, 78)(9, 82)(10, 86)(11, 89)(12, 85)(13, 54)(14, 53)(15, 90)(16, 51)(17, 88)(18, 91)(19, 94)(20, 52)(21, 81)(22, 84)(23, 79)(24, 80)(25, 93)(26, 55)(27, 83)(28, 92)(29, 87)(30, 96)(31, 68)(32, 77)(33, 74)(34, 59)(35, 76)(36, 57)(37, 71)(38, 69)(39, 64)(40, 58)(41, 67)(42, 75)(43, 60)(44, 73)(45, 63)(46, 70)(47, 62)(48, 95)(97, 147)(98, 153)(99, 158)(100, 154)(101, 166)(102, 145)(103, 171)(104, 150)(105, 149)(106, 175)(107, 146)(108, 188)(109, 185)(110, 183)(111, 182)(112, 178)(113, 181)(114, 179)(115, 174)(116, 186)(117, 148)(118, 191)(119, 189)(120, 190)(121, 184)(122, 187)(123, 177)(124, 151)(125, 180)(126, 155)(127, 161)(128, 152)(129, 159)(130, 173)(131, 164)(132, 168)(133, 170)(134, 169)(135, 192)(136, 172)(137, 160)(138, 167)(139, 165)(140, 162)(141, 156)(142, 157)(143, 163)(144, 176)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.715
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.722 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 8, 8})
Quotient :: loop^2
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^-2, (Y3 * Y1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (Y2 * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^-1)^2, Y3^2 * Y2^-1 * Y1^3, Y1 * Y2^-1 * Y3^-2 * Y2^-2, Y3^6, Y3 * Y2^-1 * Y1 * Y3 * Y1^-2, Y2^-1 * Y1^-1 * Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 20, 68, 116, 164, 43, 91, 139, 187, 25, 73, 121, 169, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 35, 83, 131, 179, 48, 96, 144, 192, 38, 86, 134, 182, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 32, 80, 128, 176, 45, 93, 141, 189, 26, 74, 122, 170, 17, 65, 113, 161)(5, 53, 101, 149, 22, 70, 118, 166, 28, 76, 124, 172, 46, 94, 142, 190, 36, 84, 132, 180, 18, 66, 114, 162)(6, 54, 102, 150, 24, 72, 120, 168, 30, 78, 126, 174, 47, 95, 143, 191, 40, 88, 136, 184, 19, 67, 115, 163)(8, 56, 104, 152, 27, 75, 123, 171, 21, 69, 117, 165, 42, 90, 138, 186, 16, 64, 112, 160, 29, 77, 125, 173)(9, 57, 105, 153, 31, 79, 127, 175, 13, 61, 109, 157, 39, 87, 135, 183, 44, 92, 140, 188, 33, 81, 129, 177)(11, 59, 107, 155, 37, 85, 133, 181, 23, 71, 119, 167, 41, 89, 137, 185, 14, 62, 110, 158, 34, 82, 130, 178)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 70)(8, 74)(9, 78)(10, 55)(11, 84)(12, 52)(13, 54)(14, 53)(15, 90)(16, 51)(17, 77)(18, 82)(19, 87)(20, 86)(21, 80)(22, 89)(23, 76)(24, 79)(25, 83)(26, 92)(27, 60)(28, 73)(29, 58)(30, 59)(31, 63)(32, 57)(33, 93)(34, 95)(35, 64)(36, 68)(37, 72)(38, 69)(39, 65)(40, 62)(41, 67)(42, 96)(43, 94)(44, 88)(45, 75)(46, 85)(47, 81)(48, 91)(97, 147)(98, 153)(99, 158)(100, 163)(101, 165)(102, 145)(103, 168)(104, 150)(105, 149)(106, 178)(107, 146)(108, 181)(109, 180)(110, 179)(111, 151)(112, 174)(113, 148)(114, 175)(115, 171)(116, 170)(117, 184)(118, 177)(119, 182)(120, 173)(121, 176)(122, 155)(123, 166)(124, 152)(125, 190)(126, 169)(127, 156)(128, 167)(129, 154)(130, 161)(131, 188)(132, 160)(133, 189)(134, 157)(135, 192)(136, 164)(137, 159)(138, 162)(139, 191)(140, 172)(141, 187)(142, 183)(143, 186)(144, 185)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.716
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.723 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, Y1 * Y2 * Y1 * Y3 * Y2^-1 * Y3^-1, Y2^6, Y3^-1 * Y1 * Y3^-3 * Y1, Y2^2 * Y1 * Y3 * Y2 * Y1 * Y3^-1, Y2^-1 * Y3^-4 * Y2^-2, Y3 * Y2^-1 * Y3 * Y2 * Y3^2 * Y2, Y2^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y2^-1, (Y1 * Y3^-1 * Y1 * Y3)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 14, 62)(5, 53, 7, 55)(6, 54, 19, 67)(8, 56, 24, 72)(10, 58, 29, 77)(11, 59, 27, 75)(12, 60, 34, 82)(13, 61, 36, 84)(15, 63, 38, 86)(16, 64, 26, 74)(17, 65, 21, 69)(18, 66, 43, 91)(20, 68, 30, 78)(22, 70, 32, 80)(23, 71, 33, 81)(25, 73, 40, 88)(28, 76, 42, 90)(31, 79, 39, 87)(35, 83, 47, 95)(37, 85, 48, 96)(41, 89, 45, 93)(44, 92, 46, 94)(97, 145, 99, 147, 107, 155, 127, 175, 113, 161, 101, 149)(98, 146, 103, 151, 117, 165, 135, 183, 123, 171, 105, 153)(100, 148, 111, 159, 136, 184, 120, 168, 128, 176, 108, 156)(102, 150, 114, 162, 138, 186, 125, 173, 129, 177, 109, 157)(104, 152, 121, 169, 134, 182, 110, 158, 130, 178, 118, 166)(106, 154, 124, 172, 139, 187, 115, 163, 132, 180, 119, 167)(112, 160, 131, 179, 140, 188, 116, 164, 133, 181, 137, 185)(122, 170, 141, 189, 144, 192, 126, 174, 142, 190, 143, 191)
	L = (1, 100)(2, 104)(3, 108)(4, 112)(5, 111)(6, 97)(7, 118)(8, 122)(9, 121)(10, 98)(11, 128)(12, 131)(13, 99)(14, 126)(15, 137)(16, 125)(17, 136)(18, 101)(19, 135)(20, 102)(21, 130)(22, 141)(23, 103)(24, 116)(25, 143)(26, 115)(27, 134)(28, 105)(29, 127)(30, 106)(31, 120)(32, 140)(33, 107)(34, 144)(35, 138)(36, 117)(37, 109)(38, 142)(39, 110)(40, 133)(41, 129)(42, 113)(43, 123)(44, 114)(45, 139)(46, 119)(47, 132)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.736
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.724 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y1 * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3)^2, Y1^6, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y3 * Y2^2 * Y3 * Y2^-2, Y1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2^-1, Y2^4 * Y1^3, Y2 * Y1 * Y3 * Y2^-1 * Y1^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 17, 65, 5, 53)(3, 51, 8, 56, 22, 70, 41, 89, 37, 85, 13, 61)(4, 52, 14, 62, 38, 86, 36, 84, 23, 71, 9, 57)(6, 54, 10, 58, 24, 72, 31, 79, 42, 90, 18, 66)(11, 59, 25, 73, 44, 92, 20, 68, 30, 78, 33, 81)(12, 60, 34, 82, 27, 75, 15, 63, 39, 87, 26, 74)(16, 64, 40, 88, 29, 77, 19, 67, 43, 91, 28, 76)(32, 80, 47, 95, 46, 94, 35, 83, 48, 96, 45, 93)(97, 145, 99, 147, 107, 155, 127, 175, 117, 165, 137, 185, 116, 164, 102, 150)(98, 146, 104, 152, 121, 169, 138, 186, 113, 161, 133, 181, 126, 174, 106, 154)(100, 148, 111, 159, 128, 176, 115, 163, 132, 180, 108, 156, 131, 179, 112, 160)(101, 149, 109, 157, 129, 177, 120, 168, 103, 151, 118, 166, 140, 188, 114, 162)(105, 153, 123, 171, 141, 189, 125, 173, 134, 182, 122, 170, 142, 190, 124, 172)(110, 158, 135, 183, 143, 191, 139, 187, 119, 167, 130, 178, 144, 192, 136, 184)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 115)(7, 119)(8, 122)(9, 98)(10, 125)(11, 128)(12, 99)(13, 130)(14, 101)(15, 137)(16, 127)(17, 134)(18, 139)(19, 102)(20, 131)(21, 132)(22, 135)(23, 103)(24, 136)(25, 141)(26, 104)(27, 133)(28, 138)(29, 106)(30, 142)(31, 112)(32, 107)(33, 143)(34, 109)(35, 116)(36, 117)(37, 123)(38, 113)(39, 118)(40, 120)(41, 111)(42, 124)(43, 114)(44, 144)(45, 121)(46, 126)(47, 129)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.734
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.725 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 13, 61, 32, 80, 15, 63, 14, 62)(6, 54, 19, 67, 20, 68, 38, 86, 16, 64, 21, 69)(8, 56, 23, 71, 17, 65, 40, 88, 26, 74, 25, 73)(10, 58, 28, 76, 18, 66, 41, 89, 27, 75, 29, 77)(12, 60, 30, 78, 34, 82, 46, 94, 36, 84, 35, 83)(22, 70, 24, 72, 39, 87, 44, 92, 42, 90, 33, 81)(31, 79, 43, 91, 37, 85, 45, 93, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 119, 167, 139, 187, 124, 172, 118, 166, 102, 150)(98, 146, 104, 152, 120, 168, 110, 158, 133, 181, 117, 165, 126, 174, 106, 154)(100, 148, 111, 159, 130, 178, 121, 169, 141, 189, 125, 173, 135, 183, 112, 160)(101, 149, 113, 161, 129, 177, 107, 155, 127, 175, 115, 163, 131, 179, 114, 162)(103, 151, 109, 157, 132, 180, 136, 184, 143, 191, 137, 185, 138, 186, 116, 164)(105, 153, 122, 170, 140, 188, 128, 176, 144, 192, 134, 182, 142, 190, 123, 171)
	L = (1, 100)(2, 105)(3, 109)(4, 103)(5, 98)(6, 116)(7, 97)(8, 113)(9, 101)(10, 114)(11, 128)(12, 130)(13, 111)(14, 107)(15, 99)(16, 102)(17, 122)(18, 123)(19, 134)(20, 112)(21, 115)(22, 135)(23, 136)(24, 140)(25, 119)(26, 104)(27, 106)(28, 137)(29, 124)(30, 142)(31, 133)(32, 110)(33, 120)(34, 132)(35, 126)(36, 108)(37, 144)(38, 117)(39, 138)(40, 121)(41, 125)(42, 118)(43, 141)(44, 129)(45, 143)(46, 131)(47, 139)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.730
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.726 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y3^6, (R * Y2 * Y3^-1)^2, Y1^2 * Y2 * Y1^2 * Y2^-1, Y1 * Y2 * Y1 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 18, 66, 5, 53)(3, 51, 13, 61, 37, 85, 34, 82, 28, 76, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60, 30, 78, 19, 67)(6, 54, 23, 71, 43, 91, 33, 81, 29, 77, 25, 73)(9, 57, 31, 79, 21, 69, 24, 72, 44, 92, 20, 68)(11, 59, 35, 83, 22, 70, 15, 63, 38, 86, 17, 65)(14, 62, 36, 84, 45, 93, 47, 95, 46, 94, 41, 89)(26, 74, 32, 80, 40, 88, 48, 96, 42, 90, 39, 87)(97, 145, 99, 147, 110, 158, 127, 175, 126, 174, 131, 179, 122, 170, 102, 150)(98, 146, 105, 153, 128, 176, 112, 160, 115, 163, 121, 169, 132, 180, 107, 155)(100, 148, 113, 161, 136, 184, 125, 173, 104, 152, 124, 172, 141, 189, 116, 164)(101, 149, 117, 165, 135, 183, 109, 157, 108, 156, 119, 167, 137, 185, 118, 166)(103, 151, 111, 159, 138, 186, 139, 187, 114, 162, 133, 181, 142, 190, 120, 168)(106, 154, 129, 177, 143, 191, 134, 182, 123, 171, 140, 188, 144, 192, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 115)(6, 120)(7, 97)(8, 103)(9, 119)(10, 101)(11, 109)(12, 98)(13, 134)(14, 136)(15, 124)(16, 118)(17, 99)(18, 126)(19, 123)(20, 102)(21, 129)(22, 130)(23, 140)(24, 125)(25, 117)(26, 141)(27, 108)(28, 131)(29, 127)(30, 104)(31, 139)(32, 143)(33, 105)(34, 107)(35, 133)(36, 144)(37, 113)(38, 112)(39, 132)(40, 142)(41, 128)(42, 110)(43, 116)(44, 121)(45, 138)(46, 122)(47, 135)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.731
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.727 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3^-2 * Y2 * Y3, Y1 * Y2^-2 * Y1 * Y3^-1, Y2^2 * Y3^3, Y1^2 * Y2^2 * Y3^-1, Y1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2, Y1^2 * Y3^-1 * Y2^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^6, (Y3^2 * Y1^-1)^2, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 36, 84, 25, 73, 5, 53)(3, 51, 13, 61, 28, 76, 40, 88, 22, 70, 16, 64)(4, 52, 18, 66, 37, 85, 12, 60, 14, 62, 21, 69)(6, 54, 27, 75, 33, 81, 45, 93, 17, 65, 29, 77)(7, 55, 32, 80, 30, 78, 24, 72, 42, 90, 10, 58)(9, 57, 38, 86, 23, 71, 15, 63, 43, 91, 19, 67)(11, 59, 44, 92, 26, 74, 34, 82, 39, 87, 31, 79)(20, 68, 41, 89, 48, 96, 47, 95, 35, 83, 46, 94)(97, 145, 99, 147, 110, 158, 134, 182, 144, 192, 140, 188, 126, 174, 102, 150)(98, 146, 105, 153, 120, 168, 112, 160, 143, 191, 125, 173, 117, 165, 107, 155)(100, 148, 115, 163, 131, 179, 127, 175, 138, 186, 113, 161, 104, 152, 118, 166)(101, 149, 119, 167, 128, 176, 109, 157, 137, 185, 123, 171, 108, 156, 122, 170)(103, 151, 129, 177, 121, 169, 124, 172, 133, 181, 111, 159, 116, 164, 130, 178)(106, 154, 136, 184, 142, 190, 141, 189, 114, 162, 135, 183, 132, 180, 139, 187)
	L = (1, 100)(2, 106)(3, 111)(4, 116)(5, 120)(6, 124)(7, 97)(8, 133)(9, 109)(10, 137)(11, 119)(12, 98)(13, 141)(14, 131)(15, 127)(16, 123)(17, 99)(18, 101)(19, 140)(20, 126)(21, 132)(22, 134)(23, 136)(24, 142)(25, 110)(26, 139)(27, 135)(28, 115)(29, 122)(30, 104)(31, 102)(32, 143)(33, 118)(34, 113)(35, 103)(36, 128)(37, 144)(38, 130)(39, 105)(40, 125)(41, 117)(42, 121)(43, 112)(44, 129)(45, 107)(46, 108)(47, 114)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.733
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.728 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * Y3 * R * Y2^-1, Y3 * Y2 * Y3^-1 * Y2 * Y3, Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y1 * Y3^-1 * Y2^-2 * Y1, Y1^2 * Y2 * Y3 * Y2, Y1^2 * Y2^-2 * Y3^-1, Y2^2 * Y3^-3, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y1 * Y2^2 * Y1 * Y3^-1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^6, (Y3^2 * Y1^-1)^2, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 36, 84, 25, 73, 5, 53)(3, 51, 13, 61, 34, 82, 39, 87, 31, 79, 16, 64)(4, 52, 18, 66, 37, 85, 12, 60, 30, 78, 21, 69)(6, 54, 27, 75, 15, 63, 43, 91, 19, 67, 29, 77)(7, 55, 32, 80, 14, 62, 24, 72, 42, 90, 10, 58)(9, 57, 38, 86, 23, 71, 33, 81, 45, 93, 17, 65)(11, 59, 44, 92, 26, 74, 28, 76, 40, 88, 22, 70)(20, 68, 41, 89, 48, 96, 47, 95, 35, 83, 46, 94)(97, 145, 99, 147, 110, 158, 134, 182, 144, 192, 140, 188, 126, 174, 102, 150)(98, 146, 105, 153, 117, 165, 112, 160, 143, 191, 125, 173, 120, 168, 107, 155)(100, 148, 115, 163, 104, 152, 127, 175, 138, 186, 113, 161, 131, 179, 118, 166)(101, 149, 119, 167, 108, 156, 109, 157, 137, 185, 123, 171, 128, 176, 122, 170)(103, 151, 129, 177, 116, 164, 124, 172, 133, 181, 111, 159, 121, 169, 130, 178)(106, 154, 136, 184, 132, 180, 141, 189, 114, 162, 135, 183, 142, 190, 139, 187)
	L = (1, 100)(2, 106)(3, 111)(4, 116)(5, 120)(6, 124)(7, 97)(8, 133)(9, 122)(10, 137)(11, 123)(12, 98)(13, 141)(14, 104)(15, 118)(16, 119)(17, 99)(18, 101)(19, 140)(20, 110)(21, 132)(22, 134)(23, 136)(24, 142)(25, 126)(26, 139)(27, 135)(28, 113)(29, 109)(30, 131)(31, 102)(32, 143)(33, 127)(34, 115)(35, 103)(36, 128)(37, 144)(38, 130)(39, 105)(40, 125)(41, 117)(42, 121)(43, 112)(44, 129)(45, 107)(46, 108)(47, 114)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.732
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.729 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (Y1^-1 * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-2 * Y3 * Y2^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, (R * Y2 * Y3)^2, Y1^6, Y2 * Y1^-1 * Y2 * Y1 * Y2^2 * Y1, Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 17, 65, 5, 53)(3, 51, 11, 59, 31, 79, 41, 89, 22, 70, 8, 56)(4, 52, 14, 62, 38, 86, 37, 85, 23, 71, 9, 57)(6, 54, 18, 66, 42, 90, 34, 82, 24, 72, 10, 58)(12, 60, 25, 73, 44, 92, 20, 68, 30, 78, 32, 80)(13, 61, 26, 74, 39, 87, 15, 63, 27, 75, 33, 81)(16, 64, 28, 76, 43, 91, 19, 67, 29, 77, 40, 88)(35, 83, 47, 95, 46, 94, 36, 84, 48, 96, 45, 93)(97, 145, 99, 147, 108, 156, 130, 178, 117, 165, 137, 185, 116, 164, 102, 150)(98, 146, 104, 152, 121, 169, 138, 186, 113, 161, 127, 175, 126, 174, 106, 154)(100, 148, 111, 159, 131, 179, 115, 163, 133, 181, 109, 157, 132, 180, 112, 160)(101, 149, 107, 155, 128, 176, 120, 168, 103, 151, 118, 166, 140, 188, 114, 162)(105, 153, 123, 171, 141, 189, 125, 173, 134, 182, 122, 170, 142, 190, 124, 172)(110, 158, 135, 183, 143, 191, 139, 187, 119, 167, 129, 177, 144, 192, 136, 184)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 115)(7, 119)(8, 122)(9, 98)(10, 125)(11, 129)(12, 131)(13, 99)(14, 101)(15, 137)(16, 130)(17, 134)(18, 139)(19, 102)(20, 132)(21, 133)(22, 135)(23, 103)(24, 136)(25, 141)(26, 104)(27, 127)(28, 138)(29, 106)(30, 142)(31, 123)(32, 143)(33, 107)(34, 112)(35, 108)(36, 116)(37, 117)(38, 113)(39, 118)(40, 120)(41, 111)(42, 124)(43, 114)(44, 144)(45, 121)(46, 126)(47, 128)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.735
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.730 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y1)^2, (Y2 * R)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^3 * Y2 * Y1^-1, (Y2 * Y1^-2)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 36, 84, 30, 78, 18, 66, 5, 53)(3, 51, 11, 59, 25, 73, 8, 56, 23, 71, 16, 64, 20, 68, 13, 61)(4, 52, 10, 58, 21, 69, 38, 86, 47, 95, 45, 93, 33, 81, 15, 63)(6, 54, 9, 57, 22, 70, 37, 85, 48, 96, 46, 94, 35, 83, 17, 65)(12, 60, 28, 76, 44, 92, 26, 74, 41, 89, 32, 80, 39, 87, 29, 77)(14, 62, 27, 75, 43, 91, 24, 72, 42, 90, 34, 82, 40, 88, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 112, 160)(102, 150, 110, 158)(103, 151, 116, 164)(105, 153, 120, 168)(106, 154, 122, 170)(107, 155, 115, 163)(109, 157, 126, 174)(111, 159, 128, 176)(113, 161, 130, 178)(114, 162, 121, 169)(117, 165, 135, 183)(118, 166, 136, 184)(119, 167, 132, 180)(123, 171, 133, 181)(124, 172, 134, 182)(125, 173, 141, 189)(127, 175, 142, 190)(129, 177, 140, 188)(131, 179, 139, 187)(137, 185, 143, 191)(138, 186, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 102)(5, 113)(6, 97)(7, 117)(8, 120)(9, 106)(10, 98)(11, 123)(12, 110)(13, 127)(14, 99)(15, 101)(16, 130)(17, 111)(18, 129)(19, 133)(20, 135)(21, 118)(22, 103)(23, 137)(24, 122)(25, 140)(26, 104)(27, 124)(28, 107)(29, 109)(30, 142)(31, 125)(32, 112)(33, 131)(34, 128)(35, 114)(36, 143)(37, 134)(38, 115)(39, 136)(40, 116)(41, 138)(42, 119)(43, 121)(44, 139)(45, 126)(46, 141)(47, 144)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.725
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.731 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1, (Y2 * Y1^-2)^2, Y3^6, Y1 * Y2 * Y3 * Y1 * Y3^-2 * Y2, Y3^-2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 38, 86, 35, 83, 19, 67, 5, 53)(3, 51, 11, 59, 27, 75, 8, 56, 25, 73, 17, 65, 22, 70, 13, 61)(4, 52, 10, 58, 23, 71, 43, 91, 20, 68, 29, 77, 41, 89, 16, 64)(6, 54, 9, 57, 24, 72, 39, 87, 15, 63, 30, 78, 44, 92, 18, 66)(12, 60, 32, 80, 48, 96, 28, 76, 37, 85, 40, 88, 45, 93, 34, 82)(14, 62, 31, 79, 47, 95, 26, 74, 33, 81, 42, 90, 46, 94, 36, 84)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 118, 166)(105, 153, 122, 170)(106, 154, 124, 172)(107, 155, 117, 165)(109, 157, 131, 179)(111, 159, 129, 177)(112, 160, 136, 184)(114, 162, 138, 186)(115, 163, 123, 171)(116, 164, 133, 181)(119, 167, 141, 189)(120, 168, 142, 190)(121, 169, 134, 182)(125, 173, 130, 178)(126, 174, 132, 180)(127, 175, 135, 183)(128, 176, 139, 187)(137, 185, 144, 192)(140, 188, 143, 191)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 127)(12, 129)(13, 132)(14, 99)(15, 134)(16, 101)(17, 138)(18, 139)(19, 137)(20, 102)(21, 135)(22, 141)(23, 140)(24, 103)(25, 133)(26, 130)(27, 144)(28, 104)(29, 131)(30, 106)(31, 136)(32, 107)(33, 121)(34, 109)(35, 126)(36, 124)(37, 110)(38, 116)(39, 112)(40, 113)(41, 120)(42, 128)(43, 117)(44, 115)(45, 143)(46, 118)(47, 123)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.726
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.732 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1 * Y3^-2, Y3^2 * Y1^2 * Y3, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1, Y2 * Y1^-1 * R * Y2 * R * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1, Y1 * Y2 * Y1^-3 * Y2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, Y2 * Y3^2 * Y2 * Y3^-2, R * Y2 * R * Y3^-1 * Y2 * Y3, Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 27, 75, 48, 96, 43, 91, 21, 69, 5, 53)(3, 51, 11, 59, 32, 80, 8, 56, 30, 78, 19, 67, 28, 76, 13, 61)(4, 52, 15, 63, 26, 74, 22, 70, 38, 86, 10, 58, 36, 84, 18, 66)(6, 54, 23, 71, 29, 77, 20, 68, 35, 83, 9, 57, 17, 65, 25, 73)(12, 60, 41, 89, 45, 93, 37, 85, 16, 64, 40, 88, 47, 95, 33, 81)(14, 62, 44, 92, 46, 94, 34, 82, 24, 72, 39, 87, 42, 90, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 112, 160)(101, 149, 115, 163)(102, 150, 120, 168)(103, 151, 124, 172)(105, 153, 130, 178)(106, 154, 133, 181)(107, 155, 123, 171)(108, 156, 134, 182)(109, 157, 139, 187)(110, 158, 131, 179)(111, 159, 129, 177)(113, 161, 138, 186)(114, 162, 137, 185)(116, 164, 135, 183)(117, 165, 128, 176)(118, 166, 136, 184)(119, 167, 127, 175)(121, 169, 140, 188)(122, 170, 141, 189)(125, 173, 142, 190)(126, 174, 144, 192)(132, 180, 143, 191)
	L = (1, 100)(2, 105)(3, 108)(4, 113)(5, 116)(6, 97)(7, 122)(8, 127)(9, 118)(10, 98)(11, 135)(12, 138)(13, 130)(14, 99)(15, 139)(16, 142)(17, 117)(18, 123)(19, 140)(20, 111)(21, 132)(22, 101)(23, 114)(24, 126)(25, 106)(26, 102)(27, 121)(28, 143)(29, 103)(30, 112)(31, 136)(32, 141)(33, 104)(34, 137)(35, 144)(36, 131)(37, 109)(38, 125)(39, 133)(40, 107)(41, 115)(42, 124)(43, 119)(44, 129)(45, 110)(46, 128)(47, 120)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.728
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.733 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 16>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^2, Y1^2 * Y3^-3, Y3 * Y1^3 * Y3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3, Y2 * Y3^-2 * Y2 * Y3^2, Y1^-1 * Y2 * Y1^3 * Y2, Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 27, 75, 48, 96, 43, 91, 21, 69, 5, 53)(3, 51, 11, 59, 32, 80, 8, 56, 30, 78, 19, 67, 28, 76, 13, 61)(4, 52, 15, 63, 29, 77, 22, 70, 38, 86, 10, 58, 26, 74, 18, 66)(6, 54, 23, 71, 17, 65, 20, 68, 36, 84, 9, 57, 34, 82, 25, 73)(12, 60, 41, 89, 47, 95, 37, 85, 16, 64, 40, 88, 45, 93, 33, 81)(14, 62, 44, 92, 42, 90, 35, 83, 24, 72, 39, 87, 46, 94, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 112, 160)(101, 149, 115, 163)(102, 150, 120, 168)(103, 151, 124, 172)(105, 153, 131, 179)(106, 154, 133, 181)(107, 155, 123, 171)(108, 156, 134, 182)(109, 157, 139, 187)(110, 158, 132, 180)(111, 159, 129, 177)(113, 161, 138, 186)(114, 162, 137, 185)(116, 164, 135, 183)(117, 165, 128, 176)(118, 166, 136, 184)(119, 167, 127, 175)(121, 169, 140, 188)(122, 170, 141, 189)(125, 173, 143, 191)(126, 174, 144, 192)(130, 178, 142, 190)
	L = (1, 100)(2, 105)(3, 108)(4, 113)(5, 116)(6, 97)(7, 125)(8, 127)(9, 114)(10, 98)(11, 135)(12, 138)(13, 131)(14, 99)(15, 139)(16, 142)(17, 103)(18, 123)(19, 140)(20, 106)(21, 122)(22, 101)(23, 118)(24, 126)(25, 111)(26, 102)(27, 121)(28, 141)(29, 132)(30, 112)(31, 137)(32, 143)(33, 104)(34, 117)(35, 136)(36, 144)(37, 109)(38, 130)(39, 129)(40, 107)(41, 115)(42, 128)(43, 119)(44, 133)(45, 110)(46, 124)(47, 120)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.727
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.734 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 118>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * R)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2, Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-3, (Y3 * Y1^-1 * Y2 * Y1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 18, 66, 35, 83, 32, 80, 17, 65, 5, 53)(3, 51, 9, 57, 19, 67, 37, 85, 46, 94, 42, 90, 31, 79, 11, 59)(4, 52, 12, 60, 20, 68, 16, 64, 26, 74, 8, 56, 24, 72, 14, 62)(7, 55, 21, 69, 36, 84, 33, 81, 45, 93, 34, 82, 15, 63, 23, 71)(10, 58, 25, 73, 38, 86, 30, 78, 44, 92, 27, 75, 43, 91, 28, 76)(13, 61, 22, 70, 39, 87, 47, 95, 41, 89, 48, 96, 40, 88, 29, 77)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 118, 166)(106, 154, 119, 167)(107, 155, 125, 173)(108, 156, 123, 171)(110, 158, 126, 174)(112, 160, 124, 172)(113, 161, 127, 175)(114, 162, 132, 180)(116, 164, 135, 183)(117, 165, 134, 182)(120, 168, 136, 184)(122, 170, 137, 185)(128, 176, 141, 189)(129, 177, 140, 188)(130, 178, 139, 187)(131, 179, 142, 190)(133, 181, 143, 191)(138, 186, 144, 192)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 123)(10, 99)(11, 126)(12, 128)(13, 129)(14, 114)(15, 125)(16, 101)(17, 120)(18, 110)(19, 134)(20, 102)(21, 136)(22, 103)(23, 137)(24, 113)(25, 138)(26, 131)(27, 105)(28, 133)(29, 111)(30, 107)(31, 139)(32, 108)(33, 109)(34, 135)(35, 122)(36, 143)(37, 124)(38, 115)(39, 130)(40, 117)(41, 119)(42, 121)(43, 127)(44, 142)(45, 144)(46, 140)(47, 132)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.724
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.735 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y1^3 * Y3 * Y1 * Y3, Y3 * Y1 * Y3 * Y1^3, Y3 * Y2 * Y3 * R * Y2 * R, Y2 * Y1^-1 * Y2 * Y1^-3, Y3 * Y1^2 * Y3 * Y1^-2, (R * Y2 * Y3)^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, Y2 * R * Y3 * Y1^-1 * Y3 * R * Y2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y2, Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 27, 75, 17, 65, 5, 53)(3, 51, 9, 57, 19, 67, 15, 63, 23, 71, 7, 55, 21, 69, 11, 59)(4, 52, 12, 60, 20, 68, 16, 64, 26, 74, 8, 56, 24, 72, 14, 62)(10, 58, 22, 70, 37, 85, 31, 79, 41, 89, 28, 76, 39, 87, 30, 78)(13, 61, 25, 73, 38, 86, 35, 83, 44, 92, 32, 80, 42, 90, 34, 82)(29, 77, 43, 91, 47, 95, 46, 94, 33, 81, 40, 88, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 123, 171)(106, 154, 125, 173)(107, 155, 114, 162)(108, 156, 128, 176)(110, 158, 131, 179)(112, 160, 130, 178)(113, 161, 117, 165)(116, 164, 134, 182)(118, 166, 136, 184)(119, 167, 132, 180)(120, 168, 138, 186)(122, 170, 140, 188)(124, 172, 139, 187)(126, 174, 142, 190)(127, 175, 141, 189)(129, 177, 137, 185)(133, 181, 143, 191)(135, 183, 144, 192)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 124)(10, 99)(11, 127)(12, 123)(13, 129)(14, 114)(15, 126)(16, 101)(17, 120)(18, 110)(19, 133)(20, 102)(21, 135)(22, 103)(23, 137)(24, 113)(25, 139)(26, 132)(27, 108)(28, 105)(29, 140)(30, 111)(31, 107)(32, 136)(33, 109)(34, 141)(35, 142)(36, 122)(37, 115)(38, 144)(39, 117)(40, 128)(41, 119)(42, 143)(43, 121)(44, 125)(45, 130)(46, 131)(47, 138)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.729
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.736 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2 * Y1^-1, Y2 * Y3^2 * Y2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y1^-2 * Y2^-1 * Y1^2 * Y2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y3^8, Y3^-2 * Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 24, 72, 42, 90, 35, 83, 19, 67, 5, 53)(3, 51, 13, 61, 25, 73, 11, 59, 28, 76, 9, 57, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 23, 71, 26, 74, 44, 92, 37, 85, 20, 68)(10, 58, 30, 78, 12, 60, 34, 82, 43, 91, 40, 88, 21, 69, 32, 80)(14, 62, 36, 84, 16, 64, 39, 87, 18, 66, 41, 89, 22, 70, 38, 86)(27, 75, 45, 93, 29, 77, 47, 95, 31, 79, 48, 96, 33, 81, 46, 94)(97, 145, 99, 147, 104, 152, 121, 169, 138, 186, 124, 172, 115, 163, 102, 150)(98, 146, 105, 153, 120, 168, 111, 159, 131, 179, 109, 157, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 118, 166, 122, 170, 110, 158, 133, 181, 112, 160)(106, 154, 127, 175, 108, 156, 129, 177, 139, 187, 123, 171, 117, 165, 125, 173)(113, 161, 132, 180, 119, 167, 135, 183, 140, 188, 137, 185, 116, 164, 134, 182)(126, 174, 141, 189, 130, 178, 143, 191, 136, 184, 144, 192, 128, 176, 142, 190)
	L = (1, 100)(2, 106)(3, 110)(4, 115)(5, 117)(6, 118)(7, 97)(8, 103)(9, 123)(10, 101)(11, 129)(12, 98)(13, 127)(14, 102)(15, 125)(16, 99)(17, 130)(18, 121)(19, 133)(20, 126)(21, 131)(22, 124)(23, 136)(24, 108)(25, 112)(26, 104)(27, 107)(28, 114)(29, 105)(30, 140)(31, 111)(32, 119)(33, 109)(34, 116)(35, 139)(36, 142)(37, 138)(38, 144)(39, 141)(40, 113)(41, 143)(42, 122)(43, 120)(44, 128)(45, 132)(46, 134)(47, 135)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.723
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.737 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-2, Y3^3, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 13, 61, 20, 68, 14, 62, 8, 56)(6, 54, 16, 64, 17, 65, 21, 69, 15, 63, 10, 58)(12, 60, 19, 67, 25, 73, 32, 80, 26, 74, 23, 71)(18, 66, 22, 70, 27, 75, 33, 81, 29, 77, 28, 76)(24, 72, 35, 83, 37, 85, 43, 91, 38, 86, 31, 79)(30, 78, 40, 88, 41, 89, 44, 92, 39, 87, 34, 82)(36, 84, 42, 90, 46, 94, 48, 96, 47, 95, 45, 93)(97, 145, 99, 147, 108, 156, 120, 168, 132, 180, 126, 174, 114, 162, 102, 150)(98, 146, 104, 152, 115, 163, 127, 175, 138, 186, 130, 178, 118, 166, 106, 154)(100, 148, 110, 158, 121, 169, 134, 182, 142, 190, 135, 183, 123, 171, 111, 159)(101, 149, 107, 155, 119, 167, 131, 179, 141, 189, 136, 184, 124, 172, 112, 160)(103, 151, 109, 157, 122, 170, 133, 181, 143, 191, 137, 185, 125, 173, 113, 161)(105, 153, 116, 164, 128, 176, 139, 187, 144, 192, 140, 188, 129, 177, 117, 165)
	L = (1, 100)(2, 105)(3, 109)(4, 103)(5, 98)(6, 113)(7, 97)(8, 107)(9, 101)(10, 112)(11, 116)(12, 121)(13, 110)(14, 99)(15, 102)(16, 117)(17, 111)(18, 123)(19, 128)(20, 104)(21, 106)(22, 129)(23, 115)(24, 133)(25, 122)(26, 108)(27, 125)(28, 118)(29, 114)(30, 137)(31, 131)(32, 119)(33, 124)(34, 136)(35, 139)(36, 142)(37, 134)(38, 120)(39, 126)(40, 140)(41, 135)(42, 144)(43, 127)(44, 130)(45, 138)(46, 143)(47, 132)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.741
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.738 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^6, Y1^6, Y3^2 * Y2 * Y1 * Y2^3, Y2 * Y1^-1 * Y2^3 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 17, 65, 5, 53)(3, 51, 13, 61, 33, 81, 44, 92, 24, 72, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60, 26, 74, 18, 66)(6, 54, 20, 68, 39, 87, 36, 84, 25, 73, 11, 59)(14, 62, 27, 75, 42, 90, 22, 70, 32, 80, 34, 82)(15, 63, 29, 77, 16, 64, 35, 83, 45, 93, 28, 76)(19, 67, 40, 88, 46, 94, 31, 79, 21, 69, 30, 78)(37, 85, 47, 95, 38, 86, 41, 89, 48, 96, 43, 91)(97, 145, 99, 147, 110, 158, 132, 180, 119, 167, 140, 188, 118, 166, 102, 150)(98, 146, 105, 153, 123, 171, 135, 183, 113, 161, 129, 177, 128, 176, 107, 155)(100, 148, 112, 160, 133, 181, 127, 175, 108, 156, 124, 172, 137, 185, 115, 163)(101, 149, 109, 157, 130, 178, 121, 169, 104, 152, 120, 168, 138, 186, 116, 164)(103, 151, 111, 159, 134, 182, 136, 184, 114, 162, 131, 179, 139, 187, 117, 165)(106, 154, 125, 173, 143, 191, 142, 190, 122, 170, 141, 189, 144, 192, 126, 174)
	L = (1, 100)(2, 106)(3, 111)(4, 113)(5, 114)(6, 117)(7, 97)(8, 103)(9, 124)(10, 101)(11, 127)(12, 98)(13, 125)(14, 133)(15, 120)(16, 99)(17, 122)(18, 119)(19, 102)(20, 126)(21, 121)(22, 137)(23, 108)(24, 141)(25, 142)(26, 104)(27, 143)(28, 140)(29, 105)(30, 107)(31, 132)(32, 144)(33, 112)(34, 139)(35, 109)(36, 136)(37, 128)(38, 110)(39, 115)(40, 116)(41, 123)(42, 134)(43, 118)(44, 131)(45, 129)(46, 135)(47, 130)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.743
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.739 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3, Y1), (Y3^-1 * Y1^-1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y1^-1 * Y3^-2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^4 * Y1^-1, Y1^-2 * Y3^2 * Y1^-2, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 17, 65, 5, 53)(3, 51, 13, 61, 33, 81, 39, 87, 24, 72, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60, 26, 74, 18, 66)(6, 54, 20, 68, 37, 85, 40, 88, 25, 73, 11, 59)(14, 62, 27, 75, 41, 89, 47, 95, 45, 93, 34, 82)(15, 63, 29, 77, 16, 64, 35, 83, 42, 90, 28, 76)(19, 67, 38, 86, 43, 91, 31, 79, 21, 69, 30, 78)(22, 70, 32, 80, 44, 92, 48, 96, 46, 94, 36, 84)(97, 145, 99, 147, 110, 158, 126, 174, 106, 154, 125, 173, 118, 166, 102, 150)(98, 146, 105, 153, 123, 171, 117, 165, 103, 151, 111, 159, 128, 176, 107, 155)(100, 148, 112, 160, 132, 180, 116, 164, 101, 149, 109, 157, 130, 178, 115, 163)(104, 152, 120, 168, 137, 185, 127, 175, 108, 156, 124, 172, 140, 188, 121, 169)(113, 161, 129, 177, 141, 189, 134, 182, 114, 162, 131, 179, 142, 190, 133, 181)(119, 167, 135, 183, 143, 191, 139, 187, 122, 170, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 106)(3, 111)(4, 113)(5, 114)(6, 117)(7, 97)(8, 103)(9, 124)(10, 101)(11, 127)(12, 98)(13, 125)(14, 132)(15, 120)(16, 99)(17, 122)(18, 119)(19, 102)(20, 126)(21, 121)(22, 130)(23, 108)(24, 138)(25, 139)(26, 104)(27, 118)(28, 135)(29, 105)(30, 107)(31, 136)(32, 110)(33, 112)(34, 142)(35, 109)(36, 141)(37, 115)(38, 116)(39, 131)(40, 134)(41, 128)(42, 129)(43, 133)(44, 123)(45, 144)(46, 143)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.744
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.740 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^-2, (Y3^-1, Y1^-1), (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, Y3^6, (R * Y2 * Y3^-1)^2, Y1^6, Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1 * Y3 * Y2^-1, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 17, 65, 5, 53)(3, 51, 13, 61, 33, 81, 45, 93, 24, 72, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60, 26, 74, 18, 66)(6, 54, 20, 68, 39, 87, 46, 94, 25, 73, 11, 59)(14, 62, 27, 75, 41, 89, 48, 96, 43, 91, 34, 82)(15, 63, 29, 77, 16, 64, 35, 83, 44, 92, 28, 76)(19, 67, 40, 88, 36, 84, 31, 79, 21, 69, 30, 78)(22, 70, 32, 80, 37, 85, 47, 95, 38, 86, 42, 90)(97, 145, 99, 147, 110, 158, 132, 180, 122, 170, 140, 188, 118, 166, 102, 150)(98, 146, 105, 153, 123, 171, 136, 184, 114, 162, 131, 179, 128, 176, 107, 155)(100, 148, 112, 160, 133, 181, 121, 169, 104, 152, 120, 168, 137, 185, 115, 163)(101, 149, 109, 157, 130, 178, 127, 175, 108, 156, 124, 172, 138, 186, 116, 164)(103, 151, 111, 159, 134, 182, 135, 183, 113, 161, 129, 177, 139, 187, 117, 165)(106, 154, 125, 173, 143, 191, 142, 190, 119, 167, 141, 189, 144, 192, 126, 174)
	L = (1, 100)(2, 106)(3, 111)(4, 113)(5, 114)(6, 117)(7, 97)(8, 103)(9, 124)(10, 101)(11, 127)(12, 98)(13, 125)(14, 133)(15, 120)(16, 99)(17, 122)(18, 119)(19, 102)(20, 126)(21, 121)(22, 137)(23, 108)(24, 140)(25, 132)(26, 104)(27, 143)(28, 141)(29, 105)(30, 107)(31, 142)(32, 144)(33, 112)(34, 128)(35, 109)(36, 135)(37, 139)(38, 110)(39, 115)(40, 116)(41, 134)(42, 123)(43, 118)(44, 129)(45, 131)(46, 136)(47, 130)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.742
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.741 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1 * Y2 * Y1^-1, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 17, 65, 29, 77, 28, 76, 16, 64, 5, 53)(3, 51, 8, 56, 18, 66, 30, 78, 40, 88, 37, 85, 25, 73, 12, 60)(4, 52, 10, 58, 19, 67, 32, 80, 41, 89, 38, 86, 26, 74, 14, 62)(6, 54, 9, 57, 20, 68, 31, 79, 42, 90, 39, 87, 27, 75, 15, 63)(11, 59, 22, 70, 33, 81, 44, 92, 47, 95, 45, 93, 35, 83, 23, 71)(13, 61, 21, 69, 34, 82, 43, 91, 48, 96, 46, 94, 36, 84, 24, 72)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(113, 161, 126, 174)(115, 163, 129, 177)(116, 164, 130, 178)(122, 170, 131, 179)(123, 171, 132, 180)(124, 172, 133, 181)(125, 173, 136, 184)(127, 175, 139, 187)(128, 176, 140, 188)(134, 182, 141, 189)(135, 183, 142, 190)(137, 185, 143, 191)(138, 186, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 102)(5, 111)(6, 97)(7, 115)(8, 117)(9, 106)(10, 98)(11, 109)(12, 120)(13, 99)(14, 101)(15, 110)(16, 122)(17, 127)(18, 129)(19, 116)(20, 103)(21, 118)(22, 104)(23, 108)(24, 119)(25, 131)(26, 123)(27, 112)(28, 135)(29, 137)(30, 139)(31, 128)(32, 113)(33, 130)(34, 114)(35, 132)(36, 121)(37, 142)(38, 124)(39, 134)(40, 143)(41, 138)(42, 125)(43, 140)(44, 126)(45, 133)(46, 141)(47, 144)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.737
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.742 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y2)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^6, Y1^2 * Y3^-3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 32, 80, 37, 85, 17, 65, 5, 53)(3, 51, 8, 56, 20, 68, 38, 86, 43, 91, 48, 96, 30, 78, 12, 60)(4, 52, 10, 58, 21, 69, 35, 83, 18, 66, 25, 73, 34, 82, 15, 63)(6, 54, 9, 57, 22, 70, 33, 81, 14, 62, 26, 74, 36, 84, 16, 64)(11, 59, 24, 72, 39, 87, 46, 94, 31, 79, 41, 89, 45, 93, 28, 76)(13, 61, 23, 71, 40, 88, 44, 92, 27, 75, 42, 90, 47, 95, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 116, 164)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 123, 171)(111, 159, 124, 172)(112, 160, 125, 173)(113, 161, 126, 174)(114, 162, 127, 175)(115, 163, 134, 182)(117, 165, 135, 183)(118, 166, 136, 184)(121, 169, 137, 185)(122, 170, 138, 186)(128, 176, 139, 187)(129, 177, 140, 188)(130, 178, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(133, 181, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 123)(12, 125)(13, 99)(14, 128)(15, 101)(16, 131)(17, 130)(18, 102)(19, 129)(20, 135)(21, 132)(22, 103)(23, 137)(24, 104)(25, 133)(26, 106)(27, 139)(28, 108)(29, 142)(30, 141)(31, 109)(32, 114)(33, 111)(34, 118)(35, 115)(36, 113)(37, 122)(38, 140)(39, 143)(40, 116)(41, 144)(42, 120)(43, 127)(44, 124)(45, 136)(46, 134)(47, 126)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.740
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.743 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y3^-1, Y3^2 * Y1 * Y3^2 * Y1^-1, Y3^6, Y3 * Y2 * Y1^-2 * Y3^2 * Y1^-2, Y1^-2 * Y2 * Y3 * Y1^2 * Y2 * Y3^-1, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 38, 86, 37, 85, 17, 65, 5, 53)(3, 51, 8, 56, 20, 68, 39, 87, 32, 80, 48, 96, 30, 78, 12, 60)(4, 52, 10, 58, 21, 69, 41, 89, 31, 79, 46, 94, 34, 82, 15, 63)(6, 54, 9, 57, 22, 70, 40, 88, 27, 75, 47, 95, 36, 84, 16, 64)(11, 59, 24, 72, 42, 90, 35, 83, 18, 66, 25, 73, 45, 93, 28, 76)(13, 61, 23, 71, 43, 91, 33, 81, 14, 62, 26, 74, 44, 92, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 116, 164)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 123, 171)(111, 159, 124, 172)(112, 160, 125, 173)(113, 161, 126, 174)(114, 162, 127, 175)(115, 163, 135, 183)(117, 165, 138, 186)(118, 166, 139, 187)(121, 169, 142, 190)(122, 170, 143, 191)(128, 176, 134, 182)(129, 177, 136, 184)(130, 178, 141, 189)(131, 179, 137, 185)(132, 180, 140, 188)(133, 181, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 117)(8, 119)(9, 121)(10, 98)(11, 123)(12, 125)(13, 99)(14, 128)(15, 101)(16, 131)(17, 130)(18, 102)(19, 136)(20, 138)(21, 140)(22, 103)(23, 142)(24, 104)(25, 144)(26, 106)(27, 134)(28, 108)(29, 137)(30, 141)(31, 109)(32, 114)(33, 111)(34, 139)(35, 135)(36, 113)(37, 143)(38, 127)(39, 129)(40, 124)(41, 115)(42, 132)(43, 116)(44, 126)(45, 118)(46, 133)(47, 120)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.738
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.744 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 x (C3 : C8) (small group id <48, 9>)
Aut   = C2 x ((C3 x D8) : C2) (small group id <96, 138>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y2 * Y1^4, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, Y3^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 17, 65, 5, 53)(4, 52, 10, 58, 19, 67, 26, 74, 11, 59, 22, 70, 31, 79, 15, 63)(6, 54, 9, 57, 20, 68, 27, 75, 13, 61, 21, 69, 33, 81, 16, 64)(14, 62, 24, 72, 34, 82, 40, 88, 25, 73, 37, 85, 43, 91, 30, 78)(18, 66, 23, 71, 35, 83, 41, 89, 28, 76, 36, 84, 44, 92, 32, 80)(29, 77, 38, 86, 45, 93, 47, 95, 39, 87, 46, 94, 48, 96, 42, 90)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 113, 161)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(114, 162, 124, 172)(115, 163, 127, 175)(116, 164, 129, 177)(119, 167, 132, 180)(120, 168, 133, 181)(125, 173, 135, 183)(126, 174, 136, 184)(128, 176, 137, 185)(130, 178, 139, 187)(131, 179, 140, 188)(134, 182, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 115)(8, 117)(9, 119)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 101)(16, 128)(17, 127)(18, 102)(19, 130)(20, 103)(21, 132)(22, 104)(23, 134)(24, 106)(25, 135)(26, 108)(27, 137)(28, 109)(29, 114)(30, 111)(31, 139)(32, 138)(33, 113)(34, 141)(35, 116)(36, 142)(37, 118)(38, 120)(39, 124)(40, 122)(41, 143)(42, 126)(43, 144)(44, 129)(45, 131)(46, 133)(47, 136)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.739
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.745 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y2^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-5 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 13, 61, 32, 80, 15, 63, 14, 62)(6, 54, 19, 67, 20, 68, 38, 86, 16, 64, 21, 69)(8, 56, 23, 71, 17, 65, 40, 88, 26, 74, 25, 73)(10, 58, 28, 76, 18, 66, 41, 89, 27, 75, 29, 77)(12, 60, 24, 72, 34, 82, 44, 92, 36, 84, 35, 83)(22, 70, 30, 78, 39, 87, 46, 94, 42, 90, 31, 79)(33, 81, 43, 91, 37, 85, 45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 124, 172, 139, 187, 119, 167, 118, 166, 102, 150)(98, 146, 104, 152, 120, 168, 117, 165, 133, 181, 110, 158, 126, 174, 106, 154)(100, 148, 111, 159, 130, 178, 125, 173, 141, 189, 121, 169, 135, 183, 112, 160)(101, 149, 113, 161, 131, 179, 115, 163, 129, 177, 107, 155, 127, 175, 114, 162)(103, 151, 109, 157, 132, 180, 137, 185, 144, 192, 136, 184, 138, 186, 116, 164)(105, 153, 122, 170, 140, 188, 134, 182, 143, 191, 128, 176, 142, 190, 123, 171)
	L = (1, 100)(2, 105)(3, 109)(4, 103)(5, 98)(6, 116)(7, 97)(8, 113)(9, 101)(10, 114)(11, 128)(12, 130)(13, 111)(14, 107)(15, 99)(16, 102)(17, 122)(18, 123)(19, 134)(20, 112)(21, 115)(22, 135)(23, 136)(24, 140)(25, 119)(26, 104)(27, 106)(28, 137)(29, 124)(30, 142)(31, 126)(32, 110)(33, 133)(34, 132)(35, 120)(36, 108)(37, 143)(38, 117)(39, 138)(40, 121)(41, 125)(42, 118)(43, 141)(44, 131)(45, 144)(46, 127)(47, 129)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.750
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.746 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), Y1^2 * Y3^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y1 * Y2^-1 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^2, Y3^6, Y1 * Y2^-3 * Y1 * Y2^-1, Y1^-1 * Y2 * Y1^-3 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 18, 66, 5, 53)(3, 51, 13, 61, 37, 85, 33, 81, 28, 76, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60, 30, 78, 19, 67)(6, 54, 23, 71, 43, 91, 34, 82, 29, 77, 25, 73)(9, 57, 31, 79, 21, 69, 15, 63, 39, 87, 17, 65)(11, 59, 35, 83, 22, 70, 24, 72, 44, 92, 20, 68)(14, 62, 32, 80, 45, 93, 48, 96, 46, 94, 41, 89)(26, 74, 36, 84, 40, 88, 47, 95, 42, 90, 38, 86)(97, 145, 99, 147, 110, 158, 131, 179, 126, 174, 127, 175, 122, 170, 102, 150)(98, 146, 105, 153, 128, 176, 121, 169, 115, 163, 112, 160, 132, 180, 107, 155)(100, 148, 113, 161, 136, 184, 125, 173, 104, 152, 124, 172, 141, 189, 116, 164)(101, 149, 117, 165, 137, 185, 119, 167, 108, 156, 109, 157, 134, 182, 118, 166)(103, 151, 111, 159, 138, 186, 139, 187, 114, 162, 133, 181, 142, 190, 120, 168)(106, 154, 129, 177, 143, 191, 140, 188, 123, 171, 135, 183, 144, 192, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 115)(6, 120)(7, 97)(8, 103)(9, 109)(10, 101)(11, 119)(12, 98)(13, 135)(14, 136)(15, 124)(16, 117)(17, 99)(18, 126)(19, 123)(20, 102)(21, 129)(22, 130)(23, 140)(24, 125)(25, 118)(26, 141)(27, 108)(28, 127)(29, 131)(30, 104)(31, 133)(32, 143)(33, 105)(34, 107)(35, 139)(36, 144)(37, 113)(38, 128)(39, 112)(40, 142)(41, 132)(42, 110)(43, 116)(44, 121)(45, 138)(46, 122)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.751
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.747 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^-2 * Y3^-2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y3, R * Y2 * Y1^-1 * R * Y2, Y2^3 * Y3^-1 * Y2 * Y3^-1, Y3^-2 * Y1^4, Y2 * Y3^-2 * Y2^-1 * Y3^-2, Y2 * Y3^2 * Y2^3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 18, 66, 5, 53)(3, 51, 13, 61, 37, 85, 44, 92, 28, 76, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60, 30, 78, 19, 67)(6, 54, 21, 69, 45, 93, 39, 87, 29, 77, 11, 59)(14, 62, 31, 79, 46, 94, 23, 71, 35, 83, 38, 86)(15, 63, 32, 80, 16, 64, 25, 73, 33, 81, 17, 65)(20, 68, 22, 70, 36, 84, 24, 72, 26, 74, 34, 82)(40, 88, 47, 95, 41, 89, 43, 91, 48, 96, 42, 90)(97, 145, 99, 147, 110, 158, 135, 183, 123, 171, 140, 188, 119, 167, 102, 150)(98, 146, 105, 153, 127, 175, 141, 189, 114, 162, 133, 181, 131, 179, 107, 155)(100, 148, 113, 161, 136, 184, 120, 168, 108, 156, 112, 160, 139, 187, 116, 164)(101, 149, 109, 157, 134, 182, 125, 173, 104, 152, 124, 172, 142, 190, 117, 165)(103, 151, 121, 169, 137, 185, 118, 166, 115, 163, 111, 159, 138, 186, 122, 170)(106, 154, 129, 177, 143, 191, 132, 180, 126, 174, 128, 176, 144, 192, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 115)(6, 118)(7, 97)(8, 103)(9, 113)(10, 101)(11, 116)(12, 98)(13, 128)(14, 136)(15, 124)(16, 99)(17, 140)(18, 126)(19, 123)(20, 135)(21, 132)(22, 125)(23, 139)(24, 102)(25, 109)(26, 117)(27, 108)(28, 129)(29, 130)(30, 104)(31, 143)(32, 105)(33, 133)(34, 141)(35, 144)(36, 107)(37, 112)(38, 138)(39, 122)(40, 131)(41, 110)(42, 119)(43, 127)(44, 121)(45, 120)(46, 137)(47, 134)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.752
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.748 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y1)^2, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y3)^2, (Y1 * Y3)^2, Y2^-1 * Y1 * Y2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-2, Y3^-2 * Y1^4, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 17, 65, 5, 53)(3, 51, 13, 61, 33, 81, 42, 90, 24, 72, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60, 26, 74, 18, 66)(6, 54, 19, 67, 37, 85, 43, 91, 25, 73, 21, 69)(9, 57, 27, 75, 16, 64, 35, 83, 39, 87, 29, 77)(11, 59, 30, 78, 20, 68, 38, 86, 40, 88, 31, 79)(14, 62, 28, 76, 41, 89, 47, 95, 45, 93, 36, 84)(22, 70, 32, 80, 44, 92, 48, 96, 46, 94, 34, 82)(97, 145, 99, 147, 110, 158, 126, 174, 106, 154, 123, 171, 118, 166, 102, 150)(98, 146, 105, 153, 124, 172, 117, 165, 103, 151, 111, 159, 128, 176, 107, 155)(100, 148, 109, 157, 130, 178, 116, 164, 101, 149, 112, 160, 132, 180, 115, 163)(104, 152, 120, 168, 137, 185, 127, 175, 108, 156, 125, 173, 140, 188, 121, 169)(113, 161, 129, 177, 141, 189, 134, 182, 114, 162, 131, 179, 142, 190, 133, 181)(119, 167, 135, 183, 143, 191, 139, 187, 122, 170, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 106)(3, 105)(4, 113)(5, 114)(6, 107)(7, 97)(8, 103)(9, 120)(10, 101)(11, 121)(12, 98)(13, 123)(14, 130)(15, 125)(16, 99)(17, 122)(18, 119)(19, 126)(20, 102)(21, 127)(22, 132)(23, 108)(24, 135)(25, 136)(26, 104)(27, 111)(28, 118)(29, 138)(30, 117)(31, 139)(32, 110)(33, 112)(34, 141)(35, 109)(36, 142)(37, 116)(38, 115)(39, 129)(40, 133)(41, 128)(42, 131)(43, 134)(44, 124)(45, 144)(46, 143)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.749
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.749 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1, Y2 * Y1^4, Y3^6, Y3^-2 * Y1^-2 * Y3^2 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 18, 66, 5, 53)(4, 52, 14, 62, 23, 71, 19, 67, 11, 59, 10, 58, 27, 75, 16, 64)(6, 54, 20, 68, 24, 72, 17, 65, 13, 61, 9, 57, 25, 73, 21, 69)(15, 63, 28, 76, 38, 86, 34, 82, 29, 77, 31, 79, 42, 90, 33, 81)(22, 70, 26, 74, 39, 87, 37, 85, 30, 78, 36, 84, 40, 88, 35, 83)(32, 80, 44, 92, 47, 95, 46, 94, 43, 91, 41, 89, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 116, 164)(106, 154, 110, 158)(111, 159, 125, 173)(112, 160, 115, 163)(113, 161, 117, 165)(118, 166, 126, 174)(119, 167, 123, 171)(120, 168, 121, 169)(122, 170, 132, 180)(124, 172, 127, 175)(128, 176, 139, 187)(129, 177, 130, 178)(131, 179, 133, 181)(134, 182, 138, 186)(135, 183, 136, 184)(137, 185, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 119)(8, 116)(9, 122)(10, 98)(11, 125)(12, 117)(13, 99)(14, 104)(15, 128)(16, 108)(17, 131)(18, 123)(19, 101)(20, 132)(21, 133)(22, 102)(23, 134)(24, 103)(25, 114)(26, 137)(27, 138)(28, 106)(29, 139)(30, 109)(31, 110)(32, 118)(33, 115)(34, 112)(35, 142)(36, 140)(37, 141)(38, 143)(39, 120)(40, 121)(41, 124)(42, 144)(43, 126)(44, 127)(45, 130)(46, 129)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.748
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.750 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y1)^2, (Y2 * R)^2, Y3^-1 * Y2 * Y3 * Y2, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^2 * Y2 * Y1^-2, (Y2 * Y1 * Y2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 36, 84, 27, 75, 18, 66, 5, 53)(3, 51, 11, 59, 20, 68, 16, 64, 25, 73, 8, 56, 23, 71, 13, 61)(4, 52, 10, 58, 21, 69, 38, 86, 47, 95, 46, 94, 33, 81, 15, 63)(6, 54, 9, 57, 22, 70, 37, 85, 48, 96, 45, 93, 35, 83, 17, 65)(12, 60, 29, 77, 39, 87, 32, 80, 44, 92, 26, 74, 41, 89, 30, 78)(14, 62, 28, 76, 40, 88, 34, 82, 43, 91, 24, 72, 42, 90, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 112, 160)(102, 150, 110, 158)(103, 151, 116, 164)(105, 153, 120, 168)(106, 154, 122, 170)(107, 155, 123, 171)(109, 157, 115, 163)(111, 159, 128, 176)(113, 161, 130, 178)(114, 162, 119, 167)(117, 165, 135, 183)(118, 166, 136, 184)(121, 169, 132, 180)(124, 172, 141, 189)(125, 173, 142, 190)(126, 174, 134, 182)(127, 175, 133, 181)(129, 177, 137, 185)(131, 179, 138, 186)(139, 187, 144, 192)(140, 188, 143, 191)
	L = (1, 100)(2, 105)(3, 108)(4, 102)(5, 113)(6, 97)(7, 117)(8, 120)(9, 106)(10, 98)(11, 124)(12, 110)(13, 127)(14, 99)(15, 101)(16, 130)(17, 111)(18, 129)(19, 133)(20, 135)(21, 118)(22, 103)(23, 137)(24, 122)(25, 140)(26, 104)(27, 141)(28, 125)(29, 107)(30, 109)(31, 126)(32, 112)(33, 131)(34, 128)(35, 114)(36, 143)(37, 134)(38, 115)(39, 136)(40, 116)(41, 138)(42, 119)(43, 121)(44, 139)(45, 142)(46, 123)(47, 144)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.745
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.751 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y2 * R)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y3^6, Y1 * Y3 * Y2 * Y1^-1 * Y3^-2 * Y2, Y3^-2 * Y1 * Y2 * Y3 * Y1^-1 * Y2, Y1^-1 * Y2 * Y3 * Y1 * Y3^-2 * Y2, Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^2 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 38, 86, 31, 79, 19, 67, 5, 53)(3, 51, 11, 59, 22, 70, 17, 65, 27, 75, 8, 56, 25, 73, 13, 61)(4, 52, 10, 58, 23, 71, 43, 91, 20, 68, 29, 77, 41, 89, 16, 64)(6, 54, 9, 57, 24, 72, 39, 87, 15, 63, 30, 78, 44, 92, 18, 66)(12, 60, 33, 81, 45, 93, 40, 88, 37, 85, 28, 76, 47, 95, 35, 83)(14, 62, 32, 80, 46, 94, 42, 90, 34, 82, 26, 74, 48, 96, 36, 84)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 118, 166)(105, 153, 122, 170)(106, 154, 124, 172)(107, 155, 127, 175)(109, 157, 117, 165)(111, 159, 130, 178)(112, 160, 136, 184)(114, 162, 138, 186)(115, 163, 121, 169)(116, 164, 133, 181)(119, 167, 141, 189)(120, 168, 142, 190)(123, 171, 134, 182)(125, 173, 129, 177)(126, 174, 128, 176)(131, 179, 139, 187)(132, 180, 135, 183)(137, 185, 143, 191)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 119)(8, 122)(9, 125)(10, 98)(11, 128)(12, 130)(13, 132)(14, 99)(15, 134)(16, 101)(17, 138)(18, 139)(19, 137)(20, 102)(21, 135)(22, 141)(23, 140)(24, 103)(25, 143)(26, 129)(27, 133)(28, 104)(29, 127)(30, 106)(31, 126)(32, 124)(33, 107)(34, 123)(35, 109)(36, 136)(37, 110)(38, 116)(39, 112)(40, 113)(41, 120)(42, 131)(43, 117)(44, 115)(45, 144)(46, 118)(47, 142)(48, 121)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.746
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.752 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = (C3 : C8) : C2 (small group id <48, 10>)
Aut   = (C2 x D24) : C2 (small group id <96, 156>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (Y2 * R)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2 * Y1^2, Y2 * Y3^2 * Y1^-1 * Y3^-1 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y3, Y3^2 * Y2 * Y1^-1 * Y3^-1 * Y1, Y3^-1 * Y1^-3 * Y3^-1 * Y1^-1, Y2 * Y3 * Y1 * Y2 * Y3 * Y1^-1, Y3^6, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y3 * Y1^-3 * Y3, Y3 * Y1^2 * Y3^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 25, 73, 44, 92, 39, 87, 20, 68, 5, 53)(3, 51, 11, 59, 26, 74, 18, 66, 31, 79, 8, 56, 29, 77, 13, 61)(4, 52, 15, 63, 27, 75, 21, 69, 37, 85, 10, 58, 36, 84, 17, 65)(6, 54, 22, 70, 28, 76, 19, 67, 35, 83, 9, 57, 33, 81, 23, 71)(12, 60, 32, 80, 45, 93, 42, 90, 24, 72, 34, 82, 48, 96, 40, 88)(14, 62, 30, 78, 46, 94, 41, 89, 16, 64, 38, 86, 47, 95, 43, 91)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 122, 170)(105, 153, 126, 174)(106, 154, 128, 176)(107, 155, 135, 183)(109, 157, 121, 169)(111, 159, 130, 178)(112, 160, 131, 179)(113, 161, 138, 186)(115, 163, 139, 187)(116, 164, 125, 173)(117, 165, 136, 184)(118, 166, 134, 182)(119, 167, 137, 185)(120, 168, 133, 181)(123, 171, 141, 189)(124, 172, 142, 190)(127, 175, 140, 188)(129, 177, 143, 191)(132, 180, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 123)(8, 126)(9, 130)(10, 98)(11, 134)(12, 131)(13, 137)(14, 99)(15, 135)(16, 127)(17, 121)(18, 139)(19, 138)(20, 132)(21, 101)(22, 128)(23, 136)(24, 102)(25, 119)(26, 141)(27, 143)(28, 103)(29, 144)(30, 111)(31, 120)(32, 104)(33, 116)(34, 107)(35, 140)(36, 142)(37, 110)(38, 106)(39, 118)(40, 114)(41, 117)(42, 109)(43, 113)(44, 133)(45, 129)(46, 122)(47, 125)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.747
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.753 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^-1, Y3^3, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (Y1 * Y3)^2, (R * Y3)^2, R * Y2^-1 * R * Y1 * Y2, Y2^4 * Y1 * Y3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y3^-1 * Y2^2 * Y1 * Y2^2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 10, 58, 26, 74, 14, 62, 13, 61)(6, 54, 15, 63, 19, 67, 27, 75, 17, 65, 20, 68)(8, 56, 23, 71, 16, 64, 22, 70, 25, 73, 18, 66)(12, 60, 31, 79, 30, 78, 21, 69, 33, 81, 32, 80)(24, 72, 29, 77, 40, 88, 28, 76, 34, 82, 41, 89)(35, 83, 39, 87, 37, 85, 36, 84, 42, 90, 38, 86)(43, 91, 45, 93, 48, 96, 44, 92, 46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 105, 153, 122, 170, 117, 165, 102, 150)(98, 146, 104, 152, 120, 168, 109, 157, 103, 151, 118, 166, 124, 172, 106, 154)(100, 148, 111, 159, 131, 179, 114, 162, 101, 149, 113, 161, 132, 180, 112, 160)(107, 155, 125, 173, 139, 187, 128, 176, 110, 158, 130, 178, 140, 188, 126, 174)(115, 163, 129, 177, 142, 190, 134, 182, 116, 164, 127, 175, 141, 189, 133, 181)(119, 167, 135, 183, 143, 191, 137, 185, 121, 169, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 105)(3, 106)(4, 103)(5, 98)(6, 115)(7, 97)(8, 112)(9, 101)(10, 110)(11, 122)(12, 126)(13, 107)(14, 99)(15, 123)(16, 121)(17, 102)(18, 119)(19, 113)(20, 111)(21, 128)(22, 114)(23, 118)(24, 136)(25, 104)(26, 109)(27, 116)(28, 137)(29, 124)(30, 129)(31, 117)(32, 127)(33, 108)(34, 120)(35, 133)(36, 134)(37, 138)(38, 135)(39, 132)(40, 130)(41, 125)(42, 131)(43, 144)(44, 143)(45, 140)(46, 139)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.754
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.754 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>)
Aut   = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1^4, Y3^2 * Y1 * Y3^2 * Y2 * Y1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 17, 65, 5, 53)(4, 52, 14, 62, 26, 74, 10, 58, 11, 59, 27, 75, 31, 79, 15, 63)(6, 54, 19, 67, 35, 83, 29, 77, 13, 61, 16, 64, 32, 80, 20, 68)(9, 57, 24, 72, 38, 86, 22, 70, 23, 71, 39, 87, 41, 89, 25, 73)(18, 66, 21, 69, 37, 85, 43, 91, 28, 76, 33, 81, 45, 93, 34, 82)(30, 78, 44, 92, 48, 96, 42, 90, 36, 84, 46, 94, 47, 95, 40, 88)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 113, 161)(105, 153, 119, 167)(106, 154, 111, 159)(110, 158, 123, 171)(112, 160, 115, 163)(114, 162, 124, 172)(116, 164, 125, 173)(117, 165, 129, 177)(118, 166, 121, 169)(120, 168, 135, 183)(122, 170, 127, 175)(126, 174, 132, 180)(128, 176, 131, 179)(130, 178, 139, 187)(133, 181, 141, 189)(134, 182, 137, 185)(136, 184, 138, 186)(140, 188, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 102)(5, 112)(6, 97)(7, 117)(8, 119)(9, 106)(10, 98)(11, 109)(12, 115)(13, 99)(14, 126)(15, 104)(16, 114)(17, 129)(18, 101)(19, 124)(20, 123)(21, 118)(22, 103)(23, 111)(24, 136)(25, 113)(26, 135)(27, 132)(28, 108)(29, 110)(30, 125)(31, 120)(32, 140)(33, 121)(34, 131)(35, 142)(36, 116)(37, 143)(38, 141)(39, 138)(40, 127)(41, 133)(42, 122)(43, 128)(44, 139)(45, 144)(46, 130)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.753
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.755 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, Y3^3, (Y2^-1 * Y1)^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2 * R * Y2^-1 * R * Y3^-1, Y3 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-4 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3 * Y2^-2 * Y1^-1, Y2^2 * Y3^-1 * Y2^-2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 7, 55, 5, 53)(3, 51, 11, 59, 13, 61, 26, 74, 14, 62, 10, 58)(6, 54, 17, 65, 19, 67, 27, 75, 15, 63, 20, 68)(8, 56, 23, 71, 18, 66, 22, 70, 25, 73, 16, 64)(12, 60, 31, 79, 32, 80, 21, 69, 33, 81, 30, 78)(24, 72, 29, 77, 41, 89, 28, 76, 34, 82, 40, 88)(35, 83, 39, 87, 37, 85, 36, 84, 42, 90, 38, 86)(43, 91, 45, 93, 48, 96, 44, 92, 46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 105, 153, 122, 170, 117, 165, 102, 150)(98, 146, 104, 152, 120, 168, 109, 157, 103, 151, 118, 166, 124, 172, 106, 154)(100, 148, 111, 159, 131, 179, 114, 162, 101, 149, 113, 161, 132, 180, 112, 160)(107, 155, 125, 173, 139, 187, 128, 176, 110, 158, 130, 178, 140, 188, 126, 174)(115, 163, 127, 175, 141, 189, 134, 182, 116, 164, 129, 177, 142, 190, 133, 181)(119, 167, 135, 183, 143, 191, 137, 185, 121, 169, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 105)(3, 109)(4, 103)(5, 98)(6, 115)(7, 97)(8, 114)(9, 101)(10, 107)(11, 122)(12, 128)(13, 110)(14, 99)(15, 102)(16, 119)(17, 123)(18, 121)(19, 111)(20, 113)(21, 126)(22, 112)(23, 118)(24, 137)(25, 104)(26, 106)(27, 116)(28, 136)(29, 124)(30, 127)(31, 117)(32, 129)(33, 108)(34, 120)(35, 133)(36, 134)(37, 138)(38, 135)(39, 132)(40, 125)(41, 130)(42, 131)(43, 144)(44, 143)(45, 140)(46, 139)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.756
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 12^8, 16^6 ]

E27.756 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (Y1 * Y3^-1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^4 * Y2, (Y2 * Y3^-1 * Y1)^2, (Y1^-1 * Y2 * Y3)^2, Y3 * Y1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 16, 64, 5, 53)(4, 52, 14, 62, 29, 77, 22, 70, 11, 59, 25, 73, 24, 72, 10, 58)(6, 54, 15, 63, 31, 79, 28, 76, 13, 61, 26, 74, 35, 83, 18, 66)(9, 57, 23, 71, 39, 87, 33, 81, 21, 69, 38, 86, 37, 85, 20, 68)(17, 65, 32, 80, 46, 94, 42, 90, 27, 75, 19, 67, 36, 84, 34, 82)(30, 78, 44, 92, 48, 96, 40, 88, 41, 89, 45, 93, 47, 95, 43, 91)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 112, 160)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 121, 169)(111, 159, 122, 170)(113, 161, 123, 171)(114, 162, 124, 172)(115, 163, 128, 176)(116, 164, 129, 177)(119, 167, 134, 182)(120, 168, 125, 173)(126, 174, 137, 185)(127, 175, 131, 179)(130, 178, 138, 186)(132, 180, 142, 190)(133, 181, 135, 183)(136, 184, 139, 187)(140, 188, 141, 189)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 102)(5, 111)(6, 97)(7, 115)(8, 117)(9, 106)(10, 98)(11, 109)(12, 122)(13, 99)(14, 126)(15, 113)(16, 128)(17, 101)(18, 110)(19, 116)(20, 103)(21, 118)(22, 104)(23, 136)(24, 119)(25, 137)(26, 123)(27, 108)(28, 121)(29, 134)(30, 114)(31, 141)(32, 129)(33, 112)(34, 127)(35, 140)(36, 143)(37, 132)(38, 139)(39, 142)(40, 120)(41, 124)(42, 131)(43, 125)(44, 138)(45, 130)(46, 144)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16, 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.755
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.757 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 4, 12})
Quotient :: edge^2
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C3 x (C8 : C2)) : C2 (small group id <96, 32>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1^-1), (R * Y3)^2, Y1^4, R * Y1 * R * Y2, Y2^4, Y2 * Y3^-3 * Y1, Y1 * Y3^2 * Y2 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y1^2, Y3 * Y1 * Y3 * Y2^-2 * Y1, Y2^-1 * Y3 * Y2^-1 * Y1^2 * Y3, Y3 * Y2 * Y1 * Y2 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 19, 67, 9, 57, 37, 85, 40, 88, 48, 96, 45, 93, 39, 87, 23, 71, 31, 79, 7, 55)(2, 50, 10, 58, 21, 69, 32, 80, 30, 78, 17, 65, 47, 95, 27, 75, 26, 74, 6, 54, 25, 73, 12, 60)(3, 51, 14, 62, 20, 68, 36, 84, 29, 77, 18, 66, 34, 82, 28, 76, 24, 72, 5, 53, 22, 70, 16, 64)(8, 56, 33, 81, 41, 89, 15, 63, 46, 94, 38, 86, 13, 61, 44, 92, 43, 91, 11, 59, 42, 90, 35, 83)(97, 98, 104, 101)(99, 105, 128, 111)(100, 113, 129, 116)(102, 107, 130, 119)(103, 123, 131, 125)(106, 134, 118, 136)(108, 140, 120, 141)(109, 132, 144, 143)(110, 135, 126, 139)(112, 127, 117, 138)(114, 133, 122, 142)(115, 121, 137, 124)(145, 147, 157, 150)(146, 153, 180, 155)(148, 162, 188, 165)(149, 159, 191, 167)(151, 172, 182, 174)(152, 176, 192, 178)(154, 183, 173, 185)(156, 175, 164, 190)(158, 179, 169, 184)(160, 177, 170, 189)(161, 181, 168, 186)(163, 166, 187, 171)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.760
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.758 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 4, 12})
Quotient :: edge^2
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C3 x (C8 : C2)) : C2 (small group id <96, 32>)
|r| :: 2
Presentation :: [ R^2, Y3^3, R * Y2 * R * Y1, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4, Y2^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 10, 58, 12, 60)(3, 51, 14, 62, 16, 64)(5, 53, 19, 67, 17, 65)(6, 54, 21, 69, 18, 66)(8, 56, 23, 71, 25, 73)(9, 57, 27, 75, 28, 76)(11, 59, 30, 78, 29, 77)(13, 61, 31, 79, 33, 81)(15, 63, 35, 83, 34, 82)(20, 68, 36, 84, 37, 85)(22, 70, 39, 87, 40, 88)(24, 72, 42, 90, 41, 89)(26, 74, 43, 91, 44, 92)(32, 80, 46, 94, 45, 93)(38, 86, 47, 95, 48, 96)(97, 98, 104, 101)(99, 105, 118, 111)(100, 108, 119, 113)(102, 107, 120, 116)(103, 106, 121, 115)(109, 122, 134, 128)(110, 124, 135, 130)(112, 123, 136, 131)(114, 126, 137, 132)(117, 125, 138, 133)(127, 140, 143, 141)(129, 139, 144, 142)(145, 147, 157, 150)(146, 153, 170, 155)(148, 160, 175, 162)(149, 159, 176, 164)(151, 158, 177, 165)(152, 166, 182, 168)(154, 172, 187, 173)(156, 171, 188, 174)(161, 179, 189, 180)(163, 178, 190, 181)(167, 184, 191, 185)(169, 183, 192, 186)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 48^4 ), ( 48^6 ) }
Outer automorphisms :: reflexible
Dual of E27.759
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.759 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 4, 12})
Quotient :: loop^2
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C3 x (C8 : C2)) : C2 (small group id <96, 32>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y1^-1), (R * Y3)^2, Y1^4, R * Y1 * R * Y2, Y2^4, Y2 * Y3^-3 * Y1, Y1 * Y3^2 * Y2 * Y3^-1, Y1 * Y3^-1 * Y2 * Y3^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y1^2, Y3 * Y1 * Y3 * Y2^-2 * Y1, Y2^-1 * Y3 * Y2^-1 * Y1^2 * Y3, Y3 * Y2 * Y1 * Y2 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 19, 67, 115, 163, 9, 57, 105, 153, 37, 85, 133, 181, 40, 88, 136, 184, 48, 96, 144, 192, 45, 93, 141, 189, 39, 87, 135, 183, 23, 71, 119, 167, 31, 79, 127, 175, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 21, 69, 117, 165, 32, 80, 128, 176, 30, 78, 126, 174, 17, 65, 113, 161, 47, 95, 143, 191, 27, 75, 123, 171, 26, 74, 122, 170, 6, 54, 102, 150, 25, 73, 121, 169, 12, 60, 108, 156)(3, 51, 99, 147, 14, 62, 110, 158, 20, 68, 116, 164, 36, 84, 132, 180, 29, 77, 125, 173, 18, 66, 114, 162, 34, 82, 130, 178, 28, 76, 124, 172, 24, 72, 120, 168, 5, 53, 101, 149, 22, 70, 118, 166, 16, 64, 112, 160)(8, 56, 104, 152, 33, 81, 129, 177, 41, 89, 137, 185, 15, 63, 111, 159, 46, 94, 142, 190, 38, 86, 134, 182, 13, 61, 109, 157, 44, 92, 140, 188, 43, 91, 139, 187, 11, 59, 107, 155, 42, 90, 138, 186, 35, 83, 131, 179)
	L = (1, 50)(2, 56)(3, 57)(4, 65)(5, 49)(6, 59)(7, 75)(8, 53)(9, 80)(10, 86)(11, 82)(12, 92)(13, 84)(14, 87)(15, 51)(16, 79)(17, 81)(18, 85)(19, 73)(20, 52)(21, 90)(22, 88)(23, 54)(24, 93)(25, 89)(26, 94)(27, 83)(28, 67)(29, 55)(30, 91)(31, 69)(32, 63)(33, 68)(34, 71)(35, 77)(36, 96)(37, 74)(38, 70)(39, 78)(40, 58)(41, 76)(42, 64)(43, 62)(44, 72)(45, 60)(46, 66)(47, 61)(48, 95)(97, 147)(98, 153)(99, 157)(100, 162)(101, 159)(102, 145)(103, 172)(104, 176)(105, 180)(106, 183)(107, 146)(108, 175)(109, 150)(110, 179)(111, 191)(112, 177)(113, 181)(114, 188)(115, 166)(116, 190)(117, 148)(118, 187)(119, 149)(120, 186)(121, 184)(122, 189)(123, 163)(124, 182)(125, 185)(126, 151)(127, 164)(128, 192)(129, 170)(130, 152)(131, 169)(132, 155)(133, 168)(134, 174)(135, 173)(136, 158)(137, 154)(138, 161)(139, 171)(140, 165)(141, 160)(142, 156)(143, 167)(144, 178)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.758
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 96 f = 40
	degree seq :: [ 48^4 ]

E27.760 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 4, 12})
Quotient :: loop^2
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C3 x (C8 : C2)) : C2 (small group id <96, 32>)
|r| :: 2
Presentation :: [ R^2, Y3^3, R * Y2 * R * Y1, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4, Y2^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 12, 60, 108, 156)(3, 51, 99, 147, 14, 62, 110, 158, 16, 64, 112, 160)(5, 53, 101, 149, 19, 67, 115, 163, 17, 65, 113, 161)(6, 54, 102, 150, 21, 69, 117, 165, 18, 66, 114, 162)(8, 56, 104, 152, 23, 71, 119, 167, 25, 73, 121, 169)(9, 57, 105, 153, 27, 75, 123, 171, 28, 76, 124, 172)(11, 59, 107, 155, 30, 78, 126, 174, 29, 77, 125, 173)(13, 61, 109, 157, 31, 79, 127, 175, 33, 81, 129, 177)(15, 63, 111, 159, 35, 83, 131, 179, 34, 82, 130, 178)(20, 68, 116, 164, 36, 84, 132, 180, 37, 85, 133, 181)(22, 70, 118, 166, 39, 87, 135, 183, 40, 88, 136, 184)(24, 72, 120, 168, 42, 90, 138, 186, 41, 89, 137, 185)(26, 74, 122, 170, 43, 91, 139, 187, 44, 92, 140, 188)(32, 80, 128, 176, 46, 94, 142, 190, 45, 93, 141, 189)(38, 86, 134, 182, 47, 95, 143, 191, 48, 96, 144, 192)
	L = (1, 50)(2, 56)(3, 57)(4, 60)(5, 49)(6, 59)(7, 58)(8, 53)(9, 70)(10, 73)(11, 72)(12, 71)(13, 74)(14, 76)(15, 51)(16, 75)(17, 52)(18, 78)(19, 55)(20, 54)(21, 77)(22, 63)(23, 65)(24, 68)(25, 67)(26, 86)(27, 88)(28, 87)(29, 90)(30, 89)(31, 92)(32, 61)(33, 91)(34, 62)(35, 64)(36, 66)(37, 69)(38, 80)(39, 82)(40, 83)(41, 84)(42, 85)(43, 96)(44, 95)(45, 79)(46, 81)(47, 93)(48, 94)(97, 147)(98, 153)(99, 157)(100, 160)(101, 159)(102, 145)(103, 158)(104, 166)(105, 170)(106, 172)(107, 146)(108, 171)(109, 150)(110, 177)(111, 176)(112, 175)(113, 179)(114, 148)(115, 178)(116, 149)(117, 151)(118, 182)(119, 184)(120, 152)(121, 183)(122, 155)(123, 188)(124, 187)(125, 154)(126, 156)(127, 162)(128, 164)(129, 165)(130, 190)(131, 189)(132, 161)(133, 163)(134, 168)(135, 192)(136, 191)(137, 167)(138, 169)(139, 173)(140, 174)(141, 180)(142, 181)(143, 185)(144, 186)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.757
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.761 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1^-1), (Y3, Y2), Y2^4, Y3^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 17, 65)(6, 54, 19, 67, 10, 58)(7, 55, 11, 59, 20, 68)(13, 61, 22, 70, 28, 76)(14, 62, 29, 77, 23, 71)(15, 63, 30, 78, 24, 72)(16, 64, 25, 73, 34, 82)(18, 66, 36, 84, 26, 74)(21, 69, 37, 85, 27, 75)(31, 79, 38, 86, 42, 90)(32, 80, 39, 87, 43, 91)(33, 81, 44, 92, 40, 88)(35, 83, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 110, 158, 127, 175, 114, 162)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 111, 159, 128, 176, 117, 165)(105, 153, 119, 167, 134, 182, 122, 170)(107, 155, 120, 168, 135, 183, 123, 171)(112, 160, 129, 177, 141, 189, 131, 179)(113, 161, 125, 173, 138, 186, 132, 180)(116, 164, 126, 174, 139, 187, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 140, 188, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 110)(4, 112)(5, 113)(6, 114)(7, 97)(8, 119)(9, 121)(10, 122)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 103)(17, 130)(18, 131)(19, 132)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 107)(26, 137)(27, 106)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 116)(35, 117)(36, 142)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 144)(43, 124)(44, 126)(45, 128)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.763
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.762 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y3, Y1), Y2^-1 * Y3^-1 * Y2 * Y1 * Y3, Y3^4 * Y1^-1, R * Y2 * R * Y1^-1 * Y2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3^2 * Y2 * Y3^2 * Y2^-1, (Y3^-1 * Y2^-1)^4, (Y1^-1 * Y3^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 18, 66)(6, 54, 20, 68, 10, 58)(7, 55, 11, 59, 21, 69)(13, 61, 27, 75, 33, 81)(14, 62, 16, 64, 28, 76)(15, 63, 31, 79, 24, 72)(17, 65, 29, 77, 26, 74)(19, 67, 30, 78, 22, 70)(23, 71, 32, 80, 25, 73)(34, 82, 36, 84, 45, 93)(35, 83, 44, 92, 38, 86)(37, 85, 40, 88, 39, 87)(41, 89, 43, 91, 42, 90)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 123, 171, 106, 154)(100, 148, 112, 160, 130, 178, 115, 163)(101, 149, 108, 156, 129, 177, 116, 164)(103, 151, 120, 168, 131, 179, 121, 169)(105, 153, 110, 158, 132, 180, 118, 166)(107, 155, 127, 175, 140, 188, 128, 176)(111, 159, 134, 182, 119, 167, 117, 165)(113, 161, 135, 183, 142, 190, 137, 185)(114, 162, 124, 172, 141, 189, 126, 174)(122, 170, 133, 181, 143, 191, 139, 187)(125, 173, 136, 184, 144, 192, 138, 186)
	L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 114)(6, 118)(7, 97)(8, 124)(9, 125)(10, 126)(11, 98)(12, 112)(13, 130)(14, 133)(15, 99)(16, 136)(17, 107)(18, 122)(19, 138)(20, 115)(21, 101)(22, 139)(23, 102)(24, 104)(25, 106)(26, 103)(27, 132)(28, 135)(29, 117)(30, 137)(31, 108)(32, 116)(33, 141)(34, 142)(35, 109)(36, 144)(37, 127)(38, 129)(39, 111)(40, 120)(41, 119)(42, 121)(43, 128)(44, 123)(45, 143)(46, 140)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.764
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.763 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-3, Y1^4, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y2), (R * Y2)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1 * Y2^-1, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y2 * Y1 * Y2^-1, (Y2^-1 * Y3)^3, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3^-2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 10, 58, 27, 75, 19, 67)(6, 54, 24, 72, 28, 76, 25, 73)(7, 55, 12, 60, 29, 77, 23, 71)(9, 57, 30, 78, 21, 69, 33, 81)(11, 59, 37, 85, 22, 70, 38, 86)(14, 62, 32, 80, 44, 92, 39, 87)(15, 63, 31, 79, 45, 93, 40, 88)(17, 65, 36, 84, 46, 94, 43, 91)(18, 66, 35, 83, 47, 95, 41, 89)(20, 68, 34, 82, 48, 96, 42, 90)(97, 145, 99, 147, 110, 158, 103, 151, 113, 161, 129, 177, 114, 162, 134, 182, 116, 164, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 127, 175, 108, 156, 130, 178, 109, 157, 131, 179, 120, 168, 132, 180, 106, 154, 128, 176, 107, 155)(101, 149, 117, 165, 136, 184, 119, 167, 138, 186, 112, 160, 137, 185, 121, 169, 139, 187, 115, 163, 135, 183, 118, 166)(104, 152, 122, 170, 140, 188, 125, 173, 142, 190, 126, 174, 143, 191, 133, 181, 144, 192, 123, 171, 141, 189, 124, 172)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 115)(6, 116)(7, 97)(8, 123)(9, 128)(10, 131)(11, 132)(12, 98)(13, 127)(14, 102)(15, 134)(16, 136)(17, 99)(18, 103)(19, 137)(20, 129)(21, 135)(22, 139)(23, 101)(24, 130)(25, 138)(26, 141)(27, 143)(28, 144)(29, 104)(30, 140)(31, 107)(32, 120)(33, 110)(34, 105)(35, 108)(36, 109)(37, 142)(38, 113)(39, 121)(40, 118)(41, 119)(42, 117)(43, 112)(44, 124)(45, 133)(46, 122)(47, 125)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.761
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.764 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C4 x (C3 : C4) (small group id <48, 11>)
Aut   = (C6 x D8) : C2 (small group id <96, 147>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-2 * Y3^-1, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1^-1, Y1^4, Y2^5 * Y3^-1, (Y3 * Y2^-1)^3, Y3^-2 * Y2^2 * Y1 * Y3 * Y2^-1 * Y1^-1, (Y1^-1 * Y2^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 10, 58, 22, 70, 15, 63)(4, 52, 9, 57, 23, 71, 18, 66)(6, 54, 12, 60, 24, 72, 21, 69)(7, 55, 11, 59, 25, 73, 20, 68)(13, 61, 29, 77, 38, 86, 32, 80)(14, 62, 27, 75, 39, 87, 34, 82)(16, 64, 30, 78, 40, 88, 35, 83)(17, 65, 26, 74, 41, 89, 36, 84)(19, 67, 28, 76, 42, 90, 37, 85)(31, 79, 43, 91, 47, 95, 45, 93)(33, 81, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 115, 163, 100, 148, 110, 158, 103, 151, 112, 160, 129, 177, 113, 161, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 106, 154, 123, 171, 108, 156, 124, 172, 140, 188, 125, 173, 107, 155)(101, 149, 114, 162, 132, 180, 141, 189, 131, 179, 111, 159, 130, 178, 117, 165, 133, 181, 142, 190, 128, 176, 116, 164)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 119, 167, 135, 183, 121, 169, 136, 184, 144, 192, 137, 185, 120, 168)
	L = (1, 100)(2, 106)(3, 110)(4, 113)(5, 111)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 103)(14, 102)(15, 128)(16, 99)(17, 127)(18, 130)(19, 129)(20, 131)(21, 101)(22, 135)(23, 137)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 139)(30, 140)(31, 112)(32, 141)(33, 109)(34, 116)(35, 142)(36, 117)(37, 114)(38, 121)(39, 120)(40, 118)(41, 143)(42, 144)(43, 124)(44, 122)(45, 133)(46, 132)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.762
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.765 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, (Y3, Y1^-1), Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^4, Y2^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 18, 66)(6, 54, 19, 67, 10, 58)(7, 55, 11, 59, 20, 68)(13, 61, 22, 70, 28, 76)(14, 62, 29, 77, 23, 71)(15, 63, 30, 78, 24, 72)(16, 64, 34, 82, 25, 73)(17, 65, 26, 74, 36, 84)(21, 69, 37, 85, 27, 75)(31, 79, 38, 86, 42, 90)(32, 80, 39, 87, 43, 91)(33, 81, 44, 92, 40, 88)(35, 83, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 112, 160, 127, 175, 110, 158)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 117, 165, 128, 176, 111, 159)(105, 153, 121, 169, 134, 182, 119, 167)(107, 155, 123, 171, 135, 183, 120, 168)(113, 161, 129, 177, 141, 189, 131, 179)(114, 162, 130, 178, 138, 186, 125, 173)(116, 164, 133, 181, 139, 187, 126, 174)(122, 170, 136, 184, 143, 191, 137, 185)(132, 180, 140, 188, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 114)(6, 112)(7, 97)(8, 119)(9, 122)(10, 121)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 131)(17, 103)(18, 132)(19, 130)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 137)(26, 107)(27, 106)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 142)(35, 117)(36, 116)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 144)(43, 124)(44, 126)(45, 128)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.769
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.766 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y3, Y1), R * Y2 * R * Y1^-1 * Y2^-1, Y3^4 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y3, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, (Y1^-1 * Y3^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 18, 66)(6, 54, 20, 68, 10, 58)(7, 55, 11, 59, 21, 69)(13, 61, 27, 75, 33, 81)(14, 62, 19, 67, 28, 76)(15, 63, 32, 80, 25, 73)(16, 64, 30, 78, 22, 70)(17, 65, 29, 77, 26, 74)(23, 71, 31, 79, 24, 72)(34, 82, 37, 85, 45, 93)(35, 83, 44, 92, 38, 86)(36, 84, 42, 90, 39, 87)(40, 88, 41, 89, 43, 91)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 123, 171, 106, 154)(100, 148, 112, 160, 130, 178, 115, 163)(101, 149, 108, 156, 129, 177, 116, 164)(103, 151, 120, 168, 131, 179, 121, 169)(105, 153, 118, 166, 133, 181, 110, 158)(107, 155, 127, 175, 140, 188, 128, 176)(111, 159, 117, 165, 119, 167, 134, 182)(113, 161, 135, 183, 142, 190, 137, 185)(114, 162, 126, 174, 141, 189, 124, 172)(122, 170, 132, 180, 143, 191, 139, 187)(125, 173, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 114)(6, 118)(7, 97)(8, 124)(9, 125)(10, 126)(11, 98)(12, 115)(13, 130)(14, 132)(15, 99)(16, 136)(17, 107)(18, 122)(19, 138)(20, 112)(21, 101)(22, 139)(23, 102)(24, 106)(25, 104)(26, 103)(27, 133)(28, 135)(29, 117)(30, 137)(31, 116)(32, 108)(33, 141)(34, 142)(35, 109)(36, 128)(37, 144)(38, 129)(39, 111)(40, 120)(41, 119)(42, 121)(43, 127)(44, 123)(45, 143)(46, 140)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.771
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.767 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3^-2 * Y2^2, Y2^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^-12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 17, 65)(6, 54, 19, 67, 10, 58)(7, 55, 11, 59, 20, 68)(13, 61, 21, 69, 26, 74)(14, 62, 27, 75, 22, 70)(15, 63, 28, 76, 23, 71)(16, 64, 31, 79, 24, 72)(18, 66, 34, 82, 25, 73)(29, 77, 35, 83, 39, 87)(30, 78, 36, 84, 40, 88)(32, 80, 43, 91, 37, 85)(33, 81, 44, 92, 38, 86)(41, 89, 45, 93, 47, 95)(42, 90, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 117, 165, 106, 154)(100, 148, 112, 160, 103, 151, 114, 162)(101, 149, 108, 156, 122, 170, 115, 163)(105, 153, 120, 168, 107, 155, 121, 169)(110, 158, 125, 173, 111, 159, 126, 174)(113, 161, 127, 175, 116, 164, 130, 178)(118, 166, 131, 179, 119, 167, 132, 180)(123, 171, 135, 183, 124, 172, 136, 184)(128, 176, 137, 185, 129, 177, 138, 186)(133, 181, 141, 189, 134, 182, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 110)(4, 109)(5, 113)(6, 111)(7, 97)(8, 118)(9, 117)(10, 119)(11, 98)(12, 123)(13, 103)(14, 102)(15, 99)(16, 128)(17, 122)(18, 129)(19, 124)(20, 101)(21, 107)(22, 106)(23, 104)(24, 133)(25, 134)(26, 116)(27, 115)(28, 108)(29, 137)(30, 138)(31, 139)(32, 114)(33, 112)(34, 140)(35, 141)(36, 142)(37, 121)(38, 120)(39, 143)(40, 144)(41, 126)(42, 125)(43, 130)(44, 127)(45, 132)(46, 131)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.770
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.768 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3, Y1), Y3^-4 * Y1, Y2 * Y1^-1 * Y2 * Y3^2, Y3 * Y1 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y3 * Y2^-1)^4, (Y1^-1 * Y2^-2)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 18, 66)(6, 54, 20, 68, 10, 58)(7, 55, 11, 59, 21, 69)(13, 61, 26, 74, 17, 65)(14, 62, 23, 71, 27, 75)(15, 63, 28, 76, 22, 70)(16, 64, 30, 78, 25, 73)(19, 67, 29, 77, 24, 72)(31, 79, 41, 89, 34, 82)(32, 80, 42, 90, 33, 81)(35, 83, 38, 86, 40, 88)(36, 84, 39, 87, 37, 85)(43, 91, 46, 94, 48, 96)(44, 92, 47, 95, 45, 93)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 122, 170, 106, 154)(100, 148, 112, 160, 117, 165, 115, 163)(101, 149, 108, 156, 113, 161, 116, 164)(103, 151, 120, 168, 105, 153, 121, 169)(107, 155, 125, 173, 114, 162, 126, 174)(110, 158, 127, 175, 118, 166, 128, 176)(111, 159, 129, 177, 119, 167, 130, 178)(123, 171, 137, 185, 124, 172, 138, 186)(131, 179, 139, 187, 133, 181, 141, 189)(132, 180, 143, 191, 134, 182, 144, 192)(135, 183, 140, 188, 136, 184, 142, 190)
	L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 114)(6, 118)(7, 97)(8, 123)(9, 109)(10, 124)(11, 98)(12, 119)(13, 117)(14, 106)(15, 99)(16, 131)(17, 107)(18, 122)(19, 133)(20, 111)(21, 101)(22, 104)(23, 102)(24, 135)(25, 136)(26, 103)(27, 116)(28, 108)(29, 132)(30, 134)(31, 139)(32, 141)(33, 143)(34, 144)(35, 120)(36, 112)(37, 121)(38, 115)(39, 126)(40, 125)(41, 142)(42, 140)(43, 129)(44, 127)(45, 130)(46, 128)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.772
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.769 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^3, Y1^4, Y1^2 * Y3^-2, Y3^4, (R * Y2)^2, (R * Y3)^2, Y1 * Y3^2 * Y1, (Y3^-1, Y2^-1), (R * Y1)^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 16, 64)(4, 52, 18, 66, 7, 55, 19, 67)(6, 54, 23, 71, 26, 74, 24, 72)(9, 57, 27, 75, 21, 69, 30, 78)(10, 58, 32, 80, 12, 60, 33, 81)(11, 59, 35, 83, 22, 70, 36, 84)(14, 62, 29, 77, 20, 68, 31, 79)(15, 63, 28, 76, 17, 65, 34, 82)(37, 85, 43, 91, 41, 89, 47, 95)(38, 86, 48, 96, 40, 88, 45, 93)(39, 87, 46, 94, 42, 90, 44, 92)(97, 145, 99, 147, 110, 158, 103, 151, 113, 161, 122, 170, 104, 152, 121, 169, 116, 164, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 124, 172, 108, 156, 127, 175, 118, 166, 101, 149, 117, 165, 130, 178, 106, 154, 125, 173, 107, 155)(109, 157, 133, 181, 119, 167, 136, 184, 114, 162, 138, 186, 112, 160, 137, 185, 120, 168, 134, 182, 115, 163, 135, 183)(123, 171, 139, 187, 131, 179, 142, 190, 128, 176, 144, 192, 126, 174, 143, 191, 132, 180, 140, 188, 129, 177, 141, 189)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 125)(10, 101)(11, 130)(12, 98)(13, 134)(14, 102)(15, 121)(16, 136)(17, 99)(18, 133)(19, 137)(20, 122)(21, 127)(22, 124)(23, 135)(24, 138)(25, 113)(26, 110)(27, 140)(28, 107)(29, 117)(30, 142)(31, 105)(32, 139)(33, 143)(34, 118)(35, 141)(36, 144)(37, 115)(38, 112)(39, 120)(40, 109)(41, 114)(42, 119)(43, 129)(44, 126)(45, 132)(46, 123)(47, 128)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.765
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.770 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^3, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y2)^2, Y1^4, Y3^4, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 27, 75, 10, 58)(6, 54, 24, 72, 28, 76, 25, 73)(7, 55, 23, 71, 29, 77, 12, 60)(9, 57, 30, 78, 21, 69, 33, 81)(11, 59, 37, 85, 22, 70, 38, 86)(14, 62, 32, 80, 44, 92, 43, 91)(15, 63, 31, 79, 45, 93, 40, 88)(17, 65, 36, 84, 46, 94, 42, 90)(19, 67, 35, 83, 47, 95, 39, 87)(20, 68, 34, 82, 48, 96, 41, 89)(97, 145, 99, 147, 110, 158, 103, 151, 113, 161, 126, 174, 115, 163, 133, 181, 116, 164, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 127, 175, 108, 156, 130, 178, 112, 160, 131, 179, 121, 169, 132, 180, 106, 154, 128, 176, 107, 155)(101, 149, 117, 165, 136, 184, 119, 167, 137, 185, 109, 157, 135, 183, 120, 168, 138, 186, 114, 162, 139, 187, 118, 166)(104, 152, 122, 170, 140, 188, 125, 173, 142, 190, 129, 177, 143, 191, 134, 182, 144, 192, 123, 171, 141, 189, 124, 172)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 114)(6, 116)(7, 97)(8, 123)(9, 128)(10, 131)(11, 132)(12, 98)(13, 136)(14, 102)(15, 133)(16, 127)(17, 99)(18, 135)(19, 103)(20, 126)(21, 139)(22, 138)(23, 101)(24, 137)(25, 130)(26, 141)(27, 143)(28, 144)(29, 104)(30, 110)(31, 107)(32, 121)(33, 140)(34, 105)(35, 108)(36, 112)(37, 113)(38, 142)(39, 119)(40, 118)(41, 117)(42, 109)(43, 120)(44, 124)(45, 134)(46, 122)(47, 125)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.767
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.771 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-2 * Y3^-1, Y2^-2 * Y3^-2, (Y3^-1, Y2), Y1^4, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y1^-2 * Y3 * Y1^-2 * Y3^-1, (Y2^-1 * Y3)^3, Y3^-2 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-2 * Y2^10 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 7, 55, 15, 63)(4, 52, 17, 65, 6, 54, 19, 67)(9, 57, 21, 69, 12, 60, 23, 71)(10, 58, 25, 73, 11, 59, 27, 75)(14, 62, 26, 74, 16, 64, 28, 76)(18, 66, 22, 70, 20, 68, 24, 72)(29, 77, 37, 85, 32, 80, 40, 88)(30, 78, 43, 91, 31, 79, 44, 92)(33, 81, 45, 93, 34, 82, 46, 94)(35, 83, 38, 86, 36, 84, 39, 87)(41, 89, 47, 95, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 129, 177, 116, 164, 100, 148, 104, 152, 103, 151, 112, 160, 130, 178, 114, 162, 102, 150)(98, 146, 105, 153, 118, 166, 137, 185, 124, 172, 106, 154, 101, 149, 108, 156, 120, 168, 138, 186, 122, 170, 107, 155)(109, 157, 125, 173, 115, 163, 132, 180, 142, 190, 126, 174, 111, 159, 128, 176, 113, 161, 131, 179, 141, 189, 127, 175)(117, 165, 133, 181, 123, 171, 140, 188, 144, 192, 134, 182, 119, 167, 136, 184, 121, 169, 139, 187, 143, 191, 135, 183)
	L = (1, 100)(2, 106)(3, 104)(4, 114)(5, 107)(6, 116)(7, 97)(8, 102)(9, 101)(10, 122)(11, 124)(12, 98)(13, 126)(14, 103)(15, 127)(16, 99)(17, 125)(18, 129)(19, 128)(20, 130)(21, 134)(22, 108)(23, 135)(24, 105)(25, 133)(26, 137)(27, 136)(28, 138)(29, 111)(30, 141)(31, 142)(32, 109)(33, 112)(34, 110)(35, 115)(36, 113)(37, 119)(38, 143)(39, 144)(40, 117)(41, 120)(42, 118)(43, 123)(44, 121)(45, 132)(46, 131)(47, 140)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.766
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.772 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = (C3 : C4) : C4 (small group id <48, 12>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 91>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^-2, (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y1^4, Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^-3 * Y3^3, Y2^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 10, 58)(4, 52, 17, 65, 23, 71, 9, 57)(6, 54, 21, 69, 24, 72, 12, 60)(7, 55, 20, 68, 25, 73, 11, 59)(14, 62, 29, 77, 38, 86, 32, 80)(15, 63, 27, 75, 39, 87, 31, 79)(16, 64, 30, 78, 40, 88, 33, 81)(18, 66, 26, 74, 41, 89, 36, 84)(19, 67, 28, 76, 42, 90, 37, 85)(34, 82, 45, 93, 47, 95, 43, 91)(35, 83, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 130, 178, 115, 163, 100, 148, 111, 159, 103, 151, 112, 160, 131, 179, 114, 162, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 106, 154, 123, 171, 108, 156, 124, 172, 140, 188, 125, 173, 107, 155)(101, 149, 113, 161, 132, 180, 141, 189, 129, 177, 109, 157, 127, 175, 117, 165, 133, 181, 142, 190, 128, 176, 116, 164)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 119, 167, 135, 183, 121, 169, 136, 184, 144, 192, 137, 185, 120, 168)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 109)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 128)(14, 103)(15, 102)(16, 99)(17, 127)(18, 130)(19, 131)(20, 129)(21, 101)(22, 135)(23, 137)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 139)(30, 140)(31, 116)(32, 141)(33, 142)(34, 112)(35, 110)(36, 117)(37, 113)(38, 121)(39, 120)(40, 118)(41, 143)(42, 144)(43, 124)(44, 122)(45, 133)(46, 132)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.768
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.773 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 4, 12})
Quotient :: edge^2
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C24 x C2) : C2 (small group id <96, 28>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^2 * Y2^-1, Y2^4, (R * Y3)^2, Y1^4, Y2 * Y3 * Y2^-1 * Y3, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y1 * Y3^2 * Y2, (Y1^-1 * Y2^-1)^4, (Y3 * Y1^-1 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 17, 65, 9, 57, 26, 74, 42, 90, 39, 87, 47, 95, 33, 81, 13, 61, 22, 70, 7, 55)(2, 50, 10, 58, 19, 67, 6, 54, 21, 69, 38, 86, 32, 80, 46, 94, 41, 89, 25, 73, 30, 78, 12, 60)(3, 51, 14, 62, 34, 82, 31, 79, 45, 93, 43, 91, 27, 75, 37, 85, 18, 66, 5, 53, 20, 68, 16, 64)(8, 56, 23, 71, 28, 76, 11, 59, 29, 77, 44, 92, 40, 88, 48, 96, 35, 83, 15, 63, 36, 84, 24, 72)(97, 98, 104, 101)(99, 109, 102, 111)(100, 108, 119, 114)(103, 106, 120, 116)(105, 121, 107, 123)(110, 129, 117, 131)(112, 118, 115, 132)(113, 126, 124, 133)(122, 137, 125, 139)(127, 135, 128, 136)(130, 143, 134, 144)(138, 142, 140, 141)(145, 147, 152, 150)(146, 153, 149, 155)(148, 160, 167, 163)(151, 158, 168, 165)(154, 161, 164, 172)(156, 170, 162, 173)(157, 175, 159, 176)(166, 178, 180, 182)(169, 183, 171, 184)(174, 186, 181, 188)(177, 189, 179, 190)(185, 191, 187, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.776
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.774 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 4, 4, 12})
Quotient :: edge^2
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C24 x C2) : C2 (small group id <96, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^4, Y2^2 * Y1^2, Y1^-1 * Y2^2 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y1^-1)^4, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 4, 52, 7, 55)(2, 50, 10, 58, 12, 60)(3, 51, 14, 62, 16, 64)(5, 53, 19, 67, 17, 65)(6, 54, 20, 68, 18, 66)(8, 56, 21, 69, 22, 70)(9, 57, 24, 72, 26, 74)(11, 59, 28, 76, 27, 75)(13, 61, 30, 78, 32, 80)(15, 63, 34, 82, 33, 81)(23, 71, 36, 84, 38, 86)(25, 73, 40, 88, 39, 87)(29, 77, 41, 89, 42, 90)(31, 79, 44, 92, 43, 91)(35, 83, 45, 93, 46, 94)(37, 85, 48, 96, 47, 95)(97, 98, 104, 101)(99, 109, 102, 111)(100, 108, 117, 113)(103, 106, 118, 115)(105, 119, 107, 121)(110, 128, 116, 129)(112, 126, 114, 130)(120, 134, 124, 135)(122, 132, 123, 136)(125, 131, 127, 133)(137, 142, 140, 143)(138, 141, 139, 144)(145, 147, 152, 150)(146, 153, 149, 155)(148, 160, 165, 162)(151, 158, 166, 164)(154, 170, 163, 171)(156, 168, 161, 172)(157, 173, 159, 175)(167, 179, 169, 181)(174, 186, 178, 187)(176, 185, 177, 188)(180, 190, 184, 191)(182, 189, 183, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 48^4 ), ( 48^6 ) }
Outer automorphisms :: reflexible
Dual of E27.775
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.775 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 4, 12})
Quotient :: loop^2
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C24 x C2) : C2 (small group id <96, 28>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^2 * Y2^-1, Y2^4, (R * Y3)^2, Y1^4, Y2 * Y3 * Y2^-1 * Y3, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y1 * Y3^2 * Y2, (Y1^-1 * Y2^-1)^4, (Y3 * Y1^-1 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 17, 65, 113, 161, 9, 57, 105, 153, 26, 74, 122, 170, 42, 90, 138, 186, 39, 87, 135, 183, 47, 95, 143, 191, 33, 81, 129, 177, 13, 61, 109, 157, 22, 70, 118, 166, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 19, 67, 115, 163, 6, 54, 102, 150, 21, 69, 117, 165, 38, 86, 134, 182, 32, 80, 128, 176, 46, 94, 142, 190, 41, 89, 137, 185, 25, 73, 121, 169, 30, 78, 126, 174, 12, 60, 108, 156)(3, 51, 99, 147, 14, 62, 110, 158, 34, 82, 130, 178, 31, 79, 127, 175, 45, 93, 141, 189, 43, 91, 139, 187, 27, 75, 123, 171, 37, 85, 133, 181, 18, 66, 114, 162, 5, 53, 101, 149, 20, 68, 116, 164, 16, 64, 112, 160)(8, 56, 104, 152, 23, 71, 119, 167, 28, 76, 124, 172, 11, 59, 107, 155, 29, 77, 125, 173, 44, 92, 140, 188, 40, 88, 136, 184, 48, 96, 144, 192, 35, 83, 131, 179, 15, 63, 111, 159, 36, 84, 132, 180, 24, 72, 120, 168)
	L = (1, 50)(2, 56)(3, 61)(4, 60)(5, 49)(6, 63)(7, 58)(8, 53)(9, 73)(10, 72)(11, 75)(12, 71)(13, 54)(14, 81)(15, 51)(16, 70)(17, 78)(18, 52)(19, 84)(20, 55)(21, 83)(22, 67)(23, 66)(24, 68)(25, 59)(26, 89)(27, 57)(28, 85)(29, 91)(30, 76)(31, 87)(32, 88)(33, 69)(34, 95)(35, 62)(36, 64)(37, 65)(38, 96)(39, 80)(40, 79)(41, 77)(42, 94)(43, 74)(44, 93)(45, 90)(46, 92)(47, 86)(48, 82)(97, 147)(98, 153)(99, 152)(100, 160)(101, 155)(102, 145)(103, 158)(104, 150)(105, 149)(106, 161)(107, 146)(108, 170)(109, 175)(110, 168)(111, 176)(112, 167)(113, 164)(114, 173)(115, 148)(116, 172)(117, 151)(118, 178)(119, 163)(120, 165)(121, 183)(122, 162)(123, 184)(124, 154)(125, 156)(126, 186)(127, 159)(128, 157)(129, 189)(130, 180)(131, 190)(132, 182)(133, 188)(134, 166)(135, 171)(136, 169)(137, 191)(138, 181)(139, 192)(140, 174)(141, 179)(142, 177)(143, 187)(144, 185)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.774
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 96 f = 40
	degree seq :: [ 48^4 ]

E27.776 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 4, 4, 12})
Quotient :: loop^2
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C24 x C2) : C2 (small group id <96, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^4, Y2^2 * Y1^2, Y1^-1 * Y2^2 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y1^-1)^4, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 12, 60, 108, 156)(3, 51, 99, 147, 14, 62, 110, 158, 16, 64, 112, 160)(5, 53, 101, 149, 19, 67, 115, 163, 17, 65, 113, 161)(6, 54, 102, 150, 20, 68, 116, 164, 18, 66, 114, 162)(8, 56, 104, 152, 21, 69, 117, 165, 22, 70, 118, 166)(9, 57, 105, 153, 24, 72, 120, 168, 26, 74, 122, 170)(11, 59, 107, 155, 28, 76, 124, 172, 27, 75, 123, 171)(13, 61, 109, 157, 30, 78, 126, 174, 32, 80, 128, 176)(15, 63, 111, 159, 34, 82, 130, 178, 33, 81, 129, 177)(23, 71, 119, 167, 36, 84, 132, 180, 38, 86, 134, 182)(25, 73, 121, 169, 40, 88, 136, 184, 39, 87, 135, 183)(29, 77, 125, 173, 41, 89, 137, 185, 42, 90, 138, 186)(31, 79, 127, 175, 44, 92, 140, 188, 43, 91, 139, 187)(35, 83, 131, 179, 45, 93, 141, 189, 46, 94, 142, 190)(37, 85, 133, 181, 48, 96, 144, 192, 47, 95, 143, 191)
	L = (1, 50)(2, 56)(3, 61)(4, 60)(5, 49)(6, 63)(7, 58)(8, 53)(9, 71)(10, 70)(11, 73)(12, 69)(13, 54)(14, 80)(15, 51)(16, 78)(17, 52)(18, 82)(19, 55)(20, 81)(21, 65)(22, 67)(23, 59)(24, 86)(25, 57)(26, 84)(27, 88)(28, 87)(29, 83)(30, 66)(31, 85)(32, 68)(33, 62)(34, 64)(35, 79)(36, 75)(37, 77)(38, 76)(39, 72)(40, 74)(41, 94)(42, 93)(43, 96)(44, 95)(45, 91)(46, 92)(47, 89)(48, 90)(97, 147)(98, 153)(99, 152)(100, 160)(101, 155)(102, 145)(103, 158)(104, 150)(105, 149)(106, 170)(107, 146)(108, 168)(109, 173)(110, 166)(111, 175)(112, 165)(113, 172)(114, 148)(115, 171)(116, 151)(117, 162)(118, 164)(119, 179)(120, 161)(121, 181)(122, 163)(123, 154)(124, 156)(125, 159)(126, 186)(127, 157)(128, 185)(129, 188)(130, 187)(131, 169)(132, 190)(133, 167)(134, 189)(135, 192)(136, 191)(137, 177)(138, 178)(139, 174)(140, 176)(141, 183)(142, 184)(143, 180)(144, 182)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.773
Transitivity :: VT+
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.777 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y3^4, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (Y3, Y1^-1), Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 17, 65)(6, 54, 19, 67, 10, 58)(7, 55, 11, 59, 20, 68)(13, 61, 22, 70, 28, 76)(14, 62, 29, 77, 23, 71)(15, 63, 30, 78, 24, 72)(16, 64, 25, 73, 34, 82)(18, 66, 36, 84, 26, 74)(21, 69, 37, 85, 27, 75)(31, 79, 38, 86, 42, 90)(32, 80, 39, 87, 43, 91)(33, 81, 44, 92, 40, 88)(35, 83, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 111, 159, 127, 175, 114, 162)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 110, 158, 128, 176, 117, 165)(105, 153, 120, 168, 134, 182, 122, 170)(107, 155, 119, 167, 135, 183, 123, 171)(112, 160, 129, 177, 141, 189, 131, 179)(113, 161, 126, 174, 138, 186, 132, 180)(116, 164, 125, 173, 139, 187, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 140, 188, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 110)(4, 112)(5, 113)(6, 117)(7, 97)(8, 119)(9, 121)(10, 123)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 103)(17, 130)(18, 102)(19, 133)(20, 101)(21, 131)(22, 134)(23, 136)(24, 104)(25, 107)(26, 106)(27, 137)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 116)(35, 114)(36, 115)(37, 142)(38, 143)(39, 118)(40, 120)(41, 122)(42, 144)(43, 124)(44, 126)(45, 128)(46, 132)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.779
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.778 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3^4 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 9, 57, 17, 65)(6, 54, 19, 67, 10, 58)(7, 55, 11, 59, 20, 68)(13, 61, 23, 71, 29, 77)(14, 62, 30, 78, 24, 72)(15, 63, 31, 79, 25, 73)(16, 64, 26, 74, 22, 70)(18, 66, 37, 85, 27, 75)(21, 69, 38, 86, 28, 76)(32, 80, 40, 88, 44, 92)(33, 81, 41, 89, 45, 93)(34, 82, 42, 90, 35, 83)(36, 84, 39, 87, 43, 91)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 119, 167, 106, 154)(100, 148, 111, 159, 128, 176, 114, 162)(101, 149, 108, 156, 125, 173, 115, 163)(103, 151, 110, 158, 129, 177, 117, 165)(105, 153, 121, 169, 136, 184, 123, 171)(107, 155, 120, 168, 137, 185, 124, 172)(112, 160, 131, 179, 142, 190, 132, 180)(113, 161, 127, 175, 140, 188, 133, 181)(116, 164, 126, 174, 141, 189, 134, 182)(118, 166, 130, 178, 143, 191, 135, 183)(122, 170, 138, 186, 144, 192, 139, 187)
	L = (1, 100)(2, 105)(3, 110)(4, 112)(5, 113)(6, 117)(7, 97)(8, 120)(9, 122)(10, 124)(11, 98)(12, 126)(13, 128)(14, 130)(15, 99)(16, 107)(17, 118)(18, 102)(19, 134)(20, 101)(21, 135)(22, 103)(23, 136)(24, 131)(25, 104)(26, 116)(27, 106)(28, 132)(29, 140)(30, 138)(31, 108)(32, 142)(33, 109)(34, 127)(35, 111)(36, 114)(37, 115)(38, 139)(39, 133)(40, 144)(41, 119)(42, 121)(43, 123)(44, 143)(45, 125)(46, 137)(47, 129)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.780
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.779 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, Y2^-3 * Y3^-1, (R * Y1)^2, (R * Y2^-1)^2, Y3^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2, Y3^-1), Y2 * Y1 * Y2 * Y1^-1, Y1^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y2^-2 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 12, 60, 23, 71, 18, 66)(6, 54, 9, 57, 24, 72, 20, 68)(7, 55, 10, 58, 25, 73, 21, 69)(13, 61, 27, 75, 38, 86, 31, 79)(14, 62, 26, 74, 39, 87, 34, 82)(16, 64, 30, 78, 40, 88, 35, 83)(17, 65, 29, 77, 41, 89, 36, 84)(19, 67, 28, 76, 42, 90, 37, 85)(32, 80, 44, 92, 47, 95, 45, 93)(33, 81, 43, 91, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 103, 151, 112, 160, 128, 176, 113, 161, 129, 177, 115, 163, 100, 148, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 108, 156, 124, 172, 139, 187, 125, 173, 140, 188, 126, 174, 106, 154, 123, 171, 107, 155)(101, 149, 116, 164, 130, 178, 114, 162, 133, 181, 142, 190, 132, 180, 141, 189, 131, 179, 117, 165, 127, 175, 111, 159)(104, 152, 118, 166, 134, 182, 121, 169, 136, 184, 143, 191, 137, 185, 144, 192, 138, 186, 119, 167, 135, 183, 120, 168)
	L = (1, 100)(2, 106)(3, 110)(4, 113)(5, 117)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 102)(14, 129)(15, 131)(16, 99)(17, 103)(18, 101)(19, 128)(20, 127)(21, 132)(22, 135)(23, 137)(24, 138)(25, 104)(26, 107)(27, 140)(28, 105)(29, 108)(30, 139)(31, 141)(32, 109)(33, 112)(34, 111)(35, 142)(36, 114)(37, 116)(38, 120)(39, 144)(40, 118)(41, 121)(42, 143)(43, 122)(44, 124)(45, 133)(46, 130)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.777
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.780 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 : C4 (small group id <48, 13>)
Aut   = (C12 x C2 x C2) : C2 (small group id <96, 137>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2), (Y3 * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, Y2^-2 * Y3^-2, (R * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^4, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3, Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2^7 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 12, 60, 23, 71, 18, 66)(6, 54, 9, 57, 24, 72, 20, 68)(7, 55, 10, 58, 25, 73, 21, 69)(13, 61, 29, 77, 38, 86, 32, 80)(14, 62, 27, 75, 39, 87, 34, 82)(16, 64, 30, 78, 40, 88, 35, 83)(17, 65, 26, 74, 41, 89, 36, 84)(19, 67, 28, 76, 42, 90, 37, 85)(31, 79, 44, 92, 47, 95, 45, 93)(33, 81, 43, 91, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 115, 163, 100, 148, 110, 158, 103, 151, 112, 160, 129, 177, 113, 161, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 106, 154, 123, 171, 108, 156, 124, 172, 140, 188, 125, 173, 107, 155)(101, 149, 116, 164, 132, 180, 142, 190, 131, 179, 117, 165, 130, 178, 114, 162, 133, 181, 141, 189, 128, 176, 111, 159)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 119, 167, 135, 183, 121, 169, 136, 184, 144, 192, 137, 185, 120, 168)
	L = (1, 100)(2, 106)(3, 110)(4, 113)(5, 117)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 103)(14, 102)(15, 131)(16, 99)(17, 127)(18, 101)(19, 129)(20, 130)(21, 128)(22, 135)(23, 137)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 139)(30, 140)(31, 112)(32, 142)(33, 109)(34, 111)(35, 141)(36, 114)(37, 116)(38, 121)(39, 120)(40, 118)(41, 143)(42, 144)(43, 124)(44, 122)(45, 132)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.778
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.781 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y1^-1), Y2^4, Y3^4, (Y3, Y2) ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 9, 57, 17, 65)(6, 54, 10, 58, 19, 67)(7, 55, 11, 59, 20, 68)(12, 60, 22, 70, 29, 77)(13, 61, 23, 71, 32, 80)(15, 63, 24, 72, 33, 81)(16, 64, 25, 73, 34, 82)(18, 66, 26, 74, 36, 84)(21, 69, 27, 75, 37, 85)(28, 76, 38, 86, 43, 91)(30, 78, 39, 87, 44, 92)(31, 79, 40, 88, 45, 93)(35, 83, 41, 89, 46, 94)(42, 90, 47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 109, 157, 124, 172, 114, 162)(101, 149, 110, 158, 125, 173, 115, 163)(103, 151, 111, 159, 126, 174, 117, 165)(105, 153, 119, 167, 134, 182, 122, 170)(107, 155, 120, 168, 135, 183, 123, 171)(112, 160, 127, 175, 138, 186, 131, 179)(113, 161, 128, 176, 139, 187, 132, 180)(116, 164, 129, 177, 140, 188, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 141, 189, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 109)(4, 112)(5, 113)(6, 114)(7, 97)(8, 119)(9, 121)(10, 122)(11, 98)(12, 124)(13, 127)(14, 128)(15, 99)(16, 103)(17, 130)(18, 131)(19, 132)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 107)(26, 137)(27, 106)(28, 138)(29, 139)(30, 108)(31, 111)(32, 141)(33, 110)(34, 116)(35, 117)(36, 142)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 126)(43, 144)(44, 125)(45, 129)(46, 133)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.782
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.782 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-3, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3, Y2), Y1^4, (Y3^-1, Y1^-1), Y3^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y2, (Y1^-1 * Y3^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 22, 70, 15, 63)(4, 52, 10, 58, 23, 71, 18, 66)(6, 54, 11, 59, 24, 72, 20, 68)(7, 55, 12, 60, 25, 73, 21, 69)(13, 61, 26, 74, 38, 86, 31, 79)(14, 62, 27, 75, 39, 87, 34, 82)(16, 64, 28, 76, 40, 88, 35, 83)(17, 65, 29, 77, 41, 89, 36, 84)(19, 67, 30, 78, 42, 90, 37, 85)(32, 80, 43, 91, 47, 95, 45, 93)(33, 81, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 103, 151, 112, 160, 128, 176, 113, 161, 129, 177, 115, 163, 100, 148, 110, 158, 102, 150)(98, 146, 105, 153, 122, 170, 108, 156, 124, 172, 139, 187, 125, 173, 140, 188, 126, 174, 106, 154, 123, 171, 107, 155)(101, 149, 111, 159, 127, 175, 117, 165, 131, 179, 141, 189, 132, 180, 142, 190, 133, 181, 114, 162, 130, 178, 116, 164)(104, 152, 118, 166, 134, 182, 121, 169, 136, 184, 143, 191, 137, 185, 144, 192, 138, 186, 119, 167, 135, 183, 120, 168)
	L = (1, 100)(2, 106)(3, 110)(4, 113)(5, 114)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 102)(14, 129)(15, 130)(16, 99)(17, 103)(18, 132)(19, 128)(20, 133)(21, 101)(22, 135)(23, 137)(24, 138)(25, 104)(26, 107)(27, 140)(28, 105)(29, 108)(30, 139)(31, 116)(32, 109)(33, 112)(34, 142)(35, 111)(36, 117)(37, 141)(38, 120)(39, 144)(40, 118)(41, 121)(42, 143)(43, 122)(44, 124)(45, 127)(46, 131)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.781
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.783 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2, Y1^-1), R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y3, Y1^-1), Y3^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 9, 57, 18, 66)(6, 54, 10, 58, 19, 67)(7, 55, 11, 59, 20, 68)(12, 60, 22, 70, 29, 77)(13, 61, 23, 71, 32, 80)(15, 63, 24, 72, 33, 81)(16, 64, 25, 73, 35, 83)(17, 65, 26, 74, 36, 84)(21, 69, 27, 75, 37, 85)(28, 76, 38, 86, 43, 91)(30, 78, 39, 87, 44, 92)(31, 79, 40, 88, 45, 93)(34, 82, 41, 89, 46, 94)(42, 90, 47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 112, 160, 124, 172, 109, 157)(101, 149, 110, 158, 125, 173, 115, 163)(103, 151, 117, 165, 126, 174, 111, 159)(105, 153, 121, 169, 134, 182, 119, 167)(107, 155, 123, 171, 135, 183, 120, 168)(113, 161, 127, 175, 138, 186, 130, 178)(114, 162, 131, 179, 139, 187, 128, 176)(116, 164, 133, 181, 140, 188, 129, 177)(122, 170, 136, 184, 143, 191, 137, 185)(132, 180, 141, 189, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 109)(4, 113)(5, 114)(6, 112)(7, 97)(8, 119)(9, 122)(10, 121)(11, 98)(12, 124)(13, 127)(14, 128)(15, 99)(16, 130)(17, 103)(18, 132)(19, 131)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 137)(26, 107)(27, 106)(28, 138)(29, 139)(30, 108)(31, 111)(32, 141)(33, 110)(34, 117)(35, 142)(36, 116)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 126)(43, 144)(44, 125)(45, 129)(46, 133)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.789
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.784 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y2, Y1^-1), (Y3, Y1^-1), (R * Y1)^2, Y3^4, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 9, 57, 17, 65)(6, 54, 10, 58, 19, 67)(7, 55, 11, 59, 20, 68)(12, 60, 22, 70, 29, 77)(13, 61, 23, 71, 32, 80)(15, 63, 24, 72, 33, 81)(16, 64, 25, 73, 34, 82)(18, 66, 26, 74, 36, 84)(21, 69, 27, 75, 37, 85)(28, 76, 38, 86, 43, 91)(30, 78, 39, 87, 44, 92)(31, 79, 40, 88, 45, 93)(35, 83, 41, 89, 46, 94)(42, 90, 47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 111, 159, 124, 172, 114, 162)(101, 149, 110, 158, 125, 173, 115, 163)(103, 151, 109, 157, 126, 174, 117, 165)(105, 153, 120, 168, 134, 182, 122, 170)(107, 155, 119, 167, 135, 183, 123, 171)(112, 160, 127, 175, 138, 186, 131, 179)(113, 161, 129, 177, 139, 187, 132, 180)(116, 164, 128, 176, 140, 188, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 141, 189, 144, 192, 142, 190)
	L = (1, 100)(2, 105)(3, 109)(4, 112)(5, 113)(6, 117)(7, 97)(8, 119)(9, 121)(10, 123)(11, 98)(12, 124)(13, 127)(14, 128)(15, 99)(16, 103)(17, 130)(18, 102)(19, 133)(20, 101)(21, 131)(22, 134)(23, 136)(24, 104)(25, 107)(26, 106)(27, 137)(28, 138)(29, 139)(30, 108)(31, 111)(32, 141)(33, 110)(34, 116)(35, 114)(36, 115)(37, 142)(38, 143)(39, 118)(40, 120)(41, 122)(42, 126)(43, 144)(44, 125)(45, 129)(46, 132)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.788
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.785 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3^2 * Y2^2, (Y2, Y1^-1), (R * Y3)^2, Y3^2 * Y2^-2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2)^4, Y3^-12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 9, 57, 17, 65)(6, 54, 10, 58, 19, 67)(7, 55, 11, 59, 20, 68)(12, 60, 21, 69, 26, 74)(13, 61, 22, 70, 28, 76)(15, 63, 23, 71, 30, 78)(16, 64, 24, 72, 32, 80)(18, 66, 25, 73, 34, 82)(27, 75, 35, 83, 40, 88)(29, 77, 36, 84, 42, 90)(31, 79, 37, 85, 43, 91)(33, 81, 38, 86, 44, 92)(39, 87, 45, 93, 47, 95)(41, 89, 46, 94, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 117, 165, 106, 154)(100, 148, 112, 160, 103, 151, 114, 162)(101, 149, 110, 158, 122, 170, 115, 163)(105, 153, 120, 168, 107, 155, 121, 169)(109, 157, 123, 171, 111, 159, 125, 173)(113, 161, 128, 176, 116, 164, 130, 178)(118, 166, 131, 179, 119, 167, 132, 180)(124, 172, 136, 184, 126, 174, 138, 186)(127, 175, 135, 183, 129, 177, 137, 185)(133, 181, 141, 189, 134, 182, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 109)(4, 108)(5, 113)(6, 111)(7, 97)(8, 118)(9, 117)(10, 119)(11, 98)(12, 103)(13, 102)(14, 124)(15, 99)(16, 127)(17, 122)(18, 129)(19, 126)(20, 101)(21, 107)(22, 106)(23, 104)(24, 133)(25, 134)(26, 116)(27, 135)(28, 115)(29, 137)(30, 110)(31, 114)(32, 139)(33, 112)(34, 140)(35, 141)(36, 142)(37, 121)(38, 120)(39, 125)(40, 143)(41, 123)(42, 144)(43, 130)(44, 128)(45, 132)(46, 131)(47, 138)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.790
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.786 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y1^-1), Y3^-3 * Y1, (R * Y1)^2, Y2^4, R * Y2 * R * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y1^4, (Y1 * Y3)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 10, 58, 23, 71, 18, 66)(6, 54, 9, 57, 24, 72, 19, 67)(7, 55, 12, 60, 25, 73, 20, 68)(13, 61, 26, 74, 38, 86, 32, 80)(14, 62, 29, 77, 39, 87, 34, 82)(16, 64, 30, 78, 40, 88, 35, 83)(17, 65, 27, 75, 41, 89, 36, 84)(21, 69, 28, 76, 42, 90, 37, 85)(31, 79, 43, 91, 47, 95, 45, 93)(33, 81, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 122, 170, 107, 155)(100, 148, 113, 161, 127, 175, 110, 158)(101, 149, 115, 163, 128, 176, 111, 159)(103, 151, 117, 165, 129, 177, 112, 160)(104, 152, 118, 166, 134, 182, 120, 168)(106, 154, 125, 173, 139, 187, 123, 171)(108, 156, 126, 174, 140, 188, 124, 172)(114, 162, 130, 178, 141, 189, 132, 180)(116, 164, 131, 179, 142, 190, 133, 181)(119, 167, 137, 185, 143, 191, 135, 183)(121, 169, 138, 186, 144, 192, 136, 184)
	L = (1, 100)(2, 106)(3, 110)(4, 108)(5, 114)(6, 113)(7, 97)(8, 119)(9, 123)(10, 121)(11, 125)(12, 98)(13, 127)(14, 126)(15, 130)(16, 99)(17, 124)(18, 103)(19, 132)(20, 101)(21, 102)(22, 135)(23, 116)(24, 137)(25, 104)(26, 139)(27, 138)(28, 105)(29, 136)(30, 107)(31, 140)(32, 141)(33, 109)(34, 112)(35, 111)(36, 117)(37, 115)(38, 143)(39, 131)(40, 118)(41, 133)(42, 120)(43, 144)(44, 122)(45, 129)(46, 128)(47, 142)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.787
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.787 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^3, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2 * Y3 * Y1 * Y3, Y2^-1 * Y3^4, Y1^2 * Y2 * Y1^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y2 * Y1^-2)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 22, 70, 6, 54, 11, 59, 29, 77, 14, 62, 3, 51, 9, 57, 21, 69, 5, 53)(4, 52, 16, 64, 28, 76, 38, 86, 19, 67, 31, 79, 44, 92, 23, 71, 13, 61, 12, 60, 35, 83, 18, 66)(7, 55, 25, 73, 30, 78, 20, 68, 24, 72, 10, 58, 32, 80, 39, 87, 15, 63, 34, 82, 43, 91, 26, 74)(17, 65, 33, 81, 46, 94, 45, 93, 27, 75, 36, 84, 47, 95, 42, 90, 37, 85, 40, 88, 48, 96, 41, 89)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 109, 157, 115, 163)(101, 149, 110, 158, 118, 166)(103, 151, 111, 159, 120, 168)(104, 152, 117, 165, 125, 173)(106, 154, 121, 169, 130, 178)(108, 156, 127, 175, 112, 160)(113, 161, 133, 181, 123, 171)(114, 162, 119, 167, 134, 182)(116, 164, 122, 170, 135, 183)(124, 172, 131, 179, 140, 188)(126, 174, 139, 187, 128, 176)(129, 177, 136, 184, 132, 180)(137, 185, 138, 186, 141, 189)(142, 190, 144, 192, 143, 191)
	L = (1, 100)(2, 106)(3, 109)(4, 113)(5, 116)(6, 115)(7, 97)(8, 124)(9, 121)(10, 129)(11, 130)(12, 98)(13, 133)(14, 122)(15, 99)(16, 107)(17, 111)(18, 118)(19, 123)(20, 137)(21, 131)(22, 135)(23, 101)(24, 102)(25, 136)(26, 138)(27, 103)(28, 142)(29, 140)(30, 104)(31, 105)(32, 125)(33, 127)(34, 132)(35, 144)(36, 108)(37, 120)(38, 110)(39, 141)(40, 112)(41, 134)(42, 114)(43, 117)(44, 143)(45, 119)(46, 139)(47, 126)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.786
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.788 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^4, Y3 * Y2^3, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y1^4, (Y3, Y2), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (Y2^-1 * Y3)^3, Y3^2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 12, 60, 27, 75, 19, 67)(6, 54, 24, 72, 28, 76, 25, 73)(7, 55, 10, 58, 29, 77, 22, 70)(9, 57, 30, 78, 21, 69, 33, 81)(11, 59, 37, 85, 23, 71, 38, 86)(14, 62, 31, 79, 44, 92, 39, 87)(15, 63, 32, 80, 45, 93, 40, 88)(17, 65, 34, 82, 46, 94, 42, 90)(18, 66, 35, 83, 47, 95, 43, 91)(20, 68, 36, 84, 48, 96, 41, 89)(97, 145, 99, 147, 110, 158, 103, 151, 113, 161, 134, 182, 114, 162, 129, 177, 116, 164, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 127, 175, 108, 156, 130, 178, 120, 168, 131, 179, 109, 157, 132, 180, 106, 154, 128, 176, 107, 155)(101, 149, 117, 165, 135, 183, 115, 163, 138, 186, 121, 169, 139, 187, 112, 160, 137, 185, 118, 166, 136, 184, 119, 167)(104, 152, 122, 170, 140, 188, 125, 173, 142, 190, 133, 181, 143, 191, 126, 174, 144, 192, 123, 171, 141, 189, 124, 172)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 118)(6, 116)(7, 97)(8, 123)(9, 128)(10, 131)(11, 132)(12, 98)(13, 130)(14, 102)(15, 129)(16, 138)(17, 99)(18, 103)(19, 101)(20, 134)(21, 136)(22, 139)(23, 137)(24, 127)(25, 135)(26, 141)(27, 143)(28, 144)(29, 104)(30, 142)(31, 107)(32, 109)(33, 113)(34, 105)(35, 108)(36, 120)(37, 140)(38, 110)(39, 119)(40, 112)(41, 121)(42, 117)(43, 115)(44, 124)(45, 126)(46, 122)(47, 125)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.784
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.789 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-3, Y3^4, (R * Y1)^2, Y1^2 * Y3^-2, (R * Y3)^2, Y3^-2 * Y1^-2, (R * Y2)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2^-2 * Y1 * Y3 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y2^-1, (Y3 * Y2^-1)^3, Y2 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 16, 64)(4, 52, 18, 66, 7, 55, 19, 67)(6, 54, 23, 71, 26, 74, 24, 72)(9, 57, 27, 75, 21, 69, 30, 78)(10, 58, 32, 80, 12, 60, 33, 81)(11, 59, 35, 83, 22, 70, 36, 84)(14, 62, 28, 76, 20, 68, 34, 82)(15, 63, 29, 77, 17, 65, 31, 79)(37, 85, 43, 91, 41, 89, 47, 95)(38, 86, 44, 92, 40, 88, 46, 94)(39, 87, 45, 93, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 103, 151, 113, 161, 122, 170, 104, 152, 121, 169, 116, 164, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 124, 172, 108, 156, 127, 175, 118, 166, 101, 149, 117, 165, 130, 178, 106, 154, 125, 173, 107, 155)(109, 157, 133, 181, 115, 163, 136, 184, 120, 168, 138, 186, 112, 160, 137, 185, 114, 162, 134, 182, 119, 167, 135, 183)(123, 171, 139, 187, 129, 177, 142, 190, 132, 180, 144, 192, 126, 174, 143, 191, 128, 176, 140, 188, 131, 179, 141, 189)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 125)(10, 101)(11, 130)(12, 98)(13, 134)(14, 102)(15, 121)(16, 136)(17, 99)(18, 138)(19, 135)(20, 122)(21, 127)(22, 124)(23, 137)(24, 133)(25, 113)(26, 110)(27, 140)(28, 107)(29, 117)(30, 142)(31, 105)(32, 144)(33, 141)(34, 118)(35, 143)(36, 139)(37, 119)(38, 112)(39, 114)(40, 109)(41, 120)(42, 115)(43, 131)(44, 126)(45, 128)(46, 123)(47, 132)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.783
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.790 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), Y2^-3 * Y3^-1, (R * Y1)^2, Y3^4, (R * Y3)^2, Y1^4, (R * Y2)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 9, 57)(4, 52, 17, 65, 23, 71, 10, 58)(6, 54, 20, 68, 24, 72, 11, 59)(7, 55, 21, 69, 25, 73, 12, 60)(14, 62, 26, 74, 38, 86, 31, 79)(15, 63, 27, 75, 39, 87, 32, 80)(16, 64, 28, 76, 40, 88, 33, 81)(18, 66, 29, 77, 41, 89, 36, 84)(19, 67, 30, 78, 42, 90, 37, 85)(34, 82, 45, 93, 47, 95, 43, 91)(35, 83, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 103, 151, 112, 160, 130, 178, 114, 162, 131, 179, 115, 163, 100, 148, 111, 159, 102, 150)(98, 146, 105, 153, 122, 170, 108, 156, 124, 172, 139, 187, 125, 173, 140, 188, 126, 174, 106, 154, 123, 171, 107, 155)(101, 149, 109, 157, 127, 175, 117, 165, 129, 177, 141, 189, 132, 180, 142, 190, 133, 181, 113, 161, 128, 176, 116, 164)(104, 152, 118, 166, 134, 182, 121, 169, 136, 184, 143, 191, 137, 185, 144, 192, 138, 186, 119, 167, 135, 183, 120, 168)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 113)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 128)(14, 102)(15, 131)(16, 99)(17, 132)(18, 103)(19, 130)(20, 133)(21, 101)(22, 135)(23, 137)(24, 138)(25, 104)(26, 107)(27, 140)(28, 105)(29, 108)(30, 139)(31, 116)(32, 142)(33, 109)(34, 110)(35, 112)(36, 117)(37, 141)(38, 120)(39, 144)(40, 118)(41, 121)(42, 143)(43, 122)(44, 124)(45, 127)(46, 129)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.785
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.791 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^3, (Y2, Y1^-1), (R * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y2^4, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3, (Y3 * Y2 * Y1^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 14, 62)(6, 54, 9, 57, 17, 65)(8, 56, 20, 68, 21, 69)(10, 58, 18, 66, 24, 72)(11, 59, 25, 73, 26, 74)(15, 63, 29, 77, 31, 79)(16, 64, 32, 80, 33, 81)(19, 67, 30, 78, 36, 84)(22, 70, 37, 85, 39, 87)(23, 71, 40, 88, 41, 89)(27, 75, 38, 86, 44, 92)(28, 76, 34, 82, 45, 93)(35, 83, 43, 91, 47, 95)(42, 90, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 102, 150)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 107, 155, 119, 167, 111, 159)(101, 149, 108, 156, 120, 168, 113, 161)(104, 152, 115, 163, 131, 179, 118, 166)(109, 157, 121, 169, 136, 184, 125, 173)(110, 158, 122, 170, 137, 185, 127, 175)(112, 160, 123, 171, 138, 186, 130, 178)(116, 164, 126, 174, 139, 187, 133, 181)(117, 165, 132, 180, 143, 191, 135, 183)(124, 172, 129, 177, 140, 188, 142, 190)(128, 176, 134, 182, 144, 192, 141, 189)
	L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 112)(6, 111)(7, 115)(8, 98)(9, 118)(10, 119)(11, 99)(12, 123)(13, 124)(14, 126)(15, 102)(16, 101)(17, 130)(18, 131)(19, 103)(20, 127)(21, 134)(22, 105)(23, 106)(24, 138)(25, 129)(26, 139)(27, 108)(28, 109)(29, 142)(30, 110)(31, 116)(32, 135)(33, 121)(34, 113)(35, 114)(36, 144)(37, 137)(38, 117)(39, 128)(40, 140)(41, 133)(42, 120)(43, 122)(44, 136)(45, 143)(46, 125)(47, 141)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.801
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.792 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^3, (Y1^-1, Y2), (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 14, 62)(6, 54, 9, 57, 17, 65)(8, 56, 20, 68, 21, 69)(10, 58, 18, 66, 24, 72)(11, 59, 25, 73, 26, 74)(15, 63, 29, 77, 31, 79)(16, 64, 32, 80, 33, 81)(19, 67, 36, 84, 37, 85)(22, 70, 30, 78, 39, 87)(23, 71, 40, 88, 41, 89)(27, 75, 44, 92, 28, 76)(34, 82, 38, 86, 46, 94)(35, 83, 45, 93, 47, 95)(42, 90, 48, 96, 43, 91)(97, 145, 99, 147, 106, 154, 102, 150)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 107, 155, 119, 167, 111, 159)(101, 149, 108, 156, 120, 168, 113, 161)(104, 152, 115, 163, 131, 179, 118, 166)(109, 157, 121, 169, 136, 184, 125, 173)(110, 158, 122, 170, 137, 185, 127, 175)(112, 160, 123, 171, 138, 186, 130, 178)(116, 164, 132, 180, 141, 189, 126, 174)(117, 165, 133, 181, 143, 191, 135, 183)(124, 172, 139, 187, 142, 190, 129, 177)(128, 176, 140, 188, 144, 192, 134, 182)
	L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 112)(6, 111)(7, 115)(8, 98)(9, 118)(10, 119)(11, 99)(12, 123)(13, 124)(14, 126)(15, 102)(16, 101)(17, 130)(18, 131)(19, 103)(20, 122)(21, 134)(22, 105)(23, 106)(24, 138)(25, 139)(26, 116)(27, 108)(28, 109)(29, 129)(30, 110)(31, 141)(32, 133)(33, 125)(34, 113)(35, 114)(36, 137)(37, 128)(38, 117)(39, 144)(40, 142)(41, 132)(42, 120)(43, 121)(44, 143)(45, 127)(46, 136)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.802
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.793 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^3, Y2^4, Y2 * Y3 * Y2^-1 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, (Y1^-1 * Y2^-1)^3, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 13, 61)(4, 52, 14, 62, 15, 63)(6, 54, 20, 68, 21, 69)(7, 55, 22, 70, 25, 73)(8, 56, 26, 74, 27, 75)(9, 57, 29, 77, 30, 78)(11, 59, 23, 71, 35, 83)(12, 60, 24, 72, 36, 84)(16, 64, 28, 76, 39, 87)(17, 65, 40, 88, 33, 81)(18, 66, 41, 89, 37, 85)(19, 67, 42, 90, 31, 79)(32, 80, 47, 95, 45, 93)(34, 82, 46, 94, 43, 91)(38, 86, 48, 96, 44, 92)(97, 145, 99, 147, 107, 155, 102, 150)(98, 146, 103, 151, 119, 167, 105, 153)(100, 148, 108, 156, 130, 178, 112, 160)(101, 149, 113, 161, 131, 179, 115, 163)(104, 152, 120, 168, 140, 188, 124, 172)(106, 154, 127, 175, 116, 164, 129, 177)(109, 157, 118, 166, 117, 165, 125, 173)(110, 158, 128, 176, 142, 190, 133, 181)(111, 159, 122, 170, 139, 187, 134, 182)(114, 162, 132, 180, 143, 191, 135, 183)(121, 169, 136, 184, 126, 174, 138, 186)(123, 171, 137, 185, 144, 192, 141, 189)
	L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 114)(6, 112)(7, 120)(8, 98)(9, 124)(10, 128)(11, 130)(12, 99)(13, 122)(14, 129)(15, 125)(16, 102)(17, 132)(18, 101)(19, 135)(20, 133)(21, 134)(22, 139)(23, 140)(24, 103)(25, 137)(26, 109)(27, 138)(28, 105)(29, 111)(30, 141)(31, 142)(32, 106)(33, 110)(34, 107)(35, 143)(36, 113)(37, 116)(38, 117)(39, 115)(40, 144)(41, 121)(42, 123)(43, 118)(44, 119)(45, 126)(46, 127)(47, 131)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.800
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.794 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^3, Y2 * Y3 * Y2^-1 * Y3, (R * Y1)^2, Y2^4, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y1 * Y2^-1)^3, Y2^-1 * Y1^-1 * Y2 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 13, 61)(4, 52, 14, 62, 15, 63)(6, 54, 20, 68, 21, 69)(7, 55, 22, 70, 25, 73)(8, 56, 26, 74, 27, 75)(9, 57, 29, 77, 30, 78)(11, 59, 23, 71, 35, 83)(12, 60, 24, 72, 36, 84)(16, 64, 28, 76, 39, 87)(17, 65, 40, 88, 31, 79)(18, 66, 41, 89, 32, 80)(19, 67, 42, 90, 33, 81)(34, 82, 46, 94, 45, 93)(37, 85, 48, 96, 43, 91)(38, 86, 47, 95, 44, 92)(97, 145, 99, 147, 107, 155, 102, 150)(98, 146, 103, 151, 119, 167, 105, 153)(100, 148, 108, 156, 130, 178, 112, 160)(101, 149, 113, 161, 131, 179, 115, 163)(104, 152, 120, 168, 139, 187, 124, 172)(106, 154, 127, 175, 116, 164, 129, 177)(109, 157, 125, 173, 117, 165, 118, 166)(110, 158, 128, 176, 142, 190, 134, 182)(111, 159, 133, 181, 141, 189, 122, 170)(114, 162, 132, 180, 143, 191, 135, 183)(121, 169, 138, 186, 126, 174, 136, 184)(123, 171, 140, 188, 144, 192, 137, 185)
	L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 114)(6, 112)(7, 120)(8, 98)(9, 124)(10, 128)(11, 130)(12, 99)(13, 133)(14, 129)(15, 118)(16, 102)(17, 132)(18, 101)(19, 135)(20, 134)(21, 122)(22, 111)(23, 139)(24, 103)(25, 140)(26, 117)(27, 136)(28, 105)(29, 141)(30, 137)(31, 142)(32, 106)(33, 110)(34, 107)(35, 143)(36, 113)(37, 109)(38, 116)(39, 115)(40, 123)(41, 126)(42, 144)(43, 119)(44, 121)(45, 125)(46, 127)(47, 131)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.799
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 6^16, 8^12 ]

E27.795 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^2 * Y1^2, Y2^2 * Y1^-2, (Y2, Y1^-1), Y2^4, (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^-1 * Y1^2 * Y3 * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59)(4, 52, 15, 63, 23, 71, 16, 64)(7, 55, 21, 69, 24, 72, 22, 70)(10, 58, 27, 75, 18, 66, 28, 76)(12, 60, 31, 79, 19, 67, 32, 80)(13, 61, 33, 81, 17, 65, 34, 82)(14, 62, 35, 83, 20, 68, 36, 84)(25, 73, 41, 89, 29, 77, 42, 90)(26, 74, 43, 91, 30, 78, 44, 92)(37, 85, 39, 87, 38, 86, 40, 88)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 109, 157, 119, 167, 113, 161)(103, 151, 110, 158, 120, 168, 116, 164)(106, 154, 121, 169, 114, 162, 125, 173)(108, 156, 122, 170, 115, 163, 126, 174)(111, 159, 129, 177, 112, 160, 130, 178)(117, 165, 131, 179, 118, 166, 132, 180)(123, 171, 137, 185, 124, 172, 138, 186)(127, 175, 139, 187, 128, 176, 140, 188)(133, 181, 141, 189, 134, 182, 142, 190)(135, 183, 143, 191, 136, 184, 144, 192)
	L = (1, 100)(2, 106)(3, 109)(4, 103)(5, 114)(6, 113)(7, 97)(8, 119)(9, 121)(10, 108)(11, 125)(12, 98)(13, 110)(14, 99)(15, 127)(16, 128)(17, 116)(18, 115)(19, 101)(20, 102)(21, 135)(22, 136)(23, 120)(24, 104)(25, 122)(26, 105)(27, 118)(28, 117)(29, 126)(30, 107)(31, 133)(32, 134)(33, 139)(34, 140)(35, 143)(36, 144)(37, 111)(38, 112)(39, 124)(40, 123)(41, 132)(42, 131)(43, 141)(44, 142)(45, 129)(46, 130)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.797
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.796 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2^-2, Y1^2 * Y2^2, (Y1^-1, Y2), Y1^4, (R * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y2^-1 * Y3^3 * Y2^-1, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59)(4, 52, 15, 63, 24, 72, 17, 65)(7, 55, 22, 70, 16, 64, 23, 71)(10, 58, 27, 75, 19, 67, 28, 76)(12, 60, 31, 79, 20, 68, 32, 80)(13, 61, 33, 81, 18, 66, 34, 82)(14, 62, 35, 83, 21, 69, 36, 84)(25, 73, 41, 89, 29, 77, 42, 90)(26, 74, 43, 91, 30, 78, 44, 92)(37, 85, 40, 88, 38, 86, 39, 87)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 109, 157, 120, 168, 114, 162)(103, 151, 110, 158, 112, 160, 117, 165)(106, 154, 121, 169, 115, 163, 125, 173)(108, 156, 122, 170, 116, 164, 126, 174)(111, 159, 129, 177, 113, 161, 130, 178)(118, 166, 131, 179, 119, 167, 132, 180)(123, 171, 137, 185, 124, 172, 138, 186)(127, 175, 139, 187, 128, 176, 140, 188)(133, 181, 141, 189, 134, 182, 142, 190)(135, 183, 143, 191, 136, 184, 144, 192)
	L = (1, 100)(2, 106)(3, 109)(4, 112)(5, 115)(6, 114)(7, 97)(8, 120)(9, 121)(10, 116)(11, 125)(12, 98)(13, 117)(14, 99)(15, 127)(16, 104)(17, 128)(18, 110)(19, 108)(20, 101)(21, 102)(22, 135)(23, 136)(24, 103)(25, 126)(26, 105)(27, 119)(28, 118)(29, 122)(30, 107)(31, 134)(32, 133)(33, 139)(34, 140)(35, 143)(36, 144)(37, 111)(38, 113)(39, 123)(40, 124)(41, 132)(42, 131)(43, 142)(44, 141)(45, 129)(46, 130)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.798
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.797 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y3^3, (Y3^-1, Y1), (Y1^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3 * Y1^4, Y3^-1 * Y1^-1 * Y2 * Y3 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y1^-2 * Y3)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 22, 70, 7, 55, 12, 60, 29, 77, 18, 66, 4, 52, 10, 58, 21, 69, 5, 53)(3, 51, 13, 61, 39, 87, 41, 89, 16, 64, 40, 88, 45, 93, 38, 86, 14, 62, 33, 81, 19, 67, 15, 63)(6, 54, 23, 71, 26, 74, 32, 80, 25, 73, 44, 92, 47, 95, 30, 78, 24, 72, 34, 82, 31, 79, 9, 57)(11, 59, 35, 83, 37, 85, 27, 75, 36, 84, 17, 65, 42, 90, 46, 94, 20, 68, 43, 91, 48, 96, 28, 76)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 115, 163)(101, 149, 116, 164, 109, 157)(103, 151, 122, 170, 123, 171)(104, 152, 124, 172, 112, 160)(106, 154, 129, 177, 130, 178)(108, 156, 133, 181, 134, 182)(110, 158, 131, 179, 127, 175)(111, 159, 132, 180, 119, 167)(114, 162, 140, 188, 138, 186)(117, 165, 120, 168, 139, 187)(118, 166, 137, 185, 128, 176)(121, 169, 135, 183, 142, 190)(125, 173, 141, 189, 143, 191)(126, 174, 136, 184, 144, 192)
	L = (1, 100)(2, 106)(3, 110)(4, 103)(5, 114)(6, 120)(7, 97)(8, 117)(9, 126)(10, 108)(11, 116)(12, 98)(13, 129)(14, 112)(15, 134)(16, 99)(17, 131)(18, 118)(19, 141)(20, 132)(21, 125)(22, 101)(23, 130)(24, 121)(25, 102)(26, 127)(27, 124)(28, 142)(29, 104)(30, 128)(31, 143)(32, 105)(33, 136)(34, 140)(35, 139)(36, 107)(37, 144)(38, 137)(39, 115)(40, 109)(41, 111)(42, 133)(43, 113)(44, 119)(45, 135)(46, 123)(47, 122)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.795
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.798 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1 * Y1, Y2^3, (Y2 * Y1)^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^2, R * Y2 * Y3 * R * Y2^-1, Y3^-1 * Y2 * Y3^2 * Y2, Y3^6, (Y3^-1 * Y2^-1)^3, Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^6, Y1 * Y2^-1 * Y3^2 * Y2^-1 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 9, 57, 16, 64, 28, 76, 39, 87, 44, 92, 25, 73, 19, 67, 7, 55, 5, 53)(3, 51, 11, 59, 12, 60, 27, 75, 17, 65, 41, 89, 42, 90, 47, 95, 38, 86, 36, 84, 14, 62, 13, 61)(6, 54, 20, 68, 21, 69, 29, 77, 34, 82, 48, 96, 46, 94, 45, 93, 23, 71, 26, 74, 22, 70, 8, 56)(10, 58, 30, 78, 31, 79, 40, 88, 35, 83, 37, 85, 43, 91, 33, 81, 18, 66, 24, 72, 32, 80, 15, 63)(97, 145, 99, 147, 102, 150)(98, 146, 104, 152, 106, 154)(100, 148, 111, 159, 113, 161)(101, 149, 114, 162, 107, 155)(103, 151, 119, 167, 120, 168)(105, 153, 123, 171, 125, 173)(108, 156, 129, 177, 130, 178)(109, 157, 131, 179, 116, 164)(110, 158, 121, 169, 133, 181)(112, 160, 117, 165, 136, 184)(115, 163, 132, 180, 122, 170)(118, 166, 134, 182, 126, 174)(124, 172, 127, 175, 143, 191)(128, 176, 141, 189, 137, 185)(135, 183, 138, 186, 142, 190)(139, 187, 140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 98)(6, 117)(7, 97)(8, 116)(9, 124)(10, 127)(11, 123)(12, 113)(13, 107)(14, 99)(15, 126)(16, 135)(17, 138)(18, 128)(19, 101)(20, 125)(21, 130)(22, 102)(23, 118)(24, 111)(25, 103)(26, 104)(27, 137)(28, 140)(29, 144)(30, 136)(31, 131)(32, 106)(33, 120)(34, 142)(35, 139)(36, 109)(37, 129)(38, 110)(39, 121)(40, 133)(41, 143)(42, 134)(43, 114)(44, 115)(45, 122)(46, 119)(47, 132)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.796
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.799 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y2^-3 * Y1^-1, (Y2, Y1^-1), Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3)^2, (Y3 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 18, 66, 13, 61)(4, 52, 9, 57, 19, 67, 15, 63)(6, 54, 10, 58, 20, 68, 11, 59)(12, 60, 21, 69, 33, 81, 27, 75)(14, 62, 22, 70, 34, 82, 31, 79)(16, 64, 23, 71, 35, 83, 29, 77)(17, 65, 24, 72, 36, 84, 25, 73)(26, 74, 37, 85, 45, 93, 44, 92)(28, 76, 38, 86, 46, 94, 43, 91)(30, 78, 39, 87, 47, 95, 42, 90)(32, 80, 40, 88, 48, 96, 41, 89)(97, 145, 99, 147, 107, 155, 101, 149, 109, 157, 116, 164, 103, 151, 114, 162, 106, 154, 98, 146, 104, 152, 102, 150)(100, 148, 110, 158, 125, 173, 111, 159, 127, 175, 131, 179, 115, 163, 130, 178, 119, 167, 105, 153, 118, 166, 112, 160)(108, 156, 122, 170, 139, 187, 123, 171, 140, 188, 142, 190, 129, 177, 141, 189, 134, 182, 117, 165, 133, 181, 124, 172)(113, 161, 128, 176, 138, 186, 121, 169, 137, 185, 143, 191, 132, 180, 144, 192, 135, 183, 120, 168, 136, 184, 126, 174)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 111)(6, 113)(7, 115)(8, 117)(9, 98)(10, 120)(11, 121)(12, 99)(13, 123)(14, 126)(15, 101)(16, 122)(17, 102)(18, 129)(19, 103)(20, 132)(21, 104)(22, 135)(23, 133)(24, 106)(25, 107)(26, 112)(27, 109)(28, 137)(29, 140)(30, 110)(31, 138)(32, 134)(33, 114)(34, 143)(35, 141)(36, 116)(37, 119)(38, 128)(39, 118)(40, 142)(41, 124)(42, 127)(43, 144)(44, 125)(45, 131)(46, 136)(47, 130)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.794
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.800 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-3 * Y1, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^4, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y2 * Y3)^2, (Y3 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 18, 66, 12, 60)(4, 52, 9, 57, 19, 67, 14, 62)(6, 54, 10, 58, 20, 68, 16, 64)(11, 59, 21, 69, 33, 81, 26, 74)(13, 61, 22, 70, 34, 82, 29, 77)(15, 63, 23, 71, 35, 83, 30, 78)(17, 65, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 45, 93, 41, 89)(27, 75, 38, 86, 46, 94, 42, 90)(28, 76, 39, 87, 47, 95, 43, 91)(32, 80, 40, 88, 48, 96, 44, 92)(97, 145, 99, 147, 106, 154, 98, 146, 104, 152, 116, 164, 103, 151, 114, 162, 112, 160, 101, 149, 108, 156, 102, 150)(100, 148, 109, 157, 119, 167, 105, 153, 118, 166, 131, 179, 115, 163, 130, 178, 126, 174, 110, 158, 125, 173, 111, 159)(107, 155, 121, 169, 134, 182, 117, 165, 133, 181, 142, 190, 129, 177, 141, 189, 138, 186, 122, 170, 137, 185, 123, 171)(113, 161, 128, 176, 135, 183, 120, 168, 136, 184, 143, 191, 132, 180, 144, 192, 139, 187, 127, 175, 140, 188, 124, 172)
	L = (1, 100)(2, 105)(3, 107)(4, 97)(5, 110)(6, 113)(7, 115)(8, 117)(9, 98)(10, 120)(11, 99)(12, 122)(13, 124)(14, 101)(15, 121)(16, 127)(17, 102)(18, 129)(19, 103)(20, 132)(21, 104)(22, 135)(23, 133)(24, 106)(25, 111)(26, 108)(27, 136)(28, 109)(29, 139)(30, 137)(31, 112)(32, 138)(33, 114)(34, 143)(35, 141)(36, 116)(37, 119)(38, 144)(39, 118)(40, 123)(41, 126)(42, 128)(43, 125)(44, 142)(45, 131)(46, 140)(47, 130)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.793
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.801 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y1^4, Y1 * Y2^3 * Y3, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y3, Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2, (R * Y2 * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * R * Y2 * Y1 * Y2^-1 * R * Y2^-1 * Y1^-1, (Y2 * Y1^-1 * Y2^-1 * Y3)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 24, 72, 14, 62)(4, 52, 9, 57, 25, 73, 16, 64)(6, 54, 20, 68, 26, 74, 22, 70)(8, 56, 27, 75, 18, 66, 29, 77)(10, 58, 31, 79, 19, 67, 33, 81)(12, 60, 21, 69, 30, 78, 36, 84)(13, 61, 23, 71, 46, 94, 37, 85)(15, 63, 28, 76, 34, 82, 41, 89)(17, 65, 32, 80, 42, 90, 39, 87)(35, 83, 43, 91, 40, 88, 45, 93)(38, 86, 44, 92, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 112, 160, 133, 181, 122, 170, 103, 151, 120, 168, 126, 174, 105, 153, 119, 167, 102, 150)(98, 146, 104, 152, 113, 161, 100, 148, 111, 159, 115, 163, 101, 149, 114, 162, 138, 186, 121, 169, 130, 178, 106, 154)(107, 155, 128, 176, 134, 182, 109, 157, 129, 177, 136, 184, 110, 158, 135, 183, 144, 192, 142, 190, 127, 175, 131, 179)(116, 164, 139, 187, 125, 173, 117, 165, 140, 188, 137, 185, 118, 166, 141, 189, 123, 171, 132, 180, 143, 191, 124, 172)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 112)(6, 117)(7, 121)(8, 124)(9, 98)(10, 128)(11, 119)(12, 118)(13, 99)(14, 133)(15, 125)(16, 101)(17, 129)(18, 137)(19, 135)(20, 126)(21, 102)(22, 108)(23, 107)(24, 142)(25, 103)(26, 132)(27, 130)(28, 104)(29, 111)(30, 116)(31, 138)(32, 106)(33, 113)(34, 123)(35, 140)(36, 122)(37, 110)(38, 141)(39, 115)(40, 143)(41, 114)(42, 127)(43, 144)(44, 131)(45, 134)(46, 120)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.791
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.802 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y2^2 * Y3 * Y1^-1 * Y2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2^-1, (Y2^-1 * Y1^-1 * R)^2, Y1 * Y2 * Y1^-1 * Y2 * Y3 * Y2, Y2 * R * Y3 * Y2^-1 * Y1 * R * Y2, Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 24, 72, 14, 62)(4, 52, 9, 57, 25, 73, 16, 64)(6, 54, 20, 68, 26, 74, 22, 70)(8, 56, 27, 75, 18, 66, 30, 78)(10, 58, 32, 80, 19, 67, 34, 82)(12, 60, 36, 84, 41, 89, 21, 69)(13, 61, 31, 79, 46, 94, 23, 71)(15, 63, 29, 77, 42, 90, 40, 88)(17, 65, 33, 81, 28, 76, 38, 86)(35, 83, 45, 93, 39, 87, 43, 91)(37, 85, 48, 96, 47, 95, 44, 92)(97, 145, 99, 147, 108, 156, 105, 153, 127, 175, 122, 170, 103, 151, 120, 168, 137, 185, 112, 160, 119, 167, 102, 150)(98, 146, 104, 152, 124, 172, 121, 169, 138, 186, 115, 163, 101, 149, 114, 162, 113, 161, 100, 148, 111, 159, 106, 154)(107, 155, 129, 177, 143, 191, 142, 190, 128, 176, 135, 183, 110, 158, 134, 182, 133, 181, 109, 157, 130, 178, 131, 179)(116, 164, 139, 187, 123, 171, 132, 180, 144, 192, 136, 184, 118, 166, 141, 189, 126, 174, 117, 165, 140, 188, 125, 173)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 112)(6, 117)(7, 121)(8, 125)(9, 98)(10, 129)(11, 127)(12, 116)(13, 99)(14, 119)(15, 126)(16, 101)(17, 130)(18, 136)(19, 134)(20, 108)(21, 102)(22, 137)(23, 110)(24, 142)(25, 103)(26, 132)(27, 138)(28, 128)(29, 104)(30, 111)(31, 107)(32, 124)(33, 106)(34, 113)(35, 144)(36, 122)(37, 139)(38, 115)(39, 140)(40, 114)(41, 118)(42, 123)(43, 133)(44, 135)(45, 143)(46, 120)(47, 141)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.792
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.803 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 6, 12})
Quotient :: edge^2
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1 * Y3^-1 * Y2^-1, (Y3 * Y1^-1)^2, Y3^2 * Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1 * Y2 * Y3^2 * Y2^-1, Y2 * Y1^2 * Y2 * Y1^-1, Y2^6, (Y2 * Y1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 13, 61, 34, 82, 31, 79, 48, 96, 29, 77, 47, 95, 40, 88, 46, 94, 22, 70, 7, 55)(2, 50, 10, 58, 33, 81, 39, 87, 14, 62, 37, 85, 21, 69, 44, 92, 45, 93, 27, 75, 6, 54, 12, 60)(3, 51, 15, 63, 19, 67, 43, 91, 35, 83, 42, 90, 26, 74, 36, 84, 24, 72, 28, 76, 9, 57, 17, 65)(5, 53, 20, 68, 25, 73, 18, 66, 11, 59, 32, 80, 8, 56, 30, 78, 38, 86, 41, 89, 16, 64, 23, 71)(97, 98, 104, 125, 117, 101)(99, 109, 107, 122, 136, 112)(100, 111, 133, 143, 132, 108)(102, 120, 134, 110, 115, 121)(103, 116, 139, 144, 126, 124)(105, 129, 127, 131, 141, 118)(106, 113, 119, 140, 138, 128)(114, 130, 135, 137, 142, 123)(145, 147, 158, 173, 170, 150)(146, 153, 160, 165, 179, 155)(148, 162, 186, 191, 185, 161)(149, 163, 175, 152, 168, 166)(151, 156, 176, 192, 181, 167)(154, 178, 187, 188, 190, 172)(157, 177, 182, 184, 189, 169)(159, 164, 171, 180, 174, 183)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.806
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.804 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 6, 6, 12})
Quotient :: edge^2
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1^-1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1 * Y2)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, Y2^6, Y1^-1 * Y3 * Y2^-1 * Y1^-2 * Y3 * Y1^-2, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3, (Y1 * Y3)^12 ]
Map:: non-degenerate
	R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 21, 69)(11, 59, 22, 70)(13, 61, 26, 74)(14, 62, 27, 75)(15, 63, 29, 77)(18, 66, 34, 82)(19, 67, 35, 83)(20, 68, 36, 84)(23, 71, 32, 80)(24, 72, 37, 85)(25, 73, 31, 79)(28, 76, 39, 87)(30, 78, 41, 89)(33, 81, 43, 91)(38, 86, 45, 93)(40, 88, 46, 94)(42, 90, 47, 95)(44, 92, 48, 96)(97, 98, 101, 107, 106, 100)(99, 103, 111, 118, 114, 104)(102, 109, 121, 117, 124, 110)(105, 115, 120, 108, 119, 116)(112, 126, 123, 130, 138, 127)(113, 128, 136, 125, 131, 129)(122, 134, 133, 135, 140, 132)(137, 141, 142, 143, 144, 139)(145, 146, 149, 155, 154, 148)(147, 151, 159, 166, 162, 152)(150, 157, 169, 165, 172, 158)(153, 163, 168, 156, 167, 164)(160, 174, 171, 178, 186, 175)(161, 176, 184, 173, 179, 177)(170, 182, 181, 183, 188, 180)(185, 189, 190, 191, 192, 187)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 48^4 ), ( 48^6 ) }
Outer automorphisms :: reflexible
Dual of E27.805
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.805 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 6, 12})
Quotient :: loop^2
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1 * Y3^-1 * Y2^-1, (Y3 * Y1^-1)^2, Y3^2 * Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1 * Y2 * Y3^2 * Y2^-1, Y2 * Y1^2 * Y2 * Y1^-1, Y2^6, (Y2 * Y1)^6 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 34, 82, 130, 178, 31, 79, 127, 175, 48, 96, 144, 192, 29, 77, 125, 173, 47, 95, 143, 191, 40, 88, 136, 184, 46, 94, 142, 190, 22, 70, 118, 166, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 33, 81, 129, 177, 39, 87, 135, 183, 14, 62, 110, 158, 37, 85, 133, 181, 21, 69, 117, 165, 44, 92, 140, 188, 45, 93, 141, 189, 27, 75, 123, 171, 6, 54, 102, 150, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 19, 67, 115, 163, 43, 91, 139, 187, 35, 83, 131, 179, 42, 90, 138, 186, 26, 74, 122, 170, 36, 84, 132, 180, 24, 72, 120, 168, 28, 76, 124, 172, 9, 57, 105, 153, 17, 65, 113, 161)(5, 53, 101, 149, 20, 68, 116, 164, 25, 73, 121, 169, 18, 66, 114, 162, 11, 59, 107, 155, 32, 80, 128, 176, 8, 56, 104, 152, 30, 78, 126, 174, 38, 86, 134, 182, 41, 89, 137, 185, 16, 64, 112, 160, 23, 71, 119, 167)
	L = (1, 50)(2, 56)(3, 61)(4, 63)(5, 49)(6, 72)(7, 68)(8, 77)(9, 81)(10, 65)(11, 74)(12, 52)(13, 59)(14, 67)(15, 85)(16, 51)(17, 71)(18, 82)(19, 73)(20, 91)(21, 53)(22, 57)(23, 92)(24, 86)(25, 54)(26, 88)(27, 66)(28, 55)(29, 69)(30, 76)(31, 83)(32, 58)(33, 79)(34, 87)(35, 93)(36, 60)(37, 95)(38, 62)(39, 89)(40, 64)(41, 94)(42, 80)(43, 96)(44, 90)(45, 70)(46, 75)(47, 84)(48, 78)(97, 147)(98, 153)(99, 158)(100, 162)(101, 163)(102, 145)(103, 156)(104, 168)(105, 160)(106, 178)(107, 146)(108, 176)(109, 177)(110, 173)(111, 164)(112, 165)(113, 148)(114, 186)(115, 175)(116, 171)(117, 179)(118, 149)(119, 151)(120, 166)(121, 157)(122, 150)(123, 180)(124, 154)(125, 170)(126, 183)(127, 152)(128, 192)(129, 182)(130, 187)(131, 155)(132, 174)(133, 167)(134, 184)(135, 159)(136, 189)(137, 161)(138, 191)(139, 188)(140, 190)(141, 169)(142, 172)(143, 185)(144, 181)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.804
Transitivity :: VT+
Graph::
	v = 4 e = 96 f = 40
	degree seq :: [ 48^4 ]

E27.806 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 6, 6, 12})
Quotient :: loop^2
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1^-1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1 * Y2)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, Y2^6, Y1^-1 * Y3 * Y2^-1 * Y1^-2 * Y3 * Y1^-2, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3, (Y1 * Y3)^12 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 3, 51, 99, 147)(2, 50, 98, 146, 6, 54, 102, 150)(4, 52, 100, 148, 9, 57, 105, 153)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(8, 56, 104, 152, 17, 65, 113, 161)(10, 58, 106, 154, 21, 69, 117, 165)(11, 59, 107, 155, 22, 70, 118, 166)(13, 61, 109, 157, 26, 74, 122, 170)(14, 62, 110, 158, 27, 75, 123, 171)(15, 63, 111, 159, 29, 77, 125, 173)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 35, 83, 131, 179)(20, 68, 116, 164, 36, 84, 132, 180)(23, 71, 119, 167, 32, 80, 128, 176)(24, 72, 120, 168, 37, 85, 133, 181)(25, 73, 121, 169, 31, 79, 127, 175)(28, 76, 124, 172, 39, 87, 135, 183)(30, 78, 126, 174, 41, 89, 137, 185)(33, 81, 129, 177, 43, 91, 139, 187)(38, 86, 134, 182, 45, 93, 141, 189)(40, 88, 136, 184, 46, 94, 142, 190)(42, 90, 138, 186, 47, 95, 143, 191)(44, 92, 140, 188, 48, 96, 144, 192)
	L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 67)(10, 52)(11, 58)(12, 71)(13, 73)(14, 54)(15, 70)(16, 78)(17, 80)(18, 56)(19, 72)(20, 57)(21, 76)(22, 66)(23, 68)(24, 60)(25, 69)(26, 86)(27, 82)(28, 62)(29, 83)(30, 75)(31, 64)(32, 88)(33, 65)(34, 90)(35, 81)(36, 74)(37, 87)(38, 85)(39, 92)(40, 77)(41, 93)(42, 79)(43, 89)(44, 84)(45, 94)(46, 95)(47, 96)(48, 91)(97, 146)(98, 149)(99, 151)(100, 145)(101, 155)(102, 157)(103, 159)(104, 147)(105, 163)(106, 148)(107, 154)(108, 167)(109, 169)(110, 150)(111, 166)(112, 174)(113, 176)(114, 152)(115, 168)(116, 153)(117, 172)(118, 162)(119, 164)(120, 156)(121, 165)(122, 182)(123, 178)(124, 158)(125, 179)(126, 171)(127, 160)(128, 184)(129, 161)(130, 186)(131, 177)(132, 170)(133, 183)(134, 181)(135, 188)(136, 173)(137, 189)(138, 175)(139, 185)(140, 180)(141, 190)(142, 191)(143, 192)(144, 187)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.803
Transitivity :: VT+
Graph::
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.807 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, Y3^3, (Y3 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2^-1, Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2, (Y3^-1 * Y1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 13, 61)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 16, 64)(8, 56, 18, 66)(9, 57, 19, 67)(10, 58, 20, 68)(12, 60, 17, 65)(21, 69, 37, 85)(22, 70, 31, 79)(23, 71, 30, 78)(24, 72, 38, 86)(25, 73, 36, 84)(26, 74, 39, 87)(27, 75, 40, 88)(28, 76, 33, 81)(29, 77, 41, 89)(32, 80, 42, 90)(34, 82, 43, 91)(35, 83, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 100, 148, 108, 156, 102, 150, 101, 149)(98, 146, 103, 151, 104, 152, 113, 161, 106, 154, 105, 153)(107, 155, 117, 165, 118, 166, 111, 159, 120, 168, 119, 167)(109, 157, 121, 169, 122, 170, 110, 158, 124, 172, 123, 171)(112, 160, 125, 173, 126, 174, 116, 164, 128, 176, 127, 175)(114, 162, 129, 177, 130, 178, 115, 163, 132, 180, 131, 179)(133, 181, 141, 189, 136, 184, 134, 182, 142, 190, 135, 183)(137, 185, 143, 191, 140, 188, 138, 186, 144, 192, 139, 187)
	L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 99)(6, 97)(7, 113)(8, 106)(9, 103)(10, 98)(11, 118)(12, 101)(13, 122)(14, 123)(15, 119)(16, 126)(17, 105)(18, 130)(19, 131)(20, 127)(21, 111)(22, 120)(23, 117)(24, 107)(25, 110)(26, 124)(27, 121)(28, 109)(29, 116)(30, 128)(31, 125)(32, 112)(33, 115)(34, 132)(35, 129)(36, 114)(37, 136)(38, 135)(39, 141)(40, 142)(41, 140)(42, 139)(43, 143)(44, 144)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.811
Graph:: bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.808 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3 * Y2 * Y3^-2, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y2^-2 * Y3 * Y2 * Y3, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3, Y1 * Y3^-1 * Y2 * Y1 * Y2, Y1 * Y3 * Y1 * Y3 * Y2^-1, Y2^6, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2 * Y1, (Y2^-1 * Y1 * Y3^-1)^2, (Y3 * Y2^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 19, 67)(6, 54, 23, 71)(7, 55, 20, 68)(8, 56, 14, 62)(9, 57, 24, 72)(10, 58, 18, 66)(12, 60, 36, 84)(13, 61, 33, 81)(16, 64, 29, 77)(17, 65, 43, 91)(21, 69, 46, 94)(22, 70, 32, 80)(25, 73, 28, 76)(26, 74, 47, 95)(27, 75, 44, 92)(30, 78, 42, 90)(31, 79, 38, 86)(34, 82, 39, 87)(35, 83, 40, 88)(37, 85, 48, 96)(41, 89, 45, 93)(97, 145, 99, 147, 108, 156, 133, 181, 117, 165, 101, 149)(98, 146, 103, 151, 123, 171, 144, 192, 127, 175, 105, 153)(100, 148, 112, 160, 138, 186, 122, 170, 118, 166, 114, 162)(102, 150, 120, 168, 109, 157, 113, 161, 140, 188, 121, 169)(104, 152, 125, 173, 139, 187, 130, 178, 128, 176, 119, 167)(106, 154, 115, 163, 124, 172, 126, 174, 132, 180, 129, 177)(107, 155, 111, 159, 137, 185, 142, 190, 143, 191, 131, 179)(110, 158, 136, 184, 134, 182, 135, 183, 141, 189, 116, 164)
	L = (1, 100)(2, 104)(3, 109)(4, 113)(5, 116)(6, 97)(7, 124)(8, 126)(9, 107)(10, 98)(11, 125)(12, 134)(13, 135)(14, 99)(15, 103)(16, 108)(17, 133)(18, 141)(19, 119)(20, 112)(21, 121)(22, 101)(23, 131)(24, 114)(25, 110)(26, 102)(27, 142)(28, 143)(29, 123)(30, 144)(31, 129)(32, 105)(33, 111)(34, 106)(35, 132)(36, 139)(37, 122)(38, 118)(39, 117)(40, 120)(41, 115)(42, 136)(43, 137)(44, 138)(45, 140)(46, 128)(47, 127)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.812
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.809 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-2, (Y3 * Y1)^2, (Y2 * R)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1^-2 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y3^-1, (Y3 * Y1^-2)^2, Y2^6, Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 28, 76, 21, 69, 5, 53)(3, 51, 13, 61, 11, 59, 25, 73, 42, 90, 16, 64)(4, 52, 17, 65, 43, 91, 47, 95, 31, 79, 18, 66)(6, 54, 23, 71, 39, 87, 14, 62, 19, 67, 24, 72)(7, 55, 27, 75, 45, 93, 38, 86, 34, 82, 10, 58)(9, 57, 32, 80, 30, 78, 35, 83, 46, 94, 22, 70)(12, 60, 37, 85, 20, 68, 41, 89, 48, 96, 29, 77)(15, 63, 33, 81, 44, 92, 26, 74, 36, 84, 40, 88)(97, 145, 99, 147, 110, 158, 124, 172, 121, 169, 102, 150)(98, 146, 105, 153, 112, 160, 117, 165, 131, 179, 107, 155)(100, 148, 111, 159, 134, 182, 143, 191, 122, 170, 103, 151)(101, 149, 115, 163, 126, 174, 104, 152, 119, 167, 118, 166)(106, 154, 129, 177, 137, 185, 141, 189, 132, 180, 108, 156)(109, 157, 128, 176, 135, 183, 138, 186, 142, 190, 120, 168)(113, 161, 116, 164, 136, 184, 127, 175, 125, 173, 140, 188)(114, 162, 130, 178, 144, 192, 139, 187, 123, 171, 133, 181)
	L = (1, 100)(2, 106)(3, 111)(4, 99)(5, 116)(6, 103)(7, 97)(8, 125)(9, 129)(10, 105)(11, 108)(12, 98)(13, 114)(14, 134)(15, 110)(16, 137)(17, 101)(18, 128)(19, 136)(20, 115)(21, 141)(22, 113)(23, 140)(24, 133)(25, 122)(26, 102)(27, 120)(28, 143)(29, 119)(30, 127)(31, 104)(32, 130)(33, 112)(34, 135)(35, 132)(36, 107)(37, 109)(38, 124)(39, 144)(40, 126)(41, 117)(42, 139)(43, 142)(44, 118)(45, 131)(46, 123)(47, 121)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.810
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.810 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-1 * Y3, Y1 * R * Y3 * R, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^-1 * R * Y2 * R, Y2 * R * Y1^-1 * Y3^-1 * Y2 * Y1^2 * R, R * Y2 * Y1^2 * Y2 * Y1 * R * Y2, Y1^-1 * Y2 * Y1^3 * Y2 * Y1^-2, (Y3 * Y2)^6, Y1^12, (Y3^-1 * Y1^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53, 11, 59, 23, 71, 37, 85, 46, 94, 44, 92, 36, 84, 22, 70, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 24, 72, 39, 87, 28, 76, 41, 89, 35, 83, 45, 93, 34, 82, 18, 66, 8, 56)(6, 54, 13, 61, 27, 75, 38, 86, 47, 95, 40, 88, 33, 81, 17, 65, 32, 80, 21, 69, 30, 78, 14, 62)(9, 57, 19, 67, 26, 74, 12, 60, 25, 73, 16, 64, 31, 79, 43, 91, 48, 96, 42, 90, 29, 77, 20, 68)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 108, 156)(103, 151, 112, 160)(104, 152, 113, 161)(106, 154, 117, 165)(107, 155, 120, 168)(109, 157, 124, 172)(110, 158, 125, 173)(111, 159, 126, 174)(114, 162, 122, 170)(115, 163, 123, 171)(116, 164, 131, 179)(118, 166, 130, 178)(119, 167, 134, 182)(121, 169, 136, 184)(127, 175, 133, 181)(128, 176, 139, 187)(129, 177, 140, 188)(132, 180, 138, 186)(135, 183, 144, 192)(137, 185, 142, 190)(141, 189, 143, 191)
	L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 115)(10, 100)(11, 119)(12, 121)(13, 123)(14, 102)(15, 120)(16, 127)(17, 128)(18, 104)(19, 122)(20, 105)(21, 126)(22, 106)(23, 133)(24, 135)(25, 112)(26, 108)(27, 134)(28, 137)(29, 116)(30, 110)(31, 139)(32, 117)(33, 113)(34, 114)(35, 141)(36, 118)(37, 142)(38, 143)(39, 124)(40, 129)(41, 131)(42, 125)(43, 144)(44, 132)(45, 130)(46, 140)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.809
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.811 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3, Y3^3, (Y2^-1 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, (Y2 * Y3^-1)^2, (R * Y3)^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2^2 * Y3 * Y2^2, Y3 * Y2^-4 * Y3 * Y2^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 10, 58, 4, 52, 5, 53)(3, 51, 11, 59, 14, 62, 26, 74, 13, 61, 9, 57)(6, 54, 16, 64, 21, 69, 28, 76, 18, 66, 19, 67)(8, 56, 23, 71, 17, 65, 15, 63, 25, 73, 22, 70)(12, 60, 31, 79, 34, 82, 45, 93, 33, 81, 30, 78)(20, 68, 40, 88, 24, 72, 43, 91, 41, 89, 37, 85)(27, 75, 35, 83, 39, 87, 36, 84, 29, 77, 38, 86)(32, 80, 44, 92, 48, 96, 42, 90, 46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 128, 176, 139, 187, 124, 172, 106, 154, 122, 170, 141, 189, 138, 186, 116, 164, 102, 150)(98, 146, 104, 152, 120, 168, 140, 188, 132, 180, 110, 158, 100, 148, 111, 159, 133, 181, 142, 190, 123, 171, 105, 153)(101, 149, 112, 160, 134, 182, 143, 191, 127, 175, 118, 166, 103, 151, 114, 162, 135, 183, 144, 192, 129, 177, 113, 161)(107, 155, 125, 173, 117, 165, 137, 185, 121, 169, 130, 178, 109, 157, 131, 179, 115, 163, 136, 184, 119, 167, 126, 174)
	L = (1, 100)(2, 101)(3, 109)(4, 103)(5, 106)(6, 114)(7, 97)(8, 121)(9, 122)(10, 98)(11, 105)(12, 129)(13, 110)(14, 99)(15, 119)(16, 115)(17, 104)(18, 117)(19, 124)(20, 137)(21, 102)(22, 111)(23, 118)(24, 116)(25, 113)(26, 107)(27, 125)(28, 112)(29, 135)(30, 141)(31, 126)(32, 142)(33, 130)(34, 108)(35, 134)(36, 131)(37, 139)(38, 132)(39, 123)(40, 133)(41, 120)(42, 140)(43, 136)(44, 143)(45, 127)(46, 144)(47, 138)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.807
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.812 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y2^2, Y1^-1 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^2 * Y1^-1 * Y3 * Y1, Y2 * Y1 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1^-2, Y3^3 * Y1^3, (Y1 * Y3)^6, Y2^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 29, 77, 20, 68, 5, 53)(3, 51, 13, 61, 37, 85, 47, 95, 35, 83, 11, 59)(4, 52, 15, 63, 12, 60, 28, 76, 42, 90, 18, 66)(6, 54, 14, 62, 38, 86, 48, 96, 30, 78, 24, 72)(7, 55, 27, 75, 41, 89, 17, 65, 19, 67, 25, 73)(9, 57, 23, 71, 21, 69, 39, 87, 40, 88, 31, 79)(10, 58, 33, 81, 32, 80, 36, 84, 43, 91, 22, 70)(16, 64, 34, 82, 45, 93, 46, 94, 44, 92, 26, 74)(97, 145, 99, 147, 106, 154, 130, 178, 137, 185, 144, 192, 125, 173, 143, 191, 132, 180, 140, 188, 121, 169, 102, 150)(98, 146, 105, 153, 123, 171, 141, 189, 138, 186, 133, 181, 116, 164, 135, 183, 115, 163, 122, 170, 111, 159, 107, 155)(100, 148, 112, 160, 129, 177, 127, 175, 104, 152, 126, 174, 124, 172, 142, 190, 139, 187, 117, 165, 101, 149, 110, 158)(103, 151, 119, 167, 118, 166, 109, 157, 114, 162, 134, 182, 113, 161, 136, 184, 128, 176, 131, 179, 108, 156, 120, 168)
	L = (1, 100)(2, 106)(3, 105)(4, 113)(5, 115)(6, 119)(7, 97)(8, 123)(9, 126)(10, 114)(11, 120)(12, 98)(13, 130)(14, 99)(15, 129)(16, 107)(17, 125)(18, 116)(19, 128)(20, 132)(21, 109)(22, 101)(23, 141)(24, 142)(25, 111)(26, 102)(27, 118)(28, 103)(29, 124)(30, 143)(31, 131)(32, 104)(33, 137)(34, 127)(35, 140)(36, 108)(37, 134)(38, 112)(39, 110)(40, 122)(41, 138)(42, 139)(43, 121)(44, 117)(45, 144)(46, 133)(47, 135)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.808
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.813 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2, Y2^-2 * Y1 * Y3^-2 * Y1, Y2^-2 * Y3^2 * Y2^-2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 18, 66)(12, 60, 27, 75)(13, 61, 28, 76)(15, 63, 22, 70)(16, 64, 30, 78)(19, 67, 35, 83)(20, 68, 36, 84)(23, 71, 38, 86)(25, 73, 33, 81)(26, 74, 41, 89)(29, 77, 37, 85)(31, 79, 39, 87)(32, 80, 40, 88)(34, 82, 45, 93)(42, 90, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 107, 155, 121, 169, 111, 159, 101, 149)(98, 146, 103, 151, 114, 162, 129, 177, 118, 166, 105, 153)(100, 148, 108, 156, 102, 150, 109, 157, 122, 170, 112, 160)(104, 152, 115, 163, 106, 154, 116, 164, 130, 178, 119, 167)(110, 158, 123, 171, 113, 161, 124, 172, 137, 185, 126, 174)(117, 165, 131, 179, 120, 168, 132, 180, 141, 189, 134, 182)(125, 173, 138, 186, 127, 175, 139, 187, 128, 176, 140, 188)(133, 181, 142, 190, 135, 183, 143, 191, 136, 184, 144, 192)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 112)(6, 97)(7, 115)(8, 118)(9, 119)(10, 98)(11, 102)(12, 101)(13, 99)(14, 125)(15, 122)(16, 121)(17, 127)(18, 106)(19, 105)(20, 103)(21, 133)(22, 130)(23, 129)(24, 135)(25, 109)(26, 107)(27, 138)(28, 139)(29, 137)(30, 140)(31, 110)(32, 113)(33, 116)(34, 114)(35, 142)(36, 143)(37, 141)(38, 144)(39, 117)(40, 120)(41, 128)(42, 126)(43, 123)(44, 124)(45, 136)(46, 134)(47, 131)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.819
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.814 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y2^-1)^2, Y2^-1 * Y3^-2 * Y2^-1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1, (Y2 * Y1 * Y3)^2, Y3^-1 * Y1 * Y2^-2 * Y1 * Y3^-1, Y2^-2 * Y3^2 * Y2^-2, Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1, (Y2^-1 * Y3)^6, (Y3^-1 * Y1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 20, 68)(8, 56, 24, 72)(9, 57, 27, 75)(10, 58, 28, 76)(12, 60, 21, 69)(13, 61, 22, 70)(14, 62, 23, 71)(16, 64, 25, 73)(17, 65, 26, 74)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(33, 81, 45, 93)(34, 82, 46, 94)(35, 83, 43, 91)(36, 84, 44, 92)(41, 89, 47, 95)(42, 90, 48, 96)(97, 145, 99, 147, 108, 156, 129, 177, 112, 160, 101, 149)(98, 146, 103, 151, 117, 165, 137, 185, 121, 169, 105, 153)(100, 148, 109, 157, 102, 150, 110, 158, 130, 178, 113, 161)(104, 152, 118, 166, 106, 154, 119, 167, 138, 186, 122, 170)(107, 155, 125, 173, 141, 189, 131, 179, 114, 162, 127, 175)(111, 159, 126, 174, 115, 163, 128, 176, 142, 190, 132, 180)(116, 164, 133, 181, 143, 191, 139, 187, 123, 171, 135, 183)(120, 168, 134, 182, 124, 172, 136, 184, 144, 192, 140, 188)
	L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 113)(6, 97)(7, 118)(8, 121)(9, 122)(10, 98)(11, 126)(12, 102)(13, 101)(14, 99)(15, 131)(16, 130)(17, 129)(18, 132)(19, 127)(20, 134)(21, 106)(22, 105)(23, 103)(24, 139)(25, 138)(26, 137)(27, 140)(28, 135)(29, 115)(30, 114)(31, 111)(32, 107)(33, 110)(34, 108)(35, 142)(36, 141)(37, 124)(38, 123)(39, 120)(40, 116)(41, 119)(42, 117)(43, 144)(44, 143)(45, 128)(46, 125)(47, 136)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.818
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.815 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3^-3, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^4 * Y2^-2, Y2^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 21, 69)(12, 60, 22, 70)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 25, 73)(16, 64, 26, 74)(17, 65, 27, 75)(18, 66, 28, 76)(19, 67, 29, 77)(20, 68, 30, 78)(31, 79, 39, 87)(32, 80, 40, 88)(33, 81, 41, 89)(34, 82, 42, 90)(35, 83, 43, 91)(36, 84, 44, 92)(37, 85, 45, 93)(38, 86, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 127, 175, 114, 162, 101, 149)(98, 146, 103, 151, 117, 165, 135, 183, 124, 172, 105, 153)(100, 148, 110, 158, 128, 176, 109, 157, 132, 180, 112, 160)(102, 150, 115, 163, 129, 177, 113, 161, 131, 179, 108, 156)(104, 152, 120, 168, 136, 184, 119, 167, 140, 188, 122, 170)(106, 154, 125, 173, 137, 185, 123, 171, 139, 187, 118, 166)(111, 159, 130, 178, 143, 191, 134, 182, 116, 164, 133, 181)(121, 169, 138, 186, 144, 192, 142, 190, 126, 174, 141, 189)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 118)(8, 121)(9, 123)(10, 98)(11, 128)(12, 130)(13, 99)(14, 101)(15, 129)(16, 127)(17, 133)(18, 132)(19, 134)(20, 102)(21, 136)(22, 138)(23, 103)(24, 105)(25, 137)(26, 135)(27, 141)(28, 140)(29, 142)(30, 106)(31, 115)(32, 143)(33, 107)(34, 112)(35, 114)(36, 116)(37, 109)(38, 110)(39, 125)(40, 144)(41, 117)(42, 122)(43, 124)(44, 126)(45, 119)(46, 120)(47, 131)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.820
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.816 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^-2, (Y2, Y1), (Y3^-1, Y2), (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^6, Y3^4 * Y2^-2, Y3 * Y1^-1 * Y3 * Y2^-2 * Y1^-1, Y3 * Y1 * Y2^2 * Y3 * Y1^-1, Y1 * Y3 * Y1^-1 * Y3 * Y2^2, (Y2^-1 * Y3 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 20, 68, 5, 53)(3, 51, 9, 57, 26, 74, 21, 69, 6, 54, 11, 59)(4, 52, 15, 63, 27, 75, 12, 60, 35, 83, 17, 65)(7, 55, 23, 71, 28, 76, 19, 67, 32, 80, 10, 58)(13, 61, 34, 82, 43, 91, 30, 78, 18, 66, 38, 86)(14, 62, 39, 87, 44, 92, 33, 81, 22, 70, 29, 77)(16, 64, 31, 79, 45, 93, 41, 89, 24, 72, 36, 84)(37, 85, 46, 94, 42, 90, 48, 96, 40, 88, 47, 95)(97, 145, 99, 147, 104, 152, 122, 170, 116, 164, 102, 150)(98, 146, 105, 153, 121, 169, 117, 165, 101, 149, 107, 155)(100, 148, 109, 157, 123, 171, 139, 187, 131, 179, 114, 162)(103, 151, 110, 158, 124, 172, 140, 188, 128, 176, 118, 166)(106, 154, 125, 173, 119, 167, 135, 183, 115, 163, 129, 177)(108, 156, 126, 174, 113, 161, 134, 182, 111, 159, 130, 178)(112, 160, 133, 181, 141, 189, 138, 186, 120, 168, 136, 184)(127, 175, 142, 190, 137, 185, 144, 192, 132, 180, 143, 191)
	L = (1, 100)(2, 106)(3, 109)(4, 112)(5, 115)(6, 114)(7, 97)(8, 123)(9, 125)(10, 127)(11, 129)(12, 98)(13, 133)(14, 99)(15, 101)(16, 124)(17, 121)(18, 136)(19, 132)(20, 131)(21, 135)(22, 102)(23, 137)(24, 103)(25, 119)(26, 139)(27, 141)(28, 104)(29, 142)(30, 105)(31, 113)(32, 116)(33, 143)(34, 107)(35, 120)(36, 108)(37, 140)(38, 117)(39, 144)(40, 110)(41, 111)(42, 118)(43, 138)(44, 122)(45, 128)(46, 134)(47, 126)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.817
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.817 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1 * Y3)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-3 * Y1, Y3 * Y1 * Y3 * Y1^-3, Y3^-1 * Y1^-1 * Y3^-3 * Y1^-1, Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1^-1, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y2 * Y1^2 * Y2 * Y1^-2, (Y1^-2 * Y2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 22, 70, 34, 82, 46, 94, 35, 83, 16, 64, 32, 80, 19, 67, 5, 53)(3, 51, 11, 59, 24, 72, 43, 91, 41, 89, 17, 65, 29, 77, 8, 56, 27, 75, 42, 90, 38, 86, 13, 61)(4, 52, 15, 63, 25, 73, 21, 69, 6, 54, 18, 66, 26, 74, 9, 57, 31, 79, 20, 68, 33, 81, 10, 58)(12, 60, 28, 76, 44, 92, 40, 88, 14, 62, 30, 78, 45, 93, 36, 84, 47, 95, 39, 87, 48, 96, 37, 85)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 120, 168)(105, 153, 124, 172)(106, 154, 126, 174)(107, 155, 131, 179)(109, 157, 130, 178)(111, 159, 132, 180)(112, 160, 123, 171)(114, 162, 133, 181)(115, 163, 134, 182)(116, 164, 136, 184)(117, 165, 135, 183)(118, 166, 137, 185)(119, 167, 138, 186)(121, 169, 140, 188)(122, 170, 141, 189)(125, 173, 142, 190)(127, 175, 143, 191)(128, 176, 139, 187)(129, 177, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 114)(6, 97)(7, 121)(8, 124)(9, 128)(10, 98)(11, 132)(12, 123)(13, 126)(14, 99)(15, 119)(16, 127)(17, 133)(18, 131)(19, 129)(20, 101)(21, 130)(22, 102)(23, 116)(24, 140)(25, 115)(26, 103)(27, 143)(28, 139)(29, 141)(30, 104)(31, 118)(32, 117)(33, 142)(34, 106)(35, 111)(36, 138)(37, 107)(38, 144)(39, 109)(40, 113)(41, 110)(42, 136)(43, 135)(44, 134)(45, 120)(46, 122)(47, 137)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.816
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.818 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^2, (R * Y3)^2, (Y1, Y2), (Y3, Y1), (Y2 * Y3^-1)^2, (R * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-3, Y2^2 * Y3^2 * Y2^2, Y2^-1 * Y1^-1 * Y2^-3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 18, 66, 5, 53)(3, 51, 9, 57, 26, 74, 43, 91, 41, 89, 15, 63)(4, 52, 10, 58, 27, 75, 20, 68, 7, 55, 12, 60)(6, 54, 11, 59, 28, 76, 44, 92, 37, 85, 19, 67)(13, 61, 29, 77, 22, 70, 34, 82, 45, 93, 39, 87)(14, 62, 30, 78, 24, 72, 36, 84, 16, 64, 31, 79)(17, 65, 32, 80, 23, 71, 35, 83, 21, 69, 33, 81)(38, 86, 46, 94, 42, 90, 48, 96, 40, 88, 47, 95)(97, 145, 99, 147, 109, 157, 133, 181, 114, 162, 137, 185, 141, 189, 124, 172, 104, 152, 122, 170, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 115, 163, 101, 149, 111, 159, 135, 183, 140, 188, 121, 169, 139, 187, 130, 178, 107, 155)(100, 148, 113, 161, 134, 182, 120, 168, 103, 151, 117, 165, 136, 184, 110, 158, 123, 171, 119, 167, 138, 186, 112, 160)(106, 154, 128, 176, 142, 190, 132, 180, 108, 156, 129, 177, 143, 191, 126, 174, 116, 164, 131, 179, 144, 192, 127, 175)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 117)(7, 97)(8, 123)(9, 126)(10, 121)(11, 129)(12, 98)(13, 134)(14, 122)(15, 127)(16, 99)(17, 133)(18, 103)(19, 131)(20, 101)(21, 124)(22, 138)(23, 102)(24, 137)(25, 116)(26, 120)(27, 114)(28, 113)(29, 142)(30, 139)(31, 105)(32, 115)(33, 140)(34, 144)(35, 107)(36, 111)(37, 119)(38, 118)(39, 143)(40, 109)(41, 112)(42, 141)(43, 132)(44, 128)(45, 136)(46, 130)(47, 125)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.814
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.819 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y3), (R * Y3)^2, Y1^2 * Y3^-2, (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-2 * Y2 * Y1 * Y2 * Y1^-1, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (Y2^-1 * Y1^-1 * R)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1^-1)^2, Y2^-1 * Y1 * Y3^2 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1 * Y2^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 19, 67, 5, 53)(3, 51, 13, 61, 28, 76, 20, 68, 37, 85, 11, 59)(4, 52, 10, 58, 29, 77, 21, 69, 7, 55, 12, 60)(6, 54, 18, 66, 30, 78, 9, 57, 31, 79, 23, 71)(14, 62, 32, 80, 24, 72, 38, 86, 45, 93, 41, 89)(15, 63, 35, 83, 26, 74, 39, 87, 16, 64, 36, 84)(17, 65, 33, 81, 25, 73, 40, 88, 22, 70, 34, 82)(42, 90, 46, 94, 44, 92, 48, 96, 43, 91, 47, 95)(97, 145, 99, 147, 110, 158, 127, 175, 115, 163, 133, 181, 141, 189, 126, 174, 104, 152, 124, 172, 120, 168, 102, 150)(98, 146, 105, 153, 128, 176, 116, 164, 101, 149, 114, 162, 137, 185, 109, 157, 123, 171, 119, 167, 134, 182, 107, 155)(100, 148, 113, 161, 138, 186, 122, 170, 103, 151, 118, 166, 139, 187, 111, 159, 125, 173, 121, 169, 140, 188, 112, 160)(106, 154, 131, 179, 142, 190, 136, 184, 108, 156, 132, 180, 143, 191, 129, 177, 117, 165, 135, 183, 144, 192, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 118)(7, 97)(8, 125)(9, 129)(10, 123)(11, 132)(12, 98)(13, 131)(14, 138)(15, 124)(16, 99)(17, 127)(18, 130)(19, 103)(20, 135)(21, 101)(22, 126)(23, 136)(24, 140)(25, 102)(26, 133)(27, 117)(28, 122)(29, 115)(30, 113)(31, 121)(32, 142)(33, 119)(34, 105)(35, 116)(36, 109)(37, 112)(38, 144)(39, 107)(40, 114)(41, 143)(42, 120)(43, 110)(44, 141)(45, 139)(46, 134)(47, 128)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.813
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.820 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C6 x D8 (small group id <48, 45>)
Aut   = C2 x D8 x S3 (small group id <96, 209>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y2^-1), Y3^-2 * Y2^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1, Y3 * Y1 * Y3 * Y1^3, (Y3^-2 * Y1^-1)^2, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3^2 * Y1 * Y2^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 20, 68, 5, 53)(3, 51, 13, 61, 28, 76, 21, 69, 37, 85, 11, 59)(4, 52, 17, 65, 29, 77, 22, 70, 40, 88, 12, 60)(6, 54, 18, 66, 30, 78, 9, 57, 32, 80, 23, 71)(7, 55, 19, 67, 31, 79, 10, 58, 36, 84, 26, 74)(14, 62, 33, 81, 24, 72, 38, 86, 46, 94, 42, 90)(15, 63, 34, 82, 25, 73, 39, 87, 47, 95, 43, 91)(16, 64, 35, 83, 45, 93, 41, 89, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 128, 176, 116, 164, 133, 181, 142, 190, 126, 174, 104, 152, 124, 172, 120, 168, 102, 150)(98, 146, 105, 153, 129, 177, 117, 165, 101, 149, 114, 162, 138, 186, 109, 157, 123, 171, 119, 167, 134, 182, 107, 155)(100, 148, 111, 159, 132, 180, 144, 192, 136, 184, 143, 191, 127, 175, 141, 189, 125, 173, 121, 169, 103, 151, 112, 160)(106, 154, 130, 178, 118, 166, 140, 188, 115, 163, 139, 187, 113, 161, 137, 185, 122, 170, 135, 183, 108, 156, 131, 179)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 125)(9, 130)(10, 129)(11, 131)(12, 98)(13, 137)(14, 132)(15, 128)(16, 99)(17, 123)(18, 139)(19, 138)(20, 136)(21, 140)(22, 101)(23, 135)(24, 103)(25, 102)(26, 134)(27, 122)(28, 121)(29, 120)(30, 141)(31, 104)(32, 144)(33, 118)(34, 117)(35, 105)(36, 116)(37, 143)(38, 108)(39, 107)(40, 142)(41, 119)(42, 113)(43, 109)(44, 114)(45, 124)(46, 127)(47, 126)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.815
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.821 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y2^6, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-2, (Y3^2 * Y2^-1)^2, Y3^2 * Y2 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^3, Y3^-2 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * Y1 * Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 8, 56)(5, 53, 18, 66)(6, 54, 10, 58)(7, 55, 23, 71)(9, 57, 30, 78)(12, 60, 24, 72)(13, 61, 27, 75)(14, 62, 33, 81)(15, 63, 25, 73)(16, 64, 28, 76)(17, 65, 31, 79)(19, 67, 29, 77)(20, 68, 32, 80)(21, 69, 26, 74)(22, 70, 34, 82)(35, 83, 42, 90)(36, 84, 48, 96)(37, 85, 44, 92)(38, 86, 45, 93)(39, 87, 46, 94)(40, 88, 47, 95)(41, 89, 43, 91)(97, 145, 99, 147, 108, 156, 132, 180, 116, 164, 101, 149)(98, 146, 103, 151, 120, 168, 139, 187, 128, 176, 105, 153)(100, 148, 111, 159, 133, 181, 110, 158, 136, 184, 113, 161)(102, 150, 117, 165, 134, 182, 115, 163, 135, 183, 109, 157)(104, 152, 123, 171, 140, 188, 122, 170, 143, 191, 125, 173)(106, 154, 129, 177, 141, 189, 127, 175, 142, 190, 121, 169)(107, 155, 130, 178, 144, 192, 124, 172, 114, 162, 131, 179)(112, 160, 126, 174, 138, 186, 119, 167, 118, 166, 137, 185)
	L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 115)(6, 97)(7, 121)(8, 124)(9, 127)(10, 98)(11, 123)(12, 133)(13, 126)(14, 99)(15, 101)(16, 134)(17, 132)(18, 125)(19, 137)(20, 136)(21, 119)(22, 102)(23, 111)(24, 140)(25, 114)(26, 103)(27, 105)(28, 141)(29, 139)(30, 113)(31, 144)(32, 143)(33, 107)(34, 106)(35, 142)(36, 117)(37, 138)(38, 108)(39, 116)(40, 118)(41, 110)(42, 135)(43, 129)(44, 131)(45, 120)(46, 128)(47, 130)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.822
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.822 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1)^2, (Y2 * Y3^-1)^2, (Y3, Y2^-1), (Y1, Y2), (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3 * Y1^-2, Y3^-2 * Y1^-1 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 19, 67, 5, 53)(3, 51, 9, 57, 26, 74, 43, 91, 41, 89, 15, 63)(4, 52, 17, 65, 27, 75, 21, 69, 36, 84, 12, 60)(6, 54, 11, 59, 28, 76, 44, 92, 37, 85, 20, 68)(7, 55, 18, 66, 29, 77, 10, 58, 33, 81, 24, 72)(13, 61, 30, 78, 22, 70, 34, 82, 46, 94, 38, 86)(14, 62, 39, 87, 23, 71, 42, 90, 47, 95, 32, 80)(16, 64, 40, 88, 45, 93, 31, 79, 48, 96, 35, 83)(97, 145, 99, 147, 109, 157, 133, 181, 115, 163, 137, 185, 142, 190, 124, 172, 104, 152, 122, 170, 118, 166, 102, 150)(98, 146, 105, 153, 126, 174, 116, 164, 101, 149, 111, 159, 134, 182, 140, 188, 121, 169, 139, 187, 130, 178, 107, 155)(100, 148, 110, 158, 129, 177, 144, 192, 132, 180, 143, 191, 125, 173, 141, 189, 123, 171, 119, 167, 103, 151, 112, 160)(106, 154, 127, 175, 117, 165, 138, 186, 114, 162, 136, 184, 113, 161, 135, 183, 120, 168, 131, 179, 108, 156, 128, 176)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 114)(6, 112)(7, 97)(8, 123)(9, 127)(10, 126)(11, 128)(12, 98)(13, 129)(14, 133)(15, 136)(16, 99)(17, 121)(18, 134)(19, 132)(20, 138)(21, 101)(22, 103)(23, 102)(24, 130)(25, 120)(26, 119)(27, 118)(28, 141)(29, 104)(30, 117)(31, 116)(32, 105)(33, 115)(34, 108)(35, 107)(36, 142)(37, 144)(38, 113)(39, 139)(40, 140)(41, 143)(42, 111)(43, 131)(44, 135)(45, 122)(46, 125)(47, 124)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.821
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 12^8, 24^4 ]

E27.823 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1, Y3^6 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(15, 63, 22, 70)(16, 64, 23, 71)(17, 65, 24, 72)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 32, 80)(30, 78, 37, 85)(31, 79, 38, 86)(39, 87, 45, 93)(40, 88, 46, 94)(41, 89, 42, 90)(43, 91, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 108, 156, 121, 169, 111, 159)(102, 150, 109, 157, 122, 170, 112, 160)(104, 152, 115, 163, 129, 177, 118, 166)(106, 154, 116, 164, 130, 178, 119, 167)(110, 158, 123, 171, 135, 183, 126, 174)(113, 161, 124, 172, 136, 184, 127, 175)(117, 165, 131, 179, 141, 189, 133, 181)(120, 168, 132, 180, 142, 190, 134, 182)(125, 173, 137, 185, 143, 191, 139, 187)(128, 176, 138, 186, 144, 192, 140, 188)
	L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 126)(16, 101)(17, 102)(18, 129)(19, 131)(20, 103)(21, 128)(22, 133)(23, 105)(24, 106)(25, 135)(26, 107)(27, 137)(28, 109)(29, 120)(30, 139)(31, 112)(32, 113)(33, 141)(34, 114)(35, 138)(36, 116)(37, 140)(38, 119)(39, 143)(40, 122)(41, 132)(42, 124)(43, 134)(44, 127)(45, 144)(46, 130)(47, 142)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.830
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.824 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^12, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 7, 55, 13, 61, 10, 58)(5, 53, 8, 56, 14, 62, 11, 59)(9, 57, 15, 63, 21, 69, 18, 66)(12, 60, 16, 64, 22, 70, 19, 67)(17, 65, 23, 71, 29, 77, 26, 74)(20, 68, 24, 72, 30, 78, 27, 75)(25, 73, 31, 79, 37, 85, 34, 82)(28, 76, 32, 80, 38, 86, 35, 83)(33, 81, 39, 87, 44, 92, 42, 90)(36, 84, 40, 88, 45, 93, 43, 91)(41, 89, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 142, 190, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152)(100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 143, 191, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155)(102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 140, 188, 144, 192, 141, 189, 134, 182, 126, 174, 118, 166, 110, 158)
	L = (1, 98)(2, 102)(3, 103)(4, 97)(5, 104)(6, 100)(7, 109)(8, 110)(9, 111)(10, 99)(11, 101)(12, 112)(13, 106)(14, 107)(15, 117)(16, 118)(17, 119)(18, 105)(19, 108)(20, 120)(21, 114)(22, 115)(23, 125)(24, 126)(25, 127)(26, 113)(27, 116)(28, 128)(29, 122)(30, 123)(31, 133)(32, 134)(33, 135)(34, 121)(35, 124)(36, 136)(37, 130)(38, 131)(39, 140)(40, 141)(41, 142)(42, 129)(43, 132)(44, 138)(45, 139)(46, 144)(47, 137)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.827
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.825 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1, Y3^-1), Y1^-1 * Y3^-2 * Y1^-1, Y3^-2 * Y1^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), (Y3 * Y1^-1)^2, (Y2, Y3^-1), (R * Y2)^2, Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1, Y2^-3 * Y1^-1 * Y3 * Y2^-3, Y2^3 * Y3 * Y2^3 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 22, 70, 18, 66)(13, 61, 23, 71, 37, 85, 31, 79)(14, 62, 24, 72, 16, 64, 25, 73)(17, 65, 26, 74, 20, 68, 28, 76)(19, 67, 27, 75, 38, 86, 34, 82)(29, 77, 39, 87, 47, 95, 45, 93)(30, 78, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 36, 84, 44, 92)(35, 83, 43, 91, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 125, 173, 140, 188, 124, 172, 108, 156, 121, 169, 137, 185, 131, 179, 115, 163, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 129, 177, 113, 161, 100, 148, 110, 158, 126, 174, 139, 187, 123, 171, 107, 155)(101, 149, 111, 159, 127, 175, 141, 189, 132, 180, 116, 164, 103, 151, 112, 160, 128, 176, 142, 190, 130, 178, 114, 162)(104, 152, 117, 165, 133, 181, 143, 191, 138, 186, 122, 170, 106, 154, 120, 168, 136, 184, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 113)(7, 97)(8, 103)(9, 120)(10, 101)(11, 122)(12, 98)(13, 126)(14, 117)(15, 121)(16, 99)(17, 118)(18, 124)(19, 129)(20, 102)(21, 112)(22, 116)(23, 136)(24, 111)(25, 105)(26, 114)(27, 138)(28, 107)(29, 139)(30, 133)(31, 137)(32, 109)(33, 134)(34, 140)(35, 135)(36, 115)(37, 128)(38, 132)(39, 144)(40, 127)(41, 119)(42, 130)(43, 143)(44, 123)(45, 131)(46, 125)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.828
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.826 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^-2, Y1^2 * Y3^2, (R * Y1)^2, (Y1^-1, Y3^-1), (Y2^-1, Y1), (R * Y2)^2, (Y2, Y3^-1), Y1^4, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2^5 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 22, 70, 18, 66)(13, 61, 23, 71, 37, 85, 31, 79)(14, 62, 24, 72, 16, 64, 25, 73)(17, 65, 26, 74, 20, 68, 28, 76)(19, 67, 27, 75, 38, 86, 34, 82)(29, 77, 39, 87, 47, 95, 46, 94)(30, 78, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 36, 84, 44, 92)(35, 83, 43, 91, 48, 96, 45, 93)(97, 145, 99, 147, 109, 157, 125, 173, 138, 186, 122, 170, 106, 154, 120, 168, 136, 184, 131, 179, 115, 163, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 132, 180, 116, 164, 103, 151, 112, 160, 128, 176, 139, 187, 123, 171, 107, 155)(100, 148, 110, 158, 126, 174, 141, 189, 130, 178, 114, 162, 101, 149, 111, 159, 127, 175, 142, 190, 129, 177, 113, 161)(104, 152, 117, 165, 133, 181, 143, 191, 140, 188, 124, 172, 108, 156, 121, 169, 137, 185, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 113)(7, 97)(8, 103)(9, 120)(10, 101)(11, 122)(12, 98)(13, 126)(14, 117)(15, 121)(16, 99)(17, 118)(18, 124)(19, 129)(20, 102)(21, 112)(22, 116)(23, 136)(24, 111)(25, 105)(26, 114)(27, 138)(28, 107)(29, 141)(30, 133)(31, 137)(32, 109)(33, 134)(34, 140)(35, 142)(36, 115)(37, 128)(38, 132)(39, 131)(40, 127)(41, 119)(42, 130)(43, 125)(44, 123)(45, 143)(46, 144)(47, 139)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.829
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.827 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, (Y3^-1, Y1), Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^12, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 37, 85, 29, 77, 21, 69, 13, 61, 5, 53)(3, 51, 8, 56, 16, 64, 24, 72, 32, 80, 40, 88, 46, 94, 43, 91, 35, 83, 27, 75, 19, 67, 11, 59)(4, 52, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 47, 95, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60)(6, 54, 10, 58, 18, 66, 26, 74, 34, 82, 42, 90, 48, 96, 45, 93, 38, 86, 30, 78, 22, 70, 14, 62)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 112, 160)(105, 153, 106, 154)(108, 156, 110, 158)(109, 157, 115, 163)(111, 159, 120, 168)(113, 161, 114, 162)(116, 164, 118, 166)(117, 165, 123, 171)(119, 167, 128, 176)(121, 169, 122, 170)(124, 172, 126, 174)(125, 173, 131, 179)(127, 175, 136, 184)(129, 177, 130, 178)(132, 180, 134, 182)(133, 181, 139, 187)(135, 183, 142, 190)(137, 185, 138, 186)(140, 188, 141, 189)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 108)(6, 97)(7, 113)(8, 106)(9, 104)(10, 98)(11, 110)(12, 107)(13, 116)(14, 101)(15, 121)(16, 114)(17, 112)(18, 103)(19, 118)(20, 115)(21, 124)(22, 109)(23, 129)(24, 122)(25, 120)(26, 111)(27, 126)(28, 123)(29, 132)(30, 117)(31, 137)(32, 130)(33, 128)(34, 119)(35, 134)(36, 131)(37, 140)(38, 125)(39, 143)(40, 138)(41, 136)(42, 127)(43, 141)(44, 139)(45, 133)(46, 144)(47, 142)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.824
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.828 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^4, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 27, 75, 12, 60, 3, 51, 8, 56, 19, 67, 31, 79, 16, 64, 5, 53)(4, 52, 9, 57, 20, 68, 33, 81, 40, 88, 26, 74, 11, 59, 22, 70, 35, 83, 43, 91, 30, 78, 15, 63)(6, 54, 10, 58, 21, 69, 34, 82, 41, 89, 28, 76, 13, 61, 23, 71, 36, 84, 44, 92, 32, 80, 17, 65)(14, 62, 24, 72, 37, 85, 45, 93, 47, 95, 39, 87, 25, 73, 38, 86, 46, 94, 48, 96, 42, 90, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 127, 175)(116, 164, 131, 179)(117, 165, 132, 180)(120, 168, 134, 182)(125, 173, 135, 183)(126, 174, 136, 184)(128, 176, 137, 185)(129, 177, 139, 187)(130, 178, 140, 188)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 122)(13, 99)(14, 102)(15, 125)(16, 126)(17, 101)(18, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 109)(26, 135)(27, 136)(28, 108)(29, 113)(30, 138)(31, 139)(32, 112)(33, 141)(34, 114)(35, 142)(36, 115)(37, 117)(38, 119)(39, 124)(40, 143)(41, 123)(42, 128)(43, 144)(44, 127)(45, 130)(46, 132)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.825
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.829 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, Y3 * Y2 * Y3^-1 * Y2, Y1 * Y2 * Y1^2 * Y3^-1 * Y1^3 * Y3^-1, Y1^2 * Y2 * Y1^4 * Y3^-2, Y1^-12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 33, 81, 41, 89, 25, 73, 40, 88, 47, 95, 31, 79, 16, 64, 5, 53)(3, 51, 8, 56, 19, 67, 34, 82, 45, 93, 29, 77, 14, 62, 24, 72, 39, 87, 43, 91, 27, 75, 12, 60)(4, 52, 9, 57, 20, 68, 35, 83, 44, 92, 28, 76, 13, 61, 23, 71, 38, 86, 46, 94, 30, 78, 15, 63)(6, 54, 10, 58, 21, 69, 36, 84, 42, 90, 26, 74, 11, 59, 22, 70, 37, 85, 48, 96, 32, 80, 17, 65)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 130, 178)(116, 164, 133, 181)(117, 165, 134, 182)(120, 168, 136, 184)(125, 173, 137, 185)(126, 174, 138, 186)(127, 175, 139, 187)(128, 176, 140, 188)(129, 177, 141, 189)(131, 179, 144, 192)(132, 180, 142, 190)(135, 183, 143, 191)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 122)(13, 99)(14, 102)(15, 125)(16, 126)(17, 101)(18, 131)(19, 133)(20, 135)(21, 103)(22, 136)(23, 104)(24, 106)(25, 109)(26, 137)(27, 138)(28, 108)(29, 113)(30, 141)(31, 142)(32, 112)(33, 140)(34, 144)(35, 139)(36, 114)(37, 143)(38, 115)(39, 117)(40, 119)(41, 124)(42, 129)(43, 132)(44, 123)(45, 128)(46, 130)(47, 134)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.826
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.830 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C12 x C4 (small group id <48, 20>)
Aut   = (C12 x C4) : C2 (small group id <96, 81>)
|r| :: 2
Presentation :: [ R^2, (Y2 * Y3^-1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1), Y2^-2 * Y3^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y3^-1), Y1^-1 * Y3 * Y1^-2 * Y2 * Y1^-1, Y2 * Y3^2 * Y2 * Y3 * Y2, (Y1^-1 * Y3^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 14, 62, 29, 77, 44, 92, 40, 88, 22, 70, 32, 80, 18, 66, 5, 53)(3, 51, 9, 57, 24, 72, 41, 89, 34, 82, 48, 96, 38, 86, 20, 68, 7, 55, 12, 60, 27, 75, 15, 63)(4, 52, 10, 58, 25, 73, 42, 90, 33, 81, 47, 95, 37, 85, 19, 67, 6, 54, 11, 59, 26, 74, 17, 65)(13, 61, 28, 76, 43, 91, 39, 87, 21, 69, 31, 79, 46, 94, 36, 84, 16, 64, 30, 78, 45, 93, 35, 83)(97, 145, 99, 147, 109, 157, 129, 177, 118, 166, 103, 151, 112, 160, 100, 148, 110, 158, 130, 178, 117, 165, 102, 150)(98, 146, 105, 153, 124, 172, 143, 191, 128, 176, 108, 156, 126, 174, 106, 154, 125, 173, 144, 192, 127, 175, 107, 155)(101, 149, 111, 159, 131, 179, 138, 186, 136, 184, 116, 164, 132, 180, 113, 161, 119, 167, 137, 185, 135, 183, 115, 163)(104, 152, 120, 168, 139, 187, 133, 181, 114, 162, 123, 171, 141, 189, 121, 169, 140, 188, 134, 182, 142, 190, 122, 170)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 113)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 130)(14, 129)(15, 119)(16, 99)(17, 131)(18, 122)(19, 132)(20, 101)(21, 103)(22, 102)(23, 138)(24, 140)(25, 139)(26, 141)(27, 104)(28, 144)(29, 143)(30, 105)(31, 108)(32, 107)(33, 117)(34, 118)(35, 137)(36, 111)(37, 142)(38, 114)(39, 116)(40, 115)(41, 136)(42, 135)(43, 134)(44, 133)(45, 120)(46, 123)(47, 127)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.823
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.831 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, R * Y2 * R * Y1 * Y2, Y3 * Y1 * Y2^-1 * Y3^-1 * Y2, Y3^6 * Y1, Y2^-1 * Y3^-3 * Y2 * Y3^-3, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 14, 62)(13, 61, 19, 67)(15, 63, 23, 71)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 24, 72)(25, 73, 27, 75)(26, 74, 29, 77)(28, 76, 31, 79)(30, 78, 36, 84)(32, 80, 38, 86)(33, 81, 34, 82)(35, 83, 37, 85)(39, 87, 41, 89)(40, 88, 43, 91)(42, 90, 44, 92)(45, 93, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 108, 156, 123, 171, 113, 161)(106, 154, 109, 157, 125, 173, 114, 162)(111, 159, 124, 172, 135, 183, 129, 177)(117, 165, 126, 174, 136, 184, 131, 179)(119, 167, 127, 175, 137, 185, 130, 178)(120, 168, 132, 180, 139, 187, 133, 181)(128, 176, 140, 188, 143, 191, 141, 189)(134, 182, 138, 186, 144, 192, 142, 190)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 110)(8, 119)(9, 112)(10, 98)(11, 121)(12, 124)(13, 99)(14, 127)(15, 128)(16, 130)(17, 129)(18, 101)(19, 103)(20, 105)(21, 102)(22, 123)(23, 134)(24, 106)(25, 135)(26, 107)(27, 137)(28, 138)(29, 118)(30, 109)(31, 140)(32, 120)(33, 142)(34, 141)(35, 114)(36, 115)(37, 116)(38, 117)(39, 143)(40, 122)(41, 144)(42, 132)(43, 125)(44, 126)(45, 131)(46, 133)(47, 139)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.852
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.832 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y3^-2, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1 * Y1, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^4 * Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 30, 78)(24, 72, 25, 73)(26, 74, 33, 81)(27, 75, 31, 79)(28, 76, 32, 80)(29, 77, 37, 85)(34, 82, 35, 83)(36, 84, 38, 86)(39, 87, 42, 90)(40, 88, 43, 91)(41, 89, 48, 96)(44, 92, 45, 93)(46, 94, 47, 95)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 118, 166, 115, 163, 126, 174)(114, 162, 122, 170, 116, 164, 129, 177)(123, 171, 135, 183, 127, 175, 138, 186)(124, 172, 136, 184, 128, 176, 139, 187)(125, 173, 142, 190, 133, 181, 143, 191)(130, 178, 140, 188, 131, 179, 141, 189)(132, 180, 137, 185, 134, 182, 144, 192)
	L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 125)(13, 127)(14, 126)(15, 101)(16, 124)(17, 128)(18, 102)(19, 133)(20, 104)(21, 135)(22, 137)(23, 138)(24, 136)(25, 139)(26, 106)(27, 142)(28, 107)(29, 141)(30, 144)(31, 143)(32, 109)(33, 111)(34, 112)(35, 113)(36, 114)(37, 140)(38, 116)(39, 134)(40, 117)(41, 130)(42, 132)(43, 119)(44, 120)(45, 121)(46, 122)(47, 129)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.853
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.833 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, R * Y2 * R * Y1 * Y2^-1, Y3 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y2^-1 * Y3 * Y2^-1, Y3^2 * Y2^-1 * Y3^-2 * Y2, Y3^-1 * Y2 * Y3^-5 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 16, 64)(13, 61, 20, 68)(14, 62, 17, 65)(15, 63, 23, 71)(18, 66, 19, 67)(21, 69, 24, 72)(25, 73, 28, 76)(26, 74, 29, 77)(27, 75, 34, 82)(30, 78, 37, 85)(31, 79, 33, 81)(32, 80, 39, 87)(35, 83, 36, 84)(38, 86, 40, 88)(41, 89, 44, 92)(42, 90, 45, 93)(43, 91, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 113, 161, 124, 172, 108, 156)(106, 154, 114, 162, 125, 173, 109, 157)(111, 159, 123, 171, 137, 185, 129, 177)(117, 165, 126, 174, 138, 186, 131, 179)(119, 167, 130, 178, 140, 188, 127, 175)(120, 168, 133, 181, 141, 189, 132, 180)(128, 176, 142, 190, 136, 184, 143, 191)(134, 182, 139, 187, 135, 183, 144, 192)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 112)(8, 119)(9, 110)(10, 98)(11, 121)(12, 123)(13, 99)(14, 127)(15, 128)(16, 130)(17, 129)(18, 101)(19, 105)(20, 103)(21, 102)(22, 124)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 140)(29, 118)(30, 109)(31, 142)(32, 141)(33, 144)(34, 143)(35, 114)(36, 115)(37, 116)(38, 117)(39, 138)(40, 120)(41, 136)(42, 122)(43, 132)(44, 134)(45, 125)(46, 126)(47, 131)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.854
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.834 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y1 * Y2 * Y1^2 * Y2^-1 * Y1, Y2^-1 * R * Y1^-1 * Y2^-1 * Y1 * R, (R * Y2 * Y3^-1)^2, Y2^2 * Y1^-1 * Y2^-2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^5 * Y1 * Y2 * Y1^-1, (Y1, Y2^-1, Y1^-1), (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 35, 83, 28, 76)(16, 64, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 38, 86, 30, 78, 41, 89)(27, 75, 44, 92, 47, 95, 45, 93)(32, 80, 42, 90, 33, 81, 43, 91)(34, 82, 39, 87, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 123, 171, 139, 187, 119, 167, 137, 185, 117, 165, 136, 184, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 128, 176, 110, 158, 122, 170, 105, 153, 121, 169, 140, 188, 120, 168, 104, 152)(100, 148, 108, 156, 124, 172, 142, 190, 129, 177, 111, 159, 126, 174, 107, 155, 125, 173, 141, 189, 127, 175, 109, 157)(102, 150, 113, 161, 131, 179, 143, 191, 138, 186, 118, 166, 134, 182, 115, 163, 133, 181, 144, 192, 132, 180, 114, 162)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 131)(21, 103)(22, 109)(23, 104)(24, 132)(25, 133)(26, 134)(27, 140)(28, 106)(29, 136)(30, 137)(31, 112)(32, 138)(33, 139)(34, 135)(35, 124)(36, 127)(37, 125)(38, 126)(39, 144)(40, 121)(41, 122)(42, 129)(43, 128)(44, 143)(45, 123)(46, 130)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.847
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.835 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1, Y2^-1 * Y1 * Y2 * Y3^-1, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2^5 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 17, 65, 22, 70, 19, 67)(9, 57, 23, 71, 16, 64, 25, 73)(11, 59, 26, 74, 18, 66, 27, 75)(14, 62, 24, 72, 37, 85, 31, 79)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 32, 80, 41, 89)(30, 78, 44, 92, 47, 95, 45, 93)(33, 81, 42, 90, 35, 83, 43, 91)(36, 84, 40, 88, 48, 96, 46, 94)(97, 145, 99, 147, 110, 158, 126, 174, 139, 187, 123, 171, 108, 156, 121, 169, 137, 185, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 136, 184, 129, 177, 113, 161, 100, 148, 109, 157, 125, 173, 140, 188, 124, 172, 107, 155)(101, 149, 112, 160, 127, 175, 142, 190, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 141, 189, 130, 178, 114, 162)(104, 152, 117, 165, 133, 181, 143, 191, 138, 186, 122, 170, 106, 154, 119, 167, 135, 183, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 105)(4, 104)(5, 108)(6, 107)(7, 97)(8, 103)(9, 117)(10, 101)(11, 118)(12, 98)(13, 119)(14, 125)(15, 121)(16, 99)(17, 122)(18, 102)(19, 123)(20, 129)(21, 112)(22, 114)(23, 111)(24, 135)(25, 109)(26, 115)(27, 113)(28, 138)(29, 133)(30, 136)(31, 137)(32, 110)(33, 134)(34, 139)(35, 116)(36, 140)(37, 128)(38, 131)(39, 127)(40, 143)(41, 120)(42, 130)(43, 124)(44, 144)(45, 132)(46, 126)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.850
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.836 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y2^-1 * Y3 * Y2 * Y1, Y1^4, Y3^4, Y1^2 * Y3^-2, (R * Y1)^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^6 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 19, 67, 22, 70, 17, 65)(9, 57, 23, 71, 15, 63, 25, 73)(11, 59, 27, 75, 18, 66, 26, 74)(14, 62, 24, 72, 37, 85, 32, 80)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 31, 79, 41, 89)(30, 78, 44, 92, 47, 95, 46, 94)(33, 81, 42, 90, 35, 83, 43, 91)(36, 84, 40, 88, 48, 96, 45, 93)(97, 145, 99, 147, 110, 158, 126, 174, 138, 186, 122, 170, 106, 154, 121, 169, 137, 185, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 136, 184, 131, 179, 115, 163, 103, 151, 109, 157, 125, 173, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 142, 190, 130, 178, 114, 162, 101, 149, 111, 159, 128, 176, 141, 189, 129, 177, 113, 161)(104, 152, 117, 165, 133, 181, 143, 191, 139, 187, 123, 171, 108, 156, 119, 167, 135, 183, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 99)(10, 101)(11, 102)(12, 98)(13, 121)(14, 127)(15, 117)(16, 119)(17, 123)(18, 118)(19, 122)(20, 129)(21, 105)(22, 107)(23, 109)(24, 137)(25, 112)(26, 113)(27, 115)(28, 138)(29, 110)(30, 141)(31, 133)(32, 135)(33, 134)(34, 139)(35, 116)(36, 142)(37, 125)(38, 131)(39, 120)(40, 126)(41, 128)(42, 130)(43, 124)(44, 132)(45, 143)(46, 144)(47, 136)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.844
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.837 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^12, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 13, 61, 7, 55)(5, 53, 11, 59, 14, 62, 8, 56)(10, 58, 15, 63, 21, 69, 17, 65)(12, 60, 16, 64, 22, 70, 19, 67)(18, 66, 25, 73, 29, 77, 23, 71)(20, 68, 27, 75, 30, 78, 24, 72)(26, 74, 31, 79, 37, 85, 33, 81)(28, 76, 32, 80, 38, 86, 35, 83)(34, 82, 41, 89, 44, 92, 39, 87)(36, 84, 43, 91, 45, 93, 40, 88)(42, 90, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 142, 190, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152)(100, 148, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 143, 191, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155)(102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 140, 188, 144, 192, 141, 189, 134, 182, 126, 174, 118, 166, 110, 158)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 100)(7, 99)(8, 101)(9, 109)(10, 111)(11, 110)(12, 112)(13, 103)(14, 104)(15, 117)(16, 118)(17, 106)(18, 121)(19, 108)(20, 123)(21, 113)(22, 115)(23, 114)(24, 116)(25, 125)(26, 127)(27, 126)(28, 128)(29, 119)(30, 120)(31, 133)(32, 134)(33, 122)(34, 137)(35, 124)(36, 139)(37, 129)(38, 131)(39, 130)(40, 132)(41, 140)(42, 142)(43, 141)(44, 135)(45, 136)(46, 144)(47, 138)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.843
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.838 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y1^-2 * Y3^-2, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y3^2 * Y1^-1, Y1^4, Y1^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^5 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 11, 59)(14, 62, 23, 71, 37, 85, 29, 77)(15, 63, 25, 73, 16, 64, 24, 72)(17, 65, 27, 75, 19, 67, 26, 74)(20, 68, 28, 76, 38, 86, 34, 82)(30, 78, 45, 93, 47, 95, 39, 87)(31, 79, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 35, 83, 43, 91)(36, 84, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 126, 174, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 129, 177, 113, 161, 100, 148, 112, 160, 127, 175, 140, 188, 124, 172, 107, 155)(101, 149, 109, 157, 125, 173, 141, 189, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 142, 190, 130, 178, 114, 162)(104, 152, 117, 165, 133, 181, 143, 191, 138, 186, 122, 170, 106, 154, 121, 169, 136, 184, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 121)(14, 127)(15, 117)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 109)(25, 105)(26, 107)(27, 114)(28, 138)(29, 137)(30, 142)(31, 133)(32, 110)(33, 134)(34, 139)(35, 116)(36, 141)(37, 128)(38, 131)(39, 132)(40, 125)(41, 119)(42, 130)(43, 124)(44, 126)(45, 144)(46, 143)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.849
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.839 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y3^2 * Y1^-2, Y3^4, Y1^-1 * Y2^-1 * Y1^-1 * Y2, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y2^5 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 11, 59)(14, 62, 23, 71, 37, 85, 29, 77)(15, 63, 25, 73, 16, 64, 24, 72)(17, 65, 27, 75, 19, 67, 26, 74)(20, 68, 28, 76, 38, 86, 34, 82)(30, 78, 45, 93, 47, 95, 39, 87)(31, 79, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 35, 83, 43, 91)(36, 84, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 126, 174, 138, 186, 122, 170, 106, 154, 121, 169, 136, 184, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 142, 190, 130, 178, 114, 162, 101, 149, 109, 157, 125, 173, 141, 189, 129, 177, 113, 161)(104, 152, 117, 165, 133, 181, 143, 191, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 144, 192, 134, 182, 118, 166)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 121)(14, 127)(15, 117)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 109)(25, 105)(26, 107)(27, 114)(28, 138)(29, 137)(30, 140)(31, 133)(32, 110)(33, 134)(34, 139)(35, 116)(36, 135)(37, 128)(38, 131)(39, 144)(40, 125)(41, 119)(42, 130)(43, 124)(44, 143)(45, 132)(46, 126)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.846
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.840 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y3 * Y1^2, (R * Y3)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1 * R)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4 * Y1 * Y2^2 * Y1, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 35, 83, 28, 76)(16, 64, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 38, 86, 30, 78, 41, 89)(27, 75, 45, 93, 34, 82, 46, 94)(32, 80, 42, 90, 33, 81, 43, 91)(39, 87, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 127, 175, 109, 157, 100, 148, 108, 156, 124, 172, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 129, 177, 111, 159, 126, 174, 107, 155, 125, 173, 142, 190, 128, 176, 110, 158, 122, 170)(115, 163, 133, 181, 143, 191, 139, 187, 119, 167, 137, 185, 117, 165, 136, 184, 144, 192, 138, 186, 118, 166, 134, 182)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 131)(21, 103)(22, 109)(23, 104)(24, 132)(25, 133)(26, 134)(27, 141)(28, 106)(29, 136)(30, 137)(31, 112)(32, 138)(33, 139)(34, 142)(35, 124)(36, 127)(37, 125)(38, 126)(39, 143)(40, 121)(41, 122)(42, 129)(43, 128)(44, 144)(45, 130)(46, 123)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.848
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.841 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y3^4, Y1^4, Y2^-1 * Y1 * Y2 * Y3^-1, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y3, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^2 * Y1^-2 * Y2^-2 * Y1^-2, Y2^-2 * Y1^-1 * Y2^-4 * Y1^-1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 17, 65, 22, 70, 19, 67)(9, 57, 23, 71, 16, 64, 25, 73)(11, 59, 26, 74, 18, 66, 27, 75)(14, 62, 24, 72, 37, 85, 31, 79)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 32, 80, 41, 89)(30, 78, 45, 93, 36, 84, 46, 94)(33, 81, 42, 90, 35, 83, 43, 91)(40, 88, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 136, 184, 130, 178, 114, 162, 101, 149, 112, 160, 127, 175, 140, 188, 124, 172, 107, 155)(100, 148, 109, 157, 125, 173, 141, 189, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 142, 190, 129, 177, 113, 161)(106, 154, 119, 167, 135, 183, 143, 191, 139, 187, 123, 171, 108, 156, 121, 169, 137, 185, 144, 192, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 105)(4, 104)(5, 108)(6, 107)(7, 97)(8, 103)(9, 117)(10, 101)(11, 118)(12, 98)(13, 119)(14, 125)(15, 121)(16, 99)(17, 122)(18, 102)(19, 123)(20, 129)(21, 112)(22, 114)(23, 111)(24, 135)(25, 109)(26, 115)(27, 113)(28, 138)(29, 133)(30, 136)(31, 137)(32, 110)(33, 134)(34, 139)(35, 116)(36, 140)(37, 128)(38, 131)(39, 127)(40, 132)(41, 120)(42, 130)(43, 124)(44, 126)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.851
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.842 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y1, Y3^4, Y1^4, Y2 * Y3 * Y2^-1 * Y1, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^-4 * Y1^-1 * Y2^-1, (Y2^-2 * Y1 * Y3^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 19, 67, 22, 70, 17, 65)(9, 57, 23, 71, 15, 63, 25, 73)(11, 59, 27, 75, 18, 66, 26, 74)(14, 62, 24, 72, 37, 85, 32, 80)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 31, 79, 41, 89)(30, 78, 45, 93, 36, 84, 46, 94)(33, 81, 42, 90, 35, 83, 43, 91)(40, 88, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 136, 184, 130, 178, 114, 162, 101, 149, 111, 159, 128, 176, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 142, 190, 131, 179, 115, 163, 103, 151, 109, 157, 125, 173, 141, 189, 129, 177, 113, 161)(106, 154, 121, 169, 137, 185, 144, 192, 139, 187, 123, 171, 108, 156, 119, 167, 135, 183, 143, 191, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 99)(10, 101)(11, 102)(12, 98)(13, 121)(14, 127)(15, 117)(16, 119)(17, 123)(18, 118)(19, 122)(20, 129)(21, 105)(22, 107)(23, 109)(24, 137)(25, 112)(26, 113)(27, 115)(28, 138)(29, 110)(30, 140)(31, 133)(32, 135)(33, 134)(34, 139)(35, 116)(36, 136)(37, 125)(38, 131)(39, 120)(40, 126)(41, 128)(42, 130)(43, 124)(44, 132)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.845
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.843 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, (R * Y2)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 38, 86, 30, 78, 22, 70, 14, 62, 5, 53)(3, 51, 8, 56, 16, 64, 24, 72, 32, 80, 40, 88, 46, 94, 43, 91, 35, 83, 27, 75, 19, 67, 11, 59)(4, 52, 10, 58, 17, 65, 26, 74, 33, 81, 42, 90, 47, 95, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60)(6, 54, 9, 57, 18, 66, 25, 73, 34, 82, 41, 89, 48, 96, 45, 93, 37, 85, 29, 77, 21, 69, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 112, 160)(105, 153, 106, 154)(108, 156, 109, 157)(110, 158, 115, 163)(111, 159, 120, 168)(113, 161, 114, 162)(116, 164, 117, 165)(118, 166, 123, 171)(119, 167, 128, 176)(121, 169, 122, 170)(124, 172, 125, 173)(126, 174, 131, 179)(127, 175, 136, 184)(129, 177, 130, 178)(132, 180, 133, 181)(134, 182, 139, 187)(135, 183, 142, 190)(137, 185, 138, 186)(140, 188, 141, 189)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 109)(6, 97)(7, 113)(8, 106)(9, 104)(10, 98)(11, 108)(12, 101)(13, 107)(14, 116)(15, 121)(16, 114)(17, 112)(18, 103)(19, 117)(20, 115)(21, 110)(22, 125)(23, 129)(24, 122)(25, 120)(26, 111)(27, 124)(28, 118)(29, 123)(30, 132)(31, 137)(32, 130)(33, 128)(34, 119)(35, 133)(36, 131)(37, 126)(38, 141)(39, 143)(40, 138)(41, 136)(42, 127)(43, 140)(44, 134)(45, 139)(46, 144)(47, 142)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.837
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.844 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y1 * Y2, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1^-1 * Y3^-1, Y1^-1 * Y2 * Y3^-1 * Y1 * Y3, Y1^-1 * Y3^2 * Y1 * Y3^2, Y3 * Y1^-4 * Y3 * Y1^-2, Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 22, 70, 39, 87, 32, 80, 15, 63, 27, 75, 44, 92, 36, 84, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 40, 88, 48, 96, 33, 81, 29, 77, 31, 79, 46, 94, 47, 95, 30, 78, 12, 60)(4, 52, 14, 62, 24, 72, 43, 91, 37, 85, 21, 69, 6, 54, 20, 68, 25, 73, 45, 93, 34, 82, 16, 64)(9, 57, 26, 74, 41, 89, 38, 86, 19, 67, 13, 61, 10, 58, 28, 76, 42, 90, 35, 83, 17, 65, 11, 59)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 110, 158)(106, 154, 116, 164)(111, 159, 125, 173)(112, 160, 113, 161)(114, 162, 126, 174)(115, 163, 117, 165)(118, 166, 136, 184)(120, 168, 122, 170)(121, 169, 124, 172)(123, 171, 127, 175)(128, 176, 129, 177)(130, 178, 131, 179)(132, 180, 143, 191)(133, 181, 134, 182)(135, 183, 144, 192)(137, 185, 139, 187)(138, 186, 141, 189)(140, 188, 142, 190)
	L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 110)(9, 123)(10, 98)(11, 125)(12, 112)(13, 99)(14, 127)(15, 102)(16, 129)(17, 128)(18, 130)(19, 101)(20, 104)(21, 108)(22, 137)(23, 122)(24, 140)(25, 103)(26, 142)(27, 106)(28, 119)(29, 109)(30, 131)(31, 116)(32, 115)(33, 117)(34, 135)(35, 144)(36, 138)(37, 114)(38, 126)(39, 133)(40, 139)(41, 132)(42, 118)(43, 143)(44, 121)(45, 136)(46, 124)(47, 141)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.836
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.845 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1^-1 * Y2 * Y3^-1, Y1^-1 * Y3^2 * Y1 * Y3^2, Y2 * Y1^-6, Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 22, 70, 30, 78, 12, 60, 3, 51, 8, 56, 23, 71, 36, 84, 18, 66, 5, 53)(4, 52, 14, 62, 24, 72, 41, 89, 35, 83, 17, 65, 11, 59, 9, 57, 26, 74, 39, 87, 34, 82, 16, 64)(6, 54, 20, 68, 25, 73, 43, 91, 38, 86, 19, 67, 13, 61, 10, 58, 28, 76, 40, 88, 37, 85, 21, 69)(15, 63, 27, 75, 42, 90, 47, 95, 46, 94, 33, 81, 29, 77, 31, 79, 44, 92, 48, 96, 45, 93, 32, 80)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 110, 158)(106, 154, 116, 164)(111, 159, 125, 173)(112, 160, 113, 161)(114, 162, 126, 174)(115, 163, 117, 165)(118, 166, 132, 180)(120, 168, 122, 170)(121, 169, 124, 172)(123, 171, 127, 175)(128, 176, 129, 177)(130, 178, 131, 179)(133, 181, 134, 182)(135, 183, 137, 185)(136, 184, 139, 187)(138, 186, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 110)(9, 123)(10, 98)(11, 125)(12, 112)(13, 99)(14, 127)(15, 102)(16, 129)(17, 128)(18, 130)(19, 101)(20, 104)(21, 108)(22, 135)(23, 122)(24, 138)(25, 103)(26, 140)(27, 106)(28, 119)(29, 109)(30, 131)(31, 116)(32, 115)(33, 117)(34, 141)(35, 142)(36, 137)(37, 114)(38, 126)(39, 143)(40, 118)(41, 144)(42, 121)(43, 132)(44, 124)(45, 133)(46, 134)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.842
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.846 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y2)^2, Y3^4, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^6, Y2 * Y3 * Y1^2 * Y3^-1 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 28, 76, 12, 60, 3, 51, 8, 56, 19, 67, 32, 80, 17, 65, 5, 53)(4, 52, 10, 58, 20, 68, 34, 82, 40, 88, 26, 74, 11, 59, 23, 71, 35, 83, 43, 91, 30, 78, 15, 63)(6, 54, 9, 57, 21, 69, 33, 81, 41, 89, 27, 75, 13, 61, 22, 70, 36, 84, 44, 92, 31, 79, 16, 64)(14, 62, 24, 72, 37, 85, 45, 93, 47, 95, 39, 87, 25, 73, 38, 86, 46, 94, 48, 96, 42, 90, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 128, 176)(116, 164, 131, 179)(117, 165, 132, 180)(120, 168, 134, 182)(125, 173, 135, 183)(126, 174, 136, 184)(127, 175, 137, 185)(129, 177, 140, 188)(130, 178, 139, 187)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 123)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 109)(26, 108)(27, 135)(28, 136)(29, 111)(30, 138)(31, 113)(32, 140)(33, 141)(34, 114)(35, 142)(36, 115)(37, 117)(38, 119)(39, 122)(40, 143)(41, 124)(42, 127)(43, 128)(44, 144)(45, 130)(46, 132)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.839
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.847 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3, (Y3 * R)^2, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, Y3^-1 * Y1 * Y2 * Y1^-1 * Y3^-1, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^-6 * Y2, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 27, 75, 11, 59, 3, 51, 8, 56, 20, 68, 34, 82, 15, 63, 5, 53)(4, 52, 12, 60, 21, 69, 39, 87, 35, 83, 18, 66, 6, 54, 17, 65, 22, 70, 40, 88, 31, 79, 13, 61)(9, 57, 23, 71, 37, 85, 36, 84, 16, 64, 26, 74, 10, 58, 25, 73, 38, 86, 33, 81, 14, 62, 24, 72)(28, 76, 41, 89, 47, 95, 46, 94, 32, 80, 44, 92, 29, 77, 42, 90, 48, 96, 45, 93, 30, 78, 43, 91)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 130, 178)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 125, 173)(126, 174, 128, 176)(127, 175, 131, 179)(129, 177, 132, 180)(133, 181, 134, 182)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 124)(13, 126)(14, 107)(15, 127)(16, 101)(17, 125)(18, 128)(19, 133)(20, 118)(21, 116)(22, 103)(23, 137)(24, 139)(25, 138)(26, 140)(27, 131)(28, 113)(29, 108)(30, 114)(31, 123)(32, 109)(33, 141)(34, 134)(35, 111)(36, 142)(37, 130)(38, 115)(39, 143)(40, 144)(41, 121)(42, 119)(43, 122)(44, 120)(45, 132)(46, 129)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.834
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.848 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^2, Y1 * Y2 * Y1^-1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3 * Y1^-2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-1 * Y2, (Y3^-1, Y1^-1)^2, Y1^-2 * Y3 * Y1^-1 * Y3^-1 * Y1^-3, (Y1^-1 * Y3^-1 * Y1 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 37, 85, 32, 80, 46, 94, 29, 77, 44, 92, 34, 82, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 38, 86, 48, 96, 30, 78, 45, 93, 28, 76, 43, 91, 47, 95, 27, 75, 11, 59)(4, 52, 12, 60, 21, 69, 41, 89, 33, 81, 14, 62, 24, 72, 9, 57, 23, 71, 39, 87, 31, 79, 13, 61)(6, 54, 17, 65, 22, 70, 42, 90, 36, 84, 16, 64, 26, 74, 10, 58, 25, 73, 40, 88, 35, 83, 18, 66)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 125, 173)(126, 174, 128, 176)(127, 175, 131, 179)(129, 177, 132, 180)(130, 178, 143, 191)(133, 181, 144, 192)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 124)(13, 126)(14, 107)(15, 127)(16, 101)(17, 125)(18, 128)(19, 135)(20, 118)(21, 116)(22, 103)(23, 139)(24, 141)(25, 140)(26, 142)(27, 131)(28, 113)(29, 108)(30, 114)(31, 123)(32, 109)(33, 144)(34, 137)(35, 111)(36, 133)(37, 129)(38, 136)(39, 134)(40, 115)(41, 143)(42, 130)(43, 121)(44, 119)(45, 122)(46, 120)(47, 138)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.840
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.849 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^4, Y1^2 * Y2 * Y1^3 * Y3^2 * Y1, Y1 * Y2 * Y1^2 * Y3 * Y1^3 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 33, 81, 41, 89, 25, 73, 40, 88, 48, 96, 32, 80, 17, 65, 5, 53)(3, 51, 8, 56, 19, 67, 34, 82, 45, 93, 29, 77, 14, 62, 24, 72, 39, 87, 44, 92, 28, 76, 12, 60)(4, 52, 10, 58, 20, 68, 36, 84, 43, 91, 27, 75, 13, 61, 22, 70, 38, 86, 46, 94, 30, 78, 15, 63)(6, 54, 9, 57, 21, 69, 35, 83, 42, 90, 26, 74, 11, 59, 23, 71, 37, 85, 47, 95, 31, 79, 16, 64)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 130, 178)(116, 164, 133, 181)(117, 165, 134, 182)(120, 168, 136, 184)(125, 173, 137, 185)(126, 174, 138, 186)(127, 175, 139, 187)(128, 176, 140, 188)(129, 177, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(135, 183, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 123)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 131)(19, 133)(20, 135)(21, 103)(22, 136)(23, 104)(24, 106)(25, 109)(26, 108)(27, 137)(28, 138)(29, 111)(30, 141)(31, 113)(32, 143)(33, 139)(34, 142)(35, 140)(36, 114)(37, 144)(38, 115)(39, 117)(40, 119)(41, 122)(42, 129)(43, 124)(44, 132)(45, 127)(46, 128)(47, 130)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.838
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.850 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, (R * Y2)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1^-1 * Y3, Y1 * Y3 * Y1^-1 * Y2 * Y3, Y1^-1 * Y3^-2 * Y1^-5 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 22, 70, 39, 87, 32, 80, 15, 63, 27, 75, 44, 92, 36, 84, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 40, 88, 48, 96, 34, 82, 29, 77, 31, 79, 46, 94, 47, 95, 30, 78, 12, 60)(4, 52, 14, 62, 24, 72, 43, 91, 37, 85, 21, 69, 6, 54, 20, 68, 25, 73, 45, 93, 33, 81, 16, 64)(9, 57, 26, 74, 41, 89, 38, 86, 19, 67, 11, 59, 10, 58, 28, 76, 42, 90, 35, 83, 17, 65, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 116, 164)(106, 154, 110, 158)(111, 159, 125, 173)(112, 160, 115, 163)(113, 161, 117, 165)(114, 162, 126, 174)(118, 166, 136, 184)(120, 168, 124, 172)(121, 169, 122, 170)(123, 171, 127, 175)(128, 176, 130, 178)(129, 177, 134, 182)(131, 179, 133, 181)(132, 180, 143, 191)(135, 183, 144, 192)(137, 185, 141, 189)(138, 186, 139, 187)(140, 188, 142, 190)
	L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 116)(9, 123)(10, 98)(11, 125)(12, 117)(13, 99)(14, 104)(15, 102)(16, 108)(17, 128)(18, 129)(19, 101)(20, 127)(21, 130)(22, 137)(23, 124)(24, 140)(25, 103)(26, 119)(27, 106)(28, 142)(29, 109)(30, 134)(31, 110)(32, 115)(33, 135)(34, 112)(35, 126)(36, 138)(37, 114)(38, 144)(39, 133)(40, 141)(41, 132)(42, 118)(43, 136)(44, 121)(45, 143)(46, 122)(47, 139)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.835
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.851 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1^-1 * Y3, Y1 * Y3 * Y1^-1 * Y2 * Y3, Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-5 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 22, 70, 39, 87, 34, 82, 29, 77, 31, 79, 46, 94, 36, 84, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 40, 88, 48, 96, 32, 80, 15, 63, 27, 75, 44, 92, 47, 95, 30, 78, 12, 60)(4, 52, 14, 62, 24, 72, 43, 91, 35, 83, 17, 65, 13, 61, 9, 57, 26, 74, 41, 89, 33, 81, 16, 64)(6, 54, 20, 68, 25, 73, 45, 93, 38, 86, 19, 67, 11, 59, 10, 58, 28, 76, 42, 90, 37, 85, 21, 69)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 116, 164)(106, 154, 110, 158)(111, 159, 125, 173)(112, 160, 115, 163)(113, 161, 117, 165)(114, 162, 126, 174)(118, 166, 136, 184)(120, 168, 124, 172)(121, 169, 122, 170)(123, 171, 127, 175)(128, 176, 130, 178)(129, 177, 134, 182)(131, 179, 133, 181)(132, 180, 143, 191)(135, 183, 144, 192)(137, 185, 141, 189)(138, 186, 139, 187)(140, 188, 142, 190)
	L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 116)(9, 123)(10, 98)(11, 125)(12, 117)(13, 99)(14, 104)(15, 102)(16, 108)(17, 128)(18, 129)(19, 101)(20, 127)(21, 130)(22, 137)(23, 124)(24, 140)(25, 103)(26, 119)(27, 106)(28, 142)(29, 109)(30, 134)(31, 110)(32, 115)(33, 144)(34, 112)(35, 126)(36, 139)(37, 114)(38, 135)(39, 131)(40, 141)(41, 143)(42, 118)(43, 136)(44, 121)(45, 132)(46, 122)(47, 138)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.841
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.852 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1 * Y2^-1 * Y1, (Y3, Y2), (Y2 * Y3^-1)^2, Y3 * Y1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y2^2 * Y3^-2, Y2 * Y1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-4 * Y2, Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1, Y2 * Y3^2 * Y2 * Y3 * Y2, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 14, 62, 29, 77, 44, 92, 40, 88, 22, 70, 32, 80, 18, 66, 5, 53)(3, 51, 10, 58, 24, 72, 42, 90, 34, 82, 47, 95, 38, 86, 19, 67, 7, 55, 11, 59, 27, 75, 15, 63)(4, 52, 9, 57, 25, 73, 41, 89, 33, 81, 48, 96, 37, 85, 20, 68, 6, 54, 12, 60, 26, 74, 17, 65)(13, 61, 28, 76, 43, 91, 39, 87, 21, 69, 31, 79, 46, 94, 36, 84, 16, 64, 30, 78, 45, 93, 35, 83)(97, 145, 99, 147, 109, 157, 129, 177, 118, 166, 103, 151, 112, 160, 100, 148, 110, 158, 130, 178, 117, 165, 102, 150)(98, 146, 105, 153, 124, 172, 143, 191, 128, 176, 108, 156, 126, 174, 106, 154, 125, 173, 144, 192, 127, 175, 107, 155)(101, 149, 113, 161, 131, 179, 138, 186, 136, 184, 116, 164, 132, 180, 111, 159, 119, 167, 137, 185, 135, 183, 115, 163)(104, 152, 120, 168, 139, 187, 133, 181, 114, 162, 123, 171, 141, 189, 121, 169, 140, 188, 134, 182, 142, 190, 122, 170)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 111)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 130)(14, 129)(15, 131)(16, 99)(17, 119)(18, 122)(19, 132)(20, 101)(21, 103)(22, 102)(23, 138)(24, 140)(25, 139)(26, 141)(27, 104)(28, 144)(29, 143)(30, 105)(31, 108)(32, 107)(33, 117)(34, 118)(35, 137)(36, 113)(37, 142)(38, 114)(39, 116)(40, 115)(41, 136)(42, 135)(43, 134)(44, 133)(45, 120)(46, 123)(47, 127)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.831
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.853 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-2, (Y3, Y2), Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y3^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y2, Y1^-1 * Y3^2 * Y1^-1 * Y3 * Y2, Y2 * Y3 * Y2^2 * Y1^-2, Y2^12, Y3^-1 * Y1 * Y2^-1 * Y1^9 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 27, 75, 45, 93, 41, 89, 17, 65, 35, 83, 48, 96, 44, 92, 22, 70, 5, 53)(3, 51, 13, 61, 28, 76, 12, 60, 40, 88, 19, 67, 4, 52, 18, 66, 29, 77, 11, 59, 37, 85, 16, 64)(6, 54, 23, 71, 30, 78, 20, 68, 34, 82, 9, 57, 7, 55, 26, 74, 31, 79, 21, 69, 36, 84, 10, 58)(14, 62, 32, 80, 46, 94, 43, 91, 24, 72, 38, 86, 15, 63, 33, 81, 47, 95, 42, 90, 25, 73, 39, 87)(97, 145, 99, 147, 110, 158, 127, 175, 144, 192, 125, 173, 143, 191, 130, 178, 141, 189, 136, 184, 120, 168, 102, 150)(98, 146, 105, 153, 128, 176, 115, 163, 140, 188, 119, 167, 138, 186, 109, 157, 137, 185, 117, 165, 134, 182, 107, 155)(100, 148, 111, 159, 126, 174, 104, 152, 124, 172, 142, 190, 132, 180, 118, 166, 133, 181, 121, 169, 103, 151, 113, 161)(101, 149, 116, 164, 135, 183, 108, 156, 131, 179, 106, 154, 129, 177, 112, 160, 123, 171, 122, 170, 139, 187, 114, 162)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 117)(6, 113)(7, 97)(8, 125)(9, 129)(10, 128)(11, 131)(12, 98)(13, 101)(14, 126)(15, 127)(16, 140)(17, 99)(18, 137)(19, 123)(20, 134)(21, 135)(22, 136)(23, 139)(24, 103)(25, 102)(26, 138)(27, 119)(28, 143)(29, 142)(30, 144)(31, 104)(32, 112)(33, 115)(34, 118)(35, 105)(36, 141)(37, 120)(38, 108)(39, 107)(40, 121)(41, 116)(42, 114)(43, 109)(44, 122)(45, 133)(46, 130)(47, 132)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.832
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.854 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x (C4 : C4) (small group id <48, 22>)
Aut   = (C2 x C4 x S3) : C2 (small group id <96, 102>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3), Y3^-1 * Y2^-1 * Y1^-2, (Y2^-1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1^-2 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y3^2 * Y2 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y2^-1 * Y1 * Y3, (Y2 * Y1)^4, Y1 * Y3^-1 * Y1 * Y2^9, Y1 * Y3^-1 * Y2^-1 * Y1^9 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 43, 91, 37, 85, 45, 93, 40, 88, 48, 96, 42, 90, 15, 63, 5, 53)(3, 51, 13, 61, 7, 55, 24, 72, 27, 75, 21, 69, 33, 81, 10, 58, 32, 80, 11, 59, 34, 82, 16, 64)(4, 52, 18, 66, 6, 54, 22, 70, 26, 74, 20, 68, 30, 78, 9, 57, 28, 76, 12, 60, 36, 84, 19, 67)(14, 62, 29, 77, 17, 65, 31, 79, 23, 71, 35, 83, 44, 92, 38, 86, 46, 94, 39, 87, 47, 95, 41, 89)(97, 145, 99, 147, 110, 158, 132, 180, 144, 192, 128, 176, 142, 190, 126, 174, 139, 187, 123, 171, 119, 167, 102, 150)(98, 146, 105, 153, 125, 173, 117, 165, 138, 186, 118, 166, 135, 183, 109, 157, 133, 181, 115, 163, 131, 179, 107, 155)(100, 148, 111, 159, 130, 178, 143, 191, 124, 172, 141, 189, 129, 177, 140, 188, 122, 170, 104, 152, 103, 151, 113, 161)(101, 149, 116, 164, 137, 185, 120, 168, 136, 184, 114, 162, 134, 182, 112, 160, 121, 169, 108, 156, 127, 175, 106, 154)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 117)(6, 113)(7, 97)(8, 102)(9, 101)(10, 125)(11, 127)(12, 98)(13, 134)(14, 130)(15, 132)(16, 131)(17, 99)(18, 133)(19, 121)(20, 138)(21, 137)(22, 136)(23, 103)(24, 135)(25, 107)(26, 119)(27, 104)(28, 142)(29, 116)(30, 140)(31, 105)(32, 141)(33, 139)(34, 144)(35, 108)(36, 143)(37, 112)(38, 115)(39, 114)(40, 109)(41, 118)(42, 120)(43, 122)(44, 123)(45, 126)(46, 129)(47, 128)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.833
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.855 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^3, (Y2^-1, Y3), (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y2, Y2^4, (R * Y2^-1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 18, 66)(12, 60, 27, 75)(13, 61, 28, 76)(15, 63, 30, 78)(16, 64, 32, 80)(19, 67, 37, 85)(20, 68, 29, 77)(22, 70, 34, 82)(23, 71, 39, 87)(25, 73, 41, 89)(26, 74, 42, 90)(31, 79, 45, 93)(33, 81, 44, 92)(35, 83, 46, 94)(36, 84, 43, 91)(38, 86, 48, 96)(40, 88, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 108, 156, 121, 169, 111, 159)(102, 150, 109, 157, 122, 170, 112, 160)(104, 152, 115, 163, 131, 179, 118, 166)(106, 154, 116, 164, 132, 180, 119, 167)(110, 158, 123, 171, 137, 185, 126, 174)(113, 161, 124, 172, 138, 186, 128, 176)(117, 165, 133, 181, 142, 190, 130, 178)(120, 168, 125, 173, 139, 187, 135, 183)(127, 175, 140, 188, 144, 192, 136, 184)(129, 177, 134, 182, 143, 191, 141, 189)
	L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 111)(6, 97)(7, 115)(8, 106)(9, 118)(10, 98)(11, 121)(12, 109)(13, 99)(14, 125)(15, 112)(16, 101)(17, 129)(18, 131)(19, 116)(20, 103)(21, 124)(22, 119)(23, 105)(24, 136)(25, 122)(26, 107)(27, 139)(28, 134)(29, 127)(30, 120)(31, 110)(32, 141)(33, 130)(34, 113)(35, 132)(36, 114)(37, 138)(38, 117)(39, 144)(40, 126)(41, 135)(42, 143)(43, 140)(44, 123)(45, 142)(46, 128)(47, 133)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.868
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.856 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, Y1^-2 * Y3^2, (R * Y1)^2, Y3^4, Y2^-1 * Y1^-1 * Y2^-2, (Y1^-1, Y3^-1), (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^2 * Y3^-2 * Y2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y1, Y3 * Y2^2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 23, 71, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 24, 72, 13, 61)(14, 62, 25, 73, 16, 64, 26, 74)(17, 65, 27, 75, 21, 69, 31, 79)(18, 66, 28, 76, 22, 70, 32, 80)(19, 67, 29, 77, 20, 68, 30, 78)(33, 81, 39, 87, 35, 83, 40, 88)(34, 82, 45, 93, 36, 84, 46, 94)(37, 85, 44, 92, 38, 86, 42, 90)(41, 89, 47, 95, 43, 91, 48, 96)(97, 145, 99, 147, 109, 157, 101, 149, 111, 159, 120, 168, 104, 152, 119, 167, 107, 155, 98, 146, 105, 153, 102, 150)(100, 148, 113, 161, 128, 176, 108, 156, 127, 175, 118, 166, 103, 151, 117, 165, 124, 172, 106, 154, 123, 171, 114, 162)(110, 158, 129, 177, 142, 190, 122, 170, 136, 184, 132, 180, 112, 160, 131, 179, 141, 189, 121, 169, 135, 183, 130, 178)(115, 163, 137, 185, 134, 182, 126, 174, 144, 192, 140, 188, 116, 164, 139, 187, 133, 181, 125, 173, 143, 191, 138, 186)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 126)(14, 119)(15, 122)(16, 99)(17, 133)(18, 135)(19, 120)(20, 102)(21, 134)(22, 136)(23, 112)(24, 116)(25, 111)(26, 105)(27, 140)(28, 131)(29, 109)(30, 107)(31, 138)(32, 129)(33, 124)(34, 137)(35, 128)(36, 139)(37, 117)(38, 113)(39, 118)(40, 114)(41, 132)(42, 123)(43, 130)(44, 127)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.865
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.857 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, Y1^2 * Y3^-2, (Y1, Y3^-1), Y2^3 * Y1^-1, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2 * Y3^2 * Y2, (Y2^-1 * Y1^-1)^3, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 23, 71, 14, 62)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 24, 72, 18, 66)(13, 61, 25, 73, 15, 63, 26, 74)(16, 64, 27, 75, 21, 69, 31, 79)(17, 65, 28, 76, 22, 70, 32, 80)(19, 67, 29, 77, 20, 68, 30, 78)(33, 81, 40, 88, 35, 83, 39, 87)(34, 82, 45, 93, 36, 84, 46, 94)(37, 85, 42, 90, 38, 86, 44, 92)(41, 89, 47, 95, 43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 98, 146, 105, 153, 120, 168, 104, 152, 119, 167, 114, 162, 101, 149, 110, 158, 102, 150)(100, 148, 112, 160, 124, 172, 106, 154, 123, 171, 118, 166, 103, 151, 117, 165, 128, 176, 108, 156, 127, 175, 113, 161)(109, 157, 129, 177, 141, 189, 121, 169, 136, 184, 132, 180, 111, 159, 131, 179, 142, 190, 122, 170, 135, 183, 130, 178)(115, 163, 137, 185, 134, 182, 125, 173, 143, 191, 140, 188, 116, 164, 139, 187, 133, 181, 126, 174, 144, 192, 138, 186)
	L = (1, 100)(2, 106)(3, 109)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 119)(14, 122)(15, 99)(16, 133)(17, 135)(18, 126)(19, 120)(20, 102)(21, 134)(22, 136)(23, 111)(24, 116)(25, 110)(26, 105)(27, 138)(28, 129)(29, 114)(30, 107)(31, 140)(32, 131)(33, 128)(34, 137)(35, 124)(36, 139)(37, 117)(38, 112)(39, 118)(40, 113)(41, 132)(42, 127)(43, 130)(44, 123)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.866
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.858 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1^4, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, (Y2^3 * Y1^-1)^2, Y1 * Y2 * R * Y2^-4 * R * Y2, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 41, 89, 29, 77)(16, 64, 38, 86, 42, 90, 39, 87)(20, 68, 25, 73, 32, 80, 30, 78)(24, 72, 37, 85, 33, 81, 35, 83)(26, 74, 34, 82, 31, 79, 36, 84)(28, 76, 43, 91, 40, 88, 44, 92)(45, 93, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 114, 162, 102, 150, 113, 161, 137, 185, 136, 184, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 139, 187, 129, 177, 109, 157, 100, 148, 108, 156, 128, 176, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 135, 183, 119, 167, 127, 175, 107, 155, 126, 174, 144, 192, 134, 182, 118, 166, 122, 170)(110, 158, 130, 178, 117, 165, 123, 171, 142, 190, 133, 181, 111, 159, 132, 180, 115, 163, 125, 173, 143, 191, 131, 179)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 121)(21, 103)(22, 109)(23, 104)(24, 133)(25, 128)(26, 130)(27, 137)(28, 139)(29, 106)(30, 116)(31, 132)(32, 126)(33, 131)(34, 127)(35, 120)(36, 122)(37, 129)(38, 138)(39, 112)(40, 140)(41, 125)(42, 135)(43, 136)(44, 124)(45, 142)(46, 144)(47, 141)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.863
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.859 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, Y2^-3 * Y1^-1, Y3^4, Y1^4, Y1^2 * Y3^-2, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3 * Y2 * Y3 * Y2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y3^-1 * Y2 * Y3 * Y2, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 23, 71, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 24, 72, 13, 61)(14, 62, 25, 73, 16, 64, 26, 74)(17, 65, 27, 75, 21, 69, 31, 79)(18, 66, 28, 76, 22, 70, 32, 80)(19, 67, 29, 77, 20, 68, 30, 78)(33, 81, 40, 88, 35, 83, 39, 87)(34, 82, 45, 93, 36, 84, 46, 94)(37, 85, 42, 90, 38, 86, 44, 92)(41, 89, 47, 95, 43, 91, 48, 96)(97, 145, 99, 147, 109, 157, 101, 149, 111, 159, 120, 168, 104, 152, 119, 167, 107, 155, 98, 146, 105, 153, 102, 150)(100, 148, 113, 161, 128, 176, 108, 156, 127, 175, 118, 166, 103, 151, 117, 165, 124, 172, 106, 154, 123, 171, 114, 162)(110, 158, 129, 177, 142, 190, 122, 170, 135, 183, 132, 180, 112, 160, 131, 179, 141, 189, 121, 169, 136, 184, 130, 178)(115, 163, 137, 185, 133, 181, 126, 174, 144, 192, 140, 188, 116, 164, 139, 187, 134, 182, 125, 173, 143, 191, 138, 186)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 126)(14, 119)(15, 122)(16, 99)(17, 133)(18, 135)(19, 120)(20, 102)(21, 134)(22, 136)(23, 112)(24, 116)(25, 111)(26, 105)(27, 138)(28, 129)(29, 109)(30, 107)(31, 140)(32, 131)(33, 128)(34, 139)(35, 124)(36, 137)(37, 117)(38, 113)(39, 118)(40, 114)(41, 130)(42, 127)(43, 132)(44, 123)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.864
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.860 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, (Y3 * Y1)^2, Y3^4, Y3^-2 * Y1^-2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^2 * Y1^-1 * Y2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3, Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 23, 71, 14, 62)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 24, 72, 18, 66)(13, 61, 25, 73, 15, 63, 26, 74)(16, 64, 27, 75, 21, 69, 31, 79)(17, 65, 28, 76, 22, 70, 32, 80)(19, 67, 29, 77, 20, 68, 30, 78)(33, 81, 39, 87, 35, 83, 40, 88)(34, 82, 45, 93, 36, 84, 46, 94)(37, 85, 44, 92, 38, 86, 42, 90)(41, 89, 47, 95, 43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 98, 146, 105, 153, 120, 168, 104, 152, 119, 167, 114, 162, 101, 149, 110, 158, 102, 150)(100, 148, 112, 160, 124, 172, 106, 154, 123, 171, 118, 166, 103, 151, 117, 165, 128, 176, 108, 156, 127, 175, 113, 161)(109, 157, 129, 177, 141, 189, 121, 169, 135, 183, 132, 180, 111, 159, 131, 179, 142, 190, 122, 170, 136, 184, 130, 178)(115, 163, 137, 185, 133, 181, 125, 173, 143, 191, 140, 188, 116, 164, 139, 187, 134, 182, 126, 174, 144, 192, 138, 186)
	L = (1, 100)(2, 106)(3, 109)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 119)(14, 122)(15, 99)(16, 133)(17, 135)(18, 126)(19, 120)(20, 102)(21, 134)(22, 136)(23, 111)(24, 116)(25, 110)(26, 105)(27, 140)(28, 131)(29, 114)(30, 107)(31, 138)(32, 129)(33, 124)(34, 139)(35, 128)(36, 137)(37, 117)(38, 112)(39, 118)(40, 113)(41, 130)(42, 123)(43, 132)(44, 127)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.867
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.861 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^3, Y1^-1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y3, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-2, Y1 * Y2 * R * Y2^2 * R * Y2, Y1 * Y2^6 * Y3, (Y2^3 * Y1^-1)^2, Y1 * Y2^2 * R * Y2^-2 * R * Y2^2, (Y3 * Y2^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 41, 89, 29, 77)(16, 64, 38, 86, 42, 90, 39, 87)(20, 68, 30, 78, 32, 80, 25, 73)(24, 72, 35, 83, 33, 81, 37, 85)(26, 74, 36, 84, 31, 79, 34, 82)(28, 76, 43, 91, 40, 88, 44, 92)(45, 93, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 138, 186, 114, 162, 102, 150, 113, 161, 137, 185, 136, 184, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 139, 187, 129, 177, 109, 157, 100, 148, 108, 156, 128, 176, 140, 188, 120, 168, 104, 152)(105, 153, 121, 169, 141, 189, 135, 183, 118, 166, 127, 175, 107, 155, 126, 174, 144, 192, 134, 182, 119, 167, 122, 170)(110, 158, 130, 178, 115, 163, 123, 171, 142, 190, 133, 181, 111, 159, 132, 180, 117, 165, 125, 173, 143, 191, 131, 179)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 126)(21, 103)(22, 109)(23, 104)(24, 131)(25, 116)(26, 132)(27, 137)(28, 139)(29, 106)(30, 128)(31, 130)(32, 121)(33, 133)(34, 122)(35, 129)(36, 127)(37, 120)(38, 138)(39, 112)(40, 140)(41, 125)(42, 135)(43, 136)(44, 124)(45, 143)(46, 141)(47, 144)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.862
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.862 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1^-1 * Y2 * Y1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, Y1^-6 * Y2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1 * Y3^-1, (Y1^-2 * Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 27, 75, 11, 59, 3, 51, 8, 56, 20, 68, 37, 85, 15, 63, 5, 53)(4, 52, 12, 60, 28, 76, 43, 91, 42, 90, 18, 66, 6, 54, 17, 65, 41, 89, 44, 92, 32, 80, 13, 61)(9, 57, 23, 71, 47, 95, 38, 86, 33, 81, 26, 74, 10, 58, 25, 73, 48, 96, 36, 84, 31, 79, 24, 72)(14, 62, 34, 82, 30, 78, 21, 69, 45, 93, 40, 88, 16, 64, 39, 87, 29, 77, 22, 70, 46, 94, 35, 83)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 133, 181)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 137, 185)(125, 173, 126, 174)(127, 175, 129, 177)(128, 176, 138, 186)(130, 178, 135, 183)(131, 179, 136, 184)(132, 180, 134, 182)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 132)(16, 101)(17, 126)(18, 129)(19, 139)(20, 118)(21, 116)(22, 103)(23, 137)(24, 130)(25, 124)(26, 135)(27, 134)(28, 119)(29, 113)(30, 108)(31, 114)(32, 136)(33, 109)(34, 122)(35, 128)(36, 123)(37, 140)(38, 111)(39, 120)(40, 138)(41, 121)(42, 131)(43, 133)(44, 115)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.861
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.863 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (Y3 * R)^2, (R * Y1)^2, Y1^-6 * Y2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1, Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, (Y1^-2 * Y3 * Y1^-1)^2, (Y1^-2 * Y3^-1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 27, 75, 11, 59, 3, 51, 8, 56, 20, 68, 37, 85, 15, 63, 5, 53)(4, 52, 12, 60, 28, 76, 43, 91, 42, 90, 18, 66, 6, 54, 17, 65, 41, 89, 44, 92, 32, 80, 13, 61)(9, 57, 23, 71, 47, 95, 38, 86, 31, 79, 26, 74, 10, 58, 25, 73, 48, 96, 36, 84, 33, 81, 24, 72)(14, 62, 34, 82, 29, 77, 21, 69, 45, 93, 40, 88, 16, 64, 39, 87, 30, 78, 22, 70, 46, 94, 35, 83)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 133, 181)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 137, 185)(125, 173, 126, 174)(127, 175, 129, 177)(128, 176, 138, 186)(130, 178, 135, 183)(131, 179, 136, 184)(132, 180, 134, 182)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 132)(16, 101)(17, 126)(18, 129)(19, 139)(20, 118)(21, 116)(22, 103)(23, 124)(24, 135)(25, 137)(26, 130)(27, 134)(28, 121)(29, 113)(30, 108)(31, 114)(32, 131)(33, 109)(34, 120)(35, 138)(36, 123)(37, 140)(38, 111)(39, 122)(40, 128)(41, 119)(42, 136)(43, 133)(44, 115)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.858
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.864 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y2 * Y1^-3, Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y3, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 26, 74, 41, 89, 16, 64, 29, 77, 38, 86, 14, 62, 20, 68, 5, 53)(3, 51, 11, 59, 17, 65, 4, 52, 15, 63, 39, 87, 36, 84, 46, 94, 23, 71, 6, 54, 22, 70, 13, 61)(8, 56, 25, 73, 30, 78, 9, 57, 28, 76, 48, 96, 44, 92, 37, 85, 32, 80, 10, 58, 31, 79, 27, 75)(18, 66, 42, 90, 35, 83, 19, 67, 43, 91, 33, 81, 24, 72, 47, 95, 34, 82, 21, 69, 45, 93, 40, 88)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 115, 163)(105, 153, 122, 170)(106, 154, 116, 164)(107, 155, 129, 177)(109, 157, 133, 181)(111, 159, 130, 178)(112, 160, 132, 180)(113, 161, 127, 175)(117, 165, 134, 182)(118, 166, 131, 179)(119, 167, 124, 172)(120, 168, 137, 185)(121, 169, 135, 183)(123, 171, 141, 189)(125, 173, 140, 188)(126, 174, 138, 186)(128, 176, 143, 191)(136, 184, 142, 190)(139, 187, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 120)(8, 122)(9, 125)(10, 98)(11, 130)(12, 132)(13, 127)(14, 99)(15, 136)(16, 102)(17, 121)(18, 103)(19, 137)(20, 104)(21, 101)(22, 129)(23, 133)(24, 134)(25, 119)(26, 140)(27, 138)(28, 109)(29, 106)(30, 139)(31, 135)(32, 141)(33, 111)(34, 142)(35, 107)(36, 110)(37, 113)(38, 114)(39, 124)(40, 118)(41, 117)(42, 144)(43, 128)(44, 116)(45, 126)(46, 131)(47, 123)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.859
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.865 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y3)^2, (Y2 * R)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, Y3^4, Y3^-1 * Y1^-3 * Y2, Y3^2 * Y1^-1 * Y3^2 * Y1, Y1 * Y2 * Y1 * Y3 * Y1 * Y3, Y1 * Y3^-1 * Y2 * Y1 * Y3^2 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 14, 62, 27, 75, 40, 88, 16, 64, 29, 77, 37, 85, 12, 60, 20, 68, 5, 53)(3, 51, 11, 59, 23, 71, 6, 54, 22, 70, 46, 94, 36, 84, 41, 89, 17, 65, 4, 52, 15, 63, 13, 61)(8, 56, 25, 73, 32, 80, 10, 58, 31, 79, 48, 96, 44, 92, 38, 86, 30, 78, 9, 57, 28, 76, 26, 74)(18, 66, 42, 90, 34, 82, 21, 69, 45, 93, 33, 81, 24, 72, 47, 95, 35, 83, 19, 67, 43, 91, 39, 87)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 116, 164)(106, 154, 123, 171)(107, 155, 129, 177)(109, 157, 134, 182)(111, 159, 130, 178)(112, 160, 132, 180)(113, 161, 127, 175)(115, 163, 133, 181)(118, 166, 131, 179)(119, 167, 124, 172)(120, 168, 136, 184)(121, 169, 142, 190)(122, 170, 139, 187)(125, 173, 140, 188)(126, 174, 143, 191)(128, 176, 138, 186)(135, 183, 137, 185)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 114)(8, 116)(9, 125)(10, 98)(11, 130)(12, 132)(13, 127)(14, 99)(15, 135)(16, 102)(17, 121)(18, 133)(19, 136)(20, 140)(21, 101)(22, 129)(23, 134)(24, 103)(25, 119)(26, 143)(27, 104)(28, 109)(29, 106)(30, 141)(31, 142)(32, 139)(33, 111)(34, 137)(35, 107)(36, 110)(37, 120)(38, 113)(39, 118)(40, 117)(41, 131)(42, 122)(43, 126)(44, 123)(45, 128)(46, 124)(47, 144)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.856
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.866 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-3 * Y2, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1, Y2 * Y3^-1 * Y1^-1 * Y3 * Y2 * Y1, Y1 * Y3^2 * Y1 * Y2 * Y3 * Y1, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 12, 60, 26, 74, 40, 88, 16, 64, 29, 77, 37, 85, 14, 62, 20, 68, 5, 53)(3, 51, 11, 59, 17, 65, 4, 52, 15, 63, 38, 86, 36, 84, 46, 94, 23, 71, 6, 54, 22, 70, 13, 61)(8, 56, 25, 73, 30, 78, 9, 57, 28, 76, 48, 96, 44, 92, 41, 89, 32, 80, 10, 58, 31, 79, 27, 75)(18, 66, 42, 90, 34, 82, 19, 67, 43, 91, 39, 87, 24, 72, 47, 95, 35, 83, 21, 69, 45, 93, 33, 81)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 115, 163)(105, 153, 122, 170)(106, 154, 116, 164)(107, 155, 129, 177)(109, 157, 121, 169)(111, 159, 130, 178)(112, 160, 132, 180)(113, 161, 124, 172)(117, 165, 133, 181)(118, 166, 131, 179)(119, 167, 127, 175)(120, 168, 136, 184)(123, 171, 139, 187)(125, 173, 140, 188)(126, 174, 143, 191)(128, 176, 138, 186)(134, 182, 137, 185)(135, 183, 142, 190)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 120)(8, 122)(9, 125)(10, 98)(11, 130)(12, 132)(13, 124)(14, 99)(15, 135)(16, 102)(17, 137)(18, 103)(19, 136)(20, 104)(21, 101)(22, 129)(23, 121)(24, 133)(25, 113)(26, 140)(27, 143)(28, 134)(29, 106)(30, 141)(31, 109)(32, 139)(33, 111)(34, 142)(35, 107)(36, 110)(37, 114)(38, 127)(39, 118)(40, 117)(41, 119)(42, 123)(43, 126)(44, 116)(45, 128)(46, 131)(47, 144)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.857
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.867 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (R * Y3)^2, (Y2 * R)^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y1)^2, Y3^4, Y1^2 * Y3 * Y2 * Y1, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3^-1 * Y2 * Y1, Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1, Y1^2 * Y3^-2 * Y1 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 14, 62, 27, 75, 39, 87, 16, 64, 29, 77, 37, 85, 12, 60, 20, 68, 5, 53)(3, 51, 11, 59, 23, 71, 6, 54, 22, 70, 46, 94, 36, 84, 41, 89, 17, 65, 4, 52, 15, 63, 13, 61)(8, 56, 25, 73, 32, 80, 10, 58, 31, 79, 48, 96, 44, 92, 40, 88, 30, 78, 9, 57, 28, 76, 26, 74)(18, 66, 42, 90, 35, 83, 21, 69, 45, 93, 38, 86, 24, 72, 47, 95, 34, 82, 19, 67, 43, 91, 33, 81)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 116, 164)(106, 154, 123, 171)(107, 155, 129, 177)(109, 157, 121, 169)(111, 159, 130, 178)(112, 160, 132, 180)(113, 161, 124, 172)(115, 163, 133, 181)(118, 166, 131, 179)(119, 167, 127, 175)(120, 168, 135, 183)(122, 170, 141, 189)(125, 173, 140, 188)(126, 174, 138, 186)(128, 176, 143, 191)(134, 182, 137, 185)(136, 184, 142, 190)(139, 187, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 114)(8, 116)(9, 125)(10, 98)(11, 130)(12, 132)(13, 124)(14, 99)(15, 134)(16, 102)(17, 136)(18, 133)(19, 135)(20, 140)(21, 101)(22, 129)(23, 121)(24, 103)(25, 113)(26, 138)(27, 104)(28, 142)(29, 106)(30, 139)(31, 109)(32, 141)(33, 111)(34, 137)(35, 107)(36, 110)(37, 120)(38, 118)(39, 117)(40, 119)(41, 131)(42, 144)(43, 128)(44, 123)(45, 126)(46, 127)(47, 122)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.860
Graph:: bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.868 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C2 (small group id <48, 33>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y3^3, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (Y2^-1 * Y3)^2, Y3 * Y1^4, Y2 * Y1 * Y2 * Y1^-1 * Y3, Y2^-1 * R * Y2 * R * Y3^-1, Y1 * Y2^-3 * Y3, (Y2 * Y1^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 7, 55, 12, 60, 32, 80, 19, 67, 4, 52, 10, 58, 21, 69, 5, 53)(3, 51, 13, 61, 39, 87, 27, 75, 17, 65, 40, 88, 46, 94, 22, 70, 15, 63, 35, 83, 31, 79, 16, 64)(6, 54, 24, 72, 45, 93, 47, 95, 28, 76, 9, 57, 33, 81, 48, 96, 25, 73, 14, 62, 41, 89, 26, 74)(11, 59, 36, 84, 20, 68, 29, 77, 38, 86, 30, 78, 44, 92, 43, 91, 37, 85, 34, 82, 42, 90, 18, 66)(97, 145, 99, 147, 110, 158, 106, 154, 131, 179, 129, 177, 128, 176, 142, 190, 143, 191, 119, 167, 123, 171, 102, 150)(98, 146, 105, 153, 130, 178, 117, 165, 141, 189, 140, 188, 115, 163, 122, 170, 125, 173, 103, 151, 121, 169, 107, 155)(100, 148, 114, 162, 109, 157, 108, 156, 133, 181, 127, 175, 104, 152, 126, 174, 118, 166, 101, 149, 116, 164, 113, 161)(111, 159, 138, 186, 137, 185, 136, 184, 139, 187, 144, 192, 135, 183, 134, 182, 124, 172, 112, 160, 132, 180, 120, 168)
	L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 115)(6, 121)(7, 97)(8, 117)(9, 120)(10, 108)(11, 133)(12, 98)(13, 131)(14, 105)(15, 113)(16, 118)(17, 99)(18, 139)(19, 119)(20, 138)(21, 128)(22, 123)(23, 101)(24, 110)(25, 124)(26, 144)(27, 112)(28, 102)(29, 114)(30, 132)(31, 142)(32, 104)(33, 141)(34, 126)(35, 136)(36, 130)(37, 134)(38, 107)(39, 127)(40, 109)(41, 129)(42, 140)(43, 125)(44, 116)(45, 137)(46, 135)(47, 122)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.855
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.869 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^4, Y3 * Y2^2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y2^-2 * Y3 * Y1, Y3^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 14, 62)(5, 53, 7, 55)(6, 54, 18, 66)(8, 56, 23, 71)(10, 58, 27, 75)(11, 59, 20, 68)(12, 60, 21, 69)(13, 61, 22, 70)(15, 63, 24, 72)(16, 64, 25, 73)(17, 65, 26, 74)(19, 67, 28, 76)(29, 77, 40, 88)(30, 78, 41, 89)(31, 79, 38, 86)(32, 80, 44, 92)(33, 81, 36, 84)(34, 82, 37, 85)(35, 83, 42, 90)(39, 87, 47, 95)(43, 91, 46, 94)(45, 93, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 116, 164, 105, 153)(100, 148, 108, 156, 119, 167, 112, 160)(102, 150, 109, 157, 123, 171, 113, 161)(104, 152, 117, 165, 110, 158, 121, 169)(106, 154, 118, 166, 114, 162, 122, 170)(111, 159, 125, 173, 134, 182, 129, 177)(115, 163, 126, 174, 138, 186, 130, 178)(120, 168, 132, 180, 127, 175, 136, 184)(124, 172, 133, 181, 131, 179, 137, 185)(128, 176, 139, 187, 143, 191, 141, 189)(135, 183, 142, 190, 140, 188, 144, 192)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 112)(6, 97)(7, 117)(8, 120)(9, 121)(10, 98)(11, 119)(12, 125)(13, 99)(14, 127)(15, 128)(16, 129)(17, 101)(18, 116)(19, 102)(20, 110)(21, 132)(22, 103)(23, 134)(24, 135)(25, 136)(26, 105)(27, 107)(28, 106)(29, 139)(30, 109)(31, 140)(32, 115)(33, 141)(34, 113)(35, 114)(36, 142)(37, 118)(38, 143)(39, 124)(40, 144)(41, 122)(42, 123)(43, 126)(44, 131)(45, 130)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.892
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.870 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = ((C4 x C2) : C2) x S3 (small group id <96, 215>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (R * Y3)^2, Y1^4, (Y3^-1, Y1^-1), Y3^4, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y3^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 9, 57, 22, 70, 18, 66)(13, 61, 28, 76, 37, 85, 31, 79)(14, 62, 27, 75, 16, 64, 26, 74)(17, 65, 25, 73, 19, 67, 24, 72)(20, 68, 23, 71, 38, 86, 34, 82)(29, 77, 44, 92, 36, 84, 39, 87)(30, 78, 42, 90, 32, 80, 43, 91)(33, 81, 40, 88, 35, 83, 41, 89)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 109, 157, 125, 173, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 127, 175, 111, 159, 101, 149, 114, 162, 130, 178, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 126, 174, 142, 190, 131, 179, 115, 163, 103, 151, 110, 158, 128, 176, 141, 189, 129, 177, 113, 161)(106, 154, 121, 169, 136, 184, 144, 192, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 143, 191, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 122)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 114)(25, 105)(26, 107)(27, 111)(28, 138)(29, 141)(30, 133)(31, 139)(32, 109)(33, 134)(34, 137)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 130)(41, 119)(42, 127)(43, 124)(44, 144)(45, 132)(46, 125)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.881
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.871 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = ((C4 x C2) : C2) x S3 (small group id <96, 215>)
|r| :: 2
Presentation :: [ R^2, (R * Y3)^2, Y1^4, Y1 * Y2 * Y1^-1 * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2^-2 * Y3^-2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y1^-1 * Y2^6 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 25, 73, 15, 63)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 9, 57, 27, 75, 21, 69)(7, 55, 22, 70, 28, 76, 10, 58)(13, 61, 33, 81, 43, 91, 38, 86)(14, 62, 32, 80, 18, 66, 30, 78)(16, 64, 34, 82, 24, 72, 35, 83)(19, 67, 29, 77, 44, 92, 41, 89)(20, 68, 31, 79, 23, 71, 36, 84)(37, 85, 48, 96, 42, 90, 45, 93)(39, 87, 46, 94, 40, 88, 47, 95)(97, 145, 99, 147, 109, 157, 133, 181, 140, 188, 123, 171, 104, 152, 121, 169, 139, 187, 138, 186, 115, 163, 102, 150)(98, 146, 105, 153, 125, 173, 141, 189, 134, 182, 111, 159, 101, 149, 117, 165, 137, 185, 144, 192, 129, 177, 107, 155)(100, 148, 114, 162, 103, 151, 120, 168, 135, 183, 119, 167, 122, 170, 110, 158, 124, 172, 112, 160, 136, 184, 116, 164)(106, 154, 128, 176, 108, 156, 132, 180, 142, 190, 131, 179, 118, 166, 126, 174, 113, 161, 127, 175, 143, 191, 130, 178)
	L = (1, 100)(2, 106)(3, 110)(4, 115)(5, 118)(6, 119)(7, 97)(8, 122)(9, 126)(10, 129)(11, 131)(12, 98)(13, 103)(14, 102)(15, 130)(16, 99)(17, 101)(18, 123)(19, 136)(20, 133)(21, 128)(22, 134)(23, 138)(24, 121)(25, 114)(26, 140)(27, 116)(28, 104)(29, 108)(30, 107)(31, 105)(32, 111)(33, 143)(34, 141)(35, 144)(36, 117)(37, 112)(38, 142)(39, 109)(40, 139)(41, 113)(42, 120)(43, 124)(44, 135)(45, 127)(46, 125)(47, 137)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.882
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.872 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y3^2, R^2, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^4, Y2^6 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 18, 66, 13, 61)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 10, 58, 20, 68, 16, 64)(11, 59, 21, 69, 33, 81, 27, 75)(12, 60, 28, 76, 34, 82, 22, 70)(15, 63, 29, 77, 35, 83, 23, 71)(17, 65, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 32, 80, 40, 88)(26, 74, 42, 90, 45, 93, 38, 86)(30, 78, 43, 91, 46, 94, 39, 87)(41, 89, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 107, 155, 121, 169, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 127, 175, 112, 160, 101, 149, 109, 157, 123, 171, 136, 184, 120, 168, 106, 154)(100, 148, 108, 156, 122, 170, 137, 185, 142, 190, 131, 179, 115, 163, 130, 178, 141, 189, 140, 188, 126, 174, 111, 159)(105, 153, 118, 166, 134, 182, 143, 191, 139, 187, 125, 173, 110, 158, 124, 172, 138, 186, 144, 192, 135, 183, 119, 167)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 101)(15, 102)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 109)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.884
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.873 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ Y3^2, R^2, Y1^4, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y2^4 * Y1^-1 * Y2^-2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 10, 58, 18, 66, 13, 61)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 8, 56, 20, 68, 16, 64)(11, 59, 24, 72, 33, 81, 27, 75)(12, 60, 28, 76, 34, 82, 23, 71)(15, 63, 29, 77, 35, 83, 22, 70)(17, 65, 21, 69, 36, 84, 31, 79)(25, 73, 40, 88, 32, 80, 37, 85)(26, 74, 42, 90, 45, 93, 39, 87)(30, 78, 43, 91, 46, 94, 38, 86)(41, 89, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 107, 155, 121, 169, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 123, 171, 109, 157, 101, 149, 112, 160, 127, 175, 136, 184, 120, 168, 106, 154)(100, 148, 108, 156, 122, 170, 137, 185, 142, 190, 131, 179, 115, 163, 130, 178, 141, 189, 140, 188, 126, 174, 111, 159)(105, 153, 118, 166, 134, 182, 143, 191, 138, 186, 124, 172, 110, 158, 125, 173, 139, 187, 144, 192, 135, 183, 119, 167)
	L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 101)(15, 102)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 109)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.887
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.874 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y1 * Y3^2 * Y2^2 * Y1, Y3^2 * Y2^-4, Y3 * Y1 * Y3^-1 * Y2^-2 * Y1^-1, Y1 * Y2^-2 * Y3^-1 * Y1^-1 * Y3, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y3^-1 * Y1^2 * Y3 * Y1^-2, Y3^6, Y3 * Y2 * Y3 * Y2 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 25, 73, 15, 63)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 9, 57, 27, 75, 20, 68)(7, 55, 21, 69, 28, 76, 10, 58)(13, 61, 34, 82, 24, 72, 32, 80)(14, 62, 30, 78, 23, 71, 35, 83)(16, 64, 39, 87, 43, 91, 33, 81)(18, 66, 36, 84, 22, 70, 29, 77)(19, 67, 41, 89, 44, 92, 31, 79)(37, 85, 47, 95, 40, 88, 45, 93)(38, 86, 48, 96, 42, 90, 46, 94)(97, 145, 99, 147, 109, 157, 133, 181, 114, 162, 123, 171, 104, 152, 121, 169, 120, 168, 136, 184, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 141, 189, 128, 176, 111, 159, 101, 149, 116, 164, 132, 180, 143, 191, 130, 178, 107, 155)(100, 148, 110, 158, 124, 172, 139, 187, 138, 186, 140, 188, 122, 170, 119, 167, 103, 151, 112, 160, 134, 182, 115, 163)(106, 154, 126, 174, 113, 161, 137, 185, 144, 192, 135, 183, 117, 165, 131, 179, 108, 156, 127, 175, 142, 190, 129, 177)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 117)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 124)(14, 123)(15, 135)(16, 99)(17, 101)(18, 138)(19, 133)(20, 131)(21, 130)(22, 134)(23, 102)(24, 103)(25, 119)(26, 118)(27, 140)(28, 104)(29, 113)(30, 111)(31, 105)(32, 144)(33, 141)(34, 142)(35, 107)(36, 108)(37, 139)(38, 109)(39, 143)(40, 112)(41, 116)(42, 120)(43, 121)(44, 136)(45, 137)(46, 125)(47, 127)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.890
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.875 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y1^4, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1)^2, Y2^5 * Y1^2 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 8, 56)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 16, 64, 20, 68, 10, 58)(12, 60, 21, 69, 33, 81, 25, 73)(13, 61, 22, 70, 34, 82, 26, 74)(15, 63, 23, 71, 35, 83, 29, 77)(17, 65, 24, 72, 36, 84, 31, 79)(27, 75, 40, 88, 32, 80, 37, 85)(28, 76, 41, 89, 45, 93, 38, 86)(30, 78, 43, 91, 46, 94, 39, 87)(42, 90, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 123, 171, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 127, 175, 112, 160, 101, 149, 107, 155, 121, 169, 136, 184, 120, 168, 106, 154)(100, 148, 109, 157, 124, 172, 138, 186, 142, 190, 131, 179, 115, 163, 130, 178, 141, 189, 140, 188, 126, 174, 111, 159)(105, 153, 118, 166, 134, 182, 143, 191, 139, 187, 125, 173, 110, 158, 122, 170, 137, 185, 144, 192, 135, 183, 119, 167)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 124)(13, 99)(14, 101)(15, 102)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 108)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.883
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.876 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (Y2 * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, Y2^-2 * Y1^-1 * Y2^4 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 10, 58)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 16, 64, 20, 68, 8, 56)(12, 60, 24, 72, 33, 81, 26, 74)(13, 61, 23, 71, 34, 82, 25, 73)(15, 63, 22, 70, 35, 83, 29, 77)(17, 65, 21, 69, 36, 84, 31, 79)(27, 75, 37, 85, 32, 80, 40, 88)(28, 76, 41, 89, 45, 93, 39, 87)(30, 78, 43, 91, 46, 94, 38, 86)(42, 90, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 122, 170, 107, 155, 101, 149, 112, 160, 127, 175, 136, 184, 120, 168, 106, 154)(100, 148, 109, 157, 124, 172, 138, 186, 142, 190, 131, 179, 115, 163, 130, 178, 141, 189, 140, 188, 126, 174, 111, 159)(105, 153, 118, 166, 134, 182, 143, 191, 137, 185, 121, 169, 110, 158, 125, 173, 139, 187, 144, 192, 135, 183, 119, 167)
	L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 121)(12, 124)(13, 99)(14, 101)(15, 102)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 107)(26, 137)(27, 138)(28, 108)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 122)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.886
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.877 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (R * Y3)^2, Y1^4, Y3^-2 * Y1^2, (Y3, Y1), Y3 * Y2 * Y3 * Y2^-1, (Y2^-1, Y1), (R * Y1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y2^6 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 22, 70, 18, 66)(13, 61, 23, 71, 37, 85, 31, 79)(14, 62, 24, 72, 16, 64, 25, 73)(17, 65, 26, 74, 19, 67, 27, 75)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 36, 84, 44, 92)(30, 78, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 35, 83, 43, 91)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 125, 173, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 130, 178, 114, 162, 101, 149, 111, 159, 127, 175, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 126, 174, 142, 190, 131, 179, 115, 163, 103, 151, 110, 158, 128, 176, 141, 189, 129, 177, 113, 161)(106, 154, 121, 169, 136, 184, 144, 192, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 143, 191, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 121)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 111)(25, 105)(26, 107)(27, 114)(28, 138)(29, 141)(30, 133)(31, 137)(32, 109)(33, 134)(34, 139)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 127)(41, 119)(42, 130)(43, 124)(44, 144)(45, 132)(46, 125)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.885
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.878 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, Y1^4, (Y2^-1 * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y2 * Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y2^-2 * Y3^-1 * Y1 * Y2^-2, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 11, 59)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 9, 57)(14, 62, 28, 76, 37, 85, 29, 77)(15, 63, 26, 74, 16, 64, 27, 75)(17, 65, 24, 72, 19, 67, 25, 73)(20, 68, 23, 71, 38, 86, 34, 82)(30, 78, 39, 87, 36, 84, 44, 92)(31, 79, 42, 90, 32, 80, 43, 91)(33, 81, 40, 88, 35, 83, 41, 89)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 125, 173, 109, 157, 101, 149, 114, 162, 130, 178, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 142, 190, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 141, 189, 129, 177, 113, 161)(106, 154, 121, 169, 136, 184, 144, 192, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 143, 191, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 122)(14, 127)(15, 117)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 114)(25, 105)(26, 107)(27, 109)(28, 138)(29, 139)(30, 141)(31, 133)(32, 110)(33, 134)(34, 137)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 130)(41, 119)(42, 125)(43, 124)(44, 144)(45, 132)(46, 126)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.888
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.879 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, (Y2, Y3^-1), (Y2 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (R * Y2)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y2^-4 * Y3^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2, Y3 * Y1 * Y3^-1 * Y2^-2 * Y1^-1, Y1^2 * Y2^-1 * Y3^-2 * Y2^-1, Y3^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 11, 59)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 20, 68, 27, 75, 9, 57)(7, 55, 21, 69, 28, 76, 10, 58)(14, 62, 34, 82, 24, 72, 32, 80)(15, 63, 35, 83, 23, 71, 30, 78)(16, 64, 33, 81, 43, 91, 37, 85)(18, 66, 36, 84, 22, 70, 29, 77)(19, 67, 31, 79, 44, 92, 41, 89)(38, 86, 45, 93, 40, 88, 47, 95)(39, 87, 48, 96, 42, 90, 46, 94)(97, 145, 99, 147, 110, 158, 134, 182, 114, 162, 123, 171, 104, 152, 121, 169, 120, 168, 136, 184, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 141, 189, 128, 176, 109, 157, 101, 149, 116, 164, 132, 180, 143, 191, 130, 178, 107, 155)(100, 148, 111, 159, 124, 172, 139, 187, 138, 186, 140, 188, 122, 170, 119, 167, 103, 151, 112, 160, 135, 183, 115, 163)(106, 154, 126, 174, 113, 161, 137, 185, 144, 192, 133, 181, 117, 165, 131, 179, 108, 156, 127, 175, 142, 190, 129, 177)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 117)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 133)(14, 124)(15, 123)(16, 99)(17, 101)(18, 138)(19, 134)(20, 131)(21, 130)(22, 135)(23, 102)(24, 103)(25, 119)(26, 118)(27, 140)(28, 104)(29, 113)(30, 109)(31, 105)(32, 144)(33, 141)(34, 142)(35, 107)(36, 108)(37, 143)(38, 139)(39, 110)(40, 112)(41, 116)(42, 120)(43, 121)(44, 136)(45, 137)(46, 125)(47, 127)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.889
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.880 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y1^4, Y2^-2 * Y3^-2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-2, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1^-2 * Y3 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y1^-1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2 * R * Y2 * R * Y1^-2, Y3 * Y2 * Y3 * Y1^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 11, 59)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 21, 69, 27, 75, 9, 57)(7, 55, 22, 70, 28, 76, 10, 58)(14, 62, 33, 81, 43, 91, 37, 85)(15, 63, 30, 78, 18, 66, 32, 80)(16, 64, 35, 83, 24, 72, 34, 82)(19, 67, 29, 77, 44, 92, 41, 89)(20, 68, 36, 84, 23, 71, 31, 79)(38, 86, 45, 93, 42, 90, 48, 96)(39, 87, 46, 94, 40, 88, 47, 95)(97, 145, 99, 147, 110, 158, 134, 182, 140, 188, 123, 171, 104, 152, 121, 169, 139, 187, 138, 186, 115, 163, 102, 150)(98, 146, 105, 153, 125, 173, 141, 189, 133, 181, 109, 157, 101, 149, 117, 165, 137, 185, 144, 192, 129, 177, 107, 155)(100, 148, 114, 162, 103, 151, 120, 168, 135, 183, 119, 167, 122, 170, 111, 159, 124, 172, 112, 160, 136, 184, 116, 164)(106, 154, 128, 176, 108, 156, 132, 180, 142, 190, 131, 179, 118, 166, 126, 174, 113, 161, 127, 175, 143, 191, 130, 178)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 119)(7, 97)(8, 122)(9, 126)(10, 129)(11, 131)(12, 98)(13, 130)(14, 103)(15, 102)(16, 99)(17, 101)(18, 123)(19, 136)(20, 134)(21, 128)(22, 133)(23, 138)(24, 121)(25, 114)(26, 140)(27, 116)(28, 104)(29, 108)(30, 107)(31, 105)(32, 109)(33, 143)(34, 141)(35, 144)(36, 117)(37, 142)(38, 112)(39, 110)(40, 139)(41, 113)(42, 120)(43, 124)(44, 135)(45, 127)(46, 125)(47, 137)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.891
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.881 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = ((C4 x C2) : C2) x S3 (small group id <96, 215>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y3 * Y1^-1 * Y3 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y3, (Y1^-2 * Y2)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 30, 78, 15, 63, 28, 76, 44, 92, 36, 84, 19, 67, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 26, 74, 8, 56, 24, 72, 17, 65, 34, 82, 42, 90, 21, 69, 13, 61)(4, 52, 10, 58, 22, 70, 40, 88, 35, 83, 18, 66, 6, 54, 9, 57, 23, 71, 39, 87, 33, 81, 16, 64)(12, 60, 32, 80, 45, 93, 48, 96, 43, 91, 27, 75, 14, 62, 31, 79, 46, 94, 47, 95, 41, 89, 25, 73)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 121, 169)(106, 154, 123, 171)(107, 155, 126, 174)(109, 157, 124, 172)(111, 159, 120, 168)(112, 160, 127, 175)(114, 162, 128, 176)(115, 163, 125, 173)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 139, 187)(122, 170, 140, 188)(129, 177, 141, 189)(130, 178, 133, 181)(131, 179, 142, 190)(132, 180, 138, 186)(135, 183, 143, 191)(136, 184, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 127)(12, 120)(13, 123)(14, 99)(15, 102)(16, 101)(17, 128)(18, 126)(19, 129)(20, 135)(21, 137)(22, 140)(23, 103)(24, 110)(25, 109)(26, 139)(27, 104)(28, 106)(29, 141)(30, 112)(31, 113)(32, 107)(33, 133)(34, 142)(35, 115)(36, 136)(37, 131)(38, 143)(39, 132)(40, 116)(41, 122)(42, 144)(43, 117)(44, 119)(45, 130)(46, 125)(47, 138)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.870
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.882 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = ((C4 x C2) : C2) x S3 (small group id <96, 215>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1, Y3 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y2 * Y3^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 42, 90, 36, 84, 47, 95, 39, 87, 48, 96, 40, 88, 19, 67, 5, 53)(3, 51, 11, 59, 35, 83, 43, 91, 28, 76, 8, 56, 26, 74, 18, 66, 41, 89, 44, 92, 24, 72, 13, 61)(4, 52, 15, 63, 25, 73, 20, 68, 34, 82, 10, 58, 32, 80, 9, 57, 30, 78, 22, 70, 6, 54, 17, 65)(12, 60, 38, 86, 46, 94, 31, 79, 16, 64, 33, 81, 21, 69, 37, 85, 45, 93, 29, 77, 14, 62, 27, 75)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 112, 160)(101, 149, 114, 162)(102, 150, 117, 165)(103, 151, 120, 168)(105, 153, 127, 175)(106, 154, 129, 177)(107, 155, 132, 180)(108, 156, 130, 178)(109, 157, 135, 183)(110, 158, 128, 176)(111, 159, 125, 173)(113, 161, 123, 171)(115, 163, 131, 179)(116, 164, 133, 181)(118, 166, 134, 182)(119, 167, 139, 187)(121, 169, 142, 190)(122, 170, 143, 191)(124, 172, 144, 192)(126, 174, 141, 189)(136, 184, 140, 188)(137, 185, 138, 186)
	L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 121)(8, 123)(9, 119)(10, 98)(11, 133)(12, 131)(13, 129)(14, 99)(15, 136)(16, 122)(17, 135)(18, 134)(19, 102)(20, 101)(21, 137)(22, 132)(23, 118)(24, 110)(25, 138)(26, 117)(27, 114)(28, 112)(29, 104)(30, 115)(31, 109)(32, 144)(33, 107)(34, 143)(35, 142)(36, 113)(37, 139)(38, 140)(39, 111)(40, 116)(41, 141)(42, 130)(43, 125)(44, 127)(45, 120)(46, 124)(47, 128)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.871
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.883 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^4, Y2 * Y1^-2 * Y3 * Y2 * Y1^-4 * Y3, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 41, 89, 33, 81, 48, 96, 40, 88, 25, 73, 13, 61, 5, 53)(3, 51, 7, 55, 15, 63, 27, 75, 42, 90, 37, 85, 22, 70, 32, 80, 47, 95, 36, 84, 21, 69, 10, 58)(4, 52, 8, 56, 16, 64, 28, 76, 43, 91, 34, 82, 19, 67, 31, 79, 46, 94, 39, 87, 24, 72, 12, 60)(9, 57, 17, 65, 29, 77, 44, 92, 38, 86, 23, 71, 11, 59, 18, 66, 30, 78, 45, 93, 35, 83, 20, 68)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 106, 154)(102, 150, 111, 159)(104, 152, 114, 162)(105, 153, 115, 163)(108, 156, 119, 167)(109, 157, 117, 165)(110, 158, 123, 171)(112, 160, 126, 174)(113, 161, 127, 175)(116, 164, 130, 178)(118, 166, 129, 177)(120, 168, 134, 182)(121, 169, 132, 180)(122, 170, 138, 186)(124, 172, 141, 189)(125, 173, 142, 190)(128, 176, 144, 192)(131, 179, 139, 187)(133, 181, 137, 185)(135, 183, 140, 188)(136, 184, 143, 191)
	L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 99)(10, 116)(11, 118)(12, 101)(13, 120)(14, 124)(15, 125)(16, 102)(17, 103)(18, 128)(19, 129)(20, 106)(21, 131)(22, 107)(23, 133)(24, 109)(25, 135)(26, 139)(27, 140)(28, 110)(29, 111)(30, 143)(31, 144)(32, 114)(33, 115)(34, 137)(35, 117)(36, 141)(37, 119)(38, 138)(39, 121)(40, 142)(41, 130)(42, 134)(43, 122)(44, 123)(45, 132)(46, 136)(47, 126)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.875
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.884 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1^-1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y1^-2 * Y2 * Y1^2 * Y2, (Y1 * Y2 * Y1^-1 * Y2)^2, (Y1^-3 * Y2)^2, Y2 * Y3 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 16, 64, 32, 80, 26, 74, 40, 88, 23, 71, 38, 86, 31, 79, 15, 63, 5, 53)(3, 51, 9, 57, 17, 65, 35, 83, 30, 78, 14, 62, 21, 69, 7, 55, 19, 67, 33, 81, 27, 75, 11, 59)(4, 52, 8, 56, 18, 66, 34, 82, 45, 93, 41, 89, 24, 72, 39, 87, 48, 96, 44, 92, 29, 77, 13, 61)(10, 58, 22, 70, 36, 84, 47, 95, 43, 91, 28, 76, 12, 60, 20, 68, 37, 85, 46, 94, 42, 90, 25, 73)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(107, 155, 122, 170)(109, 157, 121, 169)(111, 159, 123, 171)(112, 160, 129, 177)(114, 162, 133, 181)(115, 163, 134, 182)(116, 164, 135, 183)(117, 165, 136, 184)(124, 172, 137, 185)(125, 173, 139, 187)(126, 174, 128, 176)(127, 175, 131, 179)(130, 178, 143, 191)(132, 180, 144, 192)(138, 186, 141, 189)(140, 188, 142, 190)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 118)(10, 99)(11, 121)(12, 117)(13, 101)(14, 124)(15, 125)(16, 130)(17, 132)(18, 102)(19, 133)(20, 103)(21, 108)(22, 105)(23, 135)(24, 136)(25, 107)(26, 137)(27, 138)(28, 110)(29, 111)(30, 139)(31, 140)(32, 141)(33, 142)(34, 112)(35, 143)(36, 113)(37, 115)(38, 144)(39, 119)(40, 120)(41, 122)(42, 123)(43, 126)(44, 127)(45, 128)(46, 129)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.872
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.885 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y3^4, (Y2 * R)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1 * Y3^-2 * Y2 * Y1^-1, Y3^2 * Y1 * Y2 * Y1^-1 * Y2, (Y2 * Y1^-3)^2, Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-3, (Y3 * Y1^2 * Y3)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 30, 78, 15, 63, 28, 76, 44, 92, 36, 84, 19, 67, 5, 53)(3, 51, 11, 59, 21, 69, 41, 89, 34, 82, 17, 65, 26, 74, 8, 56, 24, 72, 38, 86, 32, 80, 13, 61)(4, 52, 10, 58, 22, 70, 40, 88, 35, 83, 18, 66, 6, 54, 9, 57, 23, 71, 39, 87, 33, 81, 16, 64)(12, 60, 25, 73, 42, 90, 47, 95, 46, 94, 31, 79, 14, 62, 27, 75, 43, 91, 48, 96, 45, 93, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 121, 169)(106, 154, 123, 171)(107, 155, 124, 172)(109, 157, 126, 174)(111, 159, 122, 170)(112, 160, 127, 175)(114, 162, 125, 173)(115, 163, 128, 176)(116, 164, 134, 182)(118, 166, 138, 186)(119, 167, 139, 187)(120, 168, 140, 188)(129, 177, 141, 189)(130, 178, 133, 181)(131, 179, 142, 190)(132, 180, 137, 185)(135, 183, 143, 191)(136, 184, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 123)(12, 122)(13, 127)(14, 99)(15, 102)(16, 101)(17, 125)(18, 126)(19, 129)(20, 135)(21, 138)(22, 140)(23, 103)(24, 139)(25, 107)(26, 110)(27, 104)(28, 106)(29, 109)(30, 112)(31, 113)(32, 141)(33, 133)(34, 142)(35, 115)(36, 136)(37, 131)(38, 143)(39, 132)(40, 116)(41, 144)(42, 120)(43, 117)(44, 119)(45, 130)(46, 128)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.877
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.886 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^4, Y1^-1 * Y2 * Y1^3 * Y3 * Y2 * Y3 * Y1^-2, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 41, 89, 36, 84, 48, 96, 40, 88, 25, 73, 13, 61, 5, 53)(3, 51, 9, 57, 19, 67, 33, 81, 47, 95, 32, 80, 23, 71, 38, 86, 42, 90, 27, 75, 15, 63, 7, 55)(4, 52, 8, 56, 16, 64, 28, 76, 43, 91, 35, 83, 21, 69, 31, 79, 46, 94, 39, 87, 24, 72, 12, 60)(10, 58, 20, 68, 34, 82, 45, 93, 30, 78, 18, 66, 11, 59, 22, 70, 37, 85, 44, 92, 29, 77, 17, 65)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 105, 153)(102, 150, 111, 159)(104, 152, 114, 162)(106, 154, 117, 165)(108, 156, 118, 166)(109, 157, 115, 163)(110, 158, 123, 171)(112, 160, 126, 174)(113, 161, 127, 175)(116, 164, 131, 179)(119, 167, 132, 180)(120, 168, 133, 181)(121, 169, 129, 177)(122, 170, 138, 186)(124, 172, 141, 189)(125, 173, 142, 190)(128, 176, 144, 192)(130, 178, 139, 187)(134, 182, 137, 185)(135, 183, 140, 188)(136, 184, 143, 191)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 116)(10, 99)(11, 119)(12, 101)(13, 120)(14, 124)(15, 125)(16, 102)(17, 103)(18, 128)(19, 130)(20, 105)(21, 132)(22, 134)(23, 107)(24, 109)(25, 135)(26, 139)(27, 140)(28, 110)(29, 111)(30, 143)(31, 144)(32, 114)(33, 141)(34, 115)(35, 137)(36, 117)(37, 138)(38, 118)(39, 121)(40, 142)(41, 131)(42, 133)(43, 122)(44, 123)(45, 129)(46, 136)(47, 126)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.876
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.887 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * R * Y2 * R, (Y1^-2 * Y2)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, (Y2 * R * Y2 * Y1^-1)^2, (Y1^-1 * Y2)^4, Y2 * Y1^5 * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 16, 64, 32, 80, 24, 72, 38, 86, 27, 75, 40, 88, 31, 79, 15, 63, 5, 53)(3, 51, 9, 57, 23, 71, 33, 81, 21, 69, 7, 55, 19, 67, 14, 62, 30, 78, 36, 84, 17, 65, 11, 59)(4, 52, 8, 56, 18, 66, 34, 82, 45, 93, 42, 90, 26, 74, 39, 87, 48, 96, 44, 92, 29, 77, 13, 61)(10, 58, 25, 73, 41, 89, 46, 94, 37, 85, 20, 68, 12, 60, 28, 76, 43, 91, 47, 95, 35, 83, 22, 70)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 120, 168)(106, 154, 122, 170)(107, 155, 123, 171)(109, 157, 121, 169)(111, 159, 119, 167)(112, 160, 129, 177)(114, 162, 133, 181)(115, 163, 134, 182)(116, 164, 135, 183)(117, 165, 136, 184)(124, 172, 138, 186)(125, 173, 139, 187)(126, 174, 128, 176)(127, 175, 132, 180)(130, 178, 143, 191)(131, 179, 144, 192)(137, 185, 141, 189)(140, 188, 142, 190)
	L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 121)(10, 99)(11, 118)(12, 115)(13, 101)(14, 124)(15, 125)(16, 130)(17, 131)(18, 102)(19, 108)(20, 103)(21, 133)(22, 107)(23, 137)(24, 138)(25, 105)(26, 134)(27, 135)(28, 110)(29, 111)(30, 139)(31, 140)(32, 141)(33, 142)(34, 112)(35, 113)(36, 143)(37, 117)(38, 122)(39, 123)(40, 144)(41, 119)(42, 120)(43, 126)(44, 127)(45, 128)(46, 129)(47, 132)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.873
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.888 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (Y1^-1 * Y2)^2, Y3^4, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1 * Y3)^2, Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-3, (Y3 * Y1^2 * Y3)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 33, 81, 29, 77, 14, 62, 24, 72, 39, 87, 32, 80, 17, 65, 5, 53)(3, 51, 11, 59, 25, 73, 41, 89, 48, 96, 40, 88, 28, 76, 44, 92, 45, 93, 34, 82, 19, 67, 8, 56)(4, 52, 10, 58, 20, 68, 36, 84, 31, 79, 16, 64, 6, 54, 9, 57, 21, 69, 35, 83, 30, 78, 15, 63)(12, 60, 27, 75, 42, 90, 46, 94, 38, 86, 22, 70, 13, 61, 26, 74, 43, 91, 47, 95, 37, 85, 23, 71)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 107, 155)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 124, 172)(111, 159, 123, 171)(112, 160, 122, 170)(113, 161, 121, 169)(114, 162, 130, 178)(116, 164, 133, 181)(117, 165, 134, 182)(120, 168, 136, 184)(125, 173, 140, 188)(126, 174, 138, 186)(127, 175, 139, 187)(128, 176, 137, 185)(129, 177, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(135, 183, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 122)(12, 124)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 131)(19, 133)(20, 135)(21, 103)(22, 136)(23, 104)(24, 106)(25, 138)(26, 140)(27, 107)(28, 109)(29, 111)(30, 129)(31, 113)(32, 132)(33, 127)(34, 142)(35, 128)(36, 114)(37, 144)(38, 115)(39, 117)(40, 119)(41, 143)(42, 141)(43, 121)(44, 123)(45, 139)(46, 137)(47, 130)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.878
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.889 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y3^2 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^6, (Y3^-1 * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-1 * Y1^2 * Y2, Y2 * Y3^-1 * Y2 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2 * Y3^-3 * Y1^-1, Y3^2 * Y2 * Y1 * Y3 * Y2 * Y1^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 20, 68, 30, 78, 44, 92, 38, 86, 15, 63, 28, 76, 17, 65, 5, 53)(3, 51, 11, 59, 31, 79, 46, 94, 35, 83, 47, 95, 36, 84, 45, 93, 34, 82, 40, 88, 22, 70, 8, 56)(4, 52, 9, 57, 23, 71, 18, 66, 6, 54, 10, 58, 24, 72, 41, 89, 37, 85, 48, 96, 33, 81, 16, 64)(12, 60, 32, 80, 42, 90, 26, 74, 13, 61, 29, 77, 19, 67, 39, 87, 43, 91, 27, 75, 14, 62, 25, 73)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 107, 155)(102, 150, 115, 163)(103, 151, 118, 166)(105, 153, 123, 171)(106, 154, 125, 173)(108, 156, 129, 177)(109, 157, 120, 168)(111, 159, 131, 179)(112, 160, 121, 169)(113, 161, 127, 175)(114, 162, 135, 183)(116, 164, 130, 178)(117, 165, 136, 184)(119, 167, 139, 187)(122, 170, 137, 185)(124, 172, 142, 190)(126, 174, 141, 189)(128, 176, 144, 192)(132, 180, 140, 188)(133, 181, 138, 186)(134, 182, 143, 191)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 112)(6, 97)(7, 119)(8, 121)(9, 124)(10, 98)(11, 128)(12, 130)(13, 99)(14, 132)(15, 133)(16, 134)(17, 129)(18, 101)(19, 127)(20, 102)(21, 114)(22, 110)(23, 113)(24, 103)(25, 141)(26, 104)(27, 143)(28, 144)(29, 107)(30, 106)(31, 138)(32, 136)(33, 140)(34, 139)(35, 109)(36, 115)(37, 116)(38, 137)(39, 142)(40, 123)(41, 117)(42, 118)(43, 131)(44, 120)(45, 135)(46, 122)(47, 125)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.879
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.890 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C12 x C2) : C2 (small group id <48, 37>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3^-2 * Y1^-4, (Y2 * Y3 * Y1)^2, Y1^-2 * R * Y2 * R * Y2, Y3^6, Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y1, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 22, 70, 34, 82, 47, 95, 39, 87, 16, 64, 32, 80, 19, 67, 5, 53)(3, 51, 11, 59, 35, 83, 42, 90, 29, 77, 8, 56, 27, 75, 18, 66, 38, 86, 44, 92, 24, 72, 13, 61)(4, 52, 9, 57, 25, 73, 20, 68, 6, 54, 10, 58, 26, 74, 43, 91, 40, 88, 48, 96, 37, 85, 17, 65)(12, 60, 36, 84, 45, 93, 31, 79, 14, 62, 28, 76, 21, 69, 41, 89, 46, 94, 30, 78, 15, 63, 33, 81)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 114, 162)(102, 150, 117, 165)(103, 151, 120, 168)(105, 153, 127, 175)(106, 154, 129, 177)(107, 155, 130, 178)(108, 156, 133, 181)(109, 157, 135, 183)(110, 158, 122, 170)(112, 160, 125, 173)(113, 161, 124, 172)(115, 163, 131, 179)(116, 164, 132, 180)(118, 166, 134, 182)(119, 167, 138, 186)(121, 169, 142, 190)(123, 171, 143, 191)(126, 174, 139, 187)(128, 176, 140, 188)(136, 184, 141, 189)(137, 185, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 113)(6, 97)(7, 121)(8, 124)(9, 128)(10, 98)(11, 132)(12, 134)(13, 129)(14, 99)(15, 123)(16, 136)(17, 135)(18, 137)(19, 133)(20, 101)(21, 131)(22, 102)(23, 116)(24, 111)(25, 115)(26, 103)(27, 117)(28, 107)(29, 110)(30, 104)(31, 109)(32, 144)(33, 114)(34, 106)(35, 141)(36, 140)(37, 143)(38, 142)(39, 139)(40, 118)(41, 138)(42, 127)(43, 119)(44, 126)(45, 120)(46, 125)(47, 122)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.874
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.891 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1 * Y2)^2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y1^2 * Y3^-1, Y3^-3 * Y1^-1 * Y3^-1 * Y1^-1, (Y2 * Y3 * Y1^-1)^2, Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y2, (R * Y2 * Y3^-1)^2, (Y3 * Y1 * Y3^-1 * Y2)^2, Y3 * Y1^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y3^2 * Y2 * Y3^-1 * Y2 * Y3^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 21, 69, 40, 88, 38, 86, 47, 95, 35, 83, 44, 92, 34, 82, 17, 65, 5, 53)(3, 51, 11, 59, 31, 79, 46, 94, 37, 85, 45, 93, 36, 84, 48, 96, 39, 87, 41, 89, 22, 70, 8, 56)(4, 52, 14, 62, 23, 71, 18, 66, 30, 78, 10, 58, 28, 76, 9, 57, 26, 74, 20, 68, 6, 54, 16, 64)(12, 60, 33, 81, 43, 91, 25, 73, 15, 63, 24, 72, 19, 67, 32, 80, 42, 90, 27, 75, 13, 61, 29, 77)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 107, 155)(102, 150, 115, 163)(103, 151, 118, 166)(105, 153, 123, 171)(106, 154, 125, 173)(108, 156, 126, 174)(109, 157, 124, 172)(110, 158, 121, 169)(112, 160, 120, 168)(113, 161, 127, 175)(114, 162, 129, 177)(116, 164, 128, 176)(117, 165, 137, 185)(119, 167, 139, 187)(122, 170, 138, 186)(130, 178, 142, 190)(131, 179, 141, 189)(132, 180, 143, 191)(133, 181, 140, 188)(134, 182, 144, 192)(135, 183, 136, 184)
	L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 119)(8, 120)(9, 117)(10, 98)(11, 128)(12, 127)(13, 99)(14, 130)(15, 132)(16, 131)(17, 102)(18, 101)(19, 135)(20, 134)(21, 116)(22, 109)(23, 136)(24, 107)(25, 104)(26, 113)(27, 141)(28, 140)(29, 144)(30, 143)(31, 139)(32, 142)(33, 137)(34, 114)(35, 110)(36, 115)(37, 111)(38, 112)(39, 138)(40, 126)(41, 121)(42, 118)(43, 133)(44, 122)(45, 125)(46, 123)(47, 124)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.880
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.892 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>)
Aut   = (D8 x S3) : C2 (small group id <96, 216>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, (Y1, Y2), (R * Y3)^2, (Y3, Y2^-1), (Y1 * Y2)^2, Y2 * Y3^-2 * Y2, (Y3 * Y2^-1)^2, Y2^-2 * Y1^-2, (R * Y1)^2, (R * Y2^-1)^2, Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y3, (Y3 * Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y3 * Y1 * Y3 * Y2^4 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 22, 70, 38, 86, 36, 84, 43, 91, 37, 85, 44, 92, 32, 80, 13, 61, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59, 23, 71, 39, 87, 47, 95, 46, 94, 48, 96, 45, 93, 31, 79, 15, 63)(4, 52, 17, 65, 7, 55, 21, 69, 24, 72, 19, 67, 28, 76, 10, 58, 27, 75, 12, 60, 30, 78, 18, 66)(14, 62, 33, 81, 16, 64, 35, 83, 20, 68, 34, 82, 40, 88, 25, 73, 41, 89, 26, 74, 42, 90, 29, 77)(97, 145, 99, 147, 109, 157, 127, 175, 140, 188, 144, 192, 139, 187, 143, 191, 134, 182, 119, 167, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 111, 159, 128, 176, 141, 189, 133, 181, 142, 190, 132, 180, 135, 183, 118, 166, 107, 155)(100, 148, 110, 158, 126, 174, 138, 186, 123, 171, 137, 185, 124, 172, 136, 184, 120, 168, 116, 164, 103, 151, 112, 160)(106, 154, 121, 169, 115, 163, 130, 178, 117, 165, 131, 179, 113, 161, 129, 177, 114, 162, 125, 173, 108, 156, 122, 170)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 103)(9, 121)(10, 101)(11, 122)(12, 98)(13, 126)(14, 127)(15, 130)(16, 99)(17, 132)(18, 118)(19, 128)(20, 102)(21, 133)(22, 108)(23, 116)(24, 104)(25, 111)(26, 105)(27, 139)(28, 134)(29, 107)(30, 140)(31, 138)(32, 117)(33, 135)(34, 141)(35, 142)(36, 114)(37, 113)(38, 120)(39, 125)(40, 119)(41, 143)(42, 144)(43, 124)(44, 123)(45, 131)(46, 129)(47, 136)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.869
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.893 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 12, 12})
Quotient :: edge^2
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-2 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y3 * Y2^-1 * Y3 * Y1 * Y2, (Y1^-1 * Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, Y3 * Y1^2 * Y2^-1 * Y3 * Y2 * Y1^-2, Y1^-1 * Y2^-1 * Y1^5 * Y2^-1, Y1^-1 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 20, 68)(6, 54, 22, 70)(7, 55, 24, 72)(8, 56, 27, 75)(10, 58, 34, 82)(11, 59, 32, 80)(12, 60, 37, 85)(14, 62, 41, 89)(15, 63, 35, 83)(16, 64, 26, 74)(17, 65, 36, 84)(18, 66, 28, 76)(19, 67, 39, 87)(21, 69, 30, 78)(23, 71, 43, 91)(25, 73, 46, 94)(29, 77, 47, 95)(31, 79, 48, 96)(33, 81, 44, 92)(38, 86, 45, 93)(40, 88, 42, 90)(97, 98, 103, 119, 138, 131, 143, 132, 144, 134, 108, 101)(99, 107, 102, 117, 121, 115, 124, 104, 122, 106, 129, 110)(100, 111, 133, 139, 127, 105, 125, 116, 136, 141, 120, 113)(109, 135, 140, 126, 112, 128, 114, 137, 142, 130, 118, 123)(145, 147, 156, 177, 192, 170, 191, 172, 186, 169, 151, 150)(146, 152, 149, 163, 182, 165, 180, 155, 179, 158, 167, 154)(148, 160, 168, 188, 184, 157, 173, 166, 175, 190, 181, 162)(153, 174, 187, 183, 159, 171, 161, 178, 189, 185, 164, 176)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.896
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.894 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 12, 12})
Quotient :: edge^2
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y1 * Y3 * Y1 * Y3^-1, Y2^2 * Y1^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, Y3^4, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y3^2 * Y1 * Y3^2, Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y1 * Y2^-5 * Y1, Y1^12 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 20, 68, 7, 55)(2, 50, 10, 58, 34, 82, 12, 60)(3, 51, 15, 63, 31, 79, 17, 65)(5, 53, 18, 66, 37, 85, 22, 70)(6, 54, 19, 67, 29, 77, 24, 72)(8, 56, 26, 74, 47, 95, 28, 76)(9, 57, 30, 78, 13, 61, 32, 80)(11, 59, 33, 81, 23, 71, 36, 84)(14, 62, 38, 86, 43, 91, 40, 88)(16, 64, 41, 89, 21, 69, 42, 90)(25, 73, 44, 92, 39, 87, 45, 93)(27, 75, 46, 94, 35, 83, 48, 96)(97, 98, 104, 121, 139, 133, 116, 130, 143, 135, 110, 101)(99, 109, 102, 119, 123, 117, 127, 105, 125, 107, 131, 112)(100, 114, 134, 141, 124, 108, 103, 118, 136, 140, 122, 106)(111, 137, 144, 129, 120, 126, 113, 138, 142, 132, 115, 128)(145, 147, 158, 179, 191, 173, 164, 175, 187, 171, 152, 150)(146, 153, 149, 165, 183, 167, 178, 157, 181, 160, 169, 155)(148, 163, 170, 190, 184, 161, 151, 168, 172, 192, 182, 159)(154, 177, 188, 185, 166, 176, 156, 180, 189, 186, 162, 174)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.895
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.895 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 12, 12})
Quotient :: loop^2
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-2 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y3 * Y2^-1 * Y3 * Y1 * Y2, (Y1^-1 * Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1, Y3 * Y1^2 * Y2^-1 * Y3 * Y2 * Y1^-2, Y1^-1 * Y2^-1 * Y1^5 * Y2^-1, Y1^-1 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 20, 68, 116, 164)(6, 54, 102, 150, 22, 70, 118, 166)(7, 55, 103, 151, 24, 72, 120, 168)(8, 56, 104, 152, 27, 75, 123, 171)(10, 58, 106, 154, 34, 82, 130, 178)(11, 59, 107, 155, 32, 80, 128, 176)(12, 60, 108, 156, 37, 85, 133, 181)(14, 62, 110, 158, 41, 89, 137, 185)(15, 63, 111, 159, 35, 83, 131, 179)(16, 64, 112, 160, 26, 74, 122, 170)(17, 65, 113, 161, 36, 84, 132, 180)(18, 66, 114, 162, 28, 76, 124, 172)(19, 67, 115, 163, 39, 87, 135, 183)(21, 69, 117, 165, 30, 78, 126, 174)(23, 71, 119, 167, 43, 91, 139, 187)(25, 73, 121, 169, 46, 94, 142, 190)(29, 77, 125, 173, 47, 95, 143, 191)(31, 79, 127, 175, 48, 96, 144, 192)(33, 81, 129, 177, 44, 92, 140, 188)(38, 86, 134, 182, 45, 93, 141, 189)(40, 88, 136, 184, 42, 90, 138, 186)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 69)(7, 71)(8, 74)(9, 77)(10, 81)(11, 54)(12, 53)(13, 87)(14, 51)(15, 85)(16, 80)(17, 52)(18, 89)(19, 76)(20, 88)(21, 73)(22, 75)(23, 90)(24, 65)(25, 67)(26, 58)(27, 61)(28, 56)(29, 68)(30, 64)(31, 57)(32, 66)(33, 62)(34, 70)(35, 95)(36, 96)(37, 91)(38, 60)(39, 92)(40, 93)(41, 94)(42, 83)(43, 79)(44, 78)(45, 72)(46, 82)(47, 84)(48, 86)(97, 147)(98, 152)(99, 156)(100, 160)(101, 163)(102, 145)(103, 150)(104, 149)(105, 174)(106, 146)(107, 179)(108, 177)(109, 173)(110, 167)(111, 171)(112, 168)(113, 178)(114, 148)(115, 182)(116, 176)(117, 180)(118, 175)(119, 154)(120, 188)(121, 151)(122, 191)(123, 161)(124, 186)(125, 166)(126, 187)(127, 190)(128, 153)(129, 192)(130, 189)(131, 158)(132, 155)(133, 162)(134, 165)(135, 159)(136, 157)(137, 164)(138, 169)(139, 183)(140, 184)(141, 185)(142, 181)(143, 172)(144, 170)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.894
Transitivity :: VT+
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.896 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 12, 12})
Quotient :: loop^2
Aut^+ = Q8 x S3 (small group id <48, 40>)
Aut   = QD16 x S3 (small group id <96, 120>)
|r| :: 2
Presentation :: [ R^2, Y2^2 * Y1^2, R * Y1 * R * Y2, Y1 * Y3 * Y1 * Y3^-1, Y2^2 * Y1^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, Y3^4, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y3^2 * Y1 * Y3^2, Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y1 * Y2^-5 * Y1, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 20, 68, 116, 164, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 34, 82, 130, 178, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 31, 79, 127, 175, 17, 65, 113, 161)(5, 53, 101, 149, 18, 66, 114, 162, 37, 85, 133, 181, 22, 70, 118, 166)(6, 54, 102, 150, 19, 67, 115, 163, 29, 77, 125, 173, 24, 72, 120, 168)(8, 56, 104, 152, 26, 74, 122, 170, 47, 95, 143, 191, 28, 76, 124, 172)(9, 57, 105, 153, 30, 78, 126, 174, 13, 61, 109, 157, 32, 80, 128, 176)(11, 59, 107, 155, 33, 81, 129, 177, 23, 71, 119, 167, 36, 84, 132, 180)(14, 62, 110, 158, 38, 86, 134, 182, 43, 91, 139, 187, 40, 88, 136, 184)(16, 64, 112, 160, 41, 89, 137, 185, 21, 69, 117, 165, 42, 90, 138, 186)(25, 73, 121, 169, 44, 92, 140, 188, 39, 87, 135, 183, 45, 93, 141, 189)(27, 75, 123, 171, 46, 94, 142, 190, 35, 83, 131, 179, 48, 96, 144, 192)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 70)(8, 73)(9, 77)(10, 52)(11, 83)(12, 55)(13, 54)(14, 53)(15, 89)(16, 51)(17, 90)(18, 86)(19, 80)(20, 82)(21, 79)(22, 88)(23, 75)(24, 78)(25, 91)(26, 58)(27, 69)(28, 60)(29, 59)(30, 65)(31, 57)(32, 63)(33, 72)(34, 95)(35, 64)(36, 67)(37, 68)(38, 93)(39, 62)(40, 92)(41, 96)(42, 94)(43, 85)(44, 74)(45, 76)(46, 84)(47, 87)(48, 81)(97, 147)(98, 153)(99, 158)(100, 163)(101, 165)(102, 145)(103, 168)(104, 150)(105, 149)(106, 177)(107, 146)(108, 180)(109, 181)(110, 179)(111, 148)(112, 169)(113, 151)(114, 174)(115, 170)(116, 175)(117, 183)(118, 176)(119, 178)(120, 172)(121, 155)(122, 190)(123, 152)(124, 192)(125, 164)(126, 154)(127, 187)(128, 156)(129, 188)(130, 157)(131, 191)(132, 189)(133, 160)(134, 159)(135, 167)(136, 161)(137, 166)(138, 162)(139, 171)(140, 185)(141, 186)(142, 184)(143, 173)(144, 182)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.893
Transitivity :: VT+
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.897 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 12, 12})
Quotient :: edge^2
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 15, 63)(6, 54, 16, 64)(7, 55, 20, 68)(8, 56, 23, 71)(10, 58, 25, 73)(11, 59, 28, 76)(12, 60, 30, 78)(14, 62, 32, 80)(17, 65, 33, 81)(18, 66, 34, 82)(19, 67, 36, 84)(21, 69, 37, 85)(22, 70, 39, 87)(24, 72, 41, 89)(26, 74, 42, 90)(27, 75, 43, 91)(29, 77, 44, 92)(31, 79, 45, 93)(35, 83, 46, 94)(38, 86, 47, 95)(40, 88, 48, 96)(97, 98, 103, 115, 131, 123, 134, 125, 136, 127, 108, 101)(99, 107, 102, 114, 117, 113, 120, 104, 118, 106, 122, 110)(100, 111, 126, 141, 144, 140, 143, 139, 142, 132, 116, 105)(109, 128, 138, 121, 135, 119, 137, 129, 133, 130, 112, 124)(145, 147, 156, 170, 184, 166, 182, 168, 179, 165, 151, 150)(146, 152, 149, 161, 175, 162, 173, 155, 171, 158, 163, 154)(148, 160, 164, 181, 190, 185, 191, 183, 192, 186, 174, 157)(153, 169, 180, 176, 187, 172, 188, 178, 189, 177, 159, 167)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.900
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.898 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 12, 12})
Quotient :: edge^2
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y2^-1)^2, (Y1 * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^2, (Y2 * Y3)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1 * Y1^-1)^2, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3 * Y2 * Y3^-1 * Y1^-1 * Y2, Y2^3 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2^-5 * Y1, Y1^12 ]
Map:: polytopal non-degenerate
	R = (1, 49, 4, 52, 20, 68, 7, 55)(2, 50, 10, 58, 34, 82, 12, 60)(3, 51, 15, 63, 31, 79, 17, 65)(5, 53, 22, 70, 37, 85, 18, 66)(6, 54, 24, 72, 29, 77, 19, 67)(8, 56, 26, 74, 47, 95, 28, 76)(9, 57, 30, 78, 13, 61, 32, 80)(11, 59, 36, 84, 23, 71, 33, 81)(14, 62, 38, 86, 43, 91, 40, 88)(16, 64, 42, 90, 21, 69, 41, 89)(25, 73, 44, 92, 39, 87, 45, 93)(27, 75, 48, 96, 35, 83, 46, 94)(97, 98, 104, 121, 139, 133, 116, 130, 143, 135, 110, 101)(99, 109, 102, 119, 123, 117, 127, 105, 125, 107, 131, 112)(100, 114, 134, 140, 124, 106, 103, 118, 136, 141, 122, 108)(111, 137, 142, 129, 115, 128, 113, 138, 144, 132, 120, 126)(145, 147, 158, 179, 191, 173, 164, 175, 187, 171, 152, 150)(146, 153, 149, 165, 183, 167, 178, 157, 181, 160, 169, 155)(148, 163, 170, 190, 184, 159, 151, 168, 172, 192, 182, 161)(154, 177, 188, 185, 162, 174, 156, 180, 189, 186, 166, 176)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.899
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.899 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 12, 12})
Quotient :: loop^2
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y2 * Y1^-1 * Y2^3 * Y1^-1, Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^12 ]
Map:: polytopal non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 16, 64, 112, 160)(7, 55, 103, 151, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 28, 76, 124, 172)(12, 60, 108, 156, 30, 78, 126, 174)(14, 62, 110, 158, 32, 80, 128, 176)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 36, 84, 132, 180)(21, 69, 117, 165, 37, 85, 133, 181)(22, 70, 118, 166, 39, 87, 135, 183)(24, 72, 120, 168, 41, 89, 137, 185)(26, 74, 122, 170, 42, 90, 138, 186)(27, 75, 123, 171, 43, 91, 139, 187)(29, 77, 125, 173, 44, 92, 140, 188)(31, 79, 127, 175, 45, 93, 141, 189)(35, 83, 131, 179, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191)(40, 88, 136, 184, 48, 96, 144, 192)
	L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 66)(7, 67)(8, 70)(9, 52)(10, 74)(11, 54)(12, 53)(13, 80)(14, 51)(15, 78)(16, 76)(17, 72)(18, 69)(19, 83)(20, 57)(21, 65)(22, 58)(23, 89)(24, 56)(25, 87)(26, 62)(27, 86)(28, 61)(29, 88)(30, 93)(31, 60)(32, 90)(33, 85)(34, 64)(35, 75)(36, 68)(37, 82)(38, 77)(39, 71)(40, 79)(41, 81)(42, 73)(43, 94)(44, 95)(45, 96)(46, 84)(47, 91)(48, 92)(97, 147)(98, 152)(99, 156)(100, 160)(101, 161)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 171)(108, 170)(109, 148)(110, 163)(111, 167)(112, 164)(113, 175)(114, 173)(115, 154)(116, 181)(117, 151)(118, 182)(119, 153)(120, 179)(121, 180)(122, 184)(123, 158)(124, 188)(125, 155)(126, 157)(127, 162)(128, 187)(129, 159)(130, 189)(131, 165)(132, 176)(133, 190)(134, 168)(135, 192)(136, 166)(137, 191)(138, 174)(139, 172)(140, 178)(141, 177)(142, 185)(143, 183)(144, 186)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.898
Transitivity :: VT+
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.900 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 12, 12})
Quotient :: loop^2
Aut^+ = (C4 x S3) : C2 (small group id <48, 41>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y2^-1)^2, (Y1 * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^2, (Y2 * Y3)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1 * Y1^-1)^2, Y3^-2 * Y2 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3 * Y2 * Y3^-1 * Y1^-1 * Y2, Y2^3 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2^-5 * Y1, Y1^12 ]
Map:: non-degenerate
	R = (1, 49, 97, 145, 4, 52, 100, 148, 20, 68, 116, 164, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 34, 82, 130, 178, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 31, 79, 127, 175, 17, 65, 113, 161)(5, 53, 101, 149, 22, 70, 118, 166, 37, 85, 133, 181, 18, 66, 114, 162)(6, 54, 102, 150, 24, 72, 120, 168, 29, 77, 125, 173, 19, 67, 115, 163)(8, 56, 104, 152, 26, 74, 122, 170, 47, 95, 143, 191, 28, 76, 124, 172)(9, 57, 105, 153, 30, 78, 126, 174, 13, 61, 109, 157, 32, 80, 128, 176)(11, 59, 107, 155, 36, 84, 132, 180, 23, 71, 119, 167, 33, 81, 129, 177)(14, 62, 110, 158, 38, 86, 134, 182, 43, 91, 139, 187, 40, 88, 136, 184)(16, 64, 112, 160, 42, 90, 138, 186, 21, 69, 117, 165, 41, 89, 137, 185)(25, 73, 121, 169, 44, 92, 140, 188, 39, 87, 135, 183, 45, 93, 141, 189)(27, 75, 123, 171, 48, 96, 144, 192, 35, 83, 131, 179, 46, 94, 142, 190)
	L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 70)(8, 73)(9, 77)(10, 55)(11, 83)(12, 52)(13, 54)(14, 53)(15, 89)(16, 51)(17, 90)(18, 86)(19, 80)(20, 82)(21, 79)(22, 88)(23, 75)(24, 78)(25, 91)(26, 60)(27, 69)(28, 58)(29, 59)(30, 63)(31, 57)(32, 65)(33, 67)(34, 95)(35, 64)(36, 72)(37, 68)(38, 92)(39, 62)(40, 93)(41, 94)(42, 96)(43, 85)(44, 76)(45, 74)(46, 81)(47, 87)(48, 84)(97, 147)(98, 153)(99, 158)(100, 163)(101, 165)(102, 145)(103, 168)(104, 150)(105, 149)(106, 177)(107, 146)(108, 180)(109, 181)(110, 179)(111, 151)(112, 169)(113, 148)(114, 174)(115, 170)(116, 175)(117, 183)(118, 176)(119, 178)(120, 172)(121, 155)(122, 190)(123, 152)(124, 192)(125, 164)(126, 156)(127, 187)(128, 154)(129, 188)(130, 157)(131, 191)(132, 189)(133, 160)(134, 161)(135, 167)(136, 159)(137, 162)(138, 166)(139, 171)(140, 185)(141, 186)(142, 184)(143, 173)(144, 182)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.897
Transitivity :: VT+
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.901 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C6 x Q8 (small group id <48, 46>)
Aut   = C2 x ((C4 x S3) : C2) (small group id <96, 213>)
|r| :: 2
Presentation :: [ R^2, (Y3 * Y1)^2, Y1^-1 * Y3^2 * Y1^-1, Y1^-2 * Y3^-2, (Y3^-1 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^4, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 11, 59)(14, 62, 23, 71, 37, 85, 29, 77)(15, 63, 25, 73, 16, 64, 24, 72)(17, 65, 27, 75, 19, 67, 26, 74)(20, 68, 28, 76, 38, 86, 34, 82)(30, 78, 44, 92, 36, 84, 39, 87)(31, 79, 40, 88, 32, 80, 41, 89)(33, 81, 42, 90, 35, 83, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 130, 178, 114, 162, 101, 149, 109, 157, 125, 173, 140, 188, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 142, 190, 131, 179, 115, 163, 103, 151, 111, 159, 128, 176, 141, 189, 129, 177, 113, 161)(106, 154, 121, 169, 136, 184, 144, 192, 139, 187, 123, 171, 108, 156, 120, 168, 137, 185, 143, 191, 138, 186, 122, 170)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 121)(14, 127)(15, 117)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 109)(25, 105)(26, 107)(27, 114)(28, 138)(29, 137)(30, 141)(31, 133)(32, 110)(33, 134)(34, 139)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 125)(41, 119)(42, 130)(43, 124)(44, 144)(45, 132)(46, 126)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.902
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 8^12, 24^4 ]

E27.902 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 12, 12})
Quotient :: dipole
Aut^+ = C6 x Q8 (small group id <48, 46>)
Aut   = C2 x ((C4 x S3) : C2) (small group id <96, 213>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y3)^2, Y3^4, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 18, 66, 33, 81, 29, 77, 14, 62, 24, 72, 39, 87, 32, 80, 17, 65, 5, 53)(3, 51, 8, 56, 19, 67, 34, 82, 45, 93, 41, 89, 25, 73, 40, 88, 48, 96, 44, 92, 28, 76, 12, 60)(4, 52, 10, 58, 20, 68, 36, 84, 31, 79, 16, 64, 6, 54, 9, 57, 21, 69, 35, 83, 30, 78, 15, 63)(11, 59, 23, 71, 37, 85, 47, 95, 43, 91, 27, 75, 13, 61, 22, 70, 38, 86, 46, 94, 42, 90, 26, 74)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 130, 178)(116, 164, 133, 181)(117, 165, 134, 182)(120, 168, 136, 184)(125, 173, 137, 185)(126, 174, 138, 186)(127, 175, 139, 187)(128, 176, 140, 188)(129, 177, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(135, 183, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 123)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 131)(19, 133)(20, 135)(21, 103)(22, 136)(23, 104)(24, 106)(25, 109)(26, 108)(27, 137)(28, 138)(29, 111)(30, 129)(31, 113)(32, 132)(33, 127)(34, 142)(35, 128)(36, 114)(37, 144)(38, 115)(39, 117)(40, 119)(41, 122)(42, 141)(43, 124)(44, 143)(45, 139)(46, 140)(47, 130)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.901
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.903 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y2^-1, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-2 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3 * Y2^-1)^8, Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 13, 61)(5, 53, 9, 57)(6, 54, 15, 63)(8, 56, 18, 66)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(14, 62, 23, 71)(17, 65, 26, 74)(19, 67, 28, 76)(22, 70, 32, 80)(24, 72, 33, 81)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(35, 83, 44, 92)(40, 88, 45, 93)(41, 89, 46, 94)(42, 90, 47, 95)(43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 102, 150, 108, 156, 110, 158)(104, 152, 106, 154, 113, 161, 115, 163)(109, 157, 111, 159, 117, 165, 119, 167)(114, 162, 116, 164, 122, 170, 124, 172)(118, 166, 120, 168, 121, 169, 127, 175)(123, 171, 125, 173, 126, 174, 131, 179)(128, 176, 129, 177, 130, 178, 135, 183)(132, 180, 133, 181, 134, 182, 140, 188)(136, 184, 137, 185, 138, 186, 139, 187)(141, 189, 142, 190, 143, 191, 144, 192)
	L = (1, 100)(2, 104)(3, 102)(4, 101)(5, 110)(6, 97)(7, 106)(8, 105)(9, 115)(10, 98)(11, 108)(12, 99)(13, 118)(14, 107)(15, 120)(16, 113)(17, 103)(18, 123)(19, 112)(20, 125)(21, 121)(22, 119)(23, 127)(24, 109)(25, 111)(26, 126)(27, 124)(28, 131)(29, 114)(30, 116)(31, 117)(32, 136)(33, 137)(34, 138)(35, 122)(36, 141)(37, 142)(38, 143)(39, 139)(40, 135)(41, 128)(42, 129)(43, 130)(44, 144)(45, 140)(46, 132)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.921
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.904 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, Y1 * Y2 * Y1 * Y2^-1, Y2^4, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1 * Y3 * Y2)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 13, 61)(5, 53, 9, 57)(6, 54, 15, 63)(8, 56, 18, 66)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(14, 62, 24, 72)(17, 65, 26, 74)(19, 67, 29, 77)(22, 70, 32, 80)(23, 71, 33, 81)(25, 73, 34, 82)(27, 75, 36, 84)(28, 76, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(35, 83, 44, 92)(40, 88, 45, 93)(41, 89, 46, 94)(42, 90, 47, 95)(43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 108, 156, 110, 158, 102, 150)(104, 152, 113, 161, 115, 163, 106, 154)(109, 157, 117, 165, 120, 168, 111, 159)(114, 162, 122, 170, 125, 173, 116, 164)(118, 166, 127, 175, 121, 169, 119, 167)(123, 171, 131, 179, 126, 174, 124, 172)(128, 176, 135, 183, 130, 178, 129, 177)(132, 180, 140, 188, 134, 182, 133, 181)(136, 184, 139, 187, 138, 186, 137, 185)(141, 189, 144, 192, 143, 191, 142, 190)
	L = (1, 100)(2, 104)(3, 108)(4, 99)(5, 102)(6, 97)(7, 113)(8, 103)(9, 106)(10, 98)(11, 110)(12, 107)(13, 118)(14, 101)(15, 119)(16, 115)(17, 112)(18, 123)(19, 105)(20, 124)(21, 127)(22, 117)(23, 109)(24, 121)(25, 111)(26, 131)(27, 122)(28, 114)(29, 126)(30, 116)(31, 120)(32, 136)(33, 137)(34, 138)(35, 125)(36, 141)(37, 142)(38, 143)(39, 139)(40, 135)(41, 128)(42, 129)(43, 130)(44, 144)(45, 140)(46, 132)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.920
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.905 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (R * Y2)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3^-4 * Y2^-2, (Y2^2 * Y1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1, Y3 * Y1 * Y3 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y2 * Y1 * Y2^-1, Y3^2 * Y1 * Y3^-2 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 20, 68)(7, 55, 22, 70)(8, 56, 26, 74)(9, 57, 29, 77)(10, 58, 31, 79)(12, 60, 23, 71)(13, 61, 24, 72)(14, 62, 25, 73)(16, 64, 27, 75)(17, 65, 28, 76)(19, 67, 30, 78)(21, 69, 32, 80)(33, 81, 47, 95)(34, 82, 46, 94)(35, 83, 44, 92)(36, 84, 43, 91)(37, 85, 48, 96)(38, 86, 42, 90)(39, 87, 41, 89)(40, 88, 45, 93)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 119, 167, 105, 153)(100, 148, 109, 157, 132, 180, 113, 161)(102, 150, 110, 158, 133, 181, 115, 163)(104, 152, 120, 168, 140, 188, 124, 172)(106, 154, 121, 169, 141, 189, 126, 174)(107, 155, 129, 177, 114, 162, 130, 178)(111, 159, 127, 175, 139, 187, 136, 184)(112, 160, 134, 182, 117, 165, 135, 183)(116, 164, 131, 179, 144, 192, 122, 170)(118, 166, 137, 185, 125, 173, 138, 186)(123, 171, 142, 190, 128, 176, 143, 191)
	L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 113)(6, 97)(7, 120)(8, 123)(9, 124)(10, 98)(11, 127)(12, 132)(13, 134)(14, 99)(15, 125)(16, 133)(17, 135)(18, 136)(19, 101)(20, 130)(21, 102)(22, 116)(23, 140)(24, 142)(25, 103)(26, 114)(27, 141)(28, 143)(29, 144)(30, 105)(31, 138)(32, 106)(33, 139)(34, 111)(35, 107)(36, 117)(37, 108)(38, 115)(39, 110)(40, 137)(41, 131)(42, 122)(43, 118)(44, 128)(45, 119)(46, 126)(47, 121)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.919
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.906 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-4, Y2^-4, Y2^4, (Y3^-1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4 * Y2^2, Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1, (Y1 * Y2^2)^2, Y3^2 * Y1 * Y3^-2 * Y1, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y2^-1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 20, 68)(7, 55, 22, 70)(8, 56, 26, 74)(9, 57, 29, 77)(10, 58, 31, 79)(12, 60, 23, 71)(13, 61, 24, 72)(14, 62, 25, 73)(16, 64, 27, 75)(17, 65, 28, 76)(19, 67, 30, 78)(21, 69, 32, 80)(33, 81, 46, 94)(34, 82, 45, 93)(35, 83, 47, 95)(36, 84, 48, 96)(37, 85, 42, 90)(38, 86, 41, 89)(39, 87, 43, 91)(40, 88, 44, 92)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 119, 167, 105, 153)(100, 148, 109, 157, 132, 180, 113, 161)(102, 150, 110, 158, 133, 181, 115, 163)(104, 152, 120, 168, 140, 188, 124, 172)(106, 154, 121, 169, 141, 189, 126, 174)(107, 155, 129, 177, 114, 162, 131, 179)(111, 159, 130, 178, 144, 192, 127, 175)(112, 160, 134, 182, 117, 165, 135, 183)(116, 164, 122, 170, 138, 186, 136, 184)(118, 166, 137, 185, 125, 173, 139, 187)(123, 171, 142, 190, 128, 176, 143, 191)
	L = (1, 100)(2, 104)(3, 109)(4, 112)(5, 113)(6, 97)(7, 120)(8, 123)(9, 124)(10, 98)(11, 130)(12, 132)(13, 134)(14, 99)(15, 118)(16, 133)(17, 135)(18, 127)(19, 101)(20, 131)(21, 102)(22, 138)(23, 140)(24, 142)(25, 103)(26, 107)(27, 141)(28, 143)(29, 116)(30, 105)(31, 139)(32, 106)(33, 144)(34, 137)(35, 111)(36, 117)(37, 108)(38, 115)(39, 110)(40, 114)(41, 136)(42, 129)(43, 122)(44, 128)(45, 119)(46, 126)(47, 121)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.918
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.907 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y1 * Y2^-2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^2 * Y2)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y3^2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3^-4, Y3 * Y2^-1 * Y3^-5 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 33, 81)(24, 72, 25, 73)(26, 74, 29, 77)(27, 75, 31, 79)(28, 76, 32, 80)(30, 78, 37, 85)(34, 82, 35, 83)(36, 84, 38, 86)(39, 87, 42, 90)(40, 88, 43, 91)(41, 89, 47, 95)(44, 92, 45, 93)(46, 94, 48, 96)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 125, 173, 115, 163, 122, 170)(114, 162, 129, 177, 116, 164, 118, 166)(123, 171, 135, 183, 127, 175, 138, 186)(124, 172, 140, 188, 128, 176, 141, 189)(126, 174, 137, 185, 133, 181, 143, 191)(130, 178, 136, 184, 131, 179, 139, 187)(132, 180, 142, 190, 134, 182, 144, 192)
	L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 126)(13, 127)(14, 129)(15, 101)(16, 130)(17, 131)(18, 102)(19, 133)(20, 104)(21, 135)(22, 137)(23, 138)(24, 140)(25, 141)(26, 106)(27, 113)(28, 107)(29, 111)(30, 136)(31, 112)(32, 109)(33, 143)(34, 144)(35, 142)(36, 114)(37, 139)(38, 116)(39, 121)(40, 117)(41, 128)(42, 120)(43, 119)(44, 132)(45, 134)(46, 122)(47, 124)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.922
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.908 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y1^-1), Y1^4, (R * Y2)^2, (Y2^-1, Y3), (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2^-2 * Y3^3, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, Y3 * Y1 * Y2 * Y3 * Y1 * Y2^-1, Y1^-2 * Y2^4, Y1^-2 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 11, 59, 27, 75, 21, 69)(7, 55, 20, 68, 28, 76, 10, 58)(13, 61, 29, 77, 22, 70, 34, 82)(14, 62, 38, 86, 46, 94, 31, 79)(16, 64, 40, 88, 47, 95, 30, 78)(18, 66, 36, 84, 45, 93, 42, 90)(19, 67, 41, 89, 48, 96, 35, 83)(23, 71, 44, 92, 39, 87, 33, 81)(24, 72, 32, 80, 37, 85, 43, 91)(97, 145, 99, 147, 109, 157, 123, 171, 104, 152, 121, 169, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 117, 165, 101, 149, 111, 159, 130, 178, 107, 155)(100, 148, 110, 158, 133, 181, 144, 192, 122, 170, 142, 190, 120, 168, 115, 163)(103, 151, 112, 160, 114, 162, 135, 183, 124, 172, 143, 191, 141, 189, 119, 167)(106, 154, 126, 174, 138, 186, 140, 188, 116, 164, 136, 184, 132, 180, 129, 177)(108, 156, 127, 175, 128, 176, 137, 185, 113, 161, 134, 182, 139, 187, 131, 179)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 116)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 133)(14, 135)(15, 136)(16, 99)(17, 101)(18, 109)(19, 112)(20, 139)(21, 140)(22, 120)(23, 102)(24, 103)(25, 142)(26, 141)(27, 144)(28, 104)(29, 138)(30, 137)(31, 105)(32, 125)(33, 127)(34, 132)(35, 107)(36, 108)(37, 124)(38, 111)(39, 123)(40, 131)(41, 117)(42, 113)(43, 130)(44, 134)(45, 118)(46, 119)(47, 121)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.917
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.909 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1, Y3), Y1^4, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, Y3 * Y2^2 * Y3^2, Y2^4 * Y1^2, Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y2^-1, Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-2 * Y3^-1 * Y2^2 * Y3^-2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 11, 59, 27, 75, 21, 69)(7, 55, 20, 68, 28, 76, 10, 58)(13, 61, 29, 77, 22, 70, 34, 82)(14, 62, 38, 86, 47, 95, 31, 79)(16, 64, 39, 87, 43, 91, 30, 78)(18, 66, 36, 84, 37, 85, 42, 90)(19, 67, 41, 89, 40, 88, 35, 83)(23, 71, 46, 94, 48, 96, 33, 81)(24, 72, 32, 80, 44, 92, 45, 93)(97, 145, 99, 147, 109, 157, 123, 171, 104, 152, 121, 169, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 117, 165, 101, 149, 111, 159, 130, 178, 107, 155)(100, 148, 110, 158, 120, 168, 136, 184, 122, 170, 143, 191, 140, 188, 115, 163)(103, 151, 112, 160, 133, 181, 144, 192, 124, 172, 139, 187, 114, 162, 119, 167)(106, 154, 126, 174, 132, 180, 142, 190, 116, 164, 135, 183, 138, 186, 129, 177)(108, 156, 127, 175, 141, 189, 137, 185, 113, 161, 134, 182, 128, 176, 131, 179)
	L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 116)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 120)(14, 119)(15, 135)(16, 99)(17, 101)(18, 118)(19, 139)(20, 141)(21, 142)(22, 140)(23, 102)(24, 103)(25, 143)(26, 133)(27, 136)(28, 104)(29, 132)(30, 131)(31, 105)(32, 130)(33, 134)(34, 138)(35, 107)(36, 108)(37, 109)(38, 111)(39, 137)(40, 112)(41, 117)(42, 113)(43, 121)(44, 124)(45, 125)(46, 127)(47, 144)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.916
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.910 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^2 * Y1^2, (Y3, Y1), (R * Y3)^2, Y1^4, Y3^4, (R * Y1^-1)^2, Y1 * Y2^-1 * Y3^-2 * Y2^-1, Y1^-1 * R * Y3^-2 * R * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 6, 54, 10, 58, 13, 61)(4, 52, 9, 57, 7, 55, 11, 59)(12, 60, 17, 65, 14, 62, 18, 66)(15, 63, 16, 64, 19, 67, 20, 68)(21, 69, 22, 70, 23, 71, 24, 72)(25, 73, 27, 75, 26, 74, 28, 76)(29, 77, 31, 79, 30, 78, 32, 80)(33, 81, 34, 82, 35, 83, 36, 84)(37, 85, 38, 86, 39, 87, 40, 88)(41, 89, 43, 91, 42, 90, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 101, 149, 109, 157, 104, 152, 106, 154, 98, 146, 102, 150)(100, 148, 111, 159, 107, 155, 116, 164, 103, 151, 115, 163, 105, 153, 112, 160)(108, 156, 117, 165, 114, 162, 120, 168, 110, 158, 119, 167, 113, 161, 118, 166)(121, 169, 129, 177, 124, 172, 132, 180, 122, 170, 131, 179, 123, 171, 130, 178)(125, 173, 133, 181, 128, 176, 136, 184, 126, 174, 135, 183, 127, 175, 134, 182)(137, 185, 141, 189, 140, 188, 144, 192, 138, 186, 142, 190, 139, 187, 143, 191)
	L = (1, 100)(2, 105)(3, 108)(4, 104)(5, 107)(6, 113)(7, 97)(8, 103)(9, 101)(10, 110)(11, 98)(12, 106)(13, 114)(14, 99)(15, 121)(16, 123)(17, 109)(18, 102)(19, 122)(20, 124)(21, 125)(22, 127)(23, 126)(24, 128)(25, 115)(26, 111)(27, 116)(28, 112)(29, 119)(30, 117)(31, 120)(32, 118)(33, 137)(34, 139)(35, 138)(36, 140)(37, 141)(38, 143)(39, 142)(40, 144)(41, 131)(42, 129)(43, 132)(44, 130)(45, 135)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.914
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.911 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2, Y3^2 * Y1^2, Y3^4, Y3^2 * Y1^-2, (Y1 * Y3)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y1 * R * Y3^-2 * R * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 16, 64, 6, 54)(4, 52, 10, 58, 7, 55, 11, 59)(12, 60, 18, 66, 13, 61, 17, 65)(14, 62, 20, 68, 19, 67, 15, 63)(21, 69, 24, 72, 23, 71, 22, 70)(25, 73, 28, 76, 26, 74, 27, 75)(29, 77, 32, 80, 30, 78, 31, 79)(33, 81, 36, 84, 35, 83, 34, 82)(37, 85, 40, 88, 39, 87, 38, 86)(41, 89, 44, 92, 42, 90, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 98, 146, 105, 153, 104, 152, 112, 160, 101, 149, 102, 150)(100, 148, 110, 158, 106, 154, 116, 164, 103, 151, 115, 163, 107, 155, 111, 159)(108, 156, 117, 165, 114, 162, 120, 168, 109, 157, 119, 167, 113, 161, 118, 166)(121, 169, 129, 177, 124, 172, 132, 180, 122, 170, 131, 179, 123, 171, 130, 178)(125, 173, 133, 181, 128, 176, 136, 184, 126, 174, 135, 183, 127, 175, 134, 182)(137, 185, 141, 189, 140, 188, 144, 192, 138, 186, 142, 190, 139, 187, 143, 191)
	L = (1, 100)(2, 106)(3, 108)(4, 104)(5, 107)(6, 113)(7, 97)(8, 103)(9, 114)(10, 101)(11, 98)(12, 112)(13, 99)(14, 121)(15, 123)(16, 109)(17, 105)(18, 102)(19, 122)(20, 124)(21, 125)(22, 127)(23, 126)(24, 128)(25, 115)(26, 110)(27, 116)(28, 111)(29, 119)(30, 117)(31, 120)(32, 118)(33, 137)(34, 139)(35, 138)(36, 140)(37, 141)(38, 143)(39, 142)(40, 144)(41, 131)(42, 129)(43, 132)(44, 130)(45, 135)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.915
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.912 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1^4, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y1^4, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^4 * Y1^2, Y1 * Y2^-1 * Y3 * Y1 * Y2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3^-1 * Y2 * Y1^-1 * Y2^2 * R * Y2^-1 * R, Y2 * Y1 * Y2 * R * Y2^-1 * Y1 * Y2^-1 * R * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2^-1 * R * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-1 * R * Y2^-1 * Y1^-1, Y2 * R * Y2 * R * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 16, 64, 24, 72)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 114, 162, 102, 150, 113, 161, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 111, 159, 124, 172, 107, 155, 123, 171, 110, 158, 122, 170)(115, 163, 125, 173, 119, 167, 128, 176, 117, 165, 127, 175, 118, 166, 126, 174)(129, 177, 137, 185, 132, 180, 140, 188, 130, 178, 139, 187, 131, 179, 138, 186)(133, 181, 141, 189, 136, 184, 144, 192, 134, 182, 143, 191, 135, 183, 142, 190)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 129)(26, 131)(27, 130)(28, 132)(29, 133)(30, 135)(31, 134)(32, 136)(33, 123)(34, 121)(35, 124)(36, 122)(37, 127)(38, 125)(39, 128)(40, 126)(41, 141)(42, 142)(43, 143)(44, 144)(45, 139)(46, 140)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.913
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.913 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1^-1 * Y2 * Y1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, (Y1^-2 * Y3)^2, (Y1^2 * Y3)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-3, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 37, 85, 29, 77, 43, 91, 32, 80, 46, 94, 47, 95, 27, 75, 11, 59, 3, 51, 8, 56, 20, 68, 38, 86, 48, 96, 30, 78, 44, 92, 31, 79, 45, 93, 35, 83, 15, 63, 5, 53)(4, 52, 12, 60, 28, 76, 39, 87, 26, 74, 10, 58, 25, 73, 14, 62, 33, 81, 41, 89, 21, 69, 18, 66, 6, 54, 17, 65, 34, 82, 40, 88, 24, 72, 9, 57, 23, 71, 16, 64, 36, 84, 42, 90, 22, 70, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 130, 178)(125, 173, 126, 174)(127, 175, 128, 176)(129, 177, 132, 180)(131, 179, 143, 191)(133, 181, 144, 192)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 130)(16, 101)(17, 126)(18, 128)(19, 135)(20, 118)(21, 116)(22, 103)(23, 139)(24, 141)(25, 140)(26, 142)(27, 124)(28, 111)(29, 113)(30, 108)(31, 114)(32, 109)(33, 133)(34, 123)(35, 138)(36, 144)(37, 132)(38, 136)(39, 134)(40, 115)(41, 131)(42, 143)(43, 121)(44, 119)(45, 122)(46, 120)(47, 137)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.912
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.914 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, Y3^-2 * Y1 * Y3^-1 * Y1 * Y2, (Y3 * Y1^-2)^2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 32, 80, 12, 60, 24, 72, 41, 89, 47, 95, 45, 93, 31, 79, 15, 63, 26, 74, 43, 91, 48, 96, 46, 94, 30, 78, 13, 61, 25, 73, 42, 90, 36, 84, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 23, 71, 16, 64, 4, 52, 14, 62, 33, 81, 39, 87, 21, 69, 10, 58, 28, 76, 17, 65, 34, 82, 44, 92, 22, 70, 8, 56, 6, 54, 19, 67, 35, 83, 40, 88, 27, 75, 9, 57)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 109, 157)(103, 151, 117, 165)(105, 153, 120, 168)(106, 154, 121, 169)(107, 155, 126, 174)(111, 159, 124, 172)(112, 160, 122, 170)(113, 161, 128, 176)(114, 162, 130, 178)(115, 163, 127, 175)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 138, 186)(123, 171, 139, 187)(125, 173, 141, 189)(129, 177, 142, 190)(131, 179, 133, 181)(132, 180, 136, 184)(135, 183, 143, 191)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 118)(8, 120)(9, 122)(10, 98)(11, 101)(12, 124)(13, 99)(14, 128)(15, 102)(16, 121)(17, 127)(18, 131)(19, 126)(20, 135)(21, 137)(22, 139)(23, 103)(24, 112)(25, 104)(26, 106)(27, 138)(28, 109)(29, 142)(30, 110)(31, 107)(32, 115)(33, 114)(34, 133)(35, 141)(36, 134)(37, 125)(38, 143)(39, 144)(40, 116)(41, 123)(42, 117)(43, 119)(44, 132)(45, 129)(46, 130)(47, 140)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.910
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.915 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y3 * Y2 * Y3^-1, Y3^4, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y2, Y3^-1 * Y1^-1 * Y3^2 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y2 * Y1^-3, Y1^18 * Y2 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 32, 80, 13, 61, 25, 73, 42, 90, 47, 95, 45, 93, 31, 79, 15, 63, 27, 75, 43, 91, 48, 96, 46, 94, 30, 78, 12, 60, 24, 72, 41, 89, 36, 84, 17, 65, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 22, 70, 19, 67, 6, 54, 16, 64, 34, 82, 40, 88, 21, 69, 9, 57, 26, 74, 18, 66, 35, 83, 44, 92, 23, 71, 8, 56, 4, 52, 14, 62, 33, 81, 39, 87, 28, 76, 10, 58)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 112, 160)(102, 150, 109, 157)(103, 151, 117, 165)(105, 153, 120, 168)(106, 154, 121, 169)(107, 155, 126, 174)(110, 158, 127, 175)(111, 159, 122, 170)(113, 161, 131, 179)(114, 162, 128, 176)(115, 163, 123, 171)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 138, 186)(124, 172, 139, 187)(125, 173, 141, 189)(129, 177, 133, 181)(130, 178, 142, 190)(132, 180, 135, 183)(136, 184, 143, 191)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 107)(6, 97)(7, 118)(8, 120)(9, 123)(10, 98)(11, 127)(12, 122)(13, 99)(14, 128)(15, 102)(16, 126)(17, 130)(18, 101)(19, 121)(20, 135)(21, 137)(22, 139)(23, 103)(24, 115)(25, 104)(26, 109)(27, 106)(28, 138)(29, 133)(30, 110)(31, 114)(32, 112)(33, 113)(34, 141)(35, 142)(36, 140)(37, 131)(38, 132)(39, 144)(40, 116)(41, 124)(42, 117)(43, 119)(44, 143)(45, 129)(46, 125)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.911
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.916 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^3, Y3^-1 * Y2 * Y3 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-2)^2, Y2 * Y1^-1 * R * Y2 * Y3 * Y1 * R, Y3^-1 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y2 * Y1^-1 * Y3^-2 * Y2 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3^3, (Y1^-1 * Y3^-1 * Y1^-1)^3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 16, 64, 30, 78, 48, 96, 37, 85, 46, 94, 20, 68, 6, 54, 10, 58, 25, 73, 17, 65, 4, 52, 9, 57, 24, 72, 33, 81, 43, 91, 47, 95, 22, 70, 32, 80, 19, 67, 5, 53)(3, 51, 11, 59, 21, 69, 28, 76, 35, 83, 44, 92, 45, 93, 18, 66, 42, 90, 38, 86, 14, 62, 34, 82, 40, 88, 36, 84, 12, 60, 29, 77, 27, 75, 8, 56, 26, 74, 31, 79, 39, 87, 41, 89, 15, 63, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 114, 162)(102, 150, 117, 165)(103, 151, 110, 158)(105, 153, 125, 173)(106, 154, 127, 175)(107, 155, 129, 177)(108, 156, 115, 163)(109, 157, 133, 181)(112, 160, 135, 183)(113, 161, 140, 188)(116, 164, 134, 182)(118, 166, 131, 179)(119, 167, 124, 172)(120, 168, 138, 186)(121, 169, 136, 184)(122, 170, 139, 187)(123, 171, 142, 190)(126, 174, 132, 180)(128, 176, 137, 185)(130, 178, 143, 191)(141, 189, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 113)(6, 97)(7, 120)(8, 114)(9, 126)(10, 98)(11, 125)(12, 131)(13, 132)(14, 99)(15, 136)(16, 139)(17, 119)(18, 137)(19, 121)(20, 101)(21, 123)(22, 102)(23, 129)(24, 144)(25, 103)(26, 138)(27, 141)(28, 104)(29, 140)(30, 143)(31, 134)(32, 106)(33, 133)(34, 107)(35, 122)(36, 124)(37, 128)(38, 109)(39, 110)(40, 117)(41, 130)(42, 111)(43, 142)(44, 127)(45, 135)(46, 115)(47, 116)(48, 118)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.909
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.917 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3, (Y1, Y3), (R * Y1)^2, (Y3 * R)^2, (Y3 * Y2 * Y3)^2, Y3 * Y2 * Y3^-1 * Y1^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-2, (Y3^-1 * Y2)^4, (Y2 * R * Y2 * Y1^-1)^2, Y3^12, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 8, 56, 14, 62, 24, 72, 36, 84, 28, 76, 43, 91, 47, 95, 26, 74, 42, 90, 46, 94, 48, 96, 30, 78, 44, 92, 45, 93, 25, 73, 41, 89, 39, 87, 18, 66, 16, 64, 6, 54, 5, 53)(3, 51, 9, 57, 10, 58, 23, 71, 27, 75, 38, 86, 37, 85, 15, 63, 35, 83, 34, 82, 13, 61, 32, 80, 33, 81, 40, 88, 17, 65, 22, 70, 21, 69, 7, 55, 19, 67, 20, 68, 31, 79, 29, 77, 12, 60, 11, 59)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 113, 161)(104, 152, 119, 167)(105, 153, 121, 169)(106, 154, 122, 170)(107, 155, 124, 172)(108, 156, 126, 174)(110, 158, 127, 175)(112, 160, 125, 173)(114, 162, 123, 171)(115, 163, 137, 185)(116, 164, 138, 186)(117, 165, 139, 187)(118, 166, 140, 188)(120, 168, 136, 184)(128, 176, 135, 183)(129, 177, 142, 190)(130, 178, 143, 191)(131, 179, 141, 189)(132, 180, 133, 181)(134, 182, 144, 192)
	L = (1, 100)(2, 104)(3, 106)(4, 110)(5, 98)(6, 97)(7, 116)(8, 120)(9, 119)(10, 123)(11, 105)(12, 99)(13, 129)(14, 132)(15, 130)(16, 101)(17, 117)(18, 102)(19, 127)(20, 125)(21, 115)(22, 103)(23, 134)(24, 124)(25, 135)(26, 142)(27, 133)(28, 143)(29, 107)(30, 141)(31, 108)(32, 136)(33, 113)(34, 128)(35, 109)(36, 139)(37, 131)(38, 111)(39, 112)(40, 118)(41, 114)(42, 144)(43, 122)(44, 121)(45, 137)(46, 126)(47, 138)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.908
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.918 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y3, Y1), (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, (R * Y3)^2, (Y1, Y2^-1), Y1^-2 * Y3^2, (R * Y1)^2, Y1 * Y3^2 * Y2^-3, Y3 * Y2^-2 * Y3 * Y2 * Y1^-1, Y2^-2 * Y1 * Y2^-1 * Y1^2, Y2 * Y1^-1 * Y2 * Y3^-2 * Y2, (R * Y2 * Y3^-1)^2, Y2^-2 * R * Y2^-1 * R * Y1, Y2^2 * Y1^5 * Y2, (Y3^-1 * Y1^-1)^4, Y2^15 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 25, 73, 43, 91, 37, 85, 18, 66, 5, 53)(3, 51, 9, 57, 26, 74, 44, 92, 40, 88, 22, 70, 34, 82, 15, 63)(4, 52, 10, 58, 27, 75, 45, 93, 39, 87, 20, 68, 7, 55, 12, 60)(6, 54, 11, 59, 28, 76, 13, 61, 29, 77, 46, 94, 38, 86, 19, 67)(14, 62, 30, 78, 47, 95, 42, 90, 24, 72, 36, 84, 16, 64, 31, 79)(17, 65, 32, 80, 48, 96, 41, 89, 23, 71, 35, 83, 21, 69, 33, 81)(97, 145, 99, 147, 109, 157, 121, 169, 140, 188, 134, 182, 114, 162, 130, 178, 107, 155, 98, 146, 105, 153, 125, 173, 139, 187, 136, 184, 115, 163, 101, 149, 111, 159, 124, 172, 104, 152, 122, 170, 142, 190, 133, 181, 118, 166, 102, 150)(100, 148, 113, 161, 126, 174, 141, 189, 137, 185, 120, 168, 103, 151, 117, 165, 127, 175, 106, 154, 128, 176, 143, 191, 135, 183, 119, 167, 132, 180, 108, 156, 129, 177, 110, 158, 123, 171, 144, 192, 138, 186, 116, 164, 131, 179, 112, 160)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 117)(7, 97)(8, 123)(9, 126)(10, 121)(11, 129)(12, 98)(13, 128)(14, 122)(15, 127)(16, 99)(17, 125)(18, 103)(19, 131)(20, 101)(21, 124)(22, 132)(23, 102)(24, 130)(25, 141)(26, 143)(27, 139)(28, 113)(29, 144)(30, 140)(31, 105)(32, 142)(33, 109)(34, 112)(35, 107)(36, 111)(37, 116)(38, 119)(39, 114)(40, 120)(41, 115)(42, 118)(43, 135)(44, 138)(45, 133)(46, 137)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.906
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.919 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-1, (Y3, Y1^-1), (Y2^-1, Y1), (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2, Y1^-1 * Y2^-1 * Y3^2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3^-3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2, Y3^-2 * Y1^-6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 41, 89, 37, 85, 18, 66, 5, 53)(3, 51, 9, 57, 24, 72, 42, 90, 40, 88, 48, 96, 35, 83, 15, 63)(4, 52, 10, 58, 25, 73, 43, 91, 38, 86, 19, 67, 7, 55, 12, 60)(6, 54, 11, 59, 26, 74, 44, 92, 36, 84, 47, 95, 33, 81, 13, 61)(14, 62, 27, 75, 45, 93, 39, 87, 22, 70, 32, 80, 16, 64, 28, 76)(17, 65, 29, 77, 46, 94, 34, 82, 21, 69, 31, 79, 20, 68, 30, 78)(97, 145, 99, 147, 109, 157, 101, 149, 111, 159, 129, 177, 114, 162, 131, 179, 143, 191, 133, 181, 144, 192, 132, 180, 137, 185, 136, 184, 140, 188, 119, 167, 138, 186, 122, 170, 104, 152, 120, 168, 107, 155, 98, 146, 105, 153, 102, 150)(100, 148, 113, 161, 128, 176, 108, 156, 126, 174, 118, 166, 103, 151, 116, 164, 135, 183, 115, 163, 127, 175, 141, 189, 134, 182, 117, 165, 123, 171, 139, 187, 130, 178, 110, 158, 121, 169, 142, 190, 124, 172, 106, 154, 125, 173, 112, 160)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 121)(9, 123)(10, 119)(11, 126)(12, 98)(13, 127)(14, 120)(15, 124)(16, 99)(17, 132)(18, 103)(19, 101)(20, 122)(21, 102)(22, 131)(23, 139)(24, 141)(25, 137)(26, 113)(27, 138)(28, 105)(29, 143)(30, 140)(31, 107)(32, 111)(33, 117)(34, 109)(35, 112)(36, 142)(37, 115)(38, 114)(39, 144)(40, 118)(41, 134)(42, 135)(43, 133)(44, 125)(45, 136)(46, 129)(47, 130)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.905
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.920 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2 * Y1^-1)^2, Y2^-1 * Y1 * R * Y2^-1 * R * Y1^-1, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, R * Y2^-1 * R * Y1 * Y2^-1 * Y1^-1, Y2^-5 * Y1^-2 * Y2^-1, Y1^2 * Y2 * Y1 * Y2^2 * Y1 * Y2, Y2^4 * Y1^-1 * Y2^-2 * Y1^-1, Y1^8, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 41, 89, 33, 81, 44, 92, 47, 95, 45, 93, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 121, 169, 136, 184, 124, 172, 108, 156, 117, 165, 138, 186, 144, 192, 135, 183, 115, 163, 130, 178, 125, 173, 139, 187, 143, 191, 134, 182, 114, 162, 102, 150, 113, 161, 133, 181, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 137, 185, 126, 174, 109, 157, 100, 148, 107, 155, 122, 170, 142, 190, 120, 168, 132, 180, 123, 171, 110, 158, 127, 175, 141, 189, 119, 167, 105, 153, 112, 160, 131, 179, 128, 176, 140, 188, 118, 166, 104, 152)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 112)(7, 115)(8, 99)(9, 113)(10, 120)(11, 114)(12, 100)(13, 117)(14, 101)(15, 127)(16, 130)(17, 132)(18, 103)(19, 131)(20, 136)(21, 104)(22, 138)(23, 106)(24, 133)(25, 137)(26, 135)(27, 108)(28, 110)(29, 109)(30, 139)(31, 134)(32, 111)(33, 140)(34, 123)(35, 124)(36, 125)(37, 126)(38, 122)(39, 116)(40, 128)(41, 129)(42, 119)(43, 118)(44, 143)(45, 144)(46, 121)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.904
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.921 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, Y3^-3 * Y1^-1, (Y3^-1, Y1^-1), Y3 * Y2 * Y1 * Y2, (Y2^-1 * Y1)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y3, Y2^-1 * Y3 * Y2^5 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2^3 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 7, 55, 12, 60, 4, 52, 10, 58, 5, 53)(3, 51, 13, 61, 21, 69, 16, 64, 27, 75, 15, 63, 26, 74, 11, 59)(6, 54, 18, 66, 22, 70, 9, 57, 23, 71, 19, 67, 25, 73, 17, 65)(14, 62, 30, 78, 37, 85, 32, 80, 43, 91, 28, 76, 42, 90, 29, 77)(20, 68, 33, 81, 38, 86, 34, 82, 39, 87, 24, 72, 40, 88, 35, 83)(31, 79, 41, 89, 36, 84, 44, 92, 47, 95, 45, 93, 48, 96, 46, 94)(97, 145, 99, 147, 110, 158, 127, 175, 136, 184, 121, 169, 106, 154, 122, 170, 138, 186, 144, 192, 135, 183, 119, 167, 108, 156, 123, 171, 139, 187, 143, 191, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 137, 185, 128, 176, 111, 159, 101, 149, 114, 162, 130, 178, 142, 190, 126, 174, 112, 160, 100, 148, 113, 161, 129, 177, 141, 189, 125, 173, 109, 157, 103, 151, 115, 163, 131, 179, 140, 188, 124, 172, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 101)(9, 102)(10, 103)(11, 123)(12, 98)(13, 122)(14, 124)(15, 117)(16, 99)(17, 119)(18, 121)(19, 118)(20, 120)(21, 107)(22, 113)(23, 114)(24, 134)(25, 105)(26, 112)(27, 109)(28, 133)(29, 139)(30, 138)(31, 141)(32, 110)(33, 136)(34, 116)(35, 135)(36, 142)(37, 125)(38, 131)(39, 129)(40, 130)(41, 144)(42, 128)(43, 126)(44, 127)(45, 132)(46, 143)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.903
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.922 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, (Y3, Y2), (R * Y1)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^2, Y1^-2 * Y2^-1 * Y3 * Y1^-2, Y2 * Y3 * Y1^-1 * Y2^-4 * Y1^-1, Y3^-2 * Y2^-1 * Y3^-1 * Y1^-1 * Y3^2 * Y1^-1, Y3^2 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1, Y3^2 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2^18 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 16, 64, 30, 78, 20, 68, 5, 53)(3, 51, 13, 61, 24, 72, 12, 60, 4, 52, 17, 65, 25, 73, 11, 59)(6, 54, 18, 66, 26, 74, 9, 57, 7, 55, 19, 67, 27, 75, 10, 58)(14, 62, 32, 80, 41, 89, 34, 82, 15, 63, 31, 79, 42, 90, 33, 81)(21, 69, 29, 77, 43, 91, 37, 85, 22, 70, 28, 76, 44, 92, 38, 86)(35, 83, 45, 93, 39, 87, 47, 95, 36, 84, 46, 94, 40, 88, 48, 96)(97, 145, 99, 147, 110, 158, 131, 179, 140, 188, 123, 171, 116, 164, 121, 169, 138, 186, 136, 184, 118, 166, 103, 151, 112, 160, 100, 148, 111, 159, 132, 180, 139, 187, 122, 170, 104, 152, 120, 168, 137, 185, 135, 183, 117, 165, 102, 150)(98, 146, 105, 153, 124, 172, 141, 189, 130, 178, 113, 161, 101, 149, 114, 162, 133, 181, 144, 192, 128, 176, 108, 156, 126, 174, 106, 154, 125, 173, 142, 190, 129, 177, 109, 157, 119, 167, 115, 163, 134, 182, 143, 191, 127, 175, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 101)(14, 132)(15, 131)(16, 99)(17, 119)(18, 134)(19, 133)(20, 120)(21, 103)(22, 102)(23, 114)(24, 138)(25, 137)(26, 116)(27, 104)(28, 142)(29, 141)(30, 105)(31, 108)(32, 107)(33, 113)(34, 109)(35, 139)(36, 140)(37, 143)(38, 144)(39, 118)(40, 117)(41, 136)(42, 135)(43, 123)(44, 122)(45, 129)(46, 130)(47, 128)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.907
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.923 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3^2 * Y1 * Y3^-2 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1, Y2^8, Y3^-1 * Y1 * Y3^-3 * Y2 * Y1 * Y3^-3 * Y2 * Y1 * Y3^-3 * Y2 * Y1 * Y3^-3 * Y2 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 18, 66)(12, 60, 27, 75)(13, 61, 28, 76)(15, 63, 22, 70)(16, 64, 30, 78)(19, 67, 31, 79)(20, 68, 34, 82)(23, 71, 29, 77)(25, 73, 35, 83)(26, 74, 41, 89)(32, 80, 43, 91)(33, 81, 38, 86)(36, 84, 42, 90)(37, 85, 44, 92)(39, 87, 45, 93)(40, 88, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 121, 169, 135, 183, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 114, 162, 131, 179, 141, 189, 134, 182, 118, 166, 105, 153)(100, 148, 108, 156, 102, 150, 109, 157, 122, 170, 136, 184, 128, 176, 112, 160)(104, 152, 115, 163, 106, 154, 116, 164, 132, 180, 142, 190, 133, 181, 119, 167)(110, 158, 123, 171, 113, 161, 124, 172, 137, 185, 143, 191, 139, 187, 126, 174)(117, 165, 127, 175, 120, 168, 130, 178, 138, 186, 144, 192, 140, 188, 125, 173)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 112)(6, 97)(7, 115)(8, 118)(9, 119)(10, 98)(11, 102)(12, 101)(13, 99)(14, 125)(15, 128)(16, 129)(17, 127)(18, 106)(19, 105)(20, 103)(21, 126)(22, 133)(23, 134)(24, 123)(25, 109)(26, 107)(27, 117)(28, 120)(29, 139)(30, 140)(31, 110)(32, 135)(33, 136)(34, 113)(35, 116)(36, 114)(37, 141)(38, 142)(39, 122)(40, 121)(41, 130)(42, 124)(43, 144)(44, 143)(45, 132)(46, 131)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.932
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.924 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-2 * Y3^-1, (Y2^-1 * Y3^-1)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, (Y3 * Y2^-1)^4, Y3^-2 * Y2^6, (Y3^-1 * Y2^-1 * Y1)^6 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 24, 72)(11, 59, 18, 66)(12, 60, 27, 75)(13, 61, 28, 76)(15, 63, 22, 70)(16, 64, 30, 78)(19, 67, 37, 85)(20, 68, 29, 77)(23, 71, 34, 82)(25, 73, 35, 83)(26, 74, 43, 91)(31, 79, 47, 95)(32, 80, 46, 94)(33, 81, 40, 88)(36, 84, 44, 92)(38, 86, 42, 90)(39, 87, 45, 93)(41, 89, 48, 96)(97, 145, 99, 147, 107, 155, 121, 169, 137, 185, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 114, 162, 131, 179, 144, 192, 136, 184, 118, 166, 105, 153)(100, 148, 108, 156, 102, 150, 109, 157, 122, 170, 138, 186, 128, 176, 112, 160)(104, 152, 115, 163, 106, 154, 116, 164, 132, 180, 143, 191, 135, 183, 119, 167)(110, 158, 123, 171, 113, 161, 124, 172, 139, 187, 134, 182, 142, 190, 126, 174)(117, 165, 133, 181, 120, 168, 125, 173, 140, 188, 127, 175, 141, 189, 130, 178)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 112)(6, 97)(7, 115)(8, 118)(9, 119)(10, 98)(11, 102)(12, 101)(13, 99)(14, 125)(15, 128)(16, 129)(17, 127)(18, 106)(19, 105)(20, 103)(21, 124)(22, 135)(23, 136)(24, 134)(25, 109)(26, 107)(27, 140)(28, 141)(29, 142)(30, 120)(31, 110)(32, 137)(33, 138)(34, 113)(35, 116)(36, 114)(37, 139)(38, 117)(39, 144)(40, 143)(41, 122)(42, 121)(43, 130)(44, 126)(45, 123)(46, 133)(47, 131)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.931
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.925 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y3 * Y1 * Y3^-2 * Y1 * Y2^-1, Y2^2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^4, Y2^8, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3^-1 * Y1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 12, 60)(10, 58, 14, 62)(15, 63, 25, 73)(16, 64, 27, 75)(17, 65, 26, 74)(18, 66, 29, 77)(19, 67, 30, 78)(20, 68, 31, 79)(21, 69, 33, 81)(22, 70, 32, 80)(23, 71, 35, 83)(24, 72, 36, 84)(28, 76, 34, 82)(37, 85, 42, 90)(38, 86, 43, 91)(39, 87, 47, 95)(40, 88, 45, 93)(41, 89, 46, 94)(44, 92, 48, 96)(97, 145, 99, 147, 104, 152, 113, 161, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 130, 178, 120, 168, 110, 158, 102, 150)(103, 151, 111, 159, 122, 170, 135, 183, 126, 174, 114, 162, 105, 153, 112, 160)(107, 155, 116, 164, 128, 176, 140, 188, 132, 180, 119, 167, 109, 157, 117, 165)(121, 169, 133, 181, 143, 191, 137, 185, 125, 173, 136, 184, 123, 171, 134, 182)(127, 175, 138, 186, 144, 192, 142, 190, 131, 179, 141, 189, 129, 177, 139, 187)
	L = (1, 100)(2, 102)(3, 97)(4, 106)(5, 98)(6, 110)(7, 112)(8, 99)(9, 114)(10, 115)(11, 117)(12, 101)(13, 119)(14, 120)(15, 103)(16, 105)(17, 104)(18, 126)(19, 124)(20, 107)(21, 109)(22, 108)(23, 132)(24, 130)(25, 134)(26, 111)(27, 136)(28, 113)(29, 137)(30, 135)(31, 139)(32, 116)(33, 141)(34, 118)(35, 142)(36, 140)(37, 121)(38, 123)(39, 122)(40, 125)(41, 143)(42, 127)(43, 129)(44, 128)(45, 131)(46, 144)(47, 133)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.928
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.926 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, Y2^-3 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1 * Y2^-1)^2, Y3 * Y1 * Y2^-2 * Y1 * Y2^-1, Y3 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 16, 64)(6, 54, 17, 65)(7, 55, 18, 66)(8, 56, 22, 70)(9, 57, 23, 71)(10, 58, 24, 72)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 100, 148, 109, 157, 102, 150, 110, 158, 101, 149)(98, 146, 103, 151, 115, 163, 104, 152, 116, 164, 106, 154, 117, 165, 105, 153)(107, 155, 121, 169, 111, 159, 122, 170, 113, 161, 124, 172, 112, 160, 123, 171)(114, 162, 125, 173, 118, 166, 126, 174, 120, 168, 128, 176, 119, 167, 127, 175)(129, 177, 137, 185, 130, 178, 138, 186, 132, 180, 140, 188, 131, 179, 139, 187)(133, 181, 141, 189, 134, 182, 142, 190, 136, 184, 144, 192, 135, 183, 143, 191)
	L = (1, 100)(2, 104)(3, 109)(4, 110)(5, 108)(6, 97)(7, 116)(8, 117)(9, 115)(10, 98)(11, 122)(12, 102)(13, 101)(14, 99)(15, 124)(16, 121)(17, 123)(18, 126)(19, 106)(20, 105)(21, 103)(22, 128)(23, 125)(24, 127)(25, 113)(26, 112)(27, 111)(28, 107)(29, 120)(30, 119)(31, 118)(32, 114)(33, 138)(34, 140)(35, 137)(36, 139)(37, 142)(38, 144)(39, 141)(40, 143)(41, 132)(42, 131)(43, 130)(44, 129)(45, 136)(46, 135)(47, 134)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.929
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.927 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, Y2^4 * Y1, (Y3 * Y1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y3^6 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 21, 69)(13, 61, 16, 64)(14, 62, 22, 70)(15, 63, 23, 71)(17, 65, 19, 67)(20, 68, 24, 72)(25, 73, 34, 82)(26, 74, 28, 76)(27, 75, 37, 85)(29, 77, 31, 79)(30, 78, 33, 81)(32, 80, 39, 87)(35, 83, 36, 84)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 43, 91)(44, 92, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 105, 153, 98, 146, 103, 151, 114, 162, 101, 149)(100, 148, 110, 158, 121, 169, 109, 157, 104, 152, 118, 166, 130, 178, 112, 160)(102, 150, 115, 163, 122, 170, 117, 165, 106, 154, 113, 161, 124, 172, 108, 156)(111, 159, 127, 175, 137, 185, 126, 174, 119, 167, 125, 173, 141, 189, 129, 177)(116, 164, 133, 181, 138, 186, 131, 179, 120, 168, 123, 171, 139, 187, 132, 180)(128, 176, 140, 188, 136, 184, 144, 192, 135, 183, 143, 191, 134, 182, 142, 190)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 117)(8, 119)(9, 115)(10, 98)(11, 121)(12, 123)(13, 99)(14, 101)(15, 128)(16, 103)(17, 131)(18, 130)(19, 132)(20, 102)(21, 133)(22, 105)(23, 135)(24, 106)(25, 137)(26, 107)(27, 140)(28, 114)(29, 109)(30, 110)(31, 112)(32, 138)(33, 118)(34, 141)(35, 142)(36, 144)(37, 143)(38, 116)(39, 139)(40, 120)(41, 136)(42, 122)(43, 124)(44, 129)(45, 134)(46, 125)(47, 126)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.930
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.928 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y1^2, (R * Y1)^2, Y1^4, Y3^4, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2, Y1), Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-6 * Y1, Y2^-1 * Y3 * Y2^3 * Y3^-1 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 26, 74, 19, 67)(13, 61, 27, 75, 41, 89, 31, 79)(14, 62, 18, 66, 16, 64, 24, 72)(17, 65, 20, 68, 23, 71, 22, 70)(21, 69, 28, 76, 42, 90, 36, 84)(29, 77, 43, 91, 48, 96, 39, 87)(30, 78, 33, 81, 32, 80, 34, 82)(35, 83, 37, 85, 38, 86, 40, 88)(44, 92, 46, 94, 45, 93, 47, 95)(97, 145, 99, 147, 109, 157, 125, 173, 124, 172, 107, 155, 98, 146, 105, 153, 123, 171, 139, 187, 138, 186, 122, 170, 104, 152, 121, 169, 137, 185, 144, 192, 132, 180, 115, 163, 101, 149, 111, 159, 127, 175, 135, 183, 117, 165, 102, 150)(100, 148, 113, 161, 131, 179, 140, 188, 130, 178, 112, 160, 106, 154, 116, 164, 133, 181, 142, 190, 126, 174, 120, 168, 103, 151, 119, 167, 134, 182, 141, 189, 129, 177, 110, 158, 108, 156, 118, 166, 136, 184, 143, 191, 128, 176, 114, 162)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 114)(10, 101)(11, 119)(12, 98)(13, 126)(14, 121)(15, 120)(16, 99)(17, 107)(18, 111)(19, 113)(20, 122)(21, 134)(22, 102)(23, 115)(24, 105)(25, 112)(26, 118)(27, 129)(28, 136)(29, 140)(30, 137)(31, 130)(32, 109)(33, 127)(34, 123)(35, 117)(36, 133)(37, 124)(38, 138)(39, 143)(40, 132)(41, 128)(42, 131)(43, 142)(44, 144)(45, 125)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.925
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.929 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^4, (R * Y3)^2, (Y2, Y1), Y3 * Y2 * Y3^-1 * Y1^-1 * Y2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, R * Y2 * R * Y1 * Y2^-1, Y2^-6 * Y1^-1, Y2^-1 * Y3 * Y2^3 * Y3^-1 * Y2^-2, Y2^-3 * Y1 * Y2^-3 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 26, 74, 19, 67)(13, 61, 27, 75, 41, 89, 31, 79)(14, 62, 24, 72, 16, 64, 18, 66)(17, 65, 22, 70, 23, 71, 20, 68)(21, 69, 28, 76, 42, 90, 36, 84)(29, 77, 39, 87, 43, 91, 45, 93)(30, 78, 34, 82, 32, 80, 33, 81)(35, 83, 40, 88, 38, 86, 37, 85)(44, 92, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 109, 157, 125, 173, 132, 180, 115, 163, 101, 149, 111, 159, 127, 175, 141, 189, 138, 186, 122, 170, 104, 152, 121, 169, 137, 185, 139, 187, 124, 172, 107, 155, 98, 146, 105, 153, 123, 171, 135, 183, 117, 165, 102, 150)(100, 148, 113, 161, 131, 179, 140, 188, 130, 178, 112, 160, 108, 156, 116, 164, 133, 181, 143, 191, 126, 174, 120, 168, 103, 151, 119, 167, 134, 182, 142, 190, 129, 177, 110, 158, 106, 154, 118, 166, 136, 184, 144, 192, 128, 176, 114, 162)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 120)(10, 101)(11, 113)(12, 98)(13, 126)(14, 121)(15, 114)(16, 99)(17, 115)(18, 105)(19, 119)(20, 122)(21, 134)(22, 102)(23, 107)(24, 111)(25, 112)(26, 118)(27, 130)(28, 133)(29, 140)(30, 137)(31, 129)(32, 109)(33, 123)(34, 127)(35, 117)(36, 136)(37, 132)(38, 138)(39, 144)(40, 124)(41, 128)(42, 131)(43, 142)(44, 139)(45, 143)(46, 125)(47, 135)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.926
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.930 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (Y2^2 * Y1^-1)^2, (Y1^-1 * Y2^-2)^2, Y2^-1 * Y1 * Y2^5 * Y1, Y2^-3 * Y1^-1 * Y2 * Y1^-1 * Y2^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-2)^2, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 24, 72)(16, 64, 31, 79, 36, 84, 20, 68)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 42, 90, 30, 78, 43, 91)(28, 76, 39, 87, 47, 95, 45, 93)(32, 80, 38, 86, 33, 81, 41, 89)(34, 82, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 134, 182, 115, 163, 133, 181, 119, 167, 139, 187, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 137, 185, 117, 165, 136, 184, 118, 166, 138, 186, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 126, 174, 107, 155, 125, 173, 110, 158, 128, 176, 142, 190, 123, 171, 109, 157, 100, 148, 108, 156, 127, 175, 141, 189, 122, 170, 105, 153, 121, 169, 111, 159, 129, 177, 140, 188, 120, 168, 104, 152)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 127)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 133)(26, 138)(27, 131)(28, 135)(29, 136)(30, 139)(31, 132)(32, 134)(33, 137)(34, 140)(35, 120)(36, 116)(37, 125)(38, 129)(39, 143)(40, 121)(41, 128)(42, 126)(43, 122)(44, 144)(45, 124)(46, 130)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.927
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.931 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y2)^2, Y3^-1 * Y2 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3^12, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 14, 62)(4, 52, 16, 64, 26, 74, 12, 60)(6, 54, 22, 70, 27, 75, 23, 71)(7, 55, 20, 68, 28, 76, 10, 58)(9, 57, 29, 77, 19, 67, 30, 78)(11, 59, 34, 82, 21, 69, 35, 83)(15, 63, 31, 79, 45, 93, 38, 86)(17, 65, 36, 84, 46, 94, 39, 87)(18, 66, 33, 81, 47, 95, 42, 90)(24, 72, 32, 80, 48, 96, 43, 91)(37, 85, 44, 92, 40, 88, 41, 89)(97, 145, 99, 147, 103, 151, 111, 159, 120, 168, 125, 173, 140, 188, 131, 179, 142, 190, 143, 191, 122, 170, 123, 171, 104, 152, 121, 169, 124, 172, 141, 189, 144, 192, 126, 174, 137, 185, 130, 178, 113, 161, 114, 162, 100, 148, 102, 150)(98, 146, 105, 153, 108, 156, 127, 175, 132, 180, 110, 158, 136, 184, 118, 166, 139, 187, 138, 186, 116, 164, 117, 165, 101, 149, 115, 163, 112, 160, 134, 182, 135, 183, 109, 157, 133, 181, 119, 167, 128, 176, 129, 177, 106, 154, 107, 155)
	L = (1, 100)(2, 106)(3, 102)(4, 113)(5, 116)(6, 114)(7, 97)(8, 122)(9, 107)(10, 128)(11, 129)(12, 98)(13, 134)(14, 127)(15, 99)(16, 101)(17, 137)(18, 130)(19, 117)(20, 139)(21, 138)(22, 110)(23, 109)(24, 103)(25, 123)(26, 142)(27, 143)(28, 104)(29, 111)(30, 141)(31, 105)(32, 133)(33, 119)(34, 126)(35, 125)(36, 108)(37, 135)(38, 115)(39, 112)(40, 132)(41, 144)(42, 118)(43, 136)(44, 120)(45, 121)(46, 140)(47, 131)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.924
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.932 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C8 x S3 (small group id <48, 4>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1, Y2^-1), (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2)^2, Y2 * Y3 * Y2 * Y1^-2, Y2^-1 * Y3^-1 * Y1^-2 * Y2^-1, Y1 * Y2^2 * Y3 * Y1, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y1, Y2^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 27, 75, 16, 64)(4, 52, 18, 66, 26, 74, 12, 60)(6, 54, 24, 72, 15, 63, 25, 73)(7, 55, 22, 70, 14, 62, 10, 58)(9, 57, 29, 77, 21, 69, 30, 78)(11, 59, 34, 82, 23, 71, 35, 83)(17, 65, 31, 79, 40, 88, 38, 86)(19, 67, 36, 84, 46, 94, 39, 87)(20, 68, 33, 81, 42, 90, 45, 93)(28, 76, 32, 80, 41, 89, 47, 95)(37, 85, 44, 92, 43, 91, 48, 96)(97, 145, 99, 147, 110, 158, 136, 184, 124, 172, 125, 173, 140, 188, 131, 179, 142, 190, 116, 164, 100, 148, 111, 159, 104, 152, 123, 171, 103, 151, 113, 161, 137, 185, 126, 174, 144, 192, 130, 178, 115, 163, 138, 186, 122, 170, 102, 150)(98, 146, 105, 153, 114, 162, 134, 182, 132, 180, 112, 160, 139, 187, 120, 168, 143, 191, 129, 177, 106, 154, 119, 167, 101, 149, 117, 165, 108, 156, 127, 175, 135, 183, 109, 157, 133, 181, 121, 169, 128, 176, 141, 189, 118, 166, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 116)(7, 97)(8, 122)(9, 119)(10, 128)(11, 129)(12, 98)(13, 134)(14, 104)(15, 138)(16, 127)(17, 99)(18, 101)(19, 140)(20, 130)(21, 107)(22, 143)(23, 141)(24, 109)(25, 112)(26, 142)(27, 102)(28, 103)(29, 113)(30, 136)(31, 105)(32, 139)(33, 121)(34, 125)(35, 126)(36, 108)(37, 132)(38, 117)(39, 114)(40, 123)(41, 110)(42, 131)(43, 135)(44, 137)(45, 120)(46, 144)(47, 133)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.923
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.933 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2)^2, Y3 * Y2^-2 * Y3 * Y2^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 13, 61)(5, 53, 9, 57)(6, 54, 15, 63)(8, 56, 18, 66)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(14, 62, 23, 71)(17, 65, 26, 74)(19, 67, 28, 76)(22, 70, 32, 80)(24, 72, 33, 81)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(35, 83, 44, 92)(40, 88, 47, 95)(41, 89, 48, 96)(42, 90, 45, 93)(43, 91, 46, 94)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 102, 150, 108, 156, 110, 158)(104, 152, 106, 154, 113, 161, 115, 163)(109, 157, 111, 159, 117, 165, 119, 167)(114, 162, 116, 164, 122, 170, 124, 172)(118, 166, 120, 168, 121, 169, 127, 175)(123, 171, 125, 173, 126, 174, 131, 179)(128, 176, 129, 177, 130, 178, 135, 183)(132, 180, 133, 181, 134, 182, 140, 188)(136, 184, 137, 185, 138, 186, 139, 187)(141, 189, 142, 190, 143, 191, 144, 192)
	L = (1, 100)(2, 104)(3, 102)(4, 101)(5, 110)(6, 97)(7, 106)(8, 105)(9, 115)(10, 98)(11, 108)(12, 99)(13, 118)(14, 107)(15, 120)(16, 113)(17, 103)(18, 123)(19, 112)(20, 125)(21, 121)(22, 119)(23, 127)(24, 109)(25, 111)(26, 126)(27, 124)(28, 131)(29, 114)(30, 116)(31, 117)(32, 136)(33, 137)(34, 138)(35, 122)(36, 141)(37, 142)(38, 143)(39, 139)(40, 135)(41, 128)(42, 129)(43, 130)(44, 144)(45, 140)(46, 132)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.947
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.934 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, Y1 * Y2^-1 * Y1 * Y2, Y2^4, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2 * Y3 * Y1 * Y3)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 13, 61)(5, 53, 9, 57)(6, 54, 15, 63)(8, 56, 18, 66)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(14, 62, 24, 72)(17, 65, 26, 74)(19, 67, 29, 77)(22, 70, 32, 80)(23, 71, 33, 81)(25, 73, 34, 82)(27, 75, 36, 84)(28, 76, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(35, 83, 44, 92)(40, 88, 47, 95)(41, 89, 48, 96)(42, 90, 45, 93)(43, 91, 46, 94)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 108, 156, 110, 158, 102, 150)(104, 152, 113, 161, 115, 163, 106, 154)(109, 157, 117, 165, 120, 168, 111, 159)(114, 162, 122, 170, 125, 173, 116, 164)(118, 166, 127, 175, 121, 169, 119, 167)(123, 171, 131, 179, 126, 174, 124, 172)(128, 176, 135, 183, 130, 178, 129, 177)(132, 180, 140, 188, 134, 182, 133, 181)(136, 184, 139, 187, 138, 186, 137, 185)(141, 189, 144, 192, 143, 191, 142, 190)
	L = (1, 100)(2, 104)(3, 108)(4, 99)(5, 102)(6, 97)(7, 113)(8, 103)(9, 106)(10, 98)(11, 110)(12, 107)(13, 118)(14, 101)(15, 119)(16, 115)(17, 112)(18, 123)(19, 105)(20, 124)(21, 127)(22, 117)(23, 109)(24, 121)(25, 111)(26, 131)(27, 122)(28, 114)(29, 126)(30, 116)(31, 120)(32, 136)(33, 137)(34, 138)(35, 125)(36, 141)(37, 142)(38, 143)(39, 139)(40, 135)(41, 128)(42, 129)(43, 130)(44, 144)(45, 140)(46, 132)(47, 133)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.946
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.935 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y1 * Y2^-2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2^-1)^2, (Y3^2 * Y2)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2 * Y3^-5 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 33, 81)(24, 72, 25, 73)(26, 74, 29, 77)(27, 75, 31, 79)(28, 76, 32, 80)(30, 78, 37, 85)(34, 82, 35, 83)(36, 84, 38, 86)(39, 87, 42, 90)(40, 88, 43, 91)(41, 89, 48, 96)(44, 92, 45, 93)(46, 94, 47, 95)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 125, 173, 115, 163, 122, 170)(114, 162, 129, 177, 116, 164, 118, 166)(123, 171, 135, 183, 127, 175, 138, 186)(124, 172, 140, 188, 128, 176, 141, 189)(126, 174, 144, 192, 133, 181, 137, 185)(130, 178, 136, 184, 131, 179, 139, 187)(132, 180, 143, 191, 134, 182, 142, 190)
	L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 126)(13, 127)(14, 129)(15, 101)(16, 130)(17, 131)(18, 102)(19, 133)(20, 104)(21, 135)(22, 137)(23, 138)(24, 140)(25, 141)(26, 106)(27, 113)(28, 107)(29, 111)(30, 139)(31, 112)(32, 109)(33, 144)(34, 142)(35, 143)(36, 114)(37, 136)(38, 116)(39, 121)(40, 117)(41, 124)(42, 120)(43, 119)(44, 134)(45, 132)(46, 122)(47, 125)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16, 48, 16, 48 ), ( 16, 48, 16, 48, 16, 48, 16, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.948
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.936 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1, Y3), (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y3^-2, Y1^-2 * Y2^-4, Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y3 * Y1^2 * Y2^-1 * Y3^2 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 9, 57)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 21, 69, 27, 75, 11, 59)(7, 55, 20, 68, 28, 76, 10, 58)(14, 62, 29, 77, 22, 70, 34, 82)(15, 63, 31, 79, 47, 95, 38, 86)(16, 64, 30, 78, 43, 91, 37, 85)(18, 66, 36, 84, 39, 87, 42, 90)(19, 67, 35, 83, 40, 88, 41, 89)(23, 71, 33, 81, 48, 96, 46, 94)(24, 72, 32, 80, 44, 92, 45, 93)(97, 145, 99, 147, 110, 158, 123, 171, 104, 152, 121, 169, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 117, 165, 101, 149, 109, 157, 130, 178, 107, 155)(100, 148, 111, 159, 120, 168, 136, 184, 122, 170, 143, 191, 140, 188, 115, 163)(103, 151, 112, 160, 135, 183, 144, 192, 124, 172, 139, 187, 114, 162, 119, 167)(106, 154, 126, 174, 132, 180, 142, 190, 116, 164, 133, 181, 138, 186, 129, 177)(108, 156, 127, 175, 141, 189, 137, 185, 113, 161, 134, 182, 128, 176, 131, 179)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 116)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 133)(14, 120)(15, 119)(16, 99)(17, 101)(18, 118)(19, 139)(20, 141)(21, 142)(22, 140)(23, 102)(24, 103)(25, 143)(26, 135)(27, 136)(28, 104)(29, 132)(30, 131)(31, 105)(32, 130)(33, 134)(34, 138)(35, 107)(36, 108)(37, 137)(38, 109)(39, 110)(40, 112)(41, 117)(42, 113)(43, 121)(44, 124)(45, 125)(46, 127)(47, 144)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.945
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.937 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1 * Y2 * Y1, Y1^4, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2^-1, Y3), (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2)^2, Y2^2 * Y3^-3, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, Y1^-2 * Y2^4, (Y2 * Y1 * Y2)^2, Y1^-1 * Y3 * Y2^-1 * Y1^-1 * Y3^-2 * Y2^-1, Y2^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 9, 57)(4, 52, 17, 65, 26, 74, 12, 60)(6, 54, 21, 69, 27, 75, 11, 59)(7, 55, 20, 68, 28, 76, 10, 58)(14, 62, 29, 77, 22, 70, 34, 82)(15, 63, 31, 79, 46, 94, 38, 86)(16, 64, 30, 78, 47, 95, 37, 85)(18, 66, 36, 84, 45, 93, 42, 90)(19, 67, 35, 83, 48, 96, 41, 89)(23, 71, 33, 81, 40, 88, 44, 92)(24, 72, 32, 80, 39, 87, 43, 91)(97, 145, 99, 147, 110, 158, 123, 171, 104, 152, 121, 169, 118, 166, 102, 150)(98, 146, 105, 153, 125, 173, 117, 165, 101, 149, 109, 157, 130, 178, 107, 155)(100, 148, 111, 159, 135, 183, 144, 192, 122, 170, 142, 190, 120, 168, 115, 163)(103, 151, 112, 160, 114, 162, 136, 184, 124, 172, 143, 191, 141, 189, 119, 167)(106, 154, 126, 174, 138, 186, 140, 188, 116, 164, 133, 181, 132, 180, 129, 177)(108, 156, 127, 175, 128, 176, 137, 185, 113, 161, 134, 182, 139, 187, 131, 179)
	L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 116)(6, 115)(7, 97)(8, 122)(9, 126)(10, 128)(11, 129)(12, 98)(13, 133)(14, 135)(15, 136)(16, 99)(17, 101)(18, 110)(19, 112)(20, 139)(21, 140)(22, 120)(23, 102)(24, 103)(25, 142)(26, 141)(27, 144)(28, 104)(29, 138)(30, 137)(31, 105)(32, 125)(33, 127)(34, 132)(35, 107)(36, 108)(37, 131)(38, 109)(39, 124)(40, 123)(41, 117)(42, 113)(43, 130)(44, 134)(45, 118)(46, 119)(47, 121)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.944
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.938 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^2 * Y1^2, Y1^4, (Y3, Y1^-1), Y3^4, (R * Y1^-1)^2, (R * Y3)^2, Y1^-1 * R * Y3^-2 * R * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 6, 54, 10, 58, 13, 61)(4, 52, 9, 57, 7, 55, 11, 59)(12, 60, 17, 65, 14, 62, 18, 66)(15, 63, 16, 64, 19, 67, 20, 68)(21, 69, 22, 70, 23, 71, 24, 72)(25, 73, 27, 75, 26, 74, 28, 76)(29, 77, 31, 79, 30, 78, 32, 80)(33, 81, 34, 82, 35, 83, 36, 84)(37, 85, 38, 86, 39, 87, 40, 88)(41, 89, 43, 91, 42, 90, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 101, 149, 109, 157, 104, 152, 106, 154, 98, 146, 102, 150)(100, 148, 111, 159, 107, 155, 116, 164, 103, 151, 115, 163, 105, 153, 112, 160)(108, 156, 117, 165, 114, 162, 120, 168, 110, 158, 119, 167, 113, 161, 118, 166)(121, 169, 129, 177, 124, 172, 132, 180, 122, 170, 131, 179, 123, 171, 130, 178)(125, 173, 133, 181, 128, 176, 136, 184, 126, 174, 135, 183, 127, 175, 134, 182)(137, 185, 142, 190, 140, 188, 143, 191, 138, 186, 141, 189, 139, 187, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 104)(5, 107)(6, 113)(7, 97)(8, 103)(9, 101)(10, 110)(11, 98)(12, 106)(13, 114)(14, 99)(15, 121)(16, 123)(17, 109)(18, 102)(19, 122)(20, 124)(21, 125)(22, 127)(23, 126)(24, 128)(25, 115)(26, 111)(27, 116)(28, 112)(29, 119)(30, 117)(31, 120)(32, 118)(33, 137)(34, 139)(35, 138)(36, 140)(37, 141)(38, 143)(39, 142)(40, 144)(41, 131)(42, 129)(43, 132)(44, 130)(45, 135)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.942
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.939 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y2^2, Y3^2 * Y1^2, Y3^2 * Y1^-2, Y1^4, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, Y1 * R * Y3^-2 * R * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 16, 64, 6, 54)(4, 52, 10, 58, 7, 55, 11, 59)(12, 60, 18, 66, 13, 61, 17, 65)(14, 62, 20, 68, 19, 67, 15, 63)(21, 69, 24, 72, 23, 71, 22, 70)(25, 73, 28, 76, 26, 74, 27, 75)(29, 77, 32, 80, 30, 78, 31, 79)(33, 81, 36, 84, 35, 83, 34, 82)(37, 85, 40, 88, 39, 87, 38, 86)(41, 89, 44, 92, 42, 90, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 98, 146, 105, 153, 104, 152, 112, 160, 101, 149, 102, 150)(100, 148, 110, 158, 106, 154, 116, 164, 103, 151, 115, 163, 107, 155, 111, 159)(108, 156, 117, 165, 114, 162, 120, 168, 109, 157, 119, 167, 113, 161, 118, 166)(121, 169, 129, 177, 124, 172, 132, 180, 122, 170, 131, 179, 123, 171, 130, 178)(125, 173, 133, 181, 128, 176, 136, 184, 126, 174, 135, 183, 127, 175, 134, 182)(137, 185, 142, 190, 140, 188, 143, 191, 138, 186, 141, 189, 139, 187, 144, 192)
	L = (1, 100)(2, 106)(3, 108)(4, 104)(5, 107)(6, 113)(7, 97)(8, 103)(9, 114)(10, 101)(11, 98)(12, 112)(13, 99)(14, 121)(15, 123)(16, 109)(17, 105)(18, 102)(19, 122)(20, 124)(21, 125)(22, 127)(23, 126)(24, 128)(25, 115)(26, 110)(27, 116)(28, 111)(29, 119)(30, 117)(31, 120)(32, 118)(33, 137)(34, 139)(35, 138)(36, 140)(37, 141)(38, 143)(39, 142)(40, 144)(41, 131)(42, 129)(43, 132)(44, 130)(45, 135)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.943
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.940 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3, Y1 * Y3^-1, (Y1, Y3), R * Y3^-1 * R * Y1^-1, Y1^3 * Y3, Y2^-3 * Y3^-1 * Y1^-1 * Y2^-1, R * Y2 * Y1^-1 * R * Y2 * Y3^-1, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-2 * Y3^-1 * Y2^2 * Y3, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1^-1 * Y2^-2 * Y3^-1 * Y2^-1, R * Y2^-1 * Y1 * Y2 * Y3 * Y1 * Y2^-1 * R * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 20, 68, 16, 64, 24, 72)(25, 73, 33, 81, 27, 75, 34, 82)(26, 74, 35, 83, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 47, 95, 43, 91, 45, 93)(42, 90, 48, 96, 44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 114, 162, 102, 150, 113, 161, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 109, 157, 100, 148, 108, 156, 120, 168, 104, 152)(105, 153, 121, 169, 111, 159, 124, 172, 107, 155, 123, 171, 110, 158, 122, 170)(115, 163, 125, 173, 119, 167, 128, 176, 117, 165, 127, 175, 118, 166, 126, 174)(129, 177, 137, 185, 132, 180, 140, 188, 130, 178, 139, 187, 131, 179, 138, 186)(133, 181, 141, 189, 136, 184, 144, 192, 134, 182, 143, 191, 135, 183, 142, 190)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 129)(26, 131)(27, 130)(28, 132)(29, 133)(30, 135)(31, 134)(32, 136)(33, 123)(34, 121)(35, 124)(36, 122)(37, 127)(38, 125)(39, 128)(40, 126)(41, 143)(42, 144)(43, 141)(44, 142)(45, 137)(46, 138)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.941
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 8^12, 16^6 ]

E27.941 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y3 * Y2 * Y3^-1 * Y2, Y1 * Y2 * Y1^-1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, (Y1^2 * Y3^-1)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y1^-2 * Y3^-1 * Y1 * Y3 * Y1^-3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 19, 67, 37, 85, 30, 78, 44, 92, 31, 79, 45, 93, 47, 95, 27, 75, 11, 59, 3, 51, 8, 56, 20, 68, 38, 86, 48, 96, 29, 77, 43, 91, 32, 80, 46, 94, 35, 83, 15, 63, 5, 53)(4, 52, 12, 60, 28, 76, 40, 88, 24, 72, 9, 57, 23, 71, 16, 64, 36, 84, 41, 89, 21, 69, 18, 66, 6, 54, 17, 65, 34, 82, 39, 87, 26, 74, 10, 58, 25, 73, 14, 62, 33, 81, 42, 90, 22, 70, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 130, 178)(125, 173, 126, 174)(127, 175, 128, 176)(129, 177, 132, 180)(131, 179, 143, 191)(133, 181, 144, 192)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)
	L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 130)(16, 101)(17, 126)(18, 128)(19, 135)(20, 118)(21, 116)(22, 103)(23, 139)(24, 141)(25, 140)(26, 142)(27, 124)(28, 111)(29, 113)(30, 108)(31, 114)(32, 109)(33, 144)(34, 123)(35, 137)(36, 133)(37, 129)(38, 136)(39, 134)(40, 115)(41, 143)(42, 131)(43, 121)(44, 119)(45, 122)(46, 120)(47, 138)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.940
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.942 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, (R * Y1)^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y2)^2, Y1^-1 * Y2 * Y1^-1 * Y3^-1, (R * Y3)^2, Y1^-1 * Y2 * Y3^2 * Y1^-1 * Y3, Y3 * Y1^-1 * Y3^-2 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y1^-1 * Y2 * Y1 * Y2 * Y1^-4, Y1^-1 * Y2 * Y3^-1 * Y1^13 * Y3^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 30, 78, 13, 61, 25, 73, 42, 90, 47, 95, 45, 93, 31, 79, 15, 63, 26, 74, 43, 91, 48, 96, 46, 94, 32, 80, 12, 60, 24, 72, 41, 89, 36, 84, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 44, 92, 22, 70, 8, 56, 6, 54, 19, 67, 35, 83, 39, 87, 21, 69, 10, 58, 28, 76, 17, 65, 34, 82, 38, 86, 23, 71, 16, 64, 4, 52, 14, 62, 33, 81, 40, 88, 27, 75, 9, 57)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 109, 157)(103, 151, 117, 165)(105, 153, 120, 168)(106, 154, 121, 169)(107, 155, 126, 174)(111, 159, 124, 172)(112, 160, 122, 170)(113, 161, 128, 176)(114, 162, 130, 178)(115, 163, 127, 175)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 138, 186)(123, 171, 139, 187)(125, 173, 141, 189)(129, 177, 133, 181)(131, 179, 142, 190)(132, 180, 135, 183)(136, 184, 143, 191)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 113)(6, 97)(7, 118)(8, 120)(9, 122)(10, 98)(11, 101)(12, 124)(13, 99)(14, 128)(15, 102)(16, 121)(17, 127)(18, 131)(19, 126)(20, 135)(21, 137)(22, 139)(23, 103)(24, 112)(25, 104)(26, 106)(27, 138)(28, 109)(29, 133)(30, 110)(31, 107)(32, 115)(33, 114)(34, 142)(35, 141)(36, 140)(37, 130)(38, 132)(39, 144)(40, 116)(41, 123)(42, 117)(43, 119)(44, 143)(45, 129)(46, 125)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.938
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.943 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y2 * Y3, (Y3^-1 * Y1^-2)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 30, 78, 12, 60, 24, 72, 41, 89, 47, 95, 45, 93, 31, 79, 15, 63, 27, 75, 43, 91, 48, 96, 46, 94, 32, 80, 13, 61, 25, 73, 42, 90, 36, 84, 17, 65, 5, 53)(3, 51, 11, 59, 29, 77, 44, 92, 23, 71, 8, 56, 4, 52, 14, 62, 33, 81, 40, 88, 21, 69, 9, 57, 26, 74, 18, 66, 35, 83, 38, 86, 22, 70, 19, 67, 6, 54, 16, 64, 34, 82, 39, 87, 28, 76, 10, 58)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 112, 160)(102, 150, 109, 157)(103, 151, 117, 165)(105, 153, 120, 168)(106, 154, 121, 169)(107, 155, 126, 174)(110, 158, 127, 175)(111, 159, 122, 170)(113, 161, 131, 179)(114, 162, 128, 176)(115, 163, 123, 171)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 138, 186)(124, 172, 139, 187)(125, 173, 141, 189)(129, 177, 142, 190)(130, 178, 133, 181)(132, 180, 136, 184)(135, 183, 143, 191)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 107)(6, 97)(7, 118)(8, 120)(9, 123)(10, 98)(11, 127)(12, 122)(13, 99)(14, 128)(15, 102)(16, 126)(17, 130)(18, 101)(19, 121)(20, 135)(21, 137)(22, 139)(23, 103)(24, 115)(25, 104)(26, 109)(27, 106)(28, 138)(29, 142)(30, 110)(31, 114)(32, 112)(33, 113)(34, 141)(35, 133)(36, 134)(37, 125)(38, 143)(39, 144)(40, 116)(41, 124)(42, 117)(43, 119)(44, 132)(45, 129)(46, 131)(47, 140)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.939
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.944 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3, (R * Y1)^2, (R * Y3^-1)^2, Y3^2 * Y1 * Y2 * Y1^-1 * Y2, Y1^-1 * Y2 * Y1 * Y3^2 * Y2, Y3 * Y2 * Y3^-1 * R * Y2 * R, Y2 * R * Y3^-2 * Y1^-1 * R * Y2 * Y1^-1, (Y3 * Y2)^4, (Y3^-1 * Y1^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 4, 52, 8, 56, 14, 62, 24, 72, 34, 82, 42, 90, 45, 93, 44, 92, 25, 73, 40, 88, 43, 91, 48, 96, 28, 76, 41, 89, 47, 95, 46, 94, 39, 87, 26, 74, 18, 66, 16, 64, 6, 54, 5, 53)(3, 51, 9, 57, 10, 58, 22, 70, 21, 69, 7, 55, 19, 67, 20, 68, 33, 81, 32, 80, 13, 61, 30, 78, 31, 79, 38, 86, 17, 65, 23, 71, 37, 85, 36, 84, 35, 83, 15, 63, 29, 77, 27, 75, 12, 60, 11, 59)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 113, 161)(104, 152, 119, 167)(105, 153, 120, 168)(106, 154, 121, 169)(107, 155, 122, 170)(108, 156, 124, 172)(110, 158, 125, 173)(112, 160, 128, 176)(114, 162, 117, 165)(115, 163, 130, 178)(116, 164, 136, 184)(118, 166, 137, 185)(123, 171, 140, 188)(126, 174, 138, 186)(127, 175, 139, 187)(129, 177, 143, 191)(131, 179, 135, 183)(132, 180, 144, 192)(133, 181, 141, 189)(134, 182, 142, 190)
	L = (1, 100)(2, 104)(3, 106)(4, 110)(5, 98)(6, 97)(7, 116)(8, 120)(9, 118)(10, 117)(11, 105)(12, 99)(13, 127)(14, 130)(15, 123)(16, 101)(17, 133)(18, 102)(19, 129)(20, 128)(21, 115)(22, 103)(23, 132)(24, 138)(25, 139)(26, 112)(27, 107)(28, 143)(29, 108)(30, 134)(31, 113)(32, 126)(33, 109)(34, 141)(35, 125)(36, 111)(37, 131)(38, 119)(39, 114)(40, 144)(41, 142)(42, 140)(43, 124)(44, 136)(45, 121)(46, 122)(47, 135)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.937
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.945 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1, Y3^-1), (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y3 * Y2 * Y1, Y2 * Y1^-2 * Y2 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-2)^2, Y1 * Y2 * Y1^-1 * Y2 * Y3^2, Y1 * Y3^-2 * Y2 * Y3 * Y1 * Y2, Y2 * Y1^-1 * R * Y3 * Y1 * Y2 * R, Y1^-1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 16, 64, 30, 78, 46, 94, 48, 96, 44, 92, 20, 68, 6, 54, 10, 58, 25, 73, 17, 65, 4, 52, 9, 57, 24, 72, 47, 95, 41, 89, 35, 83, 22, 70, 32, 80, 19, 67, 5, 53)(3, 51, 11, 59, 21, 69, 29, 77, 27, 75, 8, 56, 26, 74, 31, 79, 40, 88, 36, 84, 14, 62, 33, 81, 38, 86, 34, 82, 12, 60, 28, 76, 45, 93, 42, 90, 43, 91, 18, 66, 37, 85, 39, 87, 15, 63, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 114, 162)(102, 150, 117, 165)(103, 151, 110, 158)(105, 153, 125, 173)(106, 154, 127, 175)(107, 155, 126, 174)(108, 156, 115, 163)(109, 157, 131, 179)(112, 160, 133, 181)(113, 161, 138, 186)(116, 164, 135, 183)(118, 166, 123, 171)(119, 167, 124, 172)(120, 168, 136, 184)(121, 169, 134, 182)(122, 170, 142, 190)(128, 176, 132, 180)(129, 177, 144, 192)(130, 178, 143, 191)(137, 185, 139, 187)(140, 188, 141, 189)
	L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 113)(6, 97)(7, 120)(8, 114)(9, 126)(10, 98)(11, 124)(12, 123)(13, 130)(14, 99)(15, 134)(16, 137)(17, 119)(18, 132)(19, 121)(20, 101)(21, 141)(22, 102)(23, 143)(24, 142)(25, 103)(26, 133)(27, 139)(28, 104)(29, 138)(30, 131)(31, 135)(32, 106)(33, 107)(34, 125)(35, 116)(36, 109)(37, 110)(38, 117)(39, 129)(40, 111)(41, 140)(42, 127)(43, 136)(44, 115)(45, 122)(46, 118)(47, 144)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.936
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.946 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3^-1, Y1 * Y3^-1, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (Y1 * R)^2, (R * Y2 * Y3^-1)^2, Y1^2 * Y2^-1 * R * Y2 * R, Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^2, Y2^-1 * Y1 * R * Y2^-1 * R * Y1^-1, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y1^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 16, 64, 34, 82, 27, 75, 12, 60, 4, 52)(3, 51, 9, 57, 17, 65, 36, 84, 29, 77, 13, 61, 21, 69, 8, 56)(5, 53, 11, 59, 18, 66, 7, 55, 19, 67, 35, 83, 28, 76, 14, 62)(10, 58, 24, 72, 37, 85, 30, 78, 43, 91, 22, 70, 42, 90, 23, 71)(15, 63, 31, 79, 38, 86, 26, 74, 39, 87, 20, 68, 40, 88, 32, 80)(25, 73, 46, 94, 47, 95, 44, 92, 48, 96, 41, 89, 33, 81, 45, 93)(97, 145, 99, 147, 106, 154, 121, 169, 134, 182, 114, 162, 102, 150, 113, 161, 133, 181, 143, 191, 135, 183, 115, 163, 130, 178, 125, 173, 139, 187, 144, 192, 136, 184, 124, 172, 108, 156, 117, 165, 138, 186, 129, 177, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 137, 185, 119, 167, 105, 153, 112, 160, 131, 179, 128, 176, 141, 189, 120, 168, 132, 180, 123, 171, 110, 158, 127, 175, 142, 190, 126, 174, 109, 157, 100, 148, 107, 155, 122, 170, 140, 188, 118, 166, 104, 152)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 112)(7, 115)(8, 99)(9, 113)(10, 120)(11, 114)(12, 100)(13, 117)(14, 101)(15, 127)(16, 130)(17, 132)(18, 103)(19, 131)(20, 136)(21, 104)(22, 138)(23, 106)(24, 133)(25, 142)(26, 135)(27, 108)(28, 110)(29, 109)(30, 139)(31, 134)(32, 111)(33, 141)(34, 123)(35, 124)(36, 125)(37, 126)(38, 122)(39, 116)(40, 128)(41, 129)(42, 119)(43, 118)(44, 144)(45, 121)(46, 143)(47, 140)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.934
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.947 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-3, Y3^-3 * Y1^-1, Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (Y3^-1, Y1^-1), (Y1 * Y3^-1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-6 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 7, 55, 12, 60, 4, 52, 10, 58, 5, 53)(3, 51, 13, 61, 21, 69, 16, 64, 27, 75, 15, 63, 26, 74, 11, 59)(6, 54, 18, 66, 22, 70, 9, 57, 23, 71, 19, 67, 25, 73, 17, 65)(14, 62, 30, 78, 37, 85, 32, 80, 43, 91, 28, 76, 42, 90, 29, 77)(20, 68, 33, 81, 38, 86, 34, 82, 39, 87, 24, 72, 40, 88, 35, 83)(31, 79, 46, 94, 47, 95, 44, 92, 48, 96, 41, 89, 36, 84, 45, 93)(97, 145, 99, 147, 110, 158, 127, 175, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 143, 191, 135, 183, 119, 167, 108, 156, 123, 171, 139, 187, 144, 192, 136, 184, 121, 169, 106, 154, 122, 170, 138, 186, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 120, 168, 137, 185, 125, 173, 109, 157, 103, 151, 115, 163, 131, 179, 141, 189, 126, 174, 112, 160, 100, 148, 113, 161, 129, 177, 142, 190, 128, 176, 111, 159, 101, 149, 114, 162, 130, 178, 140, 188, 124, 172, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 101)(9, 102)(10, 103)(11, 123)(12, 98)(13, 122)(14, 124)(15, 117)(16, 99)(17, 119)(18, 121)(19, 118)(20, 120)(21, 107)(22, 113)(23, 114)(24, 134)(25, 105)(26, 112)(27, 109)(28, 133)(29, 139)(30, 138)(31, 137)(32, 110)(33, 136)(34, 116)(35, 135)(36, 140)(37, 125)(38, 131)(39, 129)(40, 130)(41, 143)(42, 128)(43, 126)(44, 127)(45, 144)(46, 132)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.933
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.948 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3^-1, Y2^-1), (R * Y2)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y1^8, Y3^2 * Y2 * Y3 * Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-4 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 16, 64, 30, 78, 20, 68, 5, 53)(3, 51, 13, 61, 24, 72, 12, 60, 4, 52, 17, 65, 25, 73, 11, 59)(6, 54, 18, 66, 26, 74, 9, 57, 7, 55, 19, 67, 27, 75, 10, 58)(14, 62, 32, 80, 41, 89, 34, 82, 15, 63, 31, 79, 42, 90, 33, 81)(21, 69, 29, 77, 43, 91, 37, 85, 22, 70, 28, 76, 44, 92, 38, 86)(35, 83, 46, 94, 40, 88, 47, 95, 36, 84, 45, 93, 39, 87, 48, 96)(97, 145, 99, 147, 110, 158, 131, 179, 139, 187, 122, 170, 104, 152, 120, 168, 137, 185, 136, 184, 118, 166, 103, 151, 112, 160, 100, 148, 111, 159, 132, 180, 140, 188, 123, 171, 116, 164, 121, 169, 138, 186, 135, 183, 117, 165, 102, 150)(98, 146, 105, 153, 124, 172, 141, 189, 129, 177, 109, 157, 119, 167, 115, 163, 134, 182, 144, 192, 128, 176, 108, 156, 126, 174, 106, 154, 125, 173, 142, 190, 130, 178, 113, 161, 101, 149, 114, 162, 133, 181, 143, 191, 127, 175, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 101)(14, 132)(15, 131)(16, 99)(17, 119)(18, 134)(19, 133)(20, 120)(21, 103)(22, 102)(23, 114)(24, 138)(25, 137)(26, 116)(27, 104)(28, 142)(29, 141)(30, 105)(31, 108)(32, 107)(33, 113)(34, 109)(35, 140)(36, 139)(37, 144)(38, 143)(39, 118)(40, 117)(41, 135)(42, 136)(43, 123)(44, 122)(45, 130)(46, 129)(47, 128)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.935
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 16^6, 48^2 ]

E27.949 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-3, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1, (Y1 * Y2^-1 * Y1 * Y2)^2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 20, 68)(7, 55, 21, 69)(8, 56, 25, 73)(9, 57, 28, 76)(10, 58, 30, 78)(12, 60, 22, 70)(13, 61, 33, 81)(14, 62, 35, 83)(16, 64, 38, 86)(17, 65, 39, 87)(19, 67, 29, 77)(23, 71, 43, 91)(24, 72, 36, 84)(26, 74, 37, 85)(27, 75, 40, 88)(31, 79, 41, 89)(32, 80, 45, 93)(34, 82, 48, 96)(42, 90, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147, 108, 156, 124, 172, 137, 185, 117, 165, 115, 163, 101, 149)(98, 146, 103, 151, 118, 166, 114, 162, 127, 175, 107, 155, 125, 173, 105, 153)(100, 148, 112, 160, 128, 176, 110, 158, 130, 178, 109, 157, 102, 150, 113, 161)(104, 152, 122, 170, 138, 186, 120, 168, 140, 188, 119, 167, 106, 154, 123, 171)(111, 159, 129, 177, 141, 189, 135, 183, 144, 192, 134, 182, 116, 164, 131, 179)(121, 169, 139, 187, 143, 191, 136, 184, 142, 190, 133, 181, 126, 174, 132, 180)
	L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 119)(8, 118)(9, 120)(10, 98)(11, 122)(12, 128)(13, 124)(14, 99)(15, 132)(16, 101)(17, 117)(18, 123)(19, 102)(20, 133)(21, 112)(22, 138)(23, 114)(24, 103)(25, 131)(26, 105)(27, 107)(28, 113)(29, 106)(30, 134)(31, 140)(32, 137)(33, 142)(34, 115)(35, 143)(36, 141)(37, 111)(38, 121)(39, 126)(40, 116)(41, 130)(42, 127)(43, 144)(44, 125)(45, 139)(46, 135)(47, 129)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.958
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.950 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y1 * Y2 * Y1, Y1 * Y2^-1 * Y3^-2 * Y1 * Y2^-1, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y2, Y3^2 * Y1 * Y2^-2 * Y1, Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y3, Y2^5 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 20, 68)(7, 55, 21, 69)(8, 56, 25, 73)(9, 57, 28, 76)(10, 58, 30, 78)(12, 60, 22, 70)(13, 61, 33, 81)(14, 62, 35, 83)(16, 64, 38, 86)(17, 65, 39, 87)(19, 67, 29, 77)(23, 71, 37, 85)(24, 72, 40, 88)(26, 74, 44, 92)(27, 75, 36, 84)(31, 79, 41, 89)(32, 80, 45, 93)(34, 82, 46, 94)(42, 90, 48, 96)(43, 91, 47, 95)(97, 145, 99, 147, 108, 156, 124, 172, 137, 185, 117, 165, 115, 163, 101, 149)(98, 146, 103, 151, 118, 166, 114, 162, 127, 175, 107, 155, 125, 173, 105, 153)(100, 148, 112, 160, 128, 176, 110, 158, 130, 178, 109, 157, 102, 150, 113, 161)(104, 152, 122, 170, 138, 186, 120, 168, 139, 187, 119, 167, 106, 154, 123, 171)(111, 159, 129, 177, 141, 189, 135, 183, 142, 190, 134, 182, 116, 164, 131, 179)(121, 169, 133, 181, 144, 192, 132, 180, 143, 191, 140, 188, 126, 174, 136, 184)
	L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 119)(8, 118)(9, 120)(10, 98)(11, 122)(12, 128)(13, 124)(14, 99)(15, 132)(16, 101)(17, 117)(18, 123)(19, 102)(20, 133)(21, 112)(22, 138)(23, 114)(24, 103)(25, 135)(26, 105)(27, 107)(28, 113)(29, 106)(30, 129)(31, 139)(32, 137)(33, 121)(34, 115)(35, 126)(36, 141)(37, 111)(38, 143)(39, 144)(40, 116)(41, 130)(42, 127)(43, 125)(44, 142)(45, 140)(46, 136)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.957
Graph:: simple bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.951 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y1 * Y3^-2 * Y1 * Y2^-1, Y2^2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^4, Y2^8, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 12, 60)(10, 58, 14, 62)(15, 63, 25, 73)(16, 64, 27, 75)(17, 65, 26, 74)(18, 66, 29, 77)(19, 67, 30, 78)(20, 68, 31, 79)(21, 69, 33, 81)(22, 70, 32, 80)(23, 71, 35, 83)(24, 72, 36, 84)(28, 76, 34, 82)(37, 85, 45, 93)(38, 86, 46, 94)(39, 87, 47, 95)(40, 88, 42, 90)(41, 89, 43, 91)(44, 92, 48, 96)(97, 145, 99, 147, 104, 152, 113, 161, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 130, 178, 120, 168, 110, 158, 102, 150)(103, 151, 111, 159, 122, 170, 135, 183, 126, 174, 114, 162, 105, 153, 112, 160)(107, 155, 116, 164, 128, 176, 140, 188, 132, 180, 119, 167, 109, 157, 117, 165)(121, 169, 133, 181, 143, 191, 137, 185, 125, 173, 136, 184, 123, 171, 134, 182)(127, 175, 138, 186, 144, 192, 142, 190, 131, 179, 141, 189, 129, 177, 139, 187)
	L = (1, 100)(2, 102)(3, 97)(4, 106)(5, 98)(6, 110)(7, 112)(8, 99)(9, 114)(10, 115)(11, 117)(12, 101)(13, 119)(14, 120)(15, 103)(16, 105)(17, 104)(18, 126)(19, 124)(20, 107)(21, 109)(22, 108)(23, 132)(24, 130)(25, 134)(26, 111)(27, 136)(28, 113)(29, 137)(30, 135)(31, 139)(32, 116)(33, 141)(34, 118)(35, 142)(36, 140)(37, 121)(38, 123)(39, 122)(40, 125)(41, 143)(42, 127)(43, 129)(44, 128)(45, 131)(46, 144)(47, 133)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.954
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.952 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, Y2^-3 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y3^-1 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 16, 64)(6, 54, 17, 65)(7, 55, 18, 66)(8, 56, 22, 70)(9, 57, 23, 71)(10, 58, 24, 72)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 108, 156, 100, 148, 109, 157, 102, 150, 110, 158, 101, 149)(98, 146, 103, 151, 115, 163, 104, 152, 116, 164, 106, 154, 117, 165, 105, 153)(107, 155, 121, 169, 111, 159, 122, 170, 113, 161, 124, 172, 112, 160, 123, 171)(114, 162, 125, 173, 118, 166, 126, 174, 120, 168, 128, 176, 119, 167, 127, 175)(129, 177, 137, 185, 130, 178, 138, 186, 132, 180, 140, 188, 131, 179, 139, 187)(133, 181, 141, 189, 134, 182, 142, 190, 136, 184, 144, 192, 135, 183, 143, 191)
	L = (1, 100)(2, 104)(3, 109)(4, 110)(5, 108)(6, 97)(7, 116)(8, 117)(9, 115)(10, 98)(11, 122)(12, 102)(13, 101)(14, 99)(15, 124)(16, 121)(17, 123)(18, 126)(19, 106)(20, 105)(21, 103)(22, 128)(23, 125)(24, 127)(25, 113)(26, 112)(27, 111)(28, 107)(29, 120)(30, 119)(31, 118)(32, 114)(33, 138)(34, 140)(35, 137)(36, 139)(37, 142)(38, 144)(39, 141)(40, 143)(41, 132)(42, 131)(43, 130)(44, 129)(45, 136)(46, 135)(47, 134)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.955
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.953 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (Y2^-1 * Y3^-1)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2^-1 * Y3^4 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 21, 69)(13, 61, 16, 64)(14, 62, 22, 70)(15, 63, 23, 71)(17, 65, 19, 67)(20, 68, 24, 72)(25, 73, 34, 82)(26, 74, 28, 76)(27, 75, 37, 85)(29, 77, 31, 79)(30, 78, 33, 81)(32, 80, 39, 87)(35, 83, 36, 84)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 43, 91)(44, 92, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 105, 153, 98, 146, 103, 151, 114, 162, 101, 149)(100, 148, 110, 158, 121, 169, 109, 157, 104, 152, 118, 166, 130, 178, 112, 160)(102, 150, 115, 163, 122, 170, 117, 165, 106, 154, 113, 161, 124, 172, 108, 156)(111, 159, 127, 175, 137, 185, 126, 174, 119, 167, 125, 173, 141, 189, 129, 177)(116, 164, 133, 181, 138, 186, 131, 179, 120, 168, 123, 171, 139, 187, 132, 180)(128, 176, 144, 192, 134, 182, 143, 191, 135, 183, 140, 188, 136, 184, 142, 190)
	L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 117)(8, 119)(9, 115)(10, 98)(11, 121)(12, 123)(13, 99)(14, 101)(15, 128)(16, 103)(17, 131)(18, 130)(19, 132)(20, 102)(21, 133)(22, 105)(23, 135)(24, 106)(25, 137)(26, 107)(27, 140)(28, 114)(29, 109)(30, 110)(31, 112)(32, 139)(33, 118)(34, 141)(35, 143)(36, 142)(37, 144)(38, 116)(39, 138)(40, 120)(41, 134)(42, 122)(43, 124)(44, 126)(45, 136)(46, 125)(47, 127)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48, 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.956
Graph:: bipartite
	v = 30 e = 96 f = 14
	degree seq :: [ 4^24, 16^6 ]

E27.954 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y1^2, (R * Y1)^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), Y1^4, (R * Y3)^2, (Y2, Y1), Y2^-1 * Y1^-1 * R * Y2 * R, Y3 * Y2 * Y3 * Y1^-1 * Y2, Y3^-1 * Y2 * Y3^-1 * Y1^-1 * Y2, Y2^6 * Y1, Y2^-1 * Y3 * Y2^3 * Y3 * Y2^-2, Y2^-3 * Y1 * Y2^-3 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 26, 74, 19, 67)(13, 61, 27, 75, 41, 89, 31, 79)(14, 62, 18, 66, 16, 64, 24, 72)(17, 65, 20, 68, 23, 71, 22, 70)(21, 69, 28, 76, 42, 90, 36, 84)(29, 77, 39, 87, 43, 91, 45, 93)(30, 78, 33, 81, 32, 80, 34, 82)(35, 83, 37, 85, 38, 86, 40, 88)(44, 92, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 125, 173, 132, 180, 115, 163, 101, 149, 111, 159, 127, 175, 141, 189, 138, 186, 122, 170, 104, 152, 121, 169, 137, 185, 139, 187, 124, 172, 107, 155, 98, 146, 105, 153, 123, 171, 135, 183, 117, 165, 102, 150)(100, 148, 113, 161, 131, 179, 142, 190, 129, 177, 110, 158, 108, 156, 118, 166, 136, 184, 143, 191, 126, 174, 120, 168, 103, 151, 119, 167, 134, 182, 140, 188, 130, 178, 112, 160, 106, 154, 116, 164, 133, 181, 144, 192, 128, 176, 114, 162)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 114)(10, 101)(11, 119)(12, 98)(13, 126)(14, 121)(15, 120)(16, 99)(17, 107)(18, 111)(19, 113)(20, 122)(21, 134)(22, 102)(23, 115)(24, 105)(25, 112)(26, 118)(27, 129)(28, 136)(29, 140)(30, 137)(31, 130)(32, 109)(33, 127)(34, 123)(35, 117)(36, 133)(37, 124)(38, 138)(39, 143)(40, 132)(41, 128)(42, 131)(43, 142)(44, 139)(45, 144)(46, 125)(47, 141)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.951
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.955 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1)^2, Y3 * Y1^-2 * Y3, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, (Y2, Y1), Y2 * Y3^-1 * Y1 * Y2 * Y3^-1, R * Y2 * R * Y1 * Y2^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-6 * Y1, Y2^-1 * Y3 * Y2^3 * Y3 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 25, 73, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 26, 74, 19, 67)(13, 61, 27, 75, 41, 89, 31, 79)(14, 62, 24, 72, 16, 64, 18, 66)(17, 65, 22, 70, 23, 71, 20, 68)(21, 69, 28, 76, 42, 90, 36, 84)(29, 77, 43, 91, 48, 96, 39, 87)(30, 78, 34, 82, 32, 80, 33, 81)(35, 83, 40, 88, 38, 86, 37, 85)(44, 92, 47, 95, 45, 93, 46, 94)(97, 145, 99, 147, 109, 157, 125, 173, 124, 172, 107, 155, 98, 146, 105, 153, 123, 171, 139, 187, 138, 186, 122, 170, 104, 152, 121, 169, 137, 185, 144, 192, 132, 180, 115, 163, 101, 149, 111, 159, 127, 175, 135, 183, 117, 165, 102, 150)(100, 148, 113, 161, 131, 179, 141, 189, 129, 177, 110, 158, 106, 154, 118, 166, 136, 184, 142, 190, 126, 174, 120, 168, 103, 151, 119, 167, 134, 182, 140, 188, 130, 178, 112, 160, 108, 156, 116, 164, 133, 181, 143, 191, 128, 176, 114, 162)
	L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 120)(10, 101)(11, 113)(12, 98)(13, 126)(14, 121)(15, 114)(16, 99)(17, 115)(18, 105)(19, 119)(20, 122)(21, 134)(22, 102)(23, 107)(24, 111)(25, 112)(26, 118)(27, 130)(28, 133)(29, 140)(30, 137)(31, 129)(32, 109)(33, 123)(34, 127)(35, 117)(36, 136)(37, 132)(38, 138)(39, 142)(40, 124)(41, 128)(42, 131)(43, 143)(44, 144)(45, 125)(46, 139)(47, 135)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.952
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.956 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y1 * R)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^-2 * Y2 * Y1^-2, Y2^2 * Y3^-1 * Y2^2 * Y1^-1, (Y2^-2 * Y1^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2^-3 * Y1^-1 * Y2^3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 35, 83, 24, 72)(16, 64, 31, 79, 36, 84, 20, 68)(25, 73, 37, 85, 29, 77, 40, 88)(26, 74, 42, 90, 30, 78, 43, 91)(28, 76, 46, 94, 47, 95, 39, 87)(32, 80, 38, 86, 33, 81, 41, 89)(34, 82, 45, 93, 48, 96, 44, 92)(97, 145, 99, 147, 106, 154, 124, 172, 137, 185, 117, 165, 136, 184, 118, 166, 138, 186, 144, 192, 132, 180, 114, 162, 102, 150, 113, 161, 131, 179, 143, 191, 134, 182, 115, 163, 133, 181, 119, 167, 139, 187, 130, 178, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 135, 183, 122, 170, 105, 153, 121, 169, 111, 159, 129, 177, 141, 189, 123, 171, 109, 157, 100, 148, 108, 156, 127, 175, 142, 190, 126, 174, 107, 155, 125, 173, 110, 158, 128, 176, 140, 188, 120, 168, 104, 152)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 127)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 133)(26, 138)(27, 131)(28, 142)(29, 136)(30, 139)(31, 132)(32, 134)(33, 137)(34, 141)(35, 120)(36, 116)(37, 125)(38, 129)(39, 124)(40, 121)(41, 128)(42, 126)(43, 122)(44, 130)(45, 144)(46, 143)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.953
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.957 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3^-1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1 * Y2^2 * Y3 * Y1, Y1 * Y3 * Y2^2 * Y1, Y3^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y3^-1, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y1, Y2^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 27, 75, 16, 64)(4, 52, 18, 66, 26, 74, 12, 60)(6, 54, 24, 72, 15, 63, 25, 73)(7, 55, 22, 70, 14, 62, 10, 58)(9, 57, 29, 77, 21, 69, 30, 78)(11, 59, 34, 82, 23, 71, 35, 83)(17, 65, 42, 90, 38, 86, 31, 79)(19, 67, 36, 84, 46, 94, 43, 91)(20, 68, 45, 93, 40, 88, 33, 81)(28, 76, 32, 80, 39, 87, 47, 95)(37, 85, 48, 96, 41, 89, 44, 92)(97, 145, 99, 147, 110, 158, 134, 182, 124, 172, 126, 174, 140, 188, 130, 178, 142, 190, 116, 164, 100, 148, 111, 159, 104, 152, 123, 171, 103, 151, 113, 161, 135, 183, 125, 173, 144, 192, 131, 179, 115, 163, 136, 184, 122, 170, 102, 150)(98, 146, 105, 153, 114, 162, 138, 186, 132, 180, 109, 157, 133, 181, 121, 169, 143, 191, 129, 177, 106, 154, 119, 167, 101, 149, 117, 165, 108, 156, 127, 175, 139, 187, 112, 160, 137, 185, 120, 168, 128, 176, 141, 189, 118, 166, 107, 155)
	L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 116)(7, 97)(8, 122)(9, 119)(10, 128)(11, 129)(12, 98)(13, 127)(14, 104)(15, 136)(16, 138)(17, 99)(18, 101)(19, 140)(20, 131)(21, 107)(22, 143)(23, 141)(24, 109)(25, 112)(26, 142)(27, 102)(28, 103)(29, 134)(30, 113)(31, 105)(32, 133)(33, 120)(34, 125)(35, 126)(36, 108)(37, 139)(38, 123)(39, 110)(40, 130)(41, 132)(42, 117)(43, 114)(44, 135)(45, 121)(46, 144)(47, 137)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.950
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.958 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 8, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 5>)
Aut   = (D8 x S3) : C2 (small group id <96, 121>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3 * Y2, (Y1^-1 * Y3^-1)^2, (Y1 * Y3^-1)^2, (Y1 * Y3^-1)^2, (Y1 * Y3)^2, (R * Y3)^2, Y1^4, (Y2 * R)^2, (R * Y1)^2, Y2^-1 * Y1^-2 * Y2 * Y1^-2, Y2 * Y3^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y3^12, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 14, 62)(4, 52, 16, 64, 26, 74, 12, 60)(6, 54, 22, 70, 27, 75, 23, 71)(7, 55, 20, 68, 28, 76, 10, 58)(9, 57, 29, 77, 19, 67, 30, 78)(11, 59, 34, 82, 21, 69, 35, 83)(15, 63, 39, 87, 45, 93, 31, 79)(17, 65, 36, 84, 46, 94, 40, 88)(18, 66, 42, 90, 47, 95, 33, 81)(24, 72, 32, 80, 48, 96, 43, 91)(37, 85, 41, 89, 38, 86, 44, 92)(97, 145, 99, 147, 103, 151, 111, 159, 120, 168, 126, 174, 140, 188, 130, 178, 142, 190, 143, 191, 122, 170, 123, 171, 104, 152, 121, 169, 124, 172, 141, 189, 144, 192, 125, 173, 137, 185, 131, 179, 113, 161, 114, 162, 100, 148, 102, 150)(98, 146, 105, 153, 108, 156, 127, 175, 132, 180, 109, 157, 133, 181, 119, 167, 139, 187, 138, 186, 116, 164, 117, 165, 101, 149, 115, 163, 112, 160, 135, 183, 136, 184, 110, 158, 134, 182, 118, 166, 128, 176, 129, 177, 106, 154, 107, 155)
	L = (1, 100)(2, 106)(3, 102)(4, 113)(5, 116)(6, 114)(7, 97)(8, 122)(9, 107)(10, 128)(11, 129)(12, 98)(13, 127)(14, 135)(15, 99)(16, 101)(17, 137)(18, 131)(19, 117)(20, 139)(21, 138)(22, 110)(23, 109)(24, 103)(25, 123)(26, 142)(27, 143)(28, 104)(29, 141)(30, 111)(31, 105)(32, 134)(33, 118)(34, 126)(35, 125)(36, 108)(37, 132)(38, 136)(39, 115)(40, 112)(41, 144)(42, 119)(43, 133)(44, 120)(45, 121)(46, 140)(47, 130)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.949
Graph:: bipartite
	v = 14 e = 96 f = 30
	degree seq :: [ 8^12, 48^2 ]

E27.959 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 24, 24})
Quotient :: dipole
Aut^+ = C24 x C2 (small group id <48, 23>)
Aut   = C2 x D48 (small group id <96, 110>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y3, Y2), (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2)^2, Y1^-1 * Y2^-8, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 10, 58, 16, 64)(11, 59, 19, 67, 25, 73)(12, 60, 20, 68, 14, 62)(15, 63, 21, 69, 18, 66)(17, 65, 22, 70, 28, 76)(23, 71, 31, 79, 37, 85)(24, 72, 32, 80, 26, 74)(27, 75, 33, 81, 30, 78)(29, 77, 34, 82, 40, 88)(35, 83, 41, 89, 45, 93)(36, 84, 43, 91, 38, 86)(39, 87, 44, 92, 42, 90)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 136, 184, 124, 172, 112, 160, 101, 149, 109, 157, 121, 169, 133, 181, 141, 189, 130, 178, 118, 166, 106, 154, 98, 146, 104, 152, 115, 163, 127, 175, 137, 185, 125, 173, 113, 161, 102, 150)(100, 148, 108, 156, 120, 168, 132, 180, 142, 190, 138, 186, 126, 174, 114, 162, 103, 151, 110, 158, 122, 170, 134, 182, 143, 191, 140, 188, 129, 177, 117, 165, 105, 153, 116, 164, 128, 176, 139, 187, 144, 192, 135, 183, 123, 171, 111, 159)
	L = (1, 100)(2, 105)(3, 108)(4, 98)(5, 103)(6, 111)(7, 97)(8, 116)(9, 101)(10, 117)(11, 120)(12, 104)(13, 110)(14, 99)(15, 106)(16, 114)(17, 123)(18, 102)(19, 128)(20, 109)(21, 112)(22, 129)(23, 132)(24, 115)(25, 122)(26, 107)(27, 118)(28, 126)(29, 135)(30, 113)(31, 139)(32, 121)(33, 124)(34, 140)(35, 142)(36, 127)(37, 134)(38, 119)(39, 130)(40, 138)(41, 144)(42, 125)(43, 133)(44, 136)(45, 143)(46, 137)(47, 131)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.960
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 6^16, 48^2 ]

E27.960 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 24, 24})
Quotient :: dipole
Aut^+ = C24 x C2 (small group id <48, 23>)
Aut   = C2 x D48 (small group id <96, 110>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y2 * Y3^-3, Y2 * Y3^-1 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, (Y1, Y3^-1), Y1^-1 * Y3 * Y2 * Y1 * Y3^2, Y1^-4 * Y3^-1 * Y1^-1 * Y2 * Y1^-3, (Y1^-1 * Y3^-1)^24 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 17, 65, 29, 77, 41, 89, 37, 85, 25, 73, 13, 61, 22, 70, 34, 82, 46, 94, 48, 96, 47, 95, 35, 83, 23, 71, 11, 59, 21, 69, 33, 81, 45, 93, 39, 87, 27, 75, 15, 63, 5, 53)(3, 51, 8, 56, 18, 66, 30, 78, 42, 90, 40, 88, 28, 76, 16, 64, 6, 54, 10, 58, 20, 68, 32, 80, 44, 92, 38, 86, 26, 74, 14, 62, 4, 52, 9, 57, 19, 67, 31, 79, 43, 91, 36, 84, 24, 72, 12, 60)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(113, 161, 126, 174)(115, 163, 129, 177)(116, 164, 130, 178)(122, 170, 131, 179)(123, 171, 132, 180)(124, 172, 133, 181)(125, 173, 138, 186)(127, 175, 141, 189)(128, 176, 142, 190)(134, 182, 143, 191)(135, 183, 139, 187)(136, 184, 137, 185)(140, 188, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 110)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 102)(12, 119)(13, 99)(14, 121)(15, 122)(16, 101)(17, 127)(18, 129)(19, 130)(20, 103)(21, 106)(22, 104)(23, 112)(24, 131)(25, 108)(26, 133)(27, 134)(28, 111)(29, 139)(30, 141)(31, 142)(32, 113)(33, 116)(34, 114)(35, 124)(36, 143)(37, 120)(38, 137)(39, 140)(40, 123)(41, 132)(42, 135)(43, 144)(44, 125)(45, 128)(46, 126)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.959
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.961 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 24, 24})
Quotient :: dipole
Aut^+ = C3 x (C8 : C2) (small group id <48, 24>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y2, Y1^-1), (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y2 * Y3^-1 * Y2^-2 * Y3 * Y2, (Y3^-1, Y2^-1)^2, Y3 * Y2 * Y3 * Y2^10 * Y1^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 10, 58, 17, 65)(11, 59, 23, 71, 31, 79)(12, 60, 24, 72, 14, 62)(15, 63, 25, 73, 21, 69)(16, 64, 26, 74, 22, 70)(18, 66, 27, 75, 20, 68)(19, 67, 28, 76, 40, 88)(29, 77, 44, 92, 39, 87)(30, 78, 43, 91, 32, 80)(33, 81, 42, 90, 35, 83)(34, 82, 45, 93, 36, 84)(37, 85, 41, 89, 38, 86)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 107, 155, 125, 173, 142, 190, 133, 181, 136, 184, 113, 161, 101, 149, 109, 157, 127, 175, 135, 183, 143, 191, 134, 182, 124, 172, 106, 154, 98, 146, 104, 152, 119, 167, 140, 188, 144, 192, 137, 185, 115, 163, 102, 150)(100, 148, 111, 159, 126, 174, 123, 171, 141, 189, 120, 168, 138, 186, 118, 166, 103, 151, 117, 165, 128, 176, 114, 162, 130, 178, 108, 156, 129, 177, 122, 170, 105, 153, 121, 169, 139, 187, 116, 164, 132, 180, 110, 158, 131, 179, 112, 160)
	L = (1, 100)(2, 105)(3, 108)(4, 98)(5, 103)(6, 114)(7, 97)(8, 120)(9, 101)(10, 123)(11, 126)(12, 104)(13, 110)(14, 99)(15, 133)(16, 125)(17, 116)(18, 106)(19, 131)(20, 102)(21, 134)(22, 135)(23, 139)(24, 109)(25, 137)(26, 140)(27, 113)(28, 129)(29, 122)(30, 119)(31, 128)(32, 107)(33, 136)(34, 142)(35, 124)(36, 143)(37, 121)(38, 111)(39, 112)(40, 138)(41, 117)(42, 115)(43, 127)(44, 118)(45, 144)(46, 141)(47, 130)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48, 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.962
Graph:: bipartite
	v = 18 e = 96 f = 26
	degree seq :: [ 6^16, 48^2 ]

E27.962 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 24, 24})
Quotient :: dipole
Aut^+ = C3 x (C8 : C2) (small group id <48, 24>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y1^-2 * Y2 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y3, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y1 * Y2 * Y1^-2 * Y2 * Y1, (Y2 * Y1^-1 * Y2 * Y1)^2, Y2 * Y1^-2 * Y3^-2 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y1^16 * Y2 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 23, 71, 42, 90, 36, 84, 46, 94, 41, 89, 14, 62, 30, 78, 44, 92, 39, 87, 47, 95, 35, 83, 45, 93, 38, 86, 12, 60, 28, 76, 43, 91, 40, 88, 48, 96, 37, 85, 19, 67, 5, 53)(3, 51, 11, 59, 24, 72, 18, 66, 32, 80, 9, 57, 31, 79, 22, 70, 6, 54, 21, 69, 26, 74, 17, 65, 29, 77, 8, 56, 27, 75, 16, 64, 4, 52, 15, 63, 25, 73, 20, 68, 34, 82, 10, 58, 33, 81, 13, 61)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 120, 168)(105, 153, 124, 172)(106, 154, 126, 174)(107, 155, 131, 179)(109, 157, 135, 183)(111, 159, 132, 180)(112, 160, 119, 167)(114, 162, 134, 182)(115, 163, 129, 177)(116, 164, 137, 185)(117, 165, 133, 181)(118, 166, 136, 184)(121, 169, 139, 187)(122, 170, 140, 188)(123, 171, 141, 189)(125, 173, 143, 191)(127, 175, 142, 190)(128, 176, 138, 186)(130, 178, 144, 192)
	L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 114)(6, 97)(7, 121)(8, 124)(9, 126)(10, 98)(11, 132)(12, 102)(13, 119)(14, 99)(15, 133)(16, 136)(17, 134)(18, 137)(19, 123)(20, 101)(21, 131)(22, 135)(23, 118)(24, 139)(25, 140)(26, 103)(27, 142)(28, 106)(29, 138)(30, 104)(31, 115)(32, 144)(33, 141)(34, 143)(35, 111)(36, 117)(37, 107)(38, 116)(39, 112)(40, 109)(41, 113)(42, 130)(43, 122)(44, 120)(45, 127)(46, 129)(47, 128)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 48, 6, 48 ), ( 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48, 6, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.961
Graph:: bipartite
	v = 26 e = 96 f = 18
	degree seq :: [ 4^24, 48^2 ]

E27.963 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^2 * Y2 * Y3^6 * Y1, Y3^4 * Y2^-2 * Y3^-2 * Y1 * Y2^-1 * Y3^-2 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 17, 65)(12, 60, 18, 66)(13, 61, 19, 67)(14, 62, 20, 68)(15, 63, 21, 69)(16, 64, 22, 70)(23, 71, 29, 77)(24, 72, 30, 78)(25, 73, 31, 79)(26, 74, 32, 80)(27, 75, 33, 81)(28, 76, 34, 82)(35, 83, 41, 89)(36, 84, 42, 90)(37, 85, 43, 91)(38, 86, 44, 92)(39, 87, 45, 93)(40, 88, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 107, 155, 110, 158)(102, 150, 108, 156, 111, 159)(104, 152, 113, 161, 116, 164)(106, 154, 114, 162, 117, 165)(109, 157, 119, 167, 122, 170)(112, 160, 120, 168, 123, 171)(115, 163, 125, 173, 128, 176)(118, 166, 126, 174, 129, 177)(121, 169, 131, 179, 134, 182)(124, 172, 132, 180, 135, 183)(127, 175, 137, 185, 140, 188)(130, 178, 138, 186, 141, 189)(133, 181, 142, 190, 144, 192)(136, 184, 143, 191, 139, 187)
	L = (1, 100)(2, 104)(3, 107)(4, 109)(5, 110)(6, 97)(7, 113)(8, 115)(9, 116)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 137)(30, 114)(31, 139)(32, 140)(33, 117)(34, 118)(35, 142)(36, 120)(37, 141)(38, 144)(39, 123)(40, 124)(41, 136)(42, 126)(43, 135)(44, 143)(45, 129)(46, 130)(47, 132)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 32, 96, 32, 96 ), ( 32, 96, 32, 96, 32, 96 ) }
Outer automorphisms :: reflexible
Dual of E27.966
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.964 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1 * Y3)^2, Y2^-3 * Y1 * Y2^2 * Y3^-1 * Y2 * Y3^-1, Y2^3 * Y3^-1 * Y2^5 * Y1^-1, (Y2^-1 * Y3)^48 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 10, 58, 16, 64)(11, 59, 19, 67, 25, 73)(12, 60, 20, 68, 14, 62)(15, 63, 21, 69, 18, 66)(17, 65, 22, 70, 28, 76)(23, 71, 31, 79, 37, 85)(24, 72, 32, 80, 26, 74)(27, 75, 33, 81, 30, 78)(29, 77, 34, 82, 40, 88)(35, 83, 43, 91, 48, 96)(36, 84, 44, 92, 38, 86)(39, 87, 45, 93, 42, 90)(41, 89, 46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 141, 189, 129, 177, 117, 165, 105, 153, 116, 164, 128, 176, 140, 188, 137, 185, 125, 173, 113, 161, 102, 150)(98, 146, 104, 152, 115, 163, 127, 175, 139, 187, 138, 186, 126, 174, 114, 162, 103, 151, 110, 158, 122, 170, 134, 182, 142, 190, 130, 178, 118, 166, 106, 154)(100, 148, 108, 156, 120, 168, 132, 180, 143, 191, 136, 184, 124, 172, 112, 160, 101, 149, 109, 157, 121, 169, 133, 181, 144, 192, 135, 183, 123, 171, 111, 159)
	L = (1, 100)(2, 105)(3, 108)(4, 98)(5, 103)(6, 111)(7, 97)(8, 116)(9, 101)(10, 117)(11, 120)(12, 104)(13, 110)(14, 99)(15, 106)(16, 114)(17, 123)(18, 102)(19, 128)(20, 109)(21, 112)(22, 129)(23, 132)(24, 115)(25, 122)(26, 107)(27, 118)(28, 126)(29, 135)(30, 113)(31, 140)(32, 121)(33, 124)(34, 141)(35, 143)(36, 127)(37, 134)(38, 119)(39, 130)(40, 138)(41, 144)(42, 125)(43, 137)(44, 133)(45, 136)(46, 131)(47, 139)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 96, 4, 96, 4, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96, 4, 96 ) }
Outer automorphisms :: reflexible
Dual of E27.965
Graph:: bipartite
	v = 19 e = 96 f = 25
	degree seq :: [ 6^16, 32^3 ]

E27.965 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^2 * Y3^-1 * Y1^6, (Y1^-1 * Y3^-1)^16 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 7, 55, 17, 65, 29, 77, 38, 86, 26, 74, 14, 62, 4, 52, 9, 57, 19, 67, 31, 79, 42, 90, 47, 95, 37, 85, 25, 73, 13, 61, 22, 70, 34, 82, 44, 92, 46, 94, 36, 84, 24, 72, 12, 60, 3, 51, 8, 56, 18, 66, 30, 78, 41, 89, 45, 93, 35, 83, 23, 71, 11, 59, 21, 69, 33, 81, 43, 91, 48, 96, 40, 88, 28, 76, 16, 64, 6, 54, 10, 58, 20, 68, 32, 80, 39, 87, 27, 75, 15, 63, 5, 53)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(113, 161, 126, 174)(115, 163, 129, 177)(116, 164, 130, 178)(122, 170, 131, 179)(123, 171, 132, 180)(124, 172, 133, 181)(125, 173, 137, 185)(127, 175, 139, 187)(128, 176, 140, 188)(134, 182, 141, 189)(135, 183, 142, 190)(136, 184, 143, 191)(138, 186, 144, 192)
	L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 110)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 102)(12, 119)(13, 99)(14, 121)(15, 122)(16, 101)(17, 127)(18, 129)(19, 130)(20, 103)(21, 106)(22, 104)(23, 112)(24, 131)(25, 108)(26, 133)(27, 134)(28, 111)(29, 138)(30, 139)(31, 140)(32, 113)(33, 116)(34, 114)(35, 124)(36, 141)(37, 120)(38, 143)(39, 125)(40, 123)(41, 144)(42, 142)(43, 128)(44, 126)(45, 136)(46, 137)(47, 132)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 32, 6, 32 ), ( 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32, 6, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.964
Graph:: bipartite
	v = 25 e = 96 f = 19
	degree seq :: [ 4^24, 96 ]

E27.966 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^2 * Y2^-2, (Y3^-1, Y1), (Y3, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1, Y2), Y3^-1 * Y1^-1 * Y2^2 * Y1 * Y3^-1, Y3 * Y2^2 * Y1^3, Y1^-1 * Y2^-1 * Y1^-2 * Y3^-1 * Y2^-1, Y1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2, Y3^2 * Y2^3 * Y1^-1 * Y3 * Y1^-1, Y3^2 * Y1^-1 * Y2 * Y1^-4, Y3^2 * Y2 * Y1^11, Y2^43 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 8, 56, 23, 71, 41, 89, 33, 81, 47, 95, 38, 86, 16, 64, 30, 78, 44, 92, 40, 88, 48, 96, 34, 82, 18, 66, 5, 53)(3, 51, 9, 57, 24, 72, 22, 70, 32, 80, 46, 94, 39, 87, 17, 65, 4, 52, 10, 58, 25, 73, 21, 69, 31, 79, 45, 93, 37, 85, 15, 63)(6, 54, 11, 59, 26, 74, 42, 90, 35, 83, 13, 61, 28, 76, 20, 68, 7, 55, 12, 60, 27, 75, 43, 91, 36, 84, 14, 62, 29, 77, 19, 67)(97, 145, 99, 147, 109, 157, 129, 177, 142, 190, 123, 171, 140, 188, 121, 169, 115, 163, 101, 149, 111, 159, 131, 179, 137, 185, 128, 176, 108, 156, 126, 174, 106, 154, 125, 173, 114, 162, 133, 181, 138, 186, 119, 167, 118, 166, 103, 151, 112, 160, 100, 148, 110, 158, 130, 178, 141, 189, 122, 170, 104, 152, 120, 168, 116, 164, 134, 182, 113, 161, 132, 180, 144, 192, 127, 175, 107, 155, 98, 146, 105, 153, 124, 172, 143, 191, 135, 183, 139, 187, 136, 184, 117, 165, 102, 150)
	L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 113)(6, 112)(7, 97)(8, 121)(9, 125)(10, 124)(11, 126)(12, 98)(13, 130)(14, 129)(15, 132)(16, 99)(17, 131)(18, 135)(19, 134)(20, 101)(21, 103)(22, 102)(23, 117)(24, 115)(25, 116)(26, 140)(27, 104)(28, 114)(29, 143)(30, 105)(31, 108)(32, 107)(33, 141)(34, 142)(35, 144)(36, 137)(37, 139)(38, 111)(39, 138)(40, 118)(41, 127)(42, 136)(43, 119)(44, 120)(45, 123)(46, 122)(47, 133)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.963
Graph:: bipartite
	v = 4 e = 96 f = 40
	degree seq :: [ 32^3, 96 ]

E27.967 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, Y3^3 * Y2^-3, Y2 * Y1 * Y3^2 * Y2 * Y3 * Y2^3, Y2^-2 * Y1 * Y3^-2 * Y1 * Y3^-3 * Y1 * Y3^-1, Y3^48 ]
Map:: non-degenerate
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 19, 67)(12, 60, 20, 68)(13, 61, 21, 69)(14, 62, 22, 70)(15, 63, 23, 71)(16, 64, 24, 72)(17, 65, 25, 73)(18, 66, 26, 74)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(33, 81, 41, 89)(34, 82, 42, 90)(43, 91, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 107, 155, 123, 171, 139, 187, 136, 184, 120, 168, 105, 153, 98, 146, 103, 151, 115, 163, 131, 179, 142, 190, 128, 176, 112, 160, 101, 149)(100, 148, 108, 156, 124, 172, 140, 188, 138, 186, 122, 170, 135, 183, 119, 167, 104, 152, 116, 164, 132, 180, 144, 192, 130, 178, 114, 162, 127, 175, 111, 159)(102, 150, 109, 157, 125, 173, 110, 158, 126, 174, 141, 189, 137, 185, 121, 169, 106, 154, 117, 165, 133, 181, 118, 166, 134, 182, 143, 191, 129, 177, 113, 161)
	L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 126)(13, 99)(14, 123)(15, 125)(16, 127)(17, 101)(18, 102)(19, 132)(20, 134)(21, 103)(22, 131)(23, 133)(24, 135)(25, 105)(26, 106)(27, 140)(28, 141)(29, 107)(30, 139)(31, 109)(32, 114)(33, 112)(34, 113)(35, 144)(36, 143)(37, 115)(38, 142)(39, 117)(40, 122)(41, 120)(42, 121)(43, 138)(44, 137)(45, 136)(46, 130)(47, 128)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 6, 96, 6, 96 ), ( 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96, 6, 96 ) }
Outer automorphisms :: reflexible
Dual of E27.968
Graph:: bipartite
	v = 27 e = 96 f = 17
	degree seq :: [ 4^24, 32^3 ]

E27.968 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 16, 48})
Quotient :: dipole
Aut^+ = C48 (small group id <48, 2>)
Aut   = D96 (small group id <96, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y1^-1, Y2^-1), (Y2, Y3), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^-4 * Y3^-1 * Y2^-4, Y2^-2 * Y3^-1 * Y2^-6, (Y2^-1 * Y3)^16 ]
Map:: non-degenerate
	R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 10, 58, 16, 64)(11, 59, 19, 67, 25, 73)(12, 60, 20, 68, 14, 62)(15, 63, 21, 69, 18, 66)(17, 65, 22, 70, 28, 76)(23, 71, 31, 79, 37, 85)(24, 72, 32, 80, 26, 74)(27, 75, 33, 81, 30, 78)(29, 77, 34, 82, 40, 88)(35, 83, 43, 91, 47, 95)(36, 84, 44, 92, 38, 86)(39, 87, 45, 93, 42, 90)(41, 89, 46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 138, 186, 126, 174, 114, 162, 103, 151, 110, 158, 122, 170, 134, 182, 144, 192, 136, 184, 124, 172, 112, 160, 101, 149, 109, 157, 121, 169, 133, 181, 143, 191, 141, 189, 129, 177, 117, 165, 105, 153, 116, 164, 128, 176, 140, 188, 142, 190, 130, 178, 118, 166, 106, 154, 98, 146, 104, 152, 115, 163, 127, 175, 139, 187, 135, 183, 123, 171, 111, 159, 100, 148, 108, 156, 120, 168, 132, 180, 137, 185, 125, 173, 113, 161, 102, 150)
	L = (1, 100)(2, 105)(3, 108)(4, 98)(5, 103)(6, 111)(7, 97)(8, 116)(9, 101)(10, 117)(11, 120)(12, 104)(13, 110)(14, 99)(15, 106)(16, 114)(17, 123)(18, 102)(19, 128)(20, 109)(21, 112)(22, 129)(23, 132)(24, 115)(25, 122)(26, 107)(27, 118)(28, 126)(29, 135)(30, 113)(31, 140)(32, 121)(33, 124)(34, 141)(35, 137)(36, 127)(37, 134)(38, 119)(39, 130)(40, 138)(41, 139)(42, 125)(43, 142)(44, 133)(45, 136)(46, 143)(47, 144)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 32, 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.967
Graph:: bipartite
	v = 17 e = 96 f = 27
	degree seq :: [ 6^16, 96 ]

E27.969 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 4, 4})
Quotient :: edge^2
Aut^+ = C13 : C4 (small group id <52, 1>)
Aut   = (C26 x C2) : C2 (small group id <104, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 53, 3, 55, 6, 58, 5, 57)(2, 54, 7, 59, 4, 56, 8, 60)(9, 61, 13, 65, 10, 62, 14, 66)(11, 63, 15, 67, 12, 64, 16, 68)(17, 69, 21, 73, 18, 70, 22, 74)(19, 71, 23, 75, 20, 72, 24, 76)(25, 77, 29, 81, 26, 78, 30, 82)(27, 79, 31, 83, 28, 80, 32, 84)(33, 85, 37, 89, 34, 86, 38, 90)(35, 87, 39, 91, 36, 88, 40, 92)(41, 93, 45, 97, 42, 94, 46, 98)(43, 95, 47, 99, 44, 96, 48, 100)(49, 101, 51, 103, 50, 102, 52, 104)(105, 106, 110, 108)(107, 113, 109, 114)(111, 115, 112, 116)(117, 121, 118, 122)(119, 123, 120, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 158, 162, 160)(159, 165, 161, 166)(163, 167, 164, 168)(169, 173, 170, 174)(171, 175, 172, 176)(177, 181, 178, 182)(179, 183, 180, 184)(185, 189, 186, 190)(187, 191, 188, 192)(193, 197, 194, 198)(195, 199, 196, 200)(201, 205, 202, 206)(203, 207, 204, 208)
	L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 16^4 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.971
Graph:: bipartite
	v = 39 e = 104 f = 13
	degree seq :: [ 4^26, 8^13 ]

E27.970 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 4, 4})
Quotient :: edge^2
Aut^+ = C13 : C4 (small group id <52, 1>)
Aut   = (C26 x C2) : C2 (small group id <104, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y3^4, Y1^-2 * Y3^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 53, 3, 55, 6, 58, 5, 57)(2, 54, 7, 59, 4, 56, 8, 60)(9, 61, 13, 65, 10, 62, 14, 66)(11, 63, 15, 67, 12, 64, 16, 68)(17, 69, 21, 73, 18, 70, 22, 74)(19, 71, 23, 75, 20, 72, 24, 76)(25, 77, 29, 81, 26, 78, 30, 82)(27, 79, 31, 83, 28, 80, 32, 84)(33, 85, 37, 89, 34, 86, 38, 90)(35, 87, 39, 91, 36, 88, 40, 92)(41, 93, 45, 97, 42, 94, 46, 98)(43, 95, 47, 99, 44, 96, 48, 100)(49, 101, 52, 104, 50, 102, 51, 103)(105, 106, 110, 108)(107, 113, 109, 114)(111, 115, 112, 116)(117, 121, 118, 122)(119, 123, 120, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 137, 134, 138)(135, 139, 136, 140)(141, 145, 142, 146)(143, 147, 144, 148)(149, 153, 150, 154)(151, 155, 152, 156)(157, 158, 162, 160)(159, 165, 161, 166)(163, 167, 164, 168)(169, 173, 170, 174)(171, 175, 172, 176)(177, 181, 178, 182)(179, 183, 180, 184)(185, 189, 186, 190)(187, 191, 188, 192)(193, 197, 194, 198)(195, 199, 196, 200)(201, 205, 202, 206)(203, 207, 204, 208)
	L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 16^4 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.972
Graph:: bipartite
	v = 39 e = 104 f = 13
	degree seq :: [ 4^26, 8^13 ]

E27.971 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 4, 4})
Quotient :: loop^2
Aut^+ = C13 : C4 (small group id <52, 1>)
Aut   = (C26 x C2) : C2 (small group id <104, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 53, 105, 157, 3, 55, 107, 159, 6, 58, 110, 162, 5, 57, 109, 161)(2, 54, 106, 158, 7, 59, 111, 163, 4, 56, 108, 160, 8, 60, 112, 164)(9, 61, 113, 165, 13, 65, 117, 169, 10, 62, 114, 166, 14, 66, 118, 170)(11, 63, 115, 167, 15, 67, 119, 171, 12, 64, 116, 168, 16, 68, 120, 172)(17, 69, 121, 173, 21, 73, 125, 177, 18, 70, 122, 174, 22, 74, 126, 178)(19, 71, 123, 175, 23, 75, 127, 179, 20, 72, 124, 176, 24, 76, 128, 180)(25, 77, 129, 181, 29, 81, 133, 185, 26, 78, 130, 182, 30, 82, 134, 186)(27, 79, 131, 183, 31, 83, 135, 187, 28, 80, 132, 184, 32, 84, 136, 188)(33, 85, 137, 189, 37, 89, 141, 193, 34, 86, 138, 190, 38, 90, 142, 194)(35, 87, 139, 191, 39, 91, 143, 195, 36, 88, 140, 192, 40, 92, 144, 196)(41, 93, 145, 197, 45, 97, 149, 201, 42, 94, 146, 198, 46, 98, 150, 202)(43, 95, 147, 199, 47, 99, 151, 203, 44, 96, 148, 200, 48, 100, 152, 204)(49, 101, 153, 205, 51, 103, 155, 207, 50, 102, 154, 206, 52, 104, 156, 208)
	L = (1, 54)(2, 58)(3, 61)(4, 53)(5, 62)(6, 56)(7, 63)(8, 64)(9, 57)(10, 55)(11, 60)(12, 59)(13, 69)(14, 70)(15, 71)(16, 72)(17, 66)(18, 65)(19, 68)(20, 67)(21, 77)(22, 78)(23, 79)(24, 80)(25, 74)(26, 73)(27, 76)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 82)(34, 81)(35, 84)(36, 83)(37, 93)(38, 94)(39, 95)(40, 96)(41, 90)(42, 89)(43, 92)(44, 91)(45, 101)(46, 102)(47, 103)(48, 104)(49, 98)(50, 97)(51, 100)(52, 99)(105, 158)(106, 162)(107, 165)(108, 157)(109, 166)(110, 160)(111, 167)(112, 168)(113, 161)(114, 159)(115, 164)(116, 163)(117, 173)(118, 174)(119, 175)(120, 176)(121, 170)(122, 169)(123, 172)(124, 171)(125, 181)(126, 182)(127, 183)(128, 184)(129, 178)(130, 177)(131, 180)(132, 179)(133, 189)(134, 190)(135, 191)(136, 192)(137, 186)(138, 185)(139, 188)(140, 187)(141, 197)(142, 198)(143, 199)(144, 200)(145, 194)(146, 193)(147, 196)(148, 195)(149, 205)(150, 206)(151, 207)(152, 208)(153, 202)(154, 201)(155, 204)(156, 203)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.969
Transitivity :: VT+
Graph::
	v = 13 e = 104 f = 39
	degree seq :: [ 16^13 ]

E27.972 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 4, 4})
Quotient :: loop^2
Aut^+ = C13 : C4 (small group id <52, 1>)
Aut   = (C26 x C2) : C2 (small group id <104, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y3^4, Y1^-2 * Y3^2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 53, 105, 157, 3, 55, 107, 159, 6, 58, 110, 162, 5, 57, 109, 161)(2, 54, 106, 158, 7, 59, 111, 163, 4, 56, 108, 160, 8, 60, 112, 164)(9, 61, 113, 165, 13, 65, 117, 169, 10, 62, 114, 166, 14, 66, 118, 170)(11, 63, 115, 167, 15, 67, 119, 171, 12, 64, 116, 168, 16, 68, 120, 172)(17, 69, 121, 173, 21, 73, 125, 177, 18, 70, 122, 174, 22, 74, 126, 178)(19, 71, 123, 175, 23, 75, 127, 179, 20, 72, 124, 176, 24, 76, 128, 180)(25, 77, 129, 181, 29, 81, 133, 185, 26, 78, 130, 182, 30, 82, 134, 186)(27, 79, 131, 183, 31, 83, 135, 187, 28, 80, 132, 184, 32, 84, 136, 188)(33, 85, 137, 189, 37, 89, 141, 193, 34, 86, 138, 190, 38, 90, 142, 194)(35, 87, 139, 191, 39, 91, 143, 195, 36, 88, 140, 192, 40, 92, 144, 196)(41, 93, 145, 197, 45, 97, 149, 201, 42, 94, 146, 198, 46, 98, 150, 202)(43, 95, 147, 199, 47, 99, 151, 203, 44, 96, 148, 200, 48, 100, 152, 204)(49, 101, 153, 205, 52, 104, 156, 208, 50, 102, 154, 206, 51, 103, 155, 207)
	L = (1, 54)(2, 58)(3, 61)(4, 53)(5, 62)(6, 56)(7, 63)(8, 64)(9, 57)(10, 55)(11, 60)(12, 59)(13, 69)(14, 70)(15, 71)(16, 72)(17, 66)(18, 65)(19, 68)(20, 67)(21, 77)(22, 78)(23, 79)(24, 80)(25, 74)(26, 73)(27, 76)(28, 75)(29, 85)(30, 86)(31, 87)(32, 88)(33, 82)(34, 81)(35, 84)(36, 83)(37, 93)(38, 94)(39, 95)(40, 96)(41, 90)(42, 89)(43, 92)(44, 91)(45, 101)(46, 102)(47, 103)(48, 104)(49, 98)(50, 97)(51, 100)(52, 99)(105, 158)(106, 162)(107, 165)(108, 157)(109, 166)(110, 160)(111, 167)(112, 168)(113, 161)(114, 159)(115, 164)(116, 163)(117, 173)(118, 174)(119, 175)(120, 176)(121, 170)(122, 169)(123, 172)(124, 171)(125, 181)(126, 182)(127, 183)(128, 184)(129, 178)(130, 177)(131, 180)(132, 179)(133, 189)(134, 190)(135, 191)(136, 192)(137, 186)(138, 185)(139, 188)(140, 187)(141, 197)(142, 198)(143, 199)(144, 200)(145, 194)(146, 193)(147, 196)(148, 195)(149, 205)(150, 206)(151, 207)(152, 208)(153, 202)(154, 201)(155, 204)(156, 203)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.970
Transitivity :: VT+
Graph::
	v = 13 e = 104 f = 39
	degree seq :: [ 16^13 ]

E27.973 :: Family: { 5P } :: Oriented family(ies): { E5b }
Signature :: (0; {4, 4, 4, 4})
Quotient :: dipole
Aut^+ = C13 : C4 (small group id <52, 3>)
Aut   = C2 x (C13 : C4) (small group id <104, 12>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2 * Y3^-1, Y2 * R^-1 * Y1 * R, (Y2 * Y1^-1)^2, Y2^4, Y1^4, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^4, Y2^-2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-2, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2, Y2^2 * Y1^-2 * Y2^2 * Y1 * Y2 * Y1^-2 ]
Map::
	R = (1, 53, 2, 54, 6, 58, 4, 56)(3, 55, 9, 61, 18, 70, 8, 60)(5, 57, 11, 63, 22, 74, 13, 65)(7, 59, 16, 68, 28, 80, 15, 67)(10, 62, 21, 73, 35, 87, 20, 72)(12, 64, 14, 66, 26, 78, 24, 76)(17, 69, 31, 83, 48, 100, 30, 82)(19, 71, 33, 85, 50, 102, 32, 84)(23, 75, 39, 91, 49, 101, 38, 90)(25, 77, 37, 89, 51, 103, 41, 93)(27, 79, 44, 96, 36, 88, 43, 95)(29, 81, 46, 98, 34, 86, 45, 97)(40, 92, 42, 94, 52, 104, 47, 99)(105, 157, 107, 159, 114, 166, 109, 161)(106, 158, 111, 163, 121, 173, 112, 164)(108, 160, 115, 167, 127, 179, 116, 168)(110, 162, 118, 170, 131, 183, 119, 171)(113, 165, 123, 175, 138, 190, 124, 176)(117, 169, 125, 177, 140, 192, 129, 181)(120, 172, 133, 185, 151, 203, 134, 186)(122, 174, 135, 187, 153, 205, 136, 188)(126, 178, 141, 193, 154, 206, 142, 194)(128, 180, 143, 195, 152, 204, 144, 196)(130, 182, 146, 198, 145, 197, 147, 199)(132, 184, 148, 200, 139, 191, 149, 201)(137, 189, 155, 207, 156, 208, 150, 202)
	L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.974 :: Family: { 5P } :: Oriented family(ies): { E5b }
Signature :: (0; {4, 4, 4, 4})
Quotient :: dipole
Aut^+ = C13 : C4 (small group id <52, 3>)
Aut   = C2 x (C13 : C4) (small group id <104, 12>)
|r| :: 4
Presentation :: [ Y3^2, R^2 * Y3, Y1^-1 * Y3 * Y2, Y1^4, Y2^4, Y2 * R^-1 * Y1 * R, Y1^4, Y1^-1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 53, 2, 54, 7, 59, 5, 57)(3, 55, 10, 62, 13, 65, 4, 56)(6, 58, 15, 67, 29, 81, 17, 69)(8, 60, 19, 71, 21, 73, 9, 61)(11, 63, 25, 77, 26, 78, 12, 64)(14, 66, 28, 80, 38, 90, 20, 72)(16, 68, 18, 70, 34, 86, 32, 84)(22, 74, 40, 92, 27, 79, 35, 87)(23, 75, 41, 93, 42, 94, 24, 76)(30, 82, 47, 99, 39, 91, 31, 83)(33, 85, 46, 98, 43, 95, 49, 101)(36, 88, 50, 102, 51, 103, 37, 89)(44, 96, 52, 104, 48, 100, 45, 97)(105, 157, 107, 159, 115, 167, 110, 162)(106, 158, 112, 164, 118, 170, 108, 160)(109, 161, 119, 171, 134, 186, 120, 172)(111, 163, 122, 174, 126, 178, 113, 165)(114, 166, 127, 179, 131, 183, 116, 168)(117, 169, 132, 184, 147, 199, 128, 180)(121, 173, 129, 181, 148, 200, 137, 189)(123, 175, 140, 192, 143, 195, 124, 176)(125, 177, 144, 196, 145, 197, 141, 193)(130, 182, 139, 191, 138, 190, 149, 201)(133, 185, 150, 202, 142, 194, 135, 187)(136, 188, 151, 203, 154, 206, 152, 204)(146, 198, 153, 205, 156, 208, 155, 207)
	L = (1, 108)(2, 113)(3, 116)(4, 105)(5, 110)(6, 109)(7, 120)(8, 124)(9, 106)(10, 128)(11, 121)(12, 107)(13, 118)(14, 117)(15, 135)(16, 111)(17, 115)(18, 139)(19, 141)(20, 112)(21, 126)(22, 125)(23, 144)(24, 114)(25, 149)(26, 131)(27, 130)(28, 150)(29, 137)(30, 136)(31, 119)(32, 134)(33, 133)(34, 152)(35, 122)(36, 151)(37, 123)(38, 143)(39, 142)(40, 127)(41, 155)(42, 147)(43, 146)(44, 153)(45, 129)(46, 132)(47, 140)(48, 138)(49, 148)(50, 156)(51, 145)(52, 154)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.975 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 54, 54})
Quotient :: dipole
Aut^+ = C54 (small group id <54, 2>)
Aut   = D108 (small group id <108, 4>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^27 * Y1, (Y3 * Y2^-1)^54 ]
Map::
	R = (1, 55, 2, 56)(3, 57, 5, 59)(4, 58, 6, 60)(7, 61, 9, 63)(8, 62, 10, 64)(11, 65, 13, 67)(12, 66, 14, 68)(15, 69, 17, 71)(16, 70, 18, 72)(19, 73, 21, 75)(20, 74, 22, 76)(23, 77, 25, 79)(24, 78, 26, 80)(27, 81, 29, 83)(28, 82, 30, 84)(31, 85, 33, 87)(32, 86, 34, 88)(35, 89, 37, 91)(36, 90, 38, 92)(39, 93, 41, 95)(40, 94, 42, 96)(43, 97, 45, 99)(44, 98, 46, 100)(47, 101, 49, 103)(48, 102, 50, 104)(51, 105, 53, 107)(52, 106, 54, 108)(109, 163, 111, 165, 115, 169, 119, 173, 123, 177, 127, 181, 131, 185, 135, 189, 139, 193, 143, 197, 147, 201, 151, 205, 155, 209, 159, 213, 162, 216, 158, 212, 154, 208, 150, 204, 146, 200, 142, 196, 138, 192, 134, 188, 130, 184, 126, 180, 122, 176, 118, 172, 114, 168, 110, 164, 113, 167, 117, 171, 121, 175, 125, 179, 129, 183, 133, 187, 137, 191, 141, 195, 145, 199, 149, 203, 153, 207, 157, 211, 161, 215, 160, 214, 156, 210, 152, 206, 148, 202, 144, 198, 140, 194, 136, 190, 132, 186, 128, 182, 124, 178, 120, 174, 116, 170, 112, 166)
	L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216)
	local type(s) :: { ( 4, 108, 4, 108 ), ( 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108, 4, 108 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 28 e = 108 f = 28
	degree seq :: [ 4^27, 108 ]

E27.976 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^27, (T2^-1 * T1^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(56, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 97, 98, 101, 102, 105, 106, 109, 110, 108, 107, 104, 103, 100, 99, 96, 95, 92, 91, 88, 87, 84, 83, 80, 79, 76, 75, 72, 71, 68, 67, 64, 63, 60, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.992
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.977 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^2, (F * T2)^2, (F * T1)^2, T1 * T2^-27 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 55, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108, 109, 110, 106, 107, 102, 103, 98, 99, 94, 95, 90, 91, 86, 87, 82, 83, 78, 79, 74, 75, 70, 71, 66, 67, 62, 63, 58, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.989
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.978 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^18, (T2^-1 * T1^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 51, 52, 46, 40, 34, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 36, 42, 48, 54, 55, 50, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 49, 53, 47, 41, 35, 29, 23, 17, 11, 5)(56, 57, 61, 58, 62, 67, 64, 68, 73, 70, 74, 79, 76, 80, 85, 82, 86, 91, 88, 92, 97, 94, 98, 103, 100, 104, 109, 106, 108, 110, 107, 102, 105, 101, 96, 99, 95, 90, 93, 89, 84, 87, 83, 78, 81, 77, 72, 75, 71, 66, 69, 65, 60, 63, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.993
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.979 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T1 * T2^-18 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 51, 50, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 49, 55, 54, 48, 42, 36, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 34, 40, 46, 52, 53, 47, 41, 35, 29, 23, 17, 11, 5)(56, 57, 61, 60, 63, 67, 66, 69, 73, 72, 75, 79, 78, 81, 85, 84, 87, 91, 90, 93, 97, 96, 99, 103, 102, 105, 109, 108, 106, 110, 107, 100, 104, 101, 94, 98, 95, 88, 92, 89, 82, 86, 83, 76, 80, 77, 70, 74, 71, 64, 68, 65, 58, 62, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.990
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.980 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^-2 * T2^-1 * T1^-2, T2^-13 * T1^-1 * T2^-1, T2^5 * T1^-1 * T2^7 * T1^-2 * T2, T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-3 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 52, 44, 36, 28, 20, 12, 4, 10, 18, 26, 34, 42, 50, 54, 46, 38, 30, 22, 14, 6, 11, 19, 27, 35, 43, 51, 55, 48, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 47, 53, 45, 37, 29, 21, 13, 5)(56, 57, 61, 67, 60, 63, 69, 75, 68, 71, 77, 83, 76, 79, 85, 91, 84, 87, 93, 99, 92, 95, 101, 107, 100, 103, 109, 104, 108, 110, 105, 96, 102, 106, 97, 88, 94, 98, 89, 80, 86, 90, 81, 72, 78, 82, 73, 64, 70, 74, 65, 58, 62, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.991
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.981 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^6, T2 * T1 * T2^8, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 31, 43, 36, 24, 12, 4, 10, 20, 32, 44, 51, 47, 35, 23, 11, 21, 33, 45, 52, 55, 53, 46, 34, 22, 14, 26, 38, 48, 54, 50, 40, 28, 16, 6, 15, 27, 39, 49, 42, 30, 18, 8, 2, 7, 17, 29, 41, 37, 25, 13, 5)(56, 57, 61, 69, 76, 65, 58, 62, 70, 81, 88, 75, 64, 72, 82, 93, 100, 87, 74, 84, 94, 103, 107, 99, 86, 96, 104, 109, 110, 106, 98, 92, 97, 105, 108, 102, 91, 80, 85, 95, 101, 90, 79, 68, 73, 83, 89, 78, 67, 60, 63, 71, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.995
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.982 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-3 * T2^-1 * T1^3, T1^-2 * T2 * T1^-5, T2^3 * T1^-1 * T2^5, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 32, 18, 8, 2, 7, 17, 31, 45, 44, 30, 16, 6, 15, 29, 43, 53, 52, 42, 28, 14, 27, 41, 51, 54, 47, 36, 22, 26, 40, 50, 55, 48, 37, 23, 11, 21, 35, 46, 49, 38, 24, 12, 4, 10, 20, 34, 39, 25, 13, 5)(56, 57, 61, 69, 81, 76, 65, 58, 62, 70, 82, 95, 90, 75, 64, 72, 84, 96, 105, 101, 89, 74, 86, 98, 106, 110, 104, 94, 88, 100, 108, 109, 103, 93, 80, 87, 99, 107, 102, 92, 79, 68, 73, 85, 97, 91, 78, 67, 60, 63, 71, 83, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.996
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.983 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^3 * T2^-1 * T1^-3, T1^-2 * T2^-2 * T1^2 * T2^2, T1^-1 * T2^-1 * T1^-6, T2^6 * T1 * T2^2, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 38, 24, 12, 4, 10, 20, 34, 46, 49, 37, 23, 11, 21, 35, 47, 54, 50, 40, 26, 22, 36, 48, 55, 52, 42, 28, 14, 27, 41, 51, 53, 44, 30, 16, 6, 15, 29, 43, 45, 32, 18, 8, 2, 7, 17, 31, 39, 25, 13, 5)(56, 57, 61, 69, 81, 78, 67, 60, 63, 71, 83, 95, 92, 79, 68, 73, 85, 97, 105, 104, 93, 80, 87, 99, 107, 109, 101, 88, 94, 100, 108, 110, 102, 89, 74, 86, 98, 106, 103, 90, 75, 64, 72, 84, 96, 91, 76, 65, 58, 62, 70, 82, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.994
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.984 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^2 * T1^2 * T2^-2 * T1^-2, T2^3 * T1^-1 * T2^2 * T1^-4, T1^4 * T2 * T1 * T2^3 * T1^2, T2^-30 * T1^-1 * T2^-2, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 42, 54, 39, 23, 11, 21, 35, 46, 28, 14, 27, 45, 52, 37, 50, 32, 18, 8, 2, 7, 17, 31, 49, 55, 40, 24, 12, 4, 10, 20, 34, 44, 26, 43, 53, 38, 22, 36, 48, 30, 16, 6, 15, 29, 47, 51, 41, 25, 13, 5)(56, 57, 61, 69, 81, 97, 110, 96, 105, 91, 76, 65, 58, 62, 70, 82, 98, 109, 95, 80, 87, 103, 90, 75, 64, 72, 84, 100, 108, 94, 79, 68, 73, 85, 101, 89, 74, 86, 102, 107, 93, 78, 67, 60, 63, 71, 83, 99, 88, 104, 106, 92, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.998
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.985 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^-4 * T1^-1, T1^-1 * T2 * T1^-12 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 22, 32, 39, 46, 49, 50, 53, 44, 35, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 38, 41, 48, 55, 52, 43, 34, 37, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 33, 40, 47, 54, 51, 42, 45, 36, 27, 14, 25, 13, 5)(56, 57, 61, 69, 81, 89, 97, 105, 103, 95, 87, 76, 65, 58, 62, 70, 80, 84, 92, 100, 108, 110, 102, 94, 86, 75, 64, 72, 79, 68, 73, 83, 91, 99, 107, 109, 101, 93, 85, 74, 78, 67, 60, 63, 71, 82, 90, 98, 106, 104, 96, 88, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.999
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.986 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^8 * T2 * T1^5, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 14, 27, 36, 45, 42, 51, 55, 48, 39, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 37, 34, 43, 52, 54, 47, 38, 41, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 35, 44, 53, 50, 46, 49, 40, 31, 22, 25, 13, 5)(56, 57, 61, 69, 81, 89, 97, 105, 102, 94, 86, 78, 67, 60, 63, 71, 74, 84, 92, 100, 108, 109, 103, 95, 87, 79, 68, 73, 75, 64, 72, 83, 91, 99, 107, 110, 104, 96, 88, 80, 76, 65, 58, 62, 70, 82, 90, 98, 106, 101, 93, 85, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.997
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.987 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1), T1 * T2^-1 * T1 * T2^-6, T2 * T1^-1 * T2 * T1^-1 * T2^5, T1^2 * T2^-3 * T1^-2 * T2^3, T2^-1 * T1^-1 * T2^-2 * T1^-6, T1^3 * T2^-1 * T1 * T2^-1 * T1^4 * T2^-2 * T1, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 30, 16, 6, 15, 29, 47, 54, 53, 44, 26, 43, 38, 22, 36, 49, 51, 40, 24, 12, 4, 10, 20, 34, 32, 18, 8, 2, 7, 17, 31, 48, 46, 28, 14, 27, 45, 37, 50, 55, 52, 42, 39, 23, 11, 21, 35, 41, 25, 13, 5)(56, 57, 61, 69, 81, 97, 95, 80, 87, 88, 103, 109, 105, 91, 76, 65, 58, 62, 70, 82, 98, 94, 79, 68, 73, 85, 101, 108, 110, 104, 90, 75, 64, 72, 84, 100, 93, 78, 67, 60, 63, 71, 83, 99, 107, 106, 96, 89, 74, 86, 102, 92, 77, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.1000
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.988 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {55, 55, 55})
Quotient :: edge
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T2 * T1 * T2 * T1 * T2, T1^-15 * T2 * T1^-1 * T2 * T1^-1, T1^-1 * T2^26 ]
Map:: non-degenerate
	R = (1, 3, 9, 11, 18, 23, 25, 30, 35, 37, 42, 47, 49, 54, 50, 52, 45, 38, 40, 33, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 36, 41, 43, 48, 53, 55, 51, 44, 46, 39, 32, 34, 27, 20, 22, 15, 6, 13, 5)(56, 57, 61, 69, 75, 81, 87, 93, 99, 105, 108, 102, 96, 90, 84, 78, 72, 64, 67, 60, 63, 70, 76, 82, 88, 94, 100, 106, 109, 103, 97, 91, 85, 79, 73, 65, 58, 62, 68, 71, 77, 83, 89, 95, 101, 107, 110, 104, 98, 92, 86, 80, 74, 66, 59)
	L = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.1001
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.989 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2^-1 * T1, (F * T2)^2, (F * T1)^2, T1^55, T2^55, (T2^-1 * T1^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 42, 97, 55, 110, 36, 91, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 43, 98, 41, 96, 50, 105, 54, 109, 35, 90, 20, 75, 9, 64, 17, 72, 29, 84, 45, 100, 40, 95, 25, 80, 32, 87, 48, 103, 53, 108, 34, 89, 19, 74, 31, 86, 47, 102, 39, 94, 24, 79, 13, 68, 18, 73, 30, 85, 46, 101, 52, 107, 33, 88, 49, 104, 38, 93, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 44, 99, 51, 106, 37, 92, 22, 77, 11, 66, 4, 59)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 83)(17, 84)(18, 85)(19, 86)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 87)(26, 97)(27, 98)(28, 99)(29, 100)(30, 101)(31, 102)(32, 103)(33, 104)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(41, 105)(42, 110)(43, 96)(44, 106)(45, 95)(46, 107)(47, 94)(48, 108)(49, 93)(50, 109)(51, 92)(52, 88)(53, 89)(54, 90)(55, 91)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.977
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.990 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^27, (T2^-1 * T1^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 7, 62, 11, 66, 15, 70, 19, 74, 23, 78, 27, 82, 31, 86, 35, 90, 39, 94, 43, 98, 47, 102, 51, 106, 55, 110, 52, 107, 48, 103, 44, 99, 40, 95, 36, 91, 32, 87, 28, 83, 24, 79, 20, 75, 16, 71, 12, 67, 8, 63, 4, 59, 2, 57, 6, 61, 10, 65, 14, 69, 18, 73, 22, 77, 26, 81, 30, 85, 34, 89, 38, 93, 42, 97, 46, 101, 50, 105, 54, 109, 53, 108, 49, 104, 45, 100, 41, 96, 37, 92, 33, 88, 29, 84, 25, 80, 21, 76, 17, 72, 13, 68, 9, 64, 5, 60)
	L = (1, 57)(2, 58)(3, 61)(4, 56)(5, 59)(6, 62)(7, 65)(8, 60)(9, 63)(10, 66)(11, 69)(12, 64)(13, 67)(14, 70)(15, 73)(16, 68)(17, 71)(18, 74)(19, 77)(20, 72)(21, 75)(22, 78)(23, 81)(24, 76)(25, 79)(26, 82)(27, 85)(28, 80)(29, 83)(30, 86)(31, 89)(32, 84)(33, 87)(34, 90)(35, 93)(36, 88)(37, 91)(38, 94)(39, 97)(40, 92)(41, 95)(42, 98)(43, 101)(44, 96)(45, 99)(46, 102)(47, 105)(48, 100)(49, 103)(50, 106)(51, 109)(52, 104)(53, 107)(54, 110)(55, 108)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.979
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.991 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^18, (T2^-1 * T1^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 15, 70, 21, 76, 27, 82, 33, 88, 39, 94, 45, 100, 51, 106, 52, 107, 46, 101, 40, 95, 34, 89, 28, 83, 22, 77, 16, 71, 10, 65, 4, 59, 6, 61, 12, 67, 18, 73, 24, 79, 30, 85, 36, 91, 42, 97, 48, 103, 54, 109, 55, 110, 50, 105, 44, 99, 38, 93, 32, 87, 26, 81, 20, 75, 14, 69, 8, 63, 2, 57, 7, 62, 13, 68, 19, 74, 25, 80, 31, 86, 37, 92, 43, 98, 49, 104, 53, 108, 47, 102, 41, 96, 35, 90, 29, 84, 23, 78, 17, 72, 11, 66, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 58)(7, 67)(8, 59)(9, 68)(10, 60)(11, 69)(12, 64)(13, 73)(14, 65)(15, 74)(16, 66)(17, 75)(18, 70)(19, 79)(20, 71)(21, 80)(22, 72)(23, 81)(24, 76)(25, 85)(26, 77)(27, 86)(28, 78)(29, 87)(30, 82)(31, 91)(32, 83)(33, 92)(34, 84)(35, 93)(36, 88)(37, 97)(38, 89)(39, 98)(40, 90)(41, 99)(42, 94)(43, 103)(44, 95)(45, 104)(46, 96)(47, 105)(48, 100)(49, 109)(50, 101)(51, 108)(52, 102)(53, 110)(54, 106)(55, 107)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.980
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.992 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T1 * T2^-18 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 15, 70, 21, 76, 27, 82, 33, 88, 39, 94, 45, 100, 51, 106, 50, 105, 44, 99, 38, 93, 32, 87, 26, 81, 20, 75, 14, 69, 8, 63, 2, 57, 7, 62, 13, 68, 19, 74, 25, 80, 31, 86, 37, 92, 43, 98, 49, 104, 55, 110, 54, 109, 48, 103, 42, 97, 36, 91, 30, 85, 24, 79, 18, 73, 12, 67, 6, 61, 4, 59, 10, 65, 16, 71, 22, 77, 28, 83, 34, 89, 40, 95, 46, 101, 52, 107, 53, 108, 47, 102, 41, 96, 35, 90, 29, 84, 23, 78, 17, 72, 11, 66, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 60)(7, 59)(8, 67)(9, 68)(10, 58)(11, 69)(12, 66)(13, 65)(14, 73)(15, 74)(16, 64)(17, 75)(18, 72)(19, 71)(20, 79)(21, 80)(22, 70)(23, 81)(24, 78)(25, 77)(26, 85)(27, 86)(28, 76)(29, 87)(30, 84)(31, 83)(32, 91)(33, 92)(34, 82)(35, 93)(36, 90)(37, 89)(38, 97)(39, 98)(40, 88)(41, 99)(42, 96)(43, 95)(44, 103)(45, 104)(46, 94)(47, 105)(48, 102)(49, 101)(50, 109)(51, 110)(52, 100)(53, 106)(54, 108)(55, 107)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.976
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.993 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^-2 * T2^-1 * T1^-2, T2^-13 * T1^-1 * T2^-1, T2^5 * T1^-1 * T2^7 * T1^-2 * T2, T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-3 * T1^-1 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 17, 72, 25, 80, 33, 88, 41, 96, 49, 104, 52, 107, 44, 99, 36, 91, 28, 83, 20, 75, 12, 67, 4, 59, 10, 65, 18, 73, 26, 81, 34, 89, 42, 97, 50, 105, 54, 109, 46, 101, 38, 93, 30, 85, 22, 77, 14, 69, 6, 61, 11, 66, 19, 74, 27, 82, 35, 90, 43, 98, 51, 106, 55, 110, 48, 103, 40, 95, 32, 87, 24, 79, 16, 71, 8, 63, 2, 57, 7, 62, 15, 70, 23, 78, 31, 86, 39, 94, 47, 102, 53, 108, 45, 100, 37, 92, 29, 84, 21, 76, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 67)(7, 66)(8, 69)(9, 70)(10, 58)(11, 59)(12, 60)(13, 71)(14, 75)(15, 74)(16, 77)(17, 78)(18, 64)(19, 65)(20, 68)(21, 79)(22, 83)(23, 82)(24, 85)(25, 86)(26, 72)(27, 73)(28, 76)(29, 87)(30, 91)(31, 90)(32, 93)(33, 94)(34, 80)(35, 81)(36, 84)(37, 95)(38, 99)(39, 98)(40, 101)(41, 102)(42, 88)(43, 89)(44, 92)(45, 103)(46, 107)(47, 106)(48, 109)(49, 108)(50, 96)(51, 97)(52, 100)(53, 110)(54, 104)(55, 105)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.978
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.994 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-1 * T1^6, T2 * T1 * T2^8, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 31, 86, 43, 98, 36, 91, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 32, 87, 44, 99, 51, 106, 47, 102, 35, 90, 23, 78, 11, 66, 21, 76, 33, 88, 45, 100, 52, 107, 55, 110, 53, 108, 46, 101, 34, 89, 22, 77, 14, 69, 26, 81, 38, 93, 48, 103, 54, 109, 50, 105, 40, 95, 28, 83, 16, 71, 6, 61, 15, 70, 27, 82, 39, 94, 49, 104, 42, 97, 30, 85, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 29, 84, 41, 96, 37, 92, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 76)(15, 81)(16, 77)(17, 82)(18, 83)(19, 84)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 85)(26, 88)(27, 93)(28, 89)(29, 94)(30, 95)(31, 96)(32, 74)(33, 75)(34, 78)(35, 79)(36, 80)(37, 97)(38, 100)(39, 103)(40, 101)(41, 104)(42, 105)(43, 92)(44, 86)(45, 87)(46, 90)(47, 91)(48, 107)(49, 109)(50, 108)(51, 98)(52, 99)(53, 102)(54, 110)(55, 106)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.983
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.995 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^3 * T2^-1 * T1^-3, T1^-2 * T2^-2 * T1^2 * T2^2, T1^-1 * T2^-1 * T1^-6, T2^6 * T1 * T2^2, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 33, 88, 38, 93, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 34, 89, 46, 101, 49, 104, 37, 92, 23, 78, 11, 66, 21, 76, 35, 90, 47, 102, 54, 109, 50, 105, 40, 95, 26, 81, 22, 77, 36, 91, 48, 103, 55, 110, 52, 107, 42, 97, 28, 83, 14, 69, 27, 82, 41, 96, 51, 106, 53, 108, 44, 99, 30, 85, 16, 71, 6, 61, 15, 70, 29, 84, 43, 98, 45, 100, 32, 87, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 31, 86, 39, 94, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 83)(17, 84)(18, 85)(19, 86)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 87)(26, 78)(27, 77)(28, 95)(29, 96)(30, 97)(31, 98)(32, 99)(33, 94)(34, 74)(35, 75)(36, 76)(37, 79)(38, 80)(39, 100)(40, 92)(41, 91)(42, 105)(43, 106)(44, 107)(45, 108)(46, 88)(47, 89)(48, 90)(49, 93)(50, 104)(51, 103)(52, 109)(53, 110)(54, 101)(55, 102)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.981
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.996 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-3 * T1 * T2^3, T1^2 * T2^2 * T1^-2 * T2^-2, T2^-1 * T1^-1 * T2^-6, T1^4 * T2 * T1^4, T1^2 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-4 * T1^2, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 33, 88, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 34, 89, 45, 100, 39, 94, 23, 78, 11, 66, 21, 76, 35, 90, 46, 101, 53, 108, 49, 104, 38, 93, 22, 77, 36, 91, 47, 102, 54, 109, 50, 105, 40, 95, 26, 81, 37, 92, 48, 103, 55, 110, 52, 107, 42, 97, 28, 83, 14, 69, 27, 82, 41, 96, 51, 106, 44, 99, 30, 85, 16, 71, 6, 61, 15, 70, 29, 84, 43, 98, 32, 87, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 31, 86, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 83)(17, 84)(18, 85)(19, 86)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 87)(26, 93)(27, 92)(28, 95)(29, 96)(30, 97)(31, 98)(32, 99)(33, 80)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 104)(41, 103)(42, 105)(43, 106)(44, 107)(45, 88)(46, 89)(47, 90)(48, 91)(49, 94)(50, 108)(51, 110)(52, 109)(53, 100)(54, 101)(55, 102)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.982
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.997 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^2 * T1^2 * T2^-2 * T1^-2, T2^3 * T1^-1 * T2^2 * T1^-4, T1^4 * T2 * T1 * T2^3 * T1^2, T2^-30 * T1^-1 * T2^-2, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 33, 88, 42, 97, 54, 109, 39, 94, 23, 78, 11, 66, 21, 76, 35, 90, 46, 101, 28, 83, 14, 69, 27, 82, 45, 100, 52, 107, 37, 92, 50, 105, 32, 87, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 31, 86, 49, 104, 55, 110, 40, 95, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 34, 89, 44, 99, 26, 81, 43, 98, 53, 108, 38, 93, 22, 77, 36, 91, 48, 103, 30, 85, 16, 71, 6, 61, 15, 70, 29, 84, 47, 102, 51, 106, 41, 96, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 83)(17, 84)(18, 85)(19, 86)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 87)(26, 97)(27, 98)(28, 99)(29, 100)(30, 101)(31, 102)(32, 103)(33, 104)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(41, 105)(42, 110)(43, 109)(44, 88)(45, 108)(46, 89)(47, 107)(48, 90)(49, 106)(50, 91)(51, 92)(52, 93)(53, 94)(54, 95)(55, 96)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.986
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.998 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^8 * T2 * T1^5, (T1^-1 * T2^-1)^55 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 14, 69, 27, 82, 36, 91, 45, 100, 42, 97, 51, 106, 55, 110, 48, 103, 39, 94, 30, 85, 33, 88, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 16, 71, 6, 61, 15, 70, 28, 83, 37, 92, 34, 89, 43, 98, 52, 107, 54, 109, 47, 102, 38, 93, 41, 96, 32, 87, 23, 78, 11, 66, 21, 76, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 29, 84, 26, 81, 35, 90, 44, 99, 53, 108, 50, 105, 46, 101, 49, 104, 40, 95, 31, 86, 22, 77, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 81)(15, 82)(16, 74)(17, 83)(18, 75)(19, 84)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 76)(26, 89)(27, 90)(28, 91)(29, 92)(30, 77)(31, 78)(32, 79)(33, 80)(34, 97)(35, 98)(36, 99)(37, 100)(38, 85)(39, 86)(40, 87)(41, 88)(42, 105)(43, 106)(44, 107)(45, 108)(46, 93)(47, 94)(48, 95)(49, 96)(50, 102)(51, 101)(52, 110)(53, 109)(54, 103)(55, 104)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.984
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.999 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-2 * T1^-1 * T2^-2, T1^-13 * T2^-1 * T1^-1, T2 * T1^-1 * T2 * T1^-5 * T2 * T1^-7, T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 12, 67, 4, 59, 10, 65, 18, 73, 21, 76, 11, 66, 19, 74, 26, 81, 29, 84, 20, 75, 27, 82, 34, 89, 37, 92, 28, 83, 35, 90, 42, 97, 45, 100, 36, 91, 43, 98, 50, 105, 53, 108, 44, 99, 51, 106, 54, 109, 46, 101, 52, 107, 55, 110, 48, 103, 38, 93, 47, 102, 49, 104, 40, 95, 30, 85, 39, 94, 41, 96, 32, 87, 22, 77, 31, 86, 33, 88, 24, 79, 14, 69, 23, 78, 25, 80, 16, 71, 6, 61, 15, 70, 17, 72, 8, 63, 2, 57, 7, 62, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 68)(10, 58)(11, 59)(12, 60)(13, 72)(14, 77)(15, 78)(16, 79)(17, 80)(18, 64)(19, 65)(20, 66)(21, 67)(22, 85)(23, 86)(24, 87)(25, 88)(26, 73)(27, 74)(28, 75)(29, 76)(30, 93)(31, 94)(32, 95)(33, 96)(34, 81)(35, 82)(36, 83)(37, 84)(38, 101)(39, 102)(40, 103)(41, 104)(42, 89)(43, 90)(44, 91)(45, 92)(46, 108)(47, 107)(48, 109)(49, 110)(50, 97)(51, 98)(52, 99)(53, 100)(54, 105)(55, 106)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.985
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.1000 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^3 * T2^-1 * T1 * T2^-2, T2^13 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 19, 74, 29, 84, 37, 92, 45, 100, 53, 108, 48, 103, 40, 95, 32, 87, 24, 79, 12, 67, 4, 59, 10, 65, 20, 75, 14, 69, 26, 81, 34, 89, 42, 97, 50, 105, 55, 110, 47, 102, 39, 94, 31, 86, 23, 78, 11, 66, 21, 76, 16, 71, 6, 61, 15, 70, 27, 82, 35, 90, 43, 98, 51, 106, 54, 109, 46, 101, 38, 93, 30, 85, 22, 77, 18, 73, 8, 63, 2, 57, 7, 62, 17, 72, 28, 83, 36, 91, 44, 99, 52, 107, 49, 104, 41, 96, 33, 88, 25, 80, 13, 68, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 69)(7, 70)(8, 71)(9, 72)(10, 58)(11, 59)(12, 60)(13, 73)(14, 74)(15, 81)(16, 75)(17, 82)(18, 76)(19, 83)(20, 64)(21, 65)(22, 66)(23, 67)(24, 68)(25, 77)(26, 84)(27, 89)(28, 90)(29, 91)(30, 78)(31, 79)(32, 80)(33, 85)(34, 92)(35, 97)(36, 98)(37, 99)(38, 86)(39, 87)(40, 88)(41, 93)(42, 100)(43, 105)(44, 106)(45, 107)(46, 94)(47, 95)(48, 96)(49, 101)(50, 108)(51, 110)(52, 109)(53, 104)(54, 102)(55, 103)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.987
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.1001 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {55, 55, 55})
Quotient :: loop
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-18 * T2 ]
Map:: non-degenerate
	R = (1, 56, 3, 58, 9, 64, 4, 59, 10, 65, 15, 70, 11, 66, 16, 71, 21, 76, 17, 72, 22, 77, 27, 82, 23, 78, 28, 83, 33, 88, 29, 84, 34, 89, 39, 94, 35, 90, 40, 95, 45, 100, 41, 96, 46, 101, 51, 106, 47, 102, 52, 107, 55, 110, 53, 108, 48, 103, 54, 109, 50, 105, 42, 97, 49, 104, 44, 99, 36, 91, 43, 98, 38, 93, 30, 85, 37, 92, 32, 87, 24, 79, 31, 86, 26, 81, 18, 73, 25, 80, 20, 75, 12, 67, 19, 74, 14, 69, 6, 61, 13, 68, 8, 63, 2, 57, 7, 62, 5, 60)
	L = (1, 57)(2, 61)(3, 62)(4, 56)(5, 63)(6, 67)(7, 68)(8, 69)(9, 60)(10, 58)(11, 59)(12, 73)(13, 74)(14, 75)(15, 64)(16, 65)(17, 66)(18, 79)(19, 80)(20, 81)(21, 70)(22, 71)(23, 72)(24, 85)(25, 86)(26, 87)(27, 76)(28, 77)(29, 78)(30, 91)(31, 92)(32, 93)(33, 82)(34, 83)(35, 84)(36, 97)(37, 98)(38, 99)(39, 88)(40, 89)(41, 90)(42, 103)(43, 104)(44, 105)(45, 94)(46, 95)(47, 96)(48, 107)(49, 109)(50, 108)(51, 100)(52, 101)(53, 102)(54, 110)(55, 106)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.988
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.1002 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^27 * Y2, Y2 * Y1^-27 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 10, 65, 14, 69, 18, 73, 22, 77, 26, 81, 30, 85, 34, 89, 38, 93, 42, 97, 46, 101, 50, 105, 54, 109, 52, 107, 48, 103, 44, 99, 40, 95, 36, 91, 32, 87, 28, 83, 24, 79, 20, 75, 16, 71, 12, 67, 8, 63, 3, 58, 5, 60, 7, 62, 11, 66, 15, 70, 19, 74, 23, 78, 27, 82, 31, 86, 35, 90, 39, 94, 43, 98, 47, 102, 51, 106, 55, 110, 53, 108, 49, 104, 45, 100, 41, 96, 37, 92, 33, 88, 29, 84, 25, 80, 21, 76, 17, 72, 13, 68, 9, 64, 4, 59)(111, 166, 113, 168, 114, 169, 118, 173, 119, 174, 122, 177, 123, 178, 126, 181, 127, 182, 130, 185, 131, 186, 134, 189, 135, 190, 138, 193, 139, 194, 142, 197, 143, 198, 146, 201, 147, 202, 150, 205, 151, 206, 154, 209, 155, 210, 158, 213, 159, 214, 162, 217, 163, 218, 164, 219, 165, 220, 160, 215, 161, 216, 156, 211, 157, 212, 152, 207, 153, 208, 148, 203, 149, 204, 144, 199, 145, 200, 140, 195, 141, 196, 136, 191, 137, 192, 132, 187, 133, 188, 128, 183, 129, 184, 124, 179, 125, 180, 120, 175, 121, 176, 116, 171, 117, 172, 112, 167, 115, 170)
	L = (1, 114)(2, 111)(3, 118)(4, 119)(5, 113)(6, 112)(7, 115)(8, 122)(9, 123)(10, 116)(11, 117)(12, 126)(13, 127)(14, 120)(15, 121)(16, 130)(17, 131)(18, 124)(19, 125)(20, 134)(21, 135)(22, 128)(23, 129)(24, 138)(25, 139)(26, 132)(27, 133)(28, 142)(29, 143)(30, 136)(31, 137)(32, 146)(33, 147)(34, 140)(35, 141)(36, 150)(37, 151)(38, 144)(39, 145)(40, 154)(41, 155)(42, 148)(43, 149)(44, 158)(45, 159)(46, 152)(47, 153)(48, 162)(49, 163)(50, 156)(51, 157)(52, 164)(53, 165)(54, 160)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1015
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1003 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y2^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y1^26 * Y3^-1, (Y3 * Y2^-1)^55 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 10, 65, 14, 69, 18, 73, 22, 77, 26, 81, 30, 85, 34, 89, 38, 93, 42, 97, 46, 101, 50, 105, 54, 109, 53, 108, 49, 104, 45, 100, 41, 96, 37, 92, 33, 88, 29, 84, 25, 80, 21, 76, 17, 72, 13, 68, 9, 64, 5, 60, 3, 58, 7, 62, 11, 66, 15, 70, 19, 74, 23, 78, 27, 82, 31, 86, 35, 90, 39, 94, 43, 98, 47, 102, 51, 106, 55, 110, 52, 107, 48, 103, 44, 99, 40, 95, 36, 91, 32, 87, 28, 83, 24, 79, 20, 75, 16, 71, 12, 67, 8, 63, 4, 59)(111, 166, 113, 168, 112, 167, 117, 172, 116, 171, 121, 176, 120, 175, 125, 180, 124, 179, 129, 184, 128, 183, 133, 188, 132, 187, 137, 192, 136, 191, 141, 196, 140, 195, 145, 200, 144, 199, 149, 204, 148, 203, 153, 208, 152, 207, 157, 212, 156, 211, 161, 216, 160, 215, 165, 220, 164, 219, 162, 217, 163, 218, 158, 213, 159, 214, 154, 209, 155, 210, 150, 205, 151, 206, 146, 201, 147, 202, 142, 197, 143, 198, 138, 193, 139, 194, 134, 189, 135, 190, 130, 185, 131, 186, 126, 181, 127, 182, 122, 177, 123, 178, 118, 173, 119, 174, 114, 169, 115, 170)
	L = (1, 114)(2, 111)(3, 115)(4, 118)(5, 119)(6, 112)(7, 113)(8, 122)(9, 123)(10, 116)(11, 117)(12, 126)(13, 127)(14, 120)(15, 121)(16, 130)(17, 131)(18, 124)(19, 125)(20, 134)(21, 135)(22, 128)(23, 129)(24, 138)(25, 139)(26, 132)(27, 133)(28, 142)(29, 143)(30, 136)(31, 137)(32, 146)(33, 147)(34, 140)(35, 141)(36, 150)(37, 151)(38, 144)(39, 145)(40, 154)(41, 155)(42, 148)(43, 149)(44, 158)(45, 159)(46, 152)(47, 153)(48, 162)(49, 163)(50, 156)(51, 157)(52, 165)(53, 164)(54, 160)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1025
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1004 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3^16 * Y1^-2 * Y2, Y3 * Y2 * Y3^7 * Y2 * Y1^-6 * Y3^-8 * Y2 * Y3^8 * Y2 * Y3^3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 12, 67, 18, 73, 24, 79, 30, 85, 36, 91, 42, 97, 48, 103, 52, 107, 46, 101, 40, 95, 34, 89, 28, 83, 22, 77, 16, 71, 10, 65, 3, 58, 7, 62, 13, 68, 19, 74, 25, 80, 31, 86, 37, 92, 43, 98, 49, 104, 54, 109, 55, 110, 51, 106, 45, 100, 39, 94, 33, 88, 27, 82, 21, 76, 15, 70, 9, 64, 5, 60, 8, 63, 14, 69, 20, 75, 26, 81, 32, 87, 38, 93, 44, 99, 50, 105, 53, 108, 47, 102, 41, 96, 35, 90, 29, 84, 23, 78, 17, 72, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 114, 169, 120, 175, 125, 180, 121, 176, 126, 181, 131, 186, 127, 182, 132, 187, 137, 192, 133, 188, 138, 193, 143, 198, 139, 194, 144, 199, 149, 204, 145, 200, 150, 205, 155, 210, 151, 206, 156, 211, 161, 216, 157, 212, 162, 217, 165, 220, 163, 218, 158, 213, 164, 219, 160, 215, 152, 207, 159, 214, 154, 209, 146, 201, 153, 208, 148, 203, 140, 195, 147, 202, 142, 197, 134, 189, 141, 196, 136, 191, 128, 183, 135, 190, 130, 185, 122, 177, 129, 184, 124, 179, 116, 171, 123, 178, 118, 173, 112, 167, 117, 172, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 119)(6, 112)(7, 113)(8, 115)(9, 125)(10, 126)(11, 127)(12, 116)(13, 117)(14, 118)(15, 131)(16, 132)(17, 133)(18, 122)(19, 123)(20, 124)(21, 137)(22, 138)(23, 139)(24, 128)(25, 129)(26, 130)(27, 143)(28, 144)(29, 145)(30, 134)(31, 135)(32, 136)(33, 149)(34, 150)(35, 151)(36, 140)(37, 141)(38, 142)(39, 155)(40, 156)(41, 157)(42, 146)(43, 147)(44, 148)(45, 161)(46, 162)(47, 163)(48, 152)(49, 153)(50, 154)(51, 165)(52, 158)(53, 160)(54, 159)(55, 164)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1027
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1005 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1^18, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 12, 67, 18, 73, 24, 79, 30, 85, 36, 91, 42, 97, 48, 103, 53, 108, 47, 102, 41, 96, 35, 90, 29, 84, 23, 78, 17, 72, 11, 66, 5, 60, 8, 63, 14, 69, 20, 75, 26, 81, 32, 87, 38, 93, 44, 99, 50, 105, 54, 109, 55, 110, 51, 106, 45, 100, 39, 94, 33, 88, 27, 82, 21, 76, 15, 70, 9, 64, 3, 58, 7, 62, 13, 68, 19, 74, 25, 80, 31, 86, 37, 92, 43, 98, 49, 104, 52, 107, 46, 101, 40, 95, 34, 89, 28, 83, 22, 77, 16, 71, 10, 65, 4, 59)(111, 166, 113, 168, 118, 173, 112, 167, 117, 172, 124, 179, 116, 171, 123, 178, 130, 185, 122, 177, 129, 184, 136, 191, 128, 183, 135, 190, 142, 197, 134, 189, 141, 196, 148, 203, 140, 195, 147, 202, 154, 209, 146, 201, 153, 208, 160, 215, 152, 207, 159, 214, 164, 219, 158, 213, 162, 217, 165, 220, 163, 218, 156, 211, 161, 216, 157, 212, 150, 205, 155, 210, 151, 206, 144, 199, 149, 204, 145, 200, 138, 193, 143, 198, 139, 194, 132, 187, 137, 192, 133, 188, 126, 181, 131, 186, 127, 182, 120, 175, 125, 180, 121, 176, 114, 169, 119, 174, 115, 170)
	L = (1, 114)(2, 111)(3, 119)(4, 120)(5, 121)(6, 112)(7, 113)(8, 115)(9, 125)(10, 126)(11, 127)(12, 116)(13, 117)(14, 118)(15, 131)(16, 132)(17, 133)(18, 122)(19, 123)(20, 124)(21, 137)(22, 138)(23, 139)(24, 128)(25, 129)(26, 130)(27, 143)(28, 144)(29, 145)(30, 134)(31, 135)(32, 136)(33, 149)(34, 150)(35, 151)(36, 140)(37, 141)(38, 142)(39, 155)(40, 156)(41, 157)(42, 146)(43, 147)(44, 148)(45, 161)(46, 162)(47, 163)(48, 152)(49, 153)(50, 154)(51, 165)(52, 159)(53, 158)(54, 160)(55, 164)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1022
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1006 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y2, Y1^-1), (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-1 * Y2^2, Y3^4 * Y1^-8 * Y3 * Y2^-1 * Y3, Y2 * Y3 * Y2 * Y3^5 * Y2 * Y1^-7, Y3^5 * Y2^-1 * Y1^-6 * Y3 * Y2^-1 * Y3^6 * Y2^-1 * Y3^5 * Y2 * Y1^-5, Y2 * Y3^3 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^4 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 22, 77, 30, 85, 38, 93, 46, 101, 53, 108, 45, 100, 37, 92, 29, 84, 21, 76, 12, 67, 5, 60, 8, 63, 16, 71, 24, 79, 32, 87, 40, 95, 48, 103, 54, 109, 50, 105, 42, 97, 34, 89, 26, 81, 18, 73, 9, 64, 13, 68, 17, 72, 25, 80, 33, 88, 41, 96, 49, 104, 55, 110, 51, 106, 43, 98, 35, 90, 27, 82, 19, 74, 10, 65, 3, 58, 7, 62, 15, 70, 23, 78, 31, 86, 39, 94, 47, 102, 52, 107, 44, 99, 36, 91, 28, 83, 20, 75, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 122, 177, 114, 169, 120, 175, 128, 183, 131, 186, 121, 176, 129, 184, 136, 191, 139, 194, 130, 185, 137, 192, 144, 199, 147, 202, 138, 193, 145, 200, 152, 207, 155, 210, 146, 201, 153, 208, 160, 215, 163, 218, 154, 209, 161, 216, 164, 219, 156, 211, 162, 217, 165, 220, 158, 213, 148, 203, 157, 212, 159, 214, 150, 205, 140, 195, 149, 204, 151, 206, 142, 197, 132, 187, 141, 196, 143, 198, 134, 189, 124, 179, 133, 188, 135, 190, 126, 181, 116, 171, 125, 180, 127, 182, 118, 173, 112, 167, 117, 172, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 128)(10, 129)(11, 130)(12, 131)(13, 119)(14, 116)(15, 117)(16, 118)(17, 123)(18, 136)(19, 137)(20, 138)(21, 139)(22, 124)(23, 125)(24, 126)(25, 127)(26, 144)(27, 145)(28, 146)(29, 147)(30, 132)(31, 133)(32, 134)(33, 135)(34, 152)(35, 153)(36, 154)(37, 155)(38, 140)(39, 141)(40, 142)(41, 143)(42, 160)(43, 161)(44, 162)(45, 163)(46, 148)(47, 149)(48, 150)(49, 151)(50, 164)(51, 165)(52, 157)(53, 156)(54, 158)(55, 159)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1024
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1007 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2 * Y3 * Y2^5, Y1^-4 * Y3^-4, Y3^-1 * Y2 * Y3^-8, Y3^-5 * Y1^50, (Y2^-1 * Y3)^55 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 38, 93, 35, 90, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 40, 95, 48, 103, 46, 101, 36, 91, 24, 79, 13, 68, 18, 73, 30, 85, 42, 97, 50, 105, 54, 109, 53, 108, 47, 102, 37, 92, 25, 80, 19, 74, 31, 86, 43, 98, 51, 106, 55, 110, 52, 107, 44, 99, 32, 87, 20, 75, 9, 64, 17, 72, 29, 84, 41, 96, 49, 104, 45, 100, 33, 88, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 39, 94, 34, 89, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 153, 208, 152, 207, 138, 193, 124, 179, 137, 192, 151, 206, 161, 216, 160, 215, 150, 205, 136, 191, 149, 204, 159, 214, 165, 220, 164, 219, 158, 213, 148, 203, 144, 199, 155, 210, 162, 217, 163, 218, 156, 211, 145, 200, 132, 187, 143, 198, 154, 209, 157, 212, 146, 201, 133, 188, 121, 176, 131, 186, 142, 197, 147, 202, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 135)(20, 142)(21, 143)(22, 144)(23, 145)(24, 146)(25, 147)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 154)(33, 155)(34, 149)(35, 148)(36, 156)(37, 157)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 141)(44, 162)(45, 159)(46, 158)(47, 163)(48, 150)(49, 151)(50, 152)(51, 153)(52, 165)(53, 164)(54, 160)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1019
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1008 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y1^-1, Y2^-1), (R * Y2)^2, Y3 * Y2^-3 * Y3^-1 * Y2^3, Y2^-1 * Y3 * Y2^-6, Y3^7 * Y2^-1 * Y3, Y1^3 * Y2 * Y1^2 * Y3^-3, Y1^3 * Y2^-1 * Y1 * Y2^-2 * Y3^-3 * Y2^-3, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-3 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^2 * Y3^-3 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 38, 93, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 40, 95, 49, 104, 39, 94, 24, 79, 13, 68, 18, 73, 30, 85, 42, 97, 50, 105, 53, 108, 45, 100, 33, 88, 25, 80, 32, 87, 44, 99, 52, 107, 54, 109, 46, 101, 34, 89, 19, 74, 31, 86, 43, 98, 51, 106, 55, 110, 47, 102, 35, 90, 20, 75, 9, 64, 17, 72, 29, 84, 41, 96, 48, 103, 36, 91, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 37, 92, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 143, 198, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 144, 199, 155, 210, 149, 204, 133, 188, 121, 176, 131, 186, 145, 200, 156, 211, 163, 218, 159, 214, 148, 203, 132, 187, 146, 201, 157, 212, 164, 219, 160, 215, 150, 205, 136, 191, 147, 202, 158, 213, 165, 220, 162, 217, 152, 207, 138, 193, 124, 179, 137, 192, 151, 206, 161, 216, 154, 209, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 153, 208, 142, 197, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 144)(20, 145)(21, 146)(22, 147)(23, 148)(24, 149)(25, 143)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 135)(33, 155)(34, 156)(35, 157)(36, 158)(37, 137)(38, 136)(39, 159)(40, 138)(41, 139)(42, 140)(43, 141)(44, 142)(45, 163)(46, 164)(47, 165)(48, 151)(49, 150)(50, 152)(51, 153)(52, 154)(53, 160)(54, 162)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1020
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1009 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y3 * Y1, (Y2, Y3), (Y3, Y2), Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y2)^2, (R * Y1)^2, Y2^6 * Y3 * Y2, Y3^-3 * Y2^-1 * Y1 * Y3^-4, Y1^5 * Y2^-1 * Y3^-3, Y3 * Y2 * Y1^-2 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3^-2 * Y1^2, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 35, 90, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 40, 95, 46, 101, 34, 89, 20, 75, 9, 64, 17, 72, 29, 84, 41, 96, 50, 105, 53, 108, 45, 100, 33, 88, 19, 74, 31, 86, 43, 98, 51, 106, 55, 110, 49, 104, 39, 94, 25, 80, 32, 87, 44, 99, 52, 107, 54, 109, 48, 103, 38, 93, 24, 79, 13, 68, 18, 73, 30, 85, 42, 97, 47, 102, 37, 92, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 36, 91, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 142, 197, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 154, 209, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 153, 208, 162, 217, 152, 207, 138, 193, 124, 179, 137, 192, 151, 206, 161, 216, 164, 219, 157, 212, 146, 201, 136, 191, 150, 205, 160, 215, 165, 220, 158, 213, 147, 202, 132, 187, 145, 200, 156, 211, 163, 218, 159, 214, 148, 203, 133, 188, 121, 176, 131, 186, 144, 199, 155, 210, 149, 204, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 143, 198, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 143)(20, 144)(21, 145)(22, 146)(23, 147)(24, 148)(25, 149)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 135)(33, 155)(34, 156)(35, 136)(36, 138)(37, 157)(38, 158)(39, 159)(40, 137)(41, 139)(42, 140)(43, 141)(44, 142)(45, 163)(46, 150)(47, 152)(48, 164)(49, 165)(50, 151)(51, 153)(52, 154)(53, 160)(54, 162)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1018
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1010 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3, Y2^-5 * Y1^5, Y1^3 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-3, Y2 * Y1 * Y3^-1 * Y2^2 * Y1 * Y2^4 * Y3^-1, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2 * Y3^3 * Y2^-2, Y2^55, Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 42, 97, 53, 108, 39, 94, 24, 79, 13, 68, 18, 73, 30, 85, 46, 101, 34, 89, 19, 74, 31, 86, 47, 102, 55, 110, 41, 96, 50, 105, 36, 91, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 43, 98, 52, 107, 38, 93, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 44, 99, 33, 88, 49, 104, 54, 109, 40, 95, 25, 80, 32, 87, 48, 103, 35, 90, 20, 75, 9, 64, 17, 72, 29, 84, 45, 100, 51, 106, 37, 92, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 143, 198, 152, 207, 162, 217, 147, 202, 160, 215, 142, 197, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 159, 214, 163, 218, 148, 203, 132, 187, 146, 201, 158, 213, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 157, 212, 164, 219, 149, 204, 133, 188, 121, 176, 131, 186, 145, 200, 156, 211, 138, 193, 124, 179, 137, 192, 155, 210, 165, 220, 150, 205, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 144, 199, 154, 209, 136, 191, 153, 208, 161, 216, 151, 206, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 144)(20, 145)(21, 146)(22, 147)(23, 148)(24, 149)(25, 150)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 135)(33, 154)(34, 156)(35, 158)(36, 160)(37, 161)(38, 162)(39, 163)(40, 164)(41, 165)(42, 136)(43, 137)(44, 138)(45, 139)(46, 140)(47, 141)(48, 142)(49, 143)(50, 151)(51, 155)(52, 153)(53, 152)(54, 159)(55, 157)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1023
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1011 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y3^-1 * Y1^-1, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3^-2 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y2^4 * Y1 * Y2^9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 19, 74, 28, 83, 35, 90, 42, 97, 45, 100, 52, 107, 54, 109, 47, 102, 40, 95, 33, 88, 30, 85, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 20, 75, 9, 64, 17, 72, 27, 82, 34, 89, 37, 92, 44, 99, 51, 106, 55, 110, 48, 103, 41, 96, 38, 93, 31, 86, 24, 79, 13, 68, 18, 73, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 26, 81, 29, 84, 36, 91, 43, 98, 50, 105, 53, 108, 49, 104, 46, 101, 39, 94, 32, 87, 25, 80, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 139, 194, 147, 202, 155, 210, 163, 218, 158, 213, 150, 205, 142, 197, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 124, 179, 136, 191, 144, 199, 152, 207, 160, 215, 165, 220, 157, 212, 149, 204, 141, 196, 133, 188, 121, 176, 131, 186, 126, 181, 116, 171, 125, 180, 137, 192, 145, 200, 153, 208, 161, 216, 164, 219, 156, 211, 148, 203, 140, 195, 132, 187, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 138, 193, 146, 201, 154, 209, 162, 217, 159, 214, 151, 206, 143, 198, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 124)(20, 126)(21, 128)(22, 135)(23, 140)(24, 141)(25, 142)(26, 125)(27, 127)(28, 129)(29, 136)(30, 143)(31, 148)(32, 149)(33, 150)(34, 137)(35, 138)(36, 139)(37, 144)(38, 151)(39, 156)(40, 157)(41, 158)(42, 145)(43, 146)(44, 147)(45, 152)(46, 159)(47, 164)(48, 165)(49, 163)(50, 153)(51, 154)(52, 155)(53, 160)(54, 162)(55, 161)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1026
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1012 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-2, Y2^11 * Y1^-1 * Y2^2, Y3^-2 * Y1 * Y2^-5 * Y3^-2 * Y2^-5, Y2^-1 * Y3^2 * Y2^-12 * Y1^3 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 25, 80, 28, 83, 35, 90, 42, 97, 49, 104, 52, 107, 55, 110, 47, 102, 38, 93, 29, 84, 32, 87, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 24, 79, 13, 68, 18, 73, 27, 82, 34, 89, 41, 96, 44, 99, 51, 106, 54, 109, 46, 101, 37, 92, 40, 95, 31, 86, 20, 75, 9, 64, 17, 72, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 26, 81, 33, 88, 36, 91, 43, 98, 50, 105, 53, 108, 45, 100, 48, 103, 39, 94, 30, 85, 19, 74, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 139, 194, 147, 202, 155, 210, 162, 217, 154, 209, 146, 201, 138, 193, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 132, 187, 142, 197, 150, 205, 158, 213, 165, 220, 161, 216, 153, 208, 145, 200, 137, 192, 126, 181, 116, 171, 125, 180, 133, 188, 121, 176, 131, 186, 141, 196, 149, 204, 157, 212, 164, 219, 160, 215, 152, 207, 144, 199, 136, 191, 124, 179, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 140, 195, 148, 203, 156, 211, 163, 218, 159, 214, 151, 206, 143, 198, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 140)(20, 141)(21, 142)(22, 129)(23, 127)(24, 125)(25, 124)(26, 126)(27, 128)(28, 135)(29, 148)(30, 149)(31, 150)(32, 139)(33, 136)(34, 137)(35, 138)(36, 143)(37, 156)(38, 157)(39, 158)(40, 147)(41, 144)(42, 145)(43, 146)(44, 151)(45, 163)(46, 164)(47, 165)(48, 155)(49, 152)(50, 153)(51, 154)(52, 159)(53, 160)(54, 161)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1017
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1013 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y1^-1, Y2), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y2^-2 * Y3 * Y2^2 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1^2 * Y3^-4, Y1^5 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y3 * Y2^2 * Y3^2 * Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^2 * Y2, Y2^-5 * Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1, Y1^-3 * Y2^-1 * Y3^-1 * Y2^-2 * Y3^-2 * Y2^-2 * Y3^-2 * Y2^-2 * Y3^-2 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 14, 69, 26, 81, 35, 90, 20, 75, 9, 64, 17, 72, 29, 84, 43, 98, 52, 107, 55, 110, 49, 104, 33, 88, 46, 101, 40, 95, 25, 80, 32, 87, 45, 100, 51, 106, 38, 93, 23, 78, 12, 67, 5, 60, 8, 63, 16, 71, 28, 83, 36, 91, 21, 76, 10, 65, 3, 58, 7, 62, 15, 70, 27, 82, 42, 97, 50, 105, 34, 89, 19, 74, 31, 86, 44, 99, 41, 96, 47, 102, 53, 108, 54, 109, 48, 103, 39, 94, 24, 79, 13, 68, 18, 73, 30, 85, 37, 92, 22, 77, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 129, 184, 143, 198, 158, 213, 148, 203, 132, 187, 146, 201, 136, 191, 152, 207, 162, 217, 157, 212, 142, 197, 128, 183, 118, 173, 112, 167, 117, 172, 127, 182, 141, 196, 156, 211, 149, 204, 133, 188, 121, 176, 131, 186, 145, 200, 160, 215, 165, 220, 163, 218, 155, 210, 140, 195, 126, 181, 116, 171, 125, 180, 139, 194, 154, 209, 150, 205, 134, 189, 122, 177, 114, 169, 120, 175, 130, 185, 144, 199, 159, 214, 164, 219, 161, 216, 147, 202, 138, 193, 124, 179, 137, 192, 153, 208, 151, 206, 135, 190, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 116)(15, 117)(16, 118)(17, 119)(18, 123)(19, 144)(20, 145)(21, 146)(22, 147)(23, 148)(24, 149)(25, 150)(26, 124)(27, 125)(28, 126)(29, 127)(30, 128)(31, 129)(32, 135)(33, 159)(34, 160)(35, 136)(36, 138)(37, 140)(38, 161)(39, 158)(40, 156)(41, 154)(42, 137)(43, 139)(44, 141)(45, 142)(46, 143)(47, 151)(48, 164)(49, 165)(50, 152)(51, 155)(52, 153)(53, 157)(54, 163)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1021
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1014 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y3, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2^-3 * Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^4 * Y1, Y2^-1 * Y1 * Y2^-16 * Y1, Y3^-54 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 56, 2, 57, 6, 61, 13, 68, 15, 70, 20, 75, 25, 80, 27, 82, 32, 87, 37, 92, 39, 94, 44, 99, 49, 104, 51, 106, 52, 107, 54, 109, 47, 102, 40, 95, 42, 97, 35, 90, 28, 83, 30, 85, 23, 78, 16, 71, 18, 73, 10, 65, 3, 58, 7, 62, 12, 67, 5, 60, 8, 63, 14, 69, 19, 74, 21, 76, 26, 81, 31, 86, 33, 88, 38, 93, 43, 98, 45, 100, 50, 105, 55, 110, 53, 108, 46, 101, 48, 103, 41, 96, 34, 89, 36, 91, 29, 84, 22, 77, 24, 79, 17, 72, 9, 64, 11, 66, 4, 59)(111, 166, 113, 168, 119, 174, 126, 181, 132, 187, 138, 193, 144, 199, 150, 205, 156, 211, 162, 217, 160, 215, 154, 209, 148, 203, 142, 197, 136, 191, 130, 185, 124, 179, 116, 171, 122, 177, 114, 169, 120, 175, 127, 182, 133, 188, 139, 194, 145, 200, 151, 206, 157, 212, 163, 218, 161, 216, 155, 210, 149, 204, 143, 198, 137, 192, 131, 186, 125, 180, 118, 173, 112, 167, 117, 172, 121, 176, 128, 183, 134, 189, 140, 195, 146, 201, 152, 207, 158, 213, 164, 219, 165, 220, 159, 214, 153, 208, 147, 202, 141, 196, 135, 190, 129, 184, 123, 178, 115, 170)
	L = (1, 114)(2, 111)(3, 120)(4, 121)(5, 122)(6, 112)(7, 113)(8, 115)(9, 127)(10, 128)(11, 119)(12, 117)(13, 116)(14, 118)(15, 123)(16, 133)(17, 134)(18, 126)(19, 124)(20, 125)(21, 129)(22, 139)(23, 140)(24, 132)(25, 130)(26, 131)(27, 135)(28, 145)(29, 146)(30, 138)(31, 136)(32, 137)(33, 141)(34, 151)(35, 152)(36, 144)(37, 142)(38, 143)(39, 147)(40, 157)(41, 158)(42, 150)(43, 148)(44, 149)(45, 153)(46, 163)(47, 164)(48, 156)(49, 154)(50, 155)(51, 159)(52, 161)(53, 165)(54, 162)(55, 160)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.1016
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.1015 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^55, (Y3 * Y2^-1)^55, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 114, 169, 116, 171, 118, 173, 120, 175, 122, 177, 124, 179, 135, 190, 146, 201, 158, 213, 165, 220, 164, 219, 163, 218, 162, 217, 160, 215, 161, 216, 159, 214, 147, 202, 157, 212, 156, 211, 155, 210, 154, 209, 153, 208, 151, 206, 149, 204, 150, 205, 152, 207, 148, 203, 145, 200, 144, 199, 143, 198, 142, 197, 141, 196, 139, 194, 137, 192, 138, 193, 140, 195, 136, 191, 134, 189, 133, 188, 132, 187, 131, 186, 130, 185, 128, 183, 126, 181, 127, 182, 129, 184, 125, 180, 123, 178, 121, 176, 119, 174, 117, 172, 115, 170, 113, 168)
	L = (1, 113)(2, 111)(3, 115)(4, 112)(5, 117)(6, 114)(7, 119)(8, 116)(9, 121)(10, 118)(11, 123)(12, 120)(13, 125)(14, 122)(15, 129)(16, 128)(17, 126)(18, 130)(19, 127)(20, 131)(21, 132)(22, 133)(23, 134)(24, 136)(25, 124)(26, 140)(27, 139)(28, 137)(29, 141)(30, 138)(31, 142)(32, 143)(33, 144)(34, 145)(35, 148)(36, 135)(37, 159)(38, 152)(39, 151)(40, 149)(41, 153)(42, 150)(43, 154)(44, 155)(45, 156)(46, 157)(47, 147)(48, 146)(49, 161)(50, 162)(51, 160)(52, 163)(53, 164)(54, 165)(55, 158)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1002
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1016 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-27, (Y3^-1 * Y1^-1)^55, (Y3 * Y2^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 115, 170, 116, 171, 119, 174, 120, 175, 123, 178, 124, 179, 127, 182, 128, 183, 131, 186, 132, 187, 135, 190, 136, 191, 139, 194, 140, 195, 143, 198, 144, 199, 147, 202, 148, 203, 151, 206, 152, 207, 155, 210, 156, 211, 159, 214, 160, 215, 163, 218, 164, 219, 165, 220, 161, 216, 162, 217, 157, 212, 158, 213, 153, 208, 154, 209, 149, 204, 150, 205, 145, 200, 146, 201, 141, 196, 142, 197, 137, 192, 138, 193, 133, 188, 134, 189, 129, 184, 130, 185, 125, 180, 126, 181, 121, 176, 122, 177, 117, 172, 118, 173, 113, 168, 114, 169)
	L = (1, 113)(2, 114)(3, 117)(4, 118)(5, 111)(6, 112)(7, 121)(8, 122)(9, 115)(10, 116)(11, 125)(12, 126)(13, 119)(14, 120)(15, 129)(16, 130)(17, 123)(18, 124)(19, 133)(20, 134)(21, 127)(22, 128)(23, 137)(24, 138)(25, 131)(26, 132)(27, 141)(28, 142)(29, 135)(30, 136)(31, 145)(32, 146)(33, 139)(34, 140)(35, 149)(36, 150)(37, 143)(38, 144)(39, 153)(40, 154)(41, 147)(42, 148)(43, 157)(44, 158)(45, 151)(46, 152)(47, 161)(48, 162)(49, 155)(50, 156)(51, 164)(52, 165)(53, 159)(54, 160)(55, 163)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1014
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1017 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3^-1 * Y2^-3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^-1 * Y2 * Y3^-17, (Y2^-1 * Y3)^55, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 115, 170, 118, 173, 122, 177, 121, 176, 124, 179, 128, 183, 127, 182, 130, 185, 134, 189, 133, 188, 136, 191, 140, 195, 139, 194, 142, 197, 146, 201, 145, 200, 148, 203, 152, 207, 151, 206, 154, 209, 158, 213, 157, 212, 160, 215, 164, 219, 163, 218, 161, 216, 165, 220, 162, 217, 155, 210, 159, 214, 156, 211, 149, 204, 153, 208, 150, 205, 143, 198, 147, 202, 144, 199, 137, 192, 141, 196, 138, 193, 131, 186, 135, 190, 132, 187, 125, 180, 129, 184, 126, 181, 119, 174, 123, 178, 120, 175, 113, 168, 117, 172, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 114)(7, 123)(8, 112)(9, 125)(10, 126)(11, 115)(12, 116)(13, 129)(14, 118)(15, 131)(16, 132)(17, 121)(18, 122)(19, 135)(20, 124)(21, 137)(22, 138)(23, 127)(24, 128)(25, 141)(26, 130)(27, 143)(28, 144)(29, 133)(30, 134)(31, 147)(32, 136)(33, 149)(34, 150)(35, 139)(36, 140)(37, 153)(38, 142)(39, 155)(40, 156)(41, 145)(42, 146)(43, 159)(44, 148)(45, 161)(46, 162)(47, 151)(48, 152)(49, 165)(50, 154)(51, 160)(52, 163)(53, 157)(54, 158)(55, 164)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1012
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1018 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^3 * Y3 * Y2^3, Y3^-9 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 136, 191, 145, 200, 134, 189, 123, 178, 128, 183, 138, 193, 148, 203, 156, 211, 146, 201, 135, 190, 140, 195, 150, 205, 158, 213, 163, 218, 157, 212, 147, 202, 152, 207, 160, 215, 164, 219, 165, 220, 161, 216, 153, 208, 141, 196, 151, 206, 159, 214, 162, 217, 154, 209, 142, 197, 129, 184, 139, 194, 149, 204, 155, 210, 143, 198, 130, 185, 119, 174, 127, 182, 137, 192, 144, 199, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 132)(15, 137)(16, 116)(17, 139)(18, 118)(19, 141)(20, 142)(21, 143)(22, 144)(23, 121)(24, 122)(25, 123)(26, 124)(27, 149)(28, 126)(29, 151)(30, 128)(31, 152)(32, 153)(33, 154)(34, 155)(35, 133)(36, 134)(37, 135)(38, 136)(39, 159)(40, 138)(41, 160)(42, 140)(43, 147)(44, 161)(45, 162)(46, 145)(47, 146)(48, 148)(49, 164)(50, 150)(51, 157)(52, 165)(53, 156)(54, 158)(55, 163)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1009
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1019 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3 * Y2^3 * Y3^-1 * Y2^-3, Y2^-2 * Y3^-2 * Y2^2 * Y3^2, Y2^-1 * Y3^-1 * Y2^-6, Y3 * Y2 * Y3^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 138, 193, 150, 205, 147, 202, 134, 189, 123, 178, 128, 183, 140, 195, 152, 207, 160, 215, 159, 214, 148, 203, 135, 190, 142, 197, 154, 209, 162, 217, 164, 219, 156, 211, 143, 198, 149, 204, 155, 210, 163, 218, 165, 220, 157, 212, 144, 199, 129, 184, 141, 196, 153, 208, 161, 216, 158, 213, 145, 200, 130, 185, 119, 174, 127, 182, 139, 194, 151, 206, 146, 201, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 132)(27, 151)(28, 124)(29, 153)(30, 126)(31, 149)(32, 128)(33, 148)(34, 156)(35, 157)(36, 158)(37, 133)(38, 134)(39, 135)(40, 136)(41, 161)(42, 138)(43, 155)(44, 140)(45, 142)(46, 159)(47, 164)(48, 165)(49, 147)(50, 150)(51, 163)(52, 152)(53, 154)(54, 160)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1007
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1020 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^2 * Y3^2 * Y2^-2 * Y3^-2, Y2^-1 * Y3^-3 * Y2 * Y3^3, Y3^-1 * Y2^-1 * Y3^-6, Y2^4 * Y3 * Y2^4, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-4 * Y2^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 148, 203, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 138, 193, 150, 205, 159, 214, 149, 204, 134, 189, 123, 178, 128, 183, 140, 195, 152, 207, 160, 215, 163, 218, 155, 210, 143, 198, 135, 190, 142, 197, 154, 209, 162, 217, 164, 219, 156, 211, 144, 199, 129, 184, 141, 196, 153, 208, 161, 216, 165, 220, 157, 212, 145, 200, 130, 185, 119, 174, 127, 182, 139, 194, 151, 206, 158, 213, 146, 201, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 147, 202, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 147)(27, 151)(28, 124)(29, 153)(30, 126)(31, 135)(32, 128)(33, 134)(34, 155)(35, 156)(36, 157)(37, 158)(38, 132)(39, 133)(40, 136)(41, 161)(42, 138)(43, 142)(44, 140)(45, 149)(46, 163)(47, 164)(48, 165)(49, 148)(50, 150)(51, 154)(52, 152)(53, 159)(54, 160)(55, 162)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1008
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1021 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-2 * Y2^-2 * Y3^2 * Y2, Y2^2 * Y3^-2 * Y2^-2 * Y3^2, Y3^-4 * Y2^-1 * Y3^-1 * Y2^-4, Y2^4 * Y3^-2 * Y2^3 * Y3^-2, Y3^30 * Y2^-1 * Y3^2, (Y2^-1 * Y3)^55, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 152, 207, 162, 217, 143, 198, 159, 214, 148, 203, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 138, 193, 154, 209, 163, 218, 144, 199, 129, 184, 141, 196, 157, 212, 149, 204, 134, 189, 123, 178, 128, 183, 140, 195, 156, 211, 164, 219, 145, 200, 130, 185, 119, 174, 127, 182, 139, 194, 155, 210, 150, 205, 135, 190, 142, 197, 158, 213, 165, 220, 146, 201, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 153, 208, 151, 206, 160, 215, 161, 216, 147, 202, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 153)(27, 155)(28, 124)(29, 157)(30, 126)(31, 159)(32, 128)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 132)(39, 133)(40, 134)(41, 135)(42, 151)(43, 150)(44, 136)(45, 149)(46, 138)(47, 148)(48, 140)(49, 147)(50, 142)(51, 158)(52, 160)(53, 152)(54, 154)(55, 156)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1013
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1022 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2 * Y3^-1 * Y2 * Y3^-3 * Y2, Y3 * Y2^5 * Y3^-1 * Y2^-5, Y2^-13 * Y3^-1, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 144, 199, 152, 207, 160, 215, 157, 212, 149, 204, 141, 196, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 129, 184, 139, 194, 147, 202, 155, 210, 163, 218, 164, 219, 158, 213, 150, 205, 142, 197, 134, 189, 123, 178, 128, 183, 130, 185, 119, 174, 127, 182, 138, 193, 146, 201, 154, 209, 162, 217, 165, 220, 159, 214, 151, 206, 143, 198, 135, 190, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 145, 200, 153, 208, 161, 216, 156, 211, 148, 203, 140, 195, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 138)(16, 116)(17, 139)(18, 118)(19, 124)(20, 126)(21, 128)(22, 135)(23, 121)(24, 122)(25, 123)(26, 145)(27, 146)(28, 147)(29, 136)(30, 143)(31, 132)(32, 133)(33, 134)(34, 153)(35, 154)(36, 155)(37, 144)(38, 151)(39, 140)(40, 141)(41, 142)(42, 161)(43, 162)(44, 163)(45, 152)(46, 159)(47, 148)(48, 149)(49, 150)(50, 156)(51, 165)(52, 164)(53, 160)(54, 157)(55, 158)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1005
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1023 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^2 * Y2 * Y3^4 * Y2 * Y3, Y2^-3 * Y3 * Y2^-1 * Y3^2 * Y2^-3, Y3^23 * Y2^-1 * Y3, Y2^2 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3 * Y2^3 * Y3^2 * Y2^-2 * Y3^2, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 152, 207, 144, 199, 129, 184, 141, 196, 151, 206, 158, 213, 164, 219, 160, 215, 148, 203, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 138, 193, 154, 209, 145, 200, 130, 185, 119, 174, 127, 182, 139, 194, 155, 210, 163, 218, 165, 220, 161, 216, 149, 204, 134, 189, 123, 178, 128, 183, 140, 195, 156, 211, 146, 201, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 153, 208, 162, 217, 159, 214, 143, 198, 150, 205, 135, 190, 142, 197, 157, 212, 147, 202, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 153)(27, 155)(28, 124)(29, 151)(30, 126)(31, 150)(32, 128)(33, 149)(34, 159)(35, 152)(36, 154)(37, 156)(38, 132)(39, 133)(40, 134)(41, 135)(42, 162)(43, 163)(44, 136)(45, 158)(46, 138)(47, 140)(48, 142)(49, 161)(50, 147)(51, 148)(52, 165)(53, 164)(54, 157)(55, 160)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1010
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1024 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2^-3 * Y3 * Y2^-1 * Y3^2, Y3^13 * Y2, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 129, 184, 138, 193, 145, 200, 152, 207, 155, 210, 162, 217, 164, 219, 157, 212, 150, 205, 143, 198, 140, 195, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 130, 185, 119, 174, 127, 182, 137, 192, 144, 199, 147, 202, 154, 209, 161, 216, 165, 220, 158, 213, 151, 206, 148, 203, 141, 196, 134, 189, 123, 178, 128, 183, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 136, 191, 139, 194, 146, 201, 153, 208, 160, 215, 163, 218, 159, 214, 156, 211, 149, 204, 142, 197, 135, 190, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 136)(15, 137)(16, 116)(17, 138)(18, 118)(19, 139)(20, 124)(21, 126)(22, 128)(23, 121)(24, 122)(25, 123)(26, 144)(27, 145)(28, 146)(29, 147)(30, 132)(31, 133)(32, 134)(33, 135)(34, 152)(35, 153)(36, 154)(37, 155)(38, 140)(39, 141)(40, 142)(41, 143)(42, 160)(43, 161)(44, 162)(45, 163)(46, 148)(47, 149)(48, 150)(49, 151)(50, 165)(51, 164)(52, 159)(53, 158)(54, 156)(55, 157)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1006
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1025 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3^-3 * Y2, (Y3, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^8 * Y3 * Y2^10, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 122, 177, 128, 183, 134, 189, 140, 195, 146, 201, 152, 207, 158, 213, 163, 218, 157, 212, 151, 206, 145, 200, 139, 194, 133, 188, 127, 182, 121, 176, 115, 170, 118, 173, 124, 179, 130, 185, 136, 191, 142, 197, 148, 203, 154, 209, 160, 215, 164, 219, 165, 220, 161, 216, 155, 210, 149, 204, 143, 198, 137, 192, 131, 186, 125, 180, 119, 174, 113, 168, 117, 172, 123, 178, 129, 184, 135, 190, 141, 196, 147, 202, 153, 208, 159, 214, 162, 217, 156, 211, 150, 205, 144, 199, 138, 193, 132, 187, 126, 181, 120, 175, 114, 169)
	L = (1, 113)(2, 117)(3, 118)(4, 119)(5, 111)(6, 123)(7, 124)(8, 112)(9, 115)(10, 125)(11, 114)(12, 129)(13, 130)(14, 116)(15, 121)(16, 131)(17, 120)(18, 135)(19, 136)(20, 122)(21, 127)(22, 137)(23, 126)(24, 141)(25, 142)(26, 128)(27, 133)(28, 143)(29, 132)(30, 147)(31, 148)(32, 134)(33, 139)(34, 149)(35, 138)(36, 153)(37, 154)(38, 140)(39, 145)(40, 155)(41, 144)(42, 159)(43, 160)(44, 146)(45, 151)(46, 161)(47, 150)(48, 162)(49, 164)(50, 152)(51, 157)(52, 165)(53, 156)(54, 158)(55, 163)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1003
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1026 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y3^-4 * Y2^-1 * Y3^-1 * Y2^-4, Y2^2 * Y3^-1 * Y2 * Y3^-2 * Y2 * Y3^-4, Y2^8 * Y3^-1 * Y2 * Y3^-1, (Y2^-1 * Y3)^55, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 124, 179, 136, 191, 152, 207, 164, 219, 145, 200, 130, 185, 119, 174, 127, 182, 139, 194, 155, 210, 150, 205, 135, 190, 142, 197, 158, 213, 162, 217, 143, 198, 159, 214, 148, 203, 133, 188, 122, 177, 115, 170, 118, 173, 126, 181, 138, 193, 154, 209, 165, 220, 146, 201, 131, 186, 120, 175, 113, 168, 117, 172, 125, 180, 137, 192, 153, 208, 151, 206, 160, 215, 163, 218, 144, 199, 129, 184, 141, 196, 157, 212, 149, 204, 134, 189, 123, 178, 128, 183, 140, 195, 156, 211, 161, 216, 147, 202, 132, 187, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 125)(7, 127)(8, 112)(9, 129)(10, 130)(11, 131)(12, 114)(13, 115)(14, 137)(15, 139)(16, 116)(17, 141)(18, 118)(19, 143)(20, 144)(21, 145)(22, 146)(23, 121)(24, 122)(25, 123)(26, 153)(27, 155)(28, 124)(29, 157)(30, 126)(31, 159)(32, 128)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 132)(39, 133)(40, 134)(41, 135)(42, 151)(43, 150)(44, 136)(45, 149)(46, 138)(47, 148)(48, 140)(49, 147)(50, 142)(51, 154)(52, 156)(53, 158)(54, 160)(55, 152)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1011
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1027 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {55, 55, 55})
Quotient :: dipole
Aut^+ = C55 (small group id <55, 2>)
Aut   = D110 (small group id <110, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^15 * Y2 * Y3 * Y2 * Y3, (Y3^-1 * Y1^-1)^55 ]
Map::
	R = (1, 56)(2, 57)(3, 58)(4, 59)(5, 60)(6, 61)(7, 62)(8, 63)(9, 64)(10, 65)(11, 66)(12, 67)(13, 68)(14, 69)(15, 70)(16, 71)(17, 72)(18, 73)(19, 74)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 80)(26, 81)(27, 82)(28, 83)(29, 84)(30, 85)(31, 86)(32, 87)(33, 88)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 96)(42, 97)(43, 98)(44, 99)(45, 100)(46, 101)(47, 102)(48, 103)(49, 104)(50, 105)(51, 106)(52, 107)(53, 108)(54, 109)(55, 110)(111, 166, 112, 167, 116, 171, 119, 174, 125, 180, 130, 185, 132, 187, 137, 192, 142, 197, 144, 199, 149, 204, 154, 209, 156, 211, 161, 216, 165, 220, 163, 218, 158, 213, 153, 208, 151, 206, 146, 201, 141, 196, 139, 194, 134, 189, 129, 184, 127, 182, 122, 177, 115, 170, 118, 173, 120, 175, 113, 168, 117, 172, 124, 179, 126, 181, 131, 186, 136, 191, 138, 193, 143, 198, 148, 203, 150, 205, 155, 210, 160, 215, 162, 217, 164, 219, 159, 214, 157, 212, 152, 207, 147, 202, 145, 200, 140, 195, 135, 190, 133, 188, 128, 183, 123, 178, 121, 176, 114, 169)
	L = (1, 113)(2, 117)(3, 119)(4, 120)(5, 111)(6, 124)(7, 125)(8, 112)(9, 126)(10, 116)(11, 118)(12, 114)(13, 115)(14, 130)(15, 131)(16, 132)(17, 121)(18, 122)(19, 123)(20, 136)(21, 137)(22, 138)(23, 127)(24, 128)(25, 129)(26, 142)(27, 143)(28, 144)(29, 133)(30, 134)(31, 135)(32, 148)(33, 149)(34, 150)(35, 139)(36, 140)(37, 141)(38, 154)(39, 155)(40, 156)(41, 145)(42, 146)(43, 147)(44, 160)(45, 161)(46, 162)(47, 151)(48, 152)(49, 153)(50, 165)(51, 164)(52, 163)(53, 157)(54, 158)(55, 159)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.1004
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.1028 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 4, 14})
Quotient :: edge^2
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, Y1^4, Y2^-1 * Y1^-2 * Y2^-1, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1^-1 * Y3^-1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y1^-1)^2, (Y3 * Y1 * Y2^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1 * Y3^5 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 4, 60, 19, 75, 38, 94, 45, 101, 28, 84, 9, 65, 26, 82, 13, 69, 34, 90, 50, 106, 40, 96, 22, 78, 7, 63)(2, 58, 10, 66, 30, 86, 47, 103, 37, 93, 18, 74, 6, 62, 21, 77, 25, 81, 43, 99, 55, 111, 48, 104, 32, 88, 12, 68)(3, 59, 14, 70, 27, 83, 44, 100, 56, 112, 49, 105, 33, 89, 17, 73, 5, 61, 20, 76, 39, 95, 52, 108, 36, 92, 16, 72)(8, 64, 23, 79, 41, 97, 53, 109, 46, 102, 29, 85, 11, 67, 31, 87, 15, 71, 35, 91, 51, 107, 54, 110, 42, 98, 24, 80)(113, 114, 120, 117)(115, 125, 118, 127)(116, 129, 135, 124)(119, 132, 136, 122)(121, 137, 123, 139)(126, 143, 133, 138)(128, 147, 130, 146)(131, 144, 153, 145)(134, 142, 154, 151)(140, 156, 141, 155)(148, 162, 149, 163)(150, 161, 165, 160)(152, 164, 166, 159)(157, 167, 158, 168)(169, 171, 176, 174)(170, 177, 173, 179)(172, 186, 191, 184)(175, 189, 192, 182)(178, 197, 188, 196)(180, 199, 185, 194)(181, 201, 183, 200)(187, 204, 209, 205)(190, 195, 210, 193)(198, 213, 207, 214)(202, 216, 203, 217)(206, 215, 221, 220)(208, 211, 222, 212)(218, 224, 219, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1031
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1029 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 4, 4, 14})
Quotient :: edge^2
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (R * Y3)^2, Y2^4, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, (Y2^-1 * Y1^-1)^7 ]
Map:: non-degenerate
	R = (1, 57, 4, 60)(2, 58, 9, 65)(3, 59, 12, 68)(5, 61, 14, 70)(6, 62, 15, 71)(7, 63, 16, 72)(8, 64, 18, 74)(10, 66, 20, 76)(11, 67, 22, 78)(13, 69, 24, 80)(17, 73, 26, 82)(19, 75, 28, 84)(21, 77, 30, 86)(23, 79, 32, 88)(25, 81, 34, 90)(27, 83, 36, 92)(29, 85, 38, 94)(31, 87, 40, 96)(33, 89, 42, 98)(35, 91, 44, 100)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(43, 99, 52, 108)(45, 101, 53, 109)(47, 103, 54, 110)(49, 105, 55, 111)(51, 107, 56, 112)(113, 114, 119, 117)(115, 123, 118, 125)(116, 126, 128, 121)(120, 129, 122, 131)(124, 136, 127, 134)(130, 140, 132, 138)(133, 141, 135, 143)(137, 145, 139, 147)(142, 152, 144, 150)(146, 156, 148, 154)(149, 157, 151, 159)(153, 161, 155, 163)(158, 166, 160, 165)(162, 168, 164, 167)(169, 171, 175, 174)(170, 176, 173, 178)(172, 183, 184, 180)(177, 188, 182, 186)(179, 189, 181, 191)(185, 193, 187, 195)(190, 200, 192, 198)(194, 204, 196, 202)(197, 205, 199, 207)(201, 209, 203, 211)(206, 216, 208, 214)(210, 220, 212, 218)(213, 219, 215, 217)(221, 223, 222, 224)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1030
Graph:: simple bipartite
	v = 56 e = 112 f = 4
	degree seq :: [ 4^56 ]

E27.1030 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 4, 14})
Quotient :: loop^2
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, Y1^4, Y2^-1 * Y1^-2 * Y2^-1, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1^-1 * Y3^-1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y1^-1)^2, (Y3 * Y1 * Y2^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1 * Y3^5 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172, 19, 75, 131, 187, 38, 94, 150, 206, 45, 101, 157, 213, 28, 84, 140, 196, 9, 65, 121, 177, 26, 82, 138, 194, 13, 69, 125, 181, 34, 90, 146, 202, 50, 106, 162, 218, 40, 96, 152, 208, 22, 78, 134, 190, 7, 63, 119, 175)(2, 58, 114, 170, 10, 66, 122, 178, 30, 86, 142, 198, 47, 103, 159, 215, 37, 93, 149, 205, 18, 74, 130, 186, 6, 62, 118, 174, 21, 77, 133, 189, 25, 81, 137, 193, 43, 99, 155, 211, 55, 111, 167, 223, 48, 104, 160, 216, 32, 88, 144, 200, 12, 68, 124, 180)(3, 59, 115, 171, 14, 70, 126, 182, 27, 83, 139, 195, 44, 100, 156, 212, 56, 112, 168, 224, 49, 105, 161, 217, 33, 89, 145, 201, 17, 73, 129, 185, 5, 61, 117, 173, 20, 76, 132, 188, 39, 95, 151, 207, 52, 108, 164, 220, 36, 92, 148, 204, 16, 72, 128, 184)(8, 64, 120, 176, 23, 79, 135, 191, 41, 97, 153, 209, 53, 109, 165, 221, 46, 102, 158, 214, 29, 85, 141, 197, 11, 67, 123, 179, 31, 87, 143, 199, 15, 71, 127, 183, 35, 91, 147, 203, 51, 107, 163, 219, 54, 110, 166, 222, 42, 98, 154, 210, 24, 80, 136, 192)
	L = (1, 58)(2, 64)(3, 69)(4, 73)(5, 57)(6, 71)(7, 76)(8, 61)(9, 81)(10, 63)(11, 83)(12, 60)(13, 62)(14, 87)(15, 59)(16, 91)(17, 79)(18, 90)(19, 88)(20, 80)(21, 82)(22, 86)(23, 68)(24, 66)(25, 67)(26, 70)(27, 65)(28, 100)(29, 99)(30, 98)(31, 77)(32, 97)(33, 75)(34, 72)(35, 74)(36, 106)(37, 107)(38, 105)(39, 78)(40, 108)(41, 89)(42, 95)(43, 84)(44, 85)(45, 111)(46, 112)(47, 96)(48, 94)(49, 109)(50, 93)(51, 92)(52, 110)(53, 104)(54, 103)(55, 102)(56, 101)(113, 171)(114, 177)(115, 176)(116, 186)(117, 179)(118, 169)(119, 189)(120, 174)(121, 173)(122, 197)(123, 170)(124, 199)(125, 201)(126, 175)(127, 200)(128, 172)(129, 194)(130, 191)(131, 204)(132, 196)(133, 192)(134, 195)(135, 184)(136, 182)(137, 190)(138, 180)(139, 210)(140, 178)(141, 188)(142, 213)(143, 185)(144, 181)(145, 183)(146, 216)(147, 217)(148, 209)(149, 187)(150, 215)(151, 214)(152, 211)(153, 205)(154, 193)(155, 222)(156, 208)(157, 207)(158, 198)(159, 221)(160, 203)(161, 202)(162, 224)(163, 223)(164, 206)(165, 220)(166, 212)(167, 218)(168, 219)
	local type(s) :: { ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1029
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 112 f = 56
	degree seq :: [ 56^4 ]

E27.1031 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 4, 4, 14})
Quotient :: loop^2
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (R * Y3)^2, Y2^4, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2, (Y2^-1 * Y1^-1)^7 ]
Map:: non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 9, 65, 121, 177)(3, 59, 115, 171, 12, 68, 124, 180)(5, 61, 117, 173, 14, 70, 126, 182)(6, 62, 118, 174, 15, 71, 127, 183)(7, 63, 119, 175, 16, 72, 128, 184)(8, 64, 120, 176, 18, 74, 130, 186)(10, 66, 122, 178, 20, 76, 132, 188)(11, 67, 123, 179, 22, 78, 134, 190)(13, 69, 125, 181, 24, 80, 136, 192)(17, 73, 129, 185, 26, 82, 138, 194)(19, 75, 131, 187, 28, 84, 140, 196)(21, 77, 133, 189, 30, 86, 142, 198)(23, 79, 135, 191, 32, 88, 144, 200)(25, 81, 137, 193, 34, 90, 146, 202)(27, 83, 139, 195, 36, 92, 148, 204)(29, 85, 141, 197, 38, 94, 150, 206)(31, 87, 143, 199, 40, 96, 152, 208)(33, 89, 145, 201, 42, 98, 154, 210)(35, 91, 147, 203, 44, 100, 156, 212)(37, 93, 149, 205, 46, 102, 158, 214)(39, 95, 151, 207, 48, 104, 160, 216)(41, 97, 153, 209, 50, 106, 162, 218)(43, 99, 155, 211, 52, 108, 164, 220)(45, 101, 157, 213, 53, 109, 165, 221)(47, 103, 159, 215, 54, 110, 166, 222)(49, 105, 161, 217, 55, 111, 167, 223)(51, 107, 163, 219, 56, 112, 168, 224)
	L = (1, 58)(2, 63)(3, 67)(4, 70)(5, 57)(6, 69)(7, 61)(8, 73)(9, 60)(10, 75)(11, 62)(12, 80)(13, 59)(14, 72)(15, 78)(16, 65)(17, 66)(18, 84)(19, 64)(20, 82)(21, 85)(22, 68)(23, 87)(24, 71)(25, 89)(26, 74)(27, 91)(28, 76)(29, 79)(30, 96)(31, 77)(32, 94)(33, 83)(34, 100)(35, 81)(36, 98)(37, 101)(38, 86)(39, 103)(40, 88)(41, 105)(42, 90)(43, 107)(44, 92)(45, 95)(46, 110)(47, 93)(48, 109)(49, 99)(50, 112)(51, 97)(52, 111)(53, 102)(54, 104)(55, 106)(56, 108)(113, 171)(114, 176)(115, 175)(116, 183)(117, 178)(118, 169)(119, 174)(120, 173)(121, 188)(122, 170)(123, 189)(124, 172)(125, 191)(126, 186)(127, 184)(128, 180)(129, 193)(130, 177)(131, 195)(132, 182)(133, 181)(134, 200)(135, 179)(136, 198)(137, 187)(138, 204)(139, 185)(140, 202)(141, 205)(142, 190)(143, 207)(144, 192)(145, 209)(146, 194)(147, 211)(148, 196)(149, 199)(150, 216)(151, 197)(152, 214)(153, 203)(154, 220)(155, 201)(156, 218)(157, 219)(158, 206)(159, 217)(160, 208)(161, 213)(162, 210)(163, 215)(164, 212)(165, 223)(166, 224)(167, 222)(168, 221)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1028
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1032 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y2)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 11, 67)(5, 61, 8, 64)(7, 63, 15, 71)(9, 65, 13, 69)(10, 66, 18, 74)(12, 68, 20, 76)(14, 70, 22, 78)(16, 72, 24, 80)(17, 73, 25, 81)(19, 75, 27, 83)(21, 77, 29, 85)(23, 79, 31, 87)(26, 82, 34, 90)(28, 84, 36, 92)(30, 86, 38, 94)(32, 88, 40, 96)(33, 89, 41, 97)(35, 91, 43, 99)(37, 93, 45, 101)(39, 95, 47, 103)(42, 98, 50, 106)(44, 100, 52, 108)(46, 102, 54, 110)(48, 104, 56, 112)(49, 105, 55, 111)(51, 107, 53, 109)(113, 169, 115, 171, 121, 177, 117, 173)(114, 170, 118, 174, 125, 181, 120, 176)(116, 172, 122, 178, 129, 185, 124, 180)(119, 175, 126, 182, 133, 189, 128, 184)(123, 179, 130, 186, 137, 193, 132, 188)(127, 183, 134, 190, 141, 197, 136, 192)(131, 187, 138, 194, 145, 201, 140, 196)(135, 191, 142, 198, 149, 205, 144, 200)(139, 195, 146, 202, 153, 209, 148, 204)(143, 199, 150, 206, 157, 213, 152, 208)(147, 203, 154, 210, 161, 217, 156, 212)(151, 207, 158, 214, 165, 221, 160, 216)(155, 211, 162, 218, 167, 223, 164, 220)(159, 215, 166, 222, 163, 219, 168, 224)
	L = (1, 116)(2, 119)(3, 122)(4, 113)(5, 124)(6, 126)(7, 114)(8, 128)(9, 129)(10, 115)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 121)(18, 138)(19, 123)(20, 140)(21, 125)(22, 142)(23, 127)(24, 144)(25, 145)(26, 130)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 137)(34, 154)(35, 139)(36, 156)(37, 141)(38, 158)(39, 143)(40, 160)(41, 161)(42, 146)(43, 163)(44, 148)(45, 165)(46, 150)(47, 167)(48, 152)(49, 153)(50, 168)(51, 155)(52, 166)(53, 157)(54, 164)(55, 159)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1039
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1033 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2 * Y3 * Y2^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y3 * Y2 * Y1 * Y3 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1, (Y3 * Y1)^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 12, 68)(5, 61, 14, 70)(6, 62, 15, 71)(7, 63, 18, 74)(8, 64, 20, 76)(10, 66, 16, 72)(11, 67, 17, 73)(13, 69, 19, 75)(21, 77, 31, 87)(22, 78, 33, 89)(23, 79, 34, 90)(24, 80, 32, 88)(25, 81, 35, 91)(26, 82, 36, 92)(27, 83, 38, 94)(28, 84, 39, 95)(29, 85, 37, 93)(30, 86, 40, 96)(41, 97, 49, 105)(42, 98, 50, 106)(43, 99, 51, 107)(44, 100, 52, 108)(45, 101, 53, 109)(46, 102, 54, 110)(47, 103, 55, 111)(48, 104, 56, 112)(113, 169, 115, 171, 122, 178, 117, 173)(114, 170, 118, 174, 128, 184, 120, 176)(116, 172, 123, 179, 136, 192, 125, 181)(119, 175, 129, 185, 141, 197, 131, 187)(121, 177, 133, 189, 126, 182, 135, 191)(124, 180, 134, 190, 144, 200, 137, 193)(127, 183, 138, 194, 132, 188, 140, 196)(130, 186, 139, 195, 149, 205, 142, 198)(143, 199, 153, 209, 146, 202, 155, 211)(145, 201, 154, 210, 147, 203, 156, 212)(148, 204, 157, 213, 151, 207, 159, 215)(150, 206, 158, 214, 152, 208, 160, 216)(161, 217, 166, 222, 163, 219, 168, 224)(162, 218, 167, 223, 164, 220, 165, 221)
	L = (1, 116)(2, 119)(3, 123)(4, 113)(5, 125)(6, 129)(7, 114)(8, 131)(9, 134)(10, 136)(11, 115)(12, 135)(13, 117)(14, 137)(15, 139)(16, 141)(17, 118)(18, 140)(19, 120)(20, 142)(21, 144)(22, 121)(23, 124)(24, 122)(25, 126)(26, 149)(27, 127)(28, 130)(29, 128)(30, 132)(31, 154)(32, 133)(33, 155)(34, 156)(35, 153)(36, 158)(37, 138)(38, 159)(39, 160)(40, 157)(41, 147)(42, 143)(43, 145)(44, 146)(45, 152)(46, 148)(47, 150)(48, 151)(49, 167)(50, 168)(51, 165)(52, 166)(53, 163)(54, 164)(55, 161)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1038
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1034 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y3^-1 * Y1)^2, Y3^7, Y2 * R * Y2^-2 * Y1 * R * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 8, 64)(5, 61, 7, 63)(6, 62, 10, 66)(11, 67, 18, 74)(12, 68, 23, 79)(13, 69, 22, 78)(14, 70, 21, 77)(15, 71, 20, 76)(16, 72, 19, 75)(17, 73, 24, 80)(25, 81, 33, 89)(26, 82, 34, 90)(27, 83, 39, 95)(28, 84, 38, 94)(29, 85, 37, 93)(30, 86, 36, 92)(31, 87, 35, 91)(32, 88, 40, 96)(41, 97, 47, 103)(42, 98, 48, 104)(43, 99, 52, 108)(44, 100, 51, 107)(45, 101, 50, 106)(46, 102, 49, 105)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 125, 181, 137, 193, 127, 183)(118, 174, 124, 180, 138, 194, 128, 184)(120, 176, 132, 188, 145, 201, 134, 190)(122, 178, 131, 187, 146, 202, 135, 191)(126, 182, 140, 196, 153, 209, 142, 198)(129, 185, 139, 195, 154, 210, 143, 199)(133, 189, 148, 204, 159, 215, 150, 206)(136, 192, 147, 203, 160, 216, 151, 207)(141, 197, 156, 212, 165, 221, 157, 213)(144, 200, 155, 211, 166, 222, 158, 214)(149, 205, 162, 218, 167, 223, 163, 219)(152, 208, 161, 217, 168, 224, 164, 220)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 128)(6, 113)(7, 131)(8, 133)(9, 135)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 117)(16, 143)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 121)(23, 151)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 144)(30, 127)(31, 158)(32, 129)(33, 159)(34, 130)(35, 161)(36, 132)(37, 152)(38, 134)(39, 164)(40, 136)(41, 165)(42, 138)(43, 156)(44, 140)(45, 142)(46, 157)(47, 167)(48, 146)(49, 162)(50, 148)(51, 150)(52, 163)(53, 166)(54, 154)(55, 168)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1040
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1035 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^4, Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * R * Y1 * Y2^2 * R * Y2^-1 * Y1, Y2^-2 * Y3^7 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 8, 64)(5, 61, 7, 63)(6, 62, 10, 66)(11, 67, 18, 74)(12, 68, 23, 79)(13, 69, 22, 78)(14, 70, 21, 77)(15, 71, 20, 76)(16, 72, 19, 75)(17, 73, 24, 80)(25, 81, 33, 89)(26, 82, 34, 90)(27, 83, 39, 95)(28, 84, 38, 94)(29, 85, 37, 93)(30, 86, 36, 92)(31, 87, 35, 91)(32, 88, 40, 96)(41, 97, 49, 105)(42, 98, 50, 106)(43, 99, 55, 111)(44, 100, 54, 110)(45, 101, 53, 109)(46, 102, 52, 108)(47, 103, 51, 107)(48, 104, 56, 112)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 125, 181, 137, 193, 127, 183)(118, 174, 124, 180, 138, 194, 128, 184)(120, 176, 132, 188, 145, 201, 134, 190)(122, 178, 131, 187, 146, 202, 135, 191)(126, 182, 140, 196, 153, 209, 142, 198)(129, 185, 139, 195, 154, 210, 143, 199)(133, 189, 148, 204, 161, 217, 150, 206)(136, 192, 147, 203, 162, 218, 151, 207)(141, 197, 156, 212, 160, 216, 158, 214)(144, 200, 155, 211, 157, 213, 159, 215)(149, 205, 164, 220, 168, 224, 166, 222)(152, 208, 163, 219, 165, 221, 167, 223)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 128)(6, 113)(7, 131)(8, 133)(9, 135)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 117)(16, 143)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 121)(23, 151)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 157)(30, 127)(31, 159)(32, 129)(33, 161)(34, 130)(35, 163)(36, 132)(37, 165)(38, 134)(39, 167)(40, 136)(41, 160)(42, 138)(43, 158)(44, 140)(45, 154)(46, 142)(47, 156)(48, 144)(49, 168)(50, 146)(51, 166)(52, 148)(53, 162)(54, 150)(55, 164)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1041
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1036 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y1^2, Y2^2 * Y1^2, (Y2, Y1), (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^4, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y3^6 * Y2^-1 * Y3, Y2^-1 * Y3^-3 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 9, 65, 6, 62, 11, 67)(4, 60, 15, 71, 21, 77, 12, 68)(7, 63, 18, 74, 22, 78, 10, 66)(13, 69, 27, 83, 17, 73, 24, 80)(14, 70, 26, 82, 19, 75, 23, 79)(16, 72, 28, 84, 37, 93, 31, 87)(20, 76, 25, 81, 38, 94, 34, 90)(29, 85, 40, 96, 33, 89, 43, 99)(30, 86, 39, 95, 35, 91, 42, 98)(32, 88, 47, 103, 51, 107, 44, 100)(36, 92, 49, 105, 52, 108, 41, 97)(45, 101, 56, 112, 48, 104, 54, 110)(46, 102, 55, 111, 50, 106, 53, 109)(113, 169, 115, 171, 120, 176, 118, 174)(114, 170, 121, 177, 117, 173, 123, 179)(116, 172, 125, 181, 133, 189, 129, 185)(119, 175, 126, 182, 134, 190, 131, 187)(122, 178, 135, 191, 130, 186, 138, 194)(124, 180, 136, 192, 127, 183, 139, 195)(128, 184, 141, 197, 149, 205, 145, 201)(132, 188, 142, 198, 150, 206, 147, 203)(137, 193, 151, 207, 146, 202, 154, 210)(140, 196, 152, 208, 143, 199, 155, 211)(144, 200, 157, 213, 163, 219, 160, 216)(148, 204, 158, 214, 164, 220, 162, 218)(153, 209, 165, 221, 161, 217, 167, 223)(156, 212, 166, 222, 159, 215, 168, 224)
	L = (1, 116)(2, 122)(3, 125)(4, 128)(5, 130)(6, 129)(7, 113)(8, 133)(9, 135)(10, 137)(11, 138)(12, 114)(13, 141)(14, 115)(15, 117)(16, 144)(17, 145)(18, 146)(19, 118)(20, 119)(21, 149)(22, 120)(23, 151)(24, 121)(25, 153)(26, 154)(27, 123)(28, 124)(29, 157)(30, 126)(31, 127)(32, 158)(33, 160)(34, 161)(35, 131)(36, 132)(37, 163)(38, 134)(39, 165)(40, 136)(41, 166)(42, 167)(43, 139)(44, 140)(45, 164)(46, 142)(47, 143)(48, 148)(49, 168)(50, 147)(51, 162)(52, 150)(53, 159)(54, 152)(55, 156)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1037
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1037 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y2)^2, Y3^4, Y1^3 * Y3 * Y1^-1 * Y3 * Y1^3, Y1^3 * Y3 * Y2 * Y1 * Y3 * Y1^-3 * Y2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 7, 63, 18, 74, 33, 89, 46, 102, 30, 86, 15, 71, 24, 80, 39, 95, 47, 103, 31, 87, 16, 72, 5, 61)(3, 59, 11, 67, 25, 81, 41, 97, 53, 109, 52, 108, 40, 96, 28, 84, 44, 100, 56, 112, 49, 105, 34, 90, 19, 75, 8, 64)(4, 60, 14, 70, 29, 85, 45, 101, 36, 92, 21, 77, 10, 66, 6, 62, 17, 73, 32, 88, 48, 104, 35, 91, 20, 76, 9, 65)(12, 68, 22, 78, 37, 93, 50, 106, 55, 111, 43, 99, 27, 83, 13, 69, 23, 79, 38, 94, 51, 107, 54, 110, 42, 98, 26, 82)(113, 169, 115, 171)(114, 170, 120, 176)(116, 172, 124, 180)(117, 173, 123, 179)(118, 174, 125, 181)(119, 175, 131, 187)(121, 177, 134, 190)(122, 178, 135, 191)(126, 182, 138, 194)(127, 183, 140, 196)(128, 184, 137, 193)(129, 185, 139, 195)(130, 186, 146, 202)(132, 188, 149, 205)(133, 189, 150, 206)(136, 192, 152, 208)(141, 197, 154, 210)(142, 198, 156, 212)(143, 199, 153, 209)(144, 200, 155, 211)(145, 201, 161, 217)(147, 203, 162, 218)(148, 204, 163, 219)(151, 207, 164, 220)(157, 213, 166, 222)(158, 214, 168, 224)(159, 215, 165, 221)(160, 216, 167, 223)
	L = (1, 116)(2, 121)(3, 124)(4, 127)(5, 126)(6, 113)(7, 132)(8, 134)(9, 136)(10, 114)(11, 138)(12, 140)(13, 115)(14, 142)(15, 118)(16, 141)(17, 117)(18, 147)(19, 149)(20, 151)(21, 119)(22, 152)(23, 120)(24, 122)(25, 154)(26, 156)(27, 123)(28, 125)(29, 158)(30, 129)(31, 157)(32, 128)(33, 160)(34, 162)(35, 159)(36, 130)(37, 164)(38, 131)(39, 133)(40, 135)(41, 166)(42, 168)(43, 137)(44, 139)(45, 145)(46, 144)(47, 148)(48, 143)(49, 167)(50, 165)(51, 146)(52, 150)(53, 163)(54, 161)(55, 153)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1036
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1038 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, R * Y2 * R * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y2^-1, Y1^-1), (Y2^-1 * Y3)^2, Y2^-7 * Y1^2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 7, 63, 5, 61)(3, 59, 8, 64, 18, 74, 13, 69)(4, 60, 9, 65, 19, 75, 15, 71)(6, 62, 10, 66, 20, 76, 16, 72)(11, 67, 21, 77, 33, 89, 27, 83)(12, 68, 22, 78, 34, 90, 28, 84)(14, 70, 23, 79, 35, 91, 30, 86)(17, 73, 24, 80, 36, 92, 31, 87)(25, 81, 37, 93, 48, 104, 43, 99)(26, 82, 38, 94, 49, 105, 44, 100)(29, 85, 39, 95, 50, 106, 46, 102)(32, 88, 40, 96, 41, 97, 47, 103)(42, 98, 51, 107, 55, 111, 54, 110)(45, 101, 52, 108, 53, 109, 56, 112)(113, 169, 115, 171, 123, 179, 137, 193, 153, 209, 148, 204, 132, 188, 119, 175, 130, 186, 145, 201, 160, 216, 144, 200, 129, 185, 118, 174)(114, 170, 120, 176, 133, 189, 149, 205, 159, 215, 143, 199, 128, 184, 117, 173, 125, 181, 139, 195, 155, 211, 152, 208, 136, 192, 122, 178)(116, 172, 126, 182, 141, 197, 157, 213, 167, 223, 161, 217, 146, 202, 131, 187, 147, 203, 162, 218, 165, 221, 154, 210, 138, 194, 124, 180)(121, 177, 135, 191, 151, 207, 164, 220, 166, 222, 156, 212, 140, 196, 127, 183, 142, 198, 158, 214, 168, 224, 163, 219, 150, 206, 134, 190)
	L = (1, 116)(2, 121)(3, 124)(4, 113)(5, 127)(6, 126)(7, 131)(8, 134)(9, 114)(10, 135)(11, 138)(12, 115)(13, 140)(14, 118)(15, 117)(16, 142)(17, 141)(18, 146)(19, 119)(20, 147)(21, 150)(22, 120)(23, 122)(24, 151)(25, 154)(26, 123)(27, 156)(28, 125)(29, 129)(30, 128)(31, 158)(32, 157)(33, 161)(34, 130)(35, 132)(36, 162)(37, 163)(38, 133)(39, 136)(40, 164)(41, 165)(42, 137)(43, 166)(44, 139)(45, 144)(46, 143)(47, 168)(48, 167)(49, 145)(50, 148)(51, 149)(52, 152)(53, 153)(54, 155)(55, 160)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1033
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1039 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^-1 * Y3)^2, Y1^4, Y2^-1 * Y1 * Y2^3 * Y1 * Y2^-3, Y2^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 7, 63, 5, 61)(3, 59, 10, 66, 18, 74, 13, 69)(4, 60, 9, 65, 19, 75, 15, 71)(6, 62, 8, 64, 20, 76, 16, 72)(11, 67, 24, 80, 33, 89, 27, 83)(12, 68, 23, 79, 34, 90, 28, 84)(14, 70, 22, 78, 35, 91, 30, 86)(17, 73, 21, 77, 36, 92, 31, 87)(25, 81, 40, 96, 48, 104, 43, 99)(26, 82, 39, 95, 49, 105, 44, 100)(29, 85, 38, 94, 50, 106, 46, 102)(32, 88, 37, 93, 41, 97, 47, 103)(42, 98, 52, 108, 55, 111, 54, 110)(45, 101, 51, 107, 53, 109, 56, 112)(113, 169, 115, 171, 123, 179, 137, 193, 153, 209, 148, 204, 132, 188, 119, 175, 130, 186, 145, 201, 160, 216, 144, 200, 129, 185, 118, 174)(114, 170, 120, 176, 133, 189, 149, 205, 155, 211, 139, 195, 125, 181, 117, 173, 128, 184, 143, 199, 159, 215, 152, 208, 136, 192, 122, 178)(116, 172, 126, 182, 141, 197, 157, 213, 167, 223, 161, 217, 146, 202, 131, 187, 147, 203, 162, 218, 165, 221, 154, 210, 138, 194, 124, 180)(121, 177, 135, 191, 151, 207, 164, 220, 168, 224, 158, 214, 142, 198, 127, 183, 140, 196, 156, 212, 166, 222, 163, 219, 150, 206, 134, 190)
	L = (1, 116)(2, 121)(3, 124)(4, 113)(5, 127)(6, 126)(7, 131)(8, 134)(9, 114)(10, 135)(11, 138)(12, 115)(13, 140)(14, 118)(15, 117)(16, 142)(17, 141)(18, 146)(19, 119)(20, 147)(21, 150)(22, 120)(23, 122)(24, 151)(25, 154)(26, 123)(27, 156)(28, 125)(29, 129)(30, 128)(31, 158)(32, 157)(33, 161)(34, 130)(35, 132)(36, 162)(37, 163)(38, 133)(39, 136)(40, 164)(41, 165)(42, 137)(43, 166)(44, 139)(45, 144)(46, 143)(47, 168)(48, 167)(49, 145)(50, 148)(51, 149)(52, 152)(53, 153)(54, 155)(55, 160)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1032
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1040 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y2)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y1^-1 * Y2^-1)^2, (Y3, Y2), Y3^-2 * Y2^-1 * Y3^-3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 13, 69, 22, 78, 11, 67)(4, 60, 12, 68, 23, 79, 17, 73)(6, 62, 18, 74, 24, 80, 9, 65)(7, 63, 10, 66, 25, 81, 19, 75)(14, 70, 29, 85, 40, 96, 32, 88)(15, 71, 33, 89, 41, 97, 30, 86)(16, 72, 31, 87, 42, 98, 28, 84)(20, 76, 26, 82, 43, 99, 36, 92)(21, 77, 37, 93, 44, 100, 27, 83)(34, 90, 49, 105, 53, 109, 47, 103)(35, 91, 48, 104, 54, 110, 50, 106)(38, 94, 51, 107, 55, 111, 45, 101)(39, 95, 46, 102, 56, 112, 52, 108)(113, 169, 115, 171, 126, 182, 146, 202, 151, 207, 133, 189, 119, 175, 128, 184, 116, 172, 127, 183, 147, 203, 150, 206, 132, 188, 118, 174)(114, 170, 121, 177, 138, 194, 157, 213, 160, 216, 142, 198, 124, 180, 140, 196, 122, 178, 139, 195, 158, 214, 159, 215, 141, 197, 123, 179)(117, 173, 130, 186, 148, 204, 163, 219, 162, 218, 145, 201, 129, 185, 143, 199, 131, 187, 149, 205, 164, 220, 161, 217, 144, 200, 125, 181)(120, 176, 134, 190, 152, 208, 165, 221, 168, 224, 156, 212, 137, 193, 154, 210, 135, 191, 153, 209, 166, 222, 167, 223, 155, 211, 136, 192)
	L = (1, 116)(2, 122)(3, 127)(4, 126)(5, 131)(6, 128)(7, 113)(8, 135)(9, 139)(10, 138)(11, 140)(12, 114)(13, 143)(14, 147)(15, 146)(16, 115)(17, 117)(18, 149)(19, 148)(20, 119)(21, 118)(22, 153)(23, 152)(24, 154)(25, 120)(26, 158)(27, 157)(28, 121)(29, 124)(30, 123)(31, 130)(32, 129)(33, 125)(34, 150)(35, 151)(36, 164)(37, 163)(38, 133)(39, 132)(40, 166)(41, 165)(42, 134)(43, 137)(44, 136)(45, 159)(46, 160)(47, 142)(48, 141)(49, 145)(50, 144)(51, 161)(52, 162)(53, 167)(54, 168)(55, 156)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1034
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1041 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (Y1 * Y2^-1)^2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2)^2, (Y1^-1 * Y2^-1)^2, Y3^-1 * Y1^-1 * Y2 * Y3 * Y2^3 * Y3 * Y1^-1, Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-4 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 13, 69, 22, 78, 11, 67)(4, 60, 12, 68, 23, 79, 17, 73)(6, 62, 18, 74, 24, 80, 9, 65)(7, 63, 10, 66, 25, 81, 19, 75)(14, 70, 29, 85, 40, 96, 32, 88)(15, 71, 33, 89, 41, 97, 30, 86)(16, 72, 31, 87, 42, 98, 28, 84)(20, 76, 26, 82, 43, 99, 36, 92)(21, 77, 37, 93, 44, 100, 27, 83)(34, 90, 49, 105, 56, 112, 47, 103)(35, 91, 48, 104, 55, 111, 50, 106)(38, 94, 53, 109, 52, 108, 45, 101)(39, 95, 46, 102, 51, 107, 54, 110)(113, 169, 115, 171, 126, 182, 146, 202, 163, 219, 156, 212, 137, 193, 154, 210, 135, 191, 153, 209, 167, 223, 150, 206, 132, 188, 118, 174)(114, 170, 121, 177, 138, 194, 157, 213, 162, 218, 145, 201, 129, 185, 143, 199, 131, 187, 149, 205, 166, 222, 159, 215, 141, 197, 123, 179)(116, 172, 127, 183, 147, 203, 164, 220, 155, 211, 136, 192, 120, 176, 134, 190, 152, 208, 168, 224, 151, 207, 133, 189, 119, 175, 128, 184)(117, 173, 130, 186, 148, 204, 165, 221, 160, 216, 142, 198, 124, 180, 140, 196, 122, 178, 139, 195, 158, 214, 161, 217, 144, 200, 125, 181)
	L = (1, 116)(2, 122)(3, 127)(4, 126)(5, 131)(6, 128)(7, 113)(8, 135)(9, 139)(10, 138)(11, 140)(12, 114)(13, 143)(14, 147)(15, 146)(16, 115)(17, 117)(18, 149)(19, 148)(20, 119)(21, 118)(22, 153)(23, 152)(24, 154)(25, 120)(26, 158)(27, 157)(28, 121)(29, 124)(30, 123)(31, 130)(32, 129)(33, 125)(34, 164)(35, 163)(36, 166)(37, 165)(38, 133)(39, 132)(40, 167)(41, 168)(42, 134)(43, 137)(44, 136)(45, 161)(46, 162)(47, 142)(48, 141)(49, 145)(50, 144)(51, 155)(52, 156)(53, 159)(54, 160)(55, 151)(56, 150)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1035
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1042 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^7 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 8, 64)(5, 61, 9, 65)(6, 62, 10, 66)(11, 67, 18, 74)(12, 68, 19, 75)(13, 69, 20, 76)(14, 70, 21, 77)(15, 71, 22, 78)(16, 72, 23, 79)(17, 73, 24, 80)(25, 81, 33, 89)(26, 82, 34, 90)(27, 83, 35, 91)(28, 84, 36, 92)(29, 85, 37, 93)(30, 86, 38, 94)(31, 87, 39, 95)(32, 88, 40, 96)(41, 97, 47, 103)(42, 98, 48, 104)(43, 99, 49, 105)(44, 100, 50, 106)(45, 101, 51, 107)(46, 102, 52, 108)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 125, 181, 137, 193, 127, 183)(118, 174, 124, 180, 138, 194, 128, 184)(120, 176, 132, 188, 145, 201, 134, 190)(122, 178, 131, 187, 146, 202, 135, 191)(126, 182, 140, 196, 153, 209, 142, 198)(129, 185, 139, 195, 154, 210, 143, 199)(133, 189, 148, 204, 159, 215, 150, 206)(136, 192, 147, 203, 160, 216, 151, 207)(141, 197, 156, 212, 165, 221, 157, 213)(144, 200, 155, 211, 166, 222, 158, 214)(149, 205, 162, 218, 167, 223, 163, 219)(152, 208, 161, 217, 168, 224, 164, 220)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 128)(6, 113)(7, 131)(8, 133)(9, 135)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 117)(16, 143)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 121)(23, 151)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 144)(30, 127)(31, 158)(32, 129)(33, 159)(34, 130)(35, 161)(36, 132)(37, 152)(38, 134)(39, 164)(40, 136)(41, 165)(42, 138)(43, 156)(44, 140)(45, 142)(46, 157)(47, 167)(48, 146)(49, 162)(50, 148)(51, 150)(52, 163)(53, 166)(54, 154)(55, 168)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1046
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1043 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 5, 61)(4, 60, 7, 63)(6, 62, 8, 64)(9, 65, 13, 69)(10, 66, 12, 68)(11, 67, 15, 71)(14, 70, 16, 72)(17, 73, 21, 77)(18, 74, 20, 76)(19, 75, 23, 79)(22, 78, 24, 80)(25, 81, 29, 85)(26, 82, 28, 84)(27, 83, 31, 87)(30, 86, 32, 88)(33, 89, 37, 93)(34, 90, 36, 92)(35, 91, 39, 95)(38, 94, 40, 96)(41, 97, 45, 101)(42, 98, 44, 100)(43, 99, 47, 103)(46, 102, 48, 104)(49, 105, 53, 109)(50, 106, 52, 108)(51, 107, 54, 110)(55, 111, 56, 112)(113, 169, 115, 171, 114, 170, 117, 173)(116, 172, 122, 178, 119, 175, 124, 180)(118, 174, 121, 177, 120, 176, 125, 181)(123, 179, 130, 186, 127, 183, 132, 188)(126, 182, 129, 185, 128, 184, 133, 189)(131, 187, 138, 194, 135, 191, 140, 196)(134, 190, 137, 193, 136, 192, 141, 197)(139, 195, 146, 202, 143, 199, 148, 204)(142, 198, 145, 201, 144, 200, 149, 205)(147, 203, 154, 210, 151, 207, 156, 212)(150, 206, 153, 209, 152, 208, 157, 213)(155, 211, 162, 218, 159, 215, 164, 220)(158, 214, 161, 217, 160, 216, 165, 221)(163, 219, 167, 223, 166, 222, 168, 224)
	L = (1, 116)(2, 119)(3, 121)(4, 123)(5, 125)(6, 113)(7, 127)(8, 114)(9, 129)(10, 115)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 137)(18, 122)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 145)(26, 130)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 153)(34, 138)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 161)(42, 146)(43, 163)(44, 148)(45, 165)(46, 150)(47, 166)(48, 152)(49, 167)(50, 154)(51, 158)(52, 156)(53, 168)(54, 160)(55, 162)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1048
Graph:: bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1044 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^7 * Y2, Y3^-4 * Y2^2 * Y3^-3 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 8, 64)(5, 61, 9, 65)(6, 62, 10, 66)(11, 67, 18, 74)(12, 68, 19, 75)(13, 69, 20, 76)(14, 70, 21, 77)(15, 71, 22, 78)(16, 72, 23, 79)(17, 73, 24, 80)(25, 81, 33, 89)(26, 82, 34, 90)(27, 83, 35, 91)(28, 84, 36, 92)(29, 85, 37, 93)(30, 86, 38, 94)(31, 87, 39, 95)(32, 88, 40, 96)(41, 97, 49, 105)(42, 98, 50, 106)(43, 99, 51, 107)(44, 100, 52, 108)(45, 101, 53, 109)(46, 102, 54, 110)(47, 103, 55, 111)(48, 104, 56, 112)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 125, 181, 137, 193, 127, 183)(118, 174, 124, 180, 138, 194, 128, 184)(120, 176, 132, 188, 145, 201, 134, 190)(122, 178, 131, 187, 146, 202, 135, 191)(126, 182, 140, 196, 153, 209, 142, 198)(129, 185, 139, 195, 154, 210, 143, 199)(133, 189, 148, 204, 161, 217, 150, 206)(136, 192, 147, 203, 162, 218, 151, 207)(141, 197, 156, 212, 168, 224, 158, 214)(144, 200, 155, 211, 165, 221, 159, 215)(149, 205, 164, 220, 160, 216, 166, 222)(152, 208, 163, 219, 157, 213, 167, 223)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 128)(6, 113)(7, 131)(8, 133)(9, 135)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 117)(16, 143)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 121)(23, 151)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 157)(30, 127)(31, 159)(32, 129)(33, 161)(34, 130)(35, 163)(36, 132)(37, 165)(38, 134)(39, 167)(40, 136)(41, 168)(42, 138)(43, 166)(44, 140)(45, 162)(46, 142)(47, 164)(48, 144)(49, 160)(50, 146)(51, 158)(52, 148)(53, 154)(54, 150)(55, 156)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1049
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1045 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^4, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^7 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 8, 64)(5, 61, 9, 65)(6, 62, 10, 66)(11, 67, 18, 74)(12, 68, 19, 75)(13, 69, 20, 76)(14, 70, 21, 77)(15, 71, 22, 78)(16, 72, 23, 79)(17, 73, 24, 80)(25, 81, 33, 89)(26, 82, 34, 90)(27, 83, 35, 91)(28, 84, 36, 92)(29, 85, 37, 93)(30, 86, 38, 94)(31, 87, 39, 95)(32, 88, 40, 96)(41, 97, 49, 105)(42, 98, 50, 106)(43, 99, 51, 107)(44, 100, 52, 108)(45, 101, 53, 109)(46, 102, 54, 110)(47, 103, 55, 111)(48, 104, 56, 112)(113, 169, 115, 171, 123, 179, 117, 173)(114, 170, 119, 175, 130, 186, 121, 177)(116, 172, 125, 181, 137, 193, 127, 183)(118, 174, 124, 180, 138, 194, 128, 184)(120, 176, 132, 188, 145, 201, 134, 190)(122, 178, 131, 187, 146, 202, 135, 191)(126, 182, 140, 196, 153, 209, 142, 198)(129, 185, 139, 195, 154, 210, 143, 199)(133, 189, 148, 204, 161, 217, 150, 206)(136, 192, 147, 203, 162, 218, 151, 207)(141, 197, 156, 212, 160, 216, 158, 214)(144, 200, 155, 211, 157, 213, 159, 215)(149, 205, 164, 220, 168, 224, 166, 222)(152, 208, 163, 219, 165, 221, 167, 223)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 128)(6, 113)(7, 131)(8, 133)(9, 135)(10, 114)(11, 137)(12, 139)(13, 115)(14, 141)(15, 117)(16, 143)(17, 118)(18, 145)(19, 147)(20, 119)(21, 149)(22, 121)(23, 151)(24, 122)(25, 153)(26, 123)(27, 155)(28, 125)(29, 157)(30, 127)(31, 159)(32, 129)(33, 161)(34, 130)(35, 163)(36, 132)(37, 165)(38, 134)(39, 167)(40, 136)(41, 160)(42, 138)(43, 158)(44, 140)(45, 154)(46, 142)(47, 156)(48, 144)(49, 168)(50, 146)(51, 166)(52, 148)(53, 162)(54, 150)(55, 164)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1047
Graph:: simple bipartite
	v = 42 e = 112 f = 18
	degree seq :: [ 4^28, 8^14 ]

E27.1046 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ R^2, Y3^-2 * Y2^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y2^-1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1, Y1^4, Y3^-1 * Y2^-6, Y3^7 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 11, 67, 22, 78, 15, 71)(4, 60, 12, 68, 23, 79, 17, 73)(6, 62, 9, 65, 24, 80, 18, 74)(7, 63, 10, 66, 25, 81, 19, 75)(13, 69, 29, 85, 40, 96, 33, 89)(14, 70, 30, 86, 41, 97, 34, 90)(16, 72, 28, 84, 42, 98, 35, 91)(20, 76, 26, 82, 43, 99, 36, 92)(21, 77, 27, 83, 44, 100, 37, 93)(31, 87, 47, 103, 53, 109, 49, 105)(32, 88, 48, 104, 54, 110, 50, 106)(38, 94, 45, 101, 55, 111, 51, 107)(39, 95, 46, 102, 56, 112, 52, 108)(113, 169, 115, 171, 125, 181, 143, 199, 151, 207, 133, 189, 119, 175, 128, 184, 116, 172, 126, 182, 144, 200, 150, 206, 132, 188, 118, 174)(114, 170, 121, 177, 138, 194, 157, 213, 160, 216, 142, 198, 124, 180, 140, 196, 122, 178, 139, 195, 158, 214, 159, 215, 141, 197, 123, 179)(117, 173, 130, 186, 148, 204, 163, 219, 162, 218, 146, 202, 129, 185, 147, 203, 131, 187, 149, 205, 164, 220, 161, 217, 145, 201, 127, 183)(120, 176, 134, 190, 152, 208, 165, 221, 168, 224, 156, 212, 137, 193, 154, 210, 135, 191, 153, 209, 166, 222, 167, 223, 155, 211, 136, 192)
	L = (1, 116)(2, 122)(3, 126)(4, 125)(5, 131)(6, 128)(7, 113)(8, 135)(9, 139)(10, 138)(11, 140)(12, 114)(13, 144)(14, 143)(15, 147)(16, 115)(17, 117)(18, 149)(19, 148)(20, 119)(21, 118)(22, 153)(23, 152)(24, 154)(25, 120)(26, 158)(27, 157)(28, 121)(29, 124)(30, 123)(31, 150)(32, 151)(33, 129)(34, 127)(35, 130)(36, 164)(37, 163)(38, 133)(39, 132)(40, 166)(41, 165)(42, 134)(43, 137)(44, 136)(45, 159)(46, 160)(47, 142)(48, 141)(49, 146)(50, 145)(51, 161)(52, 162)(53, 167)(54, 168)(55, 156)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1042
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1047 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^4, (R * Y2)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y1^2 * Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y1^-2 * Y2^2 * Y1^-2 * Y2^-2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^5, Y1^-1 * Y2 * Y3 * Y1^-1 * Y3^-1 * Y2^-3 * Y3^-1, Y2^-2 * Y3^-1 * Y2^-3 * Y1^-2 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 11, 67, 22, 78, 15, 71)(4, 60, 12, 68, 23, 79, 17, 73)(6, 62, 9, 65, 24, 80, 18, 74)(7, 63, 10, 66, 25, 81, 19, 75)(13, 69, 29, 85, 40, 96, 33, 89)(14, 70, 30, 86, 41, 97, 34, 90)(16, 72, 28, 84, 42, 98, 35, 91)(20, 76, 26, 82, 43, 99, 36, 92)(21, 77, 27, 83, 44, 100, 37, 93)(31, 87, 47, 103, 56, 112, 51, 107)(32, 88, 48, 104, 55, 111, 52, 108)(38, 94, 45, 101, 50, 106, 53, 109)(39, 95, 46, 102, 49, 105, 54, 110)(113, 169, 115, 171, 125, 181, 143, 199, 161, 217, 156, 212, 137, 193, 154, 210, 135, 191, 153, 209, 167, 223, 150, 206, 132, 188, 118, 174)(114, 170, 121, 177, 138, 194, 157, 213, 164, 220, 146, 202, 129, 185, 147, 203, 131, 187, 149, 205, 166, 222, 159, 215, 141, 197, 123, 179)(116, 172, 126, 182, 144, 200, 162, 218, 155, 211, 136, 192, 120, 176, 134, 190, 152, 208, 168, 224, 151, 207, 133, 189, 119, 175, 128, 184)(117, 173, 130, 186, 148, 204, 165, 221, 160, 216, 142, 198, 124, 180, 140, 196, 122, 178, 139, 195, 158, 214, 163, 219, 145, 201, 127, 183)
	L = (1, 116)(2, 122)(3, 126)(4, 125)(5, 131)(6, 128)(7, 113)(8, 135)(9, 139)(10, 138)(11, 140)(12, 114)(13, 144)(14, 143)(15, 147)(16, 115)(17, 117)(18, 149)(19, 148)(20, 119)(21, 118)(22, 153)(23, 152)(24, 154)(25, 120)(26, 158)(27, 157)(28, 121)(29, 124)(30, 123)(31, 162)(32, 161)(33, 129)(34, 127)(35, 130)(36, 166)(37, 165)(38, 133)(39, 132)(40, 167)(41, 168)(42, 134)(43, 137)(44, 136)(45, 163)(46, 164)(47, 142)(48, 141)(49, 155)(50, 156)(51, 146)(52, 145)(53, 159)(54, 160)(55, 151)(56, 150)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1045
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1048 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1 * Y3^-1 * Y1, Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y1^-2, (Y3, Y2^-1), Y2 * Y3^-1 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y2^2, Y1^4, Y3^14, Y3^6 * Y2 * Y1 * Y2^-7 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 11, 67, 4, 60, 12, 68)(6, 62, 9, 65, 7, 63, 10, 66)(13, 69, 19, 75, 14, 70, 20, 76)(15, 71, 17, 73, 16, 72, 18, 74)(21, 77, 27, 83, 22, 78, 28, 84)(23, 79, 25, 81, 24, 80, 26, 82)(29, 85, 35, 91, 30, 86, 36, 92)(31, 87, 33, 89, 32, 88, 34, 90)(37, 93, 43, 99, 38, 94, 44, 100)(39, 95, 41, 97, 40, 96, 42, 98)(45, 101, 51, 107, 46, 102, 52, 108)(47, 103, 49, 105, 48, 104, 50, 106)(53, 109, 55, 111, 54, 110, 56, 112)(113, 169, 115, 171, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 159, 215, 151, 207, 143, 199, 135, 191, 127, 183, 118, 174)(114, 170, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 167, 223, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179)(116, 172, 126, 182, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 119, 175, 120, 176)(117, 173, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 168, 224, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180)
	L = (1, 116)(2, 122)(3, 126)(4, 125)(5, 121)(6, 120)(7, 113)(8, 115)(9, 130)(10, 129)(11, 117)(12, 114)(13, 134)(14, 133)(15, 119)(16, 118)(17, 138)(18, 137)(19, 124)(20, 123)(21, 142)(22, 141)(23, 128)(24, 127)(25, 146)(26, 145)(27, 132)(28, 131)(29, 150)(30, 149)(31, 136)(32, 135)(33, 154)(34, 153)(35, 140)(36, 139)(37, 158)(38, 157)(39, 144)(40, 143)(41, 162)(42, 161)(43, 148)(44, 147)(45, 166)(46, 165)(47, 152)(48, 151)(49, 168)(50, 167)(51, 156)(52, 155)(53, 160)(54, 159)(55, 164)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1043
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1049 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 14})
Quotient :: dipole
Aut^+ = C2 x (C7 : C4) (small group id <56, 6>)
Aut   = C2 x ((C14 x C2) : C2) (small group id <112, 36>)
|r| :: 2
Presentation :: [ R^2, Y2^-2 * Y3^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1^-2 * Y2^-2 * Y3^-2 * Y2^-3, Y2^-2 * Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y2^-2, Y3^-1 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58, 8, 64, 5, 61)(3, 59, 11, 67, 22, 78, 15, 71)(4, 60, 12, 68, 23, 79, 17, 73)(6, 62, 9, 65, 24, 80, 18, 74)(7, 63, 10, 66, 25, 81, 19, 75)(13, 69, 29, 85, 40, 96, 33, 89)(14, 70, 30, 86, 41, 97, 34, 90)(16, 72, 28, 84, 42, 98, 35, 91)(20, 76, 26, 82, 43, 99, 36, 92)(21, 77, 27, 83, 44, 100, 37, 93)(31, 87, 47, 103, 55, 111, 51, 107)(32, 88, 48, 104, 56, 112, 52, 108)(38, 94, 45, 101, 49, 105, 53, 109)(39, 95, 46, 102, 50, 106, 54, 110)(113, 169, 115, 171, 125, 181, 143, 199, 161, 217, 155, 211, 136, 192, 120, 176, 134, 190, 152, 208, 167, 223, 150, 206, 132, 188, 118, 174)(114, 170, 121, 177, 138, 194, 157, 213, 163, 219, 145, 201, 127, 183, 117, 173, 130, 186, 148, 204, 165, 221, 159, 215, 141, 197, 123, 179)(116, 172, 126, 182, 144, 200, 162, 218, 156, 212, 137, 193, 154, 210, 135, 191, 153, 209, 168, 224, 151, 207, 133, 189, 119, 175, 128, 184)(122, 178, 139, 195, 158, 214, 164, 220, 146, 202, 129, 185, 147, 203, 131, 187, 149, 205, 166, 222, 160, 216, 142, 198, 124, 180, 140, 196)
	L = (1, 116)(2, 122)(3, 126)(4, 125)(5, 131)(6, 128)(7, 113)(8, 135)(9, 139)(10, 138)(11, 140)(12, 114)(13, 144)(14, 143)(15, 147)(16, 115)(17, 117)(18, 149)(19, 148)(20, 119)(21, 118)(22, 153)(23, 152)(24, 154)(25, 120)(26, 158)(27, 157)(28, 121)(29, 124)(30, 123)(31, 162)(32, 161)(33, 129)(34, 127)(35, 130)(36, 166)(37, 165)(38, 133)(39, 132)(40, 168)(41, 167)(42, 134)(43, 137)(44, 136)(45, 164)(46, 163)(47, 142)(48, 141)(49, 156)(50, 155)(51, 146)(52, 145)(53, 160)(54, 159)(55, 151)(56, 150)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1044
Graph:: bipartite
	v = 18 e = 112 f = 42
	degree seq :: [ 8^14, 28^4 ]

E27.1050 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, R * Y2 * R * Y3, (R * Y1)^2, Y2 * Y1^2 * Y3 * Y1^-2, Y1^-2 * Y3 * Y1^2 * Y2, Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y2, Y1^-11 * Y3 * Y1^-3 * Y3 ]
Map::
	R = (1, 58, 2, 61, 5, 67, 11, 76, 20, 85, 29, 93, 37, 101, 45, 109, 53, 105, 49, 97, 41, 89, 33, 81, 25, 72, 16, 80, 24, 71, 15, 79, 23, 88, 32, 96, 40, 104, 48, 112, 56, 108, 52, 100, 44, 92, 36, 84, 28, 75, 19, 66, 10, 60, 4, 57)(3, 63, 7, 68, 12, 78, 22, 86, 30, 95, 39, 102, 46, 111, 55, 107, 51, 99, 43, 91, 35, 83, 27, 74, 18, 65, 9, 70, 14, 62, 6, 69, 13, 77, 21, 87, 31, 94, 38, 103, 47, 110, 54, 106, 50, 98, 42, 90, 34, 82, 26, 73, 17, 64, 8, 59)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 53)(52, 55)(57, 59)(58, 62)(60, 65)(61, 68)(63, 71)(64, 72)(66, 73)(67, 77)(69, 79)(70, 80)(74, 81)(75, 83)(76, 86)(78, 88)(82, 89)(84, 90)(85, 94)(87, 96)(91, 97)(92, 99)(93, 102)(95, 104)(98, 105)(100, 106)(101, 110)(103, 112)(107, 109)(108, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1051 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y1^-2 * Y3 * Y1^-2 * Y2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1, Y1^11 * Y3 * Y1^-3 * Y3 ]
Map::
	R = (1, 58, 2, 61, 5, 67, 11, 76, 20, 85, 29, 93, 37, 101, 45, 109, 53, 106, 50, 98, 42, 90, 34, 82, 26, 72, 16, 79, 23, 73, 17, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 108, 52, 100, 44, 92, 36, 84, 28, 75, 19, 66, 10, 60, 4, 57)(3, 63, 7, 71, 15, 81, 25, 89, 33, 97, 41, 105, 49, 110, 54, 103, 47, 94, 38, 87, 31, 77, 21, 70, 14, 62, 6, 69, 13, 65, 9, 74, 18, 83, 27, 91, 35, 99, 43, 107, 51, 111, 55, 102, 46, 95, 39, 86, 30, 78, 22, 68, 12, 64, 8, 59)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 53)(52, 55)(57, 59)(58, 62)(60, 65)(61, 68)(63, 72)(64, 73)(66, 71)(67, 77)(69, 79)(70, 80)(74, 82)(75, 83)(76, 86)(78, 88)(81, 90)(84, 89)(85, 94)(87, 96)(91, 98)(92, 99)(93, 102)(95, 104)(97, 106)(100, 105)(101, 110)(103, 112)(107, 109)(108, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1052 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-2 * Y3 * Y2 * Y1^-2, (Y2 * Y1^2)^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, (Y3 * Y1^-2)^2, Y2 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 74, 18, 69, 13, 81, 25, 95, 39, 109, 53, 107, 51, 85, 29, 98, 42, 89, 33, 101, 45, 84, 28, 97, 41, 88, 32, 100, 44, 90, 34, 102, 46, 92, 36, 104, 48, 112, 56, 106, 50, 87, 31, 66, 10, 78, 22, 73, 17, 61, 5, 57)(3, 65, 9, 83, 27, 105, 49, 86, 30, 103, 47, 110, 54, 94, 38, 82, 26, 64, 8, 80, 24, 72, 16, 79, 23, 63, 7, 77, 21, 71, 15, 93, 37, 99, 43, 111, 55, 108, 52, 91, 35, 96, 40, 76, 20, 70, 14, 60, 4, 68, 12, 75, 19, 67, 11, 59)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 34)(14, 36)(16, 18)(17, 27)(20, 39)(21, 41)(22, 43)(23, 44)(24, 46)(26, 48)(29, 47)(31, 52)(33, 49)(35, 51)(37, 45)(38, 53)(40, 56)(42, 55)(50, 54)(57, 60)(58, 64)(59, 66)(61, 72)(62, 76)(63, 78)(65, 85)(67, 89)(68, 84)(69, 91)(70, 88)(71, 87)(73, 75)(74, 94)(77, 98)(79, 101)(80, 97)(81, 103)(82, 100)(83, 106)(86, 104)(90, 96)(92, 108)(93, 107)(95, 111)(99, 112)(102, 110)(105, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1053
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1053 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y3 * Y1^-4, Y2 * Y1^2 * Y3 * Y1^-2, Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1^-1, (Y1^-1 * Y3)^4, (Y2 * Y3)^7 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 74, 18, 66, 10, 78, 22, 95, 39, 109, 53, 105, 49, 89, 33, 102, 46, 92, 36, 104, 48, 83, 27, 97, 41, 86, 30, 100, 44, 84, 28, 98, 42, 87, 31, 101, 45, 112, 56, 108, 52, 91, 35, 69, 13, 81, 25, 73, 17, 61, 5, 57)(3, 65, 9, 76, 20, 70, 14, 60, 4, 68, 12, 88, 32, 107, 51, 90, 34, 99, 43, 110, 54, 94, 38, 79, 23, 63, 7, 77, 21, 71, 15, 82, 26, 64, 8, 80, 24, 72, 16, 93, 37, 103, 47, 111, 55, 106, 50, 85, 29, 96, 40, 75, 19, 67, 11, 59)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 27)(10, 29)(11, 30)(12, 33)(14, 36)(16, 35)(17, 20)(18, 38)(21, 41)(22, 43)(23, 44)(24, 46)(26, 48)(28, 40)(31, 50)(32, 52)(34, 45)(37, 49)(39, 55)(42, 54)(47, 56)(51, 53)(57, 60)(58, 64)(59, 66)(61, 72)(62, 76)(63, 78)(65, 84)(67, 87)(68, 83)(69, 90)(70, 86)(71, 74)(73, 88)(75, 95)(77, 98)(79, 101)(80, 97)(81, 103)(82, 100)(85, 105)(89, 99)(91, 106)(92, 107)(93, 104)(94, 109)(96, 112)(102, 111)(108, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1052
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1054 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1^13 * Y3 * Y1^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 69, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 106, 50, 98, 42, 90, 34, 82, 26, 74, 18, 66, 10, 72, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 108, 52, 100, 44, 92, 36, 84, 28, 76, 20, 68, 12, 61, 5, 57)(3, 65, 9, 73, 17, 81, 25, 89, 33, 97, 41, 105, 49, 110, 54, 103, 47, 94, 38, 87, 31, 78, 22, 71, 15, 63, 7, 60, 4, 67, 11, 75, 19, 83, 27, 91, 35, 99, 43, 107, 51, 111, 55, 102, 46, 95, 39, 86, 30, 79, 23, 70, 14, 64, 8, 59)
	L = (1, 3)(2, 7)(4, 10)(5, 11)(6, 14)(8, 16)(9, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 27)(21, 30)(23, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 53)(52, 55)(57, 60)(58, 64)(59, 66)(61, 65)(62, 71)(63, 72)(67, 74)(68, 75)(69, 79)(70, 80)(73, 82)(76, 81)(77, 87)(78, 88)(83, 90)(84, 91)(85, 95)(86, 96)(89, 98)(92, 97)(93, 103)(94, 104)(99, 106)(100, 107)(101, 111)(102, 112)(105, 109)(108, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1055 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-2 * Y3 * Y1 * Y2 * Y1^-1, (Y1 * Y2 * Y1)^2, (Y3 * Y1^-2)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3, Y1^-2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^19 * Y3 * Y1^-1 * Y2 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 74, 18, 94, 38, 92, 36, 104, 48, 111, 55, 105, 49, 87, 31, 66, 10, 78, 22, 96, 40, 84, 28, 99, 43, 88, 32, 102, 46, 91, 35, 69, 13, 81, 25, 97, 41, 110, 54, 107, 51, 85, 29, 100, 44, 89, 33, 73, 17, 61, 5, 57)(3, 65, 9, 83, 27, 101, 45, 112, 56, 103, 47, 109, 53, 98, 42, 76, 20, 70, 14, 60, 4, 68, 12, 79, 23, 63, 7, 77, 21, 71, 15, 93, 37, 108, 52, 86, 30, 106, 50, 90, 34, 95, 39, 82, 26, 64, 8, 80, 24, 72, 16, 75, 19, 67, 11, 59)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 18)(14, 36)(16, 35)(17, 27)(20, 41)(21, 43)(22, 45)(23, 46)(24, 38)(26, 48)(29, 50)(31, 47)(33, 52)(34, 49)(37, 40)(39, 54)(42, 55)(44, 56)(51, 53)(57, 60)(58, 64)(59, 66)(61, 72)(62, 76)(63, 78)(65, 85)(67, 89)(68, 84)(69, 90)(70, 88)(71, 87)(73, 79)(74, 95)(75, 96)(77, 100)(80, 99)(81, 103)(82, 102)(83, 105)(86, 97)(91, 98)(92, 106)(93, 107)(94, 109)(101, 110)(104, 112)(108, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1056
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1056 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-2 * Y2)^2, Y1^-1 * Y2 * Y1 * Y3 * Y1^-2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1, Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3, Y2 * Y3 * Y1^10, Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 74, 18, 94, 38, 87, 31, 102, 46, 111, 55, 105, 49, 91, 35, 69, 13, 81, 25, 98, 42, 83, 27, 99, 43, 86, 30, 101, 45, 85, 29, 66, 10, 78, 22, 96, 40, 110, 54, 107, 51, 89, 33, 103, 47, 92, 36, 73, 17, 61, 5, 57)(3, 65, 9, 82, 26, 64, 8, 80, 24, 72, 16, 93, 37, 108, 52, 90, 34, 106, 50, 84, 28, 95, 39, 79, 23, 63, 7, 77, 21, 71, 15, 76, 20, 70, 14, 60, 4, 68, 12, 88, 32, 104, 48, 112, 56, 100, 44, 109, 53, 97, 41, 75, 19, 67, 11, 59)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 27)(10, 28)(11, 30)(12, 33)(14, 36)(16, 35)(17, 26)(18, 39)(20, 42)(21, 43)(22, 44)(23, 45)(24, 47)(29, 41)(31, 50)(32, 49)(34, 40)(37, 51)(38, 53)(46, 56)(48, 54)(52, 55)(57, 60)(58, 64)(59, 66)(61, 72)(62, 76)(63, 78)(65, 74)(67, 87)(68, 83)(69, 90)(70, 86)(71, 85)(73, 88)(75, 96)(77, 94)(79, 102)(80, 99)(81, 104)(82, 101)(84, 105)(89, 106)(91, 100)(92, 108)(93, 98)(95, 110)(97, 111)(103, 112)(107, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1055
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1057 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1 * Y3 * Y1)^2, Y3^-3 * Y1 * Y3^-9 * Y1 * Y3^-2 ]
Map::
	R = (1, 57, 3, 59, 8, 64, 17, 73, 26, 82, 34, 90, 42, 98, 50, 106, 55, 111, 47, 103, 39, 95, 31, 87, 23, 79, 13, 69, 21, 77, 11, 67, 20, 76, 29, 85, 37, 93, 45, 101, 53, 109, 52, 108, 44, 100, 36, 92, 28, 84, 19, 75, 10, 66, 4, 60)(2, 58, 5, 61, 12, 68, 22, 78, 30, 86, 38, 94, 46, 102, 54, 110, 51, 107, 43, 99, 35, 91, 27, 83, 18, 74, 9, 65, 16, 72, 7, 63, 15, 71, 25, 81, 33, 89, 41, 97, 49, 105, 56, 112, 48, 104, 40, 96, 32, 88, 24, 80, 14, 70, 6, 62)(113, 114)(115, 119)(116, 121)(117, 123)(118, 125)(120, 124)(122, 126)(127, 132)(128, 133)(129, 137)(130, 135)(131, 139)(134, 141)(136, 143)(138, 142)(140, 144)(145, 149)(146, 153)(147, 151)(148, 155)(150, 157)(152, 159)(154, 158)(156, 160)(161, 165)(162, 168)(163, 167)(164, 166)(169, 170)(171, 175)(172, 177)(173, 179)(174, 181)(176, 180)(178, 182)(183, 188)(184, 189)(185, 193)(186, 191)(187, 195)(190, 197)(192, 199)(194, 198)(196, 200)(201, 205)(202, 209)(203, 207)(204, 211)(206, 213)(208, 215)(210, 214)(212, 216)(217, 221)(218, 224)(219, 223)(220, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1067
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1058 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^3 * Y2 * Y3^-11 * Y1 ]
Map::
	R = (1, 57, 3, 59, 8, 64, 17, 73, 26, 82, 34, 90, 42, 98, 50, 106, 53, 109, 45, 101, 37, 93, 29, 85, 21, 77, 11, 67, 20, 76, 13, 69, 23, 79, 31, 87, 39, 95, 47, 103, 55, 111, 52, 108, 44, 100, 36, 92, 28, 84, 19, 75, 10, 66, 4, 60)(2, 58, 5, 61, 12, 68, 22, 78, 30, 86, 38, 94, 46, 102, 54, 110, 49, 105, 41, 97, 33, 89, 25, 81, 16, 72, 7, 63, 15, 71, 9, 65, 18, 74, 27, 83, 35, 91, 43, 99, 51, 107, 56, 112, 48, 104, 40, 96, 32, 88, 24, 80, 14, 70, 6, 62)(113, 114)(115, 119)(116, 121)(117, 123)(118, 125)(120, 126)(122, 124)(127, 132)(128, 135)(129, 137)(130, 133)(131, 139)(134, 141)(136, 143)(138, 144)(140, 142)(145, 151)(146, 153)(147, 149)(148, 155)(150, 157)(152, 159)(154, 160)(156, 158)(161, 167)(162, 166)(163, 165)(164, 168)(169, 170)(171, 175)(172, 177)(173, 179)(174, 181)(176, 182)(178, 180)(183, 188)(184, 191)(185, 193)(186, 189)(187, 195)(190, 197)(192, 199)(194, 200)(196, 198)(201, 207)(202, 209)(203, 205)(204, 211)(206, 213)(208, 215)(210, 216)(212, 214)(217, 223)(218, 222)(219, 221)(220, 224)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1068
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1059 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^2 * Y2)^2, Y3^-3 * Y2 * Y1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y2, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 ]
Map::
	R = (1, 57, 4, 60, 14, 70, 29, 85, 9, 65, 28, 84, 50, 106, 55, 111, 47, 103, 22, 78, 46, 102, 25, 81, 45, 101, 21, 77, 44, 100, 24, 80, 48, 104, 30, 86, 52, 108, 31, 87, 38, 94, 53, 109, 43, 99, 20, 76, 6, 62, 19, 75, 17, 73, 5, 61)(2, 58, 7, 63, 23, 79, 40, 96, 18, 74, 39, 95, 54, 110, 51, 107, 36, 92, 13, 69, 35, 91, 16, 72, 34, 90, 12, 68, 33, 89, 15, 71, 37, 93, 41, 97, 56, 112, 42, 98, 27, 83, 49, 105, 32, 88, 11, 67, 3, 59, 10, 66, 26, 82, 8, 64)(113, 114)(115, 121)(116, 124)(117, 127)(118, 130)(119, 133)(120, 136)(122, 142)(123, 143)(125, 140)(126, 138)(128, 141)(129, 135)(131, 153)(132, 154)(134, 151)(137, 152)(139, 159)(144, 162)(145, 156)(146, 160)(147, 164)(148, 150)(149, 157)(155, 166)(158, 168)(161, 165)(163, 167)(169, 171)(170, 174)(172, 181)(173, 184)(175, 190)(176, 193)(177, 195)(178, 189)(179, 192)(180, 187)(182, 200)(183, 188)(185, 194)(186, 206)(191, 211)(196, 207)(197, 219)(198, 217)(199, 210)(201, 214)(202, 213)(203, 212)(204, 216)(205, 215)(208, 223)(209, 221)(218, 224)(220, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1070
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1060 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-2 * Y1 * Y2 * Y3^-2, Y1 * Y2 * Y3 * Y2 * Y1 * Y3^-1, Y2 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 ]
Map::
	R = (1, 57, 4, 60, 14, 70, 20, 76, 6, 62, 19, 75, 42, 98, 53, 109, 38, 94, 30, 86, 52, 108, 32, 88, 45, 101, 21, 77, 44, 100, 24, 80, 47, 103, 22, 78, 46, 102, 25, 81, 48, 104, 54, 110, 51, 107, 29, 85, 9, 65, 28, 84, 17, 73, 5, 61)(2, 58, 7, 63, 23, 79, 11, 67, 3, 59, 10, 66, 31, 87, 49, 105, 27, 83, 41, 97, 56, 112, 43, 99, 34, 90, 12, 68, 33, 89, 15, 71, 36, 92, 13, 69, 35, 91, 16, 72, 37, 93, 50, 106, 55, 111, 40, 96, 18, 74, 39, 95, 26, 82, 8, 64)(113, 114)(115, 121)(116, 124)(117, 127)(118, 130)(119, 133)(120, 136)(122, 142)(123, 144)(125, 140)(126, 138)(128, 141)(129, 135)(131, 153)(132, 155)(134, 151)(137, 152)(139, 160)(143, 163)(145, 156)(146, 159)(147, 164)(148, 157)(149, 150)(154, 167)(158, 168)(161, 165)(162, 166)(169, 171)(170, 174)(172, 181)(173, 184)(175, 190)(176, 193)(177, 195)(178, 189)(179, 192)(180, 187)(182, 191)(183, 188)(185, 199)(186, 206)(194, 210)(196, 218)(197, 208)(198, 209)(200, 217)(201, 214)(202, 216)(203, 212)(204, 215)(205, 213)(207, 222)(211, 221)(219, 224)(220, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1069
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1061 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2, Y3^6 * Y2 * Y3^-8 * Y1 ]
Map::
	R = (1, 57, 4, 60, 11, 67, 19, 75, 27, 83, 35, 91, 43, 99, 51, 107, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70, 6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 53, 109, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 5, 61)(2, 58, 7, 63, 15, 71, 23, 79, 31, 87, 39, 95, 47, 103, 55, 111, 50, 106, 42, 98, 34, 90, 26, 82, 18, 74, 10, 66, 3, 59, 9, 65, 17, 73, 25, 81, 33, 89, 41, 97, 49, 105, 56, 112, 48, 104, 40, 96, 32, 88, 24, 80, 16, 72, 8, 64)(113, 114)(115, 118)(116, 122)(117, 121)(119, 126)(120, 125)(123, 128)(124, 127)(129, 134)(130, 133)(131, 138)(132, 137)(135, 142)(136, 141)(139, 144)(140, 143)(145, 150)(146, 149)(147, 154)(148, 153)(151, 158)(152, 157)(155, 160)(156, 159)(161, 166)(162, 165)(163, 167)(164, 168)(169, 171)(170, 174)(172, 176)(173, 175)(177, 182)(178, 181)(179, 186)(180, 185)(183, 190)(184, 189)(187, 192)(188, 191)(193, 198)(194, 197)(195, 202)(196, 201)(199, 206)(200, 205)(203, 208)(204, 207)(209, 214)(210, 213)(211, 218)(212, 217)(215, 222)(216, 221)(219, 224)(220, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1071
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1062 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^3 * Y1 * Y3^-1 * Y2, Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y2, (Y3^2 * Y2)^2, (Y1 * Y3^2)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1, Y3 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2, Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^84 ]
Map::
	R = (1, 57, 4, 60, 14, 70, 30, 86, 51, 107, 32, 88, 52, 108, 54, 110, 44, 100, 20, 76, 6, 62, 19, 75, 42, 98, 21, 77, 45, 101, 24, 80, 48, 104, 29, 85, 9, 65, 28, 84, 38, 94, 53, 109, 47, 103, 22, 78, 46, 102, 25, 81, 17, 73, 5, 61)(2, 58, 7, 63, 23, 79, 41, 97, 55, 111, 43, 99, 56, 112, 50, 106, 33, 89, 11, 67, 3, 59, 10, 66, 31, 87, 12, 68, 34, 90, 15, 71, 37, 93, 40, 96, 18, 74, 39, 95, 27, 83, 49, 105, 36, 92, 13, 69, 35, 91, 16, 72, 26, 82, 8, 64)(113, 114)(115, 121)(116, 124)(117, 127)(118, 130)(119, 133)(120, 136)(122, 142)(123, 144)(125, 140)(126, 138)(128, 141)(129, 135)(131, 153)(132, 155)(134, 151)(137, 152)(139, 156)(143, 160)(145, 150)(146, 157)(147, 163)(148, 164)(149, 154)(158, 167)(159, 168)(161, 165)(162, 166)(169, 171)(170, 174)(172, 181)(173, 184)(175, 190)(176, 193)(177, 195)(178, 189)(179, 192)(180, 187)(182, 201)(183, 188)(185, 199)(186, 206)(191, 212)(194, 210)(196, 211)(197, 218)(198, 217)(200, 207)(202, 214)(203, 213)(204, 216)(205, 215)(208, 222)(209, 221)(219, 224)(220, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1073
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1063 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2, Y3 * Y1 * Y2 * Y3^-1 * Y2 * Y1, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1, Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y3 ]
Map::
	R = (1, 57, 4, 60, 14, 70, 22, 78, 47, 103, 25, 81, 48, 104, 53, 109, 38, 94, 29, 85, 9, 65, 28, 84, 46, 102, 21, 77, 45, 101, 24, 80, 44, 100, 20, 76, 6, 62, 19, 75, 42, 98, 54, 110, 52, 108, 30, 86, 51, 107, 32, 88, 17, 73, 5, 61)(2, 58, 7, 63, 23, 79, 13, 69, 36, 92, 16, 72, 37, 93, 49, 105, 27, 83, 40, 96, 18, 74, 39, 95, 35, 91, 12, 68, 34, 90, 15, 71, 33, 89, 11, 67, 3, 59, 10, 66, 31, 87, 50, 106, 56, 112, 41, 97, 55, 111, 43, 99, 26, 82, 8, 64)(113, 114)(115, 121)(116, 124)(117, 127)(118, 130)(119, 133)(120, 136)(122, 142)(123, 144)(125, 140)(126, 138)(128, 141)(129, 135)(131, 153)(132, 155)(134, 151)(137, 152)(139, 154)(143, 150)(145, 158)(146, 157)(147, 156)(148, 163)(149, 164)(159, 167)(160, 168)(161, 165)(162, 166)(169, 171)(170, 174)(172, 181)(173, 184)(175, 190)(176, 193)(177, 195)(178, 189)(179, 192)(180, 187)(182, 201)(183, 188)(185, 199)(186, 206)(191, 212)(194, 210)(196, 218)(197, 209)(198, 208)(200, 217)(202, 215)(203, 216)(204, 213)(205, 214)(207, 222)(211, 221)(219, 224)(220, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1072
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1064 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = C2 x C4 x D14 (small group id <112, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y2^5 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-4 * Y2 * Y1^-1, Y1^28, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 4, 60)(2, 58, 6, 62)(3, 59, 8, 64)(5, 61, 12, 68)(7, 63, 16, 72)(9, 65, 18, 74)(10, 66, 19, 75)(11, 67, 21, 77)(13, 69, 23, 79)(14, 70, 24, 80)(15, 71, 26, 82)(17, 73, 28, 84)(20, 76, 30, 86)(22, 78, 32, 88)(25, 81, 34, 90)(27, 83, 36, 92)(29, 85, 38, 94)(31, 87, 40, 96)(33, 89, 42, 98)(35, 91, 44, 100)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(43, 99, 52, 108)(45, 101, 54, 110)(47, 103, 56, 112)(49, 105, 55, 111)(51, 107, 53, 109)(113, 114, 117, 123, 132, 141, 149, 157, 165, 164, 156, 148, 140, 130, 135, 131, 136, 144, 152, 160, 168, 161, 153, 145, 137, 127, 119, 115)(116, 121, 128, 139, 146, 155, 162, 166, 159, 150, 143, 133, 126, 118, 125, 120, 129, 138, 147, 154, 163, 167, 158, 151, 142, 134, 124, 122)(169, 171, 175, 183, 193, 201, 209, 217, 224, 216, 208, 200, 192, 187, 191, 186, 196, 204, 212, 220, 221, 213, 205, 197, 188, 179, 173, 170)(172, 178, 180, 190, 198, 207, 214, 223, 219, 210, 203, 194, 185, 176, 181, 174, 182, 189, 199, 206, 215, 222, 218, 211, 202, 195, 184, 177)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1074
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1065 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^-2, (Y1, Y2^-1), R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3, Y1^-7 * Y2^7, Y1^28, Y2^28 ]
Map:: polytopal non-degenerate
	R = (1, 57, 4, 60)(2, 58, 9, 65)(3, 59, 12, 68)(5, 61, 15, 71)(6, 62, 14, 70)(7, 63, 17, 73)(8, 64, 19, 75)(10, 66, 20, 76)(11, 67, 22, 78)(13, 69, 24, 80)(16, 72, 26, 82)(18, 74, 28, 84)(21, 77, 30, 86)(23, 79, 32, 88)(25, 81, 34, 90)(27, 83, 36, 92)(29, 85, 38, 94)(31, 87, 40, 96)(33, 89, 42, 98)(35, 91, 44, 100)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(43, 99, 52, 108)(45, 101, 53, 109)(47, 103, 54, 110)(49, 105, 55, 111)(51, 107, 56, 112)(113, 114, 119, 128, 137, 145, 153, 161, 159, 149, 143, 133, 125, 115, 120, 118, 122, 130, 139, 147, 155, 163, 157, 151, 141, 135, 123, 117)(116, 124, 134, 142, 150, 158, 165, 167, 164, 154, 148, 138, 132, 121, 131, 127, 136, 144, 152, 160, 166, 168, 162, 156, 146, 140, 129, 126)(169, 171, 179, 189, 197, 205, 213, 217, 211, 201, 195, 184, 178, 170, 176, 173, 181, 191, 199, 207, 215, 219, 209, 203, 193, 186, 175, 174)(172, 177, 185, 194, 202, 210, 218, 223, 222, 214, 208, 198, 192, 180, 187, 182, 188, 196, 204, 212, 220, 224, 221, 216, 206, 200, 190, 183)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1075
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1066 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y2^-1, Y1), R * Y2 * R * Y1, (Y3 * Y2^-1)^2, (Y3 * Y1 * Y2^-1)^2, Y1^-1 * Y2^5 * Y1^-1 * Y2^5 * Y1^-1 * Y2, Y1^-2 * Y2^4 * Y1^-1 * Y2 * Y1^-6, Y1^-2 * Y2^26 ]
Map:: polytopal non-degenerate
	R = (1, 57, 4, 60)(2, 58, 9, 65)(3, 59, 12, 68)(5, 61, 14, 70)(6, 62, 15, 71)(7, 63, 17, 73)(8, 64, 19, 75)(10, 66, 20, 76)(11, 67, 22, 78)(13, 69, 24, 80)(16, 72, 26, 82)(18, 74, 28, 84)(21, 77, 30, 86)(23, 79, 32, 88)(25, 81, 34, 90)(27, 83, 36, 92)(29, 85, 38, 94)(31, 87, 40, 96)(33, 89, 42, 98)(35, 91, 44, 100)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(43, 99, 52, 108)(45, 101, 53, 109)(47, 103, 54, 110)(49, 105, 55, 111)(51, 107, 56, 112)(113, 114, 119, 128, 137, 145, 153, 161, 159, 149, 143, 133, 125, 115, 120, 118, 122, 130, 139, 147, 155, 163, 157, 151, 141, 135, 123, 117)(116, 126, 134, 144, 150, 160, 165, 168, 164, 156, 148, 140, 132, 127, 131, 124, 136, 142, 152, 158, 166, 167, 162, 154, 146, 138, 129, 121)(169, 171, 179, 189, 197, 205, 213, 217, 211, 201, 195, 184, 178, 170, 176, 173, 181, 191, 199, 207, 215, 219, 209, 203, 193, 186, 175, 174)(172, 183, 185, 196, 202, 212, 218, 224, 222, 216, 208, 200, 192, 182, 187, 177, 188, 194, 204, 210, 220, 223, 221, 214, 206, 198, 190, 180)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1076
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1067 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1 * Y3 * Y1)^2, Y3^-3 * Y1 * Y3^-9 * Y1 * Y3^-2 ]
Map::
	R = (1, 57, 113, 169, 3, 59, 115, 171, 8, 64, 120, 176, 17, 73, 129, 185, 26, 82, 138, 194, 34, 90, 146, 202, 42, 98, 154, 210, 50, 106, 162, 218, 55, 111, 167, 223, 47, 103, 159, 215, 39, 95, 151, 207, 31, 87, 143, 199, 23, 79, 135, 191, 13, 69, 125, 181, 21, 77, 133, 189, 11, 67, 123, 179, 20, 76, 132, 188, 29, 85, 141, 197, 37, 93, 149, 205, 45, 101, 157, 213, 53, 109, 165, 221, 52, 108, 164, 220, 44, 100, 156, 212, 36, 92, 148, 204, 28, 84, 140, 196, 19, 75, 131, 187, 10, 66, 122, 178, 4, 60, 116, 172)(2, 58, 114, 170, 5, 61, 117, 173, 12, 68, 124, 180, 22, 78, 134, 190, 30, 86, 142, 198, 38, 94, 150, 206, 46, 102, 158, 214, 54, 110, 166, 222, 51, 107, 163, 219, 43, 99, 155, 211, 35, 91, 147, 203, 27, 83, 139, 195, 18, 74, 130, 186, 9, 65, 121, 177, 16, 72, 128, 184, 7, 63, 119, 175, 15, 71, 127, 183, 25, 81, 137, 193, 33, 89, 145, 201, 41, 97, 153, 209, 49, 105, 161, 217, 56, 112, 168, 224, 48, 104, 160, 216, 40, 96, 152, 208, 32, 88, 144, 200, 24, 80, 136, 192, 14, 70, 126, 182, 6, 62, 118, 174)
	L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 67)(6, 69)(7, 59)(8, 68)(9, 60)(10, 70)(11, 61)(12, 64)(13, 62)(14, 66)(15, 76)(16, 77)(17, 81)(18, 79)(19, 83)(20, 71)(21, 72)(22, 85)(23, 74)(24, 87)(25, 73)(26, 86)(27, 75)(28, 88)(29, 78)(30, 82)(31, 80)(32, 84)(33, 93)(34, 97)(35, 95)(36, 99)(37, 89)(38, 101)(39, 91)(40, 103)(41, 90)(42, 102)(43, 92)(44, 104)(45, 94)(46, 98)(47, 96)(48, 100)(49, 109)(50, 112)(51, 111)(52, 110)(53, 105)(54, 108)(55, 107)(56, 106)(113, 170)(114, 169)(115, 175)(116, 177)(117, 179)(118, 181)(119, 171)(120, 180)(121, 172)(122, 182)(123, 173)(124, 176)(125, 174)(126, 178)(127, 188)(128, 189)(129, 193)(130, 191)(131, 195)(132, 183)(133, 184)(134, 197)(135, 186)(136, 199)(137, 185)(138, 198)(139, 187)(140, 200)(141, 190)(142, 194)(143, 192)(144, 196)(145, 205)(146, 209)(147, 207)(148, 211)(149, 201)(150, 213)(151, 203)(152, 215)(153, 202)(154, 214)(155, 204)(156, 216)(157, 206)(158, 210)(159, 208)(160, 212)(161, 221)(162, 224)(163, 223)(164, 222)(165, 217)(166, 220)(167, 219)(168, 218)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1057
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1068 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y2 * R * Y1, Y3^-2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^3 * Y2 * Y3^-11 * Y1 ]
Map::
	R = (1, 57, 113, 169, 3, 59, 115, 171, 8, 64, 120, 176, 17, 73, 129, 185, 26, 82, 138, 194, 34, 90, 146, 202, 42, 98, 154, 210, 50, 106, 162, 218, 53, 109, 165, 221, 45, 101, 157, 213, 37, 93, 149, 205, 29, 85, 141, 197, 21, 77, 133, 189, 11, 67, 123, 179, 20, 76, 132, 188, 13, 69, 125, 181, 23, 79, 135, 191, 31, 87, 143, 199, 39, 95, 151, 207, 47, 103, 159, 215, 55, 111, 167, 223, 52, 108, 164, 220, 44, 100, 156, 212, 36, 92, 148, 204, 28, 84, 140, 196, 19, 75, 131, 187, 10, 66, 122, 178, 4, 60, 116, 172)(2, 58, 114, 170, 5, 61, 117, 173, 12, 68, 124, 180, 22, 78, 134, 190, 30, 86, 142, 198, 38, 94, 150, 206, 46, 102, 158, 214, 54, 110, 166, 222, 49, 105, 161, 217, 41, 97, 153, 209, 33, 89, 145, 201, 25, 81, 137, 193, 16, 72, 128, 184, 7, 63, 119, 175, 15, 71, 127, 183, 9, 65, 121, 177, 18, 74, 130, 186, 27, 83, 139, 195, 35, 91, 147, 203, 43, 99, 155, 211, 51, 107, 163, 219, 56, 112, 168, 224, 48, 104, 160, 216, 40, 96, 152, 208, 32, 88, 144, 200, 24, 80, 136, 192, 14, 70, 126, 182, 6, 62, 118, 174)
	L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 67)(6, 69)(7, 59)(8, 70)(9, 60)(10, 68)(11, 61)(12, 66)(13, 62)(14, 64)(15, 76)(16, 79)(17, 81)(18, 77)(19, 83)(20, 71)(21, 74)(22, 85)(23, 72)(24, 87)(25, 73)(26, 88)(27, 75)(28, 86)(29, 78)(30, 84)(31, 80)(32, 82)(33, 95)(34, 97)(35, 93)(36, 99)(37, 91)(38, 101)(39, 89)(40, 103)(41, 90)(42, 104)(43, 92)(44, 102)(45, 94)(46, 100)(47, 96)(48, 98)(49, 111)(50, 110)(51, 109)(52, 112)(53, 107)(54, 106)(55, 105)(56, 108)(113, 170)(114, 169)(115, 175)(116, 177)(117, 179)(118, 181)(119, 171)(120, 182)(121, 172)(122, 180)(123, 173)(124, 178)(125, 174)(126, 176)(127, 188)(128, 191)(129, 193)(130, 189)(131, 195)(132, 183)(133, 186)(134, 197)(135, 184)(136, 199)(137, 185)(138, 200)(139, 187)(140, 198)(141, 190)(142, 196)(143, 192)(144, 194)(145, 207)(146, 209)(147, 205)(148, 211)(149, 203)(150, 213)(151, 201)(152, 215)(153, 202)(154, 216)(155, 204)(156, 214)(157, 206)(158, 212)(159, 208)(160, 210)(161, 223)(162, 222)(163, 221)(164, 224)(165, 219)(166, 218)(167, 217)(168, 220)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1058
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1069 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^2 * Y2)^2, Y3^-3 * Y2 * Y1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y2, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 14, 70, 126, 182, 29, 85, 141, 197, 9, 65, 121, 177, 28, 84, 140, 196, 50, 106, 162, 218, 55, 111, 167, 223, 47, 103, 159, 215, 22, 78, 134, 190, 46, 102, 158, 214, 25, 81, 137, 193, 45, 101, 157, 213, 21, 77, 133, 189, 44, 100, 156, 212, 24, 80, 136, 192, 48, 104, 160, 216, 30, 86, 142, 198, 52, 108, 164, 220, 31, 87, 143, 199, 38, 94, 150, 206, 53, 109, 165, 221, 43, 99, 155, 211, 20, 76, 132, 188, 6, 62, 118, 174, 19, 75, 131, 187, 17, 73, 129, 185, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 23, 79, 135, 191, 40, 96, 152, 208, 18, 74, 130, 186, 39, 95, 151, 207, 54, 110, 166, 222, 51, 107, 163, 219, 36, 92, 148, 204, 13, 69, 125, 181, 35, 91, 147, 203, 16, 72, 128, 184, 34, 90, 146, 202, 12, 68, 124, 180, 33, 89, 145, 201, 15, 71, 127, 183, 37, 93, 149, 205, 41, 97, 153, 209, 56, 112, 168, 224, 42, 98, 154, 210, 27, 83, 139, 195, 49, 105, 161, 217, 32, 88, 144, 200, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 26, 82, 138, 194, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 68)(5, 71)(6, 74)(7, 77)(8, 80)(9, 59)(10, 86)(11, 87)(12, 60)(13, 84)(14, 82)(15, 61)(16, 85)(17, 79)(18, 62)(19, 97)(20, 98)(21, 63)(22, 95)(23, 73)(24, 64)(25, 96)(26, 70)(27, 103)(28, 69)(29, 72)(30, 66)(31, 67)(32, 106)(33, 100)(34, 104)(35, 108)(36, 94)(37, 101)(38, 92)(39, 78)(40, 81)(41, 75)(42, 76)(43, 110)(44, 89)(45, 93)(46, 112)(47, 83)(48, 90)(49, 109)(50, 88)(51, 111)(52, 91)(53, 105)(54, 99)(55, 107)(56, 102)(113, 171)(114, 174)(115, 169)(116, 181)(117, 184)(118, 170)(119, 190)(120, 193)(121, 195)(122, 189)(123, 192)(124, 187)(125, 172)(126, 200)(127, 188)(128, 173)(129, 194)(130, 206)(131, 180)(132, 183)(133, 178)(134, 175)(135, 211)(136, 179)(137, 176)(138, 185)(139, 177)(140, 207)(141, 219)(142, 217)(143, 210)(144, 182)(145, 214)(146, 213)(147, 212)(148, 216)(149, 215)(150, 186)(151, 196)(152, 223)(153, 221)(154, 199)(155, 191)(156, 203)(157, 202)(158, 201)(159, 205)(160, 204)(161, 198)(162, 224)(163, 197)(164, 222)(165, 209)(166, 220)(167, 208)(168, 218)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1060
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1070 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-2 * Y1 * Y2 * Y3^-2, Y1 * Y2 * Y3 * Y2 * Y1 * Y3^-1, Y2 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 14, 70, 126, 182, 20, 76, 132, 188, 6, 62, 118, 174, 19, 75, 131, 187, 42, 98, 154, 210, 53, 109, 165, 221, 38, 94, 150, 206, 30, 86, 142, 198, 52, 108, 164, 220, 32, 88, 144, 200, 45, 101, 157, 213, 21, 77, 133, 189, 44, 100, 156, 212, 24, 80, 136, 192, 47, 103, 159, 215, 22, 78, 134, 190, 46, 102, 158, 214, 25, 81, 137, 193, 48, 104, 160, 216, 54, 110, 166, 222, 51, 107, 163, 219, 29, 85, 141, 197, 9, 65, 121, 177, 28, 84, 140, 196, 17, 73, 129, 185, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 23, 79, 135, 191, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 31, 87, 143, 199, 49, 105, 161, 217, 27, 83, 139, 195, 41, 97, 153, 209, 56, 112, 168, 224, 43, 99, 155, 211, 34, 90, 146, 202, 12, 68, 124, 180, 33, 89, 145, 201, 15, 71, 127, 183, 36, 92, 148, 204, 13, 69, 125, 181, 35, 91, 147, 203, 16, 72, 128, 184, 37, 93, 149, 205, 50, 106, 162, 218, 55, 111, 167, 223, 40, 96, 152, 208, 18, 74, 130, 186, 39, 95, 151, 207, 26, 82, 138, 194, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 68)(5, 71)(6, 74)(7, 77)(8, 80)(9, 59)(10, 86)(11, 88)(12, 60)(13, 84)(14, 82)(15, 61)(16, 85)(17, 79)(18, 62)(19, 97)(20, 99)(21, 63)(22, 95)(23, 73)(24, 64)(25, 96)(26, 70)(27, 104)(28, 69)(29, 72)(30, 66)(31, 107)(32, 67)(33, 100)(34, 103)(35, 108)(36, 101)(37, 94)(38, 93)(39, 78)(40, 81)(41, 75)(42, 111)(43, 76)(44, 89)(45, 92)(46, 112)(47, 90)(48, 83)(49, 109)(50, 110)(51, 87)(52, 91)(53, 105)(54, 106)(55, 98)(56, 102)(113, 171)(114, 174)(115, 169)(116, 181)(117, 184)(118, 170)(119, 190)(120, 193)(121, 195)(122, 189)(123, 192)(124, 187)(125, 172)(126, 191)(127, 188)(128, 173)(129, 199)(130, 206)(131, 180)(132, 183)(133, 178)(134, 175)(135, 182)(136, 179)(137, 176)(138, 210)(139, 177)(140, 218)(141, 208)(142, 209)(143, 185)(144, 217)(145, 214)(146, 216)(147, 212)(148, 215)(149, 213)(150, 186)(151, 222)(152, 197)(153, 198)(154, 194)(155, 221)(156, 203)(157, 205)(158, 201)(159, 204)(160, 202)(161, 200)(162, 196)(163, 224)(164, 223)(165, 211)(166, 207)(167, 220)(168, 219)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1059
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1071 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2, Y3^6 * Y2 * Y3^-8 * Y1 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 11, 67, 123, 179, 19, 75, 131, 187, 27, 83, 139, 195, 35, 91, 147, 203, 43, 99, 155, 211, 51, 107, 163, 219, 54, 110, 166, 222, 46, 102, 158, 214, 38, 94, 150, 206, 30, 86, 142, 198, 22, 78, 134, 190, 14, 70, 126, 182, 6, 62, 118, 174, 13, 69, 125, 181, 21, 77, 133, 189, 29, 85, 141, 197, 37, 93, 149, 205, 45, 101, 157, 213, 53, 109, 165, 221, 52, 108, 164, 220, 44, 100, 156, 212, 36, 92, 148, 204, 28, 84, 140, 196, 20, 76, 132, 188, 12, 68, 124, 180, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 15, 71, 127, 183, 23, 79, 135, 191, 31, 87, 143, 199, 39, 95, 151, 207, 47, 103, 159, 215, 55, 111, 167, 223, 50, 106, 162, 218, 42, 98, 154, 210, 34, 90, 146, 202, 26, 82, 138, 194, 18, 74, 130, 186, 10, 66, 122, 178, 3, 59, 115, 171, 9, 65, 121, 177, 17, 73, 129, 185, 25, 81, 137, 193, 33, 89, 145, 201, 41, 97, 153, 209, 49, 105, 161, 217, 56, 112, 168, 224, 48, 104, 160, 216, 40, 96, 152, 208, 32, 88, 144, 200, 24, 80, 136, 192, 16, 72, 128, 184, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 62)(4, 66)(5, 65)(6, 59)(7, 70)(8, 69)(9, 61)(10, 60)(11, 72)(12, 71)(13, 64)(14, 63)(15, 68)(16, 67)(17, 78)(18, 77)(19, 82)(20, 81)(21, 74)(22, 73)(23, 86)(24, 85)(25, 76)(26, 75)(27, 88)(28, 87)(29, 80)(30, 79)(31, 84)(32, 83)(33, 94)(34, 93)(35, 98)(36, 97)(37, 90)(38, 89)(39, 102)(40, 101)(41, 92)(42, 91)(43, 104)(44, 103)(45, 96)(46, 95)(47, 100)(48, 99)(49, 110)(50, 109)(51, 111)(52, 112)(53, 106)(54, 105)(55, 107)(56, 108)(113, 171)(114, 174)(115, 169)(116, 176)(117, 175)(118, 170)(119, 173)(120, 172)(121, 182)(122, 181)(123, 186)(124, 185)(125, 178)(126, 177)(127, 190)(128, 189)(129, 180)(130, 179)(131, 192)(132, 191)(133, 184)(134, 183)(135, 188)(136, 187)(137, 198)(138, 197)(139, 202)(140, 201)(141, 194)(142, 193)(143, 206)(144, 205)(145, 196)(146, 195)(147, 208)(148, 207)(149, 200)(150, 199)(151, 204)(152, 203)(153, 214)(154, 213)(155, 218)(156, 217)(157, 210)(158, 209)(159, 222)(160, 221)(161, 212)(162, 211)(163, 224)(164, 223)(165, 216)(166, 215)(167, 220)(168, 219)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1061
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1072 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^3 * Y1 * Y3^-1 * Y2, Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y2, (Y3^2 * Y2)^2, (Y1 * Y3^2)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1, Y3 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2, Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^84 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 14, 70, 126, 182, 30, 86, 142, 198, 51, 107, 163, 219, 32, 88, 144, 200, 52, 108, 164, 220, 54, 110, 166, 222, 44, 100, 156, 212, 20, 76, 132, 188, 6, 62, 118, 174, 19, 75, 131, 187, 42, 98, 154, 210, 21, 77, 133, 189, 45, 101, 157, 213, 24, 80, 136, 192, 48, 104, 160, 216, 29, 85, 141, 197, 9, 65, 121, 177, 28, 84, 140, 196, 38, 94, 150, 206, 53, 109, 165, 221, 47, 103, 159, 215, 22, 78, 134, 190, 46, 102, 158, 214, 25, 81, 137, 193, 17, 73, 129, 185, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 23, 79, 135, 191, 41, 97, 153, 209, 55, 111, 167, 223, 43, 99, 155, 211, 56, 112, 168, 224, 50, 106, 162, 218, 33, 89, 145, 201, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 31, 87, 143, 199, 12, 68, 124, 180, 34, 90, 146, 202, 15, 71, 127, 183, 37, 93, 149, 205, 40, 96, 152, 208, 18, 74, 130, 186, 39, 95, 151, 207, 27, 83, 139, 195, 49, 105, 161, 217, 36, 92, 148, 204, 13, 69, 125, 181, 35, 91, 147, 203, 16, 72, 128, 184, 26, 82, 138, 194, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 68)(5, 71)(6, 74)(7, 77)(8, 80)(9, 59)(10, 86)(11, 88)(12, 60)(13, 84)(14, 82)(15, 61)(16, 85)(17, 79)(18, 62)(19, 97)(20, 99)(21, 63)(22, 95)(23, 73)(24, 64)(25, 96)(26, 70)(27, 100)(28, 69)(29, 72)(30, 66)(31, 104)(32, 67)(33, 94)(34, 101)(35, 107)(36, 108)(37, 98)(38, 89)(39, 78)(40, 81)(41, 75)(42, 93)(43, 76)(44, 83)(45, 90)(46, 111)(47, 112)(48, 87)(49, 109)(50, 110)(51, 91)(52, 92)(53, 105)(54, 106)(55, 102)(56, 103)(113, 171)(114, 174)(115, 169)(116, 181)(117, 184)(118, 170)(119, 190)(120, 193)(121, 195)(122, 189)(123, 192)(124, 187)(125, 172)(126, 201)(127, 188)(128, 173)(129, 199)(130, 206)(131, 180)(132, 183)(133, 178)(134, 175)(135, 212)(136, 179)(137, 176)(138, 210)(139, 177)(140, 211)(141, 218)(142, 217)(143, 185)(144, 207)(145, 182)(146, 214)(147, 213)(148, 216)(149, 215)(150, 186)(151, 200)(152, 222)(153, 221)(154, 194)(155, 196)(156, 191)(157, 203)(158, 202)(159, 205)(160, 204)(161, 198)(162, 197)(163, 224)(164, 223)(165, 209)(166, 208)(167, 220)(168, 219)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1063
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1073 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = (C4 x D14) : C2 (small group id <112, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2, Y3 * Y1 * Y2 * Y3^-1 * Y2 * Y1, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1, Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y3 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 14, 70, 126, 182, 22, 78, 134, 190, 47, 103, 159, 215, 25, 81, 137, 193, 48, 104, 160, 216, 53, 109, 165, 221, 38, 94, 150, 206, 29, 85, 141, 197, 9, 65, 121, 177, 28, 84, 140, 196, 46, 102, 158, 214, 21, 77, 133, 189, 45, 101, 157, 213, 24, 80, 136, 192, 44, 100, 156, 212, 20, 76, 132, 188, 6, 62, 118, 174, 19, 75, 131, 187, 42, 98, 154, 210, 54, 110, 166, 222, 52, 108, 164, 220, 30, 86, 142, 198, 51, 107, 163, 219, 32, 88, 144, 200, 17, 73, 129, 185, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 23, 79, 135, 191, 13, 69, 125, 181, 36, 92, 148, 204, 16, 72, 128, 184, 37, 93, 149, 205, 49, 105, 161, 217, 27, 83, 139, 195, 40, 96, 152, 208, 18, 74, 130, 186, 39, 95, 151, 207, 35, 91, 147, 203, 12, 68, 124, 180, 34, 90, 146, 202, 15, 71, 127, 183, 33, 89, 145, 201, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 31, 87, 143, 199, 50, 106, 162, 218, 56, 112, 168, 224, 41, 97, 153, 209, 55, 111, 167, 223, 43, 99, 155, 211, 26, 82, 138, 194, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 68)(5, 71)(6, 74)(7, 77)(8, 80)(9, 59)(10, 86)(11, 88)(12, 60)(13, 84)(14, 82)(15, 61)(16, 85)(17, 79)(18, 62)(19, 97)(20, 99)(21, 63)(22, 95)(23, 73)(24, 64)(25, 96)(26, 70)(27, 98)(28, 69)(29, 72)(30, 66)(31, 94)(32, 67)(33, 102)(34, 101)(35, 100)(36, 107)(37, 108)(38, 87)(39, 78)(40, 81)(41, 75)(42, 83)(43, 76)(44, 91)(45, 90)(46, 89)(47, 111)(48, 112)(49, 109)(50, 110)(51, 92)(52, 93)(53, 105)(54, 106)(55, 103)(56, 104)(113, 171)(114, 174)(115, 169)(116, 181)(117, 184)(118, 170)(119, 190)(120, 193)(121, 195)(122, 189)(123, 192)(124, 187)(125, 172)(126, 201)(127, 188)(128, 173)(129, 199)(130, 206)(131, 180)(132, 183)(133, 178)(134, 175)(135, 212)(136, 179)(137, 176)(138, 210)(139, 177)(140, 218)(141, 209)(142, 208)(143, 185)(144, 217)(145, 182)(146, 215)(147, 216)(148, 213)(149, 214)(150, 186)(151, 222)(152, 198)(153, 197)(154, 194)(155, 221)(156, 191)(157, 204)(158, 205)(159, 202)(160, 203)(161, 200)(162, 196)(163, 224)(164, 223)(165, 211)(166, 207)(167, 220)(168, 219)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1062
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1074 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = C2 x C4 x D14 (small group id <112, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y2^5 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-4 * Y2 * Y1^-1, Y1^28, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 6, 62, 118, 174)(3, 59, 115, 171, 8, 64, 120, 176)(5, 61, 117, 173, 12, 68, 124, 180)(7, 63, 119, 175, 16, 72, 128, 184)(9, 65, 121, 177, 18, 74, 130, 186)(10, 66, 122, 178, 19, 75, 131, 187)(11, 67, 123, 179, 21, 77, 133, 189)(13, 69, 125, 181, 23, 79, 135, 191)(14, 70, 126, 182, 24, 80, 136, 192)(15, 71, 127, 183, 26, 82, 138, 194)(17, 73, 129, 185, 28, 84, 140, 196)(20, 76, 132, 188, 30, 86, 142, 198)(22, 78, 134, 190, 32, 88, 144, 200)(25, 81, 137, 193, 34, 90, 146, 202)(27, 83, 139, 195, 36, 92, 148, 204)(29, 85, 141, 197, 38, 94, 150, 206)(31, 87, 143, 199, 40, 96, 152, 208)(33, 89, 145, 201, 42, 98, 154, 210)(35, 91, 147, 203, 44, 100, 156, 212)(37, 93, 149, 205, 46, 102, 158, 214)(39, 95, 151, 207, 48, 104, 160, 216)(41, 97, 153, 209, 50, 106, 162, 218)(43, 99, 155, 211, 52, 108, 164, 220)(45, 101, 157, 213, 54, 110, 166, 222)(47, 103, 159, 215, 56, 112, 168, 224)(49, 105, 161, 217, 55, 111, 167, 223)(51, 107, 163, 219, 53, 109, 165, 221)
	L = (1, 58)(2, 61)(3, 57)(4, 65)(5, 67)(6, 69)(7, 59)(8, 73)(9, 72)(10, 60)(11, 76)(12, 66)(13, 64)(14, 62)(15, 63)(16, 83)(17, 82)(18, 79)(19, 80)(20, 85)(21, 70)(22, 68)(23, 75)(24, 88)(25, 71)(26, 91)(27, 90)(28, 74)(29, 93)(30, 78)(31, 77)(32, 96)(33, 81)(34, 99)(35, 98)(36, 84)(37, 101)(38, 87)(39, 86)(40, 104)(41, 89)(42, 107)(43, 106)(44, 92)(45, 109)(46, 95)(47, 94)(48, 112)(49, 97)(50, 110)(51, 111)(52, 100)(53, 108)(54, 103)(55, 102)(56, 105)(113, 171)(114, 169)(115, 175)(116, 178)(117, 170)(118, 182)(119, 183)(120, 181)(121, 172)(122, 180)(123, 173)(124, 190)(125, 174)(126, 189)(127, 193)(128, 177)(129, 176)(130, 196)(131, 191)(132, 179)(133, 199)(134, 198)(135, 186)(136, 187)(137, 201)(138, 185)(139, 184)(140, 204)(141, 188)(142, 207)(143, 206)(144, 192)(145, 209)(146, 195)(147, 194)(148, 212)(149, 197)(150, 215)(151, 214)(152, 200)(153, 217)(154, 203)(155, 202)(156, 220)(157, 205)(158, 223)(159, 222)(160, 208)(161, 224)(162, 211)(163, 210)(164, 221)(165, 213)(166, 218)(167, 219)(168, 216)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1064
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1075 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-2 * Y1^-2, (Y1, Y2^-1), R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y3, Y1^-7 * Y2^7, Y1^28, Y2^28 ]
Map:: polytopal non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 9, 65, 121, 177)(3, 59, 115, 171, 12, 68, 124, 180)(5, 61, 117, 173, 15, 71, 127, 183)(6, 62, 118, 174, 14, 70, 126, 182)(7, 63, 119, 175, 17, 73, 129, 185)(8, 64, 120, 176, 19, 75, 131, 187)(10, 66, 122, 178, 20, 76, 132, 188)(11, 67, 123, 179, 22, 78, 134, 190)(13, 69, 125, 181, 24, 80, 136, 192)(16, 72, 128, 184, 26, 82, 138, 194)(18, 74, 130, 186, 28, 84, 140, 196)(21, 77, 133, 189, 30, 86, 142, 198)(23, 79, 135, 191, 32, 88, 144, 200)(25, 81, 137, 193, 34, 90, 146, 202)(27, 83, 139, 195, 36, 92, 148, 204)(29, 85, 141, 197, 38, 94, 150, 206)(31, 87, 143, 199, 40, 96, 152, 208)(33, 89, 145, 201, 42, 98, 154, 210)(35, 91, 147, 203, 44, 100, 156, 212)(37, 93, 149, 205, 46, 102, 158, 214)(39, 95, 151, 207, 48, 104, 160, 216)(41, 97, 153, 209, 50, 106, 162, 218)(43, 99, 155, 211, 52, 108, 164, 220)(45, 101, 157, 213, 53, 109, 165, 221)(47, 103, 159, 215, 54, 110, 166, 222)(49, 105, 161, 217, 55, 111, 167, 223)(51, 107, 163, 219, 56, 112, 168, 224)
	L = (1, 58)(2, 63)(3, 64)(4, 68)(5, 57)(6, 66)(7, 72)(8, 62)(9, 75)(10, 74)(11, 61)(12, 78)(13, 59)(14, 60)(15, 80)(16, 81)(17, 70)(18, 83)(19, 71)(20, 65)(21, 69)(22, 86)(23, 67)(24, 88)(25, 89)(26, 76)(27, 91)(28, 73)(29, 79)(30, 94)(31, 77)(32, 96)(33, 97)(34, 84)(35, 99)(36, 82)(37, 87)(38, 102)(39, 85)(40, 104)(41, 105)(42, 92)(43, 107)(44, 90)(45, 95)(46, 109)(47, 93)(48, 110)(49, 103)(50, 100)(51, 101)(52, 98)(53, 111)(54, 112)(55, 108)(56, 106)(113, 171)(114, 176)(115, 179)(116, 177)(117, 181)(118, 169)(119, 174)(120, 173)(121, 185)(122, 170)(123, 189)(124, 187)(125, 191)(126, 188)(127, 172)(128, 178)(129, 194)(130, 175)(131, 182)(132, 196)(133, 197)(134, 183)(135, 199)(136, 180)(137, 186)(138, 202)(139, 184)(140, 204)(141, 205)(142, 192)(143, 207)(144, 190)(145, 195)(146, 210)(147, 193)(148, 212)(149, 213)(150, 200)(151, 215)(152, 198)(153, 203)(154, 218)(155, 201)(156, 220)(157, 217)(158, 208)(159, 219)(160, 206)(161, 211)(162, 223)(163, 209)(164, 224)(165, 216)(166, 214)(167, 222)(168, 221)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1065
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1076 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-2 * Y1^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y2^-1, Y1), R * Y2 * R * Y1, (Y3 * Y2^-1)^2, (Y3 * Y1 * Y2^-1)^2, Y1^-1 * Y2^5 * Y1^-1 * Y2^5 * Y1^-1 * Y2, Y1^-2 * Y2^4 * Y1^-1 * Y2 * Y1^-6, Y1^-2 * Y2^26 ]
Map:: polytopal non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 9, 65, 121, 177)(3, 59, 115, 171, 12, 68, 124, 180)(5, 61, 117, 173, 14, 70, 126, 182)(6, 62, 118, 174, 15, 71, 127, 183)(7, 63, 119, 175, 17, 73, 129, 185)(8, 64, 120, 176, 19, 75, 131, 187)(10, 66, 122, 178, 20, 76, 132, 188)(11, 67, 123, 179, 22, 78, 134, 190)(13, 69, 125, 181, 24, 80, 136, 192)(16, 72, 128, 184, 26, 82, 138, 194)(18, 74, 130, 186, 28, 84, 140, 196)(21, 77, 133, 189, 30, 86, 142, 198)(23, 79, 135, 191, 32, 88, 144, 200)(25, 81, 137, 193, 34, 90, 146, 202)(27, 83, 139, 195, 36, 92, 148, 204)(29, 85, 141, 197, 38, 94, 150, 206)(31, 87, 143, 199, 40, 96, 152, 208)(33, 89, 145, 201, 42, 98, 154, 210)(35, 91, 147, 203, 44, 100, 156, 212)(37, 93, 149, 205, 46, 102, 158, 214)(39, 95, 151, 207, 48, 104, 160, 216)(41, 97, 153, 209, 50, 106, 162, 218)(43, 99, 155, 211, 52, 108, 164, 220)(45, 101, 157, 213, 53, 109, 165, 221)(47, 103, 159, 215, 54, 110, 166, 222)(49, 105, 161, 217, 55, 111, 167, 223)(51, 107, 163, 219, 56, 112, 168, 224)
	L = (1, 58)(2, 63)(3, 64)(4, 70)(5, 57)(6, 66)(7, 72)(8, 62)(9, 60)(10, 74)(11, 61)(12, 80)(13, 59)(14, 78)(15, 75)(16, 81)(17, 65)(18, 83)(19, 68)(20, 71)(21, 69)(22, 88)(23, 67)(24, 86)(25, 89)(26, 73)(27, 91)(28, 76)(29, 79)(30, 96)(31, 77)(32, 94)(33, 97)(34, 82)(35, 99)(36, 84)(37, 87)(38, 104)(39, 85)(40, 102)(41, 105)(42, 90)(43, 107)(44, 92)(45, 95)(46, 110)(47, 93)(48, 109)(49, 103)(50, 98)(51, 101)(52, 100)(53, 112)(54, 111)(55, 106)(56, 108)(113, 171)(114, 176)(115, 179)(116, 183)(117, 181)(118, 169)(119, 174)(120, 173)(121, 188)(122, 170)(123, 189)(124, 172)(125, 191)(126, 187)(127, 185)(128, 178)(129, 196)(130, 175)(131, 177)(132, 194)(133, 197)(134, 180)(135, 199)(136, 182)(137, 186)(138, 204)(139, 184)(140, 202)(141, 205)(142, 190)(143, 207)(144, 192)(145, 195)(146, 212)(147, 193)(148, 210)(149, 213)(150, 198)(151, 215)(152, 200)(153, 203)(154, 220)(155, 201)(156, 218)(157, 217)(158, 206)(159, 219)(160, 208)(161, 211)(162, 224)(163, 209)(164, 223)(165, 214)(166, 216)(167, 221)(168, 222)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1066
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1077 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * Y1 * Y2 * Y1)^2, Y2^13 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 11, 67)(6, 62, 13, 69)(8, 64, 12, 68)(10, 66, 14, 70)(15, 71, 20, 76)(16, 72, 21, 77)(17, 73, 25, 81)(18, 74, 23, 79)(19, 75, 27, 83)(22, 78, 29, 85)(24, 80, 31, 87)(26, 82, 30, 86)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 41, 97)(35, 91, 39, 95)(36, 92, 43, 99)(38, 94, 45, 101)(40, 96, 47, 103)(42, 98, 46, 102)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 56, 112)(51, 107, 55, 111)(52, 108, 54, 110)(113, 169, 115, 171, 120, 176, 129, 185, 138, 194, 146, 202, 154, 210, 162, 218, 167, 223, 159, 215, 151, 207, 143, 199, 135, 191, 125, 181, 133, 189, 123, 179, 132, 188, 141, 197, 149, 205, 157, 213, 165, 221, 164, 220, 156, 212, 148, 204, 140, 196, 131, 187, 122, 178, 116, 172)(114, 170, 117, 173, 124, 180, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 163, 219, 155, 211, 147, 203, 139, 195, 130, 186, 121, 177, 128, 184, 119, 175, 127, 183, 137, 193, 145, 201, 153, 209, 161, 217, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 126, 182, 118, 174)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1078 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, (Y2^-1 * Y1)^4, Y2^11 * Y1 * Y2^-3 * Y1, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 11, 67)(6, 62, 13, 69)(8, 64, 14, 70)(10, 66, 12, 68)(15, 71, 20, 76)(16, 72, 23, 79)(17, 73, 25, 81)(18, 74, 21, 77)(19, 75, 27, 83)(22, 78, 29, 85)(24, 80, 31, 87)(26, 82, 32, 88)(28, 84, 30, 86)(33, 89, 39, 95)(34, 90, 41, 97)(35, 91, 37, 93)(36, 92, 43, 99)(38, 94, 45, 101)(40, 96, 47, 103)(42, 98, 48, 104)(44, 100, 46, 102)(49, 105, 55, 111)(50, 106, 54, 110)(51, 107, 53, 109)(52, 108, 56, 112)(113, 169, 115, 171, 120, 176, 129, 185, 138, 194, 146, 202, 154, 210, 162, 218, 165, 221, 157, 213, 149, 205, 141, 197, 133, 189, 123, 179, 132, 188, 125, 181, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 164, 220, 156, 212, 148, 204, 140, 196, 131, 187, 122, 178, 116, 172)(114, 170, 117, 173, 124, 180, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 161, 217, 153, 209, 145, 201, 137, 193, 128, 184, 119, 175, 127, 183, 121, 177, 130, 186, 139, 195, 147, 203, 155, 211, 163, 219, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 126, 182, 118, 174)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1079 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2^-1, Y3 * Y2^14, (Y2^7 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 7, 63)(5, 61, 13, 69)(6, 62, 11, 67)(8, 64, 12, 68)(10, 66, 15, 71)(14, 70, 16, 72)(17, 73, 19, 75)(18, 74, 25, 81)(20, 76, 21, 77)(22, 78, 29, 85)(23, 79, 27, 83)(24, 80, 28, 84)(26, 82, 31, 87)(30, 86, 32, 88)(33, 89, 35, 91)(34, 90, 41, 97)(36, 92, 37, 93)(38, 94, 45, 101)(39, 95, 43, 99)(40, 96, 44, 100)(42, 98, 47, 103)(46, 102, 48, 104)(49, 105, 51, 107)(50, 106, 56, 112)(52, 108, 53, 109)(54, 110, 55, 111)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 116, 172, 123, 179, 131, 187, 139, 195, 147, 203, 155, 211, 163, 219, 166, 222, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182, 117, 173)(114, 170, 118, 174, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 165, 221, 157, 213, 149, 205, 141, 197, 133, 189, 125, 181, 119, 175, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)
	L = (1, 116)(2, 119)(3, 123)(4, 113)(5, 124)(6, 121)(7, 114)(8, 125)(9, 118)(10, 131)(11, 115)(12, 117)(13, 120)(14, 132)(15, 129)(16, 133)(17, 127)(18, 139)(19, 122)(20, 126)(21, 128)(22, 140)(23, 137)(24, 141)(25, 135)(26, 147)(27, 130)(28, 134)(29, 136)(30, 148)(31, 145)(32, 149)(33, 143)(34, 155)(35, 138)(36, 142)(37, 144)(38, 156)(39, 153)(40, 157)(41, 151)(42, 163)(43, 146)(44, 150)(45, 152)(46, 164)(47, 161)(48, 165)(49, 159)(50, 166)(51, 154)(52, 158)(53, 160)(54, 162)(55, 168)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1080 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2, Y3 * Y2^14, Y2^7 * Y1 * Y2^-7 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 7, 63)(5, 61, 13, 69)(6, 62, 12, 68)(8, 64, 11, 67)(10, 66, 16, 72)(14, 70, 15, 71)(17, 73, 19, 75)(18, 74, 25, 81)(20, 76, 21, 77)(22, 78, 29, 85)(23, 79, 28, 84)(24, 80, 27, 83)(26, 82, 32, 88)(30, 86, 31, 87)(33, 89, 35, 91)(34, 90, 41, 97)(36, 92, 37, 93)(38, 94, 45, 101)(39, 95, 44, 100)(40, 96, 43, 99)(42, 98, 48, 104)(46, 102, 47, 103)(49, 105, 51, 107)(50, 106, 55, 111)(52, 108, 53, 109)(54, 110, 56, 112)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 116, 172, 123, 179, 131, 187, 139, 195, 147, 203, 155, 211, 163, 219, 166, 222, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182, 117, 173)(114, 170, 118, 174, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 167, 223, 161, 217, 153, 209, 145, 201, 137, 193, 129, 185, 121, 177, 119, 175, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)
	L = (1, 116)(2, 119)(3, 123)(4, 113)(5, 124)(6, 125)(7, 114)(8, 121)(9, 120)(10, 131)(11, 115)(12, 117)(13, 118)(14, 132)(15, 133)(16, 129)(17, 128)(18, 139)(19, 122)(20, 126)(21, 127)(22, 140)(23, 141)(24, 137)(25, 136)(26, 147)(27, 130)(28, 134)(29, 135)(30, 148)(31, 149)(32, 145)(33, 144)(34, 155)(35, 138)(36, 142)(37, 143)(38, 156)(39, 157)(40, 153)(41, 152)(42, 163)(43, 146)(44, 150)(45, 151)(46, 164)(47, 165)(48, 161)(49, 160)(50, 166)(51, 154)(52, 158)(53, 159)(54, 162)(55, 168)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1081 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3^-2 * Y2^-1 * Y1, (Y2^-1 * Y1 * Y2^-1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1, Y2^4 * Y3^-3, Y3^7 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 23, 79)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 39, 95)(18, 74, 22, 78)(19, 75, 29, 85)(20, 76, 25, 81)(24, 80, 45, 101)(26, 82, 52, 108)(31, 87, 44, 100)(33, 89, 51, 107)(34, 90, 55, 111)(35, 91, 53, 109)(36, 92, 54, 110)(37, 93, 56, 112)(38, 94, 46, 102)(40, 96, 48, 104)(41, 97, 49, 105)(42, 98, 47, 103)(43, 99, 50, 106)(113, 169, 115, 171, 124, 180, 145, 201, 149, 205, 157, 213, 154, 210, 131, 187, 118, 174, 126, 182, 147, 203, 150, 206, 127, 183, 133, 189, 156, 212, 139, 195, 132, 188, 148, 204, 152, 208, 128, 184, 116, 172, 125, 181, 146, 202, 164, 220, 155, 211, 153, 209, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 158, 214, 162, 218, 144, 200, 167, 223, 141, 197, 122, 178, 136, 192, 160, 216, 163, 219, 137, 193, 123, 179, 143, 199, 129, 185, 142, 198, 161, 217, 165, 221, 138, 194, 120, 176, 135, 191, 159, 215, 151, 207, 168, 224, 166, 222, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 146)(13, 133)(14, 115)(15, 149)(16, 150)(17, 141)(18, 152)(19, 117)(20, 118)(21, 157)(22, 159)(23, 123)(24, 119)(25, 162)(26, 163)(27, 131)(28, 165)(29, 121)(30, 122)(31, 167)(32, 166)(33, 164)(34, 156)(35, 124)(36, 126)(37, 155)(38, 145)(39, 129)(40, 147)(41, 148)(42, 130)(43, 132)(44, 154)(45, 153)(46, 151)(47, 143)(48, 134)(49, 136)(50, 168)(51, 158)(52, 139)(53, 160)(54, 161)(55, 140)(56, 142)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1085
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1082 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y2^-1, Y2^-4 * Y3^2, (Y2^-2 * Y1)^2, Y3^7, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^3 * Y2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 14, 70)(9, 65, 16, 72)(12, 68, 24, 80)(13, 69, 28, 84)(15, 71, 26, 82)(18, 74, 21, 77)(19, 75, 35, 91)(20, 76, 23, 79)(22, 78, 33, 89)(25, 81, 29, 85)(27, 83, 31, 87)(30, 86, 42, 98)(32, 88, 45, 101)(34, 90, 44, 100)(36, 92, 39, 95)(37, 93, 50, 106)(38, 94, 41, 97)(40, 96, 49, 105)(43, 99, 46, 102)(47, 103, 55, 111)(48, 104, 54, 110)(51, 107, 53, 109)(52, 108, 56, 112)(113, 169, 115, 171, 124, 180, 141, 197, 127, 183, 144, 200, 159, 215, 164, 220, 150, 206, 161, 217, 148, 204, 131, 187, 118, 174, 126, 182, 143, 199, 128, 184, 116, 172, 125, 181, 142, 198, 158, 214, 146, 202, 160, 216, 163, 219, 149, 205, 132, 188, 145, 201, 130, 186, 117, 173)(114, 170, 119, 175, 133, 189, 147, 203, 135, 191, 152, 208, 165, 221, 168, 224, 156, 212, 157, 213, 154, 210, 137, 193, 122, 178, 123, 179, 139, 195, 129, 185, 120, 176, 134, 190, 151, 207, 162, 218, 153, 209, 166, 222, 167, 223, 155, 211, 138, 194, 140, 196, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 134)(8, 135)(9, 129)(10, 114)(11, 119)(12, 142)(13, 144)(14, 115)(15, 146)(16, 141)(17, 147)(18, 143)(19, 117)(20, 118)(21, 151)(22, 152)(23, 153)(24, 139)(25, 121)(26, 122)(27, 133)(28, 123)(29, 158)(30, 159)(31, 124)(32, 160)(33, 126)(34, 150)(35, 162)(36, 130)(37, 131)(38, 132)(39, 165)(40, 166)(41, 156)(42, 136)(43, 137)(44, 138)(45, 140)(46, 164)(47, 163)(48, 161)(49, 145)(50, 168)(51, 148)(52, 149)(53, 167)(54, 157)(55, 154)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1083 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1, Y2^-4 * Y3^-2, (Y2^-1 * Y1 * Y2^-1)^2, Y3^7, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-3, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-4 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 13, 69)(9, 65, 19, 75)(12, 68, 25, 81)(14, 70, 28, 84)(15, 71, 26, 82)(16, 72, 36, 92)(18, 74, 21, 77)(20, 76, 23, 79)(22, 78, 32, 88)(24, 80, 29, 85)(27, 83, 30, 86)(31, 87, 43, 99)(33, 89, 45, 101)(34, 90, 44, 100)(35, 91, 51, 107)(37, 93, 39, 95)(38, 94, 41, 97)(40, 96, 48, 104)(42, 98, 46, 102)(47, 103, 56, 112)(49, 105, 54, 110)(50, 106, 55, 111)(52, 108, 53, 109)(113, 169, 115, 171, 124, 180, 141, 197, 132, 188, 145, 201, 159, 215, 162, 218, 146, 202, 160, 216, 149, 205, 128, 184, 116, 172, 125, 181, 142, 198, 131, 187, 118, 174, 126, 182, 143, 199, 158, 214, 150, 206, 161, 217, 164, 220, 147, 203, 127, 183, 144, 200, 130, 186, 117, 173)(114, 170, 119, 175, 133, 189, 148, 204, 138, 194, 152, 208, 165, 221, 167, 223, 153, 209, 157, 213, 155, 211, 136, 192, 120, 176, 123, 179, 139, 195, 129, 185, 122, 178, 134, 190, 151, 207, 163, 219, 156, 212, 166, 222, 168, 224, 154, 210, 135, 191, 140, 196, 137, 193, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 123)(8, 135)(9, 136)(10, 114)(11, 140)(12, 142)(13, 144)(14, 115)(15, 146)(16, 147)(17, 121)(18, 149)(19, 117)(20, 118)(21, 139)(22, 119)(23, 153)(24, 154)(25, 155)(26, 122)(27, 137)(28, 157)(29, 131)(30, 130)(31, 124)(32, 160)(33, 126)(34, 150)(35, 162)(36, 129)(37, 164)(38, 132)(39, 133)(40, 134)(41, 156)(42, 167)(43, 168)(44, 138)(45, 166)(46, 141)(47, 143)(48, 161)(49, 145)(50, 158)(51, 148)(52, 159)(53, 151)(54, 152)(55, 163)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1084
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1084 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y1 * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y2^-4 * Y3^-1, (Y2^-2 * Y1)^2, Y1 * Y2 * Y3^-1 * Y1 * Y3^2 * Y2^-1, Y3^7, Y3^-1 * Y2^-1 * Y3^-3 * Y1 * Y2 * Y1, Y1 * Y2^-1 * Y1 * Y3^-1 * Y2^2 * Y3^-2 * Y2^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 34, 90)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 40, 96)(18, 74, 22, 78)(19, 75, 43, 99)(20, 76, 25, 81)(23, 79, 47, 103)(24, 80, 37, 93)(26, 82, 39, 95)(29, 85, 51, 107)(31, 87, 46, 102)(33, 89, 38, 94)(35, 91, 50, 106)(36, 92, 49, 105)(41, 97, 48, 104)(42, 98, 45, 101)(44, 100, 52, 108)(53, 109, 56, 112)(54, 110, 55, 111)(113, 169, 115, 171, 124, 180, 131, 187, 118, 174, 126, 182, 147, 203, 156, 212, 132, 188, 149, 205, 167, 223, 163, 219, 157, 213, 133, 189, 158, 214, 139, 195, 150, 206, 159, 215, 168, 224, 151, 207, 127, 183, 148, 204, 153, 209, 128, 184, 116, 172, 125, 181, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 141, 197, 122, 178, 136, 192, 160, 216, 164, 220, 142, 198, 144, 200, 165, 221, 155, 211, 145, 201, 123, 179, 143, 199, 129, 185, 154, 210, 146, 202, 166, 222, 152, 208, 137, 193, 161, 217, 162, 218, 138, 194, 120, 176, 135, 191, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 130)(13, 148)(14, 115)(15, 150)(16, 151)(17, 155)(18, 153)(19, 117)(20, 118)(21, 149)(22, 140)(23, 161)(24, 119)(25, 154)(26, 152)(27, 163)(28, 162)(29, 121)(30, 122)(31, 165)(32, 136)(33, 142)(34, 123)(35, 124)(36, 159)(37, 126)(38, 157)(39, 139)(40, 129)(41, 168)(42, 145)(43, 164)(44, 131)(45, 132)(46, 167)(47, 133)(48, 134)(49, 146)(50, 166)(51, 156)(52, 141)(53, 160)(54, 143)(55, 147)(56, 158)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1083
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1085 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (R * Y3)^2, Y3^-1 * Y2^4, (Y1 * Y2^-2)^2, Y3^7, Y3^-1 * Y1 * Y3 * Y2 * Y3 * Y1 * Y2^-1, Y1 * Y2 * Y3^3 * Y1 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1, Y3^-2 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 34, 90)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 40, 96)(18, 74, 22, 78)(19, 75, 42, 98)(20, 76, 25, 81)(23, 79, 36, 92)(24, 80, 47, 103)(26, 82, 51, 107)(29, 85, 44, 100)(31, 87, 46, 102)(33, 89, 45, 101)(35, 91, 52, 108)(37, 93, 49, 105)(38, 94, 41, 97)(39, 95, 50, 106)(43, 99, 48, 104)(53, 109, 55, 111)(54, 110, 56, 112)(113, 169, 115, 171, 124, 180, 128, 184, 116, 172, 125, 181, 147, 203, 151, 207, 127, 183, 148, 204, 167, 223, 163, 219, 150, 206, 133, 189, 158, 214, 139, 195, 157, 213, 159, 215, 168, 224, 156, 212, 132, 188, 149, 205, 155, 211, 131, 187, 118, 174, 126, 182, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 138, 194, 120, 176, 135, 191, 160, 216, 162, 218, 137, 193, 146, 202, 166, 222, 152, 208, 145, 201, 123, 179, 143, 199, 129, 185, 153, 209, 144, 200, 165, 221, 154, 210, 142, 198, 161, 217, 164, 220, 141, 197, 122, 178, 136, 192, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 147)(13, 148)(14, 115)(15, 150)(16, 151)(17, 154)(18, 124)(19, 117)(20, 118)(21, 159)(22, 160)(23, 146)(24, 119)(25, 145)(26, 162)(27, 156)(28, 134)(29, 121)(30, 122)(31, 165)(32, 161)(33, 153)(34, 123)(35, 167)(36, 133)(37, 126)(38, 157)(39, 163)(40, 129)(41, 142)(42, 141)(43, 130)(44, 131)(45, 132)(46, 168)(47, 149)(48, 166)(49, 136)(50, 152)(51, 139)(52, 140)(53, 164)(54, 143)(55, 158)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1081
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1086 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-2 * Y1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y3 * Y2 * Y3 * Y1, Y2^4 * Y3^-1 * Y2^2, Y3^-2 * Y2 * Y3^-3 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 23, 79)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 39, 95)(18, 74, 22, 78)(19, 75, 29, 85)(20, 76, 25, 81)(24, 80, 45, 101)(26, 82, 52, 108)(31, 87, 44, 100)(33, 89, 51, 107)(34, 90, 55, 111)(35, 91, 53, 109)(36, 92, 54, 110)(37, 93, 56, 112)(38, 94, 46, 102)(40, 96, 48, 104)(41, 97, 49, 105)(42, 98, 47, 103)(43, 99, 50, 106)(113, 169, 115, 171, 124, 180, 145, 201, 152, 208, 128, 184, 116, 172, 125, 181, 146, 202, 164, 220, 155, 211, 150, 206, 127, 183, 133, 189, 156, 212, 139, 195, 132, 188, 148, 204, 149, 205, 157, 213, 154, 210, 131, 187, 118, 174, 126, 182, 147, 203, 153, 209, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 158, 214, 165, 221, 138, 194, 120, 176, 135, 191, 159, 215, 151, 207, 168, 224, 163, 219, 137, 193, 123, 179, 143, 199, 129, 185, 142, 198, 161, 217, 162, 218, 144, 200, 167, 223, 141, 197, 122, 178, 136, 192, 160, 216, 166, 222, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 146)(13, 133)(14, 115)(15, 149)(16, 150)(17, 141)(18, 152)(19, 117)(20, 118)(21, 157)(22, 159)(23, 123)(24, 119)(25, 162)(26, 163)(27, 131)(28, 165)(29, 121)(30, 122)(31, 167)(32, 166)(33, 164)(34, 156)(35, 124)(36, 126)(37, 147)(38, 148)(39, 129)(40, 155)(41, 145)(42, 130)(43, 132)(44, 154)(45, 153)(46, 151)(47, 143)(48, 134)(49, 136)(50, 160)(51, 161)(52, 139)(53, 168)(54, 158)(55, 140)(56, 142)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1088
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1087 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y3^-3 * Y2^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2, Y1 * Y2^-1 * Y1 * Y3^2 * Y2 * Y3^2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2, Y2^8 * Y3^2, Y3^2 * Y2^8, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 34, 90)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 38, 94)(18, 74, 22, 78)(19, 75, 40, 96)(20, 76, 25, 81)(23, 79, 35, 91)(24, 80, 45, 101)(26, 82, 47, 103)(29, 85, 41, 97)(31, 87, 44, 100)(33, 89, 42, 98)(36, 92, 39, 95)(37, 93, 46, 102)(43, 99, 48, 104)(49, 105, 52, 108)(50, 106, 55, 111)(51, 107, 56, 112)(53, 109, 54, 110)(113, 169, 115, 171, 124, 180, 147, 203, 164, 220, 159, 215, 168, 224, 155, 211, 132, 188, 128, 184, 116, 172, 125, 181, 148, 204, 133, 189, 156, 212, 139, 195, 154, 210, 131, 187, 118, 174, 126, 182, 127, 183, 149, 205, 165, 221, 157, 213, 167, 223, 153, 209, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 146, 202, 162, 218, 150, 206, 166, 222, 160, 216, 142, 198, 138, 194, 120, 176, 135, 191, 145, 201, 123, 179, 143, 199, 129, 185, 151, 207, 141, 197, 122, 178, 136, 192, 137, 193, 158, 214, 163, 219, 144, 200, 161, 217, 152, 208, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 148)(13, 149)(14, 115)(15, 124)(16, 126)(17, 152)(18, 132)(19, 117)(20, 118)(21, 157)(22, 145)(23, 158)(24, 119)(25, 134)(26, 136)(27, 153)(28, 142)(29, 121)(30, 122)(31, 161)(32, 150)(33, 163)(34, 123)(35, 133)(36, 165)(37, 147)(38, 129)(39, 140)(40, 160)(41, 155)(42, 130)(43, 131)(44, 167)(45, 159)(46, 146)(47, 139)(48, 141)(49, 166)(50, 143)(51, 162)(52, 156)(53, 164)(54, 151)(55, 168)(56, 154)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1089
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1088 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y3^3 * Y2^2, (Y2^-1 * Y1 * Y2^-1)^2, Y1 * Y3^-1 * Y2 * Y1 * Y2^-3, Y3 * Y2^-18, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 17, 73)(6, 62, 8, 64)(7, 63, 21, 77)(9, 65, 27, 83)(12, 68, 28, 84)(13, 69, 34, 90)(14, 70, 32, 88)(15, 71, 30, 86)(16, 72, 39, 95)(18, 74, 22, 78)(19, 75, 42, 98)(20, 76, 25, 81)(23, 79, 45, 101)(24, 80, 35, 91)(26, 82, 43, 99)(29, 85, 48, 104)(31, 87, 44, 100)(33, 89, 40, 96)(36, 92, 41, 97)(37, 93, 46, 102)(38, 94, 47, 103)(49, 105, 56, 112)(50, 106, 52, 108)(51, 107, 54, 110)(53, 109, 55, 111)(113, 169, 115, 171, 124, 180, 147, 203, 164, 220, 160, 216, 166, 222, 150, 206, 127, 183, 131, 187, 118, 174, 126, 182, 148, 204, 133, 189, 156, 212, 139, 195, 152, 208, 128, 184, 116, 172, 125, 181, 132, 188, 149, 205, 165, 221, 157, 213, 168, 224, 155, 211, 130, 186, 117, 173)(114, 170, 119, 175, 134, 190, 144, 200, 161, 217, 154, 210, 167, 223, 159, 215, 137, 193, 141, 197, 122, 178, 136, 192, 145, 201, 123, 179, 143, 199, 129, 185, 153, 209, 138, 194, 120, 176, 135, 191, 142, 198, 158, 214, 163, 219, 146, 202, 162, 218, 151, 207, 140, 196, 121, 177)
	L = (1, 116)(2, 120)(3, 125)(4, 127)(5, 128)(6, 113)(7, 135)(8, 137)(9, 138)(10, 114)(11, 144)(12, 132)(13, 131)(14, 115)(15, 130)(16, 150)(17, 154)(18, 152)(19, 117)(20, 118)(21, 147)(22, 142)(23, 141)(24, 119)(25, 140)(26, 159)(27, 160)(28, 153)(29, 121)(30, 122)(31, 161)(32, 158)(33, 134)(34, 123)(35, 149)(36, 124)(37, 126)(38, 155)(39, 129)(40, 166)(41, 167)(42, 146)(43, 139)(44, 164)(45, 133)(46, 136)(47, 151)(48, 157)(49, 163)(50, 143)(51, 145)(52, 165)(53, 148)(54, 168)(55, 162)(56, 156)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1086
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1089 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, (Y1 * Y3)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y3^-6 * Y2 * Y1 * Y2^-1, Y3^2 * Y2^-1 * Y1 * Y2 * Y3^-3 * Y1 * Y3, (Y3 * Y2^-1)^28 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 15, 71)(6, 62, 8, 64)(7, 63, 17, 73)(9, 65, 21, 77)(12, 68, 24, 80)(13, 69, 22, 78)(14, 70, 29, 85)(16, 72, 19, 75)(18, 74, 33, 89)(20, 76, 38, 94)(23, 79, 32, 88)(25, 81, 39, 95)(26, 82, 41, 97)(27, 83, 40, 96)(28, 84, 46, 102)(30, 86, 34, 90)(31, 87, 36, 92)(35, 91, 49, 105)(37, 93, 54, 110)(42, 98, 55, 111)(43, 99, 51, 107)(44, 100, 56, 112)(45, 101, 53, 109)(47, 103, 50, 106)(48, 104, 52, 108)(113, 169, 115, 171, 118, 174, 124, 180, 128, 184, 138, 194, 143, 199, 155, 211, 160, 216, 161, 217, 162, 218, 145, 201, 146, 202, 129, 185, 144, 200, 133, 189, 151, 207, 150, 206, 167, 223, 166, 222, 156, 212, 157, 213, 139, 195, 140, 196, 125, 181, 126, 182, 116, 172, 117, 173)(114, 170, 119, 175, 122, 178, 130, 186, 134, 190, 147, 203, 152, 208, 163, 219, 168, 224, 153, 209, 154, 210, 136, 192, 137, 193, 123, 179, 135, 191, 127, 183, 142, 198, 141, 197, 159, 215, 158, 214, 164, 220, 165, 221, 148, 204, 149, 205, 131, 187, 132, 188, 120, 176, 121, 177)
	L = (1, 116)(2, 120)(3, 117)(4, 125)(5, 126)(6, 113)(7, 121)(8, 131)(9, 132)(10, 114)(11, 136)(12, 115)(13, 139)(14, 140)(15, 123)(16, 118)(17, 145)(18, 119)(19, 148)(20, 149)(21, 129)(22, 122)(23, 137)(24, 153)(25, 154)(26, 124)(27, 156)(28, 157)(29, 127)(30, 135)(31, 128)(32, 146)(33, 161)(34, 162)(35, 130)(36, 164)(37, 165)(38, 133)(39, 144)(40, 134)(41, 163)(42, 168)(43, 138)(44, 167)(45, 166)(46, 141)(47, 142)(48, 143)(49, 155)(50, 160)(51, 147)(52, 159)(53, 158)(54, 150)(55, 151)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1087
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1090 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C4 x D14 (small group id <56, 4>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, (Y1 * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, R * Y1 * Y2 * R * Y2^-1 * Y1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2, Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-3 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1, Y3^4 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 11, 67)(4, 60, 10, 66)(5, 61, 14, 70)(6, 62, 8, 64)(7, 63, 17, 73)(9, 65, 20, 76)(12, 68, 25, 81)(13, 69, 22, 78)(15, 71, 29, 85)(16, 72, 19, 75)(18, 74, 34, 90)(21, 77, 38, 94)(23, 79, 32, 88)(24, 80, 37, 93)(26, 82, 42, 98)(27, 83, 40, 96)(28, 84, 33, 89)(30, 86, 46, 102)(31, 87, 36, 92)(35, 91, 50, 106)(39, 95, 54, 110)(41, 97, 53, 109)(43, 99, 51, 107)(44, 100, 56, 112)(45, 101, 49, 105)(47, 103, 55, 111)(48, 104, 52, 108)(113, 169, 115, 171, 116, 172, 124, 180, 125, 181, 138, 194, 139, 195, 155, 211, 156, 212, 162, 218, 161, 217, 146, 202, 145, 201, 129, 185, 144, 200, 132, 188, 149, 205, 150, 206, 165, 221, 166, 222, 160, 216, 159, 215, 143, 199, 142, 198, 128, 184, 127, 183, 118, 174, 117, 173)(114, 170, 119, 175, 120, 176, 130, 186, 131, 187, 147, 203, 148, 204, 163, 219, 164, 220, 154, 210, 153, 209, 137, 193, 136, 192, 123, 179, 135, 191, 126, 182, 140, 196, 141, 197, 157, 213, 158, 214, 168, 224, 167, 223, 152, 208, 151, 207, 134, 190, 133, 189, 122, 178, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 125)(5, 115)(6, 113)(7, 130)(8, 131)(9, 119)(10, 114)(11, 126)(12, 138)(13, 139)(14, 141)(15, 117)(16, 118)(17, 132)(18, 147)(19, 148)(20, 150)(21, 121)(22, 122)(23, 140)(24, 135)(25, 123)(26, 155)(27, 156)(28, 157)(29, 158)(30, 127)(31, 128)(32, 149)(33, 144)(34, 129)(35, 163)(36, 164)(37, 165)(38, 166)(39, 133)(40, 134)(41, 136)(42, 137)(43, 162)(44, 161)(45, 168)(46, 167)(47, 142)(48, 143)(49, 145)(50, 146)(51, 154)(52, 153)(53, 160)(54, 159)(55, 151)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1091 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^28 ]
Map::
	R = (1, 58, 2, 61, 5, 65, 9, 69, 13, 73, 17, 77, 21, 81, 25, 87, 31, 89, 33, 91, 35, 93, 37, 95, 39, 97, 41, 100, 44, 112, 56, 110, 54, 108, 52, 106, 50, 104, 48, 102, 46, 84, 28, 80, 24, 76, 20, 72, 16, 68, 12, 64, 8, 60, 4, 57)(3, 63, 7, 67, 11, 71, 15, 75, 19, 79, 23, 83, 27, 86, 30, 85, 29, 88, 32, 90, 34, 92, 36, 94, 38, 96, 40, 98, 42, 101, 45, 111, 55, 109, 53, 107, 51, 105, 49, 103, 47, 99, 43, 82, 26, 78, 22, 74, 18, 70, 14, 66, 10, 62, 6, 59)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 43)(28, 30)(29, 46)(31, 47)(32, 48)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 45)(42, 44)(57, 59)(58, 62)(60, 63)(61, 66)(64, 67)(65, 70)(68, 71)(69, 74)(72, 75)(73, 78)(76, 79)(77, 82)(80, 83)(81, 99)(84, 86)(85, 102)(87, 103)(88, 104)(89, 105)(90, 106)(91, 107)(92, 108)(93, 109)(94, 110)(95, 111)(96, 112)(97, 101)(98, 100)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1092 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1^-3, (Y3 * Y2)^7, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 70, 14, 68, 12, 74, 18, 80, 24, 87, 31, 86, 30, 90, 34, 96, 40, 103, 47, 102, 46, 106, 50, 111, 55, 108, 52, 101, 45, 105, 49, 99, 43, 92, 36, 85, 29, 89, 33, 83, 27, 76, 20, 66, 10, 73, 17, 69, 13, 61, 5, 57)(3, 65, 9, 75, 19, 81, 25, 77, 21, 84, 28, 91, 35, 97, 41, 93, 37, 100, 44, 107, 51, 112, 56, 109, 53, 110, 54, 104, 48, 98, 42, 94, 38, 95, 39, 88, 32, 82, 26, 78, 22, 79, 23, 72, 16, 64, 8, 60, 4, 67, 11, 71, 15, 63, 7, 59)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 28)(22, 30)(23, 31)(26, 34)(27, 35)(29, 37)(32, 40)(33, 41)(36, 44)(38, 46)(39, 47)(42, 50)(43, 51)(45, 53)(48, 55)(49, 56)(52, 54)(57, 60)(58, 64)(59, 66)(61, 67)(62, 72)(63, 73)(65, 76)(68, 78)(69, 71)(70, 79)(74, 82)(75, 83)(77, 85)(80, 88)(81, 89)(84, 92)(86, 94)(87, 95)(90, 98)(91, 99)(93, 101)(96, 104)(97, 105)(100, 108)(102, 109)(103, 110)(106, 112)(107, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1096
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1093 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1^-3, (Y2 * Y3)^7, (Y2 * Y1^-2 * Y3)^14 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 70, 14, 66, 10, 73, 17, 80, 24, 87, 31, 83, 27, 89, 33, 96, 40, 103, 47, 99, 43, 105, 49, 111, 55, 109, 53, 102, 46, 106, 50, 100, 44, 93, 37, 86, 30, 90, 34, 84, 28, 77, 21, 68, 12, 74, 18, 69, 13, 61, 5, 57)(3, 65, 9, 72, 16, 64, 8, 60, 4, 67, 11, 76, 20, 82, 26, 78, 22, 85, 29, 92, 36, 98, 42, 94, 38, 101, 45, 108, 52, 112, 56, 107, 51, 110, 54, 104, 48, 97, 41, 91, 35, 95, 39, 88, 32, 81, 25, 75, 19, 79, 23, 71, 15, 63, 7, 59)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 25)(20, 28)(22, 30)(24, 32)(26, 34)(27, 35)(29, 37)(31, 39)(33, 41)(36, 44)(38, 46)(40, 48)(42, 50)(43, 51)(45, 53)(47, 54)(49, 56)(52, 55)(57, 60)(58, 64)(59, 66)(61, 67)(62, 72)(63, 73)(65, 70)(68, 78)(69, 76)(71, 80)(74, 82)(75, 83)(77, 85)(79, 87)(81, 89)(84, 92)(86, 94)(88, 96)(90, 98)(91, 99)(93, 101)(95, 103)(97, 105)(100, 108)(102, 107)(104, 111)(106, 112)(109, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1094
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1094 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, Y1^-8 * Y3 * Y2, Y1^-1 * Y3 * Y2 * Y1^3 * Y2 * Y3 * Y1^-2, Y1^-2 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y1^-4 * Y3 * Y1 * Y2 * Y1^-3, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 70, 14, 82, 26, 98, 42, 94, 38, 79, 23, 68, 12, 74, 18, 86, 30, 102, 46, 92, 36, 105, 49, 112, 56, 109, 53, 96, 40, 106, 50, 90, 34, 76, 20, 66, 10, 73, 17, 85, 29, 101, 45, 97, 41, 81, 25, 69, 13, 61, 5, 57)(3, 65, 9, 75, 19, 89, 33, 107, 51, 111, 55, 103, 47, 87, 31, 77, 21, 91, 35, 104, 48, 88, 32, 80, 24, 95, 39, 108, 52, 110, 54, 100, 44, 84, 28, 72, 16, 64, 8, 60, 4, 67, 11, 78, 22, 93, 37, 99, 43, 83, 27, 71, 15, 63, 7, 59)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 43)(28, 46)(29, 47)(32, 50)(34, 48)(36, 44)(37, 42)(39, 53)(41, 51)(45, 55)(49, 54)(52, 56)(57, 60)(58, 64)(59, 66)(61, 67)(62, 72)(63, 73)(65, 76)(68, 80)(69, 78)(70, 84)(71, 85)(74, 88)(75, 90)(77, 92)(79, 95)(81, 93)(82, 100)(83, 101)(86, 104)(87, 105)(89, 106)(91, 102)(94, 108)(96, 107)(97, 99)(98, 110)(103, 112)(109, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1093
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1095 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^-1 * Y2 * Y1^2 * Y3 * Y2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-4, Y1^28 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 70, 14, 82, 26, 93, 37, 101, 45, 109, 53, 106, 50, 98, 42, 90, 34, 79, 23, 68, 12, 74, 18, 86, 30, 76, 20, 66, 10, 73, 17, 85, 29, 95, 39, 103, 47, 111, 55, 108, 52, 100, 44, 92, 36, 81, 25, 69, 13, 61, 5, 57)(3, 65, 9, 75, 19, 88, 32, 80, 24, 91, 35, 99, 43, 107, 51, 112, 56, 104, 48, 96, 40, 87, 31, 77, 21, 84, 28, 72, 16, 64, 8, 60, 4, 67, 11, 78, 22, 89, 33, 97, 41, 105, 49, 110, 54, 102, 46, 94, 38, 83, 27, 71, 15, 63, 7, 59)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 28)(22, 34)(24, 36)(25, 32)(26, 38)(29, 40)(33, 42)(35, 44)(37, 46)(39, 48)(41, 50)(43, 52)(45, 54)(47, 56)(49, 53)(51, 55)(57, 60)(58, 64)(59, 66)(61, 67)(62, 72)(63, 73)(65, 76)(68, 80)(69, 78)(70, 84)(71, 85)(74, 88)(75, 86)(77, 82)(79, 91)(81, 89)(83, 95)(87, 93)(90, 99)(92, 97)(94, 103)(96, 101)(98, 107)(100, 105)(102, 111)(104, 109)(106, 112)(108, 110)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1096 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: halfedge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-2, Y1^-4 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-4, Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 58, 2, 62, 6, 70, 14, 82, 26, 93, 37, 101, 45, 109, 53, 106, 50, 98, 42, 90, 34, 76, 20, 66, 10, 73, 17, 85, 29, 79, 23, 68, 12, 74, 18, 86, 30, 95, 39, 103, 47, 111, 55, 108, 52, 100, 44, 92, 36, 81, 25, 69, 13, 61, 5, 57)(3, 65, 9, 75, 19, 89, 33, 97, 41, 105, 49, 110, 54, 102, 46, 94, 38, 84, 28, 72, 16, 64, 8, 60, 4, 67, 11, 78, 22, 87, 31, 77, 21, 91, 35, 99, 43, 107, 51, 112, 56, 104, 48, 96, 40, 88, 32, 80, 24, 83, 27, 71, 15, 63, 7, 59)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 29)(24, 26)(25, 33)(28, 39)(32, 37)(34, 43)(36, 41)(38, 47)(40, 45)(42, 51)(44, 49)(46, 55)(48, 53)(50, 56)(52, 54)(57, 60)(58, 64)(59, 66)(61, 67)(62, 72)(63, 73)(65, 76)(68, 80)(69, 78)(70, 84)(71, 85)(74, 88)(75, 90)(77, 92)(79, 83)(81, 87)(82, 94)(86, 96)(89, 98)(91, 100)(93, 102)(95, 104)(97, 106)(99, 108)(101, 110)(103, 112)(105, 109)(107, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1092
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1097 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^28 ]
Map::
	R = (1, 57, 3, 59, 7, 63, 11, 67, 15, 71, 19, 75, 23, 79, 27, 83, 33, 89, 30, 86, 34, 90, 37, 93, 39, 95, 41, 97, 43, 99, 45, 101, 56, 112, 54, 110, 51, 107, 48, 104, 50, 106, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64, 4, 60)(2, 58, 5, 61, 9, 65, 13, 69, 17, 73, 21, 77, 25, 81, 35, 91, 31, 87, 29, 85, 32, 88, 36, 92, 38, 94, 40, 96, 42, 98, 44, 100, 47, 103, 55, 111, 53, 109, 49, 105, 52, 108, 46, 102, 26, 82, 22, 78, 18, 74, 14, 70, 10, 66, 6, 62)(113, 114)(115, 118)(116, 117)(119, 122)(120, 121)(123, 126)(124, 125)(127, 130)(128, 129)(131, 134)(132, 133)(135, 138)(136, 137)(139, 158)(140, 147)(141, 160)(142, 161)(143, 162)(144, 163)(145, 164)(146, 165)(148, 166)(149, 167)(150, 168)(151, 159)(152, 157)(153, 156)(154, 155)(169, 170)(171, 174)(172, 173)(175, 178)(176, 177)(179, 182)(180, 181)(183, 186)(184, 185)(187, 190)(188, 189)(191, 194)(192, 193)(195, 214)(196, 203)(197, 216)(198, 217)(199, 218)(200, 219)(201, 220)(202, 221)(204, 222)(205, 223)(206, 224)(207, 215)(208, 213)(209, 212)(210, 211)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1104
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1098 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y1, (Y2 * Y1)^7, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ]
Map::
	R = (1, 57, 4, 60, 12, 68, 21, 77, 9, 65, 20, 76, 30, 86, 37, 93, 27, 83, 36, 92, 46, 102, 52, 108, 43, 99, 51, 107, 56, 112, 49, 105, 39, 95, 48, 104, 42, 98, 33, 89, 23, 79, 32, 88, 26, 82, 16, 72, 6, 62, 15, 71, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 25, 81, 14, 70, 24, 80, 34, 90, 41, 97, 31, 87, 40, 96, 50, 106, 55, 111, 47, 103, 54, 110, 53, 109, 45, 101, 35, 91, 44, 100, 38, 94, 29, 85, 19, 75, 28, 84, 22, 78, 11, 67, 3, 59, 10, 66, 18, 74, 8, 64)(113, 114)(115, 121)(116, 120)(117, 119)(118, 126)(122, 133)(123, 132)(124, 130)(125, 129)(127, 137)(128, 136)(131, 139)(134, 142)(135, 143)(138, 146)(140, 149)(141, 148)(144, 153)(145, 152)(147, 155)(150, 158)(151, 159)(154, 162)(156, 164)(157, 163)(160, 167)(161, 166)(165, 168)(169, 171)(170, 174)(172, 179)(173, 178)(175, 184)(176, 183)(177, 187)(180, 190)(181, 186)(182, 191)(185, 194)(188, 197)(189, 196)(192, 201)(193, 200)(195, 203)(198, 206)(199, 207)(202, 210)(204, 213)(205, 212)(208, 217)(209, 216)(211, 215)(214, 221)(218, 224)(219, 223)(220, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1107
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1099 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^3 * Y2 * Y3^-1 * Y1, (Y2 * Y1)^7, (Y3 * Y1 * Y2)^28 ]
Map::
	R = (1, 57, 4, 60, 12, 68, 16, 72, 6, 62, 15, 71, 26, 82, 33, 89, 23, 79, 32, 88, 42, 98, 49, 105, 39, 95, 48, 104, 56, 112, 52, 108, 43, 99, 51, 107, 46, 102, 37, 93, 27, 83, 36, 92, 30, 86, 21, 77, 9, 65, 20, 76, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 11, 67, 3, 59, 10, 66, 22, 78, 29, 85, 19, 75, 28, 84, 38, 94, 45, 101, 35, 91, 44, 100, 53, 109, 55, 111, 47, 103, 54, 110, 50, 106, 41, 97, 31, 87, 40, 96, 34, 90, 25, 81, 14, 70, 24, 80, 18, 74, 8, 64)(113, 114)(115, 121)(116, 120)(117, 119)(118, 126)(122, 133)(123, 132)(124, 130)(125, 129)(127, 137)(128, 136)(131, 139)(134, 142)(135, 143)(138, 146)(140, 149)(141, 148)(144, 153)(145, 152)(147, 155)(150, 158)(151, 159)(154, 162)(156, 164)(157, 163)(160, 167)(161, 166)(165, 168)(169, 171)(170, 174)(172, 179)(173, 178)(175, 184)(176, 183)(177, 187)(180, 185)(181, 190)(182, 191)(186, 194)(188, 197)(189, 196)(192, 201)(193, 200)(195, 203)(198, 206)(199, 207)(202, 210)(204, 213)(205, 212)(208, 217)(209, 216)(211, 215)(214, 221)(218, 224)(219, 223)(220, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1108
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1100 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3^-1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-7 * Y1 * Y3 * Y2, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-3 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 4, 60, 12, 68, 24, 80, 40, 96, 48, 104, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 47, 103, 33, 89, 51, 107, 55, 111, 44, 100, 26, 82, 43, 99, 37, 93, 21, 77, 9, 65, 20, 76, 36, 92, 53, 109, 41, 97, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 49, 105, 39, 95, 23, 79, 11, 67, 3, 59, 10, 66, 22, 78, 38, 94, 42, 98, 54, 110, 52, 108, 35, 91, 19, 75, 34, 90, 46, 102, 28, 84, 14, 70, 27, 83, 45, 101, 56, 112, 50, 106, 32, 88, 18, 74, 8, 64)(113, 114)(115, 121)(116, 120)(117, 119)(118, 126)(122, 133)(123, 132)(124, 130)(125, 129)(127, 140)(128, 139)(131, 145)(134, 149)(135, 148)(136, 144)(137, 143)(138, 154)(141, 158)(142, 157)(146, 159)(147, 163)(150, 155)(151, 165)(152, 162)(153, 161)(156, 166)(160, 168)(164, 167)(169, 171)(170, 174)(172, 179)(173, 178)(175, 184)(176, 183)(177, 187)(180, 191)(181, 190)(182, 194)(185, 198)(186, 197)(188, 203)(189, 202)(192, 207)(193, 206)(195, 212)(196, 211)(199, 216)(200, 215)(201, 218)(204, 220)(205, 214)(208, 217)(209, 210)(213, 223)(219, 224)(221, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1105
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1101 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2 * Y3^-4 * Y1, Y3^-4 * Y2 * Y3 * Y1 * Y3^-3 * Y2 * Y1 * Y2 * Y1, Y3^16 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 4, 60, 12, 68, 24, 80, 26, 82, 38, 94, 47, 103, 56, 112, 49, 105, 44, 100, 35, 91, 21, 77, 9, 65, 20, 76, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 40, 96, 45, 101, 54, 110, 51, 107, 42, 98, 33, 89, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 19, 75, 34, 90, 43, 99, 52, 108, 53, 109, 48, 104, 39, 95, 28, 84, 14, 70, 27, 83, 23, 79, 11, 67, 3, 59, 10, 66, 22, 78, 36, 92, 41, 97, 50, 106, 55, 111, 46, 102, 37, 93, 32, 88, 18, 74, 8, 64)(113, 114)(115, 121)(116, 120)(117, 119)(118, 126)(122, 133)(123, 132)(124, 130)(125, 129)(127, 140)(128, 139)(131, 145)(134, 147)(135, 142)(136, 144)(137, 143)(138, 149)(141, 151)(146, 154)(148, 156)(150, 158)(152, 160)(153, 161)(155, 163)(157, 165)(159, 167)(162, 168)(164, 166)(169, 171)(170, 174)(172, 179)(173, 178)(175, 184)(176, 183)(177, 187)(180, 191)(181, 190)(182, 194)(185, 198)(186, 197)(188, 199)(189, 202)(192, 195)(193, 204)(196, 206)(200, 208)(201, 209)(203, 211)(205, 213)(207, 215)(210, 218)(212, 220)(214, 222)(216, 224)(217, 221)(219, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1106
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1102 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-4 * Y1 * Y2 * Y1 * Y2 * Y1, Y3^28, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 4, 60, 12, 68, 24, 80, 33, 89, 42, 98, 51, 107, 54, 110, 45, 101, 40, 96, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 21, 77, 9, 65, 20, 76, 35, 91, 44, 100, 49, 105, 56, 112, 47, 103, 38, 94, 26, 82, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 37, 93, 46, 102, 55, 111, 50, 106, 41, 97, 36, 92, 23, 79, 11, 67, 3, 59, 10, 66, 22, 78, 28, 84, 14, 70, 27, 83, 39, 95, 48, 104, 53, 109, 52, 108, 43, 99, 34, 90, 19, 75, 32, 88, 18, 74, 8, 64)(113, 114)(115, 121)(116, 120)(117, 119)(118, 126)(122, 133)(123, 132)(124, 130)(125, 129)(127, 140)(128, 139)(131, 145)(134, 141)(135, 147)(136, 144)(137, 143)(138, 149)(142, 151)(146, 154)(148, 156)(150, 158)(152, 160)(153, 161)(155, 163)(157, 165)(159, 167)(162, 168)(164, 166)(169, 171)(170, 174)(172, 179)(173, 178)(175, 184)(176, 183)(177, 187)(180, 191)(181, 190)(182, 194)(185, 198)(186, 197)(188, 202)(189, 200)(192, 204)(193, 196)(195, 206)(199, 208)(201, 209)(203, 211)(205, 213)(207, 215)(210, 218)(212, 220)(214, 222)(216, 224)(217, 221)(219, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1109
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1103 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^28, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 4, 60)(2, 58, 6, 62)(3, 59, 8, 64)(5, 61, 10, 66)(7, 63, 12, 68)(9, 65, 14, 70)(11, 67, 16, 72)(13, 69, 18, 74)(15, 71, 20, 76)(17, 73, 22, 78)(19, 75, 24, 80)(21, 77, 26, 82)(23, 79, 28, 84)(25, 81, 49, 105)(27, 83, 45, 101)(29, 85, 52, 108)(30, 86, 48, 104)(31, 87, 53, 109)(32, 88, 47, 103)(33, 89, 46, 102)(34, 90, 50, 106)(35, 91, 54, 110)(36, 92, 44, 100)(37, 93, 43, 99)(38, 94, 55, 111)(39, 95, 56, 112)(40, 96, 41, 97)(42, 98, 51, 107)(113, 114, 117, 121, 125, 129, 133, 137, 151, 147, 143, 141, 142, 145, 149, 153, 156, 159, 162, 167, 163, 139, 135, 131, 127, 123, 119, 115)(116, 120, 124, 128, 132, 136, 140, 157, 154, 150, 146, 144, 148, 152, 155, 158, 160, 164, 165, 166, 168, 161, 138, 134, 130, 126, 122, 118)(169, 171, 175, 179, 183, 187, 191, 195, 219, 223, 218, 215, 212, 209, 205, 201, 198, 197, 199, 203, 207, 193, 189, 185, 181, 177, 173, 170)(172, 174, 178, 182, 186, 190, 194, 217, 224, 222, 221, 220, 216, 214, 211, 208, 204, 200, 202, 206, 210, 213, 196, 192, 188, 184, 180, 176)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1110
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1104 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^28 ]
Map::
	R = (1, 57, 113, 169, 3, 59, 115, 171, 7, 63, 119, 175, 11, 67, 123, 179, 15, 71, 127, 183, 19, 75, 131, 187, 23, 79, 135, 191, 27, 83, 139, 195, 49, 105, 161, 217, 55, 111, 167, 223, 52, 108, 164, 220, 50, 106, 162, 218, 46, 102, 158, 214, 44, 100, 156, 212, 42, 98, 154, 210, 39, 95, 151, 207, 36, 92, 148, 204, 32, 88, 144, 200, 29, 85, 141, 197, 31, 87, 143, 199, 35, 91, 147, 203, 28, 84, 140, 196, 24, 80, 136, 192, 20, 76, 132, 188, 16, 72, 128, 184, 12, 68, 124, 180, 8, 64, 120, 176, 4, 60, 116, 172)(2, 58, 114, 170, 5, 61, 117, 173, 9, 65, 121, 177, 13, 69, 125, 181, 17, 73, 129, 185, 21, 77, 133, 189, 25, 81, 137, 193, 47, 103, 159, 215, 53, 109, 165, 221, 54, 110, 166, 222, 51, 107, 163, 219, 56, 112, 168, 224, 48, 104, 160, 216, 45, 101, 157, 213, 43, 99, 155, 211, 41, 97, 153, 209, 38, 94, 150, 206, 34, 90, 146, 202, 30, 86, 142, 198, 33, 89, 145, 201, 37, 93, 149, 205, 40, 96, 152, 208, 26, 82, 138, 194, 22, 78, 134, 190, 18, 74, 130, 186, 14, 70, 126, 182, 10, 66, 122, 178, 6, 62, 118, 174)
	L = (1, 58)(2, 57)(3, 62)(4, 61)(5, 60)(6, 59)(7, 66)(8, 65)(9, 64)(10, 63)(11, 70)(12, 69)(13, 68)(14, 67)(15, 74)(16, 73)(17, 72)(18, 71)(19, 78)(20, 77)(21, 76)(22, 75)(23, 82)(24, 81)(25, 80)(26, 79)(27, 96)(28, 103)(29, 107)(30, 108)(31, 110)(32, 112)(33, 111)(34, 106)(35, 109)(36, 104)(37, 105)(38, 102)(39, 101)(40, 83)(41, 100)(42, 99)(43, 98)(44, 97)(45, 95)(46, 94)(47, 84)(48, 92)(49, 93)(50, 90)(51, 85)(52, 86)(53, 91)(54, 87)(55, 89)(56, 88)(113, 170)(114, 169)(115, 174)(116, 173)(117, 172)(118, 171)(119, 178)(120, 177)(121, 176)(122, 175)(123, 182)(124, 181)(125, 180)(126, 179)(127, 186)(128, 185)(129, 184)(130, 183)(131, 190)(132, 189)(133, 188)(134, 187)(135, 194)(136, 193)(137, 192)(138, 191)(139, 208)(140, 215)(141, 219)(142, 220)(143, 222)(144, 224)(145, 223)(146, 218)(147, 221)(148, 216)(149, 217)(150, 214)(151, 213)(152, 195)(153, 212)(154, 211)(155, 210)(156, 209)(157, 207)(158, 206)(159, 196)(160, 204)(161, 205)(162, 202)(163, 197)(164, 198)(165, 203)(166, 199)(167, 201)(168, 200)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1097
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1105 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y1, (Y2 * Y1)^7, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 12, 68, 124, 180, 21, 77, 133, 189, 9, 65, 121, 177, 20, 76, 132, 188, 30, 86, 142, 198, 37, 93, 149, 205, 27, 83, 139, 195, 36, 92, 148, 204, 46, 102, 158, 214, 52, 108, 164, 220, 43, 99, 155, 211, 51, 107, 163, 219, 56, 112, 168, 224, 49, 105, 161, 217, 39, 95, 151, 207, 48, 104, 160, 216, 42, 98, 154, 210, 33, 89, 145, 201, 23, 79, 135, 191, 32, 88, 144, 200, 26, 82, 138, 194, 16, 72, 128, 184, 6, 62, 118, 174, 15, 71, 127, 183, 13, 69, 125, 181, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 17, 73, 129, 185, 25, 81, 137, 193, 14, 70, 126, 182, 24, 80, 136, 192, 34, 90, 146, 202, 41, 97, 153, 209, 31, 87, 143, 199, 40, 96, 152, 208, 50, 106, 162, 218, 55, 111, 167, 223, 47, 103, 159, 215, 54, 110, 166, 222, 53, 109, 165, 221, 45, 101, 157, 213, 35, 91, 147, 203, 44, 100, 156, 212, 38, 94, 150, 206, 29, 85, 141, 197, 19, 75, 131, 187, 28, 84, 140, 196, 22, 78, 134, 190, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 18, 74, 130, 186, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 64)(5, 63)(6, 70)(7, 61)(8, 60)(9, 59)(10, 77)(11, 76)(12, 74)(13, 73)(14, 62)(15, 81)(16, 80)(17, 69)(18, 68)(19, 83)(20, 67)(21, 66)(22, 86)(23, 87)(24, 72)(25, 71)(26, 90)(27, 75)(28, 93)(29, 92)(30, 78)(31, 79)(32, 97)(33, 96)(34, 82)(35, 99)(36, 85)(37, 84)(38, 102)(39, 103)(40, 89)(41, 88)(42, 106)(43, 91)(44, 108)(45, 107)(46, 94)(47, 95)(48, 111)(49, 110)(50, 98)(51, 101)(52, 100)(53, 112)(54, 105)(55, 104)(56, 109)(113, 171)(114, 174)(115, 169)(116, 179)(117, 178)(118, 170)(119, 184)(120, 183)(121, 187)(122, 173)(123, 172)(124, 190)(125, 186)(126, 191)(127, 176)(128, 175)(129, 194)(130, 181)(131, 177)(132, 197)(133, 196)(134, 180)(135, 182)(136, 201)(137, 200)(138, 185)(139, 203)(140, 189)(141, 188)(142, 206)(143, 207)(144, 193)(145, 192)(146, 210)(147, 195)(148, 213)(149, 212)(150, 198)(151, 199)(152, 217)(153, 216)(154, 202)(155, 215)(156, 205)(157, 204)(158, 221)(159, 211)(160, 209)(161, 208)(162, 224)(163, 223)(164, 222)(165, 214)(166, 220)(167, 219)(168, 218)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1100
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1106 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^3 * Y2 * Y3^-1 * Y1, (Y2 * Y1)^7, (Y3 * Y1 * Y2)^28 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 12, 68, 124, 180, 16, 72, 128, 184, 6, 62, 118, 174, 15, 71, 127, 183, 26, 82, 138, 194, 33, 89, 145, 201, 23, 79, 135, 191, 32, 88, 144, 200, 42, 98, 154, 210, 49, 105, 161, 217, 39, 95, 151, 207, 48, 104, 160, 216, 56, 112, 168, 224, 52, 108, 164, 220, 43, 99, 155, 211, 51, 107, 163, 219, 46, 102, 158, 214, 37, 93, 149, 205, 27, 83, 139, 195, 36, 92, 148, 204, 30, 86, 142, 198, 21, 77, 133, 189, 9, 65, 121, 177, 20, 76, 132, 188, 13, 69, 125, 181, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 17, 73, 129, 185, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 22, 78, 134, 190, 29, 85, 141, 197, 19, 75, 131, 187, 28, 84, 140, 196, 38, 94, 150, 206, 45, 101, 157, 213, 35, 91, 147, 203, 44, 100, 156, 212, 53, 109, 165, 221, 55, 111, 167, 223, 47, 103, 159, 215, 54, 110, 166, 222, 50, 106, 162, 218, 41, 97, 153, 209, 31, 87, 143, 199, 40, 96, 152, 208, 34, 90, 146, 202, 25, 81, 137, 193, 14, 70, 126, 182, 24, 80, 136, 192, 18, 74, 130, 186, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 64)(5, 63)(6, 70)(7, 61)(8, 60)(9, 59)(10, 77)(11, 76)(12, 74)(13, 73)(14, 62)(15, 81)(16, 80)(17, 69)(18, 68)(19, 83)(20, 67)(21, 66)(22, 86)(23, 87)(24, 72)(25, 71)(26, 90)(27, 75)(28, 93)(29, 92)(30, 78)(31, 79)(32, 97)(33, 96)(34, 82)(35, 99)(36, 85)(37, 84)(38, 102)(39, 103)(40, 89)(41, 88)(42, 106)(43, 91)(44, 108)(45, 107)(46, 94)(47, 95)(48, 111)(49, 110)(50, 98)(51, 101)(52, 100)(53, 112)(54, 105)(55, 104)(56, 109)(113, 171)(114, 174)(115, 169)(116, 179)(117, 178)(118, 170)(119, 184)(120, 183)(121, 187)(122, 173)(123, 172)(124, 185)(125, 190)(126, 191)(127, 176)(128, 175)(129, 180)(130, 194)(131, 177)(132, 197)(133, 196)(134, 181)(135, 182)(136, 201)(137, 200)(138, 186)(139, 203)(140, 189)(141, 188)(142, 206)(143, 207)(144, 193)(145, 192)(146, 210)(147, 195)(148, 213)(149, 212)(150, 198)(151, 199)(152, 217)(153, 216)(154, 202)(155, 215)(156, 205)(157, 204)(158, 221)(159, 211)(160, 209)(161, 208)(162, 224)(163, 223)(164, 222)(165, 214)(166, 220)(167, 219)(168, 218)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1101
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1107 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3^-1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-7 * Y1 * Y3 * Y2, Y2 * Y1 * Y2 * Y3 * Y1 * Y3^-3 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 12, 68, 124, 180, 24, 80, 136, 192, 40, 96, 152, 208, 48, 104, 160, 216, 30, 86, 142, 198, 16, 72, 128, 184, 6, 62, 118, 174, 15, 71, 127, 183, 29, 85, 141, 197, 47, 103, 159, 215, 33, 89, 145, 201, 51, 107, 163, 219, 55, 111, 167, 223, 44, 100, 156, 212, 26, 82, 138, 194, 43, 99, 155, 211, 37, 93, 149, 205, 21, 77, 133, 189, 9, 65, 121, 177, 20, 76, 132, 188, 36, 92, 148, 204, 53, 109, 165, 221, 41, 97, 153, 209, 25, 81, 137, 193, 13, 69, 125, 181, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 17, 73, 129, 185, 31, 87, 143, 199, 49, 105, 161, 217, 39, 95, 151, 207, 23, 79, 135, 191, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 22, 78, 134, 190, 38, 94, 150, 206, 42, 98, 154, 210, 54, 110, 166, 222, 52, 108, 164, 220, 35, 91, 147, 203, 19, 75, 131, 187, 34, 90, 146, 202, 46, 102, 158, 214, 28, 84, 140, 196, 14, 70, 126, 182, 27, 83, 139, 195, 45, 101, 157, 213, 56, 112, 168, 224, 50, 106, 162, 218, 32, 88, 144, 200, 18, 74, 130, 186, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 64)(5, 63)(6, 70)(7, 61)(8, 60)(9, 59)(10, 77)(11, 76)(12, 74)(13, 73)(14, 62)(15, 84)(16, 83)(17, 69)(18, 68)(19, 89)(20, 67)(21, 66)(22, 93)(23, 92)(24, 88)(25, 87)(26, 98)(27, 72)(28, 71)(29, 102)(30, 101)(31, 81)(32, 80)(33, 75)(34, 103)(35, 107)(36, 79)(37, 78)(38, 99)(39, 109)(40, 106)(41, 105)(42, 82)(43, 94)(44, 110)(45, 86)(46, 85)(47, 90)(48, 112)(49, 97)(50, 96)(51, 91)(52, 111)(53, 95)(54, 100)(55, 108)(56, 104)(113, 171)(114, 174)(115, 169)(116, 179)(117, 178)(118, 170)(119, 184)(120, 183)(121, 187)(122, 173)(123, 172)(124, 191)(125, 190)(126, 194)(127, 176)(128, 175)(129, 198)(130, 197)(131, 177)(132, 203)(133, 202)(134, 181)(135, 180)(136, 207)(137, 206)(138, 182)(139, 212)(140, 211)(141, 186)(142, 185)(143, 216)(144, 215)(145, 218)(146, 189)(147, 188)(148, 220)(149, 214)(150, 193)(151, 192)(152, 217)(153, 210)(154, 209)(155, 196)(156, 195)(157, 223)(158, 205)(159, 200)(160, 199)(161, 208)(162, 201)(163, 224)(164, 204)(165, 222)(166, 221)(167, 213)(168, 219)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1098
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1108 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2 * Y3^-4 * Y1, Y3^-4 * Y2 * Y3 * Y1 * Y3^-3 * Y2 * Y1 * Y2 * Y1, Y3^16 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 12, 68, 124, 180, 24, 80, 136, 192, 26, 82, 138, 194, 38, 94, 150, 206, 47, 103, 159, 215, 56, 112, 168, 224, 49, 105, 161, 217, 44, 100, 156, 212, 35, 91, 147, 203, 21, 77, 133, 189, 9, 65, 121, 177, 20, 76, 132, 188, 30, 86, 142, 198, 16, 72, 128, 184, 6, 62, 118, 174, 15, 71, 127, 183, 29, 85, 141, 197, 40, 96, 152, 208, 45, 101, 157, 213, 54, 110, 166, 222, 51, 107, 163, 219, 42, 98, 154, 210, 33, 89, 145, 201, 25, 81, 137, 193, 13, 69, 125, 181, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 17, 73, 129, 185, 31, 87, 143, 199, 19, 75, 131, 187, 34, 90, 146, 202, 43, 99, 155, 211, 52, 108, 164, 220, 53, 109, 165, 221, 48, 104, 160, 216, 39, 95, 151, 207, 28, 84, 140, 196, 14, 70, 126, 182, 27, 83, 139, 195, 23, 79, 135, 191, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 22, 78, 134, 190, 36, 92, 148, 204, 41, 97, 153, 209, 50, 106, 162, 218, 55, 111, 167, 223, 46, 102, 158, 214, 37, 93, 149, 205, 32, 88, 144, 200, 18, 74, 130, 186, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 64)(5, 63)(6, 70)(7, 61)(8, 60)(9, 59)(10, 77)(11, 76)(12, 74)(13, 73)(14, 62)(15, 84)(16, 83)(17, 69)(18, 68)(19, 89)(20, 67)(21, 66)(22, 91)(23, 86)(24, 88)(25, 87)(26, 93)(27, 72)(28, 71)(29, 95)(30, 79)(31, 81)(32, 80)(33, 75)(34, 98)(35, 78)(36, 100)(37, 82)(38, 102)(39, 85)(40, 104)(41, 105)(42, 90)(43, 107)(44, 92)(45, 109)(46, 94)(47, 111)(48, 96)(49, 97)(50, 112)(51, 99)(52, 110)(53, 101)(54, 108)(55, 103)(56, 106)(113, 171)(114, 174)(115, 169)(116, 179)(117, 178)(118, 170)(119, 184)(120, 183)(121, 187)(122, 173)(123, 172)(124, 191)(125, 190)(126, 194)(127, 176)(128, 175)(129, 198)(130, 197)(131, 177)(132, 199)(133, 202)(134, 181)(135, 180)(136, 195)(137, 204)(138, 182)(139, 192)(140, 206)(141, 186)(142, 185)(143, 188)(144, 208)(145, 209)(146, 189)(147, 211)(148, 193)(149, 213)(150, 196)(151, 215)(152, 200)(153, 201)(154, 218)(155, 203)(156, 220)(157, 205)(158, 222)(159, 207)(160, 224)(161, 221)(162, 210)(163, 223)(164, 212)(165, 217)(166, 214)(167, 219)(168, 216)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1099
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1109 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-4 * Y1 * Y2 * Y1 * Y2 * Y1, Y3^28, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 57, 113, 169, 4, 60, 116, 172, 12, 68, 124, 180, 24, 80, 136, 192, 33, 89, 145, 201, 42, 98, 154, 210, 51, 107, 163, 219, 54, 110, 166, 222, 45, 101, 157, 213, 40, 96, 152, 208, 30, 86, 142, 198, 16, 72, 128, 184, 6, 62, 118, 174, 15, 71, 127, 183, 29, 85, 141, 197, 21, 77, 133, 189, 9, 65, 121, 177, 20, 76, 132, 188, 35, 91, 147, 203, 44, 100, 156, 212, 49, 105, 161, 217, 56, 112, 168, 224, 47, 103, 159, 215, 38, 94, 150, 206, 26, 82, 138, 194, 25, 81, 137, 193, 13, 69, 125, 181, 5, 61, 117, 173)(2, 58, 114, 170, 7, 63, 119, 175, 17, 73, 129, 185, 31, 87, 143, 199, 37, 93, 149, 205, 46, 102, 158, 214, 55, 111, 167, 223, 50, 106, 162, 218, 41, 97, 153, 209, 36, 92, 148, 204, 23, 79, 135, 191, 11, 67, 123, 179, 3, 59, 115, 171, 10, 66, 122, 178, 22, 78, 134, 190, 28, 84, 140, 196, 14, 70, 126, 182, 27, 83, 139, 195, 39, 95, 151, 207, 48, 104, 160, 216, 53, 109, 165, 221, 52, 108, 164, 220, 43, 99, 155, 211, 34, 90, 146, 202, 19, 75, 131, 187, 32, 88, 144, 200, 18, 74, 130, 186, 8, 64, 120, 176)
	L = (1, 58)(2, 57)(3, 65)(4, 64)(5, 63)(6, 70)(7, 61)(8, 60)(9, 59)(10, 77)(11, 76)(12, 74)(13, 73)(14, 62)(15, 84)(16, 83)(17, 69)(18, 68)(19, 89)(20, 67)(21, 66)(22, 85)(23, 91)(24, 88)(25, 87)(26, 93)(27, 72)(28, 71)(29, 78)(30, 95)(31, 81)(32, 80)(33, 75)(34, 98)(35, 79)(36, 100)(37, 82)(38, 102)(39, 86)(40, 104)(41, 105)(42, 90)(43, 107)(44, 92)(45, 109)(46, 94)(47, 111)(48, 96)(49, 97)(50, 112)(51, 99)(52, 110)(53, 101)(54, 108)(55, 103)(56, 106)(113, 171)(114, 174)(115, 169)(116, 179)(117, 178)(118, 170)(119, 184)(120, 183)(121, 187)(122, 173)(123, 172)(124, 191)(125, 190)(126, 194)(127, 176)(128, 175)(129, 198)(130, 197)(131, 177)(132, 202)(133, 200)(134, 181)(135, 180)(136, 204)(137, 196)(138, 182)(139, 206)(140, 193)(141, 186)(142, 185)(143, 208)(144, 189)(145, 209)(146, 188)(147, 211)(148, 192)(149, 213)(150, 195)(151, 215)(152, 199)(153, 201)(154, 218)(155, 203)(156, 220)(157, 205)(158, 222)(159, 207)(160, 224)(161, 221)(162, 210)(163, 223)(164, 212)(165, 217)(166, 214)(167, 219)(168, 216)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1102
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1110 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1, Y1^28, Y2^28 ]
Map:: non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 6, 62, 118, 174)(3, 59, 115, 171, 8, 64, 120, 176)(5, 61, 117, 173, 10, 66, 122, 178)(7, 63, 119, 175, 12, 68, 124, 180)(9, 65, 121, 177, 14, 70, 126, 182)(11, 67, 123, 179, 16, 72, 128, 184)(13, 69, 125, 181, 18, 74, 130, 186)(15, 71, 127, 183, 20, 76, 132, 188)(17, 73, 129, 185, 22, 78, 134, 190)(19, 75, 131, 187, 24, 80, 136, 192)(21, 77, 133, 189, 26, 82, 138, 194)(23, 79, 135, 191, 28, 84, 140, 196)(25, 81, 137, 193, 43, 99, 155, 211)(27, 83, 139, 195, 33, 89, 145, 201)(29, 85, 141, 197, 47, 103, 159, 215)(30, 86, 142, 198, 49, 105, 161, 217)(31, 87, 143, 199, 45, 101, 157, 213)(32, 88, 144, 200, 52, 108, 164, 220)(34, 90, 146, 202, 55, 111, 167, 223)(35, 91, 147, 203, 56, 112, 168, 224)(36, 92, 148, 204, 53, 109, 165, 221)(37, 93, 149, 205, 51, 107, 163, 219)(38, 94, 150, 206, 50, 106, 162, 218)(39, 95, 151, 207, 54, 110, 166, 222)(40, 96, 152, 208, 48, 104, 160, 216)(41, 97, 153, 209, 46, 102, 158, 214)(42, 98, 154, 210, 44, 100, 156, 212)
	L = (1, 58)(2, 61)(3, 57)(4, 64)(5, 65)(6, 60)(7, 59)(8, 68)(9, 69)(10, 62)(11, 63)(12, 72)(13, 73)(14, 66)(15, 67)(16, 76)(17, 77)(18, 70)(19, 71)(20, 80)(21, 81)(22, 74)(23, 75)(24, 84)(25, 85)(26, 78)(27, 79)(28, 89)(29, 86)(30, 88)(31, 90)(32, 91)(33, 87)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 97)(40, 98)(41, 100)(42, 102)(43, 82)(44, 104)(45, 83)(46, 110)(47, 99)(48, 106)(49, 103)(50, 109)(51, 112)(52, 105)(53, 111)(54, 107)(55, 101)(56, 108)(113, 171)(114, 169)(115, 175)(116, 174)(117, 170)(118, 178)(119, 179)(120, 172)(121, 173)(122, 182)(123, 183)(124, 176)(125, 177)(126, 186)(127, 187)(128, 180)(129, 181)(130, 190)(131, 191)(132, 184)(133, 185)(134, 194)(135, 195)(136, 188)(137, 189)(138, 211)(139, 213)(140, 192)(141, 193)(142, 197)(143, 201)(144, 198)(145, 196)(146, 199)(147, 200)(148, 202)(149, 203)(150, 204)(151, 205)(152, 206)(153, 207)(154, 208)(155, 215)(156, 209)(157, 223)(158, 210)(159, 217)(160, 212)(161, 220)(162, 216)(163, 222)(164, 224)(165, 218)(166, 214)(167, 221)(168, 219)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1103
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1111 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C28 x C2 (small group id <56, 8>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^28, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 5, 61)(4, 60, 6, 62)(7, 63, 9, 65)(8, 64, 10, 66)(11, 67, 13, 69)(12, 68, 14, 70)(15, 71, 17, 73)(16, 72, 18, 74)(19, 75, 21, 77)(20, 76, 22, 78)(23, 79, 25, 81)(24, 80, 26, 82)(27, 83, 37, 93)(28, 84, 47, 103)(29, 85, 30, 86)(31, 87, 33, 89)(32, 88, 34, 90)(35, 91, 36, 92)(38, 94, 39, 95)(40, 96, 41, 97)(42, 98, 43, 99)(44, 100, 45, 101)(46, 102, 56, 112)(48, 104, 49, 105)(50, 106, 52, 108)(51, 107, 53, 109)(54, 110, 55, 111)(113, 169, 115, 171, 119, 175, 123, 179, 127, 183, 131, 187, 135, 191, 139, 195, 144, 200, 141, 197, 143, 199, 147, 203, 150, 206, 152, 208, 154, 210, 156, 212, 158, 214, 163, 219, 160, 216, 162, 218, 166, 222, 140, 196, 136, 192, 132, 188, 128, 184, 124, 180, 120, 176, 116, 172)(114, 170, 117, 173, 121, 177, 125, 181, 129, 185, 133, 189, 137, 193, 149, 205, 146, 202, 142, 198, 145, 201, 148, 204, 151, 207, 153, 209, 155, 211, 157, 213, 168, 224, 165, 221, 161, 217, 164, 220, 167, 223, 159, 215, 138, 194, 134, 190, 130, 186, 126, 182, 122, 178, 118, 174)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1112 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^28, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 5, 61)(7, 63, 10, 66)(8, 64, 9, 65)(11, 67, 14, 70)(12, 68, 13, 69)(15, 71, 18, 74)(16, 72, 17, 73)(19, 75, 22, 78)(20, 76, 21, 77)(23, 79, 26, 82)(24, 80, 25, 81)(27, 83, 44, 100)(28, 84, 49, 105)(29, 85, 50, 106)(30, 86, 48, 104)(31, 87, 53, 109)(32, 88, 47, 103)(33, 89, 52, 108)(34, 90, 46, 102)(35, 91, 54, 110)(36, 92, 45, 101)(37, 93, 55, 111)(38, 94, 43, 99)(39, 95, 56, 112)(40, 96, 42, 98)(41, 97, 51, 107)(113, 169, 115, 171, 119, 175, 123, 179, 127, 183, 131, 187, 135, 191, 139, 195, 163, 219, 167, 223, 164, 220, 160, 216, 158, 214, 155, 211, 152, 208, 148, 204, 144, 200, 141, 197, 143, 199, 147, 203, 151, 207, 140, 196, 136, 192, 132, 188, 128, 184, 124, 180, 120, 176, 116, 172)(114, 170, 117, 173, 121, 177, 125, 181, 129, 185, 133, 189, 137, 193, 161, 217, 168, 224, 166, 222, 165, 221, 162, 218, 159, 215, 157, 213, 154, 210, 150, 206, 146, 202, 142, 198, 145, 201, 149, 205, 153, 209, 156, 212, 138, 194, 134, 190, 130, 186, 126, 182, 122, 178, 118, 174)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1113 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C28 x C2 (small group id <56, 8>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^14 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 7, 63)(5, 61, 8, 64)(9, 65, 13, 69)(10, 66, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 52, 108)(50, 106, 53, 109)(51, 107, 54, 110)(55, 111, 56, 112)(113, 169, 115, 171, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176, 114, 170, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(116, 172, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 167, 223, 166, 222, 159, 215, 151, 207, 143, 199, 135, 191, 127, 183, 119, 175, 126, 182, 134, 190, 142, 198, 150, 206, 158, 214, 165, 221, 168, 224, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179)
	L = (1, 116)(2, 119)(3, 122)(4, 113)(5, 123)(6, 126)(7, 114)(8, 127)(9, 130)(10, 115)(11, 117)(12, 131)(13, 134)(14, 118)(15, 120)(16, 135)(17, 138)(18, 121)(19, 124)(20, 139)(21, 142)(22, 125)(23, 128)(24, 143)(25, 146)(26, 129)(27, 132)(28, 147)(29, 150)(30, 133)(31, 136)(32, 151)(33, 154)(34, 137)(35, 140)(36, 155)(37, 158)(38, 141)(39, 144)(40, 159)(41, 162)(42, 145)(43, 148)(44, 163)(45, 165)(46, 149)(47, 152)(48, 166)(49, 167)(50, 153)(51, 156)(52, 168)(53, 157)(54, 160)(55, 161)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1114
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1114 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C28 x C2 (small group id <56, 8>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y2^2 * Y1 * Y3 * Y2^-2 * Y1, Y2^4 * Y3 * Y2^10 * Y1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 7, 63)(5, 61, 8, 64)(9, 65, 13, 69)(10, 66, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 169, 115, 171, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 167, 223, 159, 215, 151, 207, 143, 199, 135, 191, 127, 183, 119, 175, 126, 182, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179, 116, 172, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)
	L = (1, 116)(2, 119)(3, 122)(4, 113)(5, 123)(6, 126)(7, 114)(8, 127)(9, 130)(10, 115)(11, 117)(12, 131)(13, 134)(14, 118)(15, 120)(16, 135)(17, 138)(18, 121)(19, 124)(20, 139)(21, 142)(22, 125)(23, 128)(24, 143)(25, 146)(26, 129)(27, 132)(28, 147)(29, 150)(30, 133)(31, 136)(32, 151)(33, 154)(34, 137)(35, 140)(36, 155)(37, 158)(38, 141)(39, 144)(40, 159)(41, 162)(42, 145)(43, 148)(44, 163)(45, 166)(46, 149)(47, 152)(48, 167)(49, 168)(50, 153)(51, 156)(52, 165)(53, 164)(54, 157)(55, 160)(56, 161)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1113
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1115 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = C28 x C2 (small group id <56, 8>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, (R * Y1)^2, Y3 * Y2^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 6, 62)(4, 60, 7, 63)(5, 61, 8, 64)(9, 65, 13, 69)(10, 66, 14, 70)(11, 67, 15, 71)(12, 68, 16, 72)(17, 73, 21, 77)(18, 74, 22, 78)(19, 75, 23, 79)(20, 76, 24, 80)(25, 81, 29, 85)(26, 82, 30, 86)(27, 83, 31, 87)(28, 84, 32, 88)(33, 89, 37, 93)(34, 90, 38, 94)(35, 91, 39, 95)(36, 92, 40, 96)(41, 97, 45, 101)(42, 98, 46, 102)(43, 99, 47, 103)(44, 100, 48, 104)(49, 105, 53, 109)(50, 106, 54, 110)(51, 107, 55, 111)(52, 108, 56, 112)(113, 169, 115, 171, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179, 116, 172, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 167, 223, 159, 215, 151, 207, 143, 199, 135, 191, 127, 183, 119, 175, 126, 182, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)
	L = (1, 116)(2, 119)(3, 122)(4, 113)(5, 123)(6, 126)(7, 114)(8, 127)(9, 130)(10, 115)(11, 117)(12, 131)(13, 134)(14, 118)(15, 120)(16, 135)(17, 138)(18, 121)(19, 124)(20, 139)(21, 142)(22, 125)(23, 128)(24, 143)(25, 146)(26, 129)(27, 132)(28, 147)(29, 150)(30, 133)(31, 136)(32, 151)(33, 154)(34, 137)(35, 140)(36, 155)(37, 158)(38, 141)(39, 144)(40, 159)(41, 162)(42, 145)(43, 148)(44, 163)(45, 166)(46, 149)(47, 152)(48, 167)(49, 164)(50, 153)(51, 156)(52, 161)(53, 168)(54, 157)(55, 160)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1116 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2 * Y1)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y2^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 8, 64)(4, 60, 7, 63)(5, 61, 6, 62)(9, 65, 16, 72)(10, 66, 15, 71)(11, 67, 14, 70)(12, 68, 13, 69)(17, 73, 24, 80)(18, 74, 23, 79)(19, 75, 22, 78)(20, 76, 21, 77)(25, 81, 32, 88)(26, 82, 31, 87)(27, 83, 30, 86)(28, 84, 29, 85)(33, 89, 40, 96)(34, 90, 39, 95)(35, 91, 38, 94)(36, 92, 37, 93)(41, 97, 48, 104)(42, 98, 47, 103)(43, 99, 46, 102)(44, 100, 45, 101)(49, 105, 56, 112)(50, 106, 55, 111)(51, 107, 54, 110)(52, 108, 53, 109)(113, 169, 115, 171, 121, 177, 129, 185, 137, 193, 145, 201, 153, 209, 161, 217, 163, 219, 155, 211, 147, 203, 139, 195, 131, 187, 123, 179, 116, 172, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 164, 220, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 165, 221, 167, 223, 159, 215, 151, 207, 143, 199, 135, 191, 127, 183, 119, 175, 126, 182, 134, 190, 142, 198, 150, 206, 158, 214, 166, 222, 168, 224, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)
	L = (1, 116)(2, 119)(3, 122)(4, 113)(5, 123)(6, 126)(7, 114)(8, 127)(9, 130)(10, 115)(11, 117)(12, 131)(13, 134)(14, 118)(15, 120)(16, 135)(17, 138)(18, 121)(19, 124)(20, 139)(21, 142)(22, 125)(23, 128)(24, 143)(25, 146)(26, 129)(27, 132)(28, 147)(29, 150)(30, 133)(31, 136)(32, 151)(33, 154)(34, 137)(35, 140)(36, 155)(37, 158)(38, 141)(39, 144)(40, 159)(41, 162)(42, 145)(43, 148)(44, 163)(45, 166)(46, 149)(47, 152)(48, 167)(49, 164)(50, 153)(51, 156)(52, 161)(53, 168)(54, 157)(55, 160)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1117 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y2^4 * Y3^-3, Y3^7, Y3^-2 * Y2^-1 * Y3^-2 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 47, 103)(28, 84, 48, 104)(29, 85, 46, 102)(30, 86, 49, 105)(31, 87, 45, 101)(32, 88, 50, 106)(33, 89, 43, 99)(34, 90, 41, 97)(35, 91, 39, 95)(36, 92, 40, 96)(37, 93, 42, 98)(38, 94, 44, 100)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 123, 179, 139, 195, 144, 200, 165, 221, 148, 204, 129, 185, 118, 174, 125, 181, 141, 197, 145, 201, 126, 182, 142, 198, 164, 220, 149, 205, 130, 186, 143, 199, 146, 202, 127, 183, 116, 172, 124, 180, 140, 196, 163, 219, 150, 206, 147, 203, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 151, 207, 156, 212, 168, 224, 160, 216, 137, 193, 122, 178, 133, 189, 153, 209, 157, 213, 134, 190, 154, 210, 167, 223, 161, 217, 138, 194, 155, 211, 158, 214, 135, 191, 120, 176, 132, 188, 152, 208, 166, 222, 162, 218, 159, 215, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 140)(12, 142)(13, 115)(14, 144)(15, 145)(16, 146)(17, 117)(18, 118)(19, 152)(20, 154)(21, 119)(22, 156)(23, 157)(24, 158)(25, 121)(26, 122)(27, 163)(28, 164)(29, 123)(30, 165)(31, 125)(32, 150)(33, 139)(34, 141)(35, 143)(36, 128)(37, 129)(38, 130)(39, 166)(40, 167)(41, 131)(42, 168)(43, 133)(44, 162)(45, 151)(46, 153)(47, 155)(48, 136)(49, 137)(50, 138)(51, 149)(52, 148)(53, 147)(54, 161)(55, 160)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1121
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1118 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (Y2^-1 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^2 * Y2^-4, Y3^7, Y3^2 * Y2 * Y3 * Y2 * Y3^2 * Y2^2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 40, 96)(28, 84, 42, 98)(29, 85, 38, 94)(30, 86, 43, 99)(31, 87, 36, 92)(32, 88, 44, 100)(33, 89, 37, 93)(34, 90, 39, 95)(35, 91, 41, 97)(45, 101, 54, 110)(46, 102, 55, 111)(47, 103, 56, 112)(48, 104, 51, 107)(49, 105, 52, 108)(50, 106, 53, 109)(113, 169, 115, 171, 123, 179, 139, 195, 126, 182, 142, 198, 158, 214, 162, 218, 147, 203, 160, 216, 145, 201, 129, 185, 118, 174, 125, 181, 141, 197, 127, 183, 116, 172, 124, 180, 140, 196, 157, 213, 144, 200, 159, 215, 161, 217, 146, 202, 130, 186, 143, 199, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 148, 204, 134, 190, 151, 207, 164, 220, 168, 224, 156, 212, 166, 222, 154, 210, 137, 193, 122, 178, 133, 189, 150, 206, 135, 191, 120, 176, 132, 188, 149, 205, 163, 219, 153, 209, 165, 221, 167, 223, 155, 211, 138, 194, 152, 208, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 140)(12, 142)(13, 115)(14, 144)(15, 139)(16, 141)(17, 117)(18, 118)(19, 149)(20, 151)(21, 119)(22, 153)(23, 148)(24, 150)(25, 121)(26, 122)(27, 157)(28, 158)(29, 123)(30, 159)(31, 125)(32, 147)(33, 128)(34, 129)(35, 130)(36, 163)(37, 164)(38, 131)(39, 165)(40, 133)(41, 156)(42, 136)(43, 137)(44, 138)(45, 162)(46, 161)(47, 160)(48, 143)(49, 145)(50, 146)(51, 168)(52, 167)(53, 166)(54, 152)(55, 154)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1119 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2), (Y2 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y2^-4, Y3^7, Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-3 * Y2, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-4 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 39, 95)(28, 84, 37, 93)(29, 85, 43, 99)(30, 86, 36, 92)(31, 87, 42, 98)(32, 88, 44, 100)(33, 89, 40, 96)(34, 90, 38, 94)(35, 91, 41, 97)(45, 101, 53, 109)(46, 102, 56, 112)(47, 103, 51, 107)(48, 104, 55, 111)(49, 105, 54, 110)(50, 106, 52, 108)(113, 169, 115, 171, 123, 179, 139, 195, 130, 186, 143, 199, 158, 214, 161, 217, 144, 200, 159, 215, 146, 202, 127, 183, 116, 172, 124, 180, 140, 196, 129, 185, 118, 174, 125, 181, 141, 197, 157, 213, 147, 203, 160, 216, 162, 218, 145, 201, 126, 182, 142, 198, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 148, 204, 138, 194, 152, 208, 164, 220, 167, 223, 153, 209, 165, 221, 155, 211, 135, 191, 120, 176, 132, 188, 149, 205, 137, 193, 122, 178, 133, 189, 150, 206, 163, 219, 156, 212, 166, 222, 168, 224, 154, 210, 134, 190, 151, 207, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 140)(12, 142)(13, 115)(14, 144)(15, 145)(16, 146)(17, 117)(18, 118)(19, 149)(20, 151)(21, 119)(22, 153)(23, 154)(24, 155)(25, 121)(26, 122)(27, 129)(28, 128)(29, 123)(30, 159)(31, 125)(32, 147)(33, 161)(34, 162)(35, 130)(36, 137)(37, 136)(38, 131)(39, 165)(40, 133)(41, 156)(42, 167)(43, 168)(44, 138)(45, 139)(46, 141)(47, 160)(48, 143)(49, 157)(50, 158)(51, 148)(52, 150)(53, 166)(54, 152)(55, 163)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1120
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1120 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3, Y2), (Y2 * Y1)^2, (R * Y2)^2, Y3 * Y2^4, Y3^7, Y2 * Y3^-3 * Y2 * Y3^-2 * Y2^2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-3 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 40, 96)(28, 84, 41, 97)(29, 85, 39, 95)(30, 86, 42, 98)(31, 87, 37, 93)(32, 88, 35, 91)(33, 89, 36, 92)(34, 90, 38, 94)(43, 99, 53, 109)(44, 100, 54, 110)(45, 101, 52, 108)(46, 102, 51, 107)(47, 103, 49, 105)(48, 104, 50, 106)(55, 111, 56, 112)(113, 169, 115, 171, 123, 179, 129, 185, 118, 174, 125, 181, 139, 195, 145, 201, 130, 186, 141, 197, 155, 211, 160, 216, 146, 202, 157, 213, 167, 223, 158, 214, 142, 198, 156, 212, 159, 215, 143, 199, 126, 182, 140, 196, 144, 200, 127, 183, 116, 172, 124, 180, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 137, 193, 122, 178, 133, 189, 147, 203, 153, 209, 138, 194, 149, 205, 161, 217, 166, 222, 154, 210, 163, 219, 168, 224, 164, 220, 150, 206, 162, 218, 165, 221, 151, 207, 134, 190, 148, 204, 152, 208, 135, 191, 120, 176, 132, 188, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 128)(12, 140)(13, 115)(14, 142)(15, 143)(16, 144)(17, 117)(18, 118)(19, 136)(20, 148)(21, 119)(22, 150)(23, 151)(24, 152)(25, 121)(26, 122)(27, 123)(28, 156)(29, 125)(30, 146)(31, 158)(32, 159)(33, 129)(34, 130)(35, 131)(36, 162)(37, 133)(38, 154)(39, 164)(40, 165)(41, 137)(42, 138)(43, 139)(44, 157)(45, 141)(46, 160)(47, 167)(48, 145)(49, 147)(50, 163)(51, 149)(52, 166)(53, 168)(54, 153)(55, 155)(56, 161)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1119
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1121 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y2^4, Y3^7, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 40, 96)(28, 84, 41, 97)(29, 85, 39, 95)(30, 86, 42, 98)(31, 87, 37, 93)(32, 88, 35, 91)(33, 89, 36, 92)(34, 90, 38, 94)(43, 99, 53, 109)(44, 100, 54, 110)(45, 101, 52, 108)(46, 102, 51, 107)(47, 103, 49, 105)(48, 104, 50, 106)(55, 111, 56, 112)(113, 169, 115, 171, 123, 179, 127, 183, 116, 172, 124, 180, 139, 195, 143, 199, 126, 182, 140, 196, 155, 211, 158, 214, 142, 198, 156, 212, 167, 223, 160, 216, 146, 202, 157, 213, 159, 215, 145, 201, 130, 186, 141, 197, 144, 200, 129, 185, 118, 174, 125, 181, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 135, 191, 120, 176, 132, 188, 147, 203, 151, 207, 134, 190, 148, 204, 161, 217, 164, 220, 150, 206, 162, 218, 168, 224, 166, 222, 154, 210, 163, 219, 165, 221, 153, 209, 138, 194, 149, 205, 152, 208, 137, 193, 122, 178, 133, 189, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 139)(12, 140)(13, 115)(14, 142)(15, 143)(16, 123)(17, 117)(18, 118)(19, 147)(20, 148)(21, 119)(22, 150)(23, 151)(24, 131)(25, 121)(26, 122)(27, 155)(28, 156)(29, 125)(30, 146)(31, 158)(32, 128)(33, 129)(34, 130)(35, 161)(36, 162)(37, 133)(38, 154)(39, 164)(40, 136)(41, 137)(42, 138)(43, 167)(44, 157)(45, 141)(46, 160)(47, 144)(48, 145)(49, 168)(50, 163)(51, 149)(52, 166)(53, 152)(54, 153)(55, 159)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1117
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1122 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^14 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 17, 73)(12, 68, 18, 74)(13, 69, 15, 71)(14, 70, 16, 72)(19, 75, 25, 81)(20, 76, 26, 82)(21, 77, 23, 79)(22, 78, 24, 80)(27, 83, 33, 89)(28, 84, 34, 90)(29, 85, 31, 87)(30, 86, 32, 88)(35, 91, 41, 97)(36, 92, 42, 98)(37, 93, 39, 95)(38, 94, 40, 96)(43, 99, 49, 105)(44, 100, 50, 106)(45, 101, 47, 103)(46, 102, 48, 104)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 116, 172, 123, 179, 124, 180, 131, 187, 132, 188, 139, 195, 140, 196, 147, 203, 148, 204, 155, 211, 156, 212, 163, 219, 164, 220, 165, 221, 158, 214, 157, 213, 150, 206, 149, 205, 142, 198, 141, 197, 134, 190, 133, 189, 126, 182, 125, 181, 118, 174, 117, 173)(114, 170, 119, 175, 120, 176, 127, 183, 128, 184, 135, 191, 136, 192, 143, 199, 144, 200, 151, 207, 152, 208, 159, 215, 160, 216, 166, 222, 167, 223, 168, 224, 162, 218, 161, 217, 154, 210, 153, 209, 146, 202, 145, 201, 138, 194, 137, 193, 130, 186, 129, 185, 122, 178, 121, 177)
	L = (1, 116)(2, 120)(3, 123)(4, 124)(5, 115)(6, 113)(7, 127)(8, 128)(9, 119)(10, 114)(11, 131)(12, 132)(13, 117)(14, 118)(15, 135)(16, 136)(17, 121)(18, 122)(19, 139)(20, 140)(21, 125)(22, 126)(23, 143)(24, 144)(25, 129)(26, 130)(27, 147)(28, 148)(29, 133)(30, 134)(31, 151)(32, 152)(33, 137)(34, 138)(35, 155)(36, 156)(37, 141)(38, 142)(39, 159)(40, 160)(41, 145)(42, 146)(43, 163)(44, 164)(45, 149)(46, 150)(47, 166)(48, 167)(49, 153)(50, 154)(51, 165)(52, 158)(53, 157)(54, 168)(55, 162)(56, 161)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1123 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^14, (Y3 * Y2^-1)^28 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 17, 73)(12, 68, 18, 74)(13, 69, 15, 71)(14, 70, 16, 72)(19, 75, 25, 81)(20, 76, 26, 82)(21, 77, 23, 79)(22, 78, 24, 80)(27, 83, 33, 89)(28, 84, 34, 90)(29, 85, 31, 87)(30, 86, 32, 88)(35, 91, 41, 97)(36, 92, 42, 98)(37, 93, 39, 95)(38, 94, 40, 96)(43, 99, 49, 105)(44, 100, 50, 106)(45, 101, 47, 103)(46, 102, 48, 104)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 118, 174, 123, 179, 126, 182, 131, 187, 134, 190, 139, 195, 142, 198, 147, 203, 150, 206, 155, 211, 158, 214, 163, 219, 164, 220, 165, 221, 156, 212, 157, 213, 148, 204, 149, 205, 140, 196, 141, 197, 132, 188, 133, 189, 124, 180, 125, 181, 116, 172, 117, 173)(114, 170, 119, 175, 122, 178, 127, 183, 130, 186, 135, 191, 138, 194, 143, 199, 146, 202, 151, 207, 154, 210, 159, 215, 162, 218, 166, 222, 167, 223, 168, 224, 160, 216, 161, 217, 152, 208, 153, 209, 144, 200, 145, 201, 136, 192, 137, 193, 128, 184, 129, 185, 120, 176, 121, 177)
	L = (1, 116)(2, 120)(3, 117)(4, 124)(5, 125)(6, 113)(7, 121)(8, 128)(9, 129)(10, 114)(11, 115)(12, 132)(13, 133)(14, 118)(15, 119)(16, 136)(17, 137)(18, 122)(19, 123)(20, 140)(21, 141)(22, 126)(23, 127)(24, 144)(25, 145)(26, 130)(27, 131)(28, 148)(29, 149)(30, 134)(31, 135)(32, 152)(33, 153)(34, 138)(35, 139)(36, 156)(37, 157)(38, 142)(39, 143)(40, 160)(41, 161)(42, 146)(43, 147)(44, 164)(45, 165)(46, 150)(47, 151)(48, 167)(49, 168)(50, 154)(51, 155)(52, 158)(53, 163)(54, 159)(55, 162)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1125
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1124 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-3, Y2 * Y3^-1 * Y2^5, Y3 * Y2^2 * Y3 * Y2^2 * Y3^2, Y3^-2 * Y2^-1 * Y3^-2 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 47, 103)(28, 84, 48, 104)(29, 85, 46, 102)(30, 86, 49, 105)(31, 87, 45, 101)(32, 88, 50, 106)(33, 89, 43, 99)(34, 90, 41, 97)(35, 91, 39, 95)(36, 92, 40, 96)(37, 93, 42, 98)(38, 94, 44, 100)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 123, 179, 139, 195, 146, 202, 127, 183, 116, 172, 124, 180, 140, 196, 163, 219, 150, 206, 145, 201, 126, 182, 142, 198, 164, 220, 149, 205, 130, 186, 143, 199, 144, 200, 165, 221, 148, 204, 129, 185, 118, 174, 125, 181, 141, 197, 147, 203, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 151, 207, 158, 214, 135, 191, 120, 176, 132, 188, 152, 208, 166, 222, 162, 218, 157, 213, 134, 190, 154, 210, 167, 223, 161, 217, 138, 194, 155, 211, 156, 212, 168, 224, 160, 216, 137, 193, 122, 178, 133, 189, 153, 209, 159, 215, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 140)(12, 142)(13, 115)(14, 144)(15, 145)(16, 146)(17, 117)(18, 118)(19, 152)(20, 154)(21, 119)(22, 156)(23, 157)(24, 158)(25, 121)(26, 122)(27, 163)(28, 164)(29, 123)(30, 165)(31, 125)(32, 141)(33, 143)(34, 150)(35, 139)(36, 128)(37, 129)(38, 130)(39, 166)(40, 167)(41, 131)(42, 168)(43, 133)(44, 153)(45, 155)(46, 162)(47, 151)(48, 136)(49, 137)(50, 138)(51, 149)(52, 148)(53, 147)(54, 161)(55, 160)(56, 159)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1126
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1125 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-2, Y3^-2 * Y2^-8, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-5 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 36, 92)(28, 84, 37, 93)(29, 85, 38, 94)(30, 86, 33, 89)(31, 87, 34, 90)(32, 88, 35, 91)(39, 95, 48, 104)(40, 96, 49, 105)(41, 97, 50, 106)(42, 98, 45, 101)(43, 99, 46, 102)(44, 100, 47, 103)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 123, 179, 139, 195, 151, 207, 163, 219, 156, 212, 144, 200, 130, 186, 127, 183, 116, 172, 124, 180, 140, 196, 152, 208, 164, 220, 155, 211, 143, 199, 129, 185, 118, 174, 125, 181, 126, 182, 141, 197, 153, 209, 165, 221, 154, 210, 142, 198, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 145, 201, 157, 213, 166, 222, 162, 218, 150, 206, 138, 194, 135, 191, 120, 176, 132, 188, 146, 202, 158, 214, 167, 223, 161, 217, 149, 205, 137, 193, 122, 178, 133, 189, 134, 190, 147, 203, 159, 215, 168, 224, 160, 216, 148, 204, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 140)(12, 141)(13, 115)(14, 123)(15, 125)(16, 130)(17, 117)(18, 118)(19, 146)(20, 147)(21, 119)(22, 131)(23, 133)(24, 138)(25, 121)(26, 122)(27, 152)(28, 153)(29, 139)(30, 144)(31, 128)(32, 129)(33, 158)(34, 159)(35, 145)(36, 150)(37, 136)(38, 137)(39, 164)(40, 165)(41, 151)(42, 156)(43, 142)(44, 143)(45, 167)(46, 168)(47, 157)(48, 162)(49, 148)(50, 149)(51, 155)(52, 154)(53, 163)(54, 161)(55, 160)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1123
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1126 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 28, 28})
Quotient :: dipole
Aut^+ = D56 (small group id <56, 5>)
Aut   = C2 x D56 (small group id <112, 29>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2^2 * Y3^2, Y2^-1 * Y3 * Y2^-3 * Y3 * Y2^-4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 57, 2, 58)(3, 59, 9, 65)(4, 60, 10, 66)(5, 61, 7, 63)(6, 62, 8, 64)(11, 67, 24, 80)(12, 68, 25, 81)(13, 69, 23, 79)(14, 70, 26, 82)(15, 71, 21, 77)(16, 72, 19, 75)(17, 73, 20, 76)(18, 74, 22, 78)(27, 83, 38, 94)(28, 84, 37, 93)(29, 85, 36, 92)(30, 86, 35, 91)(31, 87, 34, 90)(32, 88, 33, 89)(39, 95, 50, 106)(40, 96, 49, 105)(41, 97, 48, 104)(42, 98, 47, 103)(43, 99, 46, 102)(44, 100, 45, 101)(51, 107, 56, 112)(52, 108, 55, 111)(53, 109, 54, 110)(113, 169, 115, 171, 123, 179, 139, 195, 151, 207, 163, 219, 154, 210, 142, 198, 126, 182, 129, 185, 118, 174, 125, 181, 140, 196, 152, 208, 164, 220, 155, 211, 143, 199, 127, 183, 116, 172, 124, 180, 130, 186, 141, 197, 153, 209, 165, 221, 156, 212, 144, 200, 128, 184, 117, 173)(114, 170, 119, 175, 131, 187, 145, 201, 157, 213, 166, 222, 160, 216, 148, 204, 134, 190, 137, 193, 122, 178, 133, 189, 146, 202, 158, 214, 167, 223, 161, 217, 149, 205, 135, 191, 120, 176, 132, 188, 138, 194, 147, 203, 159, 215, 168, 224, 162, 218, 150, 206, 136, 192, 121, 177)
	L = (1, 116)(2, 120)(3, 124)(4, 126)(5, 127)(6, 113)(7, 132)(8, 134)(9, 135)(10, 114)(11, 130)(12, 129)(13, 115)(14, 128)(15, 142)(16, 143)(17, 117)(18, 118)(19, 138)(20, 137)(21, 119)(22, 136)(23, 148)(24, 149)(25, 121)(26, 122)(27, 141)(28, 123)(29, 125)(30, 144)(31, 154)(32, 155)(33, 147)(34, 131)(35, 133)(36, 150)(37, 160)(38, 161)(39, 153)(40, 139)(41, 140)(42, 156)(43, 163)(44, 164)(45, 159)(46, 145)(47, 146)(48, 162)(49, 166)(50, 167)(51, 165)(52, 151)(53, 152)(54, 168)(55, 157)(56, 158)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 56, 4, 56 ), ( 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1124
Graph:: bipartite
	v = 30 e = 112 f = 30
	degree seq :: [ 4^28, 56^2 ]

E27.1127 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 28, 28})
Quotient :: edge^2
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = C14 x D8 (small group id <112, 38>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^7 * Y1^-2 * Y3 * Y1^-5 * Y3, Y2^28, Y1^28 ]
Map:: non-degenerate
	R = (1, 57, 4, 60)(2, 58, 6, 62)(3, 59, 8, 64)(5, 61, 12, 68)(7, 63, 16, 72)(9, 65, 18, 74)(10, 66, 19, 75)(11, 67, 21, 77)(13, 69, 23, 79)(14, 70, 24, 80)(15, 71, 26, 82)(17, 73, 28, 84)(20, 76, 30, 86)(22, 78, 32, 88)(25, 81, 34, 90)(27, 83, 36, 92)(29, 85, 38, 94)(31, 87, 40, 96)(33, 89, 42, 98)(35, 91, 44, 100)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(43, 99, 52, 108)(45, 101, 54, 110)(47, 103, 56, 112)(49, 105, 55, 111)(51, 107, 53, 109)(113, 114, 117, 123, 132, 141, 149, 157, 165, 164, 156, 148, 140, 131, 136, 130, 135, 144, 152, 160, 168, 161, 153, 145, 137, 127, 119, 115)(116, 121, 124, 134, 142, 151, 158, 167, 163, 154, 147, 138, 129, 120, 126, 118, 125, 133, 143, 150, 159, 166, 162, 155, 146, 139, 128, 122)(169, 171, 175, 183, 193, 201, 209, 217, 224, 216, 208, 200, 191, 186, 192, 187, 196, 204, 212, 220, 221, 213, 205, 197, 188, 179, 173, 170)(172, 178, 184, 195, 202, 211, 218, 222, 215, 206, 199, 189, 181, 174, 182, 176, 185, 194, 203, 210, 219, 223, 214, 207, 198, 190, 180, 177)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1128
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.1128 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 28, 28})
Quotient :: loop^2
Aut^+ = C7 x D8 (small group id <56, 9>)
Aut   = C14 x D8 (small group id <112, 38>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^7 * Y1^-2 * Y3 * Y1^-5 * Y3, Y2^28, Y1^28 ]
Map:: non-degenerate
	R = (1, 57, 113, 169, 4, 60, 116, 172)(2, 58, 114, 170, 6, 62, 118, 174)(3, 59, 115, 171, 8, 64, 120, 176)(5, 61, 117, 173, 12, 68, 124, 180)(7, 63, 119, 175, 16, 72, 128, 184)(9, 65, 121, 177, 18, 74, 130, 186)(10, 66, 122, 178, 19, 75, 131, 187)(11, 67, 123, 179, 21, 77, 133, 189)(13, 69, 125, 181, 23, 79, 135, 191)(14, 70, 126, 182, 24, 80, 136, 192)(15, 71, 127, 183, 26, 82, 138, 194)(17, 73, 129, 185, 28, 84, 140, 196)(20, 76, 132, 188, 30, 86, 142, 198)(22, 78, 134, 190, 32, 88, 144, 200)(25, 81, 137, 193, 34, 90, 146, 202)(27, 83, 139, 195, 36, 92, 148, 204)(29, 85, 141, 197, 38, 94, 150, 206)(31, 87, 143, 199, 40, 96, 152, 208)(33, 89, 145, 201, 42, 98, 154, 210)(35, 91, 147, 203, 44, 100, 156, 212)(37, 93, 149, 205, 46, 102, 158, 214)(39, 95, 151, 207, 48, 104, 160, 216)(41, 97, 153, 209, 50, 106, 162, 218)(43, 99, 155, 211, 52, 108, 164, 220)(45, 101, 157, 213, 54, 110, 166, 222)(47, 103, 159, 215, 56, 112, 168, 224)(49, 105, 161, 217, 55, 111, 167, 223)(51, 107, 163, 219, 53, 109, 165, 221)
	L = (1, 58)(2, 61)(3, 57)(4, 65)(5, 67)(6, 69)(7, 59)(8, 70)(9, 68)(10, 60)(11, 76)(12, 78)(13, 77)(14, 62)(15, 63)(16, 66)(17, 64)(18, 79)(19, 80)(20, 85)(21, 87)(22, 86)(23, 88)(24, 74)(25, 71)(26, 73)(27, 72)(28, 75)(29, 93)(30, 95)(31, 94)(32, 96)(33, 81)(34, 83)(35, 82)(36, 84)(37, 101)(38, 103)(39, 102)(40, 104)(41, 89)(42, 91)(43, 90)(44, 92)(45, 109)(46, 111)(47, 110)(48, 112)(49, 97)(50, 99)(51, 98)(52, 100)(53, 108)(54, 106)(55, 107)(56, 105)(113, 171)(114, 169)(115, 175)(116, 178)(117, 170)(118, 182)(119, 183)(120, 185)(121, 172)(122, 184)(123, 173)(124, 177)(125, 174)(126, 176)(127, 193)(128, 195)(129, 194)(130, 192)(131, 196)(132, 179)(133, 181)(134, 180)(135, 186)(136, 187)(137, 201)(138, 203)(139, 202)(140, 204)(141, 188)(142, 190)(143, 189)(144, 191)(145, 209)(146, 211)(147, 210)(148, 212)(149, 197)(150, 199)(151, 198)(152, 200)(153, 217)(154, 219)(155, 218)(156, 220)(157, 205)(158, 207)(159, 206)(160, 208)(161, 224)(162, 222)(163, 223)(164, 221)(165, 213)(166, 215)(167, 214)(168, 216)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1127
Transitivity :: VT+
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.1129 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^2, (F * T1)^2, (F * T2)^2, T1^28, (T2^-1 * T1^-1)^56 ]
Map:: non-degenerate
	R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 27, 26, 31, 30, 35, 34, 39, 38, 43, 42, 47, 46, 51, 50, 55, 54, 56, 52, 53, 48, 49, 44, 45, 40, 41, 36, 37, 32, 33, 28, 29, 24, 25, 20, 21, 16, 17, 12, 13, 8, 9, 4, 5)(57, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72, 68, 64, 60)(59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 112, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69, 65, 61)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1146
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1130 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T1 * T2^2, (F * T2)^2, (F * T1)^2, T1^28 ]
Map:: non-degenerate
	R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 54, 55, 50, 51, 46, 47, 42, 43, 38, 39, 34, 35, 30, 31, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(57, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69, 65, 60)(59, 61, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 112, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72, 68, 64)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1144
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1131 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^17, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 3, 9, 16, 22, 28, 34, 40, 46, 52, 54, 48, 42, 36, 30, 24, 18, 12, 4, 10, 6, 14, 20, 26, 32, 38, 44, 50, 56, 53, 47, 41, 35, 29, 23, 17, 11, 8, 2, 7, 15, 21, 27, 33, 39, 45, 51, 55, 49, 43, 37, 31, 25, 19, 13, 5)(57, 58, 62, 65, 71, 76, 78, 83, 88, 90, 95, 100, 102, 107, 112, 110, 105, 103, 98, 93, 91, 86, 81, 79, 74, 69, 67, 60)(59, 63, 70, 72, 77, 82, 84, 89, 94, 96, 101, 106, 108, 111, 109, 104, 99, 97, 92, 87, 85, 80, 75, 73, 68, 61, 64, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1147
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1132 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^2, T1 * T2^-18 ]
Map:: non-degenerate
	R = (1, 3, 9, 16, 22, 28, 34, 40, 46, 52, 51, 45, 39, 33, 27, 21, 15, 8, 2, 7, 11, 18, 24, 30, 36, 42, 48, 54, 56, 50, 44, 38, 32, 26, 20, 14, 6, 12, 4, 10, 17, 23, 29, 35, 41, 47, 53, 55, 49, 43, 37, 31, 25, 19, 13, 5)(57, 58, 62, 69, 71, 76, 81, 83, 88, 93, 95, 100, 105, 107, 112, 109, 102, 104, 97, 90, 92, 85, 78, 80, 73, 65, 67, 60)(59, 63, 68, 61, 64, 70, 75, 77, 82, 87, 89, 94, 99, 101, 106, 111, 108, 110, 103, 96, 98, 91, 84, 86, 79, 72, 74, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1143
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1133 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T1^3 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-9 * T1, (T2^-1 * T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 30, 40, 50, 46, 36, 26, 14, 23, 11, 21, 32, 42, 52, 49, 39, 29, 18, 8, 2, 7, 17, 28, 38, 48, 56, 54, 44, 34, 24, 12, 4, 10, 20, 31, 41, 51, 47, 37, 27, 16, 6, 15, 22, 33, 43, 53, 55, 45, 35, 25, 13, 5)(57, 58, 62, 70, 80, 69, 74, 83, 92, 100, 91, 95, 103, 106, 112, 111, 108, 97, 86, 94, 99, 88, 76, 65, 73, 78, 67, 60)(59, 63, 71, 79, 68, 61, 64, 72, 82, 90, 81, 85, 93, 102, 110, 101, 105, 107, 96, 104, 109, 98, 87, 75, 84, 89, 77, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1145
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1134 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1 * T2^5, T2 * T1^-1 * T2 * T1^-8, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 32, 37, 23, 11, 21, 33, 44, 49, 36, 22, 34, 45, 53, 55, 48, 35, 46, 38, 50, 56, 54, 47, 40, 26, 39, 51, 52, 42, 28, 14, 27, 41, 43, 30, 16, 6, 15, 29, 31, 18, 8, 2, 7, 17, 25, 13, 5)(57, 58, 62, 70, 82, 94, 101, 89, 76, 65, 73, 85, 97, 107, 112, 111, 105, 93, 80, 69, 74, 86, 98, 103, 91, 78, 67, 60)(59, 63, 71, 83, 95, 106, 109, 100, 88, 75, 81, 87, 99, 108, 110, 104, 92, 79, 68, 61, 64, 72, 84, 96, 102, 90, 77, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1150
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1135 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1 * T2^2 * T1^2 * T2 * T1^3 * T2, T1^2 * T2^-1 * T1^2 * T2^-5 * T1, T2 * T1 * T2^9, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 42, 40, 24, 12, 4, 10, 20, 34, 52, 44, 26, 43, 39, 23, 11, 21, 35, 53, 46, 28, 14, 27, 45, 38, 22, 36, 54, 48, 30, 16, 6, 15, 29, 47, 37, 55, 50, 32, 18, 8, 2, 7, 17, 31, 49, 56, 41, 25, 13, 5)(57, 58, 62, 70, 82, 98, 97, 106, 110, 91, 76, 65, 73, 85, 101, 95, 80, 69, 74, 86, 102, 108, 89, 105, 93, 78, 67, 60)(59, 63, 71, 83, 99, 96, 81, 88, 104, 109, 90, 75, 87, 103, 94, 79, 68, 61, 64, 72, 84, 100, 107, 112, 111, 92, 77, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1152
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1136 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^-6 * T2^4, T1^5 * T2^6 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 50, 32, 18, 8, 2, 7, 17, 31, 49, 52, 37, 48, 30, 16, 6, 15, 29, 47, 53, 38, 22, 36, 46, 28, 14, 27, 45, 54, 39, 23, 11, 21, 35, 44, 26, 43, 55, 40, 24, 12, 4, 10, 20, 34, 42, 56, 41, 25, 13, 5)(57, 58, 62, 70, 82, 98, 89, 105, 109, 95, 80, 69, 74, 86, 102, 91, 76, 65, 73, 85, 101, 111, 97, 106, 93, 78, 67, 60)(59, 63, 71, 83, 99, 112, 107, 108, 94, 79, 68, 61, 64, 72, 84, 100, 90, 75, 87, 103, 110, 96, 81, 88, 104, 92, 77, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1148
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1137 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^-4, T1^13 * T2^-2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 37, 44, 51, 46, 53, 47, 55, 50, 41, 31, 40, 34, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 36, 43, 38, 45, 52, 56, 54, 49, 39, 48, 42, 33, 23, 32, 26, 16, 6, 15, 13, 5)(57, 58, 62, 70, 79, 87, 95, 103, 108, 100, 92, 84, 76, 65, 73, 69, 74, 82, 90, 98, 106, 110, 102, 94, 86, 78, 67, 60)(59, 63, 71, 80, 88, 96, 104, 111, 112, 107, 99, 91, 83, 75, 68, 61, 64, 72, 81, 89, 97, 105, 109, 101, 93, 85, 77, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1151
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1138 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2^3 * T1^-1 * T2, T1^6 * T2 * T1 * T2 * T1^6, T2^-2 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 16, 6, 15, 26, 33, 23, 32, 42, 49, 39, 48, 52, 56, 54, 45, 36, 43, 38, 29, 20, 27, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 34, 41, 31, 40, 50, 55, 47, 53, 44, 51, 46, 37, 28, 35, 30, 21, 11, 19, 13, 5)(57, 58, 62, 70, 79, 87, 95, 103, 110, 102, 94, 86, 78, 69, 74, 65, 73, 82, 90, 98, 106, 108, 100, 92, 84, 76, 67, 60)(59, 63, 71, 80, 88, 96, 104, 109, 101, 93, 85, 77, 68, 61, 64, 72, 81, 89, 97, 105, 111, 112, 107, 99, 91, 83, 75, 66)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 112^28 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1149
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 56 f = 1
	degree seq :: [ 28^2, 56 ]

E27.1139 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^3, (F * T2)^2, (F * T1)^2, T2^-18 * T1^2, T2^-9 * T1 * T2^9 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 51, 54, 48, 42, 36, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 34, 40, 46, 52, 56, 50, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 49, 55, 53, 47, 41, 35, 29, 23, 17, 11, 5)(57, 58, 62, 61, 64, 68, 67, 70, 74, 73, 76, 80, 79, 82, 86, 85, 88, 92, 91, 94, 98, 97, 100, 104, 103, 106, 110, 109, 112, 107, 111, 108, 101, 105, 102, 95, 99, 96, 89, 93, 90, 83, 87, 84, 77, 81, 78, 71, 75, 72, 65, 69, 66, 59, 63, 60)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1153
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1140 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T2 * T1 * T2^10, (T1^-1 * T2^-1)^28 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 29, 39, 49, 42, 32, 22, 12, 4, 10, 20, 30, 40, 50, 55, 51, 41, 31, 21, 11, 14, 24, 34, 44, 52, 56, 54, 46, 36, 26, 16, 6, 15, 25, 35, 45, 53, 48, 38, 28, 18, 8, 2, 7, 17, 27, 37, 47, 43, 33, 23, 13, 5)(57, 58, 62, 70, 66, 59, 63, 71, 80, 76, 65, 73, 81, 90, 86, 75, 83, 91, 100, 96, 85, 93, 101, 108, 106, 95, 103, 109, 112, 111, 105, 99, 104, 110, 107, 98, 89, 94, 102, 97, 88, 79, 84, 92, 87, 78, 69, 74, 82, 77, 68, 61, 64, 72, 67, 60)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1154
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1141 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-1, T1^-3 * T2 * T1^-6, T2^3 * T1^-1 * T2 * T1^-2 * T2^2 * T1^5, (T2^-2 * T1^-2)^14 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 23, 11, 21, 35, 46, 53, 48, 37, 39, 49, 55, 52, 43, 28, 14, 27, 42, 32, 18, 8, 2, 7, 17, 31, 24, 12, 4, 10, 20, 34, 45, 38, 22, 36, 47, 54, 56, 51, 41, 26, 40, 50, 44, 30, 16, 6, 15, 29, 25, 13, 5)(57, 58, 62, 70, 82, 95, 92, 77, 66, 59, 63, 71, 83, 96, 105, 103, 91, 76, 65, 73, 85, 98, 106, 111, 110, 102, 90, 75, 87, 81, 88, 100, 108, 112, 109, 101, 89, 80, 69, 74, 86, 99, 107, 104, 94, 79, 68, 61, 64, 72, 84, 97, 93, 78, 67, 60)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1155
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1142 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {28, 56, 56})
Quotient :: edge
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T2^9 * T1^-1 * T2 * T1^-1, T1^2 * T2 * T1^-1 * T2^-2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^2 * T2 * T1^-1 * T2^-2 * T1^2 * T2^-2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 43, 50, 40, 30, 16, 6, 15, 29, 22, 36, 46, 54, 55, 48, 38, 26, 24, 12, 4, 10, 20, 34, 44, 52, 42, 32, 18, 8, 2, 7, 17, 31, 41, 51, 56, 49, 39, 28, 14, 27, 23, 11, 21, 35, 45, 53, 47, 37, 25, 13, 5)(57, 58, 62, 70, 82, 81, 88, 96, 105, 111, 109, 100, 89, 97, 92, 77, 66, 59, 63, 71, 83, 80, 69, 74, 86, 95, 104, 103, 108, 99, 107, 102, 91, 76, 65, 73, 85, 79, 68, 61, 64, 72, 84, 94, 93, 98, 106, 112, 110, 101, 90, 75, 87, 78, 67, 60)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1156
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1143 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^2, (F * T1)^2, (F * T2)^2, T1^28, (T2^-1 * T1^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 2, 58, 7, 63, 6, 62, 11, 67, 10, 66, 15, 71, 14, 70, 19, 75, 18, 74, 23, 79, 22, 78, 27, 83, 26, 82, 31, 87, 30, 86, 35, 91, 34, 90, 39, 95, 38, 94, 43, 99, 42, 98, 47, 103, 46, 102, 51, 107, 50, 106, 55, 111, 54, 110, 56, 112, 52, 108, 53, 109, 48, 104, 49, 105, 44, 100, 45, 101, 40, 96, 41, 97, 36, 92, 37, 93, 32, 88, 33, 89, 28, 84, 29, 85, 24, 80, 25, 81, 20, 76, 21, 77, 16, 72, 17, 73, 12, 68, 13, 69, 8, 64, 9, 65, 4, 60, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 59)(6, 66)(7, 67)(8, 60)(9, 61)(10, 70)(11, 71)(12, 64)(13, 65)(14, 74)(15, 75)(16, 68)(17, 69)(18, 78)(19, 79)(20, 72)(21, 73)(22, 82)(23, 83)(24, 76)(25, 77)(26, 86)(27, 87)(28, 80)(29, 81)(30, 90)(31, 91)(32, 84)(33, 85)(34, 94)(35, 95)(36, 88)(37, 89)(38, 98)(39, 99)(40, 92)(41, 93)(42, 102)(43, 103)(44, 96)(45, 97)(46, 106)(47, 107)(48, 100)(49, 101)(50, 110)(51, 111)(52, 104)(53, 105)(54, 108)(55, 112)(56, 109)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1132
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1144 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T1 * T2^2, (F * T2)^2, (F * T1)^2, T1^28 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 4, 60, 8, 64, 9, 65, 12, 68, 13, 69, 16, 72, 17, 73, 20, 76, 21, 77, 24, 80, 25, 81, 28, 84, 29, 85, 32, 88, 33, 89, 36, 92, 37, 93, 40, 96, 41, 97, 44, 100, 45, 101, 48, 104, 49, 105, 52, 108, 53, 109, 56, 112, 54, 110, 55, 111, 50, 106, 51, 107, 46, 102, 47, 103, 42, 98, 43, 99, 38, 94, 39, 95, 34, 90, 35, 91, 30, 86, 31, 87, 26, 82, 27, 83, 22, 78, 23, 79, 18, 74, 19, 75, 14, 70, 15, 71, 10, 66, 11, 67, 6, 62, 7, 63, 2, 58, 5, 61)
	L = (1, 58)(2, 62)(3, 61)(4, 57)(5, 63)(6, 66)(7, 67)(8, 59)(9, 60)(10, 70)(11, 71)(12, 64)(13, 65)(14, 74)(15, 75)(16, 68)(17, 69)(18, 78)(19, 79)(20, 72)(21, 73)(22, 82)(23, 83)(24, 76)(25, 77)(26, 86)(27, 87)(28, 80)(29, 81)(30, 90)(31, 91)(32, 84)(33, 85)(34, 94)(35, 95)(36, 88)(37, 89)(38, 98)(39, 99)(40, 92)(41, 93)(42, 102)(43, 103)(44, 96)(45, 97)(46, 106)(47, 107)(48, 100)(49, 101)(50, 110)(51, 111)(52, 104)(53, 105)(54, 109)(55, 112)(56, 108)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1130
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1145 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^17, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 16, 72, 22, 78, 28, 84, 34, 90, 40, 96, 46, 102, 52, 108, 54, 110, 48, 104, 42, 98, 36, 92, 30, 86, 24, 80, 18, 74, 12, 68, 4, 60, 10, 66, 6, 62, 14, 70, 20, 76, 26, 82, 32, 88, 38, 94, 44, 100, 50, 106, 56, 112, 53, 109, 47, 103, 41, 97, 35, 91, 29, 85, 23, 79, 17, 73, 11, 67, 8, 64, 2, 58, 7, 63, 15, 71, 21, 77, 27, 83, 33, 89, 39, 95, 45, 101, 51, 107, 55, 111, 49, 105, 43, 99, 37, 93, 31, 87, 25, 81, 19, 75, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 65)(7, 70)(8, 66)(9, 71)(10, 59)(11, 60)(12, 61)(13, 67)(14, 72)(15, 76)(16, 77)(17, 68)(18, 69)(19, 73)(20, 78)(21, 82)(22, 83)(23, 74)(24, 75)(25, 79)(26, 84)(27, 88)(28, 89)(29, 80)(30, 81)(31, 85)(32, 90)(33, 94)(34, 95)(35, 86)(36, 87)(37, 91)(38, 96)(39, 100)(40, 101)(41, 92)(42, 93)(43, 97)(44, 102)(45, 106)(46, 107)(47, 98)(48, 99)(49, 103)(50, 108)(51, 112)(52, 111)(53, 104)(54, 105)(55, 109)(56, 110)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1133
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1146 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^2, T1 * T2^-18 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 16, 72, 22, 78, 28, 84, 34, 90, 40, 96, 46, 102, 52, 108, 51, 107, 45, 101, 39, 95, 33, 89, 27, 83, 21, 77, 15, 71, 8, 64, 2, 58, 7, 63, 11, 67, 18, 74, 24, 80, 30, 86, 36, 92, 42, 98, 48, 104, 54, 110, 56, 112, 50, 106, 44, 100, 38, 94, 32, 88, 26, 82, 20, 76, 14, 70, 6, 62, 12, 68, 4, 60, 10, 66, 17, 73, 23, 79, 29, 85, 35, 91, 41, 97, 47, 103, 53, 109, 55, 111, 49, 105, 43, 99, 37, 93, 31, 87, 25, 81, 19, 75, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 69)(7, 68)(8, 70)(9, 67)(10, 59)(11, 60)(12, 61)(13, 71)(14, 75)(15, 76)(16, 74)(17, 65)(18, 66)(19, 77)(20, 81)(21, 82)(22, 80)(23, 72)(24, 73)(25, 83)(26, 87)(27, 88)(28, 86)(29, 78)(30, 79)(31, 89)(32, 93)(33, 94)(34, 92)(35, 84)(36, 85)(37, 95)(38, 99)(39, 100)(40, 98)(41, 90)(42, 91)(43, 101)(44, 105)(45, 106)(46, 104)(47, 96)(48, 97)(49, 107)(50, 111)(51, 112)(52, 110)(53, 102)(54, 103)(55, 108)(56, 109)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1129
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1147 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T1^3 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-9 * T1, (T2^-1 * T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 30, 86, 40, 96, 50, 106, 46, 102, 36, 92, 26, 82, 14, 70, 23, 79, 11, 67, 21, 77, 32, 88, 42, 98, 52, 108, 49, 105, 39, 95, 29, 85, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 28, 84, 38, 94, 48, 104, 56, 112, 54, 110, 44, 100, 34, 90, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 31, 87, 41, 97, 51, 107, 47, 103, 37, 93, 27, 83, 16, 72, 6, 62, 15, 71, 22, 78, 33, 89, 43, 99, 53, 109, 55, 111, 45, 101, 35, 91, 25, 81, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 80)(15, 79)(16, 82)(17, 78)(18, 83)(19, 84)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 85)(26, 90)(27, 92)(28, 89)(29, 93)(30, 94)(31, 75)(32, 76)(33, 77)(34, 81)(35, 95)(36, 100)(37, 102)(38, 99)(39, 103)(40, 104)(41, 86)(42, 87)(43, 88)(44, 91)(45, 105)(46, 110)(47, 106)(48, 109)(49, 107)(50, 112)(51, 96)(52, 97)(53, 98)(54, 101)(55, 108)(56, 111)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1131
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1148 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1 * T2^5, T2 * T1^-1 * T2 * T1^-8, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 32, 88, 37, 93, 23, 79, 11, 67, 21, 77, 33, 89, 44, 100, 49, 105, 36, 92, 22, 78, 34, 90, 45, 101, 53, 109, 55, 111, 48, 104, 35, 91, 46, 102, 38, 94, 50, 106, 56, 112, 54, 110, 47, 103, 40, 96, 26, 82, 39, 95, 51, 107, 52, 108, 42, 98, 28, 84, 14, 70, 27, 83, 41, 97, 43, 99, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 31, 87, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 25, 81, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 81)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 87)(26, 94)(27, 95)(28, 96)(29, 97)(30, 98)(31, 99)(32, 75)(33, 76)(34, 77)(35, 78)(36, 79)(37, 80)(38, 101)(39, 106)(40, 102)(41, 107)(42, 103)(43, 108)(44, 88)(45, 89)(46, 90)(47, 91)(48, 92)(49, 93)(50, 109)(51, 112)(52, 110)(53, 100)(54, 104)(55, 105)(56, 111)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1136
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1149 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1 * T2^2 * T1^2 * T2 * T1^3 * T2, T1^2 * T2^-1 * T1^2 * T2^-5 * T1, T2 * T1 * T2^9, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 33, 89, 51, 107, 42, 98, 40, 96, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 34, 90, 52, 108, 44, 100, 26, 82, 43, 99, 39, 95, 23, 79, 11, 67, 21, 77, 35, 91, 53, 109, 46, 102, 28, 84, 14, 70, 27, 83, 45, 101, 38, 94, 22, 78, 36, 92, 54, 110, 48, 104, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 47, 103, 37, 93, 55, 111, 50, 106, 32, 88, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 31, 87, 49, 105, 56, 112, 41, 97, 25, 81, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 88)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 106)(42, 97)(43, 96)(44, 107)(45, 95)(46, 108)(47, 94)(48, 109)(49, 93)(50, 110)(51, 112)(52, 89)(53, 90)(54, 91)(55, 92)(56, 111)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1138
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1150 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^-6 * T2^4, T1^5 * T2^6 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 33, 89, 51, 107, 50, 106, 32, 88, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 31, 87, 49, 105, 52, 108, 37, 93, 48, 104, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 47, 103, 53, 109, 38, 94, 22, 78, 36, 92, 46, 102, 28, 84, 14, 70, 27, 83, 45, 101, 54, 110, 39, 95, 23, 79, 11, 67, 21, 77, 35, 91, 44, 100, 26, 82, 43, 99, 55, 111, 40, 96, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 34, 90, 42, 98, 56, 112, 41, 97, 25, 81, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 88)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 106)(42, 89)(43, 112)(44, 90)(45, 111)(46, 91)(47, 110)(48, 92)(49, 109)(50, 93)(51, 108)(52, 94)(53, 95)(54, 96)(55, 97)(56, 107)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1134
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1151 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^-4, T1^13 * T2^-2 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 11, 67, 21, 77, 28, 84, 35, 91, 30, 86, 37, 93, 44, 100, 51, 107, 46, 102, 53, 109, 47, 103, 55, 111, 50, 106, 41, 97, 31, 87, 40, 96, 34, 90, 25, 81, 14, 70, 24, 80, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 12, 68, 4, 60, 10, 66, 20, 76, 27, 83, 22, 78, 29, 85, 36, 92, 43, 99, 38, 94, 45, 101, 52, 108, 56, 112, 54, 110, 49, 105, 39, 95, 48, 104, 42, 98, 33, 89, 23, 79, 32, 88, 26, 82, 16, 72, 6, 62, 15, 71, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 79)(15, 80)(16, 81)(17, 69)(18, 82)(19, 68)(20, 65)(21, 66)(22, 67)(23, 87)(24, 88)(25, 89)(26, 90)(27, 75)(28, 76)(29, 77)(30, 78)(31, 95)(32, 96)(33, 97)(34, 98)(35, 83)(36, 84)(37, 85)(38, 86)(39, 103)(40, 104)(41, 105)(42, 106)(43, 91)(44, 92)(45, 93)(46, 94)(47, 108)(48, 111)(49, 109)(50, 110)(51, 99)(52, 100)(53, 101)(54, 102)(55, 112)(56, 107)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1137
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1152 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-1 * T2^3 * T1^-1 * T2, T1^6 * T2 * T1 * T2 * T1^6, T2^-2 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 16, 72, 6, 62, 15, 71, 26, 82, 33, 89, 23, 79, 32, 88, 42, 98, 49, 105, 39, 95, 48, 104, 52, 108, 56, 112, 54, 110, 45, 101, 36, 92, 43, 99, 38, 94, 29, 85, 20, 76, 27, 83, 22, 78, 12, 68, 4, 60, 10, 66, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 25, 81, 14, 70, 24, 80, 34, 90, 41, 97, 31, 87, 40, 96, 50, 106, 55, 111, 47, 103, 53, 109, 44, 100, 51, 107, 46, 102, 37, 93, 28, 84, 35, 91, 30, 86, 21, 77, 11, 67, 19, 75, 13, 69, 5, 61)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 79)(15, 80)(16, 81)(17, 82)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 87)(24, 88)(25, 89)(26, 90)(27, 75)(28, 76)(29, 77)(30, 78)(31, 95)(32, 96)(33, 97)(34, 98)(35, 83)(36, 84)(37, 85)(38, 86)(39, 103)(40, 104)(41, 105)(42, 106)(43, 91)(44, 92)(45, 93)(46, 94)(47, 110)(48, 109)(49, 111)(50, 108)(51, 99)(52, 100)(53, 101)(54, 102)(55, 112)(56, 107)
	local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1135
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 56 f = 3
	degree seq :: [ 112 ]

E27.1153 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^28, (T2^-1 * T1^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 7, 63, 11, 67, 15, 71, 19, 75, 23, 79, 27, 83, 31, 87, 35, 91, 39, 95, 43, 99, 47, 103, 51, 107, 55, 111, 53, 109, 49, 105, 45, 101, 41, 97, 37, 93, 33, 89, 29, 85, 25, 81, 21, 77, 17, 73, 13, 69, 9, 65, 5, 61)(2, 58, 6, 62, 10, 66, 14, 70, 18, 74, 22, 78, 26, 82, 30, 86, 34, 90, 38, 94, 42, 98, 46, 102, 50, 106, 54, 110, 56, 112, 52, 108, 48, 104, 44, 100, 40, 96, 36, 92, 32, 88, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64, 4, 60)
	L = (1, 58)(2, 59)(3, 62)(4, 57)(5, 60)(6, 63)(7, 66)(8, 61)(9, 64)(10, 67)(11, 70)(12, 65)(13, 68)(14, 71)(15, 74)(16, 69)(17, 72)(18, 75)(19, 78)(20, 73)(21, 76)(22, 79)(23, 82)(24, 77)(25, 80)(26, 83)(27, 86)(28, 81)(29, 84)(30, 87)(31, 90)(32, 85)(33, 88)(34, 91)(35, 94)(36, 89)(37, 92)(38, 95)(39, 98)(40, 93)(41, 96)(42, 99)(43, 102)(44, 97)(45, 100)(46, 103)(47, 106)(48, 101)(49, 104)(50, 107)(51, 110)(52, 105)(53, 108)(54, 111)(55, 112)(56, 109)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1139
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1154 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2 * T1^3, T2^2 * T1^-1 * T2 * T1^-1 * T2^6, T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-1 * T1^2 * T2^-1 * T1^2 * T2^-1 * T1^2 * T2^-1 * T1^2 * T2^-1 * T1, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^3 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 31, 87, 43, 99, 40, 96, 28, 84, 16, 72, 6, 62, 15, 71, 27, 83, 39, 95, 51, 107, 56, 112, 54, 110, 47, 103, 35, 91, 23, 79, 11, 67, 21, 77, 33, 89, 45, 101, 49, 105, 37, 93, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 29, 85, 41, 97, 52, 108, 50, 106, 38, 94, 26, 82, 14, 70, 22, 78, 34, 90, 46, 102, 53, 109, 55, 111, 48, 104, 36, 92, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 32, 88, 44, 100, 42, 98, 30, 86, 18, 74, 8, 64)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 79)(15, 78)(16, 82)(17, 83)(18, 84)(19, 85)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 86)(26, 91)(27, 90)(28, 94)(29, 95)(30, 96)(31, 97)(32, 75)(33, 76)(34, 77)(35, 80)(36, 81)(37, 98)(38, 103)(39, 102)(40, 106)(41, 107)(42, 99)(43, 108)(44, 87)(45, 88)(46, 89)(47, 92)(48, 93)(49, 100)(50, 110)(51, 109)(52, 112)(53, 101)(54, 104)(55, 105)(56, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1140
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1155 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^2 * T2^-3 * T1^-1 * T2 * T1^-1 * T2^2, T2 * T1 * T2^2 * T1 * T2^2 * T1^2 * T2, T1^-3 * T2^-1 * T1^-1 * T2^-5, T1^3 * T2^-2 * T1 * T2^-1 * T1 * T2^-2 * T1, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 19, 75, 33, 89, 51, 107, 37, 93, 55, 111, 48, 104, 30, 86, 16, 72, 6, 62, 15, 71, 29, 85, 47, 103, 39, 95, 23, 79, 11, 67, 21, 77, 35, 91, 53, 109, 44, 100, 26, 82, 43, 99, 41, 97, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 49, 105, 38, 94, 22, 78, 36, 92, 54, 110, 46, 102, 28, 84, 14, 70, 27, 83, 45, 101, 40, 96, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 34, 90, 52, 108, 42, 98, 56, 112, 50, 106, 32, 88, 18, 74, 8, 64)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 88)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 106)(42, 107)(43, 112)(44, 108)(45, 97)(46, 109)(47, 96)(48, 110)(49, 95)(50, 111)(51, 94)(52, 89)(53, 90)(54, 91)(55, 92)(56, 93)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1141
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1156 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {28, 56, 56})
Quotient :: loop
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1^-1, T2), T2^-1 * T1 * T2^-2 * T1, T1^18 * T2, (T1^-1 * T2^-1)^56 ]
Map:: non-degenerate
	R = (1, 57, 3, 59, 9, 65, 6, 62, 15, 71, 22, 78, 20, 76, 27, 83, 34, 90, 32, 88, 39, 95, 46, 102, 44, 100, 51, 107, 56, 112, 54, 110, 47, 103, 49, 105, 42, 98, 35, 91, 37, 93, 30, 86, 23, 79, 25, 81, 18, 74, 11, 67, 13, 69, 5, 61)(2, 58, 7, 63, 16, 72, 14, 70, 21, 77, 28, 84, 26, 82, 33, 89, 40, 96, 38, 94, 45, 101, 52, 108, 50, 106, 53, 109, 55, 111, 48, 104, 41, 97, 43, 99, 36, 92, 29, 85, 31, 87, 24, 80, 17, 73, 19, 75, 12, 68, 4, 60, 10, 66, 8, 64)
	L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 65)(9, 72)(10, 59)(11, 60)(12, 61)(13, 66)(14, 76)(15, 77)(16, 78)(17, 67)(18, 68)(19, 69)(20, 82)(21, 83)(22, 84)(23, 73)(24, 74)(25, 75)(26, 88)(27, 89)(28, 90)(29, 79)(30, 80)(31, 81)(32, 94)(33, 95)(34, 96)(35, 85)(36, 86)(37, 87)(38, 100)(39, 101)(40, 102)(41, 91)(42, 92)(43, 93)(44, 106)(45, 107)(46, 108)(47, 97)(48, 98)(49, 99)(50, 110)(51, 109)(52, 112)(53, 103)(54, 104)(55, 105)(56, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1142
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.1157 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^28, Y1^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 10, 66, 14, 70, 18, 74, 22, 78, 26, 82, 30, 86, 34, 90, 38, 94, 42, 98, 46, 102, 50, 106, 54, 110, 53, 109, 49, 105, 45, 101, 41, 97, 37, 93, 33, 89, 29, 85, 25, 81, 21, 77, 17, 73, 13, 69, 9, 65, 4, 60)(3, 59, 5, 61, 7, 63, 11, 67, 15, 71, 19, 75, 23, 79, 27, 83, 31, 87, 35, 91, 39, 95, 43, 99, 47, 103, 51, 107, 55, 111, 56, 112, 52, 108, 48, 104, 44, 100, 40, 96, 36, 92, 32, 88, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64)(113, 169, 115, 171, 116, 172, 120, 176, 121, 177, 124, 180, 125, 181, 128, 184, 129, 185, 132, 188, 133, 189, 136, 192, 137, 193, 140, 196, 141, 197, 144, 200, 145, 201, 148, 204, 149, 205, 152, 208, 153, 209, 156, 212, 157, 213, 160, 216, 161, 217, 164, 220, 165, 221, 168, 224, 166, 222, 167, 223, 162, 218, 163, 219, 158, 214, 159, 215, 154, 210, 155, 211, 150, 206, 151, 207, 146, 202, 147, 203, 142, 198, 143, 199, 138, 194, 139, 195, 134, 190, 135, 191, 130, 186, 131, 187, 126, 182, 127, 183, 122, 178, 123, 179, 118, 174, 119, 175, 114, 170, 117, 173)
	L = (1, 116)(2, 113)(3, 120)(4, 121)(5, 115)(6, 114)(7, 117)(8, 124)(9, 125)(10, 118)(11, 119)(12, 128)(13, 129)(14, 122)(15, 123)(16, 132)(17, 133)(18, 126)(19, 127)(20, 136)(21, 137)(22, 130)(23, 131)(24, 140)(25, 141)(26, 134)(27, 135)(28, 144)(29, 145)(30, 138)(31, 139)(32, 148)(33, 149)(34, 142)(35, 143)(36, 152)(37, 153)(38, 146)(39, 147)(40, 156)(41, 157)(42, 150)(43, 151)(44, 160)(45, 161)(46, 154)(47, 155)(48, 164)(49, 165)(50, 158)(51, 159)(52, 168)(53, 166)(54, 162)(55, 163)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1176
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1158 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y3^28, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 10, 66, 14, 70, 18, 74, 22, 78, 26, 82, 30, 86, 34, 90, 38, 94, 42, 98, 46, 102, 50, 106, 54, 110, 52, 108, 48, 104, 44, 100, 40, 96, 36, 92, 32, 88, 28, 84, 24, 80, 20, 76, 16, 72, 12, 68, 8, 64, 4, 60)(3, 59, 7, 63, 11, 67, 15, 71, 19, 75, 23, 79, 27, 83, 31, 87, 35, 91, 39, 95, 43, 99, 47, 103, 51, 107, 55, 111, 56, 112, 53, 109, 49, 105, 45, 101, 41, 97, 37, 93, 33, 89, 29, 85, 25, 81, 21, 77, 17, 73, 13, 69, 9, 65, 5, 61)(113, 169, 115, 171, 114, 170, 119, 175, 118, 174, 123, 179, 122, 178, 127, 183, 126, 182, 131, 187, 130, 186, 135, 191, 134, 190, 139, 195, 138, 194, 143, 199, 142, 198, 147, 203, 146, 202, 151, 207, 150, 206, 155, 211, 154, 210, 159, 215, 158, 214, 163, 219, 162, 218, 167, 223, 166, 222, 168, 224, 164, 220, 165, 221, 160, 216, 161, 217, 156, 212, 157, 213, 152, 208, 153, 209, 148, 204, 149, 205, 144, 200, 145, 201, 140, 196, 141, 197, 136, 192, 137, 193, 132, 188, 133, 189, 128, 184, 129, 185, 124, 180, 125, 181, 120, 176, 121, 177, 116, 172, 117, 173)
	L = (1, 116)(2, 113)(3, 117)(4, 120)(5, 121)(6, 114)(7, 115)(8, 124)(9, 125)(10, 118)(11, 119)(12, 128)(13, 129)(14, 122)(15, 123)(16, 132)(17, 133)(18, 126)(19, 127)(20, 136)(21, 137)(22, 130)(23, 131)(24, 140)(25, 141)(26, 134)(27, 135)(28, 144)(29, 145)(30, 138)(31, 139)(32, 148)(33, 149)(34, 142)(35, 143)(36, 152)(37, 153)(38, 146)(39, 147)(40, 156)(41, 157)(42, 150)(43, 151)(44, 160)(45, 161)(46, 154)(47, 155)(48, 164)(49, 165)(50, 158)(51, 159)(52, 166)(53, 168)(54, 162)(55, 163)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1178
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1159 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y2), (R * Y1)^2, (Y3^-1, Y2^-1), Y2^4 * Y3^-1 * Y2^2, Y2 * Y3 * Y2 * Y3^8, Y1^6 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y1^2 * Y2^-1 * Y1^3 * Y3^-4 * Y2^-1, Y2 * Y1 * Y2 * Y3^-3 * Y2^2 * Y3^3 * Y2^2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^3 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 38, 94, 45, 101, 33, 89, 20, 76, 9, 65, 17, 73, 29, 85, 41, 97, 51, 107, 56, 112, 55, 111, 49, 105, 37, 93, 24, 80, 13, 69, 18, 74, 30, 86, 42, 98, 47, 103, 35, 91, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 39, 95, 50, 106, 53, 109, 44, 100, 32, 88, 19, 75, 25, 81, 31, 87, 43, 99, 52, 108, 54, 110, 48, 104, 36, 92, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 40, 96, 46, 102, 34, 90, 21, 77, 10, 66)(113, 169, 115, 171, 121, 177, 131, 187, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 144, 200, 149, 205, 135, 191, 123, 179, 133, 189, 145, 201, 156, 212, 161, 217, 148, 204, 134, 190, 146, 202, 157, 213, 165, 221, 167, 223, 160, 216, 147, 203, 158, 214, 150, 206, 162, 218, 168, 224, 166, 222, 159, 215, 152, 208, 138, 194, 151, 207, 163, 219, 164, 220, 154, 210, 140, 196, 126, 182, 139, 195, 153, 209, 155, 211, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 143, 199, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 137, 193, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 144)(20, 145)(21, 146)(22, 147)(23, 148)(24, 149)(25, 131)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 137)(32, 156)(33, 157)(34, 158)(35, 159)(36, 160)(37, 161)(38, 138)(39, 139)(40, 140)(41, 141)(42, 142)(43, 143)(44, 165)(45, 150)(46, 152)(47, 154)(48, 166)(49, 167)(50, 151)(51, 153)(52, 155)(53, 162)(54, 164)(55, 168)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1182
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1160 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (R * Y2)^2, (Y2, Y1^-1), (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^-3 * Y1^-1 * Y2^3, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2 * Y2^2, Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y1^-4, Y3^3 * Y2^-1 * Y3 * Y2^-3 * Y1^-2, Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y3^-2 * Y2^-3, Y2^-1 * Y3^-1 * Y1^2 * Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-2, Y1^28, Y2^-1 * Y3^-1 * Y1^2 * Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 42, 98, 41, 97, 50, 106, 54, 110, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 45, 101, 39, 95, 24, 80, 13, 69, 18, 74, 30, 86, 46, 102, 52, 108, 33, 89, 49, 105, 37, 93, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 43, 99, 40, 96, 25, 81, 32, 88, 48, 104, 53, 109, 34, 90, 19, 75, 31, 87, 47, 103, 38, 94, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 44, 100, 51, 107, 56, 112, 55, 111, 36, 92, 21, 77, 10, 66)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 163, 219, 154, 210, 152, 208, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 146, 202, 164, 220, 156, 212, 138, 194, 155, 211, 151, 207, 135, 191, 123, 179, 133, 189, 147, 203, 165, 221, 158, 214, 140, 196, 126, 182, 139, 195, 157, 213, 150, 206, 134, 190, 148, 204, 166, 222, 160, 216, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 159, 215, 149, 205, 167, 223, 162, 218, 144, 200, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 143, 199, 161, 217, 168, 224, 153, 209, 137, 193, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 146)(20, 147)(21, 148)(22, 149)(23, 150)(24, 151)(25, 152)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 137)(33, 164)(34, 165)(35, 166)(36, 167)(37, 161)(38, 159)(39, 157)(40, 155)(41, 154)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 153)(51, 156)(52, 158)(53, 160)(54, 162)(55, 168)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1184
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1161 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (Y3^-1, Y2^-1), Y2 * Y3 * Y2^-1 * Y1, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y1^-1), Y2 * Y3^-3 * Y2^-1 * Y1^-3, Y2 * Y3 * Y2^3 * Y1^-5, Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-3, Y2 * Y3^-3 * Y1 * Y2^5 * Y3^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^4 * Y1 * Y3^-1, Y2 * Y3 * Y2^3 * Y1^23, (Y2^-1 * Y3)^56 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 42, 98, 33, 89, 49, 105, 53, 109, 39, 95, 24, 80, 13, 69, 18, 74, 30, 86, 46, 102, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 45, 101, 55, 111, 41, 97, 50, 106, 37, 93, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 43, 99, 56, 112, 51, 107, 52, 108, 38, 94, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 44, 100, 34, 90, 19, 75, 31, 87, 47, 103, 54, 110, 40, 96, 25, 81, 32, 88, 48, 104, 36, 92, 21, 77, 10, 66)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 163, 219, 162, 218, 144, 200, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 143, 199, 161, 217, 164, 220, 149, 205, 160, 216, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 159, 215, 165, 221, 150, 206, 134, 190, 148, 204, 158, 214, 140, 196, 126, 182, 139, 195, 157, 213, 166, 222, 151, 207, 135, 191, 123, 179, 133, 189, 147, 203, 156, 212, 138, 194, 155, 211, 167, 223, 152, 208, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 146, 202, 154, 210, 168, 224, 153, 209, 137, 193, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 146)(20, 147)(21, 148)(22, 149)(23, 150)(24, 151)(25, 152)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 137)(33, 154)(34, 156)(35, 158)(36, 160)(37, 162)(38, 164)(39, 165)(40, 166)(41, 167)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 153)(51, 168)(52, 163)(53, 161)(54, 159)(55, 157)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1180
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1162 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1 * Y2^17, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 9, 65, 15, 71, 20, 76, 22, 78, 27, 83, 32, 88, 34, 90, 39, 95, 44, 100, 46, 102, 51, 107, 56, 112, 54, 110, 49, 105, 47, 103, 42, 98, 37, 93, 35, 91, 30, 86, 25, 81, 23, 79, 18, 74, 13, 69, 11, 67, 4, 60)(3, 59, 7, 63, 14, 70, 16, 72, 21, 77, 26, 82, 28, 84, 33, 89, 38, 94, 40, 96, 45, 101, 50, 106, 52, 108, 55, 111, 53, 109, 48, 104, 43, 99, 41, 97, 36, 92, 31, 87, 29, 85, 24, 80, 19, 75, 17, 73, 12, 68, 5, 61, 8, 64, 10, 66)(113, 169, 115, 171, 121, 177, 128, 184, 134, 190, 140, 196, 146, 202, 152, 208, 158, 214, 164, 220, 166, 222, 160, 216, 154, 210, 148, 204, 142, 198, 136, 192, 130, 186, 124, 180, 116, 172, 122, 178, 118, 174, 126, 182, 132, 188, 138, 194, 144, 200, 150, 206, 156, 212, 162, 218, 168, 224, 165, 221, 159, 215, 153, 209, 147, 203, 141, 197, 135, 191, 129, 185, 123, 179, 120, 176, 114, 170, 119, 175, 127, 183, 133, 189, 139, 195, 145, 201, 151, 207, 157, 213, 163, 219, 167, 223, 161, 217, 155, 211, 149, 205, 143, 199, 137, 193, 131, 187, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 118)(10, 120)(11, 125)(12, 129)(13, 130)(14, 119)(15, 121)(16, 126)(17, 131)(18, 135)(19, 136)(20, 127)(21, 128)(22, 132)(23, 137)(24, 141)(25, 142)(26, 133)(27, 134)(28, 138)(29, 143)(30, 147)(31, 148)(32, 139)(33, 140)(34, 144)(35, 149)(36, 153)(37, 154)(38, 145)(39, 146)(40, 150)(41, 155)(42, 159)(43, 160)(44, 151)(45, 152)(46, 156)(47, 161)(48, 165)(49, 166)(50, 157)(51, 158)(52, 162)(53, 167)(54, 168)(55, 164)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1179
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1163 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^-3 * Y2^2, Y3 * Y2^18 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 13, 69, 15, 71, 20, 76, 25, 81, 27, 83, 32, 88, 37, 93, 39, 95, 44, 100, 49, 105, 51, 107, 56, 112, 53, 109, 46, 102, 48, 104, 41, 97, 34, 90, 36, 92, 29, 85, 22, 78, 24, 80, 17, 73, 9, 65, 11, 67, 4, 60)(3, 59, 7, 63, 12, 68, 5, 61, 8, 64, 14, 70, 19, 75, 21, 77, 26, 82, 31, 87, 33, 89, 38, 94, 43, 99, 45, 101, 50, 106, 55, 111, 52, 108, 54, 110, 47, 103, 40, 96, 42, 98, 35, 91, 28, 84, 30, 86, 23, 79, 16, 72, 18, 74, 10, 66)(113, 169, 115, 171, 121, 177, 128, 184, 134, 190, 140, 196, 146, 202, 152, 208, 158, 214, 164, 220, 163, 219, 157, 213, 151, 207, 145, 201, 139, 195, 133, 189, 127, 183, 120, 176, 114, 170, 119, 175, 123, 179, 130, 186, 136, 192, 142, 198, 148, 204, 154, 210, 160, 216, 166, 222, 168, 224, 162, 218, 156, 212, 150, 206, 144, 200, 138, 194, 132, 188, 126, 182, 118, 174, 124, 180, 116, 172, 122, 178, 129, 185, 135, 191, 141, 197, 147, 203, 153, 209, 159, 215, 165, 221, 167, 223, 161, 217, 155, 211, 149, 205, 143, 199, 137, 193, 131, 187, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 129)(10, 130)(11, 121)(12, 119)(13, 118)(14, 120)(15, 125)(16, 135)(17, 136)(18, 128)(19, 126)(20, 127)(21, 131)(22, 141)(23, 142)(24, 134)(25, 132)(26, 133)(27, 137)(28, 147)(29, 148)(30, 140)(31, 138)(32, 139)(33, 143)(34, 153)(35, 154)(36, 146)(37, 144)(38, 145)(39, 149)(40, 159)(41, 160)(42, 152)(43, 150)(44, 151)(45, 155)(46, 165)(47, 166)(48, 158)(49, 156)(50, 157)(51, 161)(52, 167)(53, 168)(54, 164)(55, 162)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1175
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1164 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2)^2, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-2, Y3^-3 * Y1^-1 * Y3 * Y1^-1, Y1^2 * Y2 * Y1 * Y2 * Y1 * Y3^-1, Y1^2 * Y2^-1 * Y1 * Y2^-9, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 24, 80, 13, 69, 18, 74, 27, 83, 36, 92, 44, 100, 35, 91, 39, 95, 47, 103, 50, 106, 56, 112, 55, 111, 52, 108, 41, 97, 30, 86, 38, 94, 43, 99, 32, 88, 20, 76, 9, 65, 17, 73, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 26, 82, 34, 90, 25, 81, 29, 85, 37, 93, 46, 102, 54, 110, 45, 101, 49, 105, 51, 107, 40, 96, 48, 104, 53, 109, 42, 98, 31, 87, 19, 75, 28, 84, 33, 89, 21, 77, 10, 66)(113, 169, 115, 171, 121, 177, 131, 187, 142, 198, 152, 208, 162, 218, 158, 214, 148, 204, 138, 194, 126, 182, 135, 191, 123, 179, 133, 189, 144, 200, 154, 210, 164, 220, 161, 217, 151, 207, 141, 197, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 140, 196, 150, 206, 160, 216, 168, 224, 166, 222, 156, 212, 146, 202, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 143, 199, 153, 209, 163, 219, 159, 215, 149, 205, 139, 195, 128, 184, 118, 174, 127, 183, 134, 190, 145, 201, 155, 211, 165, 221, 167, 223, 157, 213, 147, 203, 137, 193, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 143)(20, 144)(21, 145)(22, 129)(23, 127)(24, 126)(25, 146)(26, 128)(27, 130)(28, 131)(29, 137)(30, 153)(31, 154)(32, 155)(33, 140)(34, 138)(35, 156)(36, 139)(37, 141)(38, 142)(39, 147)(40, 163)(41, 164)(42, 165)(43, 150)(44, 148)(45, 166)(46, 149)(47, 151)(48, 152)(49, 157)(50, 159)(51, 161)(52, 167)(53, 160)(54, 158)(55, 168)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1177
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1165 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y2)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y2^-4 * Y1^2, Y1^5 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-6, Y3^28, Y1^28, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 23, 79, 31, 87, 39, 95, 47, 103, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 13, 69, 18, 74, 9, 65, 17, 73, 26, 82, 34, 90, 42, 98, 50, 106, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 24, 80, 32, 88, 40, 96, 48, 104, 53, 109, 45, 101, 37, 93, 29, 85, 21, 77, 12, 68, 5, 61, 8, 64, 16, 72, 25, 81, 33, 89, 41, 97, 49, 105, 55, 111, 56, 112, 51, 107, 43, 99, 35, 91, 27, 83, 19, 75, 10, 66)(113, 169, 115, 171, 121, 177, 128, 184, 118, 174, 127, 183, 138, 194, 145, 201, 135, 191, 144, 200, 154, 210, 161, 217, 151, 207, 160, 216, 164, 220, 168, 224, 166, 222, 157, 213, 148, 204, 155, 211, 150, 206, 141, 197, 132, 188, 139, 195, 134, 190, 124, 180, 116, 172, 122, 178, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 137, 193, 126, 182, 136, 192, 146, 202, 153, 209, 143, 199, 152, 208, 162, 218, 167, 223, 159, 215, 165, 221, 156, 212, 163, 219, 158, 214, 149, 205, 140, 196, 147, 203, 142, 198, 133, 189, 123, 179, 131, 187, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 130)(10, 131)(11, 132)(12, 133)(13, 134)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 139)(20, 140)(21, 141)(22, 142)(23, 126)(24, 127)(25, 128)(26, 129)(27, 147)(28, 148)(29, 149)(30, 150)(31, 135)(32, 136)(33, 137)(34, 138)(35, 155)(36, 156)(37, 157)(38, 158)(39, 143)(40, 144)(41, 145)(42, 146)(43, 163)(44, 164)(45, 165)(46, 166)(47, 151)(48, 152)(49, 153)(50, 154)(51, 168)(52, 162)(53, 160)(54, 159)(55, 161)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1181
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1166 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1 * Y3, (Y2, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-4 * Y1^-1, Y1^4 * Y2^-1 * Y3^-2 * Y1 * Y3^-6 * Y2^-1, Y1^4 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-7, Y1^8 * Y3^-5 * Y2^-2, Y2^2 * Y3^3 * Y2 * Y1^-2 * Y2 * Y3^4 * Y2 * Y1^-1 * Y2 * Y3, Y3^28, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 23, 79, 31, 87, 39, 95, 47, 103, 52, 108, 44, 100, 36, 92, 28, 84, 20, 76, 9, 65, 17, 73, 13, 69, 18, 74, 26, 82, 34, 90, 42, 98, 50, 106, 54, 110, 46, 102, 38, 94, 30, 86, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 24, 80, 32, 88, 40, 96, 48, 104, 55, 111, 56, 112, 51, 107, 43, 99, 35, 91, 27, 83, 19, 75, 12, 68, 5, 61, 8, 64, 16, 72, 25, 81, 33, 89, 41, 97, 49, 105, 53, 109, 45, 101, 37, 93, 29, 85, 21, 77, 10, 66)(113, 169, 115, 171, 121, 177, 131, 187, 123, 179, 133, 189, 140, 196, 147, 203, 142, 198, 149, 205, 156, 212, 163, 219, 158, 214, 165, 221, 159, 215, 167, 223, 162, 218, 153, 209, 143, 199, 152, 208, 146, 202, 137, 193, 126, 182, 136, 192, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 124, 180, 116, 172, 122, 178, 132, 188, 139, 195, 134, 190, 141, 197, 148, 204, 155, 211, 150, 206, 157, 213, 164, 220, 168, 224, 166, 222, 161, 217, 151, 207, 160, 216, 154, 210, 145, 201, 135, 191, 144, 200, 138, 194, 128, 184, 118, 174, 127, 183, 125, 181, 117, 173)
	L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 131)(13, 129)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 139)(20, 140)(21, 141)(22, 142)(23, 126)(24, 127)(25, 128)(26, 130)(27, 147)(28, 148)(29, 149)(30, 150)(31, 135)(32, 136)(33, 137)(34, 138)(35, 155)(36, 156)(37, 157)(38, 158)(39, 143)(40, 144)(41, 145)(42, 146)(43, 163)(44, 164)(45, 165)(46, 166)(47, 151)(48, 152)(49, 153)(50, 154)(51, 168)(52, 159)(53, 161)(54, 162)(55, 160)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1183
Graph:: bipartite
	v = 3 e = 112 f = 57
	degree seq :: [ 56^2, 112 ]

E27.1167 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2, R * Y2 * R * Y3, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^-1 * Y1^-19, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 12, 68, 18, 74, 24, 80, 30, 86, 36, 92, 42, 98, 48, 104, 54, 110, 51, 107, 45, 101, 39, 95, 33, 89, 27, 83, 21, 77, 15, 71, 9, 65, 5, 61, 8, 64, 14, 70, 20, 76, 26, 82, 32, 88, 38, 94, 44, 100, 50, 106, 56, 112, 52, 108, 46, 102, 40, 96, 34, 90, 28, 84, 22, 78, 16, 72, 10, 66, 3, 59, 7, 63, 13, 69, 19, 75, 25, 81, 31, 87, 37, 93, 43, 99, 49, 105, 55, 111, 53, 109, 47, 103, 41, 97, 35, 91, 29, 85, 23, 79, 17, 73, 11, 67, 4, 60)(113, 169, 115, 171, 121, 177, 116, 172, 122, 178, 127, 183, 123, 179, 128, 184, 133, 189, 129, 185, 134, 190, 139, 195, 135, 191, 140, 196, 145, 201, 141, 197, 146, 202, 151, 207, 147, 203, 152, 208, 157, 213, 153, 209, 158, 214, 163, 219, 159, 215, 164, 220, 166, 222, 165, 221, 168, 224, 160, 216, 167, 223, 162, 218, 154, 210, 161, 217, 156, 212, 148, 204, 155, 211, 150, 206, 142, 198, 149, 205, 144, 200, 136, 192, 143, 199, 138, 194, 130, 186, 137, 193, 132, 188, 124, 180, 131, 187, 126, 182, 118, 174, 125, 181, 120, 176, 114, 170, 119, 175, 117, 173)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 125)(7, 117)(8, 114)(9, 116)(10, 127)(11, 128)(12, 131)(13, 120)(14, 118)(15, 123)(16, 133)(17, 134)(18, 137)(19, 126)(20, 124)(21, 129)(22, 139)(23, 140)(24, 143)(25, 132)(26, 130)(27, 135)(28, 145)(29, 146)(30, 149)(31, 138)(32, 136)(33, 141)(34, 151)(35, 152)(36, 155)(37, 144)(38, 142)(39, 147)(40, 157)(41, 158)(42, 161)(43, 150)(44, 148)(45, 153)(46, 163)(47, 164)(48, 167)(49, 156)(50, 154)(51, 159)(52, 166)(53, 168)(54, 165)(55, 162)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1171
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1168 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), Y1^-1 * Y2^2 * Y1 * Y2^-2, Y2^-2 * Y1 * Y2^-3, Y1^-3 * Y2^-2 * Y1^3 * Y2^2, Y1^-3 * Y2^-1 * Y1^-8, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 24, 80, 34, 90, 44, 100, 42, 98, 32, 88, 22, 78, 12, 68, 5, 61, 8, 64, 16, 72, 26, 82, 36, 92, 46, 102, 52, 108, 51, 107, 43, 99, 33, 89, 23, 79, 13, 69, 18, 74, 28, 84, 38, 94, 48, 104, 54, 110, 56, 112, 55, 111, 49, 105, 39, 95, 29, 85, 19, 75, 9, 65, 17, 73, 27, 83, 37, 93, 47, 103, 53, 109, 50, 106, 40, 96, 30, 86, 20, 76, 10, 66, 3, 59, 7, 63, 15, 71, 25, 81, 35, 91, 45, 101, 41, 97, 31, 87, 21, 77, 11, 67, 4, 60)(113, 169, 115, 171, 121, 177, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 140, 196, 128, 184, 118, 174, 127, 183, 139, 195, 150, 206, 138, 194, 126, 182, 137, 193, 149, 205, 160, 216, 148, 204, 136, 192, 147, 203, 159, 215, 166, 222, 158, 214, 146, 202, 157, 213, 165, 221, 168, 224, 164, 220, 156, 212, 153, 209, 162, 218, 167, 223, 163, 219, 154, 210, 143, 199, 152, 208, 161, 217, 155, 211, 144, 200, 133, 189, 142, 198, 151, 207, 145, 201, 134, 190, 123, 179, 132, 188, 141, 197, 135, 191, 124, 180, 116, 172, 122, 178, 131, 187, 125, 181, 117, 173)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 130)(10, 131)(11, 132)(12, 116)(13, 117)(14, 137)(15, 139)(16, 118)(17, 140)(18, 120)(19, 125)(20, 141)(21, 142)(22, 123)(23, 124)(24, 147)(25, 149)(26, 126)(27, 150)(28, 128)(29, 135)(30, 151)(31, 152)(32, 133)(33, 134)(34, 157)(35, 159)(36, 136)(37, 160)(38, 138)(39, 145)(40, 161)(41, 162)(42, 143)(43, 144)(44, 153)(45, 165)(46, 146)(47, 166)(48, 148)(49, 155)(50, 167)(51, 154)(52, 156)(53, 168)(54, 158)(55, 163)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1173
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1169 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2, Y1), (R * Y3)^2, (R * Y1)^2, Y1 * Y2^2 * Y1^5, Y2^-3 * Y1^-2 * Y2^3 * Y1^2, Y2^8 * Y1^-1 * Y2, Y2^-3 * Y1^4 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-5 * Y1^3, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 24, 80, 13, 69, 18, 74, 30, 86, 40, 96, 49, 105, 48, 104, 38, 94, 44, 100, 52, 108, 56, 112, 54, 110, 46, 102, 34, 90, 19, 75, 31, 87, 41, 97, 36, 92, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 39, 95, 37, 93, 25, 81, 32, 88, 42, 98, 50, 106, 55, 111, 53, 109, 45, 101, 33, 89, 43, 99, 51, 107, 47, 103, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 22, 78, 11, 67, 4, 60)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 156, 212, 144, 200, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 143, 199, 155, 211, 164, 220, 154, 210, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 153, 209, 163, 219, 168, 224, 162, 218, 152, 208, 140, 196, 126, 182, 139, 195, 134, 190, 148, 204, 159, 215, 166, 222, 167, 223, 161, 217, 151, 207, 138, 194, 135, 191, 123, 179, 133, 189, 147, 203, 158, 214, 165, 221, 160, 216, 149, 205, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 146, 202, 157, 213, 150, 206, 137, 193, 125, 181, 117, 173)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 135)(27, 134)(28, 126)(29, 153)(30, 128)(31, 155)(32, 130)(33, 156)(34, 157)(35, 158)(36, 159)(37, 136)(38, 137)(39, 138)(40, 140)(41, 163)(42, 142)(43, 164)(44, 144)(45, 150)(46, 165)(47, 166)(48, 149)(49, 151)(50, 152)(51, 168)(52, 154)(53, 160)(54, 167)(55, 161)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1174
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1170 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y1^-1 * Y2^-1 * Y1^-1 * Y2^-4 * Y1^-1, Y1^-1 * Y2 * Y1^-9 * Y2, Y2^2 * Y1^-1 * Y2 * Y1^-2 * Y2^3 * Y1^-4 * Y2, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 38, 94, 48, 104, 45, 101, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 25, 81, 32, 88, 42, 98, 52, 108, 56, 112, 53, 109, 43, 99, 33, 89, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 40, 96, 50, 106, 46, 102, 36, 92, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 39, 95, 49, 105, 55, 111, 54, 110, 44, 100, 34, 90, 19, 75, 31, 87, 24, 80, 13, 69, 18, 74, 30, 86, 41, 97, 51, 107, 47, 103, 37, 93, 22, 78, 11, 67, 4, 60)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 134, 190, 148, 204, 157, 213, 166, 222, 168, 224, 163, 219, 152, 208, 138, 194, 151, 207, 144, 200, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 143, 199, 135, 191, 123, 179, 133, 189, 147, 203, 156, 212, 165, 221, 159, 215, 162, 218, 150, 206, 161, 217, 154, 210, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 146, 202, 155, 211, 149, 205, 158, 214, 160, 216, 167, 223, 164, 220, 153, 209, 140, 196, 126, 182, 139, 195, 137, 193, 125, 181, 117, 173)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 151)(27, 137)(28, 126)(29, 136)(30, 128)(31, 135)(32, 130)(33, 134)(34, 155)(35, 156)(36, 157)(37, 158)(38, 161)(39, 144)(40, 138)(41, 140)(42, 142)(43, 149)(44, 165)(45, 166)(46, 160)(47, 162)(48, 167)(49, 154)(50, 150)(51, 152)(52, 153)(53, 159)(54, 168)(55, 164)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1172
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.1171 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2 * Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^28, (Y3^-1 * Y1^-1)^56, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 122, 178, 126, 182, 130, 186, 134, 190, 138, 194, 142, 198, 146, 202, 150, 206, 154, 210, 158, 214, 162, 218, 166, 222, 165, 221, 161, 217, 157, 213, 153, 209, 149, 205, 145, 201, 141, 197, 137, 193, 133, 189, 129, 185, 125, 181, 121, 177, 116, 172)(115, 171, 117, 173, 119, 175, 123, 179, 127, 183, 131, 187, 135, 191, 139, 195, 143, 199, 147, 203, 151, 207, 155, 211, 159, 215, 163, 219, 167, 223, 168, 224, 164, 220, 160, 216, 156, 212, 152, 208, 148, 204, 144, 200, 140, 196, 136, 192, 132, 188, 128, 184, 124, 180, 120, 176)
	L = (1, 115)(2, 117)(3, 116)(4, 120)(5, 113)(6, 119)(7, 114)(8, 121)(9, 124)(10, 123)(11, 118)(12, 125)(13, 128)(14, 127)(15, 122)(16, 129)(17, 132)(18, 131)(19, 126)(20, 133)(21, 136)(22, 135)(23, 130)(24, 137)(25, 140)(26, 139)(27, 134)(28, 141)(29, 144)(30, 143)(31, 138)(32, 145)(33, 148)(34, 147)(35, 142)(36, 149)(37, 152)(38, 151)(39, 146)(40, 153)(41, 156)(42, 155)(43, 150)(44, 157)(45, 160)(46, 159)(47, 154)(48, 161)(49, 164)(50, 163)(51, 158)(52, 165)(53, 168)(54, 167)(55, 162)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1167
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1172 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^3 * Y3^2, Y2 * Y3^-18, Y2 * Y3^-18, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^56 ]
Map::
	R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 125, 181, 127, 183, 132, 188, 137, 193, 139, 195, 144, 200, 149, 205, 151, 207, 156, 212, 161, 217, 163, 219, 168, 224, 165, 221, 158, 214, 160, 216, 153, 209, 146, 202, 148, 204, 141, 197, 134, 190, 136, 192, 129, 185, 121, 177, 123, 179, 116, 172)(115, 171, 119, 175, 124, 180, 117, 173, 120, 176, 126, 182, 131, 187, 133, 189, 138, 194, 143, 199, 145, 201, 150, 206, 155, 211, 157, 213, 162, 218, 167, 223, 164, 220, 166, 222, 159, 215, 152, 208, 154, 210, 147, 203, 140, 196, 142, 198, 135, 191, 128, 184, 130, 186, 122, 178)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 124)(7, 123)(8, 114)(9, 128)(10, 129)(11, 130)(12, 116)(13, 117)(14, 118)(15, 120)(16, 134)(17, 135)(18, 136)(19, 125)(20, 126)(21, 127)(22, 140)(23, 141)(24, 142)(25, 131)(26, 132)(27, 133)(28, 146)(29, 147)(30, 148)(31, 137)(32, 138)(33, 139)(34, 152)(35, 153)(36, 154)(37, 143)(38, 144)(39, 145)(40, 158)(41, 159)(42, 160)(43, 149)(44, 150)(45, 151)(46, 164)(47, 165)(48, 166)(49, 155)(50, 156)(51, 157)(52, 163)(53, 167)(54, 168)(55, 161)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1170
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1173 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, Y3^-6 * Y2, Y2^5 * Y3 * Y2 * Y3 * Y2^3, Y2^-1 * Y3 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^56 ]
Map::
	R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 126, 182, 138, 194, 150, 206, 160, 216, 148, 204, 136, 192, 125, 181, 130, 186, 142, 198, 154, 210, 163, 219, 168, 224, 165, 221, 156, 212, 144, 200, 132, 188, 121, 177, 129, 185, 141, 197, 153, 209, 158, 214, 146, 202, 134, 190, 123, 179, 116, 172)(115, 171, 119, 175, 127, 183, 139, 195, 151, 207, 159, 215, 147, 203, 135, 191, 124, 180, 117, 173, 120, 176, 128, 184, 140, 196, 152, 208, 162, 218, 167, 223, 161, 217, 149, 205, 137, 193, 131, 187, 143, 199, 155, 211, 164, 220, 166, 222, 157, 213, 145, 201, 133, 189, 122, 178)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 130)(20, 137)(21, 144)(22, 145)(23, 123)(24, 124)(25, 125)(26, 151)(27, 153)(28, 126)(29, 155)(30, 128)(31, 142)(32, 149)(33, 156)(34, 157)(35, 134)(36, 135)(37, 136)(38, 159)(39, 158)(40, 138)(41, 164)(42, 140)(43, 154)(44, 161)(45, 165)(46, 166)(47, 146)(48, 147)(49, 148)(50, 150)(51, 152)(52, 163)(53, 167)(54, 168)(55, 160)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1168
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1174 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, Y2^2 * Y3^-2 * Y2^-2 * Y3^2, Y3 * Y2^-1 * Y3^2 * Y2^-5 * Y3, Y2^2 * Y3 * Y2^2 * Y3^5 * Y2, Y3^2 * Y2^-1 * Y3^2 * Y2^23, (Y2^-1 * Y3)^56, (Y3^-1 * Y1^-1)^56 ]
Map::
	R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 126, 182, 138, 194, 154, 210, 145, 201, 161, 217, 165, 221, 151, 207, 136, 192, 125, 181, 130, 186, 142, 198, 158, 214, 147, 203, 132, 188, 121, 177, 129, 185, 141, 197, 157, 213, 167, 223, 153, 209, 162, 218, 149, 205, 134, 190, 123, 179, 116, 172)(115, 171, 119, 175, 127, 183, 139, 195, 155, 211, 168, 224, 163, 219, 164, 220, 150, 206, 135, 191, 124, 180, 117, 173, 120, 176, 128, 184, 140, 196, 156, 212, 146, 202, 131, 187, 143, 199, 159, 215, 166, 222, 152, 208, 137, 193, 144, 200, 160, 216, 148, 204, 133, 189, 122, 178)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 155)(27, 157)(28, 126)(29, 159)(30, 128)(31, 161)(32, 130)(33, 163)(34, 154)(35, 156)(36, 158)(37, 160)(38, 134)(39, 135)(40, 136)(41, 137)(42, 168)(43, 167)(44, 138)(45, 166)(46, 140)(47, 165)(48, 142)(49, 164)(50, 144)(51, 162)(52, 149)(53, 150)(54, 151)(55, 152)(56, 153)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.1169
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.1175 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^-2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^28, (Y3 * Y2^-1)^28, (Y3^-1 * Y1^-1)^56 ]
Map::
	R = (1, 57, 2, 58, 3, 59, 6, 62, 7, 63, 10, 66, 11, 67, 14, 70, 15, 71, 18, 74, 19, 75, 22, 78, 23, 79, 26, 82, 27, 83, 30, 86, 31, 87, 34, 90, 35, 91, 38, 94, 39, 95, 42, 98, 43, 99, 46, 102, 47, 103, 50, 106, 51, 107, 54, 110, 55, 111, 56, 112, 53, 109, 52, 108, 49, 105, 48, 104, 45, 101, 44, 100, 41, 97, 40, 96, 37, 93, 36, 92, 33, 89, 32, 88, 29, 85, 28, 84, 25, 81, 24, 80, 21, 77, 20, 76, 17, 73, 16, 72, 13, 69, 12, 68, 9, 65, 8, 64, 5, 61, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 118)(3, 119)(4, 114)(5, 113)(6, 122)(7, 123)(8, 116)(9, 117)(10, 126)(11, 127)(12, 120)(13, 121)(14, 130)(15, 131)(16, 124)(17, 125)(18, 134)(19, 135)(20, 128)(21, 129)(22, 138)(23, 139)(24, 132)(25, 133)(26, 142)(27, 143)(28, 136)(29, 137)(30, 146)(31, 147)(32, 140)(33, 141)(34, 150)(35, 151)(36, 144)(37, 145)(38, 154)(39, 155)(40, 148)(41, 149)(42, 158)(43, 159)(44, 152)(45, 153)(46, 162)(47, 163)(48, 156)(49, 157)(50, 166)(51, 167)(52, 160)(53, 161)(54, 168)(55, 165)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1163
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1176 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3 * Y1^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^28, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 5, 61, 6, 62, 9, 65, 10, 66, 13, 69, 14, 70, 17, 73, 18, 74, 21, 77, 22, 78, 25, 81, 26, 82, 29, 85, 30, 86, 33, 89, 34, 90, 37, 93, 38, 94, 41, 97, 42, 98, 45, 101, 46, 102, 49, 105, 50, 106, 53, 109, 54, 110, 55, 111, 56, 112, 51, 107, 52, 108, 47, 103, 48, 104, 43, 99, 44, 100, 39, 95, 40, 96, 35, 91, 36, 92, 31, 87, 32, 88, 27, 83, 28, 84, 23, 79, 24, 80, 19, 75, 20, 76, 15, 71, 16, 72, 11, 67, 12, 68, 7, 63, 8, 64, 3, 59, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 116)(3, 119)(4, 120)(5, 113)(6, 114)(7, 123)(8, 124)(9, 117)(10, 118)(11, 127)(12, 128)(13, 121)(14, 122)(15, 131)(16, 132)(17, 125)(18, 126)(19, 135)(20, 136)(21, 129)(22, 130)(23, 139)(24, 140)(25, 133)(26, 134)(27, 143)(28, 144)(29, 137)(30, 138)(31, 147)(32, 148)(33, 141)(34, 142)(35, 151)(36, 152)(37, 145)(38, 146)(39, 155)(40, 156)(41, 149)(42, 150)(43, 159)(44, 160)(45, 153)(46, 154)(47, 163)(48, 164)(49, 157)(50, 158)(51, 167)(52, 168)(53, 161)(54, 162)(55, 165)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1157
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1177 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1^7 * Y3 * Y1^11, (Y3 * Y2^-1)^28, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 20, 76, 26, 82, 32, 88, 38, 94, 44, 100, 50, 106, 54, 110, 48, 104, 42, 98, 36, 92, 30, 86, 24, 80, 18, 74, 12, 68, 5, 61, 8, 64, 9, 65, 16, 72, 22, 78, 28, 84, 34, 90, 40, 96, 46, 102, 52, 108, 56, 112, 55, 111, 49, 105, 43, 99, 37, 93, 31, 87, 25, 81, 19, 75, 13, 69, 10, 66, 3, 59, 7, 63, 15, 71, 21, 77, 27, 83, 33, 89, 39, 95, 45, 101, 51, 107, 53, 109, 47, 103, 41, 97, 35, 91, 29, 85, 23, 79, 17, 73, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 128)(8, 114)(9, 118)(10, 120)(11, 125)(12, 116)(13, 117)(14, 133)(15, 134)(16, 126)(17, 131)(18, 123)(19, 124)(20, 139)(21, 140)(22, 132)(23, 137)(24, 129)(25, 130)(26, 145)(27, 146)(28, 138)(29, 143)(30, 135)(31, 136)(32, 151)(33, 152)(34, 144)(35, 149)(36, 141)(37, 142)(38, 157)(39, 158)(40, 150)(41, 155)(42, 147)(43, 148)(44, 163)(45, 164)(46, 156)(47, 161)(48, 153)(49, 154)(50, 165)(51, 168)(52, 162)(53, 167)(54, 159)(55, 160)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1164
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1178 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1^-18 * Y3, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 20, 76, 26, 82, 32, 88, 38, 94, 44, 100, 50, 106, 54, 110, 48, 104, 42, 98, 36, 92, 30, 86, 24, 80, 18, 74, 10, 66, 3, 59, 7, 63, 13, 69, 16, 72, 22, 78, 28, 84, 34, 90, 40, 96, 46, 102, 52, 108, 56, 112, 53, 109, 47, 103, 41, 97, 35, 91, 29, 85, 23, 79, 17, 73, 9, 65, 12, 68, 5, 61, 8, 64, 15, 71, 21, 77, 27, 83, 33, 89, 39, 95, 45, 101, 51, 107, 55, 111, 49, 105, 43, 99, 37, 93, 31, 87, 25, 81, 19, 75, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 125)(7, 124)(8, 114)(9, 123)(10, 129)(11, 130)(12, 116)(13, 117)(14, 128)(15, 118)(16, 120)(17, 131)(18, 135)(19, 136)(20, 134)(21, 126)(22, 127)(23, 137)(24, 141)(25, 142)(26, 140)(27, 132)(28, 133)(29, 143)(30, 147)(31, 148)(32, 146)(33, 138)(34, 139)(35, 149)(36, 153)(37, 154)(38, 152)(39, 144)(40, 145)(41, 155)(42, 159)(43, 160)(44, 158)(45, 150)(46, 151)(47, 161)(48, 165)(49, 166)(50, 164)(51, 156)(52, 157)(53, 167)(54, 168)(55, 162)(56, 163)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1158
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1179 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^2 * Y3^5, Y1^10 * Y3^-3, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 36, 92, 46, 102, 51, 107, 41, 97, 31, 87, 19, 75, 24, 80, 13, 69, 18, 74, 29, 85, 39, 95, 49, 105, 53, 109, 43, 99, 33, 89, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 37, 93, 47, 103, 56, 112, 55, 111, 45, 101, 35, 91, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 38, 94, 48, 104, 52, 108, 42, 98, 32, 88, 20, 76, 9, 65, 17, 73, 25, 81, 30, 86, 40, 96, 50, 106, 54, 110, 44, 100, 34, 90, 22, 78, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 137)(16, 118)(17, 136)(18, 120)(19, 135)(20, 143)(21, 144)(22, 145)(23, 123)(24, 124)(25, 125)(26, 149)(27, 142)(28, 126)(29, 128)(30, 130)(31, 147)(32, 153)(33, 154)(34, 155)(35, 134)(36, 159)(37, 152)(38, 138)(39, 140)(40, 141)(41, 157)(42, 163)(43, 164)(44, 165)(45, 146)(46, 168)(47, 162)(48, 148)(49, 150)(50, 151)(51, 167)(52, 158)(53, 160)(54, 161)(55, 156)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1162
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1180 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^3, Y3^2 * Y1^-1 * Y3 * Y1^-1 * Y3^6, Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1, (Y3 * Y2^-1)^28, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^3 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 26, 82, 35, 91, 24, 80, 13, 69, 18, 74, 28, 84, 38, 94, 47, 103, 36, 92, 25, 81, 30, 86, 40, 96, 50, 106, 54, 110, 48, 104, 37, 93, 42, 98, 43, 99, 52, 108, 56, 112, 55, 111, 49, 105, 44, 100, 31, 87, 41, 97, 51, 107, 53, 109, 45, 101, 32, 88, 19, 75, 29, 85, 39, 95, 46, 102, 33, 89, 20, 76, 9, 65, 17, 73, 27, 83, 34, 90, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 22, 78, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 134)(15, 139)(16, 118)(17, 141)(18, 120)(19, 143)(20, 144)(21, 145)(22, 146)(23, 123)(24, 124)(25, 125)(26, 126)(27, 151)(28, 128)(29, 153)(30, 130)(31, 155)(32, 156)(33, 157)(34, 158)(35, 135)(36, 136)(37, 137)(38, 138)(39, 163)(40, 140)(41, 164)(42, 142)(43, 152)(44, 154)(45, 161)(46, 165)(47, 147)(48, 148)(49, 149)(50, 150)(51, 168)(52, 162)(53, 167)(54, 159)(55, 160)(56, 166)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1161
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1181 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^3 * Y1^-2, Y3^-4 * Y1^-1 * Y3^-1 * Y1^-3 * Y3^-1, Y1 * Y3^-5 * Y1^5, (Y3 * Y2^-1)^28, (Y1^-1 * Y3^-1)^56 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 42, 98, 51, 107, 38, 94, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 44, 100, 52, 108, 33, 89, 49, 105, 39, 95, 24, 80, 13, 69, 18, 74, 30, 86, 46, 102, 53, 109, 34, 90, 19, 75, 31, 87, 47, 103, 40, 96, 25, 81, 32, 88, 48, 104, 54, 110, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 45, 101, 41, 97, 50, 106, 55, 111, 36, 92, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 43, 99, 56, 112, 37, 93, 22, 78, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 155)(27, 157)(28, 126)(29, 159)(30, 128)(31, 161)(32, 130)(33, 163)(34, 164)(35, 165)(36, 166)(37, 167)(38, 134)(39, 135)(40, 136)(41, 137)(42, 168)(43, 153)(44, 138)(45, 152)(46, 140)(47, 151)(48, 142)(49, 150)(50, 144)(51, 149)(52, 154)(53, 156)(54, 158)(55, 160)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1165
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1182 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3 * Y1^-1 * Y3^3 * Y1^-2, Y3^3 * Y1^2 * Y3^-3 * Y1^-2, Y3 * Y1^3 * Y3 * Y1 * Y3 * Y1^2 * Y3^2, (Y3 * Y2^-1)^28, (Y1^-1 * Y3^-1)^56 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 42, 98, 51, 107, 36, 92, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 43, 99, 56, 112, 41, 97, 50, 106, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 45, 101, 55, 111, 40, 96, 25, 81, 32, 88, 48, 104, 34, 90, 19, 75, 31, 87, 47, 103, 54, 110, 39, 95, 24, 80, 13, 69, 18, 74, 30, 86, 46, 102, 33, 89, 49, 105, 53, 109, 38, 94, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 44, 100, 52, 108, 37, 93, 22, 78, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 155)(27, 157)(28, 126)(29, 159)(30, 128)(31, 161)(32, 130)(33, 156)(34, 158)(35, 160)(36, 162)(37, 163)(38, 134)(39, 135)(40, 136)(41, 137)(42, 168)(43, 167)(44, 138)(45, 166)(46, 140)(47, 165)(48, 142)(49, 164)(50, 144)(51, 153)(52, 154)(53, 149)(54, 150)(55, 151)(56, 152)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1159
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1183 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-13 * Y1^2, (Y3 * Y2^-1)^28 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 13, 69, 18, 74, 24, 80, 31, 87, 30, 86, 34, 90, 40, 96, 47, 103, 46, 102, 50, 106, 51, 107, 56, 112, 53, 109, 44, 100, 35, 91, 41, 97, 37, 93, 28, 84, 19, 75, 25, 81, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 12, 68, 5, 61, 8, 64, 16, 72, 23, 79, 22, 78, 26, 82, 32, 88, 39, 95, 38, 94, 42, 98, 48, 104, 55, 111, 54, 110, 52, 108, 43, 99, 49, 105, 45, 101, 36, 92, 27, 83, 33, 89, 29, 85, 20, 76, 9, 65, 17, 73, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 124)(15, 123)(16, 118)(17, 137)(18, 120)(19, 139)(20, 140)(21, 141)(22, 125)(23, 126)(24, 128)(25, 145)(26, 130)(27, 147)(28, 148)(29, 149)(30, 134)(31, 135)(32, 136)(33, 153)(34, 138)(35, 155)(36, 156)(37, 157)(38, 142)(39, 143)(40, 144)(41, 161)(42, 146)(43, 163)(44, 164)(45, 165)(46, 150)(47, 151)(48, 152)(49, 168)(50, 154)(51, 160)(52, 162)(53, 166)(54, 158)(55, 159)(56, 167)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1166
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1184 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {28, 56, 56})
Quotient :: dipole
Aut^+ = C56 (small group id <56, 2>)
Aut   = D112 (small group id <112, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1 * Y3^12, (Y3 * Y2^-1)^28, (Y1^-1 * Y3^-1)^56 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 14, 70, 9, 65, 17, 73, 24, 80, 31, 87, 27, 83, 33, 89, 40, 96, 47, 103, 43, 99, 49, 105, 54, 110, 56, 112, 52, 108, 45, 101, 38, 94, 42, 98, 36, 92, 29, 85, 22, 78, 26, 82, 20, 76, 12, 68, 5, 61, 8, 64, 16, 72, 10, 66, 3, 59, 7, 63, 15, 71, 23, 79, 19, 75, 25, 81, 32, 88, 39, 95, 35, 91, 41, 97, 48, 104, 55, 111, 51, 107, 53, 109, 46, 102, 50, 106, 44, 100, 37, 93, 30, 86, 34, 90, 28, 84, 21, 77, 13, 69, 18, 74, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 126)(11, 128)(12, 116)(13, 117)(14, 135)(15, 136)(16, 118)(17, 137)(18, 120)(19, 139)(20, 123)(21, 124)(22, 125)(23, 143)(24, 144)(25, 145)(26, 130)(27, 147)(28, 132)(29, 133)(30, 134)(31, 151)(32, 152)(33, 153)(34, 138)(35, 155)(36, 140)(37, 141)(38, 142)(39, 159)(40, 160)(41, 161)(42, 146)(43, 163)(44, 148)(45, 149)(46, 150)(47, 167)(48, 166)(49, 165)(50, 154)(51, 164)(52, 156)(53, 157)(54, 158)(55, 168)(56, 162)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56, 112 ), ( 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112, 56, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.1160
Graph:: bipartite
	v = 57 e = 112 f = 3
	degree seq :: [ 2^56, 112 ]

E27.1185 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^3 * T2^-3, T1^-9 * T2^9, T1^16 * T2^3, T2^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 14, 23, 30, 34, 41, 48, 52, 57, 50, 43, 39, 32, 25, 21, 12, 4, 10, 16, 6, 15, 24, 28, 35, 42, 46, 53, 56, 49, 45, 38, 31, 27, 20, 11, 18, 8, 2, 7, 17, 22, 29, 36, 40, 47, 54, 55, 51, 44, 37, 33, 26, 19, 13, 5)(58, 59, 63, 71, 79, 85, 91, 97, 103, 109, 112, 106, 100, 94, 88, 82, 76, 68, 61)(60, 64, 72, 80, 86, 92, 98, 104, 110, 114, 108, 102, 96, 90, 84, 78, 70, 75, 67)(62, 65, 73, 66, 74, 81, 87, 93, 99, 105, 111, 113, 107, 101, 95, 89, 83, 77, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1212
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1186 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1 * T2^-1 * T1 * T2^-2 * T1^4, T2 * T1 * T2^8, T2^2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 47, 40, 24, 12, 4, 10, 20, 34, 48, 55, 51, 39, 23, 11, 21, 35, 26, 42, 52, 57, 50, 38, 22, 36, 28, 14, 27, 43, 53, 56, 49, 37, 30, 16, 6, 15, 29, 44, 54, 46, 32, 18, 8, 2, 7, 17, 31, 45, 41, 25, 13, 5)(58, 59, 63, 71, 83, 91, 76, 88, 101, 110, 114, 108, 97, 82, 89, 94, 79, 68, 61)(60, 64, 72, 84, 99, 105, 90, 102, 111, 113, 107, 96, 81, 70, 75, 87, 93, 78, 67)(62, 65, 73, 85, 92, 77, 66, 74, 86, 100, 109, 112, 104, 98, 103, 106, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1225
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1187 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^5 * T2, T2^8 * T1^-1 * T2, T1 * T2^-1 * T1 * T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2^3 * T1, T1^2 * T2^-1 * T1 * T2^-2 * T1^3 * T2^-3 * T1, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 46, 32, 18, 8, 2, 7, 17, 31, 45, 54, 44, 30, 16, 6, 15, 29, 37, 50, 57, 53, 43, 28, 14, 27, 38, 22, 36, 49, 56, 52, 42, 26, 39, 23, 11, 21, 35, 48, 55, 51, 40, 24, 12, 4, 10, 20, 34, 47, 41, 25, 13, 5)(58, 59, 63, 71, 83, 97, 82, 89, 101, 110, 113, 105, 91, 76, 88, 94, 79, 68, 61)(60, 64, 72, 84, 96, 81, 70, 75, 87, 100, 109, 112, 104, 90, 102, 107, 93, 78, 67)(62, 65, 73, 85, 99, 108, 98, 103, 111, 114, 106, 92, 77, 66, 74, 86, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1210
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1188 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^-4 * T2^-1 * T1^-1 * T2^-2 * T1^-2, T1^2 * T2^-1 * T1 * T2^-1 * T1 * T2^-4 * T1, T2 * T1 * T2^3 * T1 * T2^5, T2^3 * T1^-1 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-1, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 42, 39, 23, 11, 21, 35, 53, 46, 28, 14, 27, 45, 37, 55, 50, 32, 18, 8, 2, 7, 17, 31, 49, 56, 40, 24, 12, 4, 10, 20, 34, 52, 44, 26, 43, 38, 22, 36, 54, 48, 30, 16, 6, 15, 29, 47, 57, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 97, 82, 89, 105, 110, 91, 76, 88, 104, 94, 79, 68, 61)(60, 64, 72, 84, 100, 96, 81, 70, 75, 87, 103, 109, 90, 106, 114, 112, 93, 78, 67)(62, 65, 73, 85, 101, 108, 113, 98, 107, 111, 92, 77, 66, 74, 86, 102, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1216
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1189 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-2 * T2^2 * T1^-4, T2^-4 * T1 * T2^-5 * T1, T1^3 * T2 * T1 * T2^5 * T1, T2^2 * T1^12 * T2, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 48, 30, 16, 6, 15, 29, 47, 54, 38, 22, 36, 44, 26, 43, 56, 40, 24, 12, 4, 10, 20, 34, 52, 50, 32, 18, 8, 2, 7, 17, 31, 49, 53, 37, 46, 28, 14, 27, 45, 55, 39, 23, 11, 21, 35, 42, 57, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 91, 76, 88, 104, 112, 97, 82, 89, 105, 94, 79, 68, 61)(60, 64, 72, 84, 100, 114, 109, 90, 106, 111, 96, 81, 70, 75, 87, 103, 93, 78, 67)(62, 65, 73, 85, 101, 92, 77, 66, 74, 86, 102, 113, 98, 107, 108, 110, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1226
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1190 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1 * T2^2, T2^-11 * T1 * T2^-1 * T1^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 29, 37, 45, 53, 50, 42, 34, 26, 14, 24, 12, 4, 10, 20, 30, 38, 46, 54, 51, 43, 35, 27, 16, 6, 15, 23, 11, 21, 31, 39, 47, 55, 52, 44, 36, 28, 18, 8, 2, 7, 17, 22, 32, 40, 48, 56, 57, 49, 41, 33, 25, 13, 5)(58, 59, 63, 71, 82, 85, 92, 99, 106, 109, 111, 102, 105, 96, 87, 76, 79, 68, 61)(60, 64, 72, 81, 70, 75, 84, 91, 98, 101, 108, 110, 113, 104, 95, 86, 89, 78, 67)(62, 65, 73, 83, 90, 93, 100, 107, 114, 112, 103, 94, 97, 88, 77, 66, 74, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1223
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1191 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^3 * T2^-1 * T1 * T2^-2, T1^-1 * T2^-1 * T1^-1 * T2^-11 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 29, 37, 45, 53, 54, 46, 38, 30, 22, 18, 8, 2, 7, 17, 28, 36, 44, 52, 55, 47, 39, 31, 23, 11, 21, 16, 6, 15, 27, 35, 43, 51, 56, 48, 40, 32, 24, 12, 4, 10, 20, 14, 26, 34, 42, 50, 57, 49, 41, 33, 25, 13, 5)(58, 59, 63, 71, 76, 85, 92, 99, 102, 109, 113, 106, 103, 96, 89, 82, 79, 68, 61)(60, 64, 72, 83, 86, 93, 100, 107, 110, 112, 105, 98, 95, 88, 81, 70, 75, 78, 67)(62, 65, 73, 77, 66, 74, 84, 91, 94, 101, 108, 114, 111, 104, 97, 90, 87, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1213
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1192 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1^-2 * T2^3, T1^-19, T1^19, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 6, 15, 22, 20, 27, 34, 32, 39, 46, 44, 51, 57, 53, 55, 48, 41, 43, 36, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 33, 40, 38, 45, 52, 50, 56, 54, 47, 49, 42, 35, 37, 30, 23, 25, 18, 11, 13, 5)(58, 59, 63, 71, 77, 83, 89, 95, 101, 107, 110, 104, 98, 92, 86, 80, 74, 68, 61)(60, 64, 72, 78, 84, 90, 96, 102, 108, 113, 112, 106, 100, 94, 88, 82, 76, 70, 67)(62, 65, 66, 73, 79, 85, 91, 97, 103, 109, 114, 111, 105, 99, 93, 87, 81, 75, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1220
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1193 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2^3 * T1^2, T1^19, T1^-19, T1^19, T1^-8 * T2^2 * T1^-9 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 11, 18, 23, 25, 30, 35, 37, 42, 47, 49, 54, 56, 50, 52, 45, 38, 40, 33, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 36, 41, 43, 48, 53, 55, 57, 51, 44, 46, 39, 32, 34, 27, 20, 22, 15, 6, 13, 5)(58, 59, 63, 71, 77, 83, 89, 95, 101, 107, 112, 106, 100, 94, 88, 82, 76, 68, 61)(60, 64, 70, 73, 79, 85, 91, 97, 103, 109, 114, 111, 105, 99, 93, 87, 81, 75, 67)(62, 65, 72, 78, 84, 90, 96, 102, 108, 113, 110, 104, 98, 92, 86, 80, 74, 66, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1224
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1194 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2 * T1^-1 * T2^2 * T1^-2, T1^-3 * T2^-1 * T1^-1 * T2^-8, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 43, 53, 52, 42, 32, 18, 8, 2, 7, 17, 31, 41, 51, 54, 44, 34, 22, 30, 16, 6, 15, 29, 40, 50, 55, 45, 35, 23, 11, 21, 28, 14, 27, 39, 49, 56, 46, 36, 24, 12, 4, 10, 20, 26, 38, 48, 57, 47, 37, 25, 13, 5)(58, 59, 63, 71, 83, 76, 88, 97, 106, 114, 110, 111, 102, 93, 82, 89, 79, 68, 61)(60, 64, 72, 84, 95, 90, 98, 107, 113, 104, 109, 101, 92, 81, 70, 75, 87, 78, 67)(62, 65, 73, 85, 77, 66, 74, 86, 96, 105, 100, 108, 112, 103, 94, 99, 91, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1221
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1195 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T1^2 * T2^-1 * T1 * T2^-8 * T1, T1^2 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 43, 53, 48, 38, 26, 24, 12, 4, 10, 20, 34, 44, 54, 49, 39, 28, 14, 27, 23, 11, 21, 35, 45, 55, 50, 40, 30, 16, 6, 15, 29, 22, 36, 46, 56, 52, 42, 32, 18, 8, 2, 7, 17, 31, 41, 51, 57, 47, 37, 25, 13, 5)(58, 59, 63, 71, 83, 82, 89, 97, 106, 110, 114, 113, 102, 91, 76, 88, 79, 68, 61)(60, 64, 72, 84, 81, 70, 75, 87, 96, 105, 104, 109, 112, 101, 90, 98, 93, 78, 67)(62, 65, 73, 85, 95, 94, 99, 107, 111, 100, 108, 103, 92, 77, 66, 74, 86, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1217
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1196 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-2 * T2 * T1^-1 * T2^5, T1 * T2 * T1 * T2 * T1 * T2 * T1^5, T1^-1 * T2^-4 * T1^-1 * T2^-3 * T1^-1 * T2^-2 * T1^-2, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 28, 14, 27, 45, 49, 56, 57, 52, 39, 23, 11, 21, 35, 32, 18, 8, 2, 7, 17, 31, 47, 44, 26, 43, 50, 37, 48, 53, 40, 24, 12, 4, 10, 20, 34, 30, 16, 6, 15, 29, 46, 55, 54, 42, 51, 38, 22, 36, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 109, 97, 82, 89, 91, 76, 88, 103, 106, 94, 79, 68, 61)(60, 64, 72, 84, 100, 108, 96, 81, 70, 75, 87, 90, 104, 112, 113, 105, 93, 78, 67)(62, 65, 73, 85, 101, 111, 114, 110, 98, 92, 77, 66, 74, 86, 102, 107, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1219
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1197 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-3 * T2^-6, T1^8 * T2^-3 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 38, 22, 36, 50, 42, 54, 55, 46, 30, 16, 6, 15, 29, 40, 24, 12, 4, 10, 20, 34, 48, 53, 37, 51, 44, 26, 43, 47, 32, 18, 8, 2, 7, 17, 31, 39, 23, 11, 21, 35, 49, 56, 57, 52, 45, 28, 14, 27, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 106, 91, 76, 88, 97, 82, 89, 103, 109, 94, 79, 68, 61)(60, 64, 72, 84, 100, 111, 113, 105, 90, 96, 81, 70, 75, 87, 102, 108, 93, 78, 67)(62, 65, 73, 85, 101, 107, 92, 77, 66, 74, 86, 98, 104, 112, 114, 110, 95, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1222
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1198 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^19, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 8, 2, 7, 14, 6, 13, 20, 12, 19, 26, 18, 25, 32, 24, 31, 38, 30, 37, 44, 36, 43, 50, 42, 49, 55, 48, 54, 57, 52, 56, 53, 46, 51, 47, 40, 45, 41, 34, 39, 35, 28, 33, 29, 22, 27, 23, 16, 21, 17, 10, 15, 11, 4, 9, 5)(58, 59, 63, 69, 75, 81, 87, 93, 99, 105, 109, 103, 97, 91, 85, 79, 73, 67, 61)(60, 64, 70, 76, 82, 88, 94, 100, 106, 111, 113, 108, 102, 96, 90, 84, 78, 72, 66)(62, 65, 71, 77, 83, 89, 95, 101, 107, 112, 114, 110, 104, 98, 92, 86, 80, 74, 68)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1215
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1199 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2^-3 * T1^-1, (F * T2)^2, (F * T1)^2, T1^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 4, 10, 15, 11, 16, 21, 17, 22, 27, 23, 28, 33, 29, 34, 39, 35, 40, 45, 41, 46, 51, 47, 52, 56, 53, 57, 55, 48, 54, 50, 42, 49, 44, 36, 43, 38, 30, 37, 32, 24, 31, 26, 18, 25, 20, 12, 19, 14, 6, 13, 8, 2, 7, 5)(58, 59, 63, 69, 75, 81, 87, 93, 99, 105, 110, 104, 98, 92, 86, 80, 74, 68, 61)(60, 64, 70, 76, 82, 88, 94, 100, 106, 111, 114, 109, 103, 97, 91, 85, 79, 73, 67)(62, 65, 71, 77, 83, 89, 95, 101, 107, 112, 113, 108, 102, 96, 90, 84, 78, 72, 66)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1218
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1200 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2, T1), (F * T1)^2, T2^-6 * T1, T2^-1 * T1^3 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-1, T2 * T1 * T2 * T1^8 * T2, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 31, 30, 16, 6, 15, 29, 43, 42, 28, 14, 27, 41, 55, 54, 40, 26, 39, 53, 46, 57, 52, 38, 51, 47, 34, 45, 56, 50, 48, 35, 22, 33, 44, 49, 36, 23, 11, 21, 32, 37, 24, 12, 4, 10, 20, 25, 13, 5)(58, 59, 63, 71, 83, 95, 107, 106, 94, 82, 76, 88, 100, 112, 103, 91, 79, 68, 61)(60, 64, 72, 84, 96, 108, 105, 93, 81, 70, 75, 87, 99, 111, 114, 102, 90, 78, 67)(62, 65, 73, 85, 97, 109, 113, 101, 89, 77, 66, 74, 86, 98, 110, 104, 92, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1211
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1201 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^5, T1^2 * T2^-1 * T1 * T2^-2 * T1^6, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 32, 37, 23, 11, 21, 33, 44, 49, 36, 22, 34, 45, 50, 57, 48, 35, 46, 52, 38, 51, 56, 47, 54, 40, 26, 39, 53, 55, 42, 28, 14, 27, 41, 43, 30, 16, 6, 15, 29, 31, 18, 8, 2, 7, 17, 25, 13, 5)(58, 59, 63, 71, 83, 95, 107, 101, 89, 76, 82, 88, 100, 112, 104, 92, 79, 68, 61)(60, 64, 72, 84, 96, 108, 114, 106, 94, 81, 70, 75, 87, 99, 111, 103, 91, 78, 67)(62, 65, 73, 85, 97, 109, 102, 90, 77, 66, 74, 86, 98, 110, 113, 105, 93, 80, 69)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 114^19 ), ( 114^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1214
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 57 f = 1
	degree seq :: [ 19^3, 57 ]

E27.1202 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^28, (T2^-1 * T1^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(58, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 100, 103, 104, 107, 108, 111, 112, 114, 113, 110, 109, 106, 105, 102, 101, 98, 97, 94, 93, 90, 89, 86, 85, 82, 81, 78, 77, 74, 73, 70, 69, 66, 65, 62, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1230
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1203 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1 * T2 * T1^3, T2^-1 * T1 * T2^-13 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 48, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 47, 55, 54, 46, 38, 30, 22, 14, 6, 11, 19, 27, 35, 43, 51, 56, 57, 52, 44, 36, 28, 20, 12, 4, 10, 18, 26, 34, 42, 50, 53, 45, 37, 29, 21, 13, 5)(58, 59, 63, 69, 62, 65, 71, 77, 70, 73, 79, 85, 78, 81, 87, 93, 86, 89, 95, 101, 94, 97, 103, 109, 102, 105, 111, 114, 110, 106, 112, 113, 107, 98, 104, 108, 99, 90, 96, 100, 91, 82, 88, 92, 83, 74, 80, 84, 75, 66, 72, 76, 67, 60, 64, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1229
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1204 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T1 * T2 * T1 * T2^10, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 29, 39, 49, 51, 41, 31, 21, 11, 14, 24, 34, 44, 54, 56, 48, 38, 28, 18, 8, 2, 7, 17, 27, 37, 47, 52, 42, 32, 22, 12, 4, 10, 20, 30, 40, 50, 57, 55, 46, 36, 26, 16, 6, 15, 25, 35, 45, 53, 43, 33, 23, 13, 5)(58, 59, 63, 71, 67, 60, 64, 72, 81, 77, 66, 74, 82, 91, 87, 76, 84, 92, 101, 97, 86, 94, 102, 111, 107, 96, 104, 110, 113, 114, 106, 109, 100, 105, 112, 108, 99, 90, 95, 103, 98, 89, 80, 85, 93, 88, 79, 70, 75, 83, 78, 69, 62, 65, 73, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1232
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1205 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^2 * T1^-2 * T2^-2 * T1^2, T2 * T1^3 * T2^-1 * T1^-3, T1^-1 * T2^-1 * T1^-6, T2^3 * T1^-1 * T2^5, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 32, 18, 8, 2, 7, 17, 31, 45, 44, 30, 16, 6, 15, 29, 43, 53, 52, 42, 28, 14, 27, 41, 51, 57, 56, 50, 40, 26, 22, 36, 47, 54, 55, 48, 37, 23, 11, 21, 35, 46, 49, 38, 24, 12, 4, 10, 20, 34, 39, 25, 13, 5)(58, 59, 63, 71, 83, 80, 69, 62, 65, 73, 85, 97, 94, 81, 70, 75, 87, 99, 107, 105, 95, 82, 89, 101, 109, 113, 112, 106, 96, 90, 102, 110, 114, 111, 103, 91, 76, 88, 100, 108, 104, 92, 77, 66, 74, 86, 98, 93, 78, 67, 60, 64, 72, 84, 79, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1233
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1206 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-4 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1^3 * T2 * T1^7, T2^4 * T1^-4 * T2 * T1^-3, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 38, 22, 36, 50, 55, 44, 26, 43, 47, 32, 18, 8, 2, 7, 17, 31, 39, 23, 11, 21, 35, 49, 54, 42, 52, 57, 46, 30, 16, 6, 15, 29, 40, 24, 12, 4, 10, 20, 34, 48, 53, 37, 51, 56, 45, 28, 14, 27, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 110, 95, 80, 69, 62, 65, 73, 85, 101, 111, 105, 90, 96, 81, 70, 75, 87, 102, 112, 106, 91, 76, 88, 97, 82, 89, 103, 113, 107, 92, 77, 66, 74, 86, 98, 104, 114, 108, 93, 78, 67, 60, 64, 72, 84, 100, 109, 94, 79, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1227
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1207 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2 * T1 * T2^4, T1^-4 * T2 * T1^-7, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 23, 11, 21, 32, 41, 45, 34, 43, 52, 57, 55, 48, 36, 47, 50, 39, 28, 14, 27, 30, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 31, 35, 22, 33, 42, 51, 53, 44, 46, 54, 56, 49, 38, 26, 37, 40, 29, 16, 6, 15, 25, 13, 5)(58, 59, 63, 71, 83, 93, 103, 100, 90, 78, 67, 60, 64, 72, 84, 94, 104, 111, 109, 99, 89, 77, 66, 74, 82, 87, 97, 107, 113, 114, 108, 98, 88, 76, 81, 70, 75, 86, 96, 106, 112, 110, 102, 92, 80, 69, 62, 65, 73, 85, 95, 105, 101, 91, 79, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1234
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1208 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^4 * T2^-1 * T1 * T2^-3, T1^-1 * T2^-1 * T1^-1 * T2^-8 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 46, 56, 48, 38, 22, 36, 30, 16, 6, 15, 29, 44, 54, 50, 40, 24, 12, 4, 10, 20, 34, 26, 42, 52, 57, 47, 37, 32, 18, 8, 2, 7, 17, 31, 45, 55, 49, 39, 23, 11, 21, 35, 28, 14, 27, 43, 53, 51, 41, 25, 13, 5)(58, 59, 63, 71, 83, 90, 102, 111, 108, 104, 95, 80, 69, 62, 65, 73, 85, 91, 76, 88, 101, 110, 114, 105, 96, 81, 70, 75, 87, 92, 77, 66, 74, 86, 100, 109, 113, 106, 97, 82, 89, 93, 78, 67, 60, 64, 72, 84, 99, 103, 112, 107, 98, 94, 79, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1228
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1209 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {19, 57, 57})
Quotient :: edge
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^-6 * T1, T2^-2 * T1^-1 * T2^-1 * T1^-6 * T2^-1, T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-5, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 30, 16, 6, 15, 29, 47, 51, 57, 44, 26, 43, 53, 38, 22, 36, 49, 55, 40, 24, 12, 4, 10, 20, 34, 32, 18, 8, 2, 7, 17, 31, 48, 46, 28, 14, 27, 45, 52, 37, 50, 56, 42, 54, 39, 23, 11, 21, 35, 41, 25, 13, 5)(58, 59, 63, 71, 83, 99, 112, 98, 91, 76, 88, 104, 109, 95, 80, 69, 62, 65, 73, 85, 101, 113, 106, 92, 77, 66, 74, 86, 102, 110, 96, 81, 70, 75, 87, 103, 114, 107, 93, 78, 67, 60, 64, 72, 84, 100, 111, 97, 82, 89, 90, 105, 108, 94, 79, 68, 61)
	L = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.1231
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.1210 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^3 * T2^-3, T1^-9 * T2^9, T1^16 * T2^3, T2^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 14, 71, 23, 80, 30, 87, 34, 91, 41, 98, 48, 105, 52, 109, 57, 114, 50, 107, 43, 100, 39, 96, 32, 89, 25, 82, 21, 78, 12, 69, 4, 61, 10, 67, 16, 73, 6, 63, 15, 72, 24, 81, 28, 85, 35, 92, 42, 99, 46, 103, 53, 110, 56, 113, 49, 106, 45, 102, 38, 95, 31, 88, 27, 84, 20, 77, 11, 68, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 22, 79, 29, 86, 36, 93, 40, 97, 47, 104, 54, 111, 55, 112, 51, 108, 44, 101, 37, 94, 33, 90, 26, 83, 19, 76, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 79)(15, 80)(16, 66)(17, 81)(18, 67)(19, 68)(20, 69)(21, 70)(22, 85)(23, 86)(24, 87)(25, 76)(26, 77)(27, 78)(28, 91)(29, 92)(30, 93)(31, 82)(32, 83)(33, 84)(34, 97)(35, 98)(36, 99)(37, 88)(38, 89)(39, 90)(40, 103)(41, 104)(42, 105)(43, 94)(44, 95)(45, 96)(46, 109)(47, 110)(48, 111)(49, 100)(50, 101)(51, 102)(52, 112)(53, 114)(54, 113)(55, 106)(56, 107)(57, 108)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1187
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1211 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1 * T2^-1 * T1 * T2^-2 * T1^4, T2 * T1 * T2^8, T2^2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 47, 104, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 48, 105, 55, 112, 51, 108, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 26, 83, 42, 99, 52, 109, 57, 114, 50, 107, 38, 95, 22, 79, 36, 93, 28, 85, 14, 71, 27, 84, 43, 100, 53, 110, 56, 113, 49, 106, 37, 94, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 44, 101, 54, 111, 46, 103, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 45, 102, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 91)(27, 99)(28, 92)(29, 100)(30, 93)(31, 101)(32, 94)(33, 102)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 103)(42, 105)(43, 109)(44, 110)(45, 111)(46, 106)(47, 98)(48, 90)(49, 95)(50, 96)(51, 97)(52, 112)(53, 114)(54, 113)(55, 104)(56, 107)(57, 108)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1200
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1212 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^5 * T2, T2^8 * T1^-1 * T2, T1 * T2^-1 * T1 * T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2^3 * T1, T1^2 * T2^-1 * T1 * T2^-2 * T1^3 * T2^-3 * T1, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 46, 103, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 45, 102, 54, 111, 44, 101, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 37, 94, 50, 107, 57, 114, 53, 110, 43, 100, 28, 85, 14, 71, 27, 84, 38, 95, 22, 79, 36, 93, 49, 106, 56, 113, 52, 109, 42, 99, 26, 83, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 48, 105, 55, 112, 51, 108, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 47, 104, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 97)(27, 96)(28, 99)(29, 95)(30, 100)(31, 94)(32, 101)(33, 102)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 103)(42, 108)(43, 109)(44, 110)(45, 107)(46, 111)(47, 90)(48, 91)(49, 92)(50, 93)(51, 98)(52, 112)(53, 113)(54, 114)(55, 104)(56, 105)(57, 106)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1185
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1213 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^-4 * T2^-1 * T1^-1 * T2^-2 * T1^-2, T1^2 * T2^-1 * T1 * T2^-1 * T1 * T2^-4 * T1, T2 * T1 * T2^3 * T1 * T2^5, T2^3 * T1^-1 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-2 * T2^-3 * T1^-1, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 51, 108, 42, 99, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 53, 110, 46, 103, 28, 85, 14, 71, 27, 84, 45, 102, 37, 94, 55, 112, 50, 107, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 49, 106, 56, 113, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 52, 109, 44, 101, 26, 83, 43, 100, 38, 95, 22, 79, 36, 93, 54, 111, 48, 105, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 47, 104, 57, 114, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 99)(27, 100)(28, 101)(29, 102)(30, 103)(31, 104)(32, 105)(33, 106)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 107)(42, 97)(43, 96)(44, 108)(45, 95)(46, 109)(47, 94)(48, 110)(49, 114)(50, 111)(51, 113)(52, 90)(53, 91)(54, 92)(55, 93)(56, 98)(57, 112)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1191
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1214 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-2 * T2^2 * T1^-4, T2^-4 * T1 * T2^-5 * T1, T1^3 * T2 * T1 * T2^5 * T1, T2^2 * T1^12 * T2, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 51, 108, 48, 105, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 47, 104, 54, 111, 38, 95, 22, 79, 36, 93, 44, 101, 26, 83, 43, 100, 56, 113, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 52, 109, 50, 107, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 49, 106, 53, 110, 37, 94, 46, 103, 28, 85, 14, 71, 27, 84, 45, 102, 55, 112, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 42, 99, 57, 114, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 99)(27, 100)(28, 101)(29, 102)(30, 103)(31, 104)(32, 105)(33, 106)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 107)(42, 91)(43, 114)(44, 92)(45, 113)(46, 93)(47, 112)(48, 94)(49, 111)(50, 108)(51, 110)(52, 90)(53, 95)(54, 96)(55, 97)(56, 98)(57, 109)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1201
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1215 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1 * T2^2, T2^-11 * T1 * T2^-1 * T1^2 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 29, 86, 37, 94, 45, 102, 53, 110, 50, 107, 42, 99, 34, 91, 26, 83, 14, 71, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 30, 87, 38, 95, 46, 103, 54, 111, 51, 108, 43, 100, 35, 92, 27, 84, 16, 73, 6, 63, 15, 72, 23, 80, 11, 68, 21, 78, 31, 88, 39, 96, 47, 104, 55, 112, 52, 109, 44, 101, 36, 93, 28, 85, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 22, 79, 32, 89, 40, 97, 48, 105, 56, 113, 57, 114, 49, 106, 41, 98, 33, 90, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 82)(15, 81)(16, 83)(17, 80)(18, 84)(19, 79)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 85)(26, 90)(27, 91)(28, 92)(29, 89)(30, 76)(31, 77)(32, 78)(33, 93)(34, 98)(35, 99)(36, 100)(37, 97)(38, 86)(39, 87)(40, 88)(41, 101)(42, 106)(43, 107)(44, 108)(45, 105)(46, 94)(47, 95)(48, 96)(49, 109)(50, 114)(51, 110)(52, 111)(53, 113)(54, 102)(55, 103)(56, 104)(57, 112)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1198
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1216 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^3 * T2^-1 * T1 * T2^-2, T1^-1 * T2^-1 * T1^-1 * T2^-11 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 29, 86, 37, 94, 45, 102, 53, 110, 54, 111, 46, 103, 38, 95, 30, 87, 22, 79, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 28, 85, 36, 93, 44, 101, 52, 109, 55, 112, 47, 104, 39, 96, 31, 88, 23, 80, 11, 68, 21, 78, 16, 73, 6, 63, 15, 72, 27, 84, 35, 92, 43, 100, 51, 108, 56, 113, 48, 105, 40, 97, 32, 89, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 14, 71, 26, 83, 34, 91, 42, 99, 50, 107, 57, 114, 49, 106, 41, 98, 33, 90, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 76)(15, 83)(16, 77)(17, 84)(18, 78)(19, 85)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 79)(26, 86)(27, 91)(28, 92)(29, 93)(30, 80)(31, 81)(32, 82)(33, 87)(34, 94)(35, 99)(36, 100)(37, 101)(38, 88)(39, 89)(40, 90)(41, 95)(42, 102)(43, 107)(44, 108)(45, 109)(46, 96)(47, 97)(48, 98)(49, 103)(50, 110)(51, 114)(52, 113)(53, 112)(54, 104)(55, 105)(56, 106)(57, 111)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1188
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1217 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1^-2 * T2^3, T1^-19, T1^19, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 6, 63, 15, 72, 22, 79, 20, 77, 27, 84, 34, 91, 32, 89, 39, 96, 46, 103, 44, 101, 51, 108, 57, 114, 53, 110, 55, 112, 48, 105, 41, 98, 43, 100, 36, 93, 29, 86, 31, 88, 24, 81, 17, 74, 19, 76, 12, 69, 4, 61, 10, 67, 8, 65, 2, 59, 7, 64, 16, 73, 14, 71, 21, 78, 28, 85, 26, 83, 33, 90, 40, 97, 38, 95, 45, 102, 52, 109, 50, 107, 56, 113, 54, 111, 47, 104, 49, 106, 42, 99, 35, 92, 37, 94, 30, 87, 23, 80, 25, 82, 18, 75, 11, 68, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 66)(9, 73)(10, 60)(11, 61)(12, 62)(13, 67)(14, 77)(15, 78)(16, 79)(17, 68)(18, 69)(19, 70)(20, 83)(21, 84)(22, 85)(23, 74)(24, 75)(25, 76)(26, 89)(27, 90)(28, 91)(29, 80)(30, 81)(31, 82)(32, 95)(33, 96)(34, 97)(35, 86)(36, 87)(37, 88)(38, 101)(39, 102)(40, 103)(41, 92)(42, 93)(43, 94)(44, 107)(45, 108)(46, 109)(47, 98)(48, 99)(49, 100)(50, 110)(51, 113)(52, 114)(53, 104)(54, 105)(55, 106)(56, 112)(57, 111)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1195
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1218 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2^3 * T1^2, T1^19, T1^-19, T1^19, T1^-8 * T2^2 * T1^-9 * T2 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 11, 68, 18, 75, 23, 80, 25, 82, 30, 87, 35, 92, 37, 94, 42, 99, 47, 104, 49, 106, 54, 111, 56, 113, 50, 107, 52, 109, 45, 102, 38, 95, 40, 97, 33, 90, 26, 83, 28, 85, 21, 78, 14, 71, 16, 73, 8, 65, 2, 59, 7, 64, 12, 69, 4, 61, 10, 67, 17, 74, 19, 76, 24, 81, 29, 86, 31, 88, 36, 93, 41, 98, 43, 100, 48, 105, 53, 110, 55, 112, 57, 114, 51, 108, 44, 101, 46, 103, 39, 96, 32, 89, 34, 91, 27, 84, 20, 77, 22, 79, 15, 72, 6, 63, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 70)(8, 72)(9, 69)(10, 60)(11, 61)(12, 62)(13, 73)(14, 77)(15, 78)(16, 79)(17, 66)(18, 67)(19, 68)(20, 83)(21, 84)(22, 85)(23, 74)(24, 75)(25, 76)(26, 89)(27, 90)(28, 91)(29, 80)(30, 81)(31, 82)(32, 95)(33, 96)(34, 97)(35, 86)(36, 87)(37, 88)(38, 101)(39, 102)(40, 103)(41, 92)(42, 93)(43, 94)(44, 107)(45, 108)(46, 109)(47, 98)(48, 99)(49, 100)(50, 112)(51, 113)(52, 114)(53, 104)(54, 105)(55, 106)(56, 110)(57, 111)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1199
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1219 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2 * T1^-1 * T2^2 * T1^-2, T1^-3 * T2^-1 * T1^-1 * T2^-8, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 43, 100, 53, 110, 52, 109, 42, 99, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 41, 98, 51, 108, 54, 111, 44, 101, 34, 91, 22, 79, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 40, 97, 50, 107, 55, 112, 45, 102, 35, 92, 23, 80, 11, 68, 21, 78, 28, 85, 14, 71, 27, 84, 39, 96, 49, 106, 56, 113, 46, 103, 36, 93, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 26, 83, 38, 95, 48, 105, 57, 114, 47, 104, 37, 94, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 76)(27, 95)(28, 77)(29, 96)(30, 78)(31, 97)(32, 79)(33, 98)(34, 80)(35, 81)(36, 82)(37, 99)(38, 90)(39, 105)(40, 106)(41, 107)(42, 91)(43, 108)(44, 92)(45, 93)(46, 94)(47, 109)(48, 100)(49, 114)(50, 113)(51, 112)(52, 101)(53, 111)(54, 102)(55, 103)(56, 104)(57, 110)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1196
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1220 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1, T1^2 * T2^-1 * T1 * T2^-8 * T1, T1^2 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 * T2 * T1^3 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 43, 100, 53, 110, 48, 105, 38, 95, 26, 83, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 44, 101, 54, 111, 49, 106, 39, 96, 28, 85, 14, 71, 27, 84, 23, 80, 11, 68, 21, 78, 35, 92, 45, 102, 55, 112, 50, 107, 40, 97, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 22, 79, 36, 93, 46, 103, 56, 113, 52, 109, 42, 99, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 41, 98, 51, 108, 57, 114, 47, 104, 37, 94, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 82)(27, 81)(28, 95)(29, 80)(30, 96)(31, 79)(32, 97)(33, 98)(34, 76)(35, 77)(36, 78)(37, 99)(38, 94)(39, 105)(40, 106)(41, 93)(42, 107)(43, 108)(44, 90)(45, 91)(46, 92)(47, 109)(48, 104)(49, 110)(50, 111)(51, 103)(52, 112)(53, 114)(54, 100)(55, 101)(56, 102)(57, 113)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1192
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1221 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-2 * T2 * T1^-1 * T2^5, T1 * T2 * T1 * T2 * T1 * T2 * T1^5, T1^-1 * T2^-4 * T1^-1 * T2^-3 * T1^-1 * T2^-2 * T1^-2, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 28, 85, 14, 71, 27, 84, 45, 102, 49, 106, 56, 113, 57, 114, 52, 109, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 47, 104, 44, 101, 26, 83, 43, 100, 50, 107, 37, 94, 48, 105, 53, 110, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 46, 103, 55, 112, 54, 111, 42, 99, 51, 108, 38, 95, 22, 79, 36, 93, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 99)(27, 100)(28, 101)(29, 102)(30, 90)(31, 103)(32, 91)(33, 104)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 92)(42, 109)(43, 108)(44, 111)(45, 107)(46, 106)(47, 112)(48, 93)(49, 94)(50, 95)(51, 96)(52, 97)(53, 98)(54, 114)(55, 113)(56, 105)(57, 110)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1194
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1222 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-3 * T2^-6, T1^8 * T2^-3 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 38, 95, 22, 79, 36, 93, 50, 107, 42, 99, 54, 111, 55, 112, 46, 103, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 40, 97, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 34, 91, 48, 105, 53, 110, 37, 94, 51, 108, 44, 101, 26, 83, 43, 100, 47, 104, 32, 89, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 49, 106, 56, 113, 57, 114, 52, 109, 45, 102, 28, 85, 14, 71, 27, 84, 41, 98, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 99)(27, 100)(28, 101)(29, 98)(30, 102)(31, 97)(32, 103)(33, 96)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 104)(42, 106)(43, 111)(44, 107)(45, 108)(46, 109)(47, 112)(48, 90)(49, 91)(50, 92)(51, 93)(52, 94)(53, 95)(54, 113)(55, 114)(56, 105)(57, 110)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1197
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1223 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^19, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 8, 65, 2, 59, 7, 64, 14, 71, 6, 63, 13, 70, 20, 77, 12, 69, 19, 76, 26, 83, 18, 75, 25, 82, 32, 89, 24, 81, 31, 88, 38, 95, 30, 87, 37, 94, 44, 101, 36, 93, 43, 100, 50, 107, 42, 99, 49, 106, 55, 112, 48, 105, 54, 111, 57, 114, 52, 109, 56, 113, 53, 110, 46, 103, 51, 108, 47, 104, 40, 97, 45, 102, 41, 98, 34, 91, 39, 96, 35, 92, 28, 85, 33, 90, 29, 86, 22, 79, 27, 84, 23, 80, 16, 73, 21, 78, 17, 74, 10, 67, 15, 72, 11, 68, 4, 61, 9, 66, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 69)(7, 70)(8, 71)(9, 60)(10, 61)(11, 62)(12, 75)(13, 76)(14, 77)(15, 66)(16, 67)(17, 68)(18, 81)(19, 82)(20, 83)(21, 72)(22, 73)(23, 74)(24, 87)(25, 88)(26, 89)(27, 78)(28, 79)(29, 80)(30, 93)(31, 94)(32, 95)(33, 84)(34, 85)(35, 86)(36, 99)(37, 100)(38, 101)(39, 90)(40, 91)(41, 92)(42, 105)(43, 106)(44, 107)(45, 96)(46, 97)(47, 98)(48, 109)(49, 111)(50, 112)(51, 102)(52, 103)(53, 104)(54, 113)(55, 114)(56, 108)(57, 110)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1190
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1224 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2^-3 * T1^-1, (F * T2)^2, (F * T1)^2, T1^19 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 4, 61, 10, 67, 15, 72, 11, 68, 16, 73, 21, 78, 17, 74, 22, 79, 27, 84, 23, 80, 28, 85, 33, 90, 29, 86, 34, 91, 39, 96, 35, 92, 40, 97, 45, 102, 41, 98, 46, 103, 51, 108, 47, 104, 52, 109, 56, 113, 53, 110, 57, 114, 55, 112, 48, 105, 54, 111, 50, 107, 42, 99, 49, 106, 44, 101, 36, 93, 43, 100, 38, 95, 30, 87, 37, 94, 32, 89, 24, 81, 31, 88, 26, 83, 18, 75, 25, 82, 20, 77, 12, 69, 19, 76, 14, 71, 6, 63, 13, 70, 8, 65, 2, 59, 7, 64, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 69)(7, 70)(8, 71)(9, 62)(10, 60)(11, 61)(12, 75)(13, 76)(14, 77)(15, 66)(16, 67)(17, 68)(18, 81)(19, 82)(20, 83)(21, 72)(22, 73)(23, 74)(24, 87)(25, 88)(26, 89)(27, 78)(28, 79)(29, 80)(30, 93)(31, 94)(32, 95)(33, 84)(34, 85)(35, 86)(36, 99)(37, 100)(38, 101)(39, 90)(40, 91)(41, 92)(42, 105)(43, 106)(44, 107)(45, 96)(46, 97)(47, 98)(48, 110)(49, 111)(50, 112)(51, 102)(52, 103)(53, 104)(54, 114)(55, 113)(56, 108)(57, 109)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1193
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1225 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2, T1), (F * T1)^2, T2^-6 * T1, T2^-1 * T1^3 * T2^-2 * T1^-1 * T2^-2 * T1^-1 * T2^-1, T2 * T1 * T2 * T1^8 * T2, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 31, 88, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 43, 100, 42, 99, 28, 85, 14, 71, 27, 84, 41, 98, 55, 112, 54, 111, 40, 97, 26, 83, 39, 96, 53, 110, 46, 103, 57, 114, 52, 109, 38, 95, 51, 108, 47, 104, 34, 91, 45, 102, 56, 113, 50, 107, 48, 105, 35, 92, 22, 79, 33, 90, 44, 101, 49, 106, 36, 93, 23, 80, 11, 68, 21, 78, 32, 89, 37, 94, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 76)(26, 95)(27, 96)(28, 97)(29, 98)(30, 99)(31, 100)(32, 77)(33, 78)(34, 79)(35, 80)(36, 81)(37, 82)(38, 107)(39, 108)(40, 109)(41, 110)(42, 111)(43, 112)(44, 89)(45, 90)(46, 91)(47, 92)(48, 93)(49, 94)(50, 106)(51, 105)(52, 113)(53, 104)(54, 114)(55, 103)(56, 101)(57, 102)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1186
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1226 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1 * T2^5, T1^2 * T2^-1 * T1 * T2^-2 * T1^6, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 24, 81, 12, 69, 4, 61, 10, 67, 20, 77, 32, 89, 37, 94, 23, 80, 11, 68, 21, 78, 33, 90, 44, 101, 49, 106, 36, 93, 22, 79, 34, 91, 45, 102, 50, 107, 57, 114, 48, 105, 35, 92, 46, 103, 52, 109, 38, 95, 51, 108, 56, 113, 47, 104, 54, 111, 40, 97, 26, 83, 39, 96, 53, 110, 55, 112, 42, 99, 28, 85, 14, 71, 27, 84, 41, 98, 43, 100, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 31, 88, 18, 75, 8, 65, 2, 59, 7, 64, 17, 74, 25, 82, 13, 70, 5, 62)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 82)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 88)(26, 95)(27, 96)(28, 97)(29, 98)(30, 99)(31, 100)(32, 76)(33, 77)(34, 78)(35, 79)(36, 80)(37, 81)(38, 107)(39, 108)(40, 109)(41, 110)(42, 111)(43, 112)(44, 89)(45, 90)(46, 91)(47, 92)(48, 93)(49, 94)(50, 101)(51, 114)(52, 102)(53, 113)(54, 103)(55, 104)(56, 105)(57, 106)
	local type(s) :: { ( 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57, 19, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.1189
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 57 f = 4
	degree seq :: [ 114 ]

E27.1227 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^3 * T2^-3, T2^-1 * T1^-18, T2^19, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 14, 71, 23, 80, 30, 87, 34, 91, 41, 98, 48, 105, 52, 109, 55, 112, 51, 108, 44, 101, 37, 94, 33, 90, 26, 83, 19, 76, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 22, 79, 29, 86, 36, 93, 40, 97, 47, 104, 54, 111, 56, 113, 49, 106, 45, 102, 38, 95, 31, 88, 27, 84, 20, 77, 11, 68, 18, 75, 8, 65)(4, 61, 10, 67, 16, 73, 6, 63, 15, 72, 24, 81, 28, 85, 35, 92, 42, 99, 46, 103, 53, 110, 57, 114, 50, 107, 43, 100, 39, 96, 32, 89, 25, 82, 21, 78, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 79)(15, 80)(16, 66)(17, 81)(18, 67)(19, 68)(20, 69)(21, 70)(22, 85)(23, 86)(24, 87)(25, 76)(26, 77)(27, 78)(28, 91)(29, 92)(30, 93)(31, 82)(32, 83)(33, 84)(34, 97)(35, 98)(36, 99)(37, 88)(38, 89)(39, 90)(40, 103)(41, 104)(42, 105)(43, 94)(44, 95)(45, 96)(46, 109)(47, 110)(48, 111)(49, 100)(50, 101)(51, 102)(52, 113)(53, 112)(54, 114)(55, 106)(56, 107)(57, 108)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1206
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1228 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T2^-3 * T1^6, T2^5 * T1 * T2^3 * T1^2, T2^-19, T2^19, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 47, 104, 50, 107, 38, 95, 22, 79, 36, 93, 28, 85, 14, 71, 27, 84, 43, 100, 53, 110, 41, 98, 25, 82, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 31, 88, 45, 102, 51, 108, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 26, 83, 42, 99, 54, 111, 55, 112, 46, 103, 32, 89, 18, 75, 8, 65)(4, 61, 10, 67, 20, 77, 34, 91, 48, 105, 56, 113, 57, 114, 49, 106, 37, 94, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 44, 101, 52, 109, 40, 97, 24, 81, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 91)(27, 99)(28, 92)(29, 100)(30, 93)(31, 101)(32, 94)(33, 102)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 103)(42, 105)(43, 111)(44, 110)(45, 109)(46, 106)(47, 108)(48, 90)(49, 95)(50, 96)(51, 97)(52, 98)(53, 112)(54, 113)(55, 114)(56, 104)(57, 107)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1208
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1229 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^19, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 15, 72, 21, 78, 27, 84, 33, 90, 39, 96, 45, 102, 51, 108, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 11, 68, 5, 62)(2, 59, 7, 64, 13, 70, 19, 76, 25, 82, 31, 88, 37, 94, 43, 100, 49, 106, 55, 112, 56, 113, 50, 107, 44, 101, 38, 95, 32, 89, 26, 83, 20, 77, 14, 71, 8, 65)(4, 61, 6, 63, 12, 69, 18, 75, 24, 81, 30, 87, 36, 93, 42, 99, 48, 105, 54, 111, 57, 114, 52, 109, 46, 103, 40, 97, 34, 91, 28, 85, 22, 79, 16, 73, 10, 67)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 60)(7, 69)(8, 61)(9, 70)(10, 62)(11, 71)(12, 66)(13, 75)(14, 67)(15, 76)(16, 68)(17, 77)(18, 72)(19, 81)(20, 73)(21, 82)(22, 74)(23, 83)(24, 78)(25, 87)(26, 79)(27, 88)(28, 80)(29, 89)(30, 84)(31, 93)(32, 85)(33, 94)(34, 86)(35, 95)(36, 90)(37, 99)(38, 91)(39, 100)(40, 92)(41, 101)(42, 96)(43, 105)(44, 97)(45, 106)(46, 98)(47, 107)(48, 102)(49, 111)(50, 103)(51, 112)(52, 104)(53, 113)(54, 108)(55, 114)(56, 109)(57, 110)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1203
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1230 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^19 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 15, 72, 21, 78, 27, 84, 33, 90, 39, 96, 45, 102, 51, 108, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 11, 68, 5, 62)(2, 59, 7, 64, 13, 70, 19, 76, 25, 82, 31, 88, 37, 94, 43, 100, 49, 106, 55, 112, 56, 113, 50, 107, 44, 101, 38, 95, 32, 89, 26, 83, 20, 77, 14, 71, 8, 65)(4, 61, 10, 67, 16, 73, 22, 79, 28, 85, 34, 91, 40, 97, 46, 103, 52, 109, 57, 114, 54, 111, 48, 105, 42, 99, 36, 93, 30, 87, 24, 81, 18, 75, 12, 69, 6, 63)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 62)(7, 61)(8, 69)(9, 70)(10, 60)(11, 71)(12, 68)(13, 67)(14, 75)(15, 76)(16, 66)(17, 77)(18, 74)(19, 73)(20, 81)(21, 82)(22, 72)(23, 83)(24, 80)(25, 79)(26, 87)(27, 88)(28, 78)(29, 89)(30, 86)(31, 85)(32, 93)(33, 94)(34, 84)(35, 95)(36, 92)(37, 91)(38, 99)(39, 100)(40, 90)(41, 101)(42, 98)(43, 97)(44, 105)(45, 106)(46, 96)(47, 107)(48, 104)(49, 103)(50, 111)(51, 112)(52, 102)(53, 113)(54, 110)(55, 109)(56, 114)(57, 108)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1202
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1231 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T1^-3 * T2^4, T2^-2 * T1^-1 * T2^-1 * T1^-11, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 14, 71, 27, 84, 36, 93, 45, 102, 42, 99, 51, 108, 55, 112, 46, 103, 49, 106, 40, 97, 31, 88, 22, 79, 25, 82, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 29, 86, 26, 83, 35, 92, 44, 101, 53, 110, 50, 107, 56, 113, 47, 104, 38, 95, 41, 98, 32, 89, 23, 80, 11, 68, 21, 78, 18, 75, 8, 65)(4, 61, 10, 67, 20, 77, 16, 73, 6, 63, 15, 72, 28, 85, 37, 94, 34, 91, 43, 100, 52, 109, 54, 111, 57, 114, 48, 105, 39, 96, 30, 87, 33, 90, 24, 81, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 76)(17, 85)(18, 77)(19, 86)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 78)(26, 91)(27, 92)(28, 93)(29, 94)(30, 79)(31, 80)(32, 81)(33, 82)(34, 99)(35, 100)(36, 101)(37, 102)(38, 87)(39, 88)(40, 89)(41, 90)(42, 107)(43, 108)(44, 109)(45, 110)(46, 95)(47, 96)(48, 97)(49, 98)(50, 114)(51, 113)(52, 112)(53, 111)(54, 103)(55, 104)(56, 105)(57, 106)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1209
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1232 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^2, T2^7 * T1^-3, T1^3 * T2 * T1^2 * T2^4 * T1, T1^3 * T2^-1 * T1^5 * T2^-1 * T1, T1^13 * T2^2 * T1^2 * T2, T1^57, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 46, 103, 28, 85, 14, 71, 27, 84, 45, 102, 55, 112, 38, 95, 22, 79, 36, 93, 51, 108, 41, 98, 25, 82, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 31, 88, 49, 106, 53, 110, 44, 101, 26, 83, 43, 100, 56, 113, 39, 96, 23, 80, 11, 68, 21, 78, 35, 92, 50, 107, 32, 89, 18, 75, 8, 65)(4, 61, 10, 67, 20, 77, 34, 91, 48, 105, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 47, 104, 54, 111, 37, 94, 52, 109, 42, 99, 57, 114, 40, 97, 24, 81, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 99)(27, 100)(28, 101)(29, 102)(30, 103)(31, 104)(32, 105)(33, 106)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 107)(42, 108)(43, 114)(44, 109)(45, 113)(46, 110)(47, 112)(48, 90)(49, 111)(50, 91)(51, 92)(52, 93)(53, 94)(54, 95)(55, 96)(56, 97)(57, 98)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1204
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1233 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-5, T1^-1 * T2^-2 * T1^2 * T2^2 * T1^-1, T1 * T2^-3 * T1^3 * T2 * T1 * T2 * T1, T1^2 * T2 * T1 * T2^8, (T1^-1 * T2^-1)^57 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 31, 88, 43, 100, 55, 112, 46, 103, 34, 91, 22, 79, 14, 71, 26, 83, 38, 95, 50, 107, 49, 106, 37, 94, 25, 82, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 29, 86, 41, 98, 53, 110, 47, 104, 35, 92, 23, 80, 11, 68, 21, 78, 33, 90, 45, 102, 57, 114, 54, 111, 42, 99, 30, 87, 18, 75, 8, 65)(4, 61, 10, 67, 20, 77, 32, 89, 44, 101, 56, 113, 52, 109, 40, 97, 28, 85, 16, 73, 6, 63, 15, 72, 27, 84, 39, 96, 51, 108, 48, 105, 36, 93, 24, 81, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 78)(15, 83)(16, 79)(17, 84)(18, 85)(19, 86)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 87)(26, 90)(27, 95)(28, 91)(29, 96)(30, 97)(31, 98)(32, 76)(33, 77)(34, 80)(35, 81)(36, 82)(37, 99)(38, 102)(39, 107)(40, 103)(41, 108)(42, 109)(43, 110)(44, 88)(45, 89)(46, 92)(47, 93)(48, 94)(49, 111)(50, 114)(51, 106)(52, 112)(53, 105)(54, 113)(55, 104)(56, 100)(57, 101)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1205
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1234 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {19, 57, 57})
Quotient :: loop
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^2 * T2 * T1 * T2^4, T2^3 * T1^-1 * T2 * T1^-8, T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 58, 3, 60, 9, 66, 19, 76, 33, 90, 22, 79, 36, 93, 45, 102, 54, 111, 48, 105, 57, 114, 52, 109, 41, 98, 28, 85, 14, 71, 27, 84, 25, 82, 13, 70, 5, 62)(2, 59, 7, 64, 17, 74, 31, 88, 23, 80, 11, 68, 21, 78, 35, 92, 44, 101, 53, 110, 47, 104, 56, 113, 51, 108, 40, 97, 26, 83, 39, 96, 32, 89, 18, 75, 8, 65)(4, 61, 10, 67, 20, 77, 34, 91, 43, 100, 37, 94, 46, 103, 55, 112, 50, 107, 38, 95, 49, 106, 42, 99, 30, 87, 16, 73, 6, 63, 15, 72, 29, 86, 24, 81, 12, 69)
	L = (1, 59)(2, 63)(3, 64)(4, 58)(5, 65)(6, 71)(7, 72)(8, 73)(9, 74)(10, 60)(11, 61)(12, 62)(13, 75)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 89)(26, 95)(27, 96)(28, 97)(29, 82)(30, 98)(31, 81)(32, 99)(33, 80)(34, 76)(35, 77)(36, 78)(37, 79)(38, 105)(39, 106)(40, 107)(41, 108)(42, 109)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(48, 110)(49, 114)(50, 111)(51, 112)(52, 113)(53, 100)(54, 101)(55, 102)(56, 103)(57, 104)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1207
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.1235 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1, Y2^2 * Y3 * Y2 * Y1^-2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y1^3 * Y2 * Y1^4 * Y3^-1 * Y2^2 * Y3^-8, Y1^19, Y2^57, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 22, 79, 28, 85, 34, 91, 40, 97, 46, 103, 52, 109, 55, 112, 49, 106, 43, 100, 37, 94, 31, 88, 25, 82, 19, 76, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 23, 80, 29, 86, 35, 92, 41, 98, 47, 104, 53, 110, 57, 114, 51, 108, 45, 102, 39, 96, 33, 90, 27, 84, 21, 78, 13, 70, 18, 75, 10, 67)(5, 62, 8, 65, 16, 73, 9, 66, 17, 74, 24, 81, 30, 87, 36, 93, 42, 99, 48, 105, 54, 111, 56, 113, 50, 107, 44, 101, 38, 95, 32, 89, 26, 83, 20, 77, 12, 69)(115, 172, 117, 174, 123, 180, 128, 185, 137, 194, 144, 201, 148, 205, 155, 212, 162, 219, 166, 223, 171, 228, 164, 221, 157, 214, 153, 210, 146, 203, 139, 196, 135, 192, 126, 183, 118, 175, 124, 181, 130, 187, 120, 177, 129, 186, 138, 195, 142, 199, 149, 206, 156, 213, 160, 217, 167, 224, 170, 227, 163, 220, 159, 216, 152, 209, 145, 202, 141, 198, 134, 191, 125, 182, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 136, 193, 143, 200, 150, 207, 154, 211, 161, 218, 168, 225, 169, 226, 165, 222, 158, 215, 151, 208, 147, 204, 140, 197, 133, 190, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 130)(10, 132)(11, 133)(12, 134)(13, 135)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 139)(20, 140)(21, 141)(22, 128)(23, 129)(24, 131)(25, 145)(26, 146)(27, 147)(28, 136)(29, 137)(30, 138)(31, 151)(32, 152)(33, 153)(34, 142)(35, 143)(36, 144)(37, 157)(38, 158)(39, 159)(40, 148)(41, 149)(42, 150)(43, 163)(44, 164)(45, 165)(46, 154)(47, 155)(48, 156)(49, 169)(50, 170)(51, 171)(52, 160)(53, 161)(54, 162)(55, 166)(56, 168)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1270
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1236 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1 * Y2^-1 * Y3^2 * Y2 * Y1, Y2^3 * Y1 * Y2^3 * Y3^-2, Y1^4 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1, Y1^2 * Y2^-2 * Y3^-6 * Y2^-1, Y1^19, Y2 * Y1^-2 * Y2 * Y3 * Y2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y1 * Y2 * Y3 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 49, 106, 34, 91, 19, 76, 31, 88, 40, 97, 25, 82, 32, 89, 46, 103, 52, 109, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 54, 111, 56, 113, 48, 105, 33, 90, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 45, 102, 51, 108, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 50, 107, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 47, 104, 55, 112, 57, 114, 53, 110, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 152, 209, 136, 193, 150, 207, 164, 221, 156, 213, 168, 225, 169, 226, 160, 217, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 162, 219, 167, 224, 151, 208, 165, 222, 158, 215, 140, 197, 157, 214, 161, 218, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 163, 220, 170, 227, 171, 228, 166, 223, 159, 216, 142, 199, 128, 185, 141, 198, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 162)(34, 163)(35, 164)(36, 165)(37, 166)(38, 167)(39, 147)(40, 145)(41, 143)(42, 140)(43, 141)(44, 142)(45, 144)(46, 146)(47, 155)(48, 170)(49, 156)(50, 158)(51, 159)(52, 160)(53, 171)(54, 157)(55, 161)(56, 168)(57, 169)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1280
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1237 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2, Y1^-1), Y3 * Y2 * Y3 * Y2 * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2^-2 * Y1 * Y3^-1 * Y2^-3, Y1^2 * Y2 * Y1 * Y2^2 * Y1 * Y3^-4, Y1^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 52, 109, 40, 97, 25, 82, 32, 89, 34, 91, 19, 76, 31, 88, 46, 103, 49, 106, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 51, 108, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 33, 90, 47, 104, 55, 112, 56, 113, 48, 105, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 54, 111, 57, 114, 53, 110, 41, 98, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 50, 107, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 142, 199, 128, 185, 141, 198, 159, 216, 163, 220, 170, 227, 171, 228, 166, 223, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 161, 218, 158, 215, 140, 197, 157, 214, 164, 221, 151, 208, 162, 219, 167, 224, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 160, 217, 169, 226, 168, 225, 156, 213, 165, 222, 152, 209, 136, 193, 150, 207, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 144)(34, 146)(35, 155)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 140)(43, 141)(44, 142)(45, 143)(46, 145)(47, 147)(48, 170)(49, 160)(50, 159)(51, 157)(52, 156)(53, 171)(54, 158)(55, 161)(56, 169)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1277
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1238 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y2^-3 * Y1^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 12, 69, 18, 75, 24, 81, 30, 87, 36, 93, 42, 99, 48, 105, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 11, 68, 4, 61)(3, 60, 7, 64, 13, 70, 19, 76, 25, 82, 31, 88, 37, 94, 43, 100, 49, 106, 54, 111, 57, 114, 52, 109, 46, 103, 40, 97, 34, 91, 28, 85, 22, 79, 16, 73, 10, 67)(5, 62, 8, 65, 14, 71, 20, 77, 26, 83, 32, 89, 38, 95, 44, 101, 50, 107, 55, 112, 56, 113, 51, 108, 45, 102, 39, 96, 33, 90, 27, 84, 21, 78, 15, 72, 9, 66)(115, 172, 117, 174, 123, 180, 118, 175, 124, 181, 129, 186, 125, 182, 130, 187, 135, 192, 131, 188, 136, 193, 141, 198, 137, 194, 142, 199, 147, 204, 143, 200, 148, 205, 153, 210, 149, 206, 154, 211, 159, 216, 155, 212, 160, 217, 165, 222, 161, 218, 166, 223, 170, 227, 167, 224, 171, 228, 169, 226, 162, 219, 168, 225, 164, 221, 156, 213, 163, 220, 158, 215, 150, 207, 157, 214, 152, 209, 144, 201, 151, 208, 146, 203, 138, 195, 145, 202, 140, 197, 132, 189, 139, 196, 134, 191, 126, 183, 133, 190, 128, 185, 120, 177, 127, 184, 122, 179, 116, 173, 121, 178, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 123)(6, 116)(7, 117)(8, 119)(9, 129)(10, 130)(11, 131)(12, 120)(13, 121)(14, 122)(15, 135)(16, 136)(17, 137)(18, 126)(19, 127)(20, 128)(21, 141)(22, 142)(23, 143)(24, 132)(25, 133)(26, 134)(27, 147)(28, 148)(29, 149)(30, 138)(31, 139)(32, 140)(33, 153)(34, 154)(35, 155)(36, 144)(37, 145)(38, 146)(39, 159)(40, 160)(41, 161)(42, 150)(43, 151)(44, 152)(45, 165)(46, 166)(47, 167)(48, 156)(49, 157)(50, 158)(51, 170)(52, 171)(53, 162)(54, 163)(55, 164)(56, 169)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1276
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1239 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 12, 69, 18, 75, 24, 81, 30, 87, 36, 93, 42, 99, 48, 105, 52, 109, 46, 103, 40, 97, 34, 91, 28, 85, 22, 79, 16, 73, 10, 67, 4, 61)(3, 60, 7, 64, 13, 70, 19, 76, 25, 82, 31, 88, 37, 94, 43, 100, 49, 106, 54, 111, 56, 113, 51, 108, 45, 102, 39, 96, 33, 90, 27, 84, 21, 78, 15, 72, 9, 66)(5, 62, 8, 65, 14, 71, 20, 77, 26, 83, 32, 89, 38, 95, 44, 101, 50, 107, 55, 112, 57, 114, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 11, 68)(115, 172, 117, 174, 122, 179, 116, 173, 121, 178, 128, 185, 120, 177, 127, 184, 134, 191, 126, 183, 133, 190, 140, 197, 132, 189, 139, 196, 146, 203, 138, 195, 145, 202, 152, 209, 144, 201, 151, 208, 158, 215, 150, 207, 157, 214, 164, 221, 156, 213, 163, 220, 169, 226, 162, 219, 168, 225, 171, 228, 166, 223, 170, 227, 167, 224, 160, 217, 165, 222, 161, 218, 154, 211, 159, 216, 155, 212, 148, 205, 153, 210, 149, 206, 142, 199, 147, 204, 143, 200, 136, 193, 141, 198, 137, 194, 130, 187, 135, 192, 131, 188, 124, 181, 129, 186, 125, 182, 118, 175, 123, 180, 119, 176)
	L = (1, 118)(2, 115)(3, 123)(4, 124)(5, 125)(6, 116)(7, 117)(8, 119)(9, 129)(10, 130)(11, 131)(12, 120)(13, 121)(14, 122)(15, 135)(16, 136)(17, 137)(18, 126)(19, 127)(20, 128)(21, 141)(22, 142)(23, 143)(24, 132)(25, 133)(26, 134)(27, 147)(28, 148)(29, 149)(30, 138)(31, 139)(32, 140)(33, 153)(34, 154)(35, 155)(36, 144)(37, 145)(38, 146)(39, 159)(40, 160)(41, 161)(42, 150)(43, 151)(44, 152)(45, 165)(46, 166)(47, 167)(48, 156)(49, 157)(50, 158)(51, 170)(52, 162)(53, 171)(54, 163)(55, 164)(56, 168)(57, 169)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1273
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1240 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y1^-1, Y2), (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y3 * Y1^-2 * Y2^3 * Y3, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-11 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 19, 76, 28, 85, 35, 92, 42, 99, 45, 102, 52, 109, 56, 113, 49, 106, 46, 103, 39, 96, 32, 89, 25, 82, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 26, 83, 29, 86, 36, 93, 43, 100, 50, 107, 53, 110, 55, 112, 48, 105, 41, 98, 38, 95, 31, 88, 24, 81, 13, 70, 18, 75, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 20, 77, 9, 66, 17, 74, 27, 84, 34, 91, 37, 94, 44, 101, 51, 108, 57, 114, 54, 111, 47, 104, 40, 97, 33, 90, 30, 87, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 143, 200, 151, 208, 159, 216, 167, 224, 168, 225, 160, 217, 152, 209, 144, 201, 136, 193, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 142, 199, 150, 207, 158, 215, 166, 223, 169, 226, 161, 218, 153, 210, 145, 202, 137, 194, 125, 182, 135, 192, 130, 187, 120, 177, 129, 186, 141, 198, 149, 206, 157, 214, 165, 222, 170, 227, 162, 219, 154, 211, 146, 203, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 128, 185, 140, 197, 148, 205, 156, 213, 164, 221, 171, 228, 163, 220, 155, 212, 147, 204, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 128)(20, 130)(21, 132)(22, 139)(23, 144)(24, 145)(25, 146)(26, 129)(27, 131)(28, 133)(29, 140)(30, 147)(31, 152)(32, 153)(33, 154)(34, 141)(35, 142)(36, 143)(37, 148)(38, 155)(39, 160)(40, 161)(41, 162)(42, 149)(43, 150)(44, 151)(45, 156)(46, 163)(47, 168)(48, 169)(49, 170)(50, 157)(51, 158)(52, 159)(53, 164)(54, 171)(55, 167)(56, 166)(57, 165)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1271
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1241 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2^-1 * Y3 * Y2 * Y1, (R * Y3)^2, (R * Y2)^2, Y1 * Y2 * Y3 * Y2^-1, (R * Y1)^2, Y1^2 * Y3 * Y2^-1 * Y3 * Y2, Y2 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-1, Y1 * Y2^-1 * Y3^-2 * Y2^-11, (Y2^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 25, 82, 28, 85, 35, 92, 42, 99, 49, 106, 52, 109, 54, 111, 45, 102, 48, 105, 39, 96, 30, 87, 19, 76, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 24, 81, 13, 70, 18, 75, 27, 84, 34, 91, 41, 98, 44, 101, 51, 108, 53, 110, 56, 113, 47, 104, 38, 95, 29, 86, 32, 89, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 26, 83, 33, 90, 36, 93, 43, 100, 50, 107, 57, 114, 55, 112, 46, 103, 37, 94, 40, 97, 31, 88, 20, 77, 9, 66, 17, 74, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 143, 200, 151, 208, 159, 216, 167, 224, 164, 221, 156, 213, 148, 205, 140, 197, 128, 185, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 144, 201, 152, 209, 160, 217, 168, 225, 165, 222, 157, 214, 149, 206, 141, 198, 130, 187, 120, 177, 129, 186, 137, 194, 125, 182, 135, 192, 145, 202, 153, 210, 161, 218, 169, 226, 166, 223, 158, 215, 150, 207, 142, 199, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 136, 193, 146, 203, 154, 211, 162, 219, 170, 227, 171, 228, 163, 220, 155, 212, 147, 204, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 144)(20, 145)(21, 146)(22, 133)(23, 131)(24, 129)(25, 128)(26, 130)(27, 132)(28, 139)(29, 152)(30, 153)(31, 154)(32, 143)(33, 140)(34, 141)(35, 142)(36, 147)(37, 160)(38, 161)(39, 162)(40, 151)(41, 148)(42, 149)(43, 150)(44, 155)(45, 168)(46, 169)(47, 170)(48, 159)(49, 156)(50, 157)(51, 158)(52, 163)(53, 165)(54, 166)(55, 171)(56, 167)(57, 164)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1281
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1242 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y2), (R * Y1)^2, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y1^3 * Y2 * Y1 * Y3^2 * Y1^-2 * Y2^-1, Y3^2 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-3, Y2 * Y3^2 * Y2 * Y3^2 * Y1^-1 * Y2 * Y1^-2, Y2^2 * Y1^-1 * Y3^2 * Y1^-3 * Y2 * Y1^-1, Y2 * Y1 * Y2^3 * Y1 * Y3^-2 * Y2^2 * Y3^-1, Y1^-2 * Y2^-6 * Y1^-1 * Y3^2, Y1^19, (Y3 * Y2^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 34, 91, 19, 76, 31, 88, 47, 104, 55, 112, 40, 97, 25, 82, 32, 89, 48, 105, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 57, 114, 52, 109, 33, 90, 49, 106, 54, 111, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 46, 103, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 56, 113, 41, 98, 50, 107, 51, 108, 53, 110, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 165, 222, 162, 219, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 161, 218, 168, 225, 152, 209, 136, 193, 150, 207, 158, 215, 140, 197, 157, 214, 170, 227, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 166, 223, 164, 221, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 163, 220, 167, 224, 151, 208, 160, 217, 142, 199, 128, 185, 141, 198, 159, 216, 169, 226, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 156, 213, 171, 228, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 166)(34, 156)(35, 158)(36, 160)(37, 162)(38, 167)(39, 168)(40, 169)(41, 170)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 155)(51, 164)(52, 171)(53, 165)(54, 163)(55, 161)(56, 159)(57, 157)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1284
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1243 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y3, Y1 * Y3, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y3, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^2 * Y3^-1 * Y2^-1 * Y1^-3, Y1^2 * Y2 * Y3^-2 * Y1 * Y3^-1 * Y2^2 * Y1, Y1^-2 * Y2^-1 * Y3^2 * Y1^-2 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2 * Y3 * Y1^-5, Y2 * Y3^-2 * Y2^8, Y1 * Y2^-5 * Y3^-3 * Y2^-1 * Y3^-1, Y1^3 * Y2^-2 * Y1 * Y2^-1 * Y3^-1 * Y2^-3, Y2^-1 * Y1^-1 * Y2^-2 * Y1^13, (Y2^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 40, 97, 25, 82, 32, 89, 48, 105, 53, 110, 34, 91, 19, 76, 31, 88, 47, 104, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 46, 103, 52, 109, 33, 90, 49, 106, 57, 114, 55, 112, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 51, 108, 56, 113, 41, 98, 50, 107, 54, 111, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 165, 222, 156, 213, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 167, 224, 160, 217, 142, 199, 128, 185, 141, 198, 159, 216, 151, 208, 169, 226, 164, 221, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 163, 220, 170, 227, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 166, 223, 158, 215, 140, 197, 157, 214, 152, 209, 136, 193, 150, 207, 168, 225, 162, 219, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 161, 218, 171, 228, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 166)(34, 167)(35, 168)(36, 169)(37, 161)(38, 159)(39, 157)(40, 156)(41, 170)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 146)(49, 147)(50, 155)(51, 158)(52, 160)(53, 162)(54, 164)(55, 171)(56, 165)(57, 163)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1274
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1244 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y3^2 * Y2^-1 * Y3^-2, Y3^2 * Y2^-1 * Y1^2 * Y2, Y2^5 * Y1 * Y2, Y2^2 * Y3^2 * Y2^-2 * Y1^2, Y1^5 * Y2^-2 * Y3^-2 * Y2^-1 * Y1 * Y3^-1, Y1^19, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 38, 95, 50, 107, 44, 101, 32, 89, 19, 76, 25, 82, 31, 88, 43, 100, 55, 112, 47, 104, 35, 92, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 51, 108, 57, 114, 49, 106, 37, 94, 24, 81, 13, 70, 18, 75, 30, 87, 42, 99, 54, 111, 46, 103, 34, 91, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 40, 97, 52, 109, 45, 102, 33, 90, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 53, 110, 56, 113, 48, 105, 36, 93, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 146, 203, 151, 208, 137, 194, 125, 182, 135, 192, 147, 204, 158, 215, 163, 220, 150, 207, 136, 193, 148, 205, 159, 216, 164, 221, 171, 228, 162, 219, 149, 206, 160, 217, 166, 223, 152, 209, 165, 222, 170, 227, 161, 218, 168, 225, 154, 211, 140, 197, 153, 210, 167, 224, 169, 226, 156, 213, 142, 199, 128, 185, 141, 198, 155, 212, 157, 214, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 145, 202, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 146)(20, 147)(21, 148)(22, 149)(23, 150)(24, 151)(25, 133)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 139)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 140)(39, 141)(40, 142)(41, 143)(42, 144)(43, 145)(44, 164)(45, 166)(46, 168)(47, 169)(48, 170)(49, 171)(50, 152)(51, 153)(52, 154)(53, 155)(54, 156)(55, 157)(56, 167)(57, 165)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1272
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1245 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^2 * Y3 * Y2^4, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-5, Y2 * Y3^-1 * Y2 * Y3^-8 * Y2, Y1^4 * Y2^-1 * Y1 * Y2^-1 * Y3^-5 * Y2^-1, Y1^5 * Y2^-1 * Y1 * Y3^-4 * Y2^-2, Y1^19, Y2^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^5 * Y3^-1 * Y1^4 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 38, 95, 50, 107, 49, 106, 37, 94, 25, 82, 19, 76, 31, 88, 43, 100, 55, 112, 46, 103, 34, 91, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 51, 108, 48, 105, 36, 93, 24, 81, 13, 70, 18, 75, 30, 87, 42, 99, 54, 111, 57, 114, 45, 102, 33, 90, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 40, 97, 52, 109, 56, 113, 44, 101, 32, 89, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 53, 110, 47, 104, 35, 92, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 157, 214, 156, 213, 142, 199, 128, 185, 141, 198, 155, 212, 169, 226, 168, 225, 154, 211, 140, 197, 153, 210, 167, 224, 160, 217, 171, 228, 166, 223, 152, 209, 165, 222, 161, 218, 148, 205, 159, 216, 170, 227, 164, 221, 162, 219, 149, 206, 136, 193, 147, 204, 158, 215, 163, 220, 150, 207, 137, 194, 125, 182, 135, 192, 146, 203, 151, 208, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 139)(20, 146)(21, 147)(22, 148)(23, 149)(24, 150)(25, 151)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 140)(39, 141)(40, 142)(41, 143)(42, 144)(43, 145)(44, 170)(45, 171)(46, 169)(47, 167)(48, 165)(49, 164)(50, 152)(51, 153)(52, 154)(53, 155)(54, 156)(55, 157)(56, 166)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1269
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1246 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y3 * Y2 * Y3 * Y2^2 * Y1^-3, Y2^9 * Y1^4, Y1^-19, Y1^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 19, 76, 31, 88, 40, 97, 49, 106, 57, 114, 53, 110, 54, 111, 45, 102, 36, 93, 25, 82, 32, 89, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 38, 95, 33, 90, 41, 98, 50, 107, 56, 113, 47, 104, 52, 109, 44, 101, 35, 92, 24, 81, 13, 70, 18, 75, 30, 87, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 20, 77, 9, 66, 17, 74, 29, 86, 39, 96, 48, 105, 43, 100, 51, 108, 55, 112, 46, 103, 37, 94, 42, 99, 34, 91, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 157, 214, 167, 224, 166, 223, 156, 213, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 155, 212, 165, 222, 168, 225, 158, 215, 148, 205, 136, 193, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 154, 211, 164, 221, 169, 226, 159, 216, 149, 206, 137, 194, 125, 182, 135, 192, 142, 199, 128, 185, 141, 198, 153, 210, 163, 220, 170, 227, 160, 217, 150, 207, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 140, 197, 152, 209, 162, 219, 171, 228, 161, 218, 151, 208, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 140)(20, 142)(21, 144)(22, 146)(23, 148)(24, 149)(25, 150)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 152)(34, 156)(35, 158)(36, 159)(37, 160)(38, 141)(39, 143)(40, 145)(41, 147)(42, 151)(43, 162)(44, 166)(45, 168)(46, 169)(47, 170)(48, 153)(49, 154)(50, 155)(51, 157)(52, 161)(53, 171)(54, 167)(55, 165)(56, 164)(57, 163)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1279
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1247 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, Y2^-2 * Y1^-1 * Y2^-1 * Y1^-2 * Y3 * Y1^-1, Y3^3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1, Y2^-9 * Y1^4, Y1^-19, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y3^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 25, 82, 32, 89, 40, 97, 49, 106, 53, 110, 57, 114, 56, 113, 45, 102, 34, 91, 19, 76, 31, 88, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 24, 81, 13, 70, 18, 75, 30, 87, 39, 96, 48, 105, 47, 104, 52, 109, 55, 112, 44, 101, 33, 90, 41, 98, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 38, 95, 37, 94, 42, 99, 50, 107, 54, 111, 43, 100, 51, 108, 46, 103, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 157, 214, 167, 224, 162, 219, 152, 209, 140, 197, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 158, 215, 168, 225, 163, 220, 153, 210, 142, 199, 128, 185, 141, 198, 137, 194, 125, 182, 135, 192, 149, 206, 159, 216, 169, 226, 164, 221, 154, 211, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 136, 193, 150, 207, 160, 217, 170, 227, 166, 223, 156, 213, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 155, 212, 165, 222, 171, 228, 161, 218, 151, 208, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 145)(23, 143)(24, 141)(25, 140)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 158)(34, 159)(35, 160)(36, 155)(37, 152)(38, 142)(39, 144)(40, 146)(41, 147)(42, 151)(43, 168)(44, 169)(45, 170)(46, 165)(47, 162)(48, 153)(49, 154)(50, 156)(51, 157)(52, 161)(53, 163)(54, 164)(55, 166)(56, 171)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1275
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1248 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y1^2 * Y2^-3, Y2 * Y3 * Y2^2 * Y3, Y1^19, Y3^11 * Y1^-8, Y1^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 20, 77, 26, 83, 32, 89, 38, 95, 44, 101, 50, 107, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 21, 78, 27, 84, 33, 90, 39, 96, 45, 102, 51, 108, 56, 113, 55, 112, 49, 106, 43, 100, 37, 94, 31, 88, 25, 82, 19, 76, 13, 70, 10, 67)(5, 62, 8, 65, 9, 66, 16, 73, 22, 79, 28, 85, 34, 91, 40, 97, 46, 103, 52, 109, 57, 114, 54, 111, 48, 105, 42, 99, 36, 93, 30, 87, 24, 81, 18, 75, 12, 69)(115, 172, 117, 174, 123, 180, 120, 177, 129, 186, 136, 193, 134, 191, 141, 198, 148, 205, 146, 203, 153, 210, 160, 217, 158, 215, 165, 222, 171, 228, 167, 224, 169, 226, 162, 219, 155, 212, 157, 214, 150, 207, 143, 200, 145, 202, 138, 195, 131, 188, 133, 190, 126, 183, 118, 175, 124, 181, 122, 179, 116, 173, 121, 178, 130, 187, 128, 185, 135, 192, 142, 199, 140, 197, 147, 204, 154, 211, 152, 209, 159, 216, 166, 223, 164, 221, 170, 227, 168, 225, 161, 218, 163, 220, 156, 213, 149, 206, 151, 208, 144, 201, 137, 194, 139, 196, 132, 189, 125, 182, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 122)(10, 127)(11, 131)(12, 132)(13, 133)(14, 120)(15, 121)(16, 123)(17, 137)(18, 138)(19, 139)(20, 128)(21, 129)(22, 130)(23, 143)(24, 144)(25, 145)(26, 134)(27, 135)(28, 136)(29, 149)(30, 150)(31, 151)(32, 140)(33, 141)(34, 142)(35, 155)(36, 156)(37, 157)(38, 146)(39, 147)(40, 148)(41, 161)(42, 162)(43, 163)(44, 152)(45, 153)(46, 154)(47, 167)(48, 168)(49, 169)(50, 158)(51, 159)(52, 160)(53, 164)(54, 171)(55, 170)(56, 165)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1278
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1249 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, Y2^3 * Y1^2, Y1^19, Y1^19, Y3 * Y2 * Y3^7 * Y2^2 * Y1^-9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 20, 77, 26, 83, 32, 89, 38, 95, 44, 101, 50, 107, 55, 112, 49, 106, 43, 100, 37, 94, 31, 88, 25, 82, 19, 76, 11, 68, 4, 61)(3, 60, 7, 64, 13, 70, 16, 73, 22, 79, 28, 85, 34, 91, 40, 97, 46, 103, 52, 109, 57, 114, 54, 111, 48, 105, 42, 99, 36, 93, 30, 87, 24, 81, 18, 75, 10, 67)(5, 62, 8, 65, 15, 72, 21, 78, 27, 84, 33, 90, 39, 96, 45, 102, 51, 108, 56, 113, 53, 110, 47, 104, 41, 98, 35, 92, 29, 86, 23, 80, 17, 74, 9, 66, 12, 69)(115, 172, 117, 174, 123, 180, 125, 182, 132, 189, 137, 194, 139, 196, 144, 201, 149, 206, 151, 208, 156, 213, 161, 218, 163, 220, 168, 225, 170, 227, 164, 221, 166, 223, 159, 216, 152, 209, 154, 211, 147, 204, 140, 197, 142, 199, 135, 192, 128, 185, 130, 187, 122, 179, 116, 173, 121, 178, 126, 183, 118, 175, 124, 181, 131, 188, 133, 190, 138, 195, 143, 200, 145, 202, 150, 207, 155, 212, 157, 214, 162, 219, 167, 224, 169, 226, 171, 228, 165, 222, 158, 215, 160, 217, 153, 210, 146, 203, 148, 205, 141, 198, 134, 191, 136, 193, 129, 186, 120, 177, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 131)(10, 132)(11, 133)(12, 123)(13, 121)(14, 120)(15, 122)(16, 127)(17, 137)(18, 138)(19, 139)(20, 128)(21, 129)(22, 130)(23, 143)(24, 144)(25, 145)(26, 134)(27, 135)(28, 136)(29, 149)(30, 150)(31, 151)(32, 140)(33, 141)(34, 142)(35, 155)(36, 156)(37, 157)(38, 146)(39, 147)(40, 148)(41, 161)(42, 162)(43, 163)(44, 152)(45, 153)(46, 154)(47, 167)(48, 168)(49, 169)(50, 158)(51, 159)(52, 160)(53, 170)(54, 171)(55, 164)(56, 165)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1282
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1250 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y1 * Y3, Y2^-1 * Y1^-1 * Y2 * Y3^-1, (R * Y2)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y1 * Y2^-1 * Y3^-5 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^4, Y2^-1 * Y3 * Y2^-8, Y3^-3 * Y1 * Y2 * Y1^-1 * Y2^3 * Y1^-1 * Y2^3 * Y1^-1 * Y2^2, Y2^-1 * Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 34, 91, 19, 76, 31, 88, 44, 101, 53, 110, 57, 114, 51, 108, 40, 97, 25, 82, 32, 89, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 42, 99, 48, 105, 33, 90, 45, 102, 54, 111, 56, 113, 50, 107, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 43, 100, 52, 109, 55, 112, 47, 104, 41, 98, 46, 103, 49, 106, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 161, 218, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 162, 219, 169, 226, 165, 222, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 140, 197, 156, 213, 166, 223, 171, 228, 164, 221, 152, 209, 136, 193, 150, 207, 142, 199, 128, 185, 141, 198, 157, 214, 167, 224, 170, 227, 163, 220, 151, 208, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 158, 215, 168, 225, 160, 217, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 159, 216, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 162)(34, 140)(35, 142)(36, 144)(37, 146)(38, 163)(39, 164)(40, 165)(41, 161)(42, 141)(43, 143)(44, 145)(45, 147)(46, 155)(47, 169)(48, 156)(49, 160)(50, 170)(51, 171)(52, 157)(53, 158)(54, 159)(55, 166)(56, 168)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1283
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1251 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y3, (R * Y1)^2, Y1 * Y2 * Y3 * Y2^-1, Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^-2, Y2 * Y1^4 * Y3^-1 * Y2^2 * Y3^-1, Y2^-8 * Y3^-1 * Y2^-1, Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y1 * Y2^2 * Y1 * Y2, Y2^-2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 40, 97, 25, 82, 32, 89, 44, 101, 53, 110, 56, 113, 48, 105, 34, 91, 19, 76, 31, 88, 37, 94, 22, 79, 11, 68, 4, 61)(3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 43, 100, 52, 109, 55, 112, 47, 104, 33, 90, 45, 102, 50, 107, 36, 93, 21, 78, 10, 67)(5, 62, 8, 65, 16, 73, 28, 85, 42, 99, 51, 108, 41, 98, 46, 103, 54, 111, 57, 114, 49, 106, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 38, 95, 23, 80, 12, 69)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 160, 217, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 159, 216, 168, 225, 158, 215, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 151, 208, 164, 221, 171, 228, 167, 224, 157, 214, 142, 199, 128, 185, 141, 198, 152, 209, 136, 193, 150, 207, 163, 220, 170, 227, 166, 223, 156, 213, 140, 197, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 162, 219, 169, 226, 165, 222, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 161, 218, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 118)(2, 115)(3, 124)(4, 125)(5, 126)(6, 116)(7, 117)(8, 119)(9, 134)(10, 135)(11, 136)(12, 137)(13, 138)(14, 120)(15, 121)(16, 122)(17, 123)(18, 127)(19, 148)(20, 149)(21, 150)(22, 151)(23, 152)(24, 153)(25, 154)(26, 128)(27, 129)(28, 130)(29, 131)(30, 132)(31, 133)(32, 139)(33, 161)(34, 162)(35, 163)(36, 164)(37, 145)(38, 143)(39, 141)(40, 140)(41, 165)(42, 142)(43, 144)(44, 146)(45, 147)(46, 155)(47, 169)(48, 170)(49, 171)(50, 159)(51, 156)(52, 157)(53, 158)(54, 160)(55, 166)(56, 167)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1268
Graph:: bipartite
	v = 4 e = 114 f = 58
	degree seq :: [ 38^3, 114 ]

E27.1252 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^-1 * Y2^2, (R * Y3)^2, (R * Y1)^2, Y1^26 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 10, 67, 14, 71, 18, 75, 22, 79, 26, 83, 30, 87, 34, 91, 38, 95, 42, 99, 46, 103, 50, 107, 54, 111, 57, 114, 53, 110, 49, 106, 45, 102, 41, 98, 37, 94, 33, 90, 29, 86, 25, 82, 21, 78, 17, 74, 13, 70, 9, 66, 5, 62, 3, 60, 7, 64, 11, 68, 15, 72, 19, 76, 23, 80, 27, 84, 31, 88, 35, 92, 39, 96, 43, 100, 47, 104, 51, 108, 55, 112, 56, 113, 52, 109, 48, 105, 44, 101, 40, 97, 36, 93, 32, 89, 28, 85, 24, 81, 20, 77, 16, 73, 12, 69, 8, 65, 4, 61)(115, 172, 117, 174, 116, 173, 121, 178, 120, 177, 125, 182, 124, 181, 129, 186, 128, 185, 133, 190, 132, 189, 137, 194, 136, 193, 141, 198, 140, 197, 145, 202, 144, 201, 149, 206, 148, 205, 153, 210, 152, 209, 157, 214, 156, 213, 161, 218, 160, 217, 165, 222, 164, 221, 169, 226, 168, 225, 170, 227, 171, 228, 166, 223, 167, 224, 162, 219, 163, 220, 158, 215, 159, 216, 154, 211, 155, 212, 150, 207, 151, 208, 146, 203, 147, 204, 142, 199, 143, 200, 138, 195, 139, 196, 134, 191, 135, 192, 130, 187, 131, 188, 126, 183, 127, 184, 122, 179, 123, 180, 118, 175, 119, 176)
	L = (1, 117)(2, 121)(3, 116)(4, 119)(5, 115)(6, 125)(7, 120)(8, 123)(9, 118)(10, 129)(11, 124)(12, 127)(13, 122)(14, 133)(15, 128)(16, 131)(17, 126)(18, 137)(19, 132)(20, 135)(21, 130)(22, 141)(23, 136)(24, 139)(25, 134)(26, 145)(27, 140)(28, 143)(29, 138)(30, 149)(31, 144)(32, 147)(33, 142)(34, 153)(35, 148)(36, 151)(37, 146)(38, 157)(39, 152)(40, 155)(41, 150)(42, 161)(43, 156)(44, 159)(45, 154)(46, 165)(47, 160)(48, 163)(49, 158)(50, 169)(51, 164)(52, 167)(53, 162)(54, 170)(55, 168)(56, 171)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1265
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1253 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y2, Y1^-1), Y2^4 * Y1, Y1^-14 * Y2, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 22, 79, 30, 87, 38, 95, 46, 103, 51, 108, 43, 100, 35, 92, 27, 84, 19, 76, 10, 67, 3, 60, 7, 64, 15, 72, 23, 80, 31, 88, 39, 96, 47, 104, 54, 111, 56, 113, 50, 107, 42, 99, 34, 91, 26, 83, 18, 75, 9, 66, 13, 70, 17, 74, 25, 82, 33, 90, 41, 98, 49, 106, 55, 112, 57, 114, 53, 110, 45, 102, 37, 94, 29, 86, 21, 78, 12, 69, 5, 62, 8, 65, 16, 73, 24, 81, 32, 89, 40, 97, 48, 105, 52, 109, 44, 101, 36, 93, 28, 85, 20, 77, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 126, 183, 118, 175, 124, 181, 132, 189, 135, 192, 125, 182, 133, 190, 140, 197, 143, 200, 134, 191, 141, 198, 148, 205, 151, 208, 142, 199, 149, 206, 156, 213, 159, 216, 150, 207, 157, 214, 164, 221, 167, 224, 158, 215, 165, 222, 170, 227, 171, 228, 166, 223, 160, 217, 168, 225, 169, 226, 162, 219, 152, 209, 161, 218, 163, 220, 154, 211, 144, 201, 153, 210, 155, 212, 146, 203, 136, 193, 145, 202, 147, 204, 138, 195, 128, 185, 137, 194, 139, 196, 130, 187, 120, 177, 129, 186, 131, 188, 122, 179, 116, 173, 121, 178, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 127)(8, 116)(9, 126)(10, 132)(11, 133)(12, 118)(13, 119)(14, 137)(15, 131)(16, 120)(17, 122)(18, 135)(19, 140)(20, 141)(21, 125)(22, 145)(23, 139)(24, 128)(25, 130)(26, 143)(27, 148)(28, 149)(29, 134)(30, 153)(31, 147)(32, 136)(33, 138)(34, 151)(35, 156)(36, 157)(37, 142)(38, 161)(39, 155)(40, 144)(41, 146)(42, 159)(43, 164)(44, 165)(45, 150)(46, 168)(47, 163)(48, 152)(49, 154)(50, 167)(51, 170)(52, 160)(53, 158)(54, 169)(55, 162)(56, 171)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1264
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1254 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^2 * Y1 * Y2^-2, Y2^4 * Y1^-1 * Y2, Y1^4 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-2 * Y2^-2, Y1 * Y2 * Y1^10 * Y2, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 24, 81, 34, 91, 44, 101, 53, 110, 43, 100, 33, 90, 23, 80, 13, 70, 18, 75, 28, 85, 38, 95, 48, 105, 55, 112, 57, 114, 50, 107, 40, 97, 30, 87, 20, 77, 10, 67, 3, 60, 7, 64, 15, 72, 25, 82, 35, 92, 45, 102, 52, 109, 42, 99, 32, 89, 22, 79, 12, 69, 5, 62, 8, 65, 16, 73, 26, 83, 36, 93, 46, 103, 54, 111, 56, 113, 49, 106, 39, 96, 29, 86, 19, 76, 9, 66, 17, 74, 27, 84, 37, 94, 47, 104, 51, 108, 41, 98, 31, 88, 21, 78, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 142, 199, 130, 187, 120, 177, 129, 186, 141, 198, 152, 209, 140, 197, 128, 185, 139, 196, 151, 208, 162, 219, 150, 207, 138, 195, 149, 206, 161, 218, 169, 226, 160, 217, 148, 205, 159, 216, 165, 222, 171, 228, 168, 225, 158, 215, 166, 223, 155, 212, 164, 221, 170, 227, 167, 224, 156, 213, 145, 202, 154, 211, 163, 220, 157, 214, 146, 203, 135, 192, 144, 201, 153, 210, 147, 204, 136, 193, 125, 182, 134, 191, 143, 200, 137, 194, 126, 183, 118, 175, 124, 181, 133, 190, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 132)(10, 133)(11, 134)(12, 118)(13, 119)(14, 139)(15, 141)(16, 120)(17, 142)(18, 122)(19, 127)(20, 143)(21, 144)(22, 125)(23, 126)(24, 149)(25, 151)(26, 128)(27, 152)(28, 130)(29, 137)(30, 153)(31, 154)(32, 135)(33, 136)(34, 159)(35, 161)(36, 138)(37, 162)(38, 140)(39, 147)(40, 163)(41, 164)(42, 145)(43, 146)(44, 166)(45, 165)(46, 148)(47, 169)(48, 150)(49, 157)(50, 170)(51, 171)(52, 155)(53, 156)(54, 158)(55, 160)(56, 167)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1262
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1255 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y1^-1 * Y2^-3 * Y1 * Y2^3, Y2^-7 * Y1^-1, Y1^2 * Y2^-1 * Y1^6, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 40, 97, 47, 104, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 50, 107, 54, 111, 46, 103, 34, 91, 19, 76, 31, 88, 43, 100, 51, 108, 56, 113, 57, 114, 53, 110, 45, 102, 33, 90, 25, 82, 32, 89, 44, 101, 52, 109, 55, 112, 49, 106, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 42, 99, 48, 105, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 159, 216, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 160, 217, 167, 224, 163, 220, 152, 209, 136, 193, 150, 207, 161, 218, 168, 225, 171, 228, 169, 226, 162, 219, 151, 208, 140, 197, 154, 211, 164, 221, 170, 227, 166, 223, 156, 213, 142, 199, 128, 185, 141, 198, 155, 212, 165, 222, 158, 215, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 157, 214, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 139, 196, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 154)(27, 155)(28, 128)(29, 157)(30, 130)(31, 139)(32, 132)(33, 138)(34, 159)(35, 160)(36, 161)(37, 140)(38, 136)(39, 137)(40, 164)(41, 165)(42, 142)(43, 146)(44, 144)(45, 153)(46, 167)(47, 168)(48, 151)(49, 152)(50, 170)(51, 158)(52, 156)(53, 163)(54, 171)(55, 162)(56, 166)(57, 169)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1261
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1256 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y1^5 * Y2 * Y1 * Y2^2, Y2 * Y1^-3 * Y2^-4 * Y1^-3, Y2 * Y1 * Y2^9, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^3 * Y1^-2 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 40, 97, 25, 82, 32, 89, 44, 101, 55, 112, 48, 105, 33, 90, 45, 102, 51, 108, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 43, 100, 54, 111, 47, 104, 53, 110, 57, 114, 50, 107, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 42, 99, 52, 109, 41, 98, 46, 103, 56, 113, 49, 106, 34, 91, 19, 76, 31, 88, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 161, 218, 166, 223, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 162, 219, 168, 225, 156, 213, 140, 197, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 163, 220, 169, 226, 157, 214, 142, 199, 128, 185, 141, 198, 152, 209, 136, 193, 150, 207, 164, 221, 170, 227, 158, 215, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 151, 208, 165, 222, 171, 228, 160, 217, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 159, 216, 167, 224, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 153)(27, 152)(28, 128)(29, 151)(30, 130)(31, 159)(32, 132)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 142)(44, 144)(45, 167)(46, 146)(47, 166)(48, 168)(49, 169)(50, 170)(51, 171)(52, 154)(53, 155)(54, 156)(55, 157)(56, 158)(57, 160)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1260
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1257 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, Y1 * Y2 * Y1^4 * Y2, Y2^-5 * Y1 * Y2^-6, Y1 * Y2^-1 * Y1 * Y2^-3 * Y1^2 * Y2^6 * Y1, Y1 * Y2^-1 * Y1^3 * Y2^-2 * Y1^3 * Y2^-2 * Y1^3 * Y2^-2 * Y1^3 * Y2^-2 * Y1^-3 * Y2^2 * Y1, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 24, 81, 13, 70, 18, 75, 27, 84, 36, 93, 44, 101, 35, 92, 39, 96, 47, 104, 54, 111, 56, 113, 50, 107, 40, 97, 48, 105, 52, 109, 42, 99, 31, 88, 19, 76, 28, 85, 33, 90, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 26, 83, 34, 91, 25, 82, 29, 86, 37, 94, 46, 103, 53, 110, 45, 102, 49, 106, 55, 112, 57, 114, 51, 108, 41, 98, 30, 87, 38, 95, 43, 100, 32, 89, 20, 77, 9, 66, 17, 74, 22, 79, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 133, 190, 144, 201, 154, 211, 163, 220, 153, 210, 143, 200, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 142, 199, 152, 209, 162, 219, 169, 226, 161, 218, 151, 208, 141, 198, 130, 187, 120, 177, 129, 186, 136, 193, 147, 204, 157, 214, 166, 223, 171, 228, 168, 225, 160, 217, 150, 207, 140, 197, 128, 185, 137, 194, 125, 182, 135, 192, 146, 203, 156, 213, 165, 222, 170, 227, 167, 224, 158, 215, 148, 205, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 145, 202, 155, 212, 164, 221, 159, 216, 149, 206, 139, 196, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 137)(15, 136)(16, 120)(17, 142)(18, 122)(19, 144)(20, 145)(21, 146)(22, 147)(23, 125)(24, 126)(25, 127)(26, 128)(27, 130)(28, 152)(29, 132)(30, 154)(31, 155)(32, 156)(33, 157)(34, 138)(35, 139)(36, 140)(37, 141)(38, 162)(39, 143)(40, 163)(41, 164)(42, 165)(43, 166)(44, 148)(45, 149)(46, 150)(47, 151)(48, 169)(49, 153)(50, 159)(51, 170)(52, 171)(53, 158)(54, 160)(55, 161)(56, 167)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1266
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1258 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y1, Y2), (R * Y1)^2, (R * Y3)^2, Y2^4 * Y1^-1 * Y2 * Y1^-3, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-8 * Y2^-1, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 52, 109, 50, 107, 40, 97, 25, 82, 32, 89, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 44, 101, 54, 111, 48, 105, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 33, 90, 46, 103, 56, 113, 57, 114, 51, 108, 41, 98, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 53, 110, 49, 106, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 34, 91, 19, 76, 31, 88, 45, 102, 55, 112, 47, 104, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 140, 197, 157, 214, 168, 225, 161, 218, 165, 222, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 142, 199, 128, 185, 141, 198, 158, 215, 169, 226, 171, 228, 164, 221, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 159, 216, 170, 227, 166, 223, 163, 220, 152, 209, 136, 193, 150, 207, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 160, 217, 156, 213, 167, 224, 162, 219, 151, 208, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 158)(28, 128)(29, 159)(30, 130)(31, 160)(32, 132)(33, 140)(34, 142)(35, 144)(36, 146)(37, 155)(38, 136)(39, 137)(40, 138)(41, 139)(42, 167)(43, 168)(44, 169)(45, 170)(46, 156)(47, 165)(48, 151)(49, 152)(50, 153)(51, 154)(52, 163)(53, 162)(54, 161)(55, 171)(56, 166)(57, 164)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1267
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1259 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), Y2 * Y1^-1 * Y2 * Y1^-6, Y1^2 * Y2 * Y1 * Y2^6 * Y1, Y2^4 * Y1^-1 * Y2^5 * Y1^-2, Y2 * Y1^-3 * Y2^-2 * Y1^-2 * Y2 * Y1^-2 * Y2^2, (Y3^-1 * Y1^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 43, 100, 55, 112, 57, 114, 49, 106, 33, 90, 46, 103, 53, 110, 40, 97, 25, 82, 32, 89, 45, 102, 51, 108, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 42, 99, 50, 107, 34, 91, 19, 76, 31, 88, 44, 101, 54, 111, 41, 98, 47, 104, 56, 113, 48, 105, 52, 109, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172, 117, 174, 123, 180, 133, 190, 147, 204, 162, 219, 165, 222, 151, 208, 142, 199, 128, 185, 141, 198, 157, 214, 168, 225, 154, 211, 138, 195, 126, 183, 118, 175, 124, 181, 134, 191, 148, 205, 163, 220, 170, 227, 159, 216, 144, 201, 130, 187, 120, 177, 129, 186, 143, 200, 158, 215, 167, 224, 153, 210, 137, 194, 125, 182, 135, 192, 149, 206, 164, 221, 171, 228, 161, 218, 146, 203, 132, 189, 122, 179, 116, 173, 121, 178, 131, 188, 145, 202, 160, 217, 166, 223, 152, 209, 136, 193, 150, 207, 140, 197, 156, 213, 169, 226, 155, 212, 139, 196, 127, 184, 119, 176)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 156)(27, 157)(28, 128)(29, 158)(30, 130)(31, 160)(32, 132)(33, 162)(34, 163)(35, 164)(36, 140)(37, 142)(38, 136)(39, 137)(40, 138)(41, 139)(42, 169)(43, 168)(44, 167)(45, 144)(46, 166)(47, 146)(48, 165)(49, 170)(50, 171)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 159)(57, 161)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1263
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.1260 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-3 * Y2^-3, Y2^-1 * Y3^18, Y2^7 * Y3^-1 * Y2^2 * Y3^-8 * Y2, Y2^19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 136, 193, 142, 199, 148, 205, 154, 211, 160, 217, 166, 223, 169, 226, 165, 222, 158, 215, 151, 208, 147, 204, 140, 197, 133, 190, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 127, 184, 132, 189, 138, 195, 144, 201, 150, 207, 156, 213, 162, 219, 168, 225, 171, 228, 164, 221, 157, 214, 153, 210, 146, 203, 139, 196, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 137, 194, 143, 200, 149, 206, 155, 212, 161, 218, 167, 224, 170, 227, 163, 220, 159, 216, 152, 209, 145, 202, 141, 198, 134, 191, 123, 180, 131, 188, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 127)(15, 126)(16, 120)(17, 125)(18, 122)(19, 139)(20, 140)(21, 141)(22, 132)(23, 128)(24, 130)(25, 145)(26, 146)(27, 147)(28, 138)(29, 136)(30, 137)(31, 151)(32, 152)(33, 153)(34, 144)(35, 142)(36, 143)(37, 157)(38, 158)(39, 159)(40, 150)(41, 148)(42, 149)(43, 163)(44, 164)(45, 165)(46, 156)(47, 154)(48, 155)(49, 169)(50, 170)(51, 171)(52, 162)(53, 160)(54, 161)(55, 168)(56, 166)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1256
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1261 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^5 * Y3, Y3^8 * Y2^-1 * Y3, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2^-1 * Y3^3 * Y2, Y2^2 * Y3^-1 * Y2 * Y3^-2 * Y2^3 * Y3^-3 * Y2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-3 * Y2^2, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 140, 197, 154, 211, 139, 196, 146, 203, 158, 215, 167, 224, 170, 227, 162, 219, 148, 205, 133, 190, 145, 202, 151, 208, 136, 193, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 141, 198, 153, 210, 138, 195, 127, 184, 132, 189, 144, 201, 157, 214, 166, 223, 169, 226, 161, 218, 147, 204, 159, 216, 164, 221, 150, 207, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 142, 199, 156, 213, 165, 222, 155, 212, 160, 217, 168, 225, 171, 228, 163, 220, 149, 206, 134, 191, 123, 180, 131, 188, 143, 200, 152, 209, 137, 194, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 153)(27, 152)(28, 128)(29, 151)(30, 130)(31, 159)(32, 132)(33, 160)(34, 161)(35, 162)(36, 163)(37, 164)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 142)(44, 144)(45, 168)(46, 146)(47, 155)(48, 169)(49, 170)(50, 171)(51, 154)(52, 156)(53, 157)(54, 158)(55, 165)(56, 166)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1255
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1262 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y3^3 * Y2^-2 * Y3^-2 * Y2 * Y3^-1 * Y2, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-3, Y2^2 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-3 * Y2, Y2^-1 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 140, 197, 156, 213, 154, 211, 139, 196, 146, 203, 162, 219, 167, 224, 148, 205, 133, 190, 145, 202, 161, 218, 151, 208, 136, 193, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 141, 198, 157, 214, 153, 210, 138, 195, 127, 184, 132, 189, 144, 201, 160, 217, 166, 223, 147, 204, 163, 220, 171, 228, 169, 226, 150, 207, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 142, 199, 158, 215, 165, 222, 170, 227, 155, 212, 164, 221, 168, 225, 149, 206, 134, 191, 123, 180, 131, 188, 143, 200, 159, 216, 152, 209, 137, 194, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 159)(28, 128)(29, 161)(30, 130)(31, 163)(32, 132)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 136)(39, 137)(40, 138)(41, 139)(42, 153)(43, 152)(44, 140)(45, 151)(46, 142)(47, 171)(48, 144)(49, 170)(50, 146)(51, 156)(52, 158)(53, 160)(54, 162)(55, 164)(56, 154)(57, 155)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1254
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1263 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^-3 * Y2^-2 * Y3^2 * Y2 * Y3 * Y2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-5, Y2^3 * Y3^2 * Y2 * Y3 * Y2 * Y3^3, Y3^2 * Y2^12 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 140, 197, 156, 213, 148, 205, 133, 190, 145, 202, 161, 218, 169, 226, 154, 211, 139, 196, 146, 203, 162, 219, 151, 208, 136, 193, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 141, 198, 157, 214, 171, 228, 166, 223, 147, 204, 163, 220, 168, 225, 153, 210, 138, 195, 127, 184, 132, 189, 144, 201, 160, 217, 150, 207, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 142, 199, 158, 215, 149, 206, 134, 191, 123, 180, 131, 188, 143, 200, 159, 216, 170, 227, 155, 212, 164, 221, 165, 222, 167, 224, 152, 209, 137, 194, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 159)(28, 128)(29, 161)(30, 130)(31, 163)(32, 132)(33, 165)(34, 166)(35, 156)(36, 158)(37, 160)(38, 136)(39, 137)(40, 138)(41, 139)(42, 171)(43, 170)(44, 140)(45, 169)(46, 142)(47, 168)(48, 144)(49, 167)(50, 146)(51, 162)(52, 164)(53, 151)(54, 152)(55, 153)(56, 154)(57, 155)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1259
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1264 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2^-3 * Y3 * Y2^-1 * Y3^2, Y3^12 * Y2^3, Y2 * Y3 * Y2 * Y3^11 * Y2, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 133, 190, 142, 199, 149, 206, 156, 213, 159, 216, 166, 223, 170, 227, 163, 220, 160, 217, 153, 210, 146, 203, 139, 196, 136, 193, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 140, 197, 143, 200, 150, 207, 157, 214, 164, 221, 167, 224, 169, 226, 162, 219, 155, 212, 152, 209, 145, 202, 138, 195, 127, 184, 132, 189, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 134, 191, 123, 180, 131, 188, 141, 198, 148, 205, 151, 208, 158, 215, 165, 222, 171, 228, 168, 225, 161, 218, 154, 211, 147, 204, 144, 201, 137, 194, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 140)(15, 141)(16, 120)(17, 142)(18, 122)(19, 143)(20, 128)(21, 130)(22, 132)(23, 125)(24, 126)(25, 127)(26, 148)(27, 149)(28, 150)(29, 151)(30, 136)(31, 137)(32, 138)(33, 139)(34, 156)(35, 157)(36, 158)(37, 159)(38, 144)(39, 145)(40, 146)(41, 147)(42, 164)(43, 165)(44, 166)(45, 167)(46, 152)(47, 153)(48, 154)(49, 155)(50, 171)(51, 170)(52, 169)(53, 168)(54, 160)(55, 161)(56, 162)(57, 163)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1253
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1265 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y2^-1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3^-3, Y2^19, Y2^19, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 134, 191, 140, 197, 146, 203, 152, 209, 158, 215, 164, 221, 167, 224, 161, 218, 155, 212, 149, 206, 143, 200, 137, 194, 131, 188, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 135, 192, 141, 198, 147, 204, 153, 210, 159, 216, 165, 222, 170, 227, 169, 226, 163, 220, 157, 214, 151, 208, 145, 202, 139, 196, 133, 190, 127, 184, 124, 181)(119, 176, 122, 179, 123, 180, 130, 187, 136, 193, 142, 199, 148, 205, 154, 211, 160, 217, 166, 223, 171, 228, 168, 225, 162, 219, 156, 213, 150, 207, 144, 201, 138, 195, 132, 189, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 130)(8, 116)(9, 120)(10, 122)(11, 127)(12, 118)(13, 119)(14, 135)(15, 136)(16, 128)(17, 133)(18, 125)(19, 126)(20, 141)(21, 142)(22, 134)(23, 139)(24, 131)(25, 132)(26, 147)(27, 148)(28, 140)(29, 145)(30, 137)(31, 138)(32, 153)(33, 154)(34, 146)(35, 151)(36, 143)(37, 144)(38, 159)(39, 160)(40, 152)(41, 157)(42, 149)(43, 150)(44, 165)(45, 166)(46, 158)(47, 163)(48, 155)(49, 156)(50, 170)(51, 171)(52, 164)(53, 169)(54, 161)(55, 162)(56, 168)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1252
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1266 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^3 * Y2^2, Y2^19, Y2^19, Y2^-8 * Y3^2 * Y2^-9 * Y3, (Y2^-1 * Y3)^57, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 134, 191, 140, 197, 146, 203, 152, 209, 158, 215, 164, 221, 169, 226, 163, 220, 157, 214, 151, 208, 145, 202, 139, 196, 133, 190, 125, 182, 118, 175)(117, 174, 121, 178, 127, 184, 130, 187, 136, 193, 142, 199, 148, 205, 154, 211, 160, 217, 166, 223, 171, 228, 168, 225, 162, 219, 156, 213, 150, 207, 144, 201, 138, 195, 132, 189, 124, 181)(119, 176, 122, 179, 129, 186, 135, 192, 141, 198, 147, 204, 153, 210, 159, 216, 165, 222, 170, 227, 167, 224, 161, 218, 155, 212, 149, 206, 143, 200, 137, 194, 131, 188, 123, 180, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 127)(7, 126)(8, 116)(9, 125)(10, 131)(11, 132)(12, 118)(13, 119)(14, 130)(15, 120)(16, 122)(17, 133)(18, 137)(19, 138)(20, 136)(21, 128)(22, 129)(23, 139)(24, 143)(25, 144)(26, 142)(27, 134)(28, 135)(29, 145)(30, 149)(31, 150)(32, 148)(33, 140)(34, 141)(35, 151)(36, 155)(37, 156)(38, 154)(39, 146)(40, 147)(41, 157)(42, 161)(43, 162)(44, 160)(45, 152)(46, 153)(47, 163)(48, 167)(49, 168)(50, 166)(51, 158)(52, 159)(53, 169)(54, 170)(55, 171)(56, 164)(57, 165)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1257
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1267 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), Y3 * Y2 * Y3 * Y2^4 * Y3, Y2^2 * Y3^-1 * Y2 * Y3^-8 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58)(2, 59)(3, 60)(4, 61)(5, 62)(6, 63)(7, 64)(8, 65)(9, 66)(10, 67)(11, 68)(12, 69)(13, 70)(14, 71)(15, 72)(16, 73)(17, 74)(18, 75)(19, 76)(20, 77)(21, 78)(22, 79)(23, 80)(24, 81)(25, 82)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 88)(32, 89)(33, 90)(34, 91)(35, 92)(36, 93)(37, 94)(38, 95)(39, 96)(40, 97)(41, 98)(42, 99)(43, 100)(44, 101)(45, 102)(46, 103)(47, 104)(48, 105)(49, 106)(50, 107)(51, 108)(52, 109)(53, 110)(54, 111)(55, 112)(56, 113)(57, 114)(115, 172, 116, 173, 120, 177, 128, 185, 140, 197, 139, 196, 146, 203, 154, 211, 163, 220, 167, 224, 171, 228, 170, 227, 159, 216, 148, 205, 133, 190, 145, 202, 136, 193, 125, 182, 118, 175)(117, 174, 121, 178, 129, 186, 141, 198, 138, 195, 127, 184, 132, 189, 144, 201, 153, 210, 162, 219, 161, 218, 166, 223, 169, 226, 158, 215, 147, 204, 155, 212, 150, 207, 135, 192, 124, 181)(119, 176, 122, 179, 130, 187, 142, 199, 152, 209, 151, 208, 156, 213, 164, 221, 168, 225, 157, 214, 165, 222, 160, 217, 149, 206, 134, 191, 123, 180, 131, 188, 143, 200, 137, 194, 126, 183)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 138)(27, 137)(28, 128)(29, 136)(30, 130)(31, 155)(32, 132)(33, 157)(34, 158)(35, 159)(36, 160)(37, 139)(38, 140)(39, 142)(40, 144)(41, 165)(42, 146)(43, 167)(44, 168)(45, 169)(46, 170)(47, 151)(48, 152)(49, 153)(50, 154)(51, 171)(52, 156)(53, 162)(54, 163)(55, 164)(56, 166)(57, 161)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.1258
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.1268 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y1^9 * Y3 * Y1^9, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 22, 79, 28, 85, 34, 91, 40, 97, 46, 103, 52, 109, 56, 113, 50, 107, 44, 101, 38, 95, 32, 89, 26, 83, 20, 77, 12, 69, 5, 62, 8, 65, 16, 73, 9, 66, 17, 74, 24, 81, 30, 87, 36, 93, 42, 99, 48, 105, 54, 111, 57, 114, 51, 108, 45, 102, 39, 96, 33, 90, 27, 84, 21, 78, 13, 70, 18, 75, 10, 67, 3, 60, 7, 64, 15, 72, 23, 80, 29, 86, 35, 92, 41, 98, 47, 104, 53, 110, 55, 112, 49, 106, 43, 100, 37, 94, 31, 88, 25, 82, 19, 76, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 128)(10, 130)(11, 132)(12, 118)(13, 119)(14, 137)(15, 138)(16, 120)(17, 136)(18, 122)(19, 127)(20, 125)(21, 126)(22, 143)(23, 144)(24, 142)(25, 135)(26, 133)(27, 134)(28, 149)(29, 150)(30, 148)(31, 141)(32, 139)(33, 140)(34, 155)(35, 156)(36, 154)(37, 147)(38, 145)(39, 146)(40, 161)(41, 162)(42, 160)(43, 153)(44, 151)(45, 152)(46, 167)(47, 168)(48, 166)(49, 159)(50, 157)(51, 158)(52, 169)(53, 171)(54, 170)(55, 165)(56, 163)(57, 164)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1251
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1269 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3^5 * Y1^-1, Y1^-2 * Y3^-1 * Y1^-7, Y1^2 * Y3 * Y1 * Y3^3 * Y1^3 * Y3^3, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 52, 109, 49, 106, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 33, 90, 47, 104, 55, 112, 56, 113, 50, 107, 40, 97, 25, 82, 32, 89, 34, 91, 19, 76, 31, 88, 46, 103, 54, 111, 57, 114, 51, 108, 41, 98, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 53, 110, 48, 105, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 159)(28, 128)(29, 160)(30, 130)(31, 161)(32, 132)(33, 142)(34, 144)(35, 146)(36, 155)(37, 162)(38, 136)(39, 137)(40, 138)(41, 139)(42, 151)(43, 167)(44, 140)(45, 168)(46, 169)(47, 158)(48, 165)(49, 152)(50, 153)(51, 154)(52, 156)(53, 171)(54, 170)(55, 166)(56, 163)(57, 164)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1245
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1270 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^2 * Y3 * Y1 * Y3^5, Y1^-3 * Y3 * Y1^-6, Y1 * Y3^-1 * Y1 * Y3^-2 * Y1^3 * Y3^-4 * Y1, (Y3 * Y2^-1)^19, Y3^-2 * Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 52, 109, 50, 107, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 47, 104, 55, 112, 57, 114, 49, 106, 34, 91, 19, 76, 31, 88, 40, 97, 25, 82, 32, 89, 46, 103, 54, 111, 56, 113, 48, 105, 33, 90, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 45, 102, 53, 110, 51, 108, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 155)(28, 128)(29, 154)(30, 130)(31, 153)(32, 132)(33, 152)(34, 162)(35, 163)(36, 164)(37, 156)(38, 136)(39, 137)(40, 138)(41, 139)(42, 166)(43, 161)(44, 140)(45, 142)(46, 144)(47, 146)(48, 165)(49, 170)(50, 171)(51, 151)(52, 169)(53, 158)(54, 159)(55, 160)(56, 167)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1235
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1271 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-7 * Y1^-3, Y1^3 * Y3 * Y1^2 * Y3 * Y1^4, Y1^3 * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-2 * Y1, Y1^-1 * Y3^2 * Y1^2 * Y3^2 * Y1^2 * Y3^3, Y1^-1 * Y3^2 * Y1^2 * Y3^2 * Y1^2 * Y3^3, (Y3 * Y2^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 51, 108, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 46, 103, 53, 110, 34, 91, 19, 76, 31, 88, 47, 104, 41, 98, 50, 107, 55, 112, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 57, 114, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 52, 109, 33, 90, 49, 106, 40, 97, 25, 82, 32, 89, 48, 105, 54, 111, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 56, 113, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 159)(28, 128)(29, 161)(30, 130)(31, 163)(32, 132)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 136)(39, 137)(40, 138)(41, 139)(42, 171)(43, 170)(44, 140)(45, 155)(46, 142)(47, 154)(48, 144)(49, 153)(50, 146)(51, 152)(52, 156)(53, 158)(54, 160)(55, 162)(56, 164)(57, 151)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1240
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1272 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^7, Y1^9 * Y3^-2, (Y3 * Y2^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 42, 99, 51, 108, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 45, 102, 56, 113, 40, 97, 25, 82, 32, 89, 48, 105, 33, 90, 49, 106, 54, 111, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 44, 101, 52, 109, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 43, 100, 57, 114, 41, 98, 50, 107, 34, 91, 19, 76, 31, 88, 47, 104, 55, 112, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 46, 103, 53, 110, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 157)(27, 159)(28, 128)(29, 161)(30, 130)(31, 163)(32, 132)(33, 160)(34, 162)(35, 164)(36, 165)(37, 166)(38, 136)(39, 137)(40, 138)(41, 139)(42, 171)(43, 170)(44, 140)(45, 169)(46, 142)(47, 168)(48, 144)(49, 167)(50, 146)(51, 155)(52, 156)(53, 158)(54, 151)(55, 152)(56, 153)(57, 154)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1244
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1273 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3^4, Y3^3 * Y1^-12, Y1^-12 * Y3^3, (Y3 * Y2^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 34, 91, 42, 99, 50, 107, 54, 111, 46, 103, 38, 95, 30, 87, 19, 76, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 27, 84, 35, 92, 43, 100, 51, 108, 55, 112, 47, 104, 39, 96, 31, 88, 20, 77, 9, 66, 17, 74, 24, 81, 13, 70, 18, 75, 28, 85, 36, 93, 44, 101, 52, 109, 56, 113, 48, 105, 40, 97, 32, 89, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 25, 82, 29, 86, 37, 94, 45, 102, 53, 110, 57, 114, 49, 106, 41, 98, 33, 90, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 139)(15, 138)(16, 120)(17, 137)(18, 122)(19, 136)(20, 144)(21, 145)(22, 146)(23, 125)(24, 126)(25, 127)(26, 143)(27, 128)(28, 130)(29, 132)(30, 147)(31, 152)(32, 153)(33, 154)(34, 151)(35, 140)(36, 141)(37, 142)(38, 155)(39, 160)(40, 161)(41, 162)(42, 159)(43, 148)(44, 149)(45, 150)(46, 163)(47, 168)(48, 169)(49, 170)(50, 167)(51, 156)(52, 157)(53, 158)(54, 171)(55, 164)(56, 165)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1239
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1274 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^4, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-11, (Y3 * Y2^-1)^19, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 34, 91, 42, 99, 50, 107, 57, 114, 49, 106, 41, 98, 33, 90, 25, 82, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 35, 92, 43, 100, 51, 108, 56, 113, 48, 105, 40, 97, 32, 89, 24, 81, 13, 70, 18, 75, 20, 77, 9, 66, 17, 74, 28, 85, 36, 93, 44, 101, 52, 109, 55, 112, 47, 104, 39, 96, 31, 88, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 19, 76, 29, 86, 37, 94, 45, 102, 53, 110, 54, 111, 46, 103, 38, 95, 30, 87, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 142)(16, 120)(17, 143)(18, 122)(19, 128)(20, 130)(21, 132)(22, 139)(23, 125)(24, 126)(25, 127)(26, 149)(27, 150)(28, 151)(29, 140)(30, 147)(31, 136)(32, 137)(33, 138)(34, 157)(35, 158)(36, 159)(37, 148)(38, 155)(39, 144)(40, 145)(41, 146)(42, 165)(43, 166)(44, 167)(45, 156)(46, 163)(47, 152)(48, 153)(49, 154)(50, 170)(51, 169)(52, 168)(53, 164)(54, 171)(55, 160)(56, 161)(57, 162)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1243
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1275 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y3^-2 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^-19, Y3^38, (Y3 * Y2^-1)^19, Y3^-57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 9, 66, 15, 72, 20, 77, 22, 79, 27, 84, 32, 89, 34, 91, 39, 96, 44, 101, 46, 103, 51, 108, 56, 113, 55, 112, 53, 110, 48, 105, 43, 100, 41, 98, 36, 93, 31, 88, 29, 86, 24, 81, 19, 76, 17, 74, 12, 69, 5, 62, 8, 65, 10, 67, 3, 60, 7, 64, 14, 71, 16, 73, 21, 78, 26, 83, 28, 85, 33, 90, 38, 95, 40, 97, 45, 102, 50, 107, 52, 109, 57, 114, 54, 111, 49, 106, 47, 104, 42, 99, 37, 94, 35, 92, 30, 87, 25, 82, 23, 80, 18, 75, 13, 70, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 128)(7, 129)(8, 116)(9, 130)(10, 120)(11, 122)(12, 118)(13, 119)(14, 134)(15, 135)(16, 136)(17, 125)(18, 126)(19, 127)(20, 140)(21, 141)(22, 142)(23, 131)(24, 132)(25, 133)(26, 146)(27, 147)(28, 148)(29, 137)(30, 138)(31, 139)(32, 152)(33, 153)(34, 154)(35, 143)(36, 144)(37, 145)(38, 158)(39, 159)(40, 160)(41, 149)(42, 150)(43, 151)(44, 164)(45, 165)(46, 166)(47, 155)(48, 156)(49, 157)(50, 170)(51, 171)(52, 169)(53, 161)(54, 162)(55, 163)(56, 168)(57, 167)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1247
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1276 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y1^3 * Y3^2, (R * Y2 * Y3^-1)^2, Y3^19, Y3^19, Y3^-19, Y3^38, (Y3 * Y2^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 13, 70, 15, 72, 20, 77, 25, 82, 27, 84, 32, 89, 37, 94, 39, 96, 44, 101, 49, 106, 51, 108, 56, 113, 52, 109, 54, 111, 47, 104, 40, 97, 42, 99, 35, 92, 28, 85, 30, 87, 23, 80, 16, 73, 18, 75, 10, 67, 3, 60, 7, 64, 12, 69, 5, 62, 8, 65, 14, 71, 19, 76, 21, 78, 26, 83, 31, 88, 33, 90, 38, 95, 43, 100, 45, 102, 50, 107, 55, 112, 57, 114, 53, 110, 46, 103, 48, 105, 41, 98, 34, 91, 36, 93, 29, 86, 22, 79, 24, 81, 17, 74, 9, 66, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 126)(7, 125)(8, 116)(9, 130)(10, 131)(11, 132)(12, 118)(13, 119)(14, 120)(15, 122)(16, 136)(17, 137)(18, 138)(19, 127)(20, 128)(21, 129)(22, 142)(23, 143)(24, 144)(25, 133)(26, 134)(27, 135)(28, 148)(29, 149)(30, 150)(31, 139)(32, 140)(33, 141)(34, 154)(35, 155)(36, 156)(37, 145)(38, 146)(39, 147)(40, 160)(41, 161)(42, 162)(43, 151)(44, 152)(45, 153)(46, 166)(47, 167)(48, 168)(49, 157)(50, 158)(51, 159)(52, 169)(53, 170)(54, 171)(55, 163)(56, 164)(57, 165)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1238
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1277 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-1 * Y3 * Y1^-2 * Y3, Y1^8 * Y3^4 * Y1, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 38, 95, 48, 105, 53, 110, 43, 100, 33, 90, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 49, 106, 57, 114, 47, 104, 37, 94, 25, 82, 32, 89, 20, 77, 9, 66, 17, 74, 29, 86, 41, 98, 51, 108, 56, 113, 46, 103, 36, 93, 24, 81, 13, 70, 18, 75, 30, 87, 19, 76, 31, 88, 42, 99, 52, 109, 55, 112, 45, 102, 35, 92, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 40, 97, 50, 107, 54, 111, 44, 101, 34, 91, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 142)(20, 144)(21, 146)(22, 147)(23, 125)(24, 126)(25, 127)(26, 153)(27, 155)(28, 128)(29, 156)(30, 130)(31, 154)(32, 132)(33, 139)(34, 157)(35, 136)(36, 137)(37, 138)(38, 163)(39, 165)(40, 140)(41, 166)(42, 164)(43, 151)(44, 167)(45, 148)(46, 149)(47, 150)(48, 171)(49, 170)(50, 152)(51, 169)(52, 168)(53, 161)(54, 162)(55, 158)(56, 159)(57, 160)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1237
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1278 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^2 * Y3 * Y1 * Y3^4, Y3^3 * Y1^-1 * Y3 * Y1^-8, (Y3 * Y2^-1)^19, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 38, 95, 48, 105, 53, 110, 43, 100, 33, 90, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 40, 97, 50, 107, 54, 111, 44, 101, 34, 91, 19, 76, 31, 88, 24, 81, 13, 70, 18, 75, 30, 87, 41, 98, 51, 108, 55, 112, 45, 102, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 25, 82, 32, 89, 42, 99, 52, 109, 56, 113, 46, 103, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 49, 106, 57, 114, 47, 104, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 153)(27, 139)(28, 128)(29, 138)(30, 130)(31, 137)(32, 132)(33, 136)(34, 157)(35, 158)(36, 159)(37, 160)(38, 163)(39, 146)(40, 140)(41, 142)(42, 144)(43, 151)(44, 167)(45, 168)(46, 169)(47, 170)(48, 171)(49, 156)(50, 152)(51, 154)(52, 155)(53, 161)(54, 162)(55, 164)(56, 165)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1248
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1279 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^6, Y3^5 * Y1 * Y3^3 * Y1^2, Y3^-19, Y3^19, (Y3 * Y2^-1)^19, Y3^-2 * Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 34, 91, 19, 76, 31, 88, 44, 101, 53, 110, 55, 112, 57, 114, 50, 107, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 42, 99, 48, 105, 33, 90, 45, 102, 52, 109, 41, 98, 46, 103, 49, 106, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 43, 100, 54, 111, 56, 113, 47, 104, 51, 108, 40, 97, 25, 82, 32, 89, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 156)(27, 157)(28, 128)(29, 158)(30, 130)(31, 159)(32, 132)(33, 161)(34, 162)(35, 140)(36, 142)(37, 144)(38, 136)(39, 137)(40, 138)(41, 139)(42, 168)(43, 167)(44, 166)(45, 165)(46, 146)(47, 164)(48, 170)(49, 151)(50, 152)(51, 153)(52, 154)(53, 155)(54, 169)(55, 160)(56, 171)(57, 163)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1246
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1280 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^3 * Y1^6, Y3^-4 * Y1^2 * Y3^-4 * Y1, Y3^19, Y3^19, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 26, 83, 40, 97, 25, 82, 32, 89, 44, 101, 47, 104, 55, 112, 56, 113, 50, 107, 35, 92, 20, 77, 9, 66, 17, 74, 29, 86, 38, 95, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 28, 85, 42, 99, 52, 109, 41, 98, 46, 103, 48, 105, 33, 90, 45, 102, 51, 108, 36, 93, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 27, 84, 39, 96, 24, 81, 13, 70, 18, 75, 30, 87, 43, 100, 54, 111, 57, 114, 53, 110, 49, 106, 34, 91, 19, 76, 31, 88, 37, 94, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 141)(15, 143)(16, 120)(17, 145)(18, 122)(19, 147)(20, 148)(21, 149)(22, 150)(23, 125)(24, 126)(25, 127)(26, 153)(27, 152)(28, 128)(29, 151)(30, 130)(31, 159)(32, 132)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 136)(39, 137)(40, 138)(41, 139)(42, 140)(43, 142)(44, 144)(45, 169)(46, 146)(47, 157)(48, 158)(49, 160)(50, 167)(51, 170)(52, 154)(53, 155)(54, 156)(55, 168)(56, 171)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1236
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1281 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^-1 * Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^19, (Y3 * Y2^-1)^19, (Y3^-1 * Y1^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 3, 60, 7, 64, 12, 69, 9, 66, 13, 70, 18, 75, 15, 72, 19, 76, 24, 81, 21, 78, 25, 82, 30, 87, 27, 84, 31, 88, 36, 93, 33, 90, 37, 94, 42, 99, 39, 96, 43, 100, 48, 105, 45, 102, 49, 106, 54, 111, 51, 108, 55, 112, 57, 114, 53, 110, 56, 113, 52, 109, 47, 104, 50, 107, 46, 103, 41, 98, 44, 101, 40, 97, 35, 92, 38, 95, 34, 91, 29, 86, 32, 89, 28, 85, 23, 80, 26, 83, 22, 79, 17, 74, 20, 77, 16, 73, 11, 68, 14, 71, 10, 67, 5, 62, 8, 65, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 120)(5, 115)(6, 126)(7, 127)(8, 116)(9, 129)(10, 118)(11, 119)(12, 132)(13, 133)(14, 122)(15, 135)(16, 124)(17, 125)(18, 138)(19, 139)(20, 128)(21, 141)(22, 130)(23, 131)(24, 144)(25, 145)(26, 134)(27, 147)(28, 136)(29, 137)(30, 150)(31, 151)(32, 140)(33, 153)(34, 142)(35, 143)(36, 156)(37, 157)(38, 146)(39, 159)(40, 148)(41, 149)(42, 162)(43, 163)(44, 152)(45, 165)(46, 154)(47, 155)(48, 168)(49, 169)(50, 158)(51, 167)(52, 160)(53, 161)(54, 171)(55, 170)(56, 164)(57, 166)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1241
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1282 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^-3 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^19, (Y3 * Y2^-1)^19 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 5, 62, 8, 65, 12, 69, 11, 68, 14, 71, 18, 75, 17, 74, 20, 77, 24, 81, 23, 80, 26, 83, 30, 87, 29, 86, 32, 89, 36, 93, 35, 92, 38, 95, 42, 99, 41, 98, 44, 101, 48, 105, 47, 104, 50, 107, 54, 111, 53, 110, 56, 113, 57, 114, 51, 108, 55, 112, 52, 109, 45, 102, 49, 106, 46, 103, 39, 96, 43, 100, 40, 97, 33, 90, 37, 94, 34, 91, 27, 84, 31, 88, 28, 85, 21, 78, 25, 82, 22, 79, 15, 72, 19, 76, 16, 73, 9, 66, 13, 70, 10, 67, 3, 60, 7, 64, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 118)(7, 127)(8, 116)(9, 129)(10, 130)(11, 119)(12, 120)(13, 133)(14, 122)(15, 135)(16, 136)(17, 125)(18, 126)(19, 139)(20, 128)(21, 141)(22, 142)(23, 131)(24, 132)(25, 145)(26, 134)(27, 147)(28, 148)(29, 137)(30, 138)(31, 151)(32, 140)(33, 153)(34, 154)(35, 143)(36, 144)(37, 157)(38, 146)(39, 159)(40, 160)(41, 149)(42, 150)(43, 163)(44, 152)(45, 165)(46, 166)(47, 155)(48, 156)(49, 169)(50, 158)(51, 167)(52, 171)(53, 161)(54, 162)(55, 170)(56, 164)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1249
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1283 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^6, Y1^-1 * Y3^-2 * Y1^2 * Y3^2 * Y1^-1, Y1 * Y3^-3 * Y1^3 * Y3 * Y1 * Y3 * Y1, Y1^2 * Y3 * Y1 * Y3^8, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 26, 83, 33, 90, 20, 77, 9, 66, 17, 74, 27, 84, 38, 95, 45, 102, 32, 89, 19, 76, 29, 86, 39, 96, 50, 107, 57, 114, 44, 101, 31, 88, 41, 98, 51, 108, 49, 106, 54, 111, 56, 113, 43, 100, 53, 110, 48, 105, 37, 94, 42, 99, 52, 109, 55, 112, 47, 104, 36, 93, 25, 82, 30, 87, 40, 97, 46, 103, 35, 92, 24, 81, 13, 70, 18, 75, 28, 85, 34, 91, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 140)(15, 141)(16, 120)(17, 143)(18, 122)(19, 145)(20, 146)(21, 147)(22, 128)(23, 125)(24, 126)(25, 127)(26, 152)(27, 153)(28, 130)(29, 155)(30, 132)(31, 157)(32, 158)(33, 159)(34, 136)(35, 137)(36, 138)(37, 139)(38, 164)(39, 165)(40, 142)(41, 167)(42, 144)(43, 169)(44, 170)(45, 171)(46, 148)(47, 149)(48, 150)(49, 151)(50, 163)(51, 162)(52, 154)(53, 161)(54, 156)(55, 160)(56, 166)(57, 168)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1250
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1284 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {19, 57, 57})
Quotient :: dipole
Aut^+ = C57 (small group id <57, 2>)
Aut   = D114 (small group id <114, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^3, Y3 * Y1^-2 * Y3^8 * Y1^-1, Y1 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 * Y1, (Y3 * Y2^-1)^19, (Y1^-1 * Y3^-1)^57 ]
Map::
	R = (1, 58, 2, 59, 6, 63, 14, 71, 23, 80, 12, 69, 5, 62, 8, 65, 16, 73, 26, 83, 35, 92, 24, 81, 13, 70, 18, 75, 28, 85, 38, 95, 47, 104, 36, 93, 25, 82, 30, 87, 40, 97, 50, 107, 56, 113, 48, 105, 37, 94, 42, 99, 52, 109, 43, 100, 53, 110, 57, 114, 49, 106, 54, 111, 44, 101, 31, 88, 41, 98, 51, 108, 55, 112, 45, 102, 32, 89, 19, 76, 29, 86, 39, 96, 46, 103, 33, 90, 20, 77, 9, 66, 17, 74, 27, 84, 34, 91, 21, 78, 10, 67, 3, 60, 7, 64, 15, 72, 22, 79, 11, 68, 4, 61)(115, 172)(116, 173)(117, 174)(118, 175)(119, 176)(120, 177)(121, 178)(122, 179)(123, 180)(124, 181)(125, 182)(126, 183)(127, 184)(128, 185)(129, 186)(130, 187)(131, 188)(132, 189)(133, 190)(134, 191)(135, 192)(136, 193)(137, 194)(138, 195)(139, 196)(140, 197)(141, 198)(142, 199)(143, 200)(144, 201)(145, 202)(146, 203)(147, 204)(148, 205)(149, 206)(150, 207)(151, 208)(152, 209)(153, 210)(154, 211)(155, 212)(156, 213)(157, 214)(158, 215)(159, 216)(160, 217)(161, 218)(162, 219)(163, 220)(164, 221)(165, 222)(166, 223)(167, 224)(168, 225)(169, 226)(170, 227)(171, 228)
	L = (1, 117)(2, 121)(3, 123)(4, 124)(5, 115)(6, 129)(7, 131)(8, 116)(9, 133)(10, 134)(11, 135)(12, 118)(13, 119)(14, 136)(15, 141)(16, 120)(17, 143)(18, 122)(19, 145)(20, 146)(21, 147)(22, 148)(23, 125)(24, 126)(25, 127)(26, 128)(27, 153)(28, 130)(29, 155)(30, 132)(31, 157)(32, 158)(33, 159)(34, 160)(35, 137)(36, 138)(37, 139)(38, 140)(39, 165)(40, 142)(41, 167)(42, 144)(43, 164)(44, 166)(45, 168)(46, 169)(47, 149)(48, 150)(49, 151)(50, 152)(51, 171)(52, 154)(53, 170)(54, 156)(55, 163)(56, 161)(57, 162)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 38, 114 ), ( 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114, 38, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.1242
Graph:: bipartite
	v = 58 e = 114 f = 4
	degree seq :: [ 2^57, 114 ]

E27.1285 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 15, 15})
Quotient :: halfedge^2
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = (C5 x A4) : C2 (small group id <120, 38>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1^-1, Y1 * Y2 * Y1^-1 * Y2 * Y3, Y1^15, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-4 ]
Map::
	R = (1, 62, 2, 66, 6, 75, 15, 83, 23, 91, 31, 99, 39, 107, 47, 114, 54, 106, 46, 98, 38, 90, 30, 82, 22, 74, 14, 65, 5, 61)(3, 68, 8, 78, 18, 84, 24, 93, 33, 102, 42, 108, 48, 116, 56, 118, 58, 111, 51, 103, 43, 95, 35, 87, 27, 79, 19, 70, 10, 63)(4, 71, 11, 76, 16, 85, 25, 94, 34, 100, 40, 109, 49, 117, 57, 119, 59, 112, 52, 104, 44, 96, 36, 88, 28, 80, 20, 72, 12, 64)(7, 77, 17, 86, 26, 92, 32, 101, 41, 110, 50, 115, 55, 120, 60, 113, 53, 105, 45, 97, 37, 89, 29, 81, 21, 73, 13, 69, 9, 67)
	L = (1, 3)(2, 7)(4, 9)(5, 12)(6, 16)(8, 11)(10, 13)(14, 21)(15, 24)(17, 18)(19, 20)(22, 27)(23, 32)(25, 26)(28, 29)(30, 36)(31, 40)(33, 34)(35, 37)(38, 45)(39, 48)(41, 42)(43, 44)(46, 51)(47, 55)(49, 50)(52, 53)(54, 59)(56, 57)(58, 60)(61, 64)(62, 68)(63, 69)(65, 73)(66, 77)(67, 71)(70, 72)(74, 79)(75, 85)(76, 78)(80, 81)(82, 88)(83, 93)(84, 86)(87, 89)(90, 97)(91, 101)(92, 94)(95, 96)(98, 103)(99, 109)(100, 102)(104, 105)(106, 112)(107, 116)(108, 110)(111, 113)(114, 120)(115, 117)(118, 119)
	local type(s) :: { ( 30^30 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph::
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.1286 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 15, 15})
Quotient :: edge^2
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = (C5 x A4) : C2 (small group id <120, 38>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y2)^2, Y3^-1 * Y2 * Y3 * Y1, Y2 * Y1 * Y3^-1 * Y1 * Y3, Y3^15 ]
Map::
	R = (1, 61, 4, 64, 12, 72, 20, 80, 28, 88, 36, 96, 44, 104, 52, 112, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 14, 74, 5, 65)(2, 62, 7, 67, 15, 75, 23, 83, 31, 91, 39, 99, 47, 107, 55, 115, 56, 116, 48, 108, 40, 100, 32, 92, 24, 84, 16, 76, 8, 68)(3, 63, 9, 69, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 57, 117, 58, 118, 50, 110, 42, 102, 34, 94, 26, 86, 18, 78, 10, 70)(6, 66, 11, 71, 19, 79, 27, 87, 35, 95, 43, 103, 51, 111, 59, 119, 60, 120, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 13, 73)(121, 122)(123, 126)(124, 129)(125, 133)(127, 131)(128, 130)(132, 139)(134, 138)(135, 137)(136, 141)(140, 143)(142, 144)(145, 147)(146, 149)(148, 153)(150, 157)(151, 155)(152, 154)(156, 163)(158, 162)(159, 161)(160, 165)(164, 167)(166, 168)(169, 171)(170, 173)(172, 177)(174, 180)(175, 179)(176, 178)(181, 183)(182, 186)(184, 191)(185, 188)(187, 189)(190, 193)(192, 195)(194, 201)(196, 198)(197, 199)(200, 205)(202, 206)(203, 207)(204, 209)(208, 215)(210, 212)(211, 213)(214, 217)(216, 219)(218, 225)(220, 222)(221, 223)(224, 229)(226, 230)(227, 231)(228, 233)(232, 239)(234, 236)(235, 237)(238, 240)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 60, 60 ), ( 60^30 ) }
Outer automorphisms :: reflexible
Dual of E27.1288
Graph:: simple bipartite
	v = 64 e = 120 f = 4
	degree seq :: [ 2^60, 30^4 ]

E27.1287 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 15, 15})
Quotient :: edge^2
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = C10 x A4 (small group id <120, 43>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^2 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y2^-2 * Y3, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3, Y1^15, Y2^15 ]
Map:: non-degenerate
	R = (1, 61, 4, 64)(2, 62, 6, 66)(3, 63, 8, 68)(5, 65, 12, 72)(7, 67, 16, 76)(9, 69, 20, 80)(10, 70, 22, 82)(11, 71, 24, 84)(13, 73, 19, 79)(14, 74, 17, 77)(15, 75, 28, 88)(18, 78, 21, 81)(23, 83, 32, 92)(25, 85, 26, 86)(27, 87, 36, 96)(29, 89, 30, 90)(31, 91, 40, 100)(33, 93, 34, 94)(35, 95, 44, 104)(37, 97, 38, 98)(39, 99, 48, 108)(41, 101, 42, 102)(43, 103, 52, 112)(45, 105, 46, 106)(47, 107, 55, 115)(49, 109, 50, 110)(51, 111, 58, 118)(53, 113, 54, 114)(56, 116, 57, 117)(59, 119, 60, 120)(121, 122, 125, 131, 143, 151, 159, 167, 171, 163, 155, 147, 135, 127, 123)(124, 129, 139, 144, 153, 162, 168, 176, 179, 172, 166, 157, 148, 141, 130)(126, 133, 146, 152, 161, 170, 175, 180, 173, 164, 158, 149, 136, 142, 134)(128, 137, 140, 132, 145, 154, 160, 169, 177, 178, 174, 165, 156, 150, 138)(181, 183, 187, 195, 207, 215, 223, 231, 227, 219, 211, 203, 191, 185, 182)(184, 190, 201, 208, 217, 226, 232, 239, 236, 228, 222, 213, 204, 199, 189)(186, 194, 202, 196, 209, 218, 224, 233, 240, 235, 230, 221, 212, 206, 193)(188, 198, 210, 216, 225, 234, 238, 237, 229, 220, 214, 205, 192, 200, 197)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 8^4 ), ( 8^15 ) }
Outer automorphisms :: reflexible
Dual of E27.1289
Graph:: simple bipartite
	v = 38 e = 120 f = 30
	degree seq :: [ 4^30, 15^8 ]

E27.1288 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 15, 15})
Quotient :: loop^2
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = (C5 x A4) : C2 (small group id <120, 38>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y2)^2, Y3^-1 * Y2 * Y3 * Y1, Y2 * Y1 * Y3^-1 * Y1 * Y3, Y3^15 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 20, 80, 140, 200, 28, 88, 148, 208, 36, 96, 156, 216, 44, 104, 164, 224, 52, 112, 172, 232, 54, 114, 174, 234, 46, 106, 166, 226, 38, 98, 158, 218, 30, 90, 150, 210, 22, 82, 142, 202, 14, 74, 134, 194, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 15, 75, 135, 195, 23, 83, 143, 203, 31, 91, 151, 211, 39, 99, 159, 219, 47, 107, 167, 227, 55, 115, 175, 235, 56, 116, 176, 236, 48, 108, 168, 228, 40, 100, 160, 220, 32, 92, 152, 212, 24, 84, 144, 204, 16, 76, 136, 196, 8, 68, 128, 188)(3, 63, 123, 183, 9, 69, 129, 189, 17, 77, 137, 197, 25, 85, 145, 205, 33, 93, 153, 213, 41, 101, 161, 221, 49, 109, 169, 229, 57, 117, 177, 237, 58, 118, 178, 238, 50, 110, 170, 230, 42, 102, 162, 222, 34, 94, 154, 214, 26, 86, 146, 206, 18, 78, 138, 198, 10, 70, 130, 190)(6, 66, 126, 186, 11, 71, 131, 191, 19, 79, 139, 199, 27, 87, 147, 207, 35, 95, 155, 215, 43, 103, 163, 223, 51, 111, 171, 231, 59, 119, 179, 239, 60, 120, 180, 240, 53, 113, 173, 233, 45, 105, 165, 225, 37, 97, 157, 217, 29, 89, 149, 209, 21, 81, 141, 201, 13, 73, 133, 193)
	L = (1, 62)(2, 61)(3, 66)(4, 69)(5, 73)(6, 63)(7, 71)(8, 70)(9, 64)(10, 68)(11, 67)(12, 79)(13, 65)(14, 78)(15, 77)(16, 81)(17, 75)(18, 74)(19, 72)(20, 83)(21, 76)(22, 84)(23, 80)(24, 82)(25, 87)(26, 89)(27, 85)(28, 93)(29, 86)(30, 97)(31, 95)(32, 94)(33, 88)(34, 92)(35, 91)(36, 103)(37, 90)(38, 102)(39, 101)(40, 105)(41, 99)(42, 98)(43, 96)(44, 107)(45, 100)(46, 108)(47, 104)(48, 106)(49, 111)(50, 113)(51, 109)(52, 117)(53, 110)(54, 120)(55, 119)(56, 118)(57, 112)(58, 116)(59, 115)(60, 114)(121, 183)(122, 186)(123, 181)(124, 191)(125, 188)(126, 182)(127, 189)(128, 185)(129, 187)(130, 193)(131, 184)(132, 195)(133, 190)(134, 201)(135, 192)(136, 198)(137, 199)(138, 196)(139, 197)(140, 205)(141, 194)(142, 206)(143, 207)(144, 209)(145, 200)(146, 202)(147, 203)(148, 215)(149, 204)(150, 212)(151, 213)(152, 210)(153, 211)(154, 217)(155, 208)(156, 219)(157, 214)(158, 225)(159, 216)(160, 222)(161, 223)(162, 220)(163, 221)(164, 229)(165, 218)(166, 230)(167, 231)(168, 233)(169, 224)(170, 226)(171, 227)(172, 239)(173, 228)(174, 236)(175, 237)(176, 234)(177, 235)(178, 240)(179, 232)(180, 238)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1286
Transitivity :: VT+
Graph::
	v = 4 e = 120 f = 64
	degree seq :: [ 60^4 ]

E27.1289 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 15, 15})
Quotient :: loop^2
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = C10 x A4 (small group id <120, 43>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^2 * Y3 * Y1 * Y3 * Y2^-1 * Y3, Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y2^-2 * Y3, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y2 * Y3 * Y1^2 * Y3 * Y1^-1 * Y3, Y1^15, Y2^15 ]
Map:: non-degenerate
	R = (1, 61, 121, 181, 4, 64, 124, 184)(2, 62, 122, 182, 6, 66, 126, 186)(3, 63, 123, 183, 8, 68, 128, 188)(5, 65, 125, 185, 12, 72, 132, 192)(7, 67, 127, 187, 16, 76, 136, 196)(9, 69, 129, 189, 20, 80, 140, 200)(10, 70, 130, 190, 22, 82, 142, 202)(11, 71, 131, 191, 24, 84, 144, 204)(13, 73, 133, 193, 19, 79, 139, 199)(14, 74, 134, 194, 17, 77, 137, 197)(15, 75, 135, 195, 28, 88, 148, 208)(18, 78, 138, 198, 21, 81, 141, 201)(23, 83, 143, 203, 32, 92, 152, 212)(25, 85, 145, 205, 26, 86, 146, 206)(27, 87, 147, 207, 36, 96, 156, 216)(29, 89, 149, 209, 30, 90, 150, 210)(31, 91, 151, 211, 40, 100, 160, 220)(33, 93, 153, 213, 34, 94, 154, 214)(35, 95, 155, 215, 44, 104, 164, 224)(37, 97, 157, 217, 38, 98, 158, 218)(39, 99, 159, 219, 48, 108, 168, 228)(41, 101, 161, 221, 42, 102, 162, 222)(43, 103, 163, 223, 52, 112, 172, 232)(45, 105, 165, 225, 46, 106, 166, 226)(47, 107, 167, 227, 55, 115, 175, 235)(49, 109, 169, 229, 50, 110, 170, 230)(51, 111, 171, 231, 58, 118, 178, 238)(53, 113, 173, 233, 54, 114, 174, 234)(56, 116, 176, 236, 57, 117, 177, 237)(59, 119, 179, 239, 60, 120, 180, 240)
	L = (1, 62)(2, 65)(3, 61)(4, 69)(5, 71)(6, 73)(7, 63)(8, 77)(9, 79)(10, 64)(11, 83)(12, 85)(13, 86)(14, 66)(15, 67)(16, 82)(17, 80)(18, 68)(19, 84)(20, 72)(21, 70)(22, 74)(23, 91)(24, 93)(25, 94)(26, 92)(27, 75)(28, 81)(29, 76)(30, 78)(31, 99)(32, 101)(33, 102)(34, 100)(35, 87)(36, 90)(37, 88)(38, 89)(39, 107)(40, 109)(41, 110)(42, 108)(43, 95)(44, 98)(45, 96)(46, 97)(47, 111)(48, 116)(49, 117)(50, 115)(51, 103)(52, 106)(53, 104)(54, 105)(55, 120)(56, 119)(57, 118)(58, 114)(59, 112)(60, 113)(121, 183)(122, 181)(123, 187)(124, 190)(125, 182)(126, 194)(127, 195)(128, 198)(129, 184)(130, 201)(131, 185)(132, 200)(133, 186)(134, 202)(135, 207)(136, 209)(137, 188)(138, 210)(139, 189)(140, 197)(141, 208)(142, 196)(143, 191)(144, 199)(145, 192)(146, 193)(147, 215)(148, 217)(149, 218)(150, 216)(151, 203)(152, 206)(153, 204)(154, 205)(155, 223)(156, 225)(157, 226)(158, 224)(159, 211)(160, 214)(161, 212)(162, 213)(163, 231)(164, 233)(165, 234)(166, 232)(167, 219)(168, 222)(169, 220)(170, 221)(171, 227)(172, 239)(173, 240)(174, 238)(175, 230)(176, 228)(177, 229)(178, 237)(179, 236)(180, 235)
	local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) }
Outer automorphisms :: reflexible
Dual of E27.1287
Transitivity :: VT+
Graph::
	v = 30 e = 120 f = 38
	degree seq :: [ 8^30 ]

E27.1290 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 15, 15})
Quotient :: dipole
Aut^+ = C5 x A4 (small group id <60, 9>)
Aut   = (C5 x A4) : C2 (small group id <120, 38>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^2, Y2^15, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 11, 71)(6, 66, 13, 73)(8, 68, 17, 77)(10, 70, 21, 81)(12, 72, 15, 75)(14, 74, 20, 80)(16, 76, 19, 79)(18, 78, 23, 83)(22, 82, 24, 84)(25, 85, 26, 86)(27, 87, 33, 93)(28, 88, 29, 89)(30, 90, 36, 96)(31, 91, 34, 94)(32, 92, 37, 97)(35, 95, 42, 102)(38, 98, 45, 105)(39, 99, 41, 101)(40, 100, 44, 104)(43, 103, 47, 107)(46, 106, 48, 108)(49, 109, 50, 110)(51, 111, 57, 117)(52, 112, 53, 113)(54, 114, 59, 119)(55, 115, 58, 118)(56, 116, 60, 120)(121, 181, 123, 183, 128, 188, 138, 198, 147, 207, 155, 215, 163, 223, 171, 231, 174, 234, 166, 226, 158, 218, 150, 210, 142, 202, 130, 190, 124, 184)(122, 182, 125, 185, 132, 192, 143, 203, 151, 211, 159, 219, 167, 227, 175, 235, 176, 236, 168, 228, 160, 220, 152, 212, 144, 204, 134, 194, 126, 186)(127, 187, 135, 195, 145, 205, 153, 213, 161, 221, 169, 229, 177, 237, 180, 240, 173, 233, 165, 225, 157, 217, 149, 209, 141, 201, 133, 193, 136, 196)(129, 189, 139, 199, 131, 191, 137, 197, 146, 206, 154, 214, 162, 222, 170, 230, 178, 238, 179, 239, 172, 232, 164, 224, 156, 216, 148, 208, 140, 200)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 34 e = 120 f = 34
	degree seq :: [ 4^30, 30^4 ]

E27.1291 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^2 * Y1 * Y3^-2 * Y1, Y1 * Y3^-3 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y3^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 6, 66)(4, 64, 11, 71)(5, 65, 13, 73)(7, 67, 17, 77)(8, 68, 19, 79)(9, 69, 21, 81)(10, 70, 23, 83)(12, 72, 18, 78)(14, 74, 20, 80)(15, 75, 30, 90)(16, 76, 32, 92)(22, 82, 31, 91)(24, 84, 33, 93)(25, 85, 44, 104)(26, 86, 46, 106)(27, 87, 45, 105)(28, 88, 48, 108)(29, 89, 49, 109)(34, 94, 43, 103)(35, 95, 52, 112)(36, 96, 42, 102)(37, 97, 41, 101)(38, 98, 39, 99)(40, 100, 55, 115)(47, 107, 53, 113)(50, 110, 54, 114)(51, 111, 60, 120)(56, 116, 59, 119)(57, 117, 58, 118)(121, 181, 123, 183)(122, 182, 126, 186)(124, 184, 129, 189)(125, 185, 130, 190)(127, 187, 135, 195)(128, 188, 136, 196)(131, 191, 141, 201)(132, 192, 142, 202)(133, 193, 143, 203)(134, 194, 144, 204)(137, 197, 150, 210)(138, 198, 151, 211)(139, 199, 152, 212)(140, 200, 153, 213)(145, 205, 159, 219)(146, 206, 160, 220)(147, 207, 161, 221)(148, 208, 162, 222)(149, 209, 163, 223)(154, 214, 169, 229)(155, 215, 171, 231)(156, 216, 168, 228)(157, 217, 165, 225)(158, 218, 164, 224)(166, 226, 175, 235)(167, 227, 176, 236)(170, 230, 177, 237)(172, 232, 180, 240)(173, 233, 179, 239)(174, 234, 178, 238)
	L = (1, 124)(2, 127)(3, 129)(4, 132)(5, 121)(6, 135)(7, 138)(8, 122)(9, 142)(10, 123)(11, 145)(12, 147)(13, 146)(14, 125)(15, 151)(16, 126)(17, 154)(18, 156)(19, 155)(20, 128)(21, 159)(22, 161)(23, 160)(24, 130)(25, 165)(26, 131)(27, 167)(28, 133)(29, 134)(30, 169)(31, 168)(32, 171)(33, 136)(34, 162)(35, 137)(36, 173)(37, 139)(38, 140)(39, 157)(40, 141)(41, 176)(42, 143)(43, 144)(44, 153)(45, 152)(46, 178)(47, 180)(48, 179)(49, 148)(50, 149)(51, 150)(52, 177)(53, 175)(54, 158)(55, 174)(56, 172)(57, 163)(58, 164)(59, 166)(60, 170)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1298
Graph:: simple bipartite
	v = 60 e = 120 f = 8
	degree seq :: [ 4^60 ]

E27.1292 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 10, 70)(5, 65, 9, 69)(6, 66, 8, 68)(11, 71, 17, 77)(12, 72, 19, 79)(13, 73, 18, 78)(14, 74, 22, 82)(15, 75, 21, 81)(16, 76, 20, 80)(23, 83, 29, 89)(24, 84, 31, 91)(25, 85, 30, 90)(26, 86, 34, 94)(27, 87, 33, 93)(28, 88, 32, 92)(35, 95, 41, 101)(36, 96, 43, 103)(37, 97, 42, 102)(38, 98, 46, 106)(39, 99, 45, 105)(40, 100, 44, 104)(47, 107, 52, 112)(48, 108, 54, 114)(49, 109, 53, 113)(50, 110, 56, 116)(51, 111, 55, 115)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183, 131, 191, 143, 203, 155, 215, 167, 227, 159, 219, 147, 207, 135, 195, 125, 185)(122, 182, 127, 187, 137, 197, 149, 209, 161, 221, 172, 232, 165, 225, 153, 213, 141, 201, 129, 189)(124, 184, 132, 192, 144, 204, 156, 216, 168, 228, 177, 237, 170, 230, 158, 218, 146, 206, 134, 194)(126, 186, 133, 193, 145, 205, 157, 217, 169, 229, 178, 238, 171, 231, 160, 220, 148, 208, 136, 196)(128, 188, 138, 198, 150, 210, 162, 222, 173, 233, 179, 239, 175, 235, 164, 224, 152, 212, 140, 200)(130, 190, 139, 199, 151, 211, 163, 223, 174, 234, 180, 240, 176, 236, 166, 226, 154, 214, 142, 202)
	L = (1, 124)(2, 128)(3, 132)(4, 126)(5, 134)(6, 121)(7, 138)(8, 130)(9, 140)(10, 122)(11, 144)(12, 133)(13, 123)(14, 136)(15, 146)(16, 125)(17, 150)(18, 139)(19, 127)(20, 142)(21, 152)(22, 129)(23, 156)(24, 145)(25, 131)(26, 148)(27, 158)(28, 135)(29, 162)(30, 151)(31, 137)(32, 154)(33, 164)(34, 141)(35, 168)(36, 157)(37, 143)(38, 160)(39, 170)(40, 147)(41, 173)(42, 163)(43, 149)(44, 166)(45, 175)(46, 153)(47, 177)(48, 169)(49, 155)(50, 171)(51, 159)(52, 179)(53, 174)(54, 161)(55, 176)(56, 165)(57, 178)(58, 167)(59, 180)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1297
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1293 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, Y1 * Y2^-1 * Y1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y3 * Y2^2 * Y3 * Y2^-2, Y2 * Y1 * Y2^2 * Y3 * Y2 * Y3 * Y2 * Y3, Y2^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 6, 66)(4, 64, 7, 67)(5, 65, 8, 68)(9, 69, 15, 75)(10, 70, 16, 76)(11, 71, 17, 77)(12, 72, 18, 78)(13, 73, 19, 79)(14, 74, 20, 80)(21, 81, 30, 90)(22, 82, 31, 91)(23, 83, 32, 92)(24, 84, 33, 93)(25, 85, 34, 94)(26, 86, 35, 95)(27, 87, 36, 96)(28, 88, 37, 97)(29, 89, 38, 98)(39, 99, 51, 111)(40, 100, 46, 106)(41, 101, 48, 108)(42, 102, 47, 107)(43, 103, 52, 112)(44, 104, 49, 109)(45, 105, 53, 113)(50, 110, 54, 114)(55, 115, 59, 119)(56, 116, 58, 118)(57, 117, 60, 120)(121, 181, 123, 183, 129, 189, 141, 201, 159, 219, 175, 235, 170, 230, 149, 209, 134, 194, 125, 185)(122, 182, 126, 186, 135, 195, 150, 210, 171, 231, 179, 239, 174, 234, 158, 218, 140, 200, 128, 188)(124, 184, 131, 191, 142, 202, 161, 221, 176, 236, 172, 232, 180, 240, 167, 227, 147, 207, 132, 192)(127, 187, 137, 197, 151, 211, 168, 228, 178, 238, 163, 223, 177, 237, 162, 222, 156, 216, 138, 198)(130, 190, 143, 203, 160, 220, 155, 215, 173, 233, 154, 214, 169, 229, 148, 208, 133, 193, 144, 204)(136, 196, 152, 212, 166, 226, 146, 206, 165, 225, 145, 205, 164, 224, 157, 217, 139, 199, 153, 213)
	L = (1, 124)(2, 127)(3, 130)(4, 121)(5, 133)(6, 136)(7, 122)(8, 139)(9, 142)(10, 123)(11, 145)(12, 146)(13, 125)(14, 147)(15, 151)(16, 126)(17, 154)(18, 155)(19, 128)(20, 156)(21, 160)(22, 129)(23, 162)(24, 163)(25, 131)(26, 132)(27, 134)(28, 168)(29, 169)(30, 166)(31, 135)(32, 167)(33, 172)(34, 137)(35, 138)(36, 140)(37, 161)(38, 164)(39, 176)(40, 141)(41, 157)(42, 143)(43, 144)(44, 158)(45, 179)(46, 150)(47, 152)(48, 148)(49, 149)(50, 180)(51, 178)(52, 153)(53, 175)(54, 177)(55, 173)(56, 159)(57, 174)(58, 171)(59, 165)(60, 170)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1296
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1294 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, (R * Y2 * Y3)^2, Y2^-2 * Y3 * Y2^2 * Y3, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-2, Y2^10, Y2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y3 * Y2^2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 7, 67)(5, 65, 14, 74)(6, 66, 17, 77)(8, 68, 22, 82)(10, 70, 18, 78)(11, 71, 20, 80)(12, 72, 19, 79)(13, 73, 23, 83)(15, 75, 21, 81)(16, 76, 24, 84)(25, 85, 44, 104)(26, 86, 46, 106)(27, 87, 42, 102)(28, 88, 38, 98)(29, 89, 45, 105)(30, 90, 47, 107)(31, 91, 41, 101)(32, 92, 37, 97)(33, 93, 49, 109)(34, 94, 35, 95)(36, 96, 52, 112)(39, 99, 51, 111)(40, 100, 53, 113)(43, 103, 55, 115)(48, 108, 54, 114)(50, 110, 56, 116)(57, 117, 59, 119)(58, 118, 60, 120)(121, 181, 123, 183, 130, 190, 147, 207, 168, 228, 172, 232, 170, 230, 154, 214, 136, 196, 125, 185)(122, 182, 126, 186, 138, 198, 157, 217, 174, 234, 166, 226, 176, 236, 164, 224, 144, 204, 128, 188)(124, 184, 132, 192, 148, 208, 169, 229, 178, 238, 167, 227, 177, 237, 165, 225, 151, 211, 133, 193)(127, 187, 140, 200, 158, 218, 175, 235, 180, 240, 173, 233, 179, 239, 171, 231, 161, 221, 141, 201)(129, 189, 145, 205, 162, 222, 142, 202, 156, 216, 137, 197, 155, 215, 152, 212, 134, 194, 146, 206)(131, 191, 149, 209, 163, 223, 143, 203, 160, 220, 139, 199, 159, 219, 153, 213, 135, 195, 150, 210)
	L = (1, 124)(2, 127)(3, 131)(4, 121)(5, 135)(6, 139)(7, 122)(8, 143)(9, 140)(10, 148)(11, 123)(12, 137)(13, 142)(14, 141)(15, 125)(16, 151)(17, 132)(18, 158)(19, 126)(20, 129)(21, 134)(22, 133)(23, 128)(24, 161)(25, 165)(26, 167)(27, 163)(28, 130)(29, 164)(30, 166)(31, 136)(32, 169)(33, 157)(34, 159)(35, 171)(36, 173)(37, 153)(38, 138)(39, 154)(40, 172)(41, 144)(42, 175)(43, 147)(44, 149)(45, 145)(46, 150)(47, 146)(48, 178)(49, 152)(50, 177)(51, 155)(52, 160)(53, 156)(54, 180)(55, 162)(56, 179)(57, 170)(58, 168)(59, 176)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1295
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1295 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-3, Y2 * Y3 * Y1^-1 * Y3 * Y1^26 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 6, 66, 15, 75, 33, 93, 51, 111, 59, 119, 57, 117, 50, 110, 56, 116, 49, 109, 26, 86, 42, 102, 24, 84, 10, 70, 3, 63, 7, 67, 16, 76, 34, 94, 27, 87, 43, 103, 54, 114, 48, 108, 55, 115, 60, 120, 58, 118, 46, 106, 32, 92, 14, 74, 5, 65)(4, 64, 11, 71, 25, 85, 35, 95, 23, 83, 47, 107, 52, 112, 36, 96, 31, 91, 44, 104, 20, 80, 8, 68, 19, 79, 41, 101, 22, 82, 9, 69, 21, 81, 45, 105, 30, 90, 13, 73, 29, 89, 38, 98, 17, 77, 37, 97, 53, 113, 40, 100, 18, 78, 39, 99, 28, 88, 12, 72)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 129, 189)(125, 185, 130, 190)(126, 186, 136, 196)(128, 188, 138, 198)(131, 191, 141, 201)(132, 192, 142, 202)(133, 193, 143, 203)(134, 194, 144, 204)(135, 195, 154, 214)(137, 197, 156, 216)(139, 199, 159, 219)(140, 200, 160, 220)(145, 205, 165, 225)(146, 206, 166, 226)(147, 207, 153, 213)(148, 208, 161, 221)(149, 209, 167, 227)(150, 210, 155, 215)(151, 211, 157, 217)(152, 212, 162, 222)(158, 218, 172, 232)(163, 223, 171, 231)(164, 224, 173, 233)(168, 228, 177, 237)(169, 229, 178, 238)(170, 230, 175, 235)(174, 234, 179, 239)(176, 236, 180, 240)
	L = (1, 124)(2, 128)(3, 129)(4, 121)(5, 133)(6, 137)(7, 138)(8, 122)(9, 123)(10, 143)(11, 146)(12, 147)(13, 125)(14, 151)(15, 155)(16, 156)(17, 126)(18, 127)(19, 162)(20, 163)(21, 166)(22, 153)(23, 130)(24, 157)(25, 168)(26, 131)(27, 132)(28, 170)(29, 169)(30, 154)(31, 134)(32, 159)(33, 142)(34, 150)(35, 135)(36, 136)(37, 144)(38, 174)(39, 152)(40, 171)(41, 175)(42, 139)(43, 140)(44, 176)(45, 177)(46, 141)(47, 178)(48, 145)(49, 149)(50, 148)(51, 160)(52, 179)(53, 180)(54, 158)(55, 161)(56, 164)(57, 165)(58, 167)(59, 172)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1294
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1296 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1, Y1^3 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^2 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1^-2, (Y3 * Y1^-1)^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 6, 66, 17, 77, 30, 90, 46, 106, 58, 118, 50, 110, 55, 115, 59, 119, 51, 111, 26, 86, 44, 104, 53, 113, 28, 88, 10, 70, 21, 81, 41, 101, 54, 114, 29, 89, 45, 105, 57, 117, 49, 109, 56, 116, 60, 120, 52, 112, 27, 87, 40, 100, 16, 76, 5, 65)(3, 63, 9, 69, 25, 85, 37, 97, 15, 75, 36, 96, 43, 103, 19, 79, 38, 98, 47, 107, 22, 82, 7, 67, 20, 80, 33, 93, 13, 73, 4, 64, 12, 72, 32, 92, 35, 95, 14, 74, 34, 94, 42, 102, 18, 78, 39, 99, 48, 108, 24, 84, 8, 68, 23, 83, 31, 91, 11, 71)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 134, 194)(126, 186, 138, 198)(128, 188, 141, 201)(129, 189, 146, 206)(131, 191, 149, 209)(132, 192, 147, 207)(133, 193, 150, 210)(135, 195, 148, 208)(136, 196, 158, 218)(137, 197, 157, 217)(139, 199, 161, 221)(140, 200, 164, 224)(142, 202, 165, 225)(143, 203, 160, 220)(144, 204, 166, 226)(145, 205, 169, 229)(151, 211, 175, 235)(152, 212, 170, 230)(153, 213, 176, 236)(154, 214, 171, 231)(155, 215, 174, 234)(156, 216, 172, 232)(159, 219, 173, 233)(162, 222, 177, 237)(163, 223, 178, 238)(167, 227, 179, 239)(168, 228, 180, 240)
	L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 135)(6, 139)(7, 141)(8, 122)(9, 147)(10, 123)(11, 150)(12, 146)(13, 149)(14, 148)(15, 125)(16, 159)(17, 155)(18, 161)(19, 126)(20, 160)(21, 127)(22, 166)(23, 164)(24, 165)(25, 170)(26, 132)(27, 129)(28, 134)(29, 133)(30, 131)(31, 176)(32, 169)(33, 175)(34, 172)(35, 137)(36, 171)(37, 174)(38, 173)(39, 136)(40, 140)(41, 138)(42, 178)(43, 177)(44, 143)(45, 144)(46, 142)(47, 180)(48, 179)(49, 152)(50, 145)(51, 156)(52, 154)(53, 158)(54, 157)(55, 153)(56, 151)(57, 163)(58, 162)(59, 168)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1293
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1297 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), (Y3 * Y2)^2, Y2 * Y3 * Y1^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1^10, (Y2 * Y1^-5)^2, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 7, 67, 19, 79, 33, 93, 45, 105, 56, 116, 44, 104, 32, 92, 18, 78, 6, 66, 10, 70, 22, 82, 36, 96, 48, 108, 58, 118, 52, 112, 40, 100, 28, 88, 15, 75, 4, 64, 9, 69, 21, 81, 35, 95, 47, 107, 55, 115, 43, 103, 31, 91, 17, 77, 5, 65)(3, 63, 11, 71, 25, 85, 34, 94, 49, 109, 60, 120, 54, 114, 42, 102, 30, 90, 27, 87, 14, 74, 8, 68, 23, 83, 38, 98, 46, 106, 59, 119, 53, 113, 41, 101, 29, 89, 16, 76, 12, 72, 24, 84, 20, 80, 37, 97, 50, 110, 57, 117, 51, 111, 39, 99, 26, 86, 13, 73)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 134, 194)(125, 185, 136, 196)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 144, 204)(130, 190, 131, 191)(133, 193, 135, 195)(137, 197, 150, 210)(138, 198, 147, 207)(139, 199, 154, 214)(141, 201, 145, 205)(142, 202, 143, 203)(146, 206, 152, 212)(148, 208, 149, 209)(151, 211, 159, 219)(153, 213, 166, 226)(155, 215, 158, 218)(156, 216, 157, 217)(160, 220, 162, 222)(161, 221, 164, 224)(163, 223, 173, 233)(165, 225, 177, 237)(167, 227, 170, 230)(168, 228, 169, 229)(171, 231, 172, 232)(174, 234, 176, 236)(175, 235, 180, 240)(178, 238, 179, 239)
	L = (1, 124)(2, 129)(3, 132)(4, 126)(5, 135)(6, 121)(7, 141)(8, 131)(9, 130)(10, 122)(11, 144)(12, 134)(13, 136)(14, 123)(15, 138)(16, 147)(17, 148)(18, 125)(19, 155)(20, 143)(21, 142)(22, 127)(23, 145)(24, 128)(25, 140)(26, 149)(27, 133)(28, 152)(29, 150)(30, 146)(31, 160)(32, 137)(33, 167)(34, 157)(35, 156)(36, 139)(37, 158)(38, 154)(39, 161)(40, 164)(41, 162)(42, 159)(43, 172)(44, 151)(45, 175)(46, 169)(47, 168)(48, 153)(49, 170)(50, 166)(51, 173)(52, 176)(53, 174)(54, 171)(55, 178)(56, 163)(57, 179)(58, 165)(59, 180)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1292
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1298 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = C10 x S3 (small group id <60, 11>)
Aut   = C2 x S3 x D10 (small group id <120, 42>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^2, (Y3^-1, Y1), (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y2^3 * Y1^-1 * Y3, Y1^-2 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y3, Y2^-1 * Y1 * Y2^-1 * Y1^7, (Y1 * Y3^-1)^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 8, 68, 27, 87, 51, 111, 58, 118, 59, 119, 44, 104, 19, 79, 5, 65)(3, 63, 13, 73, 28, 88, 11, 71, 36, 96, 49, 109, 55, 115, 50, 110, 43, 103, 16, 76)(4, 64, 10, 70, 7, 67, 12, 72, 30, 90, 52, 112, 57, 117, 60, 120, 42, 102, 20, 80)(6, 66, 22, 82, 29, 89, 41, 101, 56, 116, 45, 105, 46, 106, 21, 81, 33, 93, 9, 69)(14, 74, 40, 100, 53, 113, 39, 99, 47, 107, 18, 78, 32, 92, 23, 83, 34, 94, 25, 85)(15, 75, 35, 95, 17, 77, 37, 97, 26, 86, 38, 98, 31, 91, 54, 114, 48, 108, 24, 84)(121, 181, 123, 183, 134, 194, 132, 192, 157, 217, 176, 236, 171, 231, 156, 216, 167, 227, 180, 240, 174, 234, 153, 213, 139, 199, 163, 223, 154, 214, 130, 190, 155, 215, 149, 209, 128, 188, 148, 208, 173, 233, 172, 232, 158, 218, 166, 226, 179, 239, 175, 235, 152, 212, 140, 200, 144, 204, 126, 186)(122, 182, 129, 189, 151, 211, 150, 210, 145, 205, 170, 230, 178, 238, 161, 221, 135, 195, 162, 222, 159, 219, 133, 193, 125, 185, 141, 201, 146, 206, 127, 187, 143, 203, 169, 229, 147, 207, 142, 202, 168, 228, 177, 237, 160, 220, 136, 196, 164, 224, 165, 225, 137, 197, 124, 184, 138, 198, 131, 191)
	L = (1, 124)(2, 130)(3, 135)(4, 139)(5, 140)(6, 143)(7, 121)(8, 127)(9, 152)(10, 125)(11, 157)(12, 122)(13, 155)(14, 142)(15, 163)(16, 144)(17, 123)(18, 166)(19, 162)(20, 164)(21, 167)(22, 154)(23, 153)(24, 170)(25, 126)(26, 148)(27, 132)(28, 137)(29, 145)(30, 128)(31, 156)(32, 141)(33, 138)(34, 129)(35, 136)(36, 146)(37, 133)(38, 131)(39, 176)(40, 149)(41, 134)(42, 179)(43, 168)(44, 180)(45, 173)(46, 159)(47, 165)(48, 175)(49, 158)(50, 174)(51, 150)(52, 147)(53, 161)(54, 169)(55, 151)(56, 160)(57, 171)(58, 172)(59, 177)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4^20 ), ( 4^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1291
Graph:: bipartite
	v = 8 e = 120 f = 60
	degree seq :: [ 20^6, 60^2 ]

E27.1299 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: halfedge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^3, Y1^-1 * Y2 * Y1^3 * Y3 * Y1^-6, Y1^-1 * Y2 * Y3 * Y1^11 * Y2 * Y3, (Y2 * Y1 * Y3)^10 ]
Map:: non-degenerate
	R = (1, 62, 2, 66, 6, 74, 14, 85, 25, 97, 37, 109, 49, 104, 44, 92, 32, 80, 20, 70, 10, 77, 17, 88, 28, 100, 40, 112, 52, 119, 59, 117, 57, 107, 47, 95, 35, 83, 23, 72, 12, 78, 18, 89, 29, 101, 41, 113, 53, 108, 48, 96, 36, 84, 24, 73, 13, 65, 5, 61)(3, 69, 9, 79, 19, 91, 31, 103, 43, 111, 51, 99, 39, 87, 27, 76, 16, 68, 8, 64, 4, 71, 11, 82, 22, 94, 34, 106, 46, 116, 56, 120, 60, 114, 54, 102, 42, 90, 30, 81, 21, 93, 33, 105, 45, 115, 55, 118, 58, 110, 50, 98, 38, 86, 26, 75, 15, 67, 7, 63)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 29)(17, 30)(20, 33)(22, 35)(24, 31)(25, 38)(27, 41)(28, 42)(32, 45)(34, 47)(36, 43)(37, 50)(39, 53)(40, 54)(44, 55)(46, 57)(48, 51)(49, 58)(52, 60)(56, 59)(61, 64)(62, 68)(63, 70)(65, 71)(66, 76)(67, 77)(69, 80)(72, 81)(73, 82)(74, 87)(75, 88)(78, 90)(79, 92)(83, 93)(84, 94)(85, 99)(86, 100)(89, 102)(91, 104)(95, 105)(96, 106)(97, 111)(98, 112)(101, 114)(103, 109)(107, 115)(108, 116)(110, 119)(113, 120)(117, 118)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1301
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.1300 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: halfedge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y2)^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-2 * Y2 * Y3 * Y1^-2, Y2 * Y1^-2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 * Y2 * Y3 * Y1^2 ]
Map:: non-degenerate
	R = (1, 62, 2, 66, 6, 74, 14, 70, 10, 77, 17, 84, 24, 91, 31, 87, 27, 93, 33, 100, 40, 107, 47, 103, 43, 109, 49, 116, 56, 120, 60, 119, 59, 113, 53, 106, 46, 110, 50, 104, 44, 97, 37, 90, 30, 94, 34, 88, 28, 81, 21, 72, 12, 78, 18, 73, 13, 65, 5, 61)(3, 69, 9, 76, 16, 68, 8, 64, 4, 71, 11, 80, 20, 86, 26, 82, 22, 89, 29, 96, 36, 102, 42, 98, 38, 105, 45, 112, 52, 118, 58, 114, 54, 117, 57, 111, 51, 115, 55, 108, 48, 101, 41, 95, 35, 99, 39, 92, 32, 85, 25, 79, 19, 83, 23, 75, 15, 67, 7, 63)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 25)(20, 28)(22, 30)(24, 32)(26, 34)(27, 35)(29, 37)(31, 39)(33, 41)(36, 44)(38, 46)(40, 48)(42, 50)(43, 51)(45, 53)(47, 55)(49, 57)(52, 59)(54, 56)(58, 60)(61, 64)(62, 68)(63, 70)(65, 71)(66, 76)(67, 77)(69, 74)(72, 82)(73, 80)(75, 84)(78, 86)(79, 87)(81, 89)(83, 91)(85, 93)(88, 96)(90, 98)(92, 100)(94, 102)(95, 103)(97, 105)(99, 107)(101, 109)(104, 112)(106, 114)(108, 116)(110, 118)(111, 119)(113, 117)(115, 120)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1302
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.1301 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: halfedge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, (Y3 * Y2)^3, Y1^10, Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 62, 2, 66, 6, 74, 14, 85, 25, 97, 37, 96, 36, 84, 24, 73, 13, 65, 5, 61)(3, 69, 9, 79, 19, 91, 31, 103, 43, 108, 48, 98, 38, 86, 26, 75, 15, 67, 7, 63)(4, 71, 11, 82, 22, 94, 34, 106, 46, 109, 49, 99, 39, 87, 27, 76, 16, 68, 8, 64)(10, 77, 17, 88, 28, 100, 40, 110, 50, 116, 56, 113, 53, 104, 44, 92, 32, 80, 20, 70)(12, 78, 18, 89, 29, 101, 41, 111, 51, 117, 57, 115, 55, 107, 47, 95, 35, 83, 23, 72)(21, 93, 33, 105, 45, 114, 54, 119, 59, 120, 60, 118, 58, 112, 52, 102, 42, 90, 30, 81)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 29)(17, 30)(20, 33)(22, 35)(24, 31)(25, 38)(27, 41)(28, 42)(32, 45)(34, 47)(36, 43)(37, 48)(39, 51)(40, 52)(44, 54)(46, 55)(49, 57)(50, 58)(53, 59)(56, 60)(61, 64)(62, 68)(63, 70)(65, 71)(66, 76)(67, 77)(69, 80)(72, 81)(73, 82)(74, 87)(75, 88)(78, 90)(79, 92)(83, 93)(84, 94)(85, 99)(86, 100)(89, 102)(91, 104)(95, 105)(96, 106)(97, 109)(98, 110)(101, 112)(103, 113)(107, 114)(108, 116)(111, 118)(115, 119)(117, 120)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1299
Transitivity :: VT+ AT
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.1302 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: halfedge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1^-1)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1^10 ]
Map:: non-degenerate
	R = (1, 62, 2, 66, 6, 74, 14, 86, 26, 99, 39, 98, 38, 85, 25, 73, 13, 65, 5, 61)(3, 69, 9, 79, 19, 93, 33, 105, 45, 110, 50, 100, 40, 87, 27, 75, 15, 67, 7, 63)(4, 71, 11, 82, 22, 95, 35, 107, 47, 111, 51, 101, 41, 88, 28, 76, 16, 68, 8, 64)(10, 77, 17, 89, 29, 102, 42, 112, 52, 118, 58, 115, 55, 106, 46, 94, 34, 80, 20, 70)(12, 78, 18, 90, 30, 103, 43, 113, 53, 119, 59, 116, 56, 108, 48, 96, 36, 83, 23, 72)(21, 92, 32, 84, 24, 97, 37, 109, 49, 117, 57, 120, 60, 114, 54, 104, 44, 91, 31, 81)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 32)(22, 36)(24, 34)(25, 33)(26, 40)(28, 43)(29, 44)(35, 48)(37, 46)(38, 45)(39, 50)(41, 53)(42, 54)(47, 56)(49, 55)(51, 59)(52, 60)(57, 58)(61, 64)(62, 68)(63, 70)(65, 71)(66, 76)(67, 77)(69, 80)(72, 84)(73, 82)(74, 88)(75, 89)(78, 92)(79, 94)(81, 90)(83, 97)(85, 95)(86, 101)(87, 102)(91, 103)(93, 106)(96, 109)(98, 107)(99, 111)(100, 112)(104, 113)(105, 115)(108, 117)(110, 118)(114, 119)(116, 120)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1300
Transitivity :: VT+ AT
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.1303 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: edge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^10, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ]
Map::
	R = (1, 61, 4, 64, 12, 72, 23, 83, 35, 95, 47, 107, 36, 96, 24, 84, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 29, 89, 41, 101, 52, 112, 42, 102, 30, 90, 18, 78, 8, 68)(3, 63, 10, 70, 21, 81, 33, 93, 45, 105, 55, 115, 46, 106, 34, 94, 22, 82, 11, 71)(6, 66, 15, 75, 27, 87, 39, 99, 50, 110, 58, 118, 51, 111, 40, 100, 28, 88, 16, 76)(9, 69, 19, 79, 31, 91, 43, 103, 53, 113, 59, 119, 54, 114, 44, 104, 32, 92, 20, 80)(14, 74, 25, 85, 37, 97, 48, 108, 56, 116, 60, 120, 57, 117, 49, 109, 38, 98, 26, 86)(121, 122)(123, 129)(124, 128)(125, 127)(126, 134)(130, 140)(131, 139)(132, 138)(133, 137)(135, 146)(136, 145)(141, 152)(142, 151)(143, 150)(144, 149)(147, 158)(148, 157)(153, 164)(154, 163)(155, 162)(156, 161)(159, 169)(160, 168)(165, 174)(166, 173)(167, 172)(170, 177)(171, 176)(175, 179)(178, 180)(181, 183)(182, 186)(184, 191)(185, 190)(187, 196)(188, 195)(189, 194)(192, 202)(193, 201)(197, 208)(198, 207)(199, 206)(200, 205)(203, 214)(204, 213)(209, 220)(210, 219)(211, 218)(212, 217)(215, 226)(216, 225)(221, 231)(222, 230)(223, 229)(224, 228)(227, 235)(232, 238)(233, 237)(234, 236)(239, 240)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 120, 120 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1309
Graph:: simple bipartite
	v = 66 e = 120 f = 2
	degree seq :: [ 2^60, 20^6 ]

E27.1304 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: edge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2 * Y3^2 * Y1 * Y2 * Y1, Y3^10, (Y3 * Y1 * Y2)^30 ]
Map::
	R = (1, 61, 4, 64, 12, 72, 24, 84, 37, 97, 49, 109, 38, 98, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 43, 103, 54, 114, 44, 104, 32, 92, 18, 78, 8, 68)(3, 63, 10, 70, 22, 82, 35, 95, 47, 107, 57, 117, 48, 108, 36, 96, 23, 83, 11, 71)(6, 66, 15, 75, 29, 89, 41, 101, 52, 112, 60, 120, 53, 113, 42, 102, 30, 90, 16, 76)(9, 69, 20, 80, 34, 94, 46, 106, 56, 116, 58, 118, 50, 110, 39, 99, 26, 86, 21, 81)(14, 74, 27, 87, 40, 100, 51, 111, 59, 119, 55, 115, 45, 105, 33, 93, 19, 79, 28, 88)(121, 122)(123, 129)(124, 128)(125, 127)(126, 134)(130, 141)(131, 140)(132, 138)(133, 137)(135, 148)(136, 147)(139, 149)(142, 146)(143, 154)(144, 152)(145, 151)(150, 160)(153, 161)(155, 159)(156, 166)(157, 164)(158, 163)(162, 171)(165, 172)(167, 170)(168, 176)(169, 174)(173, 179)(175, 180)(177, 178)(181, 183)(182, 186)(184, 191)(185, 190)(187, 196)(188, 195)(189, 199)(192, 203)(193, 202)(194, 206)(197, 210)(198, 209)(200, 213)(201, 208)(204, 216)(205, 215)(207, 219)(211, 222)(212, 221)(214, 225)(217, 228)(218, 227)(220, 230)(223, 233)(224, 232)(226, 235)(229, 237)(231, 238)(234, 240)(236, 239)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 120, 120 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1310
Graph:: simple bipartite
	v = 66 e = 120 f = 2
	degree seq :: [ 2^60, 20^6 ]

E27.1305 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: edge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^8 * Y1 * Y3^-2 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ]
Map::
	R = (1, 61, 4, 64, 12, 72, 23, 83, 35, 95, 47, 107, 56, 116, 44, 104, 32, 92, 20, 80, 9, 69, 19, 79, 31, 91, 43, 103, 55, 115, 60, 120, 52, 112, 40, 100, 28, 88, 16, 76, 6, 66, 15, 75, 27, 87, 39, 99, 51, 111, 48, 108, 36, 96, 24, 84, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 29, 89, 41, 101, 53, 113, 59, 119, 50, 110, 38, 98, 26, 86, 14, 74, 25, 85, 37, 97, 49, 109, 58, 118, 57, 117, 46, 106, 34, 94, 22, 82, 11, 71, 3, 63, 10, 70, 21, 81, 33, 93, 45, 105, 54, 114, 42, 102, 30, 90, 18, 78, 8, 68)(121, 122)(123, 129)(124, 128)(125, 127)(126, 134)(130, 140)(131, 139)(132, 138)(133, 137)(135, 146)(136, 145)(141, 152)(142, 151)(143, 150)(144, 149)(147, 158)(148, 157)(153, 164)(154, 163)(155, 162)(156, 161)(159, 170)(160, 169)(165, 176)(166, 175)(167, 174)(168, 173)(171, 179)(172, 178)(177, 180)(181, 183)(182, 186)(184, 191)(185, 190)(187, 196)(188, 195)(189, 194)(192, 202)(193, 201)(197, 208)(198, 207)(199, 206)(200, 205)(203, 214)(204, 213)(209, 220)(210, 219)(211, 218)(212, 217)(215, 226)(216, 225)(221, 232)(222, 231)(223, 230)(224, 229)(227, 237)(228, 234)(233, 240)(235, 239)(236, 238)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 40 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1307
Graph:: simple bipartite
	v = 62 e = 120 f = 6
	degree seq :: [ 2^60, 60^2 ]

E27.1306 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 10, 30})
Quotient :: edge^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y1, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ]
Map::
	R = (1, 61, 4, 64, 12, 72, 21, 81, 9, 69, 20, 80, 30, 90, 37, 97, 27, 87, 36, 96, 46, 106, 53, 113, 43, 103, 52, 112, 55, 115, 60, 120, 58, 118, 49, 109, 39, 99, 48, 108, 42, 102, 33, 93, 23, 83, 32, 92, 26, 86, 16, 76, 6, 66, 15, 75, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 25, 85, 14, 74, 24, 84, 34, 94, 41, 101, 31, 91, 40, 100, 50, 110, 57, 117, 47, 107, 56, 116, 51, 111, 59, 119, 54, 114, 45, 105, 35, 95, 44, 104, 38, 98, 29, 89, 19, 79, 28, 88, 22, 82, 11, 71, 3, 63, 10, 70, 18, 78, 8, 68)(121, 122)(123, 129)(124, 128)(125, 127)(126, 134)(130, 141)(131, 140)(132, 138)(133, 137)(135, 145)(136, 144)(139, 147)(142, 150)(143, 151)(146, 154)(148, 157)(149, 156)(152, 161)(153, 160)(155, 163)(158, 166)(159, 167)(162, 170)(164, 173)(165, 172)(168, 177)(169, 176)(171, 178)(174, 175)(179, 180)(181, 183)(182, 186)(184, 191)(185, 190)(187, 196)(188, 195)(189, 199)(192, 202)(193, 198)(194, 203)(197, 206)(200, 209)(201, 208)(204, 213)(205, 212)(207, 215)(210, 218)(211, 219)(214, 222)(216, 225)(217, 224)(220, 229)(221, 228)(223, 231)(226, 234)(227, 235)(230, 238)(232, 236)(233, 239)(237, 240)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 40 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1308
Graph:: simple bipartite
	v = 62 e = 120 f = 6
	degree seq :: [ 2^60, 60^2 ]

E27.1307 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 10, 30})
Quotient :: loop^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^10, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 23, 83, 143, 203, 35, 95, 155, 215, 47, 107, 167, 227, 36, 96, 156, 216, 24, 84, 144, 204, 13, 73, 133, 193, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 17, 77, 137, 197, 29, 89, 149, 209, 41, 101, 161, 221, 52, 112, 172, 232, 42, 102, 162, 222, 30, 90, 150, 210, 18, 78, 138, 198, 8, 68, 128, 188)(3, 63, 123, 183, 10, 70, 130, 190, 21, 81, 141, 201, 33, 93, 153, 213, 45, 105, 165, 225, 55, 115, 175, 235, 46, 106, 166, 226, 34, 94, 154, 214, 22, 82, 142, 202, 11, 71, 131, 191)(6, 66, 126, 186, 15, 75, 135, 195, 27, 87, 147, 207, 39, 99, 159, 219, 50, 110, 170, 230, 58, 118, 178, 238, 51, 111, 171, 231, 40, 100, 160, 220, 28, 88, 148, 208, 16, 76, 136, 196)(9, 69, 129, 189, 19, 79, 139, 199, 31, 91, 151, 211, 43, 103, 163, 223, 53, 113, 173, 233, 59, 119, 179, 239, 54, 114, 174, 234, 44, 104, 164, 224, 32, 92, 152, 212, 20, 80, 140, 200)(14, 74, 134, 194, 25, 85, 145, 205, 37, 97, 157, 217, 48, 108, 168, 228, 56, 116, 176, 236, 60, 120, 180, 240, 57, 117, 177, 237, 49, 109, 169, 229, 38, 98, 158, 218, 26, 86, 146, 206)
	L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 74)(7, 65)(8, 64)(9, 63)(10, 80)(11, 79)(12, 78)(13, 77)(14, 66)(15, 86)(16, 85)(17, 73)(18, 72)(19, 71)(20, 70)(21, 92)(22, 91)(23, 90)(24, 89)(25, 76)(26, 75)(27, 98)(28, 97)(29, 84)(30, 83)(31, 82)(32, 81)(33, 104)(34, 103)(35, 102)(36, 101)(37, 88)(38, 87)(39, 109)(40, 108)(41, 96)(42, 95)(43, 94)(44, 93)(45, 114)(46, 113)(47, 112)(48, 100)(49, 99)(50, 117)(51, 116)(52, 107)(53, 106)(54, 105)(55, 119)(56, 111)(57, 110)(58, 120)(59, 115)(60, 118)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 196)(128, 195)(129, 194)(130, 185)(131, 184)(132, 202)(133, 201)(134, 189)(135, 188)(136, 187)(137, 208)(138, 207)(139, 206)(140, 205)(141, 193)(142, 192)(143, 214)(144, 213)(145, 200)(146, 199)(147, 198)(148, 197)(149, 220)(150, 219)(151, 218)(152, 217)(153, 204)(154, 203)(155, 226)(156, 225)(157, 212)(158, 211)(159, 210)(160, 209)(161, 231)(162, 230)(163, 229)(164, 228)(165, 216)(166, 215)(167, 235)(168, 224)(169, 223)(170, 222)(171, 221)(172, 238)(173, 237)(174, 236)(175, 227)(176, 234)(177, 233)(178, 232)(179, 240)(180, 239)
	local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1305
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 120 f = 62
	degree seq :: [ 40^6 ]

E27.1308 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 10, 30})
Quotient :: loop^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2 * Y3^2 * Y1 * Y2 * Y1, Y3^10, (Y3 * Y1 * Y2)^30 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 24, 84, 144, 204, 37, 97, 157, 217, 49, 109, 169, 229, 38, 98, 158, 218, 25, 85, 145, 205, 13, 73, 133, 193, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 17, 77, 137, 197, 31, 91, 151, 211, 43, 103, 163, 223, 54, 114, 174, 234, 44, 104, 164, 224, 32, 92, 152, 212, 18, 78, 138, 198, 8, 68, 128, 188)(3, 63, 123, 183, 10, 70, 130, 190, 22, 82, 142, 202, 35, 95, 155, 215, 47, 107, 167, 227, 57, 117, 177, 237, 48, 108, 168, 228, 36, 96, 156, 216, 23, 83, 143, 203, 11, 71, 131, 191)(6, 66, 126, 186, 15, 75, 135, 195, 29, 89, 149, 209, 41, 101, 161, 221, 52, 112, 172, 232, 60, 120, 180, 240, 53, 113, 173, 233, 42, 102, 162, 222, 30, 90, 150, 210, 16, 76, 136, 196)(9, 69, 129, 189, 20, 80, 140, 200, 34, 94, 154, 214, 46, 106, 166, 226, 56, 116, 176, 236, 58, 118, 178, 238, 50, 110, 170, 230, 39, 99, 159, 219, 26, 86, 146, 206, 21, 81, 141, 201)(14, 74, 134, 194, 27, 87, 147, 207, 40, 100, 160, 220, 51, 111, 171, 231, 59, 119, 179, 239, 55, 115, 175, 235, 45, 105, 165, 225, 33, 93, 153, 213, 19, 79, 139, 199, 28, 88, 148, 208)
	L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 74)(7, 65)(8, 64)(9, 63)(10, 81)(11, 80)(12, 78)(13, 77)(14, 66)(15, 88)(16, 87)(17, 73)(18, 72)(19, 89)(20, 71)(21, 70)(22, 86)(23, 94)(24, 92)(25, 91)(26, 82)(27, 76)(28, 75)(29, 79)(30, 100)(31, 85)(32, 84)(33, 101)(34, 83)(35, 99)(36, 106)(37, 104)(38, 103)(39, 95)(40, 90)(41, 93)(42, 111)(43, 98)(44, 97)(45, 112)(46, 96)(47, 110)(48, 116)(49, 114)(50, 107)(51, 102)(52, 105)(53, 119)(54, 109)(55, 120)(56, 108)(57, 118)(58, 117)(59, 113)(60, 115)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 196)(128, 195)(129, 199)(130, 185)(131, 184)(132, 203)(133, 202)(134, 206)(135, 188)(136, 187)(137, 210)(138, 209)(139, 189)(140, 213)(141, 208)(142, 193)(143, 192)(144, 216)(145, 215)(146, 194)(147, 219)(148, 201)(149, 198)(150, 197)(151, 222)(152, 221)(153, 200)(154, 225)(155, 205)(156, 204)(157, 228)(158, 227)(159, 207)(160, 230)(161, 212)(162, 211)(163, 233)(164, 232)(165, 214)(166, 235)(167, 218)(168, 217)(169, 237)(170, 220)(171, 238)(172, 224)(173, 223)(174, 240)(175, 226)(176, 239)(177, 229)(178, 231)(179, 236)(180, 234)
	local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1306
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 120 f = 62
	degree seq :: [ 40^6 ]

E27.1309 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 10, 30})
Quotient :: loop^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^8 * Y1 * Y3^-2 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 23, 83, 143, 203, 35, 95, 155, 215, 47, 107, 167, 227, 56, 116, 176, 236, 44, 104, 164, 224, 32, 92, 152, 212, 20, 80, 140, 200, 9, 69, 129, 189, 19, 79, 139, 199, 31, 91, 151, 211, 43, 103, 163, 223, 55, 115, 175, 235, 60, 120, 180, 240, 52, 112, 172, 232, 40, 100, 160, 220, 28, 88, 148, 208, 16, 76, 136, 196, 6, 66, 126, 186, 15, 75, 135, 195, 27, 87, 147, 207, 39, 99, 159, 219, 51, 111, 171, 231, 48, 108, 168, 228, 36, 96, 156, 216, 24, 84, 144, 204, 13, 73, 133, 193, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 17, 77, 137, 197, 29, 89, 149, 209, 41, 101, 161, 221, 53, 113, 173, 233, 59, 119, 179, 239, 50, 110, 170, 230, 38, 98, 158, 218, 26, 86, 146, 206, 14, 74, 134, 194, 25, 85, 145, 205, 37, 97, 157, 217, 49, 109, 169, 229, 58, 118, 178, 238, 57, 117, 177, 237, 46, 106, 166, 226, 34, 94, 154, 214, 22, 82, 142, 202, 11, 71, 131, 191, 3, 63, 123, 183, 10, 70, 130, 190, 21, 81, 141, 201, 33, 93, 153, 213, 45, 105, 165, 225, 54, 114, 174, 234, 42, 102, 162, 222, 30, 90, 150, 210, 18, 78, 138, 198, 8, 68, 128, 188)
	L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 74)(7, 65)(8, 64)(9, 63)(10, 80)(11, 79)(12, 78)(13, 77)(14, 66)(15, 86)(16, 85)(17, 73)(18, 72)(19, 71)(20, 70)(21, 92)(22, 91)(23, 90)(24, 89)(25, 76)(26, 75)(27, 98)(28, 97)(29, 84)(30, 83)(31, 82)(32, 81)(33, 104)(34, 103)(35, 102)(36, 101)(37, 88)(38, 87)(39, 110)(40, 109)(41, 96)(42, 95)(43, 94)(44, 93)(45, 116)(46, 115)(47, 114)(48, 113)(49, 100)(50, 99)(51, 119)(52, 118)(53, 108)(54, 107)(55, 106)(56, 105)(57, 120)(58, 112)(59, 111)(60, 117)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 196)(128, 195)(129, 194)(130, 185)(131, 184)(132, 202)(133, 201)(134, 189)(135, 188)(136, 187)(137, 208)(138, 207)(139, 206)(140, 205)(141, 193)(142, 192)(143, 214)(144, 213)(145, 200)(146, 199)(147, 198)(148, 197)(149, 220)(150, 219)(151, 218)(152, 217)(153, 204)(154, 203)(155, 226)(156, 225)(157, 212)(158, 211)(159, 210)(160, 209)(161, 232)(162, 231)(163, 230)(164, 229)(165, 216)(166, 215)(167, 237)(168, 234)(169, 224)(170, 223)(171, 222)(172, 221)(173, 240)(174, 228)(175, 239)(176, 238)(177, 227)(178, 236)(179, 235)(180, 233)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1303
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 120 f = 66
	degree seq :: [ 120^2 ]

E27.1310 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 10, 30})
Quotient :: loop^2
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y1, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y3^-2 * Y1 * Y2 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 12, 72, 132, 192, 21, 81, 141, 201, 9, 69, 129, 189, 20, 80, 140, 200, 30, 90, 150, 210, 37, 97, 157, 217, 27, 87, 147, 207, 36, 96, 156, 216, 46, 106, 166, 226, 53, 113, 173, 233, 43, 103, 163, 223, 52, 112, 172, 232, 55, 115, 175, 235, 60, 120, 180, 240, 58, 118, 178, 238, 49, 109, 169, 229, 39, 99, 159, 219, 48, 108, 168, 228, 42, 102, 162, 222, 33, 93, 153, 213, 23, 83, 143, 203, 32, 92, 152, 212, 26, 86, 146, 206, 16, 76, 136, 196, 6, 66, 126, 186, 15, 75, 135, 195, 13, 73, 133, 193, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 17, 77, 137, 197, 25, 85, 145, 205, 14, 74, 134, 194, 24, 84, 144, 204, 34, 94, 154, 214, 41, 101, 161, 221, 31, 91, 151, 211, 40, 100, 160, 220, 50, 110, 170, 230, 57, 117, 177, 237, 47, 107, 167, 227, 56, 116, 176, 236, 51, 111, 171, 231, 59, 119, 179, 239, 54, 114, 174, 234, 45, 105, 165, 225, 35, 95, 155, 215, 44, 104, 164, 224, 38, 98, 158, 218, 29, 89, 149, 209, 19, 79, 139, 199, 28, 88, 148, 208, 22, 82, 142, 202, 11, 71, 131, 191, 3, 63, 123, 183, 10, 70, 130, 190, 18, 78, 138, 198, 8, 68, 128, 188)
	L = (1, 62)(2, 61)(3, 69)(4, 68)(5, 67)(6, 74)(7, 65)(8, 64)(9, 63)(10, 81)(11, 80)(12, 78)(13, 77)(14, 66)(15, 85)(16, 84)(17, 73)(18, 72)(19, 87)(20, 71)(21, 70)(22, 90)(23, 91)(24, 76)(25, 75)(26, 94)(27, 79)(28, 97)(29, 96)(30, 82)(31, 83)(32, 101)(33, 100)(34, 86)(35, 103)(36, 89)(37, 88)(38, 106)(39, 107)(40, 93)(41, 92)(42, 110)(43, 95)(44, 113)(45, 112)(46, 98)(47, 99)(48, 117)(49, 116)(50, 102)(51, 118)(52, 105)(53, 104)(54, 115)(55, 114)(56, 109)(57, 108)(58, 111)(59, 120)(60, 119)(121, 183)(122, 186)(123, 181)(124, 191)(125, 190)(126, 182)(127, 196)(128, 195)(129, 199)(130, 185)(131, 184)(132, 202)(133, 198)(134, 203)(135, 188)(136, 187)(137, 206)(138, 193)(139, 189)(140, 209)(141, 208)(142, 192)(143, 194)(144, 213)(145, 212)(146, 197)(147, 215)(148, 201)(149, 200)(150, 218)(151, 219)(152, 205)(153, 204)(154, 222)(155, 207)(156, 225)(157, 224)(158, 210)(159, 211)(160, 229)(161, 228)(162, 214)(163, 231)(164, 217)(165, 216)(166, 234)(167, 235)(168, 221)(169, 220)(170, 238)(171, 223)(172, 236)(173, 239)(174, 226)(175, 227)(176, 232)(177, 240)(178, 230)(179, 233)(180, 237)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1304
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 120 f = 66
	degree seq :: [ 120^2 ]

E27.1311 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y3, Y2), (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y2^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 21, 81)(12, 72, 22, 82)(13, 73, 20, 80)(14, 74, 19, 79)(15, 75, 17, 77)(16, 76, 18, 78)(23, 83, 33, 93)(24, 84, 34, 94)(25, 85, 32, 92)(26, 86, 31, 91)(27, 87, 29, 89)(28, 88, 30, 90)(35, 95, 45, 105)(36, 96, 46, 106)(37, 97, 44, 104)(38, 98, 43, 103)(39, 99, 41, 101)(40, 100, 42, 102)(47, 107, 52, 112)(48, 108, 56, 116)(49, 109, 55, 115)(50, 110, 54, 114)(51, 111, 53, 113)(57, 117, 60, 120)(58, 118, 59, 119)(121, 181, 123, 183, 131, 191, 143, 203, 155, 215, 167, 227, 159, 219, 147, 207, 135, 195, 125, 185)(122, 182, 127, 187, 137, 197, 149, 209, 161, 221, 172, 232, 165, 225, 153, 213, 141, 201, 129, 189)(124, 184, 132, 192, 144, 204, 156, 216, 168, 228, 177, 237, 170, 230, 158, 218, 146, 206, 134, 194)(126, 186, 133, 193, 145, 205, 157, 217, 169, 229, 178, 238, 171, 231, 160, 220, 148, 208, 136, 196)(128, 188, 138, 198, 150, 210, 162, 222, 173, 233, 179, 239, 175, 235, 164, 224, 152, 212, 140, 200)(130, 190, 139, 199, 151, 211, 163, 223, 174, 234, 180, 240, 176, 236, 166, 226, 154, 214, 142, 202)
	L = (1, 124)(2, 128)(3, 132)(4, 126)(5, 134)(6, 121)(7, 138)(8, 130)(9, 140)(10, 122)(11, 144)(12, 133)(13, 123)(14, 136)(15, 146)(16, 125)(17, 150)(18, 139)(19, 127)(20, 142)(21, 152)(22, 129)(23, 156)(24, 145)(25, 131)(26, 148)(27, 158)(28, 135)(29, 162)(30, 151)(31, 137)(32, 154)(33, 164)(34, 141)(35, 168)(36, 157)(37, 143)(38, 160)(39, 170)(40, 147)(41, 173)(42, 163)(43, 149)(44, 166)(45, 175)(46, 153)(47, 177)(48, 169)(49, 155)(50, 171)(51, 159)(52, 179)(53, 174)(54, 161)(55, 176)(56, 165)(57, 178)(58, 167)(59, 180)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1315
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1312 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^-2 * Y3^3, Y2^10, Y2^20 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 23, 83)(14, 74, 26, 86)(15, 75, 21, 81)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 22, 82)(27, 87, 36, 96)(28, 88, 37, 97)(29, 89, 38, 98)(30, 90, 33, 93)(31, 91, 34, 94)(32, 92, 35, 95)(39, 99, 48, 108)(40, 100, 49, 109)(41, 101, 50, 110)(42, 102, 45, 105)(43, 103, 46, 106)(44, 104, 47, 107)(51, 111, 56, 116)(52, 112, 59, 119)(53, 113, 60, 120)(54, 114, 57, 117)(55, 115, 58, 118)(121, 181, 123, 183, 131, 191, 147, 207, 159, 219, 171, 231, 162, 222, 150, 210, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 153, 213, 165, 225, 176, 236, 168, 228, 156, 216, 144, 204, 129, 189)(124, 184, 132, 192, 148, 208, 160, 220, 172, 232, 175, 235, 164, 224, 152, 212, 138, 198, 135, 195)(126, 186, 133, 193, 134, 194, 149, 209, 161, 221, 173, 233, 174, 234, 163, 223, 151, 211, 137, 197)(128, 188, 140, 200, 154, 214, 166, 226, 177, 237, 180, 240, 170, 230, 158, 218, 146, 206, 143, 203)(130, 190, 141, 201, 142, 202, 155, 215, 167, 227, 178, 238, 179, 239, 169, 229, 157, 217, 145, 205)
	L = (1, 124)(2, 128)(3, 132)(4, 134)(5, 135)(6, 121)(7, 140)(8, 142)(9, 143)(10, 122)(11, 148)(12, 149)(13, 123)(14, 131)(15, 133)(16, 138)(17, 125)(18, 126)(19, 154)(20, 155)(21, 127)(22, 139)(23, 141)(24, 146)(25, 129)(26, 130)(27, 160)(28, 161)(29, 147)(30, 152)(31, 136)(32, 137)(33, 166)(34, 167)(35, 153)(36, 158)(37, 144)(38, 145)(39, 172)(40, 173)(41, 159)(42, 164)(43, 150)(44, 151)(45, 177)(46, 178)(47, 165)(48, 170)(49, 156)(50, 157)(51, 175)(52, 174)(53, 171)(54, 162)(55, 163)(56, 180)(57, 179)(58, 176)(59, 168)(60, 169)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1316
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1313 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y3^3 * Y2^4, Y2^2 * Y3^-6 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 23, 83)(14, 74, 26, 86)(15, 75, 21, 81)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 22, 82)(27, 87, 47, 107)(28, 88, 48, 108)(29, 89, 46, 106)(30, 90, 49, 109)(31, 91, 45, 105)(32, 92, 50, 110)(33, 93, 43, 103)(34, 94, 41, 101)(35, 95, 39, 99)(36, 96, 40, 100)(37, 97, 42, 102)(38, 98, 44, 104)(51, 111, 60, 120)(52, 112, 59, 119)(53, 113, 58, 118)(54, 114, 57, 117)(55, 115, 56, 116)(121, 181, 123, 183, 131, 191, 147, 207, 158, 218, 173, 233, 152, 212, 155, 215, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 159, 219, 170, 230, 178, 238, 164, 224, 167, 227, 144, 204, 129, 189)(124, 184, 132, 192, 148, 208, 157, 217, 138, 198, 151, 211, 172, 232, 175, 235, 154, 214, 135, 195)(126, 186, 133, 193, 149, 209, 171, 231, 174, 234, 153, 213, 134, 194, 150, 210, 156, 216, 137, 197)(128, 188, 140, 200, 160, 220, 169, 229, 146, 206, 163, 223, 177, 237, 180, 240, 166, 226, 143, 203)(130, 190, 141, 201, 161, 221, 176, 236, 179, 239, 165, 225, 142, 202, 162, 222, 168, 228, 145, 205)
	L = (1, 124)(2, 128)(3, 132)(4, 134)(5, 135)(6, 121)(7, 140)(8, 142)(9, 143)(10, 122)(11, 148)(12, 150)(13, 123)(14, 152)(15, 153)(16, 154)(17, 125)(18, 126)(19, 160)(20, 162)(21, 127)(22, 164)(23, 165)(24, 166)(25, 129)(26, 130)(27, 157)(28, 156)(29, 131)(30, 155)(31, 133)(32, 172)(33, 173)(34, 174)(35, 175)(36, 136)(37, 137)(38, 138)(39, 169)(40, 168)(41, 139)(42, 167)(43, 141)(44, 177)(45, 178)(46, 179)(47, 180)(48, 144)(49, 145)(50, 146)(51, 147)(52, 149)(53, 151)(54, 158)(55, 171)(56, 159)(57, 161)(58, 163)(59, 170)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1318
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1314 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, (R * Y3)^2, Y2^4 * Y3^-3, Y2^2 * Y3^6, Y2^2 * Y3^6 ]
Map:: non-degenerate
	R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 23, 83)(14, 74, 26, 86)(15, 75, 21, 81)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 22, 82)(27, 87, 47, 107)(28, 88, 48, 108)(29, 89, 46, 106)(30, 90, 49, 109)(31, 91, 45, 105)(32, 92, 50, 110)(33, 93, 43, 103)(34, 94, 41, 101)(35, 95, 39, 99)(36, 96, 40, 100)(37, 97, 42, 102)(38, 98, 44, 104)(51, 111, 60, 120)(52, 112, 59, 119)(53, 113, 58, 118)(54, 114, 57, 117)(55, 115, 56, 116)(121, 181, 123, 183, 131, 191, 147, 207, 152, 212, 173, 233, 158, 218, 155, 215, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 159, 219, 164, 224, 178, 238, 170, 230, 167, 227, 144, 204, 129, 189)(124, 184, 132, 192, 148, 208, 171, 231, 174, 234, 157, 217, 138, 198, 151, 211, 154, 214, 135, 195)(126, 186, 133, 193, 149, 209, 153, 213, 134, 194, 150, 210, 172, 232, 175, 235, 156, 216, 137, 197)(128, 188, 140, 200, 160, 220, 176, 236, 179, 239, 169, 229, 146, 206, 163, 223, 166, 226, 143, 203)(130, 190, 141, 201, 161, 221, 165, 225, 142, 202, 162, 222, 177, 237, 180, 240, 168, 228, 145, 205)
	L = (1, 124)(2, 128)(3, 132)(4, 134)(5, 135)(6, 121)(7, 140)(8, 142)(9, 143)(10, 122)(11, 148)(12, 150)(13, 123)(14, 152)(15, 153)(16, 154)(17, 125)(18, 126)(19, 160)(20, 162)(21, 127)(22, 164)(23, 165)(24, 166)(25, 129)(26, 130)(27, 171)(28, 172)(29, 131)(30, 173)(31, 133)(32, 174)(33, 147)(34, 149)(35, 151)(36, 136)(37, 137)(38, 138)(39, 176)(40, 177)(41, 139)(42, 178)(43, 141)(44, 179)(45, 159)(46, 161)(47, 163)(48, 144)(49, 145)(50, 146)(51, 175)(52, 158)(53, 157)(54, 156)(55, 155)(56, 180)(57, 170)(58, 169)(59, 168)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 60, 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1317
Graph:: simple bipartite
	v = 36 e = 120 f = 32
	degree seq :: [ 4^30, 20^6 ]

E27.1315 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^10, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 7, 67, 17, 77, 29, 89, 41, 101, 52, 112, 40, 100, 28, 88, 16, 76, 6, 66, 10, 70, 20, 80, 32, 92, 44, 104, 54, 114, 50, 110, 38, 98, 26, 86, 14, 74, 4, 64, 9, 69, 19, 79, 31, 91, 43, 103, 51, 111, 39, 99, 27, 87, 15, 75, 5, 65)(3, 63, 11, 71, 23, 83, 35, 95, 47, 107, 57, 117, 56, 116, 46, 106, 34, 94, 22, 82, 13, 73, 25, 85, 37, 97, 49, 109, 59, 119, 60, 120, 55, 115, 45, 105, 33, 93, 21, 81, 12, 72, 24, 84, 36, 96, 48, 108, 58, 118, 53, 113, 42, 102, 30, 90, 18, 78, 8, 68)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 138, 198)(129, 189, 142, 202)(130, 190, 141, 201)(134, 194, 145, 205)(135, 195, 143, 203)(136, 196, 144, 204)(137, 197, 150, 210)(139, 199, 154, 214)(140, 200, 153, 213)(146, 206, 157, 217)(147, 207, 155, 215)(148, 208, 156, 216)(149, 209, 162, 222)(151, 211, 166, 226)(152, 212, 165, 225)(158, 218, 169, 229)(159, 219, 167, 227)(160, 220, 168, 228)(161, 221, 173, 233)(163, 223, 176, 236)(164, 224, 175, 235)(170, 230, 179, 239)(171, 231, 177, 237)(172, 232, 178, 238)(174, 234, 180, 240)
	L = (1, 124)(2, 129)(3, 132)(4, 126)(5, 134)(6, 121)(7, 139)(8, 141)(9, 130)(10, 122)(11, 144)(12, 133)(13, 123)(14, 136)(15, 146)(16, 125)(17, 151)(18, 153)(19, 140)(20, 127)(21, 142)(22, 128)(23, 156)(24, 145)(25, 131)(26, 148)(27, 158)(28, 135)(29, 163)(30, 165)(31, 152)(32, 137)(33, 154)(34, 138)(35, 168)(36, 157)(37, 143)(38, 160)(39, 170)(40, 147)(41, 171)(42, 175)(43, 164)(44, 149)(45, 166)(46, 150)(47, 178)(48, 169)(49, 155)(50, 172)(51, 174)(52, 159)(53, 180)(54, 161)(55, 176)(56, 162)(57, 173)(58, 179)(59, 167)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1311
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1316 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3, (Y2 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^15, (Y3^-1 * Y1^-1)^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 4, 64, 8, 68, 12, 72, 16, 76, 20, 80, 24, 84, 28, 88, 32, 92, 36, 96, 40, 100, 44, 104, 48, 108, 52, 112, 56, 116, 54, 114, 53, 113, 46, 106, 45, 105, 38, 98, 37, 97, 30, 90, 29, 89, 22, 82, 21, 81, 14, 74, 13, 73, 6, 66, 5, 65)(3, 63, 9, 69, 10, 70, 17, 77, 18, 78, 25, 85, 26, 86, 33, 93, 34, 94, 41, 101, 42, 102, 49, 109, 50, 110, 57, 117, 58, 118, 60, 120, 59, 119, 55, 115, 51, 111, 47, 107, 43, 103, 39, 99, 35, 95, 31, 91, 27, 87, 23, 83, 19, 79, 15, 75, 11, 71, 7, 67)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 131, 191)(125, 185, 129, 189)(126, 186, 130, 190)(128, 188, 135, 195)(132, 192, 139, 199)(133, 193, 137, 197)(134, 194, 138, 198)(136, 196, 143, 203)(140, 200, 147, 207)(141, 201, 145, 205)(142, 202, 146, 206)(144, 204, 151, 211)(148, 208, 155, 215)(149, 209, 153, 213)(150, 210, 154, 214)(152, 212, 159, 219)(156, 216, 163, 223)(157, 217, 161, 221)(158, 218, 162, 222)(160, 220, 167, 227)(164, 224, 171, 231)(165, 225, 169, 229)(166, 226, 170, 230)(168, 228, 175, 235)(172, 232, 179, 239)(173, 233, 177, 237)(174, 234, 178, 238)(176, 236, 180, 240)
	L = (1, 124)(2, 128)(3, 130)(4, 132)(5, 122)(6, 121)(7, 129)(8, 136)(9, 137)(10, 138)(11, 123)(12, 140)(13, 125)(14, 126)(15, 127)(16, 144)(17, 145)(18, 146)(19, 131)(20, 148)(21, 133)(22, 134)(23, 135)(24, 152)(25, 153)(26, 154)(27, 139)(28, 156)(29, 141)(30, 142)(31, 143)(32, 160)(33, 161)(34, 162)(35, 147)(36, 164)(37, 149)(38, 150)(39, 151)(40, 168)(41, 169)(42, 170)(43, 155)(44, 172)(45, 157)(46, 158)(47, 159)(48, 176)(49, 177)(50, 178)(51, 163)(52, 174)(53, 165)(54, 166)(55, 167)(56, 173)(57, 180)(58, 179)(59, 171)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1312
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1317 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-6 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 7, 67, 17, 77, 6, 66, 10, 70, 20, 80, 33, 93, 18, 78, 24, 84, 36, 96, 49, 109, 34, 94, 40, 100, 46, 106, 54, 114, 50, 110, 47, 107, 30, 90, 39, 99, 48, 108, 31, 91, 14, 74, 23, 83, 32, 92, 15, 75, 4, 64, 9, 69, 16, 76, 5, 65)(3, 63, 11, 71, 25, 85, 22, 82, 13, 73, 27, 87, 41, 101, 38, 98, 29, 89, 43, 103, 55, 115, 53, 113, 45, 105, 57, 117, 58, 118, 60, 120, 59, 119, 52, 112, 44, 104, 56, 116, 51, 111, 37, 97, 28, 88, 42, 102, 35, 95, 21, 81, 12, 72, 26, 86, 19, 79, 8, 68)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 139, 199)(129, 189, 142, 202)(130, 190, 141, 201)(134, 194, 149, 209)(135, 195, 147, 207)(136, 196, 145, 205)(137, 197, 146, 206)(138, 198, 148, 208)(140, 200, 155, 215)(143, 203, 158, 218)(144, 204, 157, 217)(150, 210, 165, 225)(151, 211, 163, 223)(152, 212, 161, 221)(153, 213, 162, 222)(154, 214, 164, 224)(156, 216, 171, 231)(159, 219, 173, 233)(160, 220, 172, 232)(166, 226, 179, 239)(167, 227, 177, 237)(168, 228, 175, 235)(169, 229, 176, 236)(170, 230, 178, 238)(174, 234, 180, 240)
	L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 136)(8, 141)(9, 143)(10, 122)(11, 146)(12, 148)(13, 123)(14, 150)(15, 151)(16, 152)(17, 125)(18, 126)(19, 155)(20, 127)(21, 157)(22, 128)(23, 159)(24, 130)(25, 139)(26, 162)(27, 131)(28, 164)(29, 133)(30, 166)(31, 167)(32, 168)(33, 137)(34, 138)(35, 171)(36, 140)(37, 172)(38, 142)(39, 174)(40, 144)(41, 145)(42, 176)(43, 147)(44, 178)(45, 149)(46, 156)(47, 160)(48, 170)(49, 153)(50, 154)(51, 179)(52, 177)(53, 158)(54, 169)(55, 161)(56, 180)(57, 163)(58, 175)(59, 165)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1314
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1318 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 10, 30})
Quotient :: dipole
Aut^+ = D60 (small group id <60, 12>)
Aut   = C2 x C2 x D30 (small group id <120, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-3 * Y1, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y1^-3 * Y3^-2 * Y1^-1, (Y1^-1 * Y3^-1)^10 ]
Map:: non-degenerate
	R = (1, 61, 2, 62, 7, 67, 19, 79, 36, 96, 49, 109, 32, 92, 15, 75, 4, 64, 9, 69, 21, 81, 38, 98, 52, 112, 35, 95, 18, 78, 26, 86, 14, 74, 25, 85, 42, 102, 51, 111, 34, 94, 17, 77, 6, 66, 10, 70, 22, 82, 39, 99, 50, 110, 33, 93, 16, 76, 5, 65)(3, 63, 11, 71, 27, 87, 45, 105, 57, 117, 54, 114, 40, 100, 23, 83, 12, 72, 28, 88, 46, 106, 58, 118, 56, 116, 44, 104, 31, 91, 43, 103, 30, 90, 48, 108, 60, 120, 55, 115, 41, 101, 24, 84, 13, 73, 29, 89, 47, 107, 59, 119, 53, 113, 37, 97, 20, 80, 8, 68)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 144, 204)(130, 190, 143, 203)(134, 194, 151, 211)(135, 195, 149, 209)(136, 196, 147, 207)(137, 197, 148, 208)(138, 198, 150, 210)(139, 199, 157, 217)(141, 201, 161, 221)(142, 202, 160, 220)(145, 205, 164, 224)(146, 206, 163, 223)(152, 212, 167, 227)(153, 213, 165, 225)(154, 214, 166, 226)(155, 215, 168, 228)(156, 216, 173, 233)(158, 218, 175, 235)(159, 219, 174, 234)(162, 222, 176, 236)(169, 229, 179, 239)(170, 230, 177, 237)(171, 231, 178, 238)(172, 232, 180, 240)
	L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 141)(8, 143)(9, 145)(10, 122)(11, 148)(12, 150)(13, 123)(14, 142)(15, 146)(16, 152)(17, 125)(18, 126)(19, 158)(20, 160)(21, 162)(22, 127)(23, 163)(24, 128)(25, 159)(26, 130)(27, 166)(28, 168)(29, 131)(30, 167)(31, 133)(32, 138)(33, 169)(34, 136)(35, 137)(36, 172)(37, 174)(38, 171)(39, 139)(40, 151)(41, 140)(42, 170)(43, 149)(44, 144)(45, 178)(46, 180)(47, 147)(48, 179)(49, 155)(50, 156)(51, 153)(52, 154)(53, 177)(54, 164)(55, 157)(56, 161)(57, 176)(58, 175)(59, 165)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1313
Graph:: bipartite
	v = 32 e = 120 f = 36
	degree seq :: [ 4^30, 60^2 ]

E27.1319 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {20, 20, 30})
Quotient :: edge
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^-2 * T2^-1 * T1^2 * T2, T1 * T2^-2 * T1^-1 * T2^2, T2^4 * T1^-1 * T2^2 * T1^-1, T2^-1 * T1^-2 * T2^-1 * T1^-4, T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1^-3 * T2^-2, T2^-2 * T1^14 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 44, 20, 6, 19, 42, 56, 60, 54, 38, 34, 13, 32, 52, 37, 17, 5)(2, 7, 22, 45, 55, 40, 18, 39, 33, 50, 59, 53, 35, 14, 4, 12, 30, 48, 26, 8)(9, 27, 49, 57, 43, 25, 41, 23, 46, 58, 47, 24, 16, 21, 11, 31, 51, 36, 15, 28)(61, 62, 66, 78, 98, 95, 77, 86, 104, 115, 120, 119, 112, 90, 70, 82, 102, 93, 73, 64)(63, 69, 79, 101, 94, 76, 65, 75, 80, 103, 114, 107, 97, 111, 89, 109, 116, 106, 92, 71)(67, 81, 99, 88, 74, 85, 68, 84, 100, 96, 113, 117, 108, 118, 105, 91, 110, 87, 72, 83)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1326
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.1320 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {20, 20, 30})
Quotient :: edge
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^3, T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1, T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1 * T2^-2 * T1^3 * T2^-2, (T2 * T1^-1)^4, T1^20, T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 10, 13, 29, 52, 59, 45, 20, 44, 47, 21, 46, 58, 32, 49, 22, 48, 51, 23, 50, 60, 34, 56, 40, 43, 19, 6, 17, 5)(2, 7, 14, 4, 12, 31, 33, 57, 39, 53, 26, 9, 25, 30, 11, 28, 42, 55, 36, 15, 35, 38, 16, 37, 54, 27, 41, 18, 24, 8)(61, 62, 66, 78, 100, 114, 120, 98, 111, 96, 109, 88, 106, 85, 104, 113, 119, 93, 73, 64)(63, 69, 77, 99, 103, 91, 94, 74, 83, 68, 82, 101, 118, 97, 107, 95, 105, 115, 89, 71)(65, 75, 79, 102, 116, 90, 110, 86, 108, 117, 92, 72, 81, 67, 80, 84, 112, 87, 70, 76)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^20 ), ( 40^30 ) }
Outer automorphisms :: reflexible
Dual of E27.1325
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.1321 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {20, 20, 30})
Quotient :: edge
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2^-2, T1^-3 * T2 * T1^-1 * T2, T1 * T2^-4 * T1 * T2^2 * T1^2, T1^2 * T2^9 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 41, 53, 54, 42, 29, 13, 23, 22, 34, 36, 49, 60, 55, 43, 38, 24, 20, 6, 19, 35, 48, 59, 47, 33, 17, 5)(2, 7, 21, 37, 50, 56, 44, 30, 14, 4, 12, 9, 25, 39, 51, 58, 46, 32, 28, 15, 11, 18, 26, 40, 52, 57, 45, 31, 16, 8)(61, 62, 66, 78, 94, 85, 87, 97, 108, 112, 120, 118, 114, 104, 93, 91, 98, 88, 73, 64)(63, 69, 79, 81, 96, 100, 101, 111, 119, 116, 115, 105, 102, 92, 77, 74, 84, 68, 83, 71)(65, 75, 80, 72, 82, 67, 70, 86, 95, 99, 109, 110, 113, 117, 107, 106, 103, 90, 89, 76)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^20 ), ( 40^30 ) }
Outer automorphisms :: reflexible
Dual of E27.1324
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.1322 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {20, 20, 30})
Quotient :: edge
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2 * T1^2, T2 * T1^-2 * T2^-1 * T1^2, T2^-1 * T1^2 * T2^-8, T2^-1 * T1 * T2^-2 * T1^11 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 26, 39, 51, 48, 35, 20, 6, 19, 22, 36, 44, 56, 60, 49, 37, 34, 23, 21, 13, 29, 42, 54, 59, 47, 33, 17, 5)(2, 7, 11, 28, 43, 52, 58, 46, 32, 18, 16, 9, 25, 27, 41, 55, 57, 45, 31, 15, 14, 4, 12, 30, 40, 53, 50, 38, 24, 8)(61, 62, 66, 78, 94, 91, 93, 98, 108, 118, 120, 115, 114, 100, 86, 88, 96, 85, 73, 64)(63, 69, 79, 74, 83, 68, 77, 92, 95, 105, 109, 110, 119, 112, 99, 101, 104, 90, 89, 71)(65, 75, 80, 84, 97, 106, 107, 117, 111, 113, 116, 103, 102, 87, 70, 72, 82, 67, 81, 76)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^20 ), ( 40^30 ) }
Outer automorphisms :: reflexible
Dual of E27.1323
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 20^3, 30^2 ]

E27.1323 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {20, 20, 30})
Quotient :: loop
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^20, (T2^-1 * T1^-1)^30 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 6, 66, 15, 75, 22, 82, 29, 89, 34, 94, 41, 101, 46, 106, 53, 113, 58, 118, 56, 116, 49, 109, 44, 104, 37, 97, 32, 92, 25, 85, 20, 80, 11, 71, 5, 65)(2, 62, 7, 67, 14, 74, 23, 83, 28, 88, 35, 95, 40, 100, 47, 107, 52, 112, 59, 119, 55, 115, 50, 110, 43, 103, 38, 98, 31, 91, 26, 86, 19, 79, 12, 72, 4, 64, 8, 68)(9, 69, 16, 76, 24, 84, 30, 90, 36, 96, 42, 102, 48, 108, 54, 114, 60, 120, 57, 117, 51, 111, 45, 105, 39, 99, 33, 93, 27, 87, 21, 81, 13, 73, 18, 78, 10, 70, 17, 77)
	L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 70)(6, 74)(7, 76)(8, 77)(9, 75)(10, 63)(11, 64)(12, 78)(13, 65)(14, 82)(15, 84)(16, 83)(17, 67)(18, 68)(19, 71)(20, 73)(21, 72)(22, 88)(23, 90)(24, 89)(25, 79)(26, 81)(27, 80)(28, 94)(29, 96)(30, 95)(31, 85)(32, 87)(33, 86)(34, 100)(35, 102)(36, 101)(37, 91)(38, 93)(39, 92)(40, 106)(41, 108)(42, 107)(43, 97)(44, 99)(45, 98)(46, 112)(47, 114)(48, 113)(49, 103)(50, 105)(51, 104)(52, 118)(53, 120)(54, 119)(55, 109)(56, 111)(57, 110)(58, 115)(59, 117)(60, 116)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1322
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1324 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {20, 20, 30})
Quotient :: loop
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^-2 * T2^-1 * T1^2 * T2, T1 * T2^-2 * T1^-1 * T2^2, T2^4 * T1^-1 * T2^2 * T1^-1, T2^-1 * T1^-2 * T2^-1 * T1^-4, T2^-1 * T1 * T2^-1 * T1 * T2^-3 * T1^-3 * T2^-2, T2^-2 * T1^14 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 10, 70, 29, 89, 44, 104, 20, 80, 6, 66, 19, 79, 42, 102, 56, 116, 60, 120, 54, 114, 38, 98, 34, 94, 13, 73, 32, 92, 52, 112, 37, 97, 17, 77, 5, 65)(2, 62, 7, 67, 22, 82, 45, 105, 55, 115, 40, 100, 18, 78, 39, 99, 33, 93, 50, 110, 59, 119, 53, 113, 35, 95, 14, 74, 4, 64, 12, 72, 30, 90, 48, 108, 26, 86, 8, 68)(9, 69, 27, 87, 49, 109, 57, 117, 43, 103, 25, 85, 41, 101, 23, 83, 46, 106, 58, 118, 47, 107, 24, 84, 16, 76, 21, 81, 11, 71, 31, 91, 51, 111, 36, 96, 15, 75, 28, 88)
	L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 84)(9, 79)(10, 82)(11, 63)(12, 83)(13, 64)(14, 85)(15, 80)(16, 65)(17, 86)(18, 98)(19, 101)(20, 103)(21, 99)(22, 102)(23, 67)(24, 100)(25, 68)(26, 104)(27, 72)(28, 74)(29, 109)(30, 70)(31, 110)(32, 71)(33, 73)(34, 76)(35, 77)(36, 113)(37, 111)(38, 95)(39, 88)(40, 96)(41, 94)(42, 93)(43, 114)(44, 115)(45, 91)(46, 92)(47, 97)(48, 118)(49, 116)(50, 87)(51, 89)(52, 90)(53, 117)(54, 107)(55, 120)(56, 106)(57, 108)(58, 105)(59, 112)(60, 119)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1321
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1325 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {20, 20, 30})
Quotient :: loop
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^2 * T1 * T2^-2, T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2^-2 * T1 * T2^2, T1^-5 * T2^2 * T1^-1, T2^-6 * T1^-2 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 10, 70, 28, 88, 49, 109, 35, 95, 13, 73, 31, 91, 38, 98, 54, 114, 60, 120, 58, 118, 44, 104, 20, 80, 6, 66, 19, 79, 42, 102, 37, 97, 17, 77, 5, 65)(2, 62, 7, 67, 22, 82, 46, 106, 36, 96, 14, 74, 4, 64, 12, 72, 29, 89, 51, 111, 59, 119, 52, 112, 34, 94, 40, 100, 18, 78, 39, 99, 56, 116, 48, 108, 26, 86, 8, 68)(9, 69, 25, 85, 47, 107, 23, 83, 16, 76, 32, 92, 11, 71, 30, 90, 50, 110, 33, 93, 53, 113, 55, 115, 43, 103, 57, 117, 41, 101, 24, 84, 45, 105, 21, 81, 15, 75, 27, 87)
	L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 81)(8, 84)(9, 79)(10, 82)(11, 63)(12, 83)(13, 64)(14, 85)(15, 80)(16, 65)(17, 86)(18, 98)(19, 101)(20, 103)(21, 99)(22, 102)(23, 67)(24, 100)(25, 68)(26, 104)(27, 108)(28, 107)(29, 70)(30, 74)(31, 71)(32, 106)(33, 72)(34, 73)(35, 76)(36, 77)(37, 105)(38, 89)(39, 115)(40, 93)(41, 114)(42, 116)(43, 91)(44, 94)(45, 118)(46, 87)(47, 97)(48, 117)(49, 96)(50, 88)(51, 92)(52, 90)(53, 95)(54, 110)(55, 111)(56, 120)(57, 112)(58, 113)(59, 109)(60, 119)
	local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1320
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1326 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {20, 20, 30})
Quotient :: loop
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^3, T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1, T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1 * T2^-2 * T1^3 * T2^-2, (T2 * T1^-1)^4, T1^20, T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 10, 70, 13, 73, 29, 89, 52, 112, 59, 119, 45, 105, 20, 80, 44, 104, 47, 107, 21, 81, 46, 106, 58, 118, 32, 92, 49, 109, 22, 82, 48, 108, 51, 111, 23, 83, 50, 110, 60, 120, 34, 94, 56, 116, 40, 100, 43, 103, 19, 79, 6, 66, 17, 77, 5, 65)(2, 62, 7, 67, 14, 74, 4, 64, 12, 72, 31, 91, 33, 93, 57, 117, 39, 99, 53, 113, 26, 86, 9, 69, 25, 85, 30, 90, 11, 71, 28, 88, 42, 102, 55, 115, 36, 96, 15, 75, 35, 95, 38, 98, 16, 76, 37, 97, 54, 114, 27, 87, 41, 101, 18, 78, 24, 84, 8, 68)
	L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 75)(6, 78)(7, 80)(8, 82)(9, 77)(10, 76)(11, 63)(12, 81)(13, 64)(14, 83)(15, 79)(16, 65)(17, 99)(18, 100)(19, 102)(20, 84)(21, 67)(22, 101)(23, 68)(24, 112)(25, 104)(26, 108)(27, 70)(28, 106)(29, 71)(30, 110)(31, 94)(32, 72)(33, 73)(34, 74)(35, 105)(36, 109)(37, 107)(38, 111)(39, 103)(40, 114)(41, 118)(42, 116)(43, 91)(44, 113)(45, 115)(46, 85)(47, 95)(48, 117)(49, 88)(50, 86)(51, 96)(52, 87)(53, 119)(54, 120)(55, 89)(56, 90)(57, 92)(58, 97)(59, 93)(60, 98)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1319
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.1327 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y3 * Y2^2 * Y1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2 * Y3^3 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2, Y3^2 * Y2^2 * Y3^2 * Y1^-2, Y3^-1 * Y1^2 * Y3^-1 * Y1^16, Y3 * Y2^-2 * Y1^2 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 18, 78, 38, 98, 29, 89, 10, 70, 22, 82, 42, 102, 56, 116, 60, 120, 59, 119, 49, 109, 36, 96, 17, 77, 26, 86, 44, 104, 34, 94, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 41, 101, 54, 114, 50, 110, 28, 88, 47, 107, 37, 97, 45, 105, 58, 118, 53, 113, 35, 95, 16, 76, 5, 65, 15, 75, 20, 80, 43, 103, 31, 91, 11, 71)(7, 67, 21, 81, 39, 99, 55, 115, 51, 111, 32, 92, 46, 106, 27, 87, 48, 108, 57, 117, 52, 112, 30, 90, 14, 74, 25, 85, 8, 68, 24, 84, 40, 100, 33, 93, 12, 72, 23, 83)(121, 181, 123, 183, 130, 190, 148, 208, 169, 229, 155, 215, 133, 193, 151, 211, 158, 218, 174, 234, 180, 240, 178, 238, 164, 224, 140, 200, 126, 186, 139, 199, 162, 222, 157, 217, 137, 197, 125, 185)(122, 182, 127, 187, 142, 202, 166, 226, 156, 216, 134, 194, 124, 184, 132, 192, 149, 209, 171, 231, 179, 239, 172, 232, 154, 214, 160, 220, 138, 198, 159, 219, 176, 236, 168, 228, 146, 206, 128, 188)(129, 189, 145, 205, 167, 227, 143, 203, 136, 196, 152, 212, 131, 191, 150, 210, 170, 230, 153, 213, 173, 233, 175, 235, 163, 223, 177, 237, 161, 221, 144, 204, 165, 225, 141, 201, 135, 195, 147, 207)
	L = (1, 124)(2, 121)(3, 131)(4, 133)(5, 136)(6, 122)(7, 143)(8, 145)(9, 123)(10, 149)(11, 151)(12, 153)(13, 154)(14, 150)(15, 125)(16, 155)(17, 156)(18, 126)(19, 129)(20, 135)(21, 127)(22, 130)(23, 132)(24, 128)(25, 134)(26, 137)(27, 166)(28, 170)(29, 158)(30, 172)(31, 163)(32, 171)(33, 160)(34, 164)(35, 173)(36, 169)(37, 167)(38, 138)(39, 141)(40, 144)(41, 139)(42, 142)(43, 140)(44, 146)(45, 157)(46, 152)(47, 148)(48, 147)(49, 179)(50, 174)(51, 175)(52, 177)(53, 178)(54, 161)(55, 159)(56, 162)(57, 168)(58, 165)(59, 180)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1334
Graph:: bipartite
	v = 6 e = 120 f = 62
	degree seq :: [ 40^6 ]

E27.1328 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^3 * Y1, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^3 * Y2^-2 * Y1 * Y2^-2, Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, (Y2 * Y1^-1)^4, Y1^20, (Y3^-1 * Y1^-1)^20 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 18, 78, 40, 100, 54, 114, 60, 120, 38, 98, 51, 111, 36, 96, 49, 109, 28, 88, 46, 106, 25, 85, 44, 104, 53, 113, 59, 119, 33, 93, 13, 73, 4, 64)(3, 63, 9, 69, 17, 77, 39, 99, 43, 103, 31, 91, 34, 94, 14, 74, 23, 83, 8, 68, 22, 82, 41, 101, 58, 118, 37, 97, 47, 107, 35, 95, 45, 105, 55, 115, 29, 89, 11, 71)(5, 65, 15, 75, 19, 79, 42, 102, 56, 116, 30, 90, 50, 110, 26, 86, 48, 108, 57, 117, 32, 92, 12, 72, 21, 81, 7, 67, 20, 80, 24, 84, 52, 112, 27, 87, 10, 70, 16, 76)(121, 181, 123, 183, 130, 190, 133, 193, 149, 209, 172, 232, 179, 239, 165, 225, 140, 200, 164, 224, 167, 227, 141, 201, 166, 226, 178, 238, 152, 212, 169, 229, 142, 202, 168, 228, 171, 231, 143, 203, 170, 230, 180, 240, 154, 214, 176, 236, 160, 220, 163, 223, 139, 199, 126, 186, 137, 197, 125, 185)(122, 182, 127, 187, 134, 194, 124, 184, 132, 192, 151, 211, 153, 213, 177, 237, 159, 219, 173, 233, 146, 206, 129, 189, 145, 205, 150, 210, 131, 191, 148, 208, 162, 222, 175, 235, 156, 216, 135, 195, 155, 215, 158, 218, 136, 196, 157, 217, 174, 234, 147, 207, 161, 221, 138, 198, 144, 204, 128, 188)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 137)(7, 134)(8, 122)(9, 145)(10, 133)(11, 148)(12, 151)(13, 149)(14, 124)(15, 155)(16, 157)(17, 125)(18, 144)(19, 126)(20, 164)(21, 166)(22, 168)(23, 170)(24, 128)(25, 150)(26, 129)(27, 161)(28, 162)(29, 172)(30, 131)(31, 153)(32, 169)(33, 177)(34, 176)(35, 158)(36, 135)(37, 174)(38, 136)(39, 173)(40, 163)(41, 138)(42, 175)(43, 139)(44, 167)(45, 140)(46, 178)(47, 141)(48, 171)(49, 142)(50, 180)(51, 143)(52, 179)(53, 146)(54, 147)(55, 156)(56, 160)(57, 159)(58, 152)(59, 165)(60, 154)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1333
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 40^3, 60^2 ]

E27.1329 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^2, Y2^9 * Y1^2, (Y3^-1 * Y1^-1)^20 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 18, 78, 34, 94, 25, 85, 27, 87, 37, 97, 48, 108, 52, 112, 60, 120, 58, 118, 54, 114, 44, 104, 33, 93, 31, 91, 38, 98, 28, 88, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 21, 81, 36, 96, 40, 100, 41, 101, 51, 111, 59, 119, 56, 116, 55, 115, 45, 105, 42, 102, 32, 92, 17, 77, 14, 74, 24, 84, 8, 68, 23, 83, 11, 71)(5, 65, 15, 75, 20, 80, 12, 72, 22, 82, 7, 67, 10, 70, 26, 86, 35, 95, 39, 99, 49, 109, 50, 110, 53, 113, 57, 117, 47, 107, 46, 106, 43, 103, 30, 90, 29, 89, 16, 76)(121, 181, 123, 183, 130, 190, 147, 207, 161, 221, 173, 233, 174, 234, 162, 222, 149, 209, 133, 193, 143, 203, 142, 202, 154, 214, 156, 216, 169, 229, 180, 240, 175, 235, 163, 223, 158, 218, 144, 204, 140, 200, 126, 186, 139, 199, 155, 215, 168, 228, 179, 239, 167, 227, 153, 213, 137, 197, 125, 185)(122, 182, 127, 187, 141, 201, 157, 217, 170, 230, 176, 236, 164, 224, 150, 210, 134, 194, 124, 184, 132, 192, 129, 189, 145, 205, 159, 219, 171, 231, 178, 238, 166, 226, 152, 212, 148, 208, 135, 195, 131, 191, 138, 198, 146, 206, 160, 220, 172, 232, 177, 237, 165, 225, 151, 211, 136, 196, 128, 188)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 141)(8, 122)(9, 145)(10, 147)(11, 138)(12, 129)(13, 143)(14, 124)(15, 131)(16, 128)(17, 125)(18, 146)(19, 155)(20, 126)(21, 157)(22, 154)(23, 142)(24, 140)(25, 159)(26, 160)(27, 161)(28, 135)(29, 133)(30, 134)(31, 136)(32, 148)(33, 137)(34, 156)(35, 168)(36, 169)(37, 170)(38, 144)(39, 171)(40, 172)(41, 173)(42, 149)(43, 158)(44, 150)(45, 151)(46, 152)(47, 153)(48, 179)(49, 180)(50, 176)(51, 178)(52, 177)(53, 174)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1331
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 40^3, 60^2 ]

E27.1330 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2, Y1 * Y2 * Y1 * Y2 * Y1^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^-9 * Y1^2, Y2^-1 * Y1^2 * Y2^-8, (Y3^-1 * Y1^-1)^20 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 18, 78, 34, 94, 31, 91, 33, 93, 38, 98, 48, 108, 58, 118, 60, 120, 55, 115, 54, 114, 40, 100, 26, 86, 28, 88, 36, 96, 25, 85, 13, 73, 4, 64)(3, 63, 9, 69, 19, 79, 14, 74, 23, 83, 8, 68, 17, 77, 32, 92, 35, 95, 45, 105, 49, 109, 50, 110, 59, 119, 52, 112, 39, 99, 41, 101, 44, 104, 30, 90, 29, 89, 11, 71)(5, 65, 15, 75, 20, 80, 24, 84, 37, 97, 46, 106, 47, 107, 57, 117, 51, 111, 53, 113, 56, 116, 43, 103, 42, 102, 27, 87, 10, 70, 12, 72, 22, 82, 7, 67, 21, 81, 16, 76)(121, 181, 123, 183, 130, 190, 146, 206, 159, 219, 171, 231, 168, 228, 155, 215, 140, 200, 126, 186, 139, 199, 142, 202, 156, 216, 164, 224, 176, 236, 180, 240, 169, 229, 157, 217, 154, 214, 143, 203, 141, 201, 133, 193, 149, 209, 162, 222, 174, 234, 179, 239, 167, 227, 153, 213, 137, 197, 125, 185)(122, 182, 127, 187, 131, 191, 148, 208, 163, 223, 172, 232, 178, 238, 166, 226, 152, 212, 138, 198, 136, 196, 129, 189, 145, 205, 147, 207, 161, 221, 175, 235, 177, 237, 165, 225, 151, 211, 135, 195, 134, 194, 124, 184, 132, 192, 150, 210, 160, 220, 173, 233, 170, 230, 158, 218, 144, 204, 128, 188)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 131)(8, 122)(9, 145)(10, 146)(11, 148)(12, 150)(13, 149)(14, 124)(15, 134)(16, 129)(17, 125)(18, 136)(19, 142)(20, 126)(21, 133)(22, 156)(23, 141)(24, 128)(25, 147)(26, 159)(27, 161)(28, 163)(29, 162)(30, 160)(31, 135)(32, 138)(33, 137)(34, 143)(35, 140)(36, 164)(37, 154)(38, 144)(39, 171)(40, 173)(41, 175)(42, 174)(43, 172)(44, 176)(45, 151)(46, 152)(47, 153)(48, 155)(49, 157)(50, 158)(51, 168)(52, 178)(53, 170)(54, 179)(55, 177)(56, 180)(57, 165)(58, 166)(59, 167)(60, 169)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1332
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 40^3, 60^2 ]

E27.1331 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3^-3, Y3 * Y2^2 * Y3^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y2^-1)^4, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^20, (Y2^-1 * Y3)^20, (Y3^-1 * Y1^-1)^30 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 138, 198, 160, 220, 178, 238, 176, 236, 148, 208, 167, 227, 145, 205, 164, 224, 158, 218, 172, 232, 156, 216, 170, 230, 175, 235, 180, 240, 151, 211, 133, 193, 124, 184)(123, 183, 129, 189, 139, 199, 162, 222, 179, 239, 157, 217, 168, 228, 155, 215, 165, 225, 174, 234, 153, 213, 134, 194, 144, 204, 128, 188, 143, 203, 141, 201, 166, 226, 159, 219, 137, 197, 131, 191)(125, 185, 135, 195, 130, 190, 147, 207, 163, 223, 154, 214, 150, 210, 132, 192, 142, 202, 127, 187, 140, 200, 161, 221, 177, 237, 149, 209, 171, 231, 146, 206, 169, 229, 173, 233, 152, 212, 136, 196)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 141)(8, 122)(9, 145)(10, 126)(11, 148)(12, 128)(13, 137)(14, 124)(15, 155)(16, 157)(17, 125)(18, 161)(19, 163)(20, 164)(21, 138)(22, 167)(23, 169)(24, 171)(25, 173)(26, 129)(27, 174)(28, 146)(29, 131)(30, 176)(31, 154)(32, 133)(33, 177)(34, 134)(35, 175)(36, 135)(37, 156)(38, 136)(39, 178)(40, 179)(41, 159)(42, 158)(43, 160)(44, 153)(45, 140)(46, 152)(47, 165)(48, 142)(49, 180)(50, 143)(51, 170)(52, 144)(53, 162)(54, 151)(55, 147)(56, 168)(57, 172)(58, 149)(59, 150)(60, 166)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 60 ), ( 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1329
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1332 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y3^-1 * Y2^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^3, Y2^2 * Y3^9, Y3^2 * Y2 * Y3^2 * Y2^11, (Y3^-1 * Y1^-1)^30 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 138, 198, 154, 214, 145, 205, 147, 207, 157, 217, 168, 228, 172, 232, 180, 240, 178, 238, 174, 234, 164, 224, 153, 213, 151, 211, 158, 218, 148, 208, 133, 193, 124, 184)(123, 183, 129, 189, 139, 199, 141, 201, 156, 216, 160, 220, 161, 221, 171, 231, 179, 239, 176, 236, 175, 235, 165, 225, 162, 222, 152, 212, 137, 197, 134, 194, 144, 204, 128, 188, 143, 203, 131, 191)(125, 185, 135, 195, 140, 200, 132, 192, 142, 202, 127, 187, 130, 190, 146, 206, 155, 215, 159, 219, 169, 229, 170, 230, 173, 233, 177, 237, 167, 227, 166, 226, 163, 223, 150, 210, 149, 209, 136, 196)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 141)(8, 122)(9, 145)(10, 147)(11, 138)(12, 129)(13, 143)(14, 124)(15, 131)(16, 128)(17, 125)(18, 146)(19, 155)(20, 126)(21, 157)(22, 154)(23, 142)(24, 140)(25, 159)(26, 160)(27, 161)(28, 135)(29, 133)(30, 134)(31, 136)(32, 148)(33, 137)(34, 156)(35, 168)(36, 169)(37, 170)(38, 144)(39, 171)(40, 172)(41, 173)(42, 149)(43, 158)(44, 150)(45, 151)(46, 152)(47, 153)(48, 179)(49, 180)(50, 176)(51, 178)(52, 177)(53, 174)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 60 ), ( 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1330
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1333 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, R * Y2 * Y3 * R * Y2^-1, Y2 * Y3^2 * Y2 * Y3^-1, Y3 * Y2 * Y3 * Y2^3, Y2 * Y3^4 * Y2 * Y3^-2 * Y2^2, Y2^2 * Y3^-9, (Y3^-1 * Y1^-1)^30 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 138, 198, 154, 214, 151, 211, 153, 213, 158, 218, 168, 228, 178, 238, 180, 240, 175, 235, 174, 234, 160, 220, 146, 206, 148, 208, 156, 216, 145, 205, 133, 193, 124, 184)(123, 183, 129, 189, 139, 199, 134, 194, 143, 203, 128, 188, 137, 197, 152, 212, 155, 215, 165, 225, 169, 229, 170, 230, 179, 239, 172, 232, 159, 219, 161, 221, 164, 224, 150, 210, 149, 209, 131, 191)(125, 185, 135, 195, 140, 200, 144, 204, 157, 217, 166, 226, 167, 227, 177, 237, 171, 231, 173, 233, 176, 236, 163, 223, 162, 222, 147, 207, 130, 190, 132, 192, 142, 202, 127, 187, 141, 201, 136, 196)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 139)(7, 131)(8, 122)(9, 145)(10, 146)(11, 148)(12, 150)(13, 149)(14, 124)(15, 134)(16, 129)(17, 125)(18, 136)(19, 142)(20, 126)(21, 133)(22, 156)(23, 141)(24, 128)(25, 147)(26, 159)(27, 161)(28, 163)(29, 162)(30, 160)(31, 135)(32, 138)(33, 137)(34, 143)(35, 140)(36, 164)(37, 154)(38, 144)(39, 171)(40, 173)(41, 175)(42, 174)(43, 172)(44, 176)(45, 151)(46, 152)(47, 153)(48, 155)(49, 157)(50, 158)(51, 168)(52, 178)(53, 170)(54, 179)(55, 177)(56, 180)(57, 165)(58, 166)(59, 167)(60, 169)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 60 ), ( 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60, 40, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1328
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1334 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {20, 20, 30})
Quotient :: dipole
Aut^+ = C5 x (C3 : C4) (small group id <60, 1>)
Aut   = (C6 x D10) : C2 (small group id <120, 12>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^3 * Y3, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1)^4, Y3 * Y1^-2 * Y3^3 * Y1^-2, Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1, Y3^20, (Y3^-1 * Y1^-1)^20, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 17, 77, 23, 83, 42, 102, 60, 120, 52, 112, 24, 84, 43, 103, 53, 113, 25, 85, 44, 104, 58, 118, 37, 97, 49, 109, 28, 88, 45, 105, 56, 116, 30, 90, 47, 107, 59, 119, 38, 98, 50, 110, 54, 114, 55, 115, 27, 87, 10, 70, 13, 73, 4, 64)(3, 63, 9, 69, 16, 76, 5, 65, 15, 75, 36, 96, 39, 99, 57, 117, 33, 93, 46, 106, 20, 80, 7, 67, 19, 79, 22, 82, 8, 68, 21, 81, 48, 108, 51, 111, 32, 92, 12, 72, 31, 91, 35, 95, 14, 74, 34, 94, 41, 101, 18, 78, 40, 100, 26, 86, 29, 89, 11, 71)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 134)(7, 133)(8, 122)(9, 144)(10, 146)(11, 148)(12, 147)(13, 153)(14, 124)(15, 145)(16, 150)(17, 125)(18, 126)(19, 163)(20, 165)(21, 164)(22, 167)(23, 128)(24, 149)(25, 129)(26, 174)(27, 168)(28, 160)(29, 162)(30, 131)(31, 172)(32, 169)(33, 175)(34, 173)(35, 176)(36, 158)(37, 135)(38, 136)(39, 137)(40, 178)(41, 179)(42, 138)(43, 166)(44, 139)(45, 177)(46, 180)(47, 140)(48, 170)(49, 141)(50, 142)(51, 143)(52, 171)(53, 151)(54, 161)(55, 156)(56, 152)(57, 157)(58, 154)(59, 155)(60, 159)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 40 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1327
Graph:: simple bipartite
	v = 62 e = 120 f = 6
	degree seq :: [ 2^60, 60^2 ]

E27.1335 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1), T1^-4 * T2^-1 * T1^-1 * T2^-3 * T1^-1, T2^-2 * T1 * T2^-4 * T1 * T2^-2 * T1, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 46, 28, 14, 27, 45, 38, 22, 36, 54, 56, 41, 25, 13, 5)(2, 7, 17, 31, 49, 59, 58, 44, 26, 43, 39, 23, 11, 21, 35, 53, 50, 32, 18, 8)(4, 10, 20, 34, 52, 48, 30, 16, 6, 15, 29, 47, 37, 55, 60, 57, 42, 40, 24, 12)(61, 62, 66, 74, 86, 102, 101, 110, 112, 93, 109, 97, 82, 71, 64)(63, 67, 75, 87, 103, 100, 85, 92, 108, 111, 119, 115, 96, 81, 70)(65, 68, 76, 88, 104, 117, 116, 113, 94, 79, 91, 107, 98, 83, 72)(69, 77, 89, 105, 99, 84, 73, 78, 90, 106, 118, 120, 114, 95, 80)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^15 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1349
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 15^4, 20^3 ]

E27.1336 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^4, T1^15 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 22, 32, 39, 46, 49, 56, 59, 51, 42, 45, 36, 27, 14, 25, 13, 5)(2, 7, 17, 23, 11, 21, 31, 38, 41, 48, 55, 58, 50, 53, 44, 35, 26, 29, 18, 8)(4, 10, 20, 30, 33, 40, 47, 54, 57, 60, 52, 43, 34, 37, 28, 16, 6, 15, 24, 12)(61, 62, 66, 74, 86, 94, 102, 110, 117, 109, 101, 93, 82, 71, 64)(63, 67, 75, 85, 89, 97, 105, 113, 120, 116, 108, 100, 92, 81, 70)(65, 68, 76, 87, 95, 103, 111, 118, 114, 106, 98, 90, 79, 83, 72)(69, 77, 84, 73, 78, 88, 96, 104, 112, 119, 115, 107, 99, 91, 80)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^15 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1347
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 15^4, 20^3 ]

E27.1337 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1^3 * T2^-4, T1^15, T1^15 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 14, 27, 36, 45, 42, 51, 59, 55, 46, 49, 40, 31, 22, 25, 13, 5)(2, 7, 17, 29, 26, 35, 44, 53, 50, 58, 56, 47, 38, 41, 32, 23, 11, 21, 18, 8)(4, 10, 20, 16, 6, 15, 28, 37, 34, 43, 52, 60, 54, 57, 48, 39, 30, 33, 24, 12)(61, 62, 66, 74, 86, 94, 102, 110, 114, 106, 98, 90, 82, 71, 64)(63, 67, 75, 87, 95, 103, 111, 118, 117, 109, 101, 93, 85, 81, 70)(65, 68, 76, 79, 89, 97, 105, 113, 120, 115, 107, 99, 91, 83, 72)(69, 77, 88, 96, 104, 112, 119, 116, 108, 100, 92, 84, 73, 78, 80)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^15 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1348
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 15^4, 20^3 ]

E27.1338 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^20, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 8, 2, 7, 14, 6, 13, 20, 12, 19, 26, 18, 25, 32, 24, 31, 38, 30, 37, 44, 36, 43, 50, 42, 49, 56, 48, 55, 60, 54, 59, 58, 52, 57, 53, 46, 51, 47, 40, 45, 41, 34, 39, 35, 28, 33, 29, 22, 27, 23, 16, 21, 17, 10, 15, 11, 4, 9, 5)(61, 62, 66, 72, 78, 84, 90, 96, 102, 108, 114, 112, 106, 100, 94, 88, 82, 76, 70, 64)(63, 67, 73, 79, 85, 91, 97, 103, 109, 115, 119, 117, 111, 105, 99, 93, 87, 81, 75, 69)(65, 68, 74, 80, 86, 92, 98, 104, 110, 116, 120, 118, 113, 107, 101, 95, 89, 83, 77, 71)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1351
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.1339 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1), (F * T1)^2, T1^-1 * T2^4 * T1 * T2^-4, T2^-9 * T1^-1, T1^-2 * T2^-2 * T1^-2 * T2^-1 * T1^-3, T1^-2 * T2^-2 * T1^4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 40, 24, 12, 4, 10, 20, 34, 52, 56, 42, 39, 23, 11, 21, 35, 53, 57, 44, 26, 43, 38, 22, 36, 54, 58, 46, 28, 14, 27, 45, 37, 55, 60, 48, 30, 16, 6, 15, 29, 47, 59, 50, 32, 18, 8, 2, 7, 17, 31, 49, 41, 25, 13, 5)(61, 62, 66, 74, 86, 102, 100, 85, 92, 108, 118, 113, 94, 79, 91, 107, 97, 82, 71, 64)(63, 67, 75, 87, 103, 99, 84, 73, 78, 90, 106, 117, 112, 93, 109, 119, 115, 96, 81, 70)(65, 68, 76, 88, 104, 116, 111, 101, 110, 120, 114, 95, 80, 69, 77, 89, 105, 98, 83, 72)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1352
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.1340 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^-3 * T1^-2 * T2^-3, T1^9 * T2^-3, T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-6, T1 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-3, T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^-2 * T1^-3 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 23, 11, 21, 35, 46, 57, 50, 37, 48, 53, 39, 52, 60, 56, 43, 28, 14, 27, 42, 32, 18, 8, 2, 7, 17, 31, 24, 12, 4, 10, 20, 34, 45, 38, 22, 36, 47, 51, 59, 58, 49, 55, 41, 26, 40, 54, 44, 30, 16, 6, 15, 29, 25, 13, 5)(61, 62, 66, 74, 86, 99, 111, 106, 94, 79, 91, 85, 92, 104, 116, 109, 97, 82, 71, 64)(63, 67, 75, 87, 100, 112, 119, 117, 105, 93, 84, 73, 78, 90, 103, 115, 108, 96, 81, 70)(65, 68, 76, 88, 101, 113, 107, 95, 80, 69, 77, 89, 102, 114, 120, 118, 110, 98, 83, 72)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 30^20 ), ( 30^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1350
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 20^3, 60 ]

E27.1341 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^2 * T1^-4, T2^15, T2^15, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 27, 35, 43, 51, 54, 46, 38, 30, 22, 13, 5)(2, 7, 17, 25, 33, 41, 49, 57, 58, 50, 42, 34, 26, 18, 8)(4, 10, 14, 23, 31, 39, 47, 55, 60, 53, 45, 37, 29, 21, 12)(6, 15, 24, 32, 40, 48, 56, 59, 52, 44, 36, 28, 20, 11, 16)(61, 62, 66, 74, 69, 77, 84, 91, 87, 93, 100, 107, 103, 109, 116, 120, 114, 118, 112, 105, 98, 102, 96, 89, 82, 86, 80, 72, 65, 68, 76, 70, 63, 67, 75, 83, 79, 85, 92, 99, 95, 101, 108, 115, 111, 117, 119, 113, 106, 110, 104, 97, 90, 94, 88, 81, 73, 78, 71, 64)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^15 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1344
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 15^4, 60 ]

E27.1342 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2 * T1^4, T2^15, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 53, 45, 37, 29, 21, 13, 5)(2, 7, 15, 23, 31, 39, 47, 55, 56, 48, 40, 32, 24, 16, 8)(4, 10, 18, 26, 34, 42, 50, 57, 59, 52, 44, 36, 28, 20, 12)(6, 11, 19, 27, 35, 43, 51, 58, 60, 54, 46, 38, 30, 22, 14)(61, 62, 66, 72, 65, 68, 74, 80, 73, 76, 82, 88, 81, 84, 90, 96, 89, 92, 98, 104, 97, 100, 106, 112, 105, 108, 114, 119, 113, 116, 120, 117, 109, 115, 118, 110, 101, 107, 111, 102, 93, 99, 103, 94, 85, 91, 95, 86, 77, 83, 87, 78, 69, 75, 79, 70, 63, 67, 71, 64)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^15 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1345
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 15^4, 60 ]

E27.1343 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {15, 20, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-7, T1^3 * T2 * T1 * T2^6, T2^3 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-2, (T1^-1 * T2^-1)^20 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 49, 53, 37, 26, 42, 57, 41, 25, 13, 5)(2, 7, 17, 31, 47, 54, 38, 22, 36, 52, 60, 48, 32, 18, 8)(4, 10, 20, 34, 50, 58, 44, 28, 14, 27, 43, 56, 40, 24, 12)(6, 15, 29, 45, 55, 39, 23, 11, 21, 35, 51, 59, 46, 30, 16)(61, 62, 66, 74, 86, 96, 81, 70, 63, 67, 75, 87, 102, 112, 95, 80, 69, 77, 89, 103, 117, 120, 111, 94, 79, 91, 105, 116, 101, 108, 119, 110, 93, 107, 115, 100, 85, 92, 106, 118, 109, 114, 99, 84, 73, 78, 90, 104, 113, 98, 83, 72, 65, 68, 76, 88, 97, 82, 71, 64)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 40^15 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1346
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 60 f = 3
	degree seq :: [ 15^4, 60 ]

E27.1344 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1), T1^-4 * T2^-1 * T1^-1 * T2^-3 * T1^-1, T2^-2 * T1 * T2^-4 * T1 * T2^-2 * T1, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 51, 111, 46, 106, 28, 88, 14, 74, 27, 87, 45, 105, 38, 98, 22, 82, 36, 96, 54, 114, 56, 116, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 49, 109, 59, 119, 58, 118, 44, 104, 26, 86, 43, 103, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 53, 113, 50, 110, 32, 92, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 34, 94, 52, 112, 48, 108, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 47, 107, 37, 97, 55, 115, 60, 120, 57, 117, 42, 102, 40, 100, 24, 84, 12, 72)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 110)(42, 101)(43, 100)(44, 117)(45, 99)(46, 118)(47, 98)(48, 111)(49, 97)(50, 112)(51, 119)(52, 93)(53, 94)(54, 95)(55, 96)(56, 113)(57, 116)(58, 120)(59, 115)(60, 114)
	local type(s) :: { ( 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1341
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1345 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^4, T1^15 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 22, 82, 32, 92, 39, 99, 46, 106, 49, 109, 56, 116, 59, 119, 51, 111, 42, 102, 45, 105, 36, 96, 27, 87, 14, 74, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 23, 83, 11, 71, 21, 81, 31, 91, 38, 98, 41, 101, 48, 108, 55, 115, 58, 118, 50, 110, 53, 113, 44, 104, 35, 95, 26, 86, 29, 89, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 30, 90, 33, 93, 40, 100, 47, 107, 54, 114, 57, 117, 60, 120, 52, 112, 43, 103, 34, 94, 37, 97, 28, 88, 16, 76, 6, 66, 15, 75, 24, 84, 12, 72)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 85)(16, 87)(17, 84)(18, 88)(19, 83)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 89)(26, 94)(27, 95)(28, 96)(29, 97)(30, 79)(31, 80)(32, 81)(33, 82)(34, 102)(35, 103)(36, 104)(37, 105)(38, 90)(39, 91)(40, 92)(41, 93)(42, 110)(43, 111)(44, 112)(45, 113)(46, 98)(47, 99)(48, 100)(49, 101)(50, 117)(51, 118)(52, 119)(53, 120)(54, 106)(55, 107)(56, 108)(57, 109)(58, 114)(59, 115)(60, 116)
	local type(s) :: { ( 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1342
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1346 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T1^3 * T2^-4, T1^15, T1^15 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 14, 74, 27, 87, 36, 96, 45, 105, 42, 102, 51, 111, 59, 119, 55, 115, 46, 106, 49, 109, 40, 100, 31, 91, 22, 82, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 29, 89, 26, 86, 35, 95, 44, 104, 53, 113, 50, 110, 58, 118, 56, 116, 47, 107, 38, 98, 41, 101, 32, 92, 23, 83, 11, 71, 21, 81, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 16, 76, 6, 66, 15, 75, 28, 88, 37, 97, 34, 94, 43, 103, 52, 112, 60, 120, 54, 114, 57, 117, 48, 108, 39, 99, 30, 90, 33, 93, 24, 84, 12, 72)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 79)(17, 88)(18, 80)(19, 89)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 81)(26, 94)(27, 95)(28, 96)(29, 97)(30, 82)(31, 83)(32, 84)(33, 85)(34, 102)(35, 103)(36, 104)(37, 105)(38, 90)(39, 91)(40, 92)(41, 93)(42, 110)(43, 111)(44, 112)(45, 113)(46, 98)(47, 99)(48, 100)(49, 101)(50, 114)(51, 118)(52, 119)(53, 120)(54, 106)(55, 107)(56, 108)(57, 109)(58, 117)(59, 116)(60, 115)
	local type(s) :: { ( 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60, 15, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1343
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 60 f = 5
	degree seq :: [ 40^3 ]

E27.1347 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^20, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 8, 68, 2, 62, 7, 67, 14, 74, 6, 66, 13, 73, 20, 80, 12, 72, 19, 79, 26, 86, 18, 78, 25, 85, 32, 92, 24, 84, 31, 91, 38, 98, 30, 90, 37, 97, 44, 104, 36, 96, 43, 103, 50, 110, 42, 102, 49, 109, 56, 116, 48, 108, 55, 115, 60, 120, 54, 114, 59, 119, 58, 118, 52, 112, 57, 117, 53, 113, 46, 106, 51, 111, 47, 107, 40, 100, 45, 105, 41, 101, 34, 94, 39, 99, 35, 95, 28, 88, 33, 93, 29, 89, 22, 82, 27, 87, 23, 83, 16, 76, 21, 81, 17, 77, 10, 70, 15, 75, 11, 71, 4, 64, 9, 69, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 72)(7, 73)(8, 74)(9, 63)(10, 64)(11, 65)(12, 78)(13, 79)(14, 80)(15, 69)(16, 70)(17, 71)(18, 84)(19, 85)(20, 86)(21, 75)(22, 76)(23, 77)(24, 90)(25, 91)(26, 92)(27, 81)(28, 82)(29, 83)(30, 96)(31, 97)(32, 98)(33, 87)(34, 88)(35, 89)(36, 102)(37, 103)(38, 104)(39, 93)(40, 94)(41, 95)(42, 108)(43, 109)(44, 110)(45, 99)(46, 100)(47, 101)(48, 114)(49, 115)(50, 116)(51, 105)(52, 106)(53, 107)(54, 112)(55, 119)(56, 120)(57, 111)(58, 113)(59, 117)(60, 118)
	local type(s) :: { ( 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1336
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1348 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1), (F * T1)^2, T1^-1 * T2^4 * T1 * T2^-4, T2^-9 * T1^-1, T1^-2 * T2^-2 * T1^-2 * T2^-1 * T1^-3, T1^-2 * T2^-2 * T1^4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 51, 111, 40, 100, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 34, 94, 52, 112, 56, 116, 42, 102, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 53, 113, 57, 117, 44, 104, 26, 86, 43, 103, 38, 98, 22, 82, 36, 96, 54, 114, 58, 118, 46, 106, 28, 88, 14, 74, 27, 87, 45, 105, 37, 97, 55, 115, 60, 120, 48, 108, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 47, 107, 59, 119, 50, 110, 32, 92, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 49, 109, 41, 101, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 110)(42, 100)(43, 99)(44, 116)(45, 98)(46, 117)(47, 97)(48, 118)(49, 119)(50, 120)(51, 101)(52, 93)(53, 94)(54, 95)(55, 96)(56, 111)(57, 112)(58, 113)(59, 115)(60, 114)
	local type(s) :: { ( 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1337
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1349 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^-3 * T1^-2 * T2^-3, T1^9 * T2^-3, T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-6, T1 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-1 * T1 * T2^-2 * T1^2 * T2^-3, T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^-2 * T1^-3 * T2 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 23, 83, 11, 71, 21, 81, 35, 95, 46, 106, 57, 117, 50, 110, 37, 97, 48, 108, 53, 113, 39, 99, 52, 112, 60, 120, 56, 116, 43, 103, 28, 88, 14, 74, 27, 87, 42, 102, 32, 92, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 34, 94, 45, 105, 38, 98, 22, 82, 36, 96, 47, 107, 51, 111, 59, 119, 58, 118, 49, 109, 55, 115, 41, 101, 26, 86, 40, 100, 54, 114, 44, 104, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 99)(27, 100)(28, 101)(29, 102)(30, 103)(31, 85)(32, 104)(33, 84)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 93)(46, 94)(47, 95)(48, 96)(49, 97)(50, 98)(51, 106)(52, 119)(53, 107)(54, 120)(55, 108)(56, 109)(57, 105)(58, 110)(59, 117)(60, 118)
	local type(s) :: { ( 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20, 15, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1335
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1350 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^2 * T1^-4, T2^15, T2^15, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 27, 87, 35, 95, 43, 103, 51, 111, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 57, 117, 58, 118, 50, 110, 42, 102, 34, 94, 26, 86, 18, 78, 8, 68)(4, 64, 10, 70, 14, 74, 23, 83, 31, 91, 39, 99, 47, 107, 55, 115, 60, 120, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 12, 72)(6, 66, 15, 75, 24, 84, 32, 92, 40, 100, 48, 108, 56, 116, 59, 119, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 11, 71, 16, 76)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 69)(15, 83)(16, 70)(17, 84)(18, 71)(19, 85)(20, 72)(21, 73)(22, 86)(23, 79)(24, 91)(25, 92)(26, 80)(27, 93)(28, 81)(29, 82)(30, 94)(31, 87)(32, 99)(33, 100)(34, 88)(35, 101)(36, 89)(37, 90)(38, 102)(39, 95)(40, 107)(41, 108)(42, 96)(43, 109)(44, 97)(45, 98)(46, 110)(47, 103)(48, 115)(49, 116)(50, 104)(51, 117)(52, 105)(53, 106)(54, 118)(55, 111)(56, 120)(57, 119)(58, 112)(59, 113)(60, 114)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1340
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.1351 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2 * T1^4, T2^15, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 13, 73, 5, 65)(2, 62, 7, 67, 15, 75, 23, 83, 31, 91, 39, 99, 47, 107, 55, 115, 56, 116, 48, 108, 40, 100, 32, 92, 24, 84, 16, 76, 8, 68)(4, 64, 10, 70, 18, 78, 26, 86, 34, 94, 42, 102, 50, 110, 57, 117, 59, 119, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 12, 72)(6, 66, 11, 71, 19, 79, 27, 87, 35, 95, 43, 103, 51, 111, 58, 118, 60, 120, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 14, 74)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 72)(7, 71)(8, 74)(9, 75)(10, 63)(11, 64)(12, 65)(13, 76)(14, 80)(15, 79)(16, 82)(17, 83)(18, 69)(19, 70)(20, 73)(21, 84)(22, 88)(23, 87)(24, 90)(25, 91)(26, 77)(27, 78)(28, 81)(29, 92)(30, 96)(31, 95)(32, 98)(33, 99)(34, 85)(35, 86)(36, 89)(37, 100)(38, 104)(39, 103)(40, 106)(41, 107)(42, 93)(43, 94)(44, 97)(45, 108)(46, 112)(47, 111)(48, 114)(49, 115)(50, 101)(51, 102)(52, 105)(53, 116)(54, 119)(55, 118)(56, 120)(57, 109)(58, 110)(59, 113)(60, 117)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1338
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.1352 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {15, 20, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-7, T1^3 * T2 * T1 * T2^6, T2^3 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-2, (T1^-1 * T2^-1)^20 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 49, 109, 53, 113, 37, 97, 26, 86, 42, 102, 57, 117, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 47, 107, 54, 114, 38, 98, 22, 82, 36, 96, 52, 112, 60, 120, 48, 108, 32, 92, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 34, 94, 50, 110, 58, 118, 44, 104, 28, 88, 14, 74, 27, 87, 43, 103, 56, 116, 40, 100, 24, 84, 12, 72)(6, 66, 15, 75, 29, 89, 45, 105, 55, 115, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 51, 111, 59, 119, 46, 106, 30, 90, 16, 76)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 96)(27, 102)(28, 97)(29, 103)(30, 104)(31, 105)(32, 106)(33, 107)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 108)(42, 112)(43, 117)(44, 113)(45, 116)(46, 118)(47, 115)(48, 119)(49, 114)(50, 93)(51, 94)(52, 95)(53, 98)(54, 99)(55, 100)(56, 101)(57, 120)(58, 109)(59, 110)(60, 111)
	local type(s) :: { ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1339
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.1353 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (Y2, Y1^-1), (R * Y2)^2, (R * Y3)^2, (Y2, Y1), (R * Y1)^2, Y1^2 * Y2^2 * Y3^2 * Y2^-2, Y3 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-4, Y3^3 * Y1^-1 * Y2^-4 * Y1^-2, Y2^3 * Y3^2 * Y2 * Y1^-1 * Y2^4, Y1^15, Y3 * Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 41, 101, 50, 110, 52, 112, 33, 93, 49, 109, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 40, 100, 25, 85, 32, 92, 48, 108, 51, 111, 59, 119, 55, 115, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 57, 117, 56, 116, 53, 113, 34, 94, 19, 79, 31, 91, 47, 107, 38, 98, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 45, 105, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 46, 106, 58, 118, 60, 120, 54, 114, 35, 95, 20, 80)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 171, 231, 166, 226, 148, 208, 134, 194, 147, 207, 165, 225, 158, 218, 142, 202, 156, 216, 174, 234, 176, 236, 161, 221, 145, 205, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 151, 211, 169, 229, 179, 239, 178, 238, 164, 224, 146, 206, 163, 223, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 173, 233, 170, 230, 152, 212, 138, 198, 128, 188)(124, 184, 130, 190, 140, 200, 154, 214, 172, 232, 168, 228, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 167, 227, 157, 217, 175, 235, 180, 240, 177, 237, 162, 222, 160, 220, 144, 204, 132, 192)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 154)(20, 155)(21, 156)(22, 157)(23, 158)(24, 159)(25, 160)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 145)(33, 172)(34, 173)(35, 174)(36, 175)(37, 169)(38, 167)(39, 165)(40, 163)(41, 162)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 161)(51, 168)(52, 170)(53, 176)(54, 180)(55, 179)(56, 177)(57, 164)(58, 166)(59, 171)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1362
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 30^4, 40^3 ]

E27.1354 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, Y1 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y3 * Y2, Y1^-3 * Y2^4, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-1 * Y2^-2, Y1^15, Y3^15, (Y2^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 34, 94, 42, 102, 50, 110, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 35, 95, 43, 103, 51, 111, 58, 118, 57, 117, 49, 109, 41, 101, 33, 93, 25, 85, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 19, 79, 29, 89, 37, 97, 45, 105, 53, 113, 60, 120, 55, 115, 47, 107, 39, 99, 31, 91, 23, 83, 12, 72)(9, 69, 17, 77, 28, 88, 36, 96, 44, 104, 52, 112, 59, 119, 56, 116, 48, 108, 40, 100, 32, 92, 24, 84, 13, 73, 18, 78, 20, 80)(121, 181, 123, 183, 129, 189, 139, 199, 134, 194, 147, 207, 156, 216, 165, 225, 162, 222, 171, 231, 179, 239, 175, 235, 166, 226, 169, 229, 160, 220, 151, 211, 142, 202, 145, 205, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 149, 209, 146, 206, 155, 215, 164, 224, 173, 233, 170, 230, 178, 238, 176, 236, 167, 227, 158, 218, 161, 221, 152, 212, 143, 203, 131, 191, 141, 201, 138, 198, 128, 188)(124, 184, 130, 190, 140, 200, 136, 196, 126, 186, 135, 195, 148, 208, 157, 217, 154, 214, 163, 223, 172, 232, 180, 240, 174, 234, 177, 237, 168, 228, 159, 219, 150, 210, 153, 213, 144, 204, 132, 192)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 136)(20, 138)(21, 145)(22, 150)(23, 151)(24, 152)(25, 153)(26, 134)(27, 135)(28, 137)(29, 139)(30, 158)(31, 159)(32, 160)(33, 161)(34, 146)(35, 147)(36, 148)(37, 149)(38, 166)(39, 167)(40, 168)(41, 169)(42, 154)(43, 155)(44, 156)(45, 157)(46, 174)(47, 175)(48, 176)(49, 177)(50, 162)(51, 163)(52, 164)(53, 165)(54, 170)(55, 180)(56, 179)(57, 178)(58, 171)(59, 172)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1364
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 30^4, 40^3 ]

E27.1355 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y2^-1 * Y3 * Y2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, Y1 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^3 * Y1^2, Y1^15, Y3^15, (Y2^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 34, 94, 42, 102, 50, 110, 57, 117, 49, 109, 41, 101, 33, 93, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 25, 85, 29, 89, 37, 97, 45, 105, 53, 113, 60, 120, 56, 116, 48, 108, 40, 100, 32, 92, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 27, 87, 35, 95, 43, 103, 51, 111, 58, 118, 54, 114, 46, 106, 38, 98, 30, 90, 19, 79, 23, 83, 12, 72)(9, 69, 17, 77, 24, 84, 13, 73, 18, 78, 28, 88, 36, 96, 44, 104, 52, 112, 59, 119, 55, 115, 47, 107, 39, 99, 31, 91, 20, 80)(121, 181, 123, 183, 129, 189, 139, 199, 142, 202, 152, 212, 159, 219, 166, 226, 169, 229, 176, 236, 179, 239, 171, 231, 162, 222, 165, 225, 156, 216, 147, 207, 134, 194, 145, 205, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 143, 203, 131, 191, 141, 201, 151, 211, 158, 218, 161, 221, 168, 228, 175, 235, 178, 238, 170, 230, 173, 233, 164, 224, 155, 215, 146, 206, 149, 209, 138, 198, 128, 188)(124, 184, 130, 190, 140, 200, 150, 210, 153, 213, 160, 220, 167, 227, 174, 234, 177, 237, 180, 240, 172, 232, 163, 223, 154, 214, 157, 217, 148, 208, 136, 196, 126, 186, 135, 195, 144, 204, 132, 192)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 150)(20, 151)(21, 152)(22, 153)(23, 139)(24, 137)(25, 135)(26, 134)(27, 136)(28, 138)(29, 145)(30, 158)(31, 159)(32, 160)(33, 161)(34, 146)(35, 147)(36, 148)(37, 149)(38, 166)(39, 167)(40, 168)(41, 169)(42, 154)(43, 155)(44, 156)(45, 157)(46, 174)(47, 175)(48, 176)(49, 177)(50, 162)(51, 163)(52, 164)(53, 165)(54, 178)(55, 179)(56, 180)(57, 170)(58, 171)(59, 172)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1363
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 30^4, 40^3 ]

E27.1356 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^-3 * Y1, R * Y2 * R * Y3, (R * Y1)^2, (Y2^-1, Y1^-1), Y1^20, (Y3^-1 * Y1^-1)^15 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 12, 72, 18, 78, 24, 84, 30, 90, 36, 96, 42, 102, 48, 108, 54, 114, 52, 112, 46, 106, 40, 100, 34, 94, 28, 88, 22, 82, 16, 76, 10, 70, 4, 64)(3, 63, 7, 67, 13, 73, 19, 79, 25, 85, 31, 91, 37, 97, 43, 103, 49, 109, 55, 115, 59, 119, 57, 117, 51, 111, 45, 105, 39, 99, 33, 93, 27, 87, 21, 81, 15, 75, 9, 69)(5, 65, 8, 68, 14, 74, 20, 80, 26, 86, 32, 92, 38, 98, 44, 104, 50, 110, 56, 116, 60, 120, 58, 118, 53, 113, 47, 107, 41, 101, 35, 95, 29, 89, 23, 83, 17, 77, 11, 71)(121, 181, 123, 183, 128, 188, 122, 182, 127, 187, 134, 194, 126, 186, 133, 193, 140, 200, 132, 192, 139, 199, 146, 206, 138, 198, 145, 205, 152, 212, 144, 204, 151, 211, 158, 218, 150, 210, 157, 217, 164, 224, 156, 216, 163, 223, 170, 230, 162, 222, 169, 229, 176, 236, 168, 228, 175, 235, 180, 240, 174, 234, 179, 239, 178, 238, 172, 232, 177, 237, 173, 233, 166, 226, 171, 231, 167, 227, 160, 220, 165, 225, 161, 221, 154, 214, 159, 219, 155, 215, 148, 208, 153, 213, 149, 209, 142, 202, 147, 207, 143, 203, 136, 196, 141, 201, 137, 197, 130, 190, 135, 195, 131, 191, 124, 184, 129, 189, 125, 185)
	L = (1, 123)(2, 127)(3, 128)(4, 129)(5, 121)(6, 133)(7, 134)(8, 122)(9, 125)(10, 135)(11, 124)(12, 139)(13, 140)(14, 126)(15, 131)(16, 141)(17, 130)(18, 145)(19, 146)(20, 132)(21, 137)(22, 147)(23, 136)(24, 151)(25, 152)(26, 138)(27, 143)(28, 153)(29, 142)(30, 157)(31, 158)(32, 144)(33, 149)(34, 159)(35, 148)(36, 163)(37, 164)(38, 150)(39, 155)(40, 165)(41, 154)(42, 169)(43, 170)(44, 156)(45, 161)(46, 171)(47, 160)(48, 175)(49, 176)(50, 162)(51, 167)(52, 177)(53, 166)(54, 179)(55, 180)(56, 168)(57, 173)(58, 172)(59, 178)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1360
Graph:: bipartite
	v = 4 e = 120 f = 64
	degree seq :: [ 40^3, 120 ]

E27.1357 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), Y2^-3 * Y1^-2 * Y2^-3, Y2 * Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-6, Y2^2 * Y1^11 * Y2, Y1 * Y2^-1 * Y1 * Y2^-2 * Y1^2 * Y2^-1 * Y1 * Y2^-2 * Y1^2 * Y2^-3, (Y3^-1 * Y1^-1)^15 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 39, 99, 51, 111, 46, 106, 34, 94, 19, 79, 31, 91, 25, 85, 32, 92, 44, 104, 56, 116, 49, 109, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 40, 100, 52, 112, 59, 119, 57, 117, 45, 105, 33, 93, 24, 84, 13, 73, 18, 78, 30, 90, 43, 103, 55, 115, 48, 108, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 41, 101, 53, 113, 47, 107, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 42, 102, 54, 114, 60, 120, 58, 118, 50, 110, 38, 98, 23, 83, 12, 72)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 143, 203, 131, 191, 141, 201, 155, 215, 166, 226, 177, 237, 170, 230, 157, 217, 168, 228, 173, 233, 159, 219, 172, 232, 180, 240, 176, 236, 163, 223, 148, 208, 134, 194, 147, 207, 162, 222, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 165, 225, 158, 218, 142, 202, 156, 216, 167, 227, 171, 231, 179, 239, 178, 238, 169, 229, 175, 235, 161, 221, 146, 206, 160, 220, 174, 234, 164, 224, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 145, 205, 133, 193, 125, 185)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 160)(27, 162)(28, 134)(29, 145)(30, 136)(31, 144)(32, 138)(33, 143)(34, 165)(35, 166)(36, 167)(37, 168)(38, 142)(39, 172)(40, 174)(41, 146)(42, 152)(43, 148)(44, 150)(45, 158)(46, 177)(47, 171)(48, 173)(49, 175)(50, 157)(51, 179)(52, 180)(53, 159)(54, 164)(55, 161)(56, 163)(57, 170)(58, 169)(59, 178)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1359
Graph:: bipartite
	v = 4 e = 120 f = 64
	degree seq :: [ 40^3, 120 ]

E27.1358 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), Y1^-1 * Y2^3 * Y1 * Y2^-3, Y2^-1 * Y1^-1 * Y2^-8, Y1^-3 * Y2^-2 * Y1^-2 * Y2^-1 * Y1^-2, (Y3^-1 * Y1^-1)^15 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 40, 100, 25, 85, 32, 92, 48, 108, 58, 118, 53, 113, 34, 94, 19, 79, 31, 91, 47, 107, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 46, 106, 57, 117, 52, 112, 33, 93, 49, 109, 59, 119, 55, 115, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 56, 116, 51, 111, 41, 101, 50, 110, 60, 120, 54, 114, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 45, 105, 38, 98, 23, 83, 12, 72)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 171, 231, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 172, 232, 176, 236, 162, 222, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 173, 233, 177, 237, 164, 224, 146, 206, 163, 223, 158, 218, 142, 202, 156, 216, 174, 234, 178, 238, 166, 226, 148, 208, 134, 194, 147, 207, 165, 225, 157, 217, 175, 235, 180, 240, 168, 228, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 167, 227, 179, 239, 170, 230, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 169, 229, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 169)(32, 138)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 142)(39, 143)(40, 144)(41, 145)(42, 159)(43, 158)(44, 146)(45, 157)(46, 148)(47, 179)(48, 150)(49, 161)(50, 152)(51, 160)(52, 176)(53, 177)(54, 178)(55, 180)(56, 162)(57, 164)(58, 166)(59, 170)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1361
Graph:: bipartite
	v = 4 e = 120 f = 64
	degree seq :: [ 40^3, 120 ]

E27.1359 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-2 * Y3^-4, Y2^-15, Y2^15, (Y2^-1 * Y3)^20, (Y3^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 134, 194, 143, 203, 151, 211, 159, 219, 167, 227, 174, 234, 166, 226, 158, 218, 150, 210, 142, 202, 131, 191, 124, 184)(123, 183, 127, 187, 135, 195, 144, 204, 152, 212, 160, 220, 168, 228, 175, 235, 180, 240, 173, 233, 165, 225, 157, 217, 149, 209, 141, 201, 130, 190)(125, 185, 128, 188, 136, 196, 145, 205, 153, 213, 161, 221, 169, 229, 176, 236, 178, 238, 171, 231, 163, 223, 155, 215, 147, 207, 139, 199, 132, 192)(129, 189, 137, 197, 133, 193, 138, 198, 146, 206, 154, 214, 162, 222, 170, 230, 177, 237, 179, 239, 172, 232, 164, 224, 156, 216, 148, 208, 140, 200)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 144)(15, 133)(16, 126)(17, 132)(18, 128)(19, 131)(20, 147)(21, 148)(22, 149)(23, 152)(24, 138)(25, 134)(26, 136)(27, 142)(28, 155)(29, 156)(30, 157)(31, 160)(32, 146)(33, 143)(34, 145)(35, 150)(36, 163)(37, 164)(38, 165)(39, 168)(40, 154)(41, 151)(42, 153)(43, 158)(44, 171)(45, 172)(46, 173)(47, 175)(48, 162)(49, 159)(50, 161)(51, 166)(52, 178)(53, 179)(54, 180)(55, 170)(56, 167)(57, 169)(58, 174)(59, 176)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 120 ), ( 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1357
Graph:: simple bipartite
	v = 64 e = 120 f = 4
	degree seq :: [ 2^60, 30^4 ]

E27.1360 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), Y3^4 * Y2^-1, Y2^15, Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-3, (Y3^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 134, 194, 142, 202, 150, 210, 158, 218, 166, 226, 171, 231, 163, 223, 155, 215, 147, 207, 139, 199, 131, 191, 124, 184)(123, 183, 127, 187, 135, 195, 143, 203, 151, 211, 159, 219, 167, 227, 174, 234, 177, 237, 170, 230, 162, 222, 154, 214, 146, 206, 138, 198, 130, 190)(125, 185, 128, 188, 136, 196, 144, 204, 152, 212, 160, 220, 168, 228, 175, 235, 178, 238, 172, 232, 164, 224, 156, 216, 148, 208, 140, 200, 132, 192)(129, 189, 137, 197, 145, 205, 153, 213, 161, 221, 169, 229, 176, 236, 180, 240, 179, 239, 173, 233, 165, 225, 157, 217, 149, 209, 141, 201, 133, 193)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 128)(10, 133)(11, 138)(12, 124)(13, 125)(14, 143)(15, 145)(16, 126)(17, 136)(18, 141)(19, 146)(20, 131)(21, 132)(22, 151)(23, 153)(24, 134)(25, 144)(26, 149)(27, 154)(28, 139)(29, 140)(30, 159)(31, 161)(32, 142)(33, 152)(34, 157)(35, 162)(36, 147)(37, 148)(38, 167)(39, 169)(40, 150)(41, 160)(42, 165)(43, 170)(44, 155)(45, 156)(46, 174)(47, 176)(48, 158)(49, 168)(50, 173)(51, 177)(52, 163)(53, 164)(54, 180)(55, 166)(56, 175)(57, 179)(58, 171)(59, 172)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 120 ), ( 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1356
Graph:: simple bipartite
	v = 64 e = 120 f = 4
	degree seq :: [ 2^60, 30^4 ]

E27.1361 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^2 * Y3^2 * Y2^-2 * Y3^-2, Y3 * Y2 * Y3^7, Y2^-2 * Y3 * Y2^-1 * Y3^3 * Y2^-4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 134, 194, 146, 206, 162, 222, 170, 230, 153, 213, 161, 221, 169, 229, 174, 234, 157, 217, 142, 202, 131, 191, 124, 184)(123, 183, 127, 187, 135, 195, 147, 207, 163, 223, 178, 238, 177, 237, 160, 220, 145, 205, 152, 212, 168, 228, 173, 233, 156, 216, 141, 201, 130, 190)(125, 185, 128, 188, 136, 196, 148, 208, 164, 224, 171, 231, 154, 214, 139, 199, 151, 211, 167, 227, 180, 240, 175, 235, 158, 218, 143, 203, 132, 192)(129, 189, 137, 197, 149, 209, 165, 225, 179, 239, 176, 236, 159, 219, 144, 204, 133, 193, 138, 198, 150, 210, 166, 226, 172, 232, 155, 215, 140, 200)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 161)(32, 138)(33, 160)(34, 170)(35, 171)(36, 172)(37, 173)(38, 142)(39, 143)(40, 144)(41, 145)(42, 178)(43, 179)(44, 146)(45, 180)(46, 148)(47, 169)(48, 150)(49, 152)(50, 177)(51, 162)(52, 164)(53, 166)(54, 168)(55, 157)(56, 158)(57, 159)(58, 176)(59, 175)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 120 ), ( 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120, 40, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1358
Graph:: simple bipartite
	v = 64 e = 120 f = 4
	degree seq :: [ 2^60, 30^4 ]

E27.1362 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3^2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^30, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 9, 69, 17, 77, 24, 84, 31, 91, 27, 87, 33, 93, 40, 100, 47, 107, 43, 103, 49, 109, 56, 116, 60, 120, 54, 114, 58, 118, 52, 112, 45, 105, 38, 98, 42, 102, 36, 96, 29, 89, 22, 82, 26, 86, 20, 80, 12, 72, 5, 65, 8, 68, 16, 76, 10, 70, 3, 63, 7, 67, 15, 75, 23, 83, 19, 79, 25, 85, 32, 92, 39, 99, 35, 95, 41, 101, 48, 108, 55, 115, 51, 111, 57, 117, 59, 119, 53, 113, 46, 106, 50, 110, 44, 104, 37, 97, 30, 90, 34, 94, 28, 88, 21, 81, 13, 73, 18, 78, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 134)(11, 136)(12, 124)(13, 125)(14, 143)(15, 144)(16, 126)(17, 145)(18, 128)(19, 147)(20, 131)(21, 132)(22, 133)(23, 151)(24, 152)(25, 153)(26, 138)(27, 155)(28, 140)(29, 141)(30, 142)(31, 159)(32, 160)(33, 161)(34, 146)(35, 163)(36, 148)(37, 149)(38, 150)(39, 167)(40, 168)(41, 169)(42, 154)(43, 171)(44, 156)(45, 157)(46, 158)(47, 175)(48, 176)(49, 177)(50, 162)(51, 174)(52, 164)(53, 165)(54, 166)(55, 180)(56, 179)(57, 178)(58, 170)(59, 172)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 40 ), ( 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1353
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1363 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^15, Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1^2 * Y3^-1, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 12, 72, 5, 65, 8, 68, 14, 74, 20, 80, 13, 73, 16, 76, 22, 82, 28, 88, 21, 81, 24, 84, 30, 90, 36, 96, 29, 89, 32, 92, 38, 98, 44, 104, 37, 97, 40, 100, 46, 106, 52, 112, 45, 105, 48, 108, 54, 114, 59, 119, 53, 113, 56, 116, 60, 120, 57, 117, 49, 109, 55, 115, 58, 118, 50, 110, 41, 101, 47, 107, 51, 111, 42, 102, 33, 93, 39, 99, 43, 103, 34, 94, 25, 85, 31, 91, 35, 95, 26, 86, 17, 77, 23, 83, 27, 87, 18, 78, 9, 69, 15, 75, 19, 79, 10, 70, 3, 63, 7, 67, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 131)(7, 135)(8, 122)(9, 137)(10, 138)(11, 139)(12, 124)(13, 125)(14, 126)(15, 143)(16, 128)(17, 145)(18, 146)(19, 147)(20, 132)(21, 133)(22, 134)(23, 151)(24, 136)(25, 153)(26, 154)(27, 155)(28, 140)(29, 141)(30, 142)(31, 159)(32, 144)(33, 161)(34, 162)(35, 163)(36, 148)(37, 149)(38, 150)(39, 167)(40, 152)(41, 169)(42, 170)(43, 171)(44, 156)(45, 157)(46, 158)(47, 175)(48, 160)(49, 173)(50, 177)(51, 178)(52, 164)(53, 165)(54, 166)(55, 176)(56, 168)(57, 179)(58, 180)(59, 172)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 40 ), ( 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1355
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1364 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^7, Y1^3 * Y3 * Y1 * Y3^6, Y3^3 * Y1^-1 * Y3 * Y1^-1 * Y3^4 * Y1^-2, (Y3 * Y2^-1)^15, (Y1^-1 * Y3^-1)^20 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 36, 96, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 27, 87, 42, 102, 52, 112, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 43, 103, 57, 117, 60, 120, 51, 111, 34, 94, 19, 79, 31, 91, 45, 105, 56, 116, 41, 101, 48, 108, 59, 119, 50, 110, 33, 93, 47, 107, 55, 115, 40, 100, 25, 85, 32, 92, 46, 106, 58, 118, 49, 109, 54, 114, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 44, 104, 53, 113, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 37, 97, 22, 82, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 162)(27, 163)(28, 134)(29, 165)(30, 136)(31, 167)(32, 138)(33, 169)(34, 170)(35, 171)(36, 172)(37, 146)(38, 142)(39, 143)(40, 144)(41, 145)(42, 177)(43, 176)(44, 148)(45, 175)(46, 150)(47, 174)(48, 152)(49, 173)(50, 178)(51, 179)(52, 180)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 164)(59, 166)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 40 ), ( 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40, 30, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1354
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1365 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y2 * Y3 * Y2^3 * Y1^-1, Y1^15, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 23, 83, 31, 91, 39, 99, 47, 107, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 24, 84, 32, 92, 40, 100, 48, 108, 55, 115, 58, 118, 51, 111, 43, 103, 35, 95, 27, 87, 19, 79, 10, 70)(5, 65, 8, 68, 16, 76, 25, 85, 33, 93, 41, 101, 49, 109, 56, 116, 59, 119, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 12, 72)(9, 69, 17, 77, 26, 86, 34, 94, 42, 102, 50, 110, 57, 117, 60, 120, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 13, 73, 18, 78)(121, 181, 123, 183, 129, 189, 136, 196, 126, 186, 135, 195, 146, 206, 153, 213, 143, 203, 152, 212, 162, 222, 169, 229, 159, 219, 168, 228, 177, 237, 179, 239, 172, 232, 178, 238, 174, 234, 165, 225, 156, 216, 163, 223, 158, 218, 149, 209, 140, 200, 147, 207, 142, 202, 132, 192, 124, 184, 130, 190, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 145, 205, 134, 194, 144, 204, 154, 214, 161, 221, 151, 211, 160, 220, 170, 230, 176, 236, 167, 227, 175, 235, 180, 240, 173, 233, 164, 224, 171, 231, 166, 226, 157, 217, 148, 208, 155, 215, 150, 210, 141, 201, 131, 191, 139, 199, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 138)(10, 139)(11, 140)(12, 141)(13, 142)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 147)(20, 148)(21, 149)(22, 150)(23, 134)(24, 135)(25, 136)(26, 137)(27, 155)(28, 156)(29, 157)(30, 158)(31, 143)(32, 144)(33, 145)(34, 146)(35, 163)(36, 164)(37, 165)(38, 166)(39, 151)(40, 152)(41, 153)(42, 154)(43, 171)(44, 172)(45, 173)(46, 174)(47, 159)(48, 160)(49, 161)(50, 162)(51, 178)(52, 167)(53, 179)(54, 180)(55, 168)(56, 169)(57, 170)(58, 175)(59, 176)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1369
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 30^4, 120 ]

E27.1366 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y2, Y3^-1), Y2^2 * Y3^-1 * Y2^2, Y1^15, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2^2 * Y3 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 22, 82, 30, 90, 38, 98, 46, 106, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 23, 83, 31, 91, 39, 99, 47, 107, 54, 114, 58, 118, 51, 111, 43, 103, 35, 95, 27, 87, 19, 79, 10, 70)(5, 65, 8, 68, 16, 76, 24, 84, 32, 92, 40, 100, 48, 108, 55, 115, 59, 119, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 12, 72)(9, 69, 13, 73, 17, 77, 25, 85, 33, 93, 41, 101, 49, 109, 56, 116, 60, 120, 57, 117, 50, 110, 42, 102, 34, 94, 26, 86, 18, 78)(121, 181, 123, 183, 129, 189, 132, 192, 124, 184, 130, 190, 138, 198, 141, 201, 131, 191, 139, 199, 146, 206, 149, 209, 140, 200, 147, 207, 154, 214, 157, 217, 148, 208, 155, 215, 162, 222, 165, 225, 156, 216, 163, 223, 170, 230, 173, 233, 164, 224, 171, 231, 177, 237, 179, 239, 172, 232, 178, 238, 180, 240, 175, 235, 166, 226, 174, 234, 176, 236, 168, 228, 158, 218, 167, 227, 169, 229, 160, 220, 150, 210, 159, 219, 161, 221, 152, 212, 142, 202, 151, 211, 153, 213, 144, 204, 134, 194, 143, 203, 145, 205, 136, 196, 126, 186, 135, 195, 137, 197, 128, 188, 122, 182, 127, 187, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 138)(10, 139)(11, 140)(12, 141)(13, 129)(14, 126)(15, 127)(16, 128)(17, 133)(18, 146)(19, 147)(20, 148)(21, 149)(22, 134)(23, 135)(24, 136)(25, 137)(26, 154)(27, 155)(28, 156)(29, 157)(30, 142)(31, 143)(32, 144)(33, 145)(34, 162)(35, 163)(36, 164)(37, 165)(38, 150)(39, 151)(40, 152)(41, 153)(42, 170)(43, 171)(44, 172)(45, 173)(46, 158)(47, 159)(48, 160)(49, 161)(50, 177)(51, 178)(52, 166)(53, 179)(54, 167)(55, 168)(56, 169)(57, 180)(58, 174)(59, 175)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1368
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 30^4, 120 ]

E27.1367 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2^2 * Y3 * Y2^6, Y1^4 * Y2 * Y1^-1 * Y2^-1 * Y1^-2 * Y3, Y2^2 * Y3^-1 * Y2 * Y3^-6 * Y2, Y1^2 * Y2 * Y1^2 * Y2^3 * Y1 * Y3^-2, Y2 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y3^-4, Y1 * Y2^-1 * Y1 * Y2^-3 * Y3 * Y2^-4, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1 * Y3^-3, Y2 * Y3 * Y2 * Y3^2 * Y2^2 * Y1^-5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 57, 117, 41, 101, 33, 93, 49, 109, 53, 113, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 56, 116, 40, 100, 25, 85, 32, 92, 48, 108, 60, 120, 52, 112, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 58, 118, 50, 110, 34, 94, 19, 79, 31, 91, 47, 107, 54, 114, 38, 98, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 45, 105, 55, 115, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 46, 106, 59, 119, 51, 111, 35, 95, 20, 80)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 169, 229, 168, 228, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 167, 227, 173, 233, 180, 240, 166, 226, 148, 208, 134, 194, 147, 207, 165, 225, 174, 234, 157, 217, 172, 232, 179, 239, 164, 224, 146, 206, 163, 223, 175, 235, 158, 218, 142, 202, 156, 216, 171, 231, 178, 238, 162, 222, 176, 236, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 170, 230, 177, 237, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 154)(20, 155)(21, 156)(22, 157)(23, 158)(24, 159)(25, 160)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 145)(33, 161)(34, 170)(35, 171)(36, 172)(37, 173)(38, 174)(39, 175)(40, 176)(41, 177)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 178)(51, 179)(52, 180)(53, 169)(54, 167)(55, 165)(56, 163)(57, 162)(58, 164)(59, 166)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1370
Graph:: bipartite
	v = 5 e = 120 f = 63
	degree seq :: [ 30^4, 120 ]

E27.1368 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^20, (Y3^-1 * Y1^-1)^15, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 12, 72, 18, 78, 24, 84, 30, 90, 36, 96, 42, 102, 48, 108, 54, 114, 52, 112, 46, 106, 40, 100, 34, 94, 28, 88, 22, 82, 16, 76, 10, 70, 4, 64)(3, 63, 7, 67, 13, 73, 19, 79, 25, 85, 31, 91, 37, 97, 43, 103, 49, 109, 55, 115, 59, 119, 57, 117, 51, 111, 45, 105, 39, 99, 33, 93, 27, 87, 21, 81, 15, 75, 9, 69)(5, 65, 8, 68, 14, 74, 20, 80, 26, 86, 32, 92, 38, 98, 44, 104, 50, 110, 56, 116, 60, 120, 58, 118, 53, 113, 47, 107, 41, 101, 35, 95, 29, 89, 23, 83, 17, 77, 11, 71)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 128)(4, 129)(5, 121)(6, 133)(7, 134)(8, 122)(9, 125)(10, 135)(11, 124)(12, 139)(13, 140)(14, 126)(15, 131)(16, 141)(17, 130)(18, 145)(19, 146)(20, 132)(21, 137)(22, 147)(23, 136)(24, 151)(25, 152)(26, 138)(27, 143)(28, 153)(29, 142)(30, 157)(31, 158)(32, 144)(33, 149)(34, 159)(35, 148)(36, 163)(37, 164)(38, 150)(39, 155)(40, 165)(41, 154)(42, 169)(43, 170)(44, 156)(45, 161)(46, 171)(47, 160)(48, 175)(49, 176)(50, 162)(51, 167)(52, 177)(53, 166)(54, 179)(55, 180)(56, 168)(57, 173)(58, 172)(59, 178)(60, 174)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 120 ), ( 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1366
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1369 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-2 * Y3^-4, Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-6, Y3^2 * Y1^11 * Y3, Y1^-2 * Y3^2 * Y1^-2 * Y3^2 * Y1^-2 * Y3^-2 * Y1^-3 * Y3, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 39, 99, 51, 111, 46, 106, 34, 94, 19, 79, 31, 91, 25, 85, 32, 92, 44, 104, 56, 116, 49, 109, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 40, 100, 52, 112, 59, 119, 57, 117, 45, 105, 33, 93, 24, 84, 13, 73, 18, 78, 30, 90, 43, 103, 55, 115, 48, 108, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 41, 101, 53, 113, 47, 107, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 42, 102, 54, 114, 60, 120, 58, 118, 50, 110, 38, 98, 23, 83, 12, 72)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 160)(27, 162)(28, 134)(29, 145)(30, 136)(31, 144)(32, 138)(33, 143)(34, 165)(35, 166)(36, 167)(37, 168)(38, 142)(39, 172)(40, 174)(41, 146)(42, 152)(43, 148)(44, 150)(45, 158)(46, 177)(47, 171)(48, 173)(49, 175)(50, 157)(51, 179)(52, 180)(53, 159)(54, 164)(55, 161)(56, 163)(57, 170)(58, 169)(59, 178)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 120 ), ( 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1365
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1370 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {15, 20, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^4 * Y1 * Y3^-4, Y1^-3 * Y3^-2 * Y1^-2 * Y3^-1 * Y1^-2, Y3^-1 * Y1^-1 * Y3^-8, Y3^-1 * Y1^4 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3 * Y3^-1, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 40, 100, 25, 85, 32, 92, 48, 108, 58, 118, 53, 113, 34, 94, 19, 79, 31, 91, 47, 107, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 46, 106, 57, 117, 52, 112, 33, 93, 49, 109, 59, 119, 55, 115, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 56, 116, 51, 111, 41, 101, 50, 110, 60, 120, 54, 114, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 45, 105, 38, 98, 23, 83, 12, 72)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 169)(32, 138)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 142)(39, 143)(40, 144)(41, 145)(42, 159)(43, 158)(44, 146)(45, 157)(46, 148)(47, 179)(48, 150)(49, 161)(50, 152)(51, 160)(52, 176)(53, 177)(54, 178)(55, 180)(56, 162)(57, 164)(58, 166)(59, 170)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 30, 120 ), ( 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120, 30, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1367
Graph:: simple bipartite
	v = 63 e = 120 f = 5
	degree seq :: [ 2^60, 40^3 ]

E27.1371 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {12, 30, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^5, T1^12 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 16, 6, 15, 29, 40, 38, 26, 37, 49, 58, 56, 46, 55, 60, 53, 43, 32, 41, 45, 34, 23, 11, 21, 25, 13, 5)(2, 7, 17, 30, 28, 14, 27, 39, 50, 48, 36, 47, 57, 59, 52, 42, 51, 54, 44, 33, 22, 31, 35, 24, 12, 4, 10, 20, 18, 8)(61, 62, 66, 74, 86, 96, 106, 102, 92, 82, 71, 64)(63, 67, 75, 87, 97, 107, 115, 111, 101, 91, 81, 70)(65, 68, 76, 88, 98, 108, 116, 112, 103, 93, 83, 72)(69, 77, 89, 99, 109, 117, 120, 114, 105, 95, 85, 80)(73, 78, 79, 90, 100, 110, 118, 119, 113, 104, 94, 84)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^12 ), ( 120^30 ) }
Outer automorphisms :: reflexible
Dual of E27.1375
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 12^5, 30^2 ]

E27.1372 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {12, 30, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T1^4 * T2 * T1 * T2 * T1^2, T2^7 * T1^-1 * T2 * T1^-1, (T1^-1 * T2^-2)^5, T2^-1 * T1^3 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 45, 30, 16, 6, 15, 29, 44, 55, 59, 53, 42, 26, 38, 22, 36, 49, 56, 52, 40, 24, 12, 4, 10, 20, 34, 47, 32, 18, 8, 2, 7, 17, 31, 46, 54, 43, 28, 14, 27, 37, 50, 57, 60, 58, 51, 39, 23, 11, 21, 35, 48, 41, 25, 13, 5)(61, 62, 66, 74, 86, 99, 84, 73, 78, 90, 103, 113, 118, 112, 101, 107, 93, 106, 115, 117, 109, 95, 80, 69, 77, 89, 97, 82, 71, 64)(63, 67, 75, 87, 98, 83, 72, 65, 68, 76, 88, 102, 111, 100, 85, 92, 105, 114, 119, 120, 116, 108, 94, 79, 91, 104, 110, 96, 81, 70)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 24^30 ), ( 24^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1376
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 60 f = 5
	degree seq :: [ 30^2, 60 ]

E27.1373 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {12, 30, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-5 * T2^5, T2^-2 * T1^-2 * T2^-1 * T1^-1 * T2^-4 * T1^-2, T2^12, T1^-20 * T2^-4, T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 42, 57, 51, 41, 25, 13, 5)(2, 7, 17, 31, 49, 56, 52, 37, 50, 32, 18, 8)(4, 10, 20, 34, 44, 26, 43, 58, 55, 40, 24, 12)(6, 15, 29, 47, 60, 53, 38, 22, 36, 48, 30, 16)(11, 21, 35, 46, 28, 14, 27, 45, 59, 54, 39, 23)(61, 62, 66, 74, 86, 102, 116, 113, 99, 84, 73, 78, 90, 106, 94, 79, 91, 107, 119, 115, 101, 110, 96, 81, 70, 63, 67, 75, 87, 103, 117, 112, 98, 83, 72, 65, 68, 76, 88, 104, 93, 109, 120, 114, 100, 85, 92, 108, 95, 80, 69, 77, 89, 105, 118, 111, 97, 82, 71, 64)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 60^12 ), ( 60^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1374
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 12^5, 60 ]

E27.1374 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {12, 30, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2^5, T1^12 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 16, 76, 6, 66, 15, 75, 29, 89, 40, 100, 38, 98, 26, 86, 37, 97, 49, 109, 58, 118, 56, 116, 46, 106, 55, 115, 60, 120, 53, 113, 43, 103, 32, 92, 41, 101, 45, 105, 34, 94, 23, 83, 11, 71, 21, 81, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 30, 90, 28, 88, 14, 74, 27, 87, 39, 99, 50, 110, 48, 108, 36, 96, 47, 107, 57, 117, 59, 119, 52, 112, 42, 102, 51, 111, 54, 114, 44, 104, 33, 93, 22, 82, 31, 91, 35, 95, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 18, 78, 8, 68)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 79)(19, 90)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 80)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 102)(47, 115)(48, 116)(49, 117)(50, 118)(51, 101)(52, 103)(53, 104)(54, 105)(55, 111)(56, 112)(57, 120)(58, 119)(59, 113)(60, 114)
	local type(s) :: { ( 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60, 12, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1373
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.1375 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {12, 30, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T1^4 * T2 * T1 * T2 * T1^2, T2^7 * T1^-1 * T2 * T1^-1, (T1^-1 * T2^-2)^5, T2^-1 * T1^3 * T2^-1 * T1^4 * T2^-1 * T1^4 * T2^-2 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 45, 105, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 44, 104, 55, 115, 59, 119, 53, 113, 42, 102, 26, 86, 38, 98, 22, 82, 36, 96, 49, 109, 56, 116, 52, 112, 40, 100, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 34, 94, 47, 107, 32, 92, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 46, 106, 54, 114, 43, 103, 28, 88, 14, 74, 27, 87, 37, 97, 50, 110, 57, 117, 60, 120, 58, 118, 51, 111, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 48, 108, 41, 101, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 99)(27, 98)(28, 102)(29, 97)(30, 103)(31, 104)(32, 105)(33, 106)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 107)(42, 111)(43, 113)(44, 110)(45, 114)(46, 115)(47, 93)(48, 94)(49, 95)(50, 96)(51, 100)(52, 101)(53, 118)(54, 119)(55, 117)(56, 108)(57, 109)(58, 112)(59, 120)(60, 116)
	local type(s) :: { ( 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30, 12, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.1371
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1376 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {12, 30, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (T1, T2^-1), (F * T2)^2, (F * T1)^2, T1^-5 * T2^5, T2^-2 * T1^-2 * T2^-1 * T1^-1 * T2^-4 * T1^-2, T2^12, T1^-20 * T2^-4, T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 42, 102, 57, 117, 51, 111, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 49, 109, 56, 116, 52, 112, 37, 97, 50, 110, 32, 92, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 34, 94, 44, 104, 26, 86, 43, 103, 58, 118, 55, 115, 40, 100, 24, 84, 12, 72)(6, 66, 15, 75, 29, 89, 47, 107, 60, 120, 53, 113, 38, 98, 22, 82, 36, 96, 48, 108, 30, 90, 16, 76)(11, 71, 21, 81, 35, 95, 46, 106, 28, 88, 14, 74, 27, 87, 45, 105, 59, 119, 54, 114, 39, 99, 23, 83)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 110)(42, 116)(43, 117)(44, 93)(45, 118)(46, 94)(47, 119)(48, 95)(49, 120)(50, 96)(51, 97)(52, 98)(53, 99)(54, 100)(55, 101)(56, 113)(57, 112)(58, 111)(59, 115)(60, 114)
	local type(s) :: { ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1372
Transitivity :: ET+ VT+ AT
Graph::
	v = 5 e = 60 f = 3
	degree seq :: [ 24^5 ]

E27.1377 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (Y2, Y1^-1), (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, Y2 * Y3 * Y2^4 * Y3, Y1^12, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 36, 96, 46, 106, 42, 102, 32, 92, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 37, 97, 47, 107, 55, 115, 51, 111, 41, 101, 31, 91, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 38, 98, 48, 108, 56, 116, 52, 112, 43, 103, 33, 93, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 39, 99, 49, 109, 57, 117, 60, 120, 54, 114, 45, 105, 35, 95, 25, 85, 20, 80)(13, 73, 18, 78, 19, 79, 30, 90, 40, 100, 50, 110, 58, 118, 59, 119, 53, 113, 44, 104, 34, 94, 24, 84)(121, 181, 123, 183, 129, 189, 139, 199, 136, 196, 126, 186, 135, 195, 149, 209, 160, 220, 158, 218, 146, 206, 157, 217, 169, 229, 178, 238, 176, 236, 166, 226, 175, 235, 180, 240, 173, 233, 163, 223, 152, 212, 161, 221, 165, 225, 154, 214, 143, 203, 131, 191, 141, 201, 145, 205, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 150, 210, 148, 208, 134, 194, 147, 207, 159, 219, 170, 230, 168, 228, 156, 216, 167, 227, 177, 237, 179, 239, 172, 232, 162, 222, 171, 231, 174, 234, 164, 224, 153, 213, 142, 202, 151, 211, 155, 215, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 138, 198, 128, 188)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 138)(20, 145)(21, 151)(22, 152)(23, 153)(24, 154)(25, 155)(26, 134)(27, 135)(28, 136)(29, 137)(30, 139)(31, 161)(32, 162)(33, 163)(34, 164)(35, 165)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 171)(42, 166)(43, 172)(44, 173)(45, 174)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 175)(52, 176)(53, 179)(54, 180)(55, 167)(56, 168)(57, 169)(58, 170)(59, 178)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1380
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 24^5, 60^2 ]

E27.1378 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), Y1^5 * Y2^2 * Y1^2, Y1 * Y2^-1 * Y1 * Y2^-7, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 43, 103, 53, 113, 58, 118, 52, 112, 41, 101, 47, 107, 33, 93, 46, 106, 55, 115, 57, 117, 49, 109, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 42, 102, 51, 111, 40, 100, 25, 85, 32, 92, 45, 105, 54, 114, 59, 119, 60, 120, 56, 116, 48, 108, 34, 94, 19, 79, 31, 91, 44, 104, 50, 110, 36, 96, 21, 81, 10, 70)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 165, 225, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 164, 224, 175, 235, 179, 239, 173, 233, 162, 222, 146, 206, 158, 218, 142, 202, 156, 216, 169, 229, 176, 236, 172, 232, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 167, 227, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 166, 226, 174, 234, 163, 223, 148, 208, 134, 194, 147, 207, 157, 217, 170, 230, 177, 237, 180, 240, 178, 238, 171, 231, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 168, 228, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 158)(27, 157)(28, 134)(29, 164)(30, 136)(31, 166)(32, 138)(33, 165)(34, 167)(35, 168)(36, 169)(37, 170)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 148)(44, 175)(45, 150)(46, 174)(47, 152)(48, 161)(49, 176)(50, 177)(51, 159)(52, 160)(53, 162)(54, 163)(55, 179)(56, 172)(57, 180)(58, 171)(59, 173)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1379
Graph:: bipartite
	v = 3 e = 120 f = 65
	degree seq :: [ 60^2, 120 ]

E27.1379 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3, Y2), Y3^-5 * Y2^-5, Y3^9 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^3 * Y2^-4, Y2^12, Y3^-20 * Y2^4, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2, (Y3^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 134, 194, 146, 206, 162, 222, 176, 236, 171, 231, 157, 217, 142, 202, 131, 191, 124, 184)(123, 183, 127, 187, 135, 195, 147, 207, 163, 223, 161, 221, 170, 230, 180, 240, 175, 235, 156, 216, 141, 201, 130, 190)(125, 185, 128, 188, 136, 196, 148, 208, 164, 224, 177, 237, 172, 232, 153, 213, 169, 229, 158, 218, 143, 203, 132, 192)(129, 189, 137, 197, 149, 209, 165, 225, 160, 220, 145, 205, 152, 212, 168, 228, 179, 239, 174, 234, 155, 215, 140, 200)(133, 193, 138, 198, 150, 210, 166, 226, 178, 238, 173, 233, 154, 214, 139, 199, 151, 211, 167, 227, 159, 219, 144, 204)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 169)(32, 138)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 142)(39, 143)(40, 144)(41, 145)(42, 161)(43, 160)(44, 146)(45, 159)(46, 148)(47, 158)(48, 150)(49, 157)(50, 152)(51, 180)(52, 176)(53, 177)(54, 178)(55, 179)(56, 170)(57, 162)(58, 164)(59, 166)(60, 168)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 60, 120 ), ( 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120, 60, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1378
Graph:: simple bipartite
	v = 65 e = 120 f = 3
	degree seq :: [ 2^60, 24^5 ]

E27.1380 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1, Y3^-1), (Y1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^5 * Y3^-5, Y1^-5 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-4, Y3^12, Y1^20 * Y3^4, (Y3 * Y2^-1)^12, (Y1^-1 * Y3^-1)^30 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 56, 116, 53, 113, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 46, 106, 34, 94, 19, 79, 31, 91, 47, 107, 59, 119, 55, 115, 41, 101, 50, 110, 36, 96, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 57, 117, 52, 112, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 33, 93, 49, 109, 60, 120, 54, 114, 40, 100, 25, 85, 32, 92, 48, 108, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 45, 105, 58, 118, 51, 111, 37, 97, 22, 82, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 169)(32, 138)(33, 162)(34, 164)(35, 166)(36, 168)(37, 170)(38, 142)(39, 143)(40, 144)(41, 145)(42, 177)(43, 178)(44, 146)(45, 179)(46, 148)(47, 180)(48, 150)(49, 176)(50, 152)(51, 161)(52, 157)(53, 158)(54, 159)(55, 160)(56, 172)(57, 171)(58, 175)(59, 174)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 24, 60 ), ( 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60, 24, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1377
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1381 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3 * Y1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2 * Y1^-1 * Y2 * Y3 * Y2^3 * Y1^-3, Y3^3 * Y2^-2 * Y1^-2 * Y2^-3 * Y1^-2, Y1^12, Y2^60, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 56, 116, 51, 111, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 57, 117, 55, 115, 41, 101, 50, 110, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 33, 93, 49, 109, 60, 120, 52, 112, 38, 98, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 45, 105, 58, 118, 54, 114, 40, 100, 25, 85, 32, 92, 48, 108, 35, 95, 20, 80)(13, 73, 18, 78, 30, 90, 46, 106, 34, 94, 19, 79, 31, 91, 47, 107, 59, 119, 53, 113, 39, 99, 24, 84)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 162, 222, 177, 237, 174, 234, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 166, 226, 148, 208, 134, 194, 147, 207, 165, 225, 179, 239, 172, 232, 157, 217, 170, 230, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 169, 229, 176, 236, 175, 235, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 164, 224, 146, 206, 163, 223, 178, 238, 173, 233, 158, 218, 142, 202, 156, 216, 168, 228, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 167, 227, 180, 240, 171, 231, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 154)(20, 155)(21, 156)(22, 157)(23, 158)(24, 159)(25, 160)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 145)(33, 164)(34, 166)(35, 168)(36, 170)(37, 171)(38, 172)(39, 173)(40, 174)(41, 175)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 161)(51, 176)(52, 180)(53, 179)(54, 178)(55, 177)(56, 162)(57, 163)(58, 165)(59, 167)(60, 169)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1382
Graph:: bipartite
	v = 6 e = 120 f = 62
	degree seq :: [ 24^5, 120 ]

E27.1382 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {12, 30, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^5 * Y3^2 * Y1^2, Y1 * Y3^-1 * Y1 * Y3^-7, Y1^-1 * Y3^-2 * Y1^4 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 43, 103, 53, 113, 58, 118, 52, 112, 41, 101, 47, 107, 33, 93, 46, 106, 55, 115, 57, 117, 49, 109, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 42, 102, 51, 111, 40, 100, 25, 85, 32, 92, 45, 105, 54, 114, 59, 119, 60, 120, 56, 116, 48, 108, 34, 94, 19, 79, 31, 91, 44, 104, 50, 110, 36, 96, 21, 81, 10, 70)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 158)(27, 157)(28, 134)(29, 164)(30, 136)(31, 166)(32, 138)(33, 165)(34, 167)(35, 168)(36, 169)(37, 170)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 148)(44, 175)(45, 150)(46, 174)(47, 152)(48, 161)(49, 176)(50, 177)(51, 159)(52, 160)(53, 162)(54, 163)(55, 179)(56, 172)(57, 180)(58, 171)(59, 173)(60, 178)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 24, 120 ), ( 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120, 24, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1381
Graph:: simple bipartite
	v = 62 e = 120 f = 6
	degree seq :: [ 2^60, 60^2 ]

E27.1383 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {10, 60, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-3 * T2^6, T1^-10, T1^10, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 28, 14, 27, 45, 56, 58, 49, 37, 48, 52, 40, 24, 12, 4, 10, 20, 34, 30, 16, 6, 15, 29, 46, 57, 54, 42, 53, 60, 51, 39, 23, 11, 21, 35, 32, 18, 8, 2, 7, 17, 31, 47, 44, 26, 43, 55, 59, 50, 38, 22, 36, 41, 25, 13, 5)(61, 62, 66, 74, 86, 102, 97, 82, 71, 64)(63, 67, 75, 87, 103, 113, 108, 96, 81, 70)(65, 68, 76, 88, 104, 114, 109, 98, 83, 72)(69, 77, 89, 105, 115, 120, 112, 101, 95, 80)(73, 78, 90, 93, 107, 117, 118, 110, 99, 84)(79, 91, 106, 116, 119, 111, 100, 85, 92, 94)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^10 ), ( 120^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1389
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 10^6, 60 ]

E27.1384 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {10, 60, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^6, T1^10, T1^10, T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-4 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 38, 22, 36, 50, 59, 55, 44, 26, 43, 47, 32, 18, 8, 2, 7, 17, 31, 39, 23, 11, 21, 35, 49, 58, 54, 42, 53, 57, 46, 30, 16, 6, 15, 29, 40, 24, 12, 4, 10, 20, 34, 48, 52, 37, 51, 60, 56, 45, 28, 14, 27, 41, 25, 13, 5)(61, 62, 66, 74, 86, 102, 97, 82, 71, 64)(63, 67, 75, 87, 103, 113, 111, 96, 81, 70)(65, 68, 76, 88, 104, 114, 112, 98, 83, 72)(69, 77, 89, 101, 107, 117, 120, 110, 95, 80)(73, 78, 90, 105, 115, 118, 108, 93, 99, 84)(79, 91, 100, 85, 92, 106, 116, 119, 109, 94)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^10 ), ( 120^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1388
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 10^6, 60 ]

E27.1385 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {10, 60, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-6 * T1, T1^10, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 31, 30, 16, 6, 15, 29, 43, 42, 28, 14, 27, 41, 53, 52, 40, 26, 39, 51, 59, 58, 50, 38, 49, 57, 60, 55, 46, 34, 45, 54, 56, 47, 35, 22, 33, 44, 48, 36, 23, 11, 21, 32, 37, 24, 12, 4, 10, 20, 25, 13, 5)(61, 62, 66, 74, 86, 98, 94, 82, 71, 64)(63, 67, 75, 87, 99, 109, 105, 93, 81, 70)(65, 68, 76, 88, 100, 110, 106, 95, 83, 72)(69, 77, 89, 101, 111, 117, 114, 104, 92, 80)(73, 78, 90, 102, 112, 118, 115, 107, 96, 84)(79, 91, 103, 113, 119, 120, 116, 108, 97, 85)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 120^10 ), ( 120^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1387
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 60 f = 1
	degree seq :: [ 10^6, 60 ]

E27.1386 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {10, 60, 60})
Quotient :: edge
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^3 * T2^-1 * T1^-3, T1^-1 * T2^-1 * T1^-6, T2^-1 * T1^-3 * T2^3 * T1^2 * T2^-1 * T1 * T2^-1, T2^3 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-2, T2^7 * T1^2 * T2^2 * T1, (T1^-1 * T2^-1)^10 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 47, 54, 40, 26, 22, 36, 50, 60, 46, 32, 18, 8, 2, 7, 17, 31, 45, 59, 51, 37, 23, 11, 21, 35, 49, 58, 44, 30, 16, 6, 15, 29, 43, 57, 52, 38, 24, 12, 4, 10, 20, 34, 48, 56, 42, 28, 14, 27, 41, 55, 53, 39, 25, 13, 5)(61, 62, 66, 74, 86, 83, 72, 65, 68, 76, 88, 100, 97, 84, 73, 78, 90, 102, 114, 111, 98, 85, 92, 104, 116, 107, 119, 112, 99, 106, 118, 108, 93, 105, 117, 113, 120, 109, 94, 79, 91, 103, 115, 110, 95, 80, 69, 77, 89, 101, 96, 81, 70, 63, 67, 75, 87, 82, 71, 64)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.1390
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.1387 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {10, 60, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-3 * T2^6, T1^-10, T1^10, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 28, 88, 14, 74, 27, 87, 45, 105, 56, 116, 58, 118, 49, 109, 37, 97, 48, 108, 52, 112, 40, 100, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 34, 94, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 46, 106, 57, 117, 54, 114, 42, 102, 53, 113, 60, 120, 51, 111, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 32, 92, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 47, 107, 44, 104, 26, 86, 43, 103, 55, 115, 59, 119, 50, 110, 38, 98, 22, 82, 36, 96, 41, 101, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 102)(27, 103)(28, 104)(29, 105)(30, 93)(31, 106)(32, 94)(33, 107)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 95)(42, 97)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 96)(49, 98)(50, 99)(51, 100)(52, 101)(53, 108)(54, 109)(55, 120)(56, 119)(57, 118)(58, 110)(59, 111)(60, 112)
	local type(s) :: { ( 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1385
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1388 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {10, 60, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^6, T1^10, T1^10, T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-4 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^2 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 38, 98, 22, 82, 36, 96, 50, 110, 59, 119, 55, 115, 44, 104, 26, 86, 43, 103, 47, 107, 32, 92, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 39, 99, 23, 83, 11, 71, 21, 81, 35, 95, 49, 109, 58, 118, 54, 114, 42, 102, 53, 113, 57, 117, 46, 106, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 40, 100, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 34, 94, 48, 108, 52, 112, 37, 97, 51, 111, 60, 120, 56, 116, 45, 105, 28, 88, 14, 74, 27, 87, 41, 101, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 102)(27, 103)(28, 104)(29, 101)(30, 105)(31, 100)(32, 106)(33, 99)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 107)(42, 97)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 93)(49, 94)(50, 95)(51, 96)(52, 98)(53, 111)(54, 112)(55, 118)(56, 119)(57, 120)(58, 108)(59, 109)(60, 110)
	local type(s) :: { ( 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1384
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1389 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {10, 60, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-6 * T1, T1^10, (T1^-1 * T2^-1)^60 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 18, 78, 8, 68, 2, 62, 7, 67, 17, 77, 31, 91, 30, 90, 16, 76, 6, 66, 15, 75, 29, 89, 43, 103, 42, 102, 28, 88, 14, 74, 27, 87, 41, 101, 53, 113, 52, 112, 40, 100, 26, 86, 39, 99, 51, 111, 59, 119, 58, 118, 50, 110, 38, 98, 49, 109, 57, 117, 60, 120, 55, 115, 46, 106, 34, 94, 45, 105, 54, 114, 56, 116, 47, 107, 35, 95, 22, 82, 33, 93, 44, 104, 48, 108, 36, 96, 23, 83, 11, 71, 21, 81, 32, 92, 37, 97, 24, 84, 12, 72, 4, 64, 10, 70, 20, 80, 25, 85, 13, 73, 5, 65)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 79)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 94)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 92)(45, 93)(46, 95)(47, 96)(48, 97)(49, 105)(50, 106)(51, 117)(52, 118)(53, 119)(54, 104)(55, 107)(56, 108)(57, 114)(58, 115)(59, 120)(60, 116)
	local type(s) :: { ( 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60, 10, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.1383
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 60 f = 7
	degree seq :: [ 120 ]

E27.1390 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {10, 60, 60})
Quotient :: loop
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1^-1, T2), (F * T1)^2, T2^-3 * T1^6, T2^-10, T2^10, T2^-2 * T1^-3 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 61, 3, 63, 9, 69, 19, 79, 33, 93, 47, 107, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 45, 105, 56, 116, 46, 106, 32, 92, 18, 78, 8, 68)(4, 64, 10, 70, 20, 80, 34, 94, 48, 108, 57, 117, 52, 112, 40, 100, 24, 84, 12, 72)(6, 66, 15, 75, 29, 89, 44, 104, 55, 115, 58, 118, 49, 109, 37, 97, 30, 90, 16, 76)(11, 71, 21, 81, 35, 95, 26, 86, 42, 102, 53, 113, 60, 120, 51, 111, 39, 99, 23, 83)(14, 74, 27, 87, 43, 103, 54, 114, 59, 119, 50, 110, 38, 98, 22, 82, 36, 96, 28, 88)
	L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 74)(7, 75)(8, 76)(9, 77)(10, 63)(11, 64)(12, 65)(13, 78)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 69)(21, 70)(22, 71)(23, 72)(24, 73)(25, 92)(26, 94)(27, 102)(28, 95)(29, 103)(30, 96)(31, 104)(32, 97)(33, 105)(34, 79)(35, 80)(36, 81)(37, 82)(38, 83)(39, 84)(40, 85)(41, 106)(42, 108)(43, 113)(44, 114)(45, 115)(46, 109)(47, 116)(48, 93)(49, 98)(50, 99)(51, 100)(52, 101)(53, 117)(54, 120)(55, 119)(56, 118)(57, 107)(58, 110)(59, 111)(60, 112)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1386
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.1391 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), (R * Y1)^2, Y3^-1 * Y2 * Y3^-2 * Y1^-3 * Y2^-1, Y2^6 * Y1^3, Y1^10, Y1^10, Y1^2 * Y2^-2 * Y1^2 * Y2^-1 * Y3^-3 * Y2^-3, Y3^30, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^3 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 53, 113, 51, 111, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 54, 114, 52, 112, 38, 98, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 41, 101, 47, 107, 57, 117, 60, 120, 50, 110, 35, 95, 20, 80)(13, 73, 18, 78, 30, 90, 45, 105, 55, 115, 58, 118, 48, 108, 33, 93, 39, 99, 24, 84)(19, 79, 31, 91, 40, 100, 25, 85, 32, 92, 46, 106, 56, 116, 59, 119, 49, 109, 34, 94)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 158, 218, 142, 202, 156, 216, 170, 230, 179, 239, 175, 235, 164, 224, 146, 206, 163, 223, 167, 227, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 169, 229, 178, 238, 174, 234, 162, 222, 173, 233, 177, 237, 166, 226, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 168, 228, 172, 232, 157, 217, 171, 231, 180, 240, 176, 236, 165, 225, 148, 208, 134, 194, 147, 207, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 154)(20, 155)(21, 156)(22, 157)(23, 158)(24, 159)(25, 160)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 145)(33, 168)(34, 169)(35, 170)(36, 171)(37, 162)(38, 172)(39, 153)(40, 151)(41, 149)(42, 146)(43, 147)(44, 148)(45, 150)(46, 152)(47, 161)(48, 178)(49, 179)(50, 180)(51, 173)(52, 174)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 175)(59, 176)(60, 177)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1397
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 20^6, 120 ]

E27.1392 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y1 * Y2^2 * Y3 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-3, Y3 * Y2 * Y3 * Y2^5 * Y3, Y1^4 * Y3^-6, Y1^10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 43, 103, 53, 113, 48, 108, 36, 96, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 44, 104, 54, 114, 49, 109, 38, 98, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 45, 105, 55, 115, 60, 120, 52, 112, 41, 101, 35, 95, 20, 80)(13, 73, 18, 78, 30, 90, 33, 93, 47, 107, 57, 117, 58, 118, 50, 110, 39, 99, 24, 84)(19, 79, 31, 91, 46, 106, 56, 116, 59, 119, 51, 111, 40, 100, 25, 85, 32, 92, 34, 94)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 148, 208, 134, 194, 147, 207, 165, 225, 176, 236, 178, 238, 169, 229, 157, 217, 168, 228, 172, 232, 160, 220, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 166, 226, 177, 237, 174, 234, 162, 222, 173, 233, 180, 240, 171, 231, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 167, 227, 164, 224, 146, 206, 163, 223, 175, 235, 179, 239, 170, 230, 158, 218, 142, 202, 156, 216, 161, 221, 145, 205, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 154)(20, 155)(21, 156)(22, 157)(23, 158)(24, 159)(25, 160)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 145)(33, 150)(34, 152)(35, 161)(36, 168)(37, 162)(38, 169)(39, 170)(40, 171)(41, 172)(42, 146)(43, 147)(44, 148)(45, 149)(46, 151)(47, 153)(48, 173)(49, 174)(50, 178)(51, 179)(52, 180)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 177)(59, 176)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1398
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 20^6, 120 ]

E27.1393 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^6, Y3^10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 38, 98, 34, 94, 22, 82, 11, 71, 4, 64)(3, 63, 7, 67, 15, 75, 27, 87, 39, 99, 49, 109, 45, 105, 33, 93, 21, 81, 10, 70)(5, 65, 8, 68, 16, 76, 28, 88, 40, 100, 50, 110, 46, 106, 35, 95, 23, 83, 12, 72)(9, 69, 17, 77, 29, 89, 41, 101, 51, 111, 57, 117, 54, 114, 44, 104, 32, 92, 20, 80)(13, 73, 18, 78, 30, 90, 42, 102, 52, 112, 58, 118, 55, 115, 47, 107, 36, 96, 24, 84)(19, 79, 31, 91, 43, 103, 53, 113, 59, 119, 60, 120, 56, 116, 48, 108, 37, 97, 25, 85)(121, 181, 123, 183, 129, 189, 139, 199, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 163, 223, 162, 222, 148, 208, 134, 194, 147, 207, 161, 221, 173, 233, 172, 232, 160, 220, 146, 206, 159, 219, 171, 231, 179, 239, 178, 238, 170, 230, 158, 218, 169, 229, 177, 237, 180, 240, 175, 235, 166, 226, 154, 214, 165, 225, 174, 234, 176, 236, 167, 227, 155, 215, 142, 202, 153, 213, 164, 224, 168, 228, 156, 216, 143, 203, 131, 191, 141, 201, 152, 212, 157, 217, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 145, 205, 133, 193, 125, 185)
	L = (1, 124)(2, 121)(3, 130)(4, 131)(5, 132)(6, 122)(7, 123)(8, 125)(9, 140)(10, 141)(11, 142)(12, 143)(13, 144)(14, 126)(15, 127)(16, 128)(17, 129)(18, 133)(19, 145)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 164)(33, 165)(34, 158)(35, 166)(36, 167)(37, 168)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 174)(45, 169)(46, 170)(47, 175)(48, 176)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 177)(55, 178)(56, 180)(57, 171)(58, 172)(59, 173)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1396
Graph:: bipartite
	v = 7 e = 120 f = 61
	degree seq :: [ 20^6, 120 ]

E27.1394 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^2 * Y1^-2 * Y2^-2 * Y1^2, Y2^-5 * Y1^-1 * Y2^-2, Y2^3 * Y1^-1 * Y2 * Y1^-7, Y2^-2 * Y1^4 * Y2^2 * Y1^-4, (Y3^-1 * Y1^-1)^10 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 40, 100, 54, 114, 47, 107, 33, 93, 25, 85, 32, 92, 46, 106, 60, 120, 50, 110, 36, 96, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 27, 87, 41, 101, 55, 115, 53, 113, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 44, 104, 58, 118, 49, 109, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 43, 103, 57, 117, 52, 112, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 42, 102, 56, 116, 48, 108, 34, 94, 19, 79, 31, 91, 45, 105, 59, 119, 51, 111, 37, 97, 22, 82, 11, 71, 4, 64)(121, 181, 123, 183, 129, 189, 139, 199, 153, 213, 144, 204, 132, 192, 124, 184, 130, 190, 140, 200, 154, 214, 167, 227, 159, 219, 143, 203, 131, 191, 141, 201, 155, 215, 168, 228, 174, 234, 173, 233, 158, 218, 142, 202, 156, 216, 169, 229, 176, 236, 160, 220, 175, 235, 172, 232, 157, 217, 170, 230, 178, 238, 162, 222, 146, 206, 161, 221, 177, 237, 171, 231, 180, 240, 164, 224, 148, 208, 134, 194, 147, 207, 163, 223, 179, 239, 166, 226, 150, 210, 136, 196, 126, 186, 135, 195, 149, 209, 165, 225, 152, 212, 138, 198, 128, 188, 122, 182, 127, 187, 137, 197, 151, 211, 145, 205, 133, 193, 125, 185)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 161)(27, 163)(28, 134)(29, 165)(30, 136)(31, 145)(32, 138)(33, 144)(34, 167)(35, 168)(36, 169)(37, 170)(38, 142)(39, 143)(40, 175)(41, 177)(42, 146)(43, 179)(44, 148)(45, 152)(46, 150)(47, 159)(48, 174)(49, 176)(50, 178)(51, 180)(52, 157)(53, 158)(54, 173)(55, 172)(56, 160)(57, 171)(58, 162)(59, 166)(60, 164)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1395
Graph:: bipartite
	v = 2 e = 120 f = 66
	degree seq :: [ 120^2 ]

E27.1395 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^3 * Y3^6, Y2^10, Y2^10, Y2^3 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-4 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^60 ]
Map::
	R = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)(121, 181, 122, 182, 126, 186, 134, 194, 146, 206, 162, 222, 157, 217, 142, 202, 131, 191, 124, 184)(123, 183, 127, 187, 135, 195, 147, 207, 163, 223, 173, 233, 171, 231, 156, 216, 141, 201, 130, 190)(125, 185, 128, 188, 136, 196, 148, 208, 164, 224, 174, 234, 172, 232, 158, 218, 143, 203, 132, 192)(129, 189, 137, 197, 149, 209, 161, 221, 167, 227, 177, 237, 180, 240, 170, 230, 155, 215, 140, 200)(133, 193, 138, 198, 150, 210, 165, 225, 175, 235, 178, 238, 168, 228, 153, 213, 159, 219, 144, 204)(139, 199, 151, 211, 160, 220, 145, 205, 152, 212, 166, 226, 176, 236, 179, 239, 169, 229, 154, 214)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 163)(27, 161)(28, 134)(29, 160)(30, 136)(31, 159)(32, 138)(33, 158)(34, 168)(35, 169)(36, 170)(37, 171)(38, 142)(39, 143)(40, 144)(41, 145)(42, 173)(43, 167)(44, 146)(45, 148)(46, 150)(47, 152)(48, 172)(49, 178)(50, 179)(51, 180)(52, 157)(53, 177)(54, 162)(55, 164)(56, 165)(57, 166)(58, 174)(59, 175)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 120, 120 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1394
Graph:: simple bipartite
	v = 66 e = 120 f = 2
	degree seq :: [ 2^60, 20^6 ]

E27.1396 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^6, Y3^2 * Y1^-1 * Y3^8 * Y1, (Y3 * Y2^-1)^10, Y3^-2 * Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 34, 94, 19, 79, 31, 91, 44, 104, 54, 114, 60, 120, 52, 112, 41, 101, 46, 106, 49, 109, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 43, 103, 53, 113, 57, 117, 47, 107, 56, 116, 58, 118, 50, 110, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 36, 96, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 27, 87, 42, 102, 48, 108, 33, 93, 45, 105, 55, 115, 59, 119, 51, 111, 40, 100, 25, 85, 32, 92, 37, 97, 22, 82, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 162)(27, 163)(28, 134)(29, 164)(30, 136)(31, 165)(32, 138)(33, 167)(34, 168)(35, 146)(36, 148)(37, 150)(38, 142)(39, 143)(40, 144)(41, 145)(42, 173)(43, 174)(44, 175)(45, 176)(46, 152)(47, 161)(48, 177)(49, 157)(50, 158)(51, 159)(52, 160)(53, 180)(54, 179)(55, 178)(56, 166)(57, 172)(58, 169)(59, 170)(60, 171)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 20, 120 ), ( 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1393
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1397 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1^3 * Y3 * Y1^2 * Y3, Y3 * Y1 * Y3 * Y1^5 * Y3, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y3^-5 * Y1, (Y3 * Y2^-1)^10, (Y1^-1 * Y3^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 40, 100, 25, 85, 32, 92, 44, 104, 54, 114, 58, 118, 48, 108, 33, 93, 45, 105, 51, 111, 36, 96, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 27, 87, 39, 99, 24, 84, 13, 73, 18, 78, 30, 90, 43, 103, 53, 113, 57, 117, 47, 107, 56, 116, 60, 120, 50, 110, 35, 95, 20, 80, 9, 69, 17, 77, 29, 89, 38, 98, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 28, 88, 42, 102, 52, 112, 41, 101, 46, 106, 55, 115, 59, 119, 49, 109, 34, 94, 19, 79, 31, 91, 37, 97, 22, 82, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 154)(21, 155)(22, 156)(23, 131)(24, 132)(25, 133)(26, 159)(27, 158)(28, 134)(29, 157)(30, 136)(31, 165)(32, 138)(33, 167)(34, 168)(35, 169)(36, 170)(37, 171)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 148)(44, 150)(45, 176)(46, 152)(47, 161)(48, 177)(49, 178)(50, 179)(51, 180)(52, 160)(53, 162)(54, 163)(55, 164)(56, 166)(57, 172)(58, 173)(59, 174)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 20, 120 ), ( 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1391
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1398 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {10, 60, 60})
Quotient :: dipole
Aut^+ = C60 (small group id <60, 4>)
Aut   = D120 (small group id <120, 28>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^6, Y3^10, (Y3 * Y2^-1)^10, (Y1^-1 * Y3^-1)^60 ]
Map::
	R = (1, 61, 2, 62, 6, 66, 14, 74, 21, 81, 10, 70, 3, 63, 7, 67, 15, 75, 26, 86, 33, 93, 20, 80, 9, 69, 17, 77, 27, 87, 38, 98, 45, 105, 32, 92, 19, 79, 29, 89, 39, 99, 49, 109, 54, 114, 44, 104, 31, 91, 41, 101, 50, 110, 57, 117, 59, 119, 53, 113, 43, 103, 52, 112, 58, 118, 60, 120, 56, 116, 48, 108, 37, 97, 42, 102, 51, 111, 55, 115, 47, 107, 36, 96, 25, 85, 30, 90, 40, 100, 46, 106, 35, 95, 24, 84, 13, 73, 18, 78, 28, 88, 34, 94, 23, 83, 12, 72, 5, 65, 8, 68, 16, 76, 22, 82, 11, 71, 4, 64)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 127)(3, 129)(4, 130)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 140)(11, 141)(12, 124)(13, 125)(14, 146)(15, 147)(16, 126)(17, 149)(18, 128)(19, 151)(20, 152)(21, 153)(22, 134)(23, 131)(24, 132)(25, 133)(26, 158)(27, 159)(28, 136)(29, 161)(30, 138)(31, 163)(32, 164)(33, 165)(34, 142)(35, 143)(36, 144)(37, 145)(38, 169)(39, 170)(40, 148)(41, 172)(42, 150)(43, 157)(44, 173)(45, 174)(46, 154)(47, 155)(48, 156)(49, 177)(50, 178)(51, 160)(52, 162)(53, 168)(54, 179)(55, 166)(56, 167)(57, 180)(58, 171)(59, 176)(60, 175)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 20, 120 ), ( 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120, 20, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.1392
Graph:: bipartite
	v = 61 e = 120 f = 7
	degree seq :: [ 2^60, 120 ]

E27.1399 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T1^9, T2^7 * T1^-3 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 45, 28, 14, 27, 44, 58, 62, 53, 38, 22, 36, 50, 41, 25, 13, 5)(2, 7, 17, 31, 48, 57, 43, 26, 42, 56, 63, 54, 39, 23, 11, 21, 35, 49, 32, 18, 8)(4, 10, 20, 34, 47, 30, 16, 6, 15, 29, 46, 59, 61, 52, 37, 51, 60, 55, 40, 24, 12)(64, 65, 69, 77, 89, 100, 85, 74, 67)(66, 70, 78, 90, 105, 114, 99, 84, 73)(68, 71, 79, 91, 106, 115, 101, 86, 75)(72, 80, 92, 107, 119, 123, 113, 98, 83)(76, 81, 93, 108, 120, 124, 116, 102, 87)(82, 94, 109, 121, 126, 118, 104, 112, 97)(88, 95, 110, 96, 111, 122, 125, 117, 103)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^9 ), ( 126^21 ) }
Outer automorphisms :: reflexible
Dual of E27.1408
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 9^7, 21^3 ]

E27.1400 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^9, T1^-3 * T2^-7 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 50, 38, 22, 36, 53, 62, 58, 45, 28, 14, 27, 44, 41, 25, 13, 5)(2, 7, 17, 31, 48, 39, 23, 11, 21, 35, 52, 61, 57, 43, 26, 42, 56, 49, 32, 18, 8)(4, 10, 20, 34, 51, 60, 55, 37, 54, 63, 59, 47, 30, 16, 6, 15, 29, 46, 40, 24, 12)(64, 65, 69, 77, 89, 100, 85, 74, 67)(66, 70, 78, 90, 105, 117, 99, 84, 73)(68, 71, 79, 91, 106, 118, 101, 86, 75)(72, 80, 92, 107, 119, 126, 116, 98, 83)(76, 81, 93, 108, 120, 123, 113, 102, 87)(82, 94, 109, 104, 112, 122, 125, 115, 97)(88, 95, 110, 121, 124, 114, 96, 111, 103)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^9 ), ( 126^21 ) }
Outer automorphisms :: reflexible
Dual of E27.1407
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 9^7, 21^3 ]

E27.1401 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2 * T1^-3 * T2, T2^15 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 29, 37, 45, 53, 61, 56, 48, 40, 32, 24, 12, 4, 10, 20, 14, 26, 34, 42, 50, 58, 63, 55, 47, 39, 31, 23, 11, 21, 16, 6, 15, 27, 35, 43, 51, 59, 62, 54, 46, 38, 30, 22, 18, 8, 2, 7, 17, 28, 36, 44, 52, 60, 57, 49, 41, 33, 25, 13, 5)(64, 65, 69, 77, 82, 91, 98, 105, 108, 115, 122, 126, 119, 112, 109, 102, 95, 88, 85, 74, 67)(66, 70, 78, 89, 92, 99, 106, 113, 116, 123, 125, 118, 111, 104, 101, 94, 87, 76, 81, 84, 73)(68, 71, 79, 83, 72, 80, 90, 97, 100, 107, 114, 121, 124, 120, 117, 110, 103, 96, 93, 86, 75)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 18^21 ), ( 18^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1410
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 63 f = 7
	degree seq :: [ 21^3, 63 ]

E27.1402 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-6 * T1, T2 * T1^2 * T2^-2 * T1^-2 * T2, T2 * T1^-2 * T2 * T1^-1 * T2^3 * T1 * T2 * T1, T2 * T1 * T2 * T1^9 * T2, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 31, 30, 16, 6, 15, 29, 43, 42, 28, 14, 27, 41, 55, 54, 40, 26, 39, 53, 58, 63, 52, 38, 51, 59, 46, 57, 62, 50, 60, 47, 34, 45, 56, 61, 48, 35, 22, 33, 44, 49, 36, 23, 11, 21, 32, 37, 24, 12, 4, 10, 20, 25, 13, 5)(64, 65, 69, 77, 89, 101, 113, 124, 112, 100, 88, 82, 94, 106, 118, 121, 109, 97, 85, 74, 67)(66, 70, 78, 90, 102, 114, 123, 111, 99, 87, 76, 81, 93, 105, 117, 126, 120, 108, 96, 84, 73)(68, 71, 79, 91, 103, 115, 125, 119, 107, 95, 83, 72, 80, 92, 104, 116, 122, 110, 98, 86, 75)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 18^21 ), ( 18^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1409
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 63 f = 7
	degree seq :: [ 21^3, 63 ]

E27.1403 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-3 * T1 * T2^3, T1^-7 * T2^-1, T2^9, (T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 39, 25, 13, 5)(2, 7, 17, 31, 45, 46, 32, 18, 8)(4, 10, 20, 34, 47, 51, 38, 24, 12)(6, 15, 29, 43, 55, 56, 44, 30, 16)(11, 21, 35, 48, 57, 59, 50, 37, 23)(14, 27, 41, 53, 61, 62, 54, 42, 28)(22, 36, 49, 58, 63, 60, 52, 40, 26)(64, 65, 69, 77, 89, 86, 75, 68, 71, 79, 91, 103, 100, 87, 76, 81, 93, 105, 115, 113, 101, 88, 95, 107, 117, 123, 122, 114, 102, 109, 119, 125, 126, 120, 110, 96, 108, 118, 124, 121, 111, 97, 82, 94, 106, 116, 112, 98, 83, 72, 80, 92, 104, 99, 84, 73, 66, 70, 78, 90, 85, 74, 67)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 42^9 ), ( 42^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1405
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 63 f = 3
	degree seq :: [ 9^7, 63 ]

E27.1404 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 21, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^9, T2^9, T2^4 * T1^7, T2^2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-4, (T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 41, 25, 13, 5)(2, 7, 17, 31, 49, 50, 32, 18, 8)(4, 10, 20, 34, 51, 59, 40, 24, 12)(6, 15, 29, 47, 55, 63, 48, 30, 16)(11, 21, 35, 52, 60, 42, 58, 39, 23)(14, 27, 45, 56, 37, 54, 62, 46, 28)(22, 36, 53, 61, 44, 26, 43, 57, 38)(64, 65, 69, 77, 89, 105, 122, 104, 113, 126, 117, 99, 84, 73, 66, 70, 78, 90, 106, 121, 103, 88, 95, 111, 125, 116, 98, 83, 72, 80, 92, 108, 120, 102, 87, 76, 81, 93, 109, 124, 115, 97, 82, 94, 110, 119, 101, 86, 75, 68, 71, 79, 91, 107, 123, 114, 96, 112, 118, 100, 85, 74, 67)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 42^9 ), ( 42^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1406
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 63 f = 3
	degree seq :: [ 9^7, 63 ]

E27.1405 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T1^9, T2^7 * T1^-3 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 33, 96, 45, 108, 28, 91, 14, 77, 27, 90, 44, 107, 58, 121, 62, 125, 53, 116, 38, 101, 22, 85, 36, 99, 50, 113, 41, 104, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 48, 111, 57, 120, 43, 106, 26, 89, 42, 105, 56, 119, 63, 126, 54, 117, 39, 102, 23, 86, 11, 74, 21, 84, 35, 98, 49, 112, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 34, 97, 47, 110, 30, 93, 16, 79, 6, 69, 15, 78, 29, 92, 46, 109, 59, 122, 61, 124, 52, 115, 37, 100, 51, 114, 60, 123, 55, 118, 40, 103, 24, 87, 12, 75)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 100)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 112)(42, 114)(43, 115)(44, 119)(45, 120)(46, 121)(47, 96)(48, 122)(49, 97)(50, 98)(51, 99)(52, 101)(53, 102)(54, 103)(55, 104)(56, 123)(57, 124)(58, 126)(59, 125)(60, 113)(61, 116)(62, 117)(63, 118)
	local type(s) :: { ( 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1403
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 63 f = 8
	degree seq :: [ 42^3 ]

E27.1406 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^9, T1^-3 * T2^-7 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 33, 96, 50, 113, 38, 101, 22, 85, 36, 99, 53, 116, 62, 125, 58, 121, 45, 108, 28, 91, 14, 77, 27, 90, 44, 107, 41, 104, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 48, 111, 39, 102, 23, 86, 11, 74, 21, 84, 35, 98, 52, 115, 61, 124, 57, 120, 43, 106, 26, 89, 42, 105, 56, 119, 49, 112, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 34, 97, 51, 114, 60, 123, 55, 118, 37, 100, 54, 117, 63, 126, 59, 122, 47, 110, 30, 93, 16, 79, 6, 69, 15, 78, 29, 92, 46, 109, 40, 103, 24, 87, 12, 75)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 100)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 112)(42, 117)(43, 118)(44, 119)(45, 120)(46, 104)(47, 121)(48, 103)(49, 122)(50, 102)(51, 96)(52, 97)(53, 98)(54, 99)(55, 101)(56, 126)(57, 123)(58, 124)(59, 125)(60, 113)(61, 114)(62, 115)(63, 116)
	local type(s) :: { ( 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63, 9, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1404
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 63 f = 8
	degree seq :: [ 42^3 ]

E27.1407 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2^-1), (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2 * T1^-3 * T2, T2^15 * T1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 29, 92, 37, 100, 45, 108, 53, 116, 61, 124, 56, 119, 48, 111, 40, 103, 32, 95, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 14, 77, 26, 89, 34, 97, 42, 105, 50, 113, 58, 121, 63, 126, 55, 118, 47, 110, 39, 102, 31, 94, 23, 86, 11, 74, 21, 84, 16, 79, 6, 69, 15, 78, 27, 90, 35, 98, 43, 106, 51, 114, 59, 122, 62, 125, 54, 117, 46, 109, 38, 101, 30, 93, 22, 85, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 28, 91, 36, 99, 44, 107, 52, 115, 60, 123, 57, 120, 49, 112, 41, 104, 33, 96, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 82)(15, 89)(16, 83)(17, 90)(18, 84)(19, 91)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 85)(26, 92)(27, 97)(28, 98)(29, 99)(30, 86)(31, 87)(32, 88)(33, 93)(34, 100)(35, 105)(36, 106)(37, 107)(38, 94)(39, 95)(40, 96)(41, 101)(42, 108)(43, 113)(44, 114)(45, 115)(46, 102)(47, 103)(48, 104)(49, 109)(50, 116)(51, 121)(52, 122)(53, 123)(54, 110)(55, 111)(56, 112)(57, 117)(58, 124)(59, 126)(60, 125)(61, 120)(62, 118)(63, 119)
	local type(s) :: { ( 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.1400
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1408 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-6 * T1, T2 * T1^2 * T2^-2 * T1^-2 * T2, T2 * T1^-2 * T2 * T1^-1 * T2^3 * T1 * T2 * T1, T2 * T1 * T2 * T1^9 * T2, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 31, 94, 30, 93, 16, 79, 6, 69, 15, 78, 29, 92, 43, 106, 42, 105, 28, 91, 14, 77, 27, 90, 41, 104, 55, 118, 54, 117, 40, 103, 26, 89, 39, 102, 53, 116, 58, 121, 63, 126, 52, 115, 38, 101, 51, 114, 59, 122, 46, 109, 57, 120, 62, 125, 50, 113, 60, 123, 47, 110, 34, 97, 45, 108, 56, 119, 61, 124, 48, 111, 35, 98, 22, 85, 33, 96, 44, 107, 49, 112, 36, 99, 23, 86, 11, 74, 21, 84, 32, 95, 37, 100, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 82)(26, 101)(27, 102)(28, 103)(29, 104)(30, 105)(31, 106)(32, 83)(33, 84)(34, 85)(35, 86)(36, 87)(37, 88)(38, 113)(39, 114)(40, 115)(41, 116)(42, 117)(43, 118)(44, 95)(45, 96)(46, 97)(47, 98)(48, 99)(49, 100)(50, 124)(51, 123)(52, 125)(53, 122)(54, 126)(55, 121)(56, 107)(57, 108)(58, 109)(59, 110)(60, 111)(61, 112)(62, 119)(63, 120)
	local type(s) :: { ( 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21, 9, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.1399
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1409 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-3 * T1 * T2^3, T1^-7 * T2^-1, T2^9, (T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 33, 96, 39, 102, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 45, 108, 46, 109, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 34, 97, 47, 110, 51, 114, 38, 101, 24, 87, 12, 75)(6, 69, 15, 78, 29, 92, 43, 106, 55, 118, 56, 119, 44, 107, 30, 93, 16, 79)(11, 74, 21, 84, 35, 98, 48, 111, 57, 120, 59, 122, 50, 113, 37, 100, 23, 86)(14, 77, 27, 90, 41, 104, 53, 116, 61, 124, 62, 125, 54, 117, 42, 105, 28, 91)(22, 85, 36, 99, 49, 112, 58, 121, 63, 126, 60, 123, 52, 115, 40, 103, 26, 89)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 86)(27, 85)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 108)(34, 82)(35, 83)(36, 84)(37, 87)(38, 88)(39, 109)(40, 100)(41, 99)(42, 115)(43, 116)(44, 117)(45, 118)(46, 119)(47, 96)(48, 97)(49, 98)(50, 101)(51, 102)(52, 113)(53, 112)(54, 123)(55, 124)(56, 125)(57, 110)(58, 111)(59, 114)(60, 122)(61, 121)(62, 126)(63, 120)
	local type(s) :: { ( 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1402
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 63 f = 4
	degree seq :: [ 18^7 ]

E27.1410 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 21, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1^-1), (F * T2)^2, (F * T1)^2, T2^9, T2^9, T2^4 * T1^7, T2^2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-4, (T1^-1 * T2^-1)^21 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 33, 96, 41, 104, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 49, 112, 50, 113, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 34, 97, 51, 114, 59, 122, 40, 103, 24, 87, 12, 75)(6, 69, 15, 78, 29, 92, 47, 110, 55, 118, 63, 126, 48, 111, 30, 93, 16, 79)(11, 74, 21, 84, 35, 98, 52, 115, 60, 123, 42, 105, 58, 121, 39, 102, 23, 86)(14, 77, 27, 90, 45, 108, 56, 119, 37, 100, 54, 117, 62, 125, 46, 109, 28, 91)(22, 85, 36, 99, 53, 116, 61, 124, 44, 107, 26, 89, 43, 106, 57, 120, 38, 101)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 105)(27, 106)(28, 107)(29, 108)(30, 109)(31, 110)(32, 111)(33, 112)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 113)(42, 122)(43, 121)(44, 123)(45, 120)(46, 124)(47, 119)(48, 125)(49, 118)(50, 126)(51, 96)(52, 97)(53, 98)(54, 99)(55, 100)(56, 101)(57, 102)(58, 103)(59, 104)(60, 114)(61, 115)(62, 116)(63, 117)
	local type(s) :: { ( 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63, 21, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1401
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 63 f = 4
	degree seq :: [ 18^7 ]

E27.1411 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y1^-1 * Y3^-1, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^9, Y3^3 * Y2^-2 * Y1^2 * Y2 * Y1 * Y2, Y2^-7 * Y1^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 37, 100, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 42, 105, 54, 117, 36, 99, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 43, 106, 55, 118, 38, 101, 23, 86, 12, 75)(9, 72, 17, 80, 29, 92, 44, 107, 56, 119, 63, 126, 53, 116, 35, 98, 20, 83)(13, 76, 18, 81, 30, 93, 45, 108, 57, 120, 60, 123, 50, 113, 39, 102, 24, 87)(19, 82, 31, 94, 46, 109, 41, 104, 49, 112, 59, 122, 62, 125, 52, 115, 34, 97)(25, 88, 32, 95, 47, 110, 58, 121, 61, 124, 51, 114, 33, 96, 48, 111, 40, 103)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 176, 239, 164, 227, 148, 211, 162, 225, 179, 242, 188, 251, 184, 247, 171, 234, 154, 217, 140, 203, 153, 216, 170, 233, 167, 230, 151, 214, 139, 202, 131, 194)(128, 191, 133, 196, 143, 206, 157, 220, 174, 237, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 178, 241, 187, 250, 183, 246, 169, 232, 152, 215, 168, 231, 182, 245, 175, 238, 158, 221, 144, 207, 134, 197)(130, 193, 136, 199, 146, 209, 160, 223, 177, 240, 186, 249, 181, 244, 163, 226, 180, 243, 189, 252, 185, 248, 173, 236, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 172, 235, 166, 229, 150, 213, 138, 201)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 160)(20, 161)(21, 162)(22, 163)(23, 164)(24, 165)(25, 166)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 151)(33, 177)(34, 178)(35, 179)(36, 180)(37, 152)(38, 181)(39, 176)(40, 174)(41, 172)(42, 153)(43, 154)(44, 155)(45, 156)(46, 157)(47, 158)(48, 159)(49, 167)(50, 186)(51, 187)(52, 188)(53, 189)(54, 168)(55, 169)(56, 170)(57, 171)(58, 173)(59, 175)(60, 183)(61, 184)(62, 185)(63, 182)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1417
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 18^7, 42^3 ]

E27.1412 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1 * Y3, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1, (R * Y2)^2, (R * Y1)^2, Y2^2 * Y3^-1 * Y2^-2 * Y1^-1, Y1^9, Y2^2 * Y3 * Y2^5 * Y1^-2, Y2^-1 * Y1^2 * Y3^-1 * Y2^-2 * Y1^2 * Y3^-1 * Y2^-2 * Y1^2 * Y3^-1 * Y2^-2 * Y1^3, Y1^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-3 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 37, 100, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 42, 105, 51, 114, 36, 99, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 43, 106, 52, 115, 38, 101, 23, 86, 12, 75)(9, 72, 17, 80, 29, 92, 44, 107, 56, 119, 60, 123, 50, 113, 35, 98, 20, 83)(13, 76, 18, 81, 30, 93, 45, 108, 57, 120, 61, 124, 53, 116, 39, 102, 24, 87)(19, 82, 31, 94, 46, 109, 58, 121, 63, 126, 55, 118, 41, 104, 49, 112, 34, 97)(25, 88, 32, 95, 47, 110, 33, 96, 48, 111, 59, 122, 62, 125, 54, 117, 40, 103)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 171, 234, 154, 217, 140, 203, 153, 216, 170, 233, 184, 247, 188, 251, 179, 242, 164, 227, 148, 211, 162, 225, 176, 239, 167, 230, 151, 214, 139, 202, 131, 194)(128, 191, 133, 196, 143, 206, 157, 220, 174, 237, 183, 246, 169, 232, 152, 215, 168, 231, 182, 245, 189, 252, 180, 243, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 175, 238, 158, 221, 144, 207, 134, 197)(130, 193, 136, 199, 146, 209, 160, 223, 173, 236, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 172, 235, 185, 248, 187, 250, 178, 241, 163, 226, 177, 240, 186, 249, 181, 244, 166, 229, 150, 213, 138, 201)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 160)(20, 161)(21, 162)(22, 163)(23, 164)(24, 165)(25, 166)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 151)(33, 173)(34, 175)(35, 176)(36, 177)(37, 152)(38, 178)(39, 179)(40, 180)(41, 181)(42, 153)(43, 154)(44, 155)(45, 156)(46, 157)(47, 158)(48, 159)(49, 167)(50, 186)(51, 168)(52, 169)(53, 187)(54, 188)(55, 189)(56, 170)(57, 171)(58, 172)(59, 174)(60, 182)(61, 183)(62, 185)(63, 184)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1418
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 18^7, 42^3 ]

E27.1413 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y2 * Y1^-1 * Y2 * Y1^-3 * Y2, Y2^15 * Y1, (Y3^-1 * Y1^-1)^9 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 19, 82, 28, 91, 35, 98, 42, 105, 45, 108, 52, 115, 59, 122, 63, 126, 56, 119, 49, 112, 46, 109, 39, 102, 32, 95, 25, 88, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 29, 92, 36, 99, 43, 106, 50, 113, 53, 116, 60, 123, 62, 125, 55, 118, 48, 111, 41, 104, 38, 101, 31, 94, 24, 87, 13, 76, 18, 81, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 20, 83, 9, 72, 17, 80, 27, 90, 34, 97, 37, 100, 44, 107, 51, 114, 58, 121, 61, 124, 57, 120, 54, 117, 47, 110, 40, 103, 33, 96, 30, 93, 23, 86, 12, 75)(127, 190, 129, 192, 135, 198, 145, 208, 155, 218, 163, 226, 171, 234, 179, 242, 187, 250, 182, 245, 174, 237, 166, 229, 158, 221, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 140, 203, 152, 215, 160, 223, 168, 231, 176, 239, 184, 247, 189, 252, 181, 244, 173, 236, 165, 228, 157, 220, 149, 212, 137, 200, 147, 210, 142, 205, 132, 195, 141, 204, 153, 216, 161, 224, 169, 232, 177, 240, 185, 248, 188, 251, 180, 243, 172, 235, 164, 227, 156, 219, 148, 211, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 154, 217, 162, 225, 170, 233, 178, 241, 186, 249, 183, 246, 175, 238, 167, 230, 159, 222, 151, 214, 139, 202, 131, 194)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 152)(15, 153)(16, 132)(17, 154)(18, 134)(19, 155)(20, 140)(21, 142)(22, 144)(23, 137)(24, 138)(25, 139)(26, 160)(27, 161)(28, 162)(29, 163)(30, 148)(31, 149)(32, 150)(33, 151)(34, 168)(35, 169)(36, 170)(37, 171)(38, 156)(39, 157)(40, 158)(41, 159)(42, 176)(43, 177)(44, 178)(45, 179)(46, 164)(47, 165)(48, 166)(49, 167)(50, 184)(51, 185)(52, 186)(53, 187)(54, 172)(55, 173)(56, 174)(57, 175)(58, 189)(59, 188)(60, 183)(61, 182)(62, 180)(63, 181)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1415
Graph:: bipartite
	v = 4 e = 126 f = 70
	degree seq :: [ 42^3, 126 ]

E27.1414 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1), Y2 * Y1^-1 * Y2^5, Y2 * Y1^2 * Y2^-2 * Y1^-2 * Y2, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^3 * Y1 * Y2 * Y1, Y2 * Y1 * Y2 * Y1^9 * Y2, (Y3^-1 * Y1^-1)^9 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 38, 101, 50, 113, 61, 124, 49, 112, 37, 100, 25, 88, 19, 82, 31, 94, 43, 106, 55, 118, 58, 121, 46, 109, 34, 97, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 39, 102, 51, 114, 60, 123, 48, 111, 36, 99, 24, 87, 13, 76, 18, 81, 30, 93, 42, 105, 54, 117, 63, 126, 57, 120, 45, 108, 33, 96, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 40, 103, 52, 115, 62, 125, 56, 119, 44, 107, 32, 95, 20, 83, 9, 72, 17, 80, 29, 92, 41, 104, 53, 116, 59, 122, 47, 110, 35, 98, 23, 86, 12, 75)(127, 190, 129, 192, 135, 198, 145, 208, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 157, 220, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 169, 232, 168, 231, 154, 217, 140, 203, 153, 216, 167, 230, 181, 244, 180, 243, 166, 229, 152, 215, 165, 228, 179, 242, 184, 247, 189, 252, 178, 241, 164, 227, 177, 240, 185, 248, 172, 235, 183, 246, 188, 251, 176, 239, 186, 249, 173, 236, 160, 223, 171, 234, 182, 245, 187, 250, 174, 237, 161, 224, 148, 211, 159, 222, 170, 233, 175, 238, 162, 225, 149, 212, 137, 200, 147, 210, 158, 221, 163, 226, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 151, 214, 139, 202, 131, 194)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 144)(20, 151)(21, 158)(22, 159)(23, 137)(24, 138)(25, 139)(26, 165)(27, 167)(28, 140)(29, 169)(30, 142)(31, 156)(32, 163)(33, 170)(34, 171)(35, 148)(36, 149)(37, 150)(38, 177)(39, 179)(40, 152)(41, 181)(42, 154)(43, 168)(44, 175)(45, 182)(46, 183)(47, 160)(48, 161)(49, 162)(50, 186)(51, 185)(52, 164)(53, 184)(54, 166)(55, 180)(56, 187)(57, 188)(58, 189)(59, 172)(60, 173)(61, 174)(62, 176)(63, 178)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1416
Graph:: bipartite
	v = 4 e = 126 f = 70
	degree seq :: [ 42^3, 126 ]

E27.1415 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^9, Y2^9, Y2^4 * Y3^-7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^63 ]
Map::
	R = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)(127, 190, 128, 191, 132, 195, 140, 203, 152, 215, 163, 226, 148, 211, 137, 200, 130, 193)(129, 192, 133, 196, 141, 204, 153, 216, 168, 231, 180, 243, 162, 225, 147, 210, 136, 199)(131, 194, 134, 197, 142, 205, 154, 217, 169, 232, 181, 244, 164, 227, 149, 212, 138, 201)(135, 198, 143, 206, 155, 218, 170, 233, 186, 249, 185, 248, 179, 242, 161, 224, 146, 209)(139, 202, 144, 207, 156, 219, 171, 234, 176, 239, 189, 252, 182, 245, 165, 228, 150, 213)(145, 208, 157, 220, 172, 235, 187, 250, 184, 247, 167, 230, 175, 238, 178, 241, 160, 223)(151, 214, 158, 221, 173, 236, 177, 240, 159, 222, 174, 237, 188, 251, 183, 246, 166, 229)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 159)(20, 160)(21, 161)(22, 162)(23, 137)(24, 138)(25, 139)(26, 168)(27, 170)(28, 140)(29, 172)(30, 142)(31, 174)(32, 144)(33, 176)(34, 177)(35, 178)(36, 179)(37, 180)(38, 148)(39, 149)(40, 150)(41, 151)(42, 186)(43, 152)(44, 187)(45, 154)(46, 188)(47, 156)(48, 189)(49, 158)(50, 169)(51, 171)(52, 173)(53, 175)(54, 185)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 184)(61, 183)(62, 182)(63, 181)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 42, 126 ), ( 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1413
Graph:: simple bipartite
	v = 70 e = 126 f = 4
	degree seq :: [ 2^63, 18^7 ]

E27.1416 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^7, Y2^9, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^-2, (Y3^-1 * Y1^-1)^63 ]
Map::
	R = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)(127, 190, 128, 191, 132, 195, 140, 203, 152, 215, 162, 225, 148, 211, 137, 200, 130, 193)(129, 192, 133, 196, 141, 204, 153, 216, 166, 229, 174, 237, 161, 224, 147, 210, 136, 199)(131, 194, 134, 197, 142, 205, 154, 217, 167, 230, 175, 238, 163, 226, 149, 212, 138, 201)(135, 198, 143, 206, 155, 218, 168, 231, 178, 241, 183, 246, 173, 236, 160, 223, 146, 209)(139, 202, 144, 207, 156, 219, 169, 232, 179, 242, 184, 247, 176, 239, 164, 227, 150, 213)(145, 208, 157, 220, 170, 233, 180, 243, 186, 249, 188, 251, 182, 245, 172, 235, 159, 222)(151, 214, 158, 221, 171, 234, 181, 244, 187, 250, 189, 252, 185, 248, 177, 240, 165, 228)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 158)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 166)(27, 168)(28, 140)(29, 170)(30, 142)(31, 171)(32, 144)(33, 151)(34, 172)(35, 173)(36, 174)(37, 148)(38, 149)(39, 150)(40, 178)(41, 152)(42, 180)(43, 154)(44, 181)(45, 156)(46, 165)(47, 182)(48, 183)(49, 162)(50, 163)(51, 164)(52, 186)(53, 167)(54, 187)(55, 169)(56, 177)(57, 188)(58, 175)(59, 176)(60, 189)(61, 179)(62, 185)(63, 184)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 42, 126 ), ( 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126, 42, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1414
Graph:: simple bipartite
	v = 70 e = 126 f = 4
	degree seq :: [ 2^63, 18^7 ]

E27.1417 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^5 * Y3 * Y1 * Y3^3 * Y1, Y3^3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-5, Y3^-1 * Y1^-1 * Y3^-4 * Y1^-4 * Y3 * Y1^-2, (Y3 * Y2^-1)^9, (Y1^-1 * Y3^-1)^21 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 42, 105, 59, 122, 41, 104, 50, 113, 63, 126, 54, 117, 36, 99, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 43, 106, 58, 121, 40, 103, 25, 88, 32, 95, 48, 111, 62, 125, 53, 116, 35, 98, 20, 83, 9, 72, 17, 80, 29, 92, 45, 108, 57, 120, 39, 102, 24, 87, 13, 76, 18, 81, 30, 93, 46, 109, 61, 124, 52, 115, 34, 97, 19, 82, 31, 94, 47, 110, 56, 119, 38, 101, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 44, 107, 60, 123, 51, 114, 33, 96, 49, 112, 55, 118, 37, 100, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 159)(20, 160)(21, 161)(22, 162)(23, 137)(24, 138)(25, 139)(26, 169)(27, 171)(28, 140)(29, 173)(30, 142)(31, 175)(32, 144)(33, 167)(34, 177)(35, 178)(36, 179)(37, 180)(38, 148)(39, 149)(40, 150)(41, 151)(42, 184)(43, 183)(44, 152)(45, 182)(46, 154)(47, 181)(48, 156)(49, 176)(50, 158)(51, 185)(52, 186)(53, 187)(54, 188)(55, 189)(56, 163)(57, 164)(58, 165)(59, 166)(60, 168)(61, 170)(62, 172)(63, 174)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 18, 42 ), ( 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1411
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1418 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3 * Y1^3 * Y3^-1 * Y1^-3, Y1^-1 * Y3^-1 * Y1^-6, Y3^-3 * Y1^-1 * Y3^-3 * Y1 * Y3^-3, (Y3 * Y2^-1)^9, (Y1^-1 * Y3^-1)^21 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 40, 103, 37, 100, 24, 87, 13, 76, 18, 81, 30, 93, 42, 105, 52, 115, 50, 113, 38, 101, 25, 88, 32, 95, 44, 107, 54, 117, 60, 123, 59, 122, 51, 114, 39, 102, 46, 109, 56, 119, 62, 125, 63, 126, 57, 120, 47, 110, 33, 96, 45, 108, 55, 118, 61, 124, 58, 121, 48, 111, 34, 97, 19, 82, 31, 94, 43, 106, 53, 116, 49, 112, 35, 98, 20, 83, 9, 72, 17, 80, 29, 92, 41, 104, 36, 99, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 159)(20, 160)(21, 161)(22, 162)(23, 137)(24, 138)(25, 139)(26, 148)(27, 167)(28, 140)(29, 169)(30, 142)(31, 171)(32, 144)(33, 165)(34, 173)(35, 174)(36, 175)(37, 149)(38, 150)(39, 151)(40, 152)(41, 179)(42, 154)(43, 181)(44, 156)(45, 172)(46, 158)(47, 177)(48, 183)(49, 184)(50, 163)(51, 164)(52, 166)(53, 187)(54, 168)(55, 182)(56, 170)(57, 185)(58, 189)(59, 176)(60, 178)(61, 188)(62, 180)(63, 186)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 18, 42 ), ( 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42, 18, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1412
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1419 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^2 * Y3^-1 * Y2^5, Y1^9, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^2 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 37, 100, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 40, 103, 49, 112, 36, 99, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 41, 104, 50, 113, 38, 101, 23, 86, 12, 75)(9, 72, 17, 80, 29, 92, 42, 105, 52, 115, 58, 121, 48, 111, 35, 98, 20, 83)(13, 76, 18, 81, 30, 93, 43, 106, 53, 116, 59, 122, 51, 114, 39, 102, 24, 87)(19, 82, 31, 94, 44, 107, 54, 117, 60, 123, 63, 126, 57, 120, 47, 110, 34, 97)(25, 88, 32, 95, 45, 108, 55, 118, 61, 124, 62, 125, 56, 119, 46, 109, 33, 96)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 160, 223, 172, 235, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 173, 236, 182, 245, 177, 240, 164, 227, 148, 211, 162, 225, 174, 237, 183, 246, 188, 251, 185, 248, 176, 239, 163, 226, 175, 238, 184, 247, 189, 252, 187, 250, 179, 242, 167, 230, 152, 215, 166, 229, 178, 241, 186, 249, 181, 244, 169, 232, 154, 217, 140, 203, 153, 216, 168, 231, 180, 243, 171, 234, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 170, 233, 158, 221, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 157, 220, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 160)(20, 161)(21, 162)(22, 163)(23, 164)(24, 165)(25, 159)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 151)(33, 172)(34, 173)(35, 174)(36, 175)(37, 152)(38, 176)(39, 177)(40, 153)(41, 154)(42, 155)(43, 156)(44, 157)(45, 158)(46, 182)(47, 183)(48, 184)(49, 166)(50, 167)(51, 185)(52, 168)(53, 169)(54, 170)(55, 171)(56, 188)(57, 189)(58, 178)(59, 179)(60, 180)(61, 181)(62, 187)(63, 186)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1422
Graph:: bipartite
	v = 8 e = 126 f = 66
	degree seq :: [ 18^7, 126 ]

E27.1420 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y3, Y1 * Y3, (Y2, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y1 * Y2 * Y3^2 * Y2^-1 * Y1, Y1^9, Y2 * Y1 * Y2^6 * Y1 * Y3^-2, Y2^2 * Y3 * Y2 * Y3 * Y2^4 * Y1^-3, (Y1^-2 * Y3^2)^9, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 37, 100, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 42, 105, 54, 117, 36, 99, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 43, 106, 55, 118, 38, 101, 23, 86, 12, 75)(9, 72, 17, 80, 29, 92, 44, 107, 59, 122, 63, 126, 53, 116, 35, 98, 20, 83)(13, 76, 18, 81, 30, 93, 45, 108, 60, 123, 50, 113, 56, 119, 39, 102, 24, 87)(19, 82, 31, 94, 46, 109, 58, 121, 41, 104, 49, 112, 62, 125, 52, 115, 34, 97)(25, 88, 32, 95, 47, 110, 61, 124, 51, 114, 33, 96, 48, 111, 57, 120, 40, 103)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 176, 239, 181, 244, 163, 226, 180, 243, 189, 252, 175, 238, 158, 221, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 157, 220, 174, 237, 182, 245, 164, 227, 148, 211, 162, 225, 179, 242, 188, 251, 173, 236, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 172, 235, 183, 246, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 178, 241, 187, 250, 171, 234, 154, 217, 140, 203, 153, 216, 170, 233, 184, 247, 166, 229, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 160, 223, 177, 240, 186, 249, 169, 232, 152, 215, 168, 231, 185, 248, 167, 230, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 160)(20, 161)(21, 162)(22, 163)(23, 164)(24, 165)(25, 166)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 151)(33, 177)(34, 178)(35, 179)(36, 180)(37, 152)(38, 181)(39, 182)(40, 183)(41, 184)(42, 153)(43, 154)(44, 155)(45, 156)(46, 157)(47, 158)(48, 159)(49, 167)(50, 186)(51, 187)(52, 188)(53, 189)(54, 168)(55, 169)(56, 176)(57, 174)(58, 172)(59, 170)(60, 171)(61, 173)(62, 175)(63, 185)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1421
Graph:: bipartite
	v = 8 e = 126 f = 66
	degree seq :: [ 18^7, 126 ]

E27.1421 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-1 * Y1 * Y3^-2, Y3^15 * Y1, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 19, 82, 28, 91, 35, 98, 42, 105, 45, 108, 52, 115, 59, 122, 63, 126, 56, 119, 49, 112, 46, 109, 39, 102, 32, 95, 25, 88, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 29, 92, 36, 99, 43, 106, 50, 113, 53, 116, 60, 123, 62, 125, 55, 118, 48, 111, 41, 104, 38, 101, 31, 94, 24, 87, 13, 76, 18, 81, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 20, 83, 9, 72, 17, 80, 27, 90, 34, 97, 37, 100, 44, 107, 51, 114, 58, 121, 61, 124, 57, 120, 54, 117, 47, 110, 40, 103, 33, 96, 30, 93, 23, 86, 12, 75)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 152)(15, 153)(16, 132)(17, 154)(18, 134)(19, 155)(20, 140)(21, 142)(22, 144)(23, 137)(24, 138)(25, 139)(26, 160)(27, 161)(28, 162)(29, 163)(30, 148)(31, 149)(32, 150)(33, 151)(34, 168)(35, 169)(36, 170)(37, 171)(38, 156)(39, 157)(40, 158)(41, 159)(42, 176)(43, 177)(44, 178)(45, 179)(46, 164)(47, 165)(48, 166)(49, 167)(50, 184)(51, 185)(52, 186)(53, 187)(54, 172)(55, 173)(56, 174)(57, 175)(58, 189)(59, 188)(60, 183)(61, 182)(62, 180)(63, 181)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 18, 126 ), ( 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1420
Graph:: simple bipartite
	v = 66 e = 126 f = 8
	degree seq :: [ 2^63, 42^3 ]

E27.1422 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 21, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^4, Y3 * Y1^-2 * Y3 * Y1^-1 * Y3^2 * Y1 * Y3^2 * Y1, Y1^6 * Y3 * Y1 * Y3^2 * Y1^3, (Y1^-1 * Y3^-1)^9, (Y3 * Y2^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 38, 101, 50, 113, 61, 124, 49, 112, 37, 100, 25, 88, 19, 82, 31, 94, 43, 106, 55, 118, 58, 121, 46, 109, 34, 97, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 27, 90, 39, 102, 51, 114, 60, 123, 48, 111, 36, 99, 24, 87, 13, 76, 18, 81, 30, 93, 42, 105, 54, 117, 63, 126, 57, 120, 45, 108, 33, 96, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 28, 91, 40, 103, 52, 115, 62, 125, 56, 119, 44, 107, 32, 95, 20, 83, 9, 72, 17, 80, 29, 92, 41, 104, 53, 116, 59, 122, 47, 110, 35, 98, 23, 86, 12, 75)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 144)(20, 151)(21, 158)(22, 159)(23, 137)(24, 138)(25, 139)(26, 165)(27, 167)(28, 140)(29, 169)(30, 142)(31, 156)(32, 163)(33, 170)(34, 171)(35, 148)(36, 149)(37, 150)(38, 177)(39, 179)(40, 152)(41, 181)(42, 154)(43, 168)(44, 175)(45, 182)(46, 183)(47, 160)(48, 161)(49, 162)(50, 186)(51, 185)(52, 164)(53, 184)(54, 166)(55, 180)(56, 187)(57, 188)(58, 189)(59, 172)(60, 173)(61, 174)(62, 176)(63, 178)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 18, 126 ), ( 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126, 18, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1419
Graph:: simple bipartite
	v = 66 e = 126 f = 8
	degree seq :: [ 2^63, 42^3 ]

E27.1423 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^7, T1^2 * T2^-9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 46, 43, 29, 16, 6, 15, 28, 42, 56, 63, 59, 50, 36, 22, 35, 49, 58, 61, 52, 38, 24, 12, 4, 10, 20, 33, 47, 45, 31, 18, 8, 2, 7, 17, 30, 44, 57, 55, 41, 27, 14, 26, 40, 54, 62, 60, 51, 37, 23, 11, 21, 34, 48, 53, 39, 25, 13, 5)(64, 65, 69, 77, 85, 74, 67)(66, 70, 78, 89, 98, 84, 73)(68, 71, 79, 90, 99, 86, 75)(72, 80, 91, 103, 112, 97, 83)(76, 81, 92, 104, 113, 100, 87)(82, 93, 105, 117, 121, 111, 96)(88, 94, 106, 118, 122, 114, 101)(95, 107, 119, 125, 124, 116, 110)(102, 108, 109, 120, 126, 123, 115)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^7 ), ( 126^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1432
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 7^9, 63 ]

E27.1424 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-3 * T2^-9, T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-5 * T1, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 46, 60, 50, 36, 22, 35, 49, 63, 59, 45, 31, 18, 8, 2, 7, 17, 30, 44, 58, 51, 37, 23, 11, 21, 34, 48, 62, 57, 43, 29, 16, 6, 15, 28, 42, 56, 52, 38, 24, 12, 4, 10, 20, 33, 47, 61, 55, 41, 27, 14, 26, 40, 54, 53, 39, 25, 13, 5)(64, 65, 69, 77, 85, 74, 67)(66, 70, 78, 89, 98, 84, 73)(68, 71, 79, 90, 99, 86, 75)(72, 80, 91, 103, 112, 97, 83)(76, 81, 92, 104, 113, 100, 87)(82, 93, 105, 117, 126, 111, 96)(88, 94, 106, 118, 123, 114, 101)(95, 107, 119, 116, 122, 125, 110)(102, 108, 120, 124, 109, 121, 115)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^7 ), ( 126^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1433
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 7^9, 63 ]

E27.1425 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-7, T1^7, T1^-3 * T2^9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 46, 55, 41, 27, 14, 26, 40, 54, 63, 52, 38, 24, 12, 4, 10, 20, 33, 47, 57, 43, 29, 16, 6, 15, 28, 42, 56, 62, 51, 37, 23, 11, 21, 34, 48, 59, 45, 31, 18, 8, 2, 7, 17, 30, 44, 58, 61, 50, 36, 22, 35, 49, 60, 53, 39, 25, 13, 5)(64, 65, 69, 77, 85, 74, 67)(66, 70, 78, 89, 98, 84, 73)(68, 71, 79, 90, 99, 86, 75)(72, 80, 91, 103, 112, 97, 83)(76, 81, 92, 104, 113, 100, 87)(82, 93, 105, 117, 123, 111, 96)(88, 94, 106, 118, 124, 114, 101)(95, 107, 119, 126, 116, 122, 110)(102, 108, 120, 109, 121, 125, 115)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^7 ), ( 126^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1430
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 7^9, 63 ]

E27.1426 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-1 * T2^9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 45, 31, 18, 8, 2, 7, 17, 30, 44, 55, 43, 29, 16, 6, 15, 28, 42, 54, 61, 53, 41, 27, 14, 26, 40, 52, 60, 63, 58, 49, 36, 22, 35, 48, 57, 62, 59, 50, 37, 23, 11, 21, 34, 47, 56, 51, 38, 24, 12, 4, 10, 20, 33, 46, 39, 25, 13, 5)(64, 65, 69, 77, 85, 74, 67)(66, 70, 78, 89, 98, 84, 73)(68, 71, 79, 90, 99, 86, 75)(72, 80, 91, 103, 111, 97, 83)(76, 81, 92, 104, 112, 100, 87)(82, 93, 105, 115, 120, 110, 96)(88, 94, 106, 116, 121, 113, 101)(95, 107, 117, 123, 125, 119, 109)(102, 108, 118, 124, 126, 122, 114)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^7 ), ( 126^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1431
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 7^9, 63 ]

E27.1427 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-1 * T2^-9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 46, 38, 24, 12, 4, 10, 20, 33, 47, 56, 51, 37, 23, 11, 21, 34, 48, 57, 62, 59, 50, 36, 22, 35, 49, 58, 63, 61, 53, 41, 27, 14, 26, 40, 52, 60, 55, 43, 29, 16, 6, 15, 28, 42, 54, 45, 31, 18, 8, 2, 7, 17, 30, 44, 39, 25, 13, 5)(64, 65, 69, 77, 85, 74, 67)(66, 70, 78, 89, 98, 84, 73)(68, 71, 79, 90, 99, 86, 75)(72, 80, 91, 103, 112, 97, 83)(76, 81, 92, 104, 113, 100, 87)(82, 93, 105, 115, 121, 111, 96)(88, 94, 106, 116, 122, 114, 101)(95, 107, 117, 123, 126, 120, 110)(102, 108, 118, 124, 125, 119, 109)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 126^7 ), ( 126^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1434
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 63 f = 1
	degree seq :: [ 7^9, 63 ]

E27.1428 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2 * T1^-1 * T2^5 * T1^-1, T1^5 * T2 * T1^5, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 28, 14, 27, 45, 56, 63, 59, 50, 37, 48, 53, 40, 24, 12, 4, 10, 20, 34, 30, 16, 6, 15, 29, 46, 57, 54, 42, 49, 58, 61, 52, 39, 23, 11, 21, 35, 32, 18, 8, 2, 7, 17, 31, 47, 44, 26, 43, 55, 62, 60, 51, 38, 22, 36, 41, 25, 13, 5)(64, 65, 69, 77, 89, 105, 113, 101, 86, 75, 68, 71, 79, 91, 107, 117, 122, 114, 102, 87, 76, 81, 93, 96, 110, 120, 126, 123, 115, 103, 88, 95, 97, 82, 94, 109, 119, 125, 124, 116, 104, 98, 83, 72, 80, 92, 108, 118, 121, 111, 99, 84, 73, 66, 70, 78, 90, 106, 112, 100, 85, 74, 67)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 14^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1436
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 63 f = 9
	degree seq :: [ 63^2 ]

E27.1429 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 63, 63})
Quotient :: edge
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^3 * T2^-1 * T1 * T2^-3 * T1, T2^9 * T1 * T2 * T1 * T2, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 46, 56, 59, 49, 39, 23, 11, 21, 35, 28, 14, 27, 43, 53, 63, 57, 47, 37, 32, 18, 8, 2, 7, 17, 31, 45, 55, 60, 50, 40, 24, 12, 4, 10, 20, 34, 26, 42, 52, 62, 58, 48, 38, 22, 36, 30, 16, 6, 15, 29, 44, 54, 61, 51, 41, 25, 13, 5)(64, 65, 69, 77, 89, 96, 108, 117, 126, 121, 112, 103, 88, 95, 99, 84, 73, 66, 70, 78, 90, 105, 109, 118, 124, 120, 111, 102, 87, 76, 81, 93, 98, 83, 72, 80, 92, 106, 115, 119, 123, 114, 110, 101, 86, 75, 68, 71, 79, 91, 97, 82, 94, 107, 116, 125, 122, 113, 104, 100, 85, 74, 67)
	L = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)
	local type(s) :: { ( 14^63 ) }
Outer automorphisms :: reflexible
Dual of E27.1435
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 63 f = 9
	degree seq :: [ 63^2 ]

E27.1430 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^7, T1^2 * T2^-9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 32, 95, 46, 109, 43, 106, 29, 92, 16, 79, 6, 69, 15, 78, 28, 91, 42, 105, 56, 119, 63, 126, 59, 122, 50, 113, 36, 99, 22, 85, 35, 98, 49, 112, 58, 121, 61, 124, 52, 115, 38, 101, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 33, 96, 47, 110, 45, 108, 31, 94, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 30, 93, 44, 107, 57, 120, 55, 118, 41, 104, 27, 90, 14, 77, 26, 89, 40, 103, 54, 117, 62, 125, 60, 123, 51, 114, 37, 100, 23, 86, 11, 74, 21, 84, 34, 97, 48, 111, 53, 116, 39, 102, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 85)(15, 89)(16, 90)(17, 91)(18, 92)(19, 93)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 94)(26, 98)(27, 99)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 82)(34, 83)(35, 84)(36, 86)(37, 87)(38, 88)(39, 108)(40, 112)(41, 113)(42, 117)(43, 118)(44, 119)(45, 109)(46, 120)(47, 95)(48, 96)(49, 97)(50, 100)(51, 101)(52, 102)(53, 110)(54, 121)(55, 122)(56, 125)(57, 126)(58, 111)(59, 114)(60, 115)(61, 116)(62, 124)(63, 123)
	local type(s) :: { ( 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1425
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1431 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-3 * T2^-9, T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-5 * T1, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 32, 95, 46, 109, 60, 123, 50, 113, 36, 99, 22, 85, 35, 98, 49, 112, 63, 126, 59, 122, 45, 108, 31, 94, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 30, 93, 44, 107, 58, 121, 51, 114, 37, 100, 23, 86, 11, 74, 21, 84, 34, 97, 48, 111, 62, 125, 57, 120, 43, 106, 29, 92, 16, 79, 6, 69, 15, 78, 28, 91, 42, 105, 56, 119, 52, 115, 38, 101, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 33, 96, 47, 110, 61, 124, 55, 118, 41, 104, 27, 90, 14, 77, 26, 89, 40, 103, 54, 117, 53, 116, 39, 102, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 85)(15, 89)(16, 90)(17, 91)(18, 92)(19, 93)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 94)(26, 98)(27, 99)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 82)(34, 83)(35, 84)(36, 86)(37, 87)(38, 88)(39, 108)(40, 112)(41, 113)(42, 117)(43, 118)(44, 119)(45, 120)(46, 121)(47, 95)(48, 96)(49, 97)(50, 100)(51, 101)(52, 102)(53, 122)(54, 126)(55, 123)(56, 116)(57, 124)(58, 115)(59, 125)(60, 114)(61, 109)(62, 110)(63, 111)
	local type(s) :: { ( 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1426
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1432 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-7, T1^7, T1^-3 * T2^9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 32, 95, 46, 109, 55, 118, 41, 104, 27, 90, 14, 77, 26, 89, 40, 103, 54, 117, 63, 126, 52, 115, 38, 101, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 33, 96, 47, 110, 57, 120, 43, 106, 29, 92, 16, 79, 6, 69, 15, 78, 28, 91, 42, 105, 56, 119, 62, 125, 51, 114, 37, 100, 23, 86, 11, 74, 21, 84, 34, 97, 48, 111, 59, 122, 45, 108, 31, 94, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 30, 93, 44, 107, 58, 121, 61, 124, 50, 113, 36, 99, 22, 85, 35, 98, 49, 112, 60, 123, 53, 116, 39, 102, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 85)(15, 89)(16, 90)(17, 91)(18, 92)(19, 93)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 94)(26, 98)(27, 99)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 82)(34, 83)(35, 84)(36, 86)(37, 87)(38, 88)(39, 108)(40, 112)(41, 113)(42, 117)(43, 118)(44, 119)(45, 120)(46, 121)(47, 95)(48, 96)(49, 97)(50, 100)(51, 101)(52, 102)(53, 122)(54, 123)(55, 124)(56, 126)(57, 109)(58, 125)(59, 110)(60, 111)(61, 114)(62, 115)(63, 116)
	local type(s) :: { ( 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1423
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1433 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-1 * T2^9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 32, 95, 45, 108, 31, 94, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 30, 93, 44, 107, 55, 118, 43, 106, 29, 92, 16, 79, 6, 69, 15, 78, 28, 91, 42, 105, 54, 117, 61, 124, 53, 116, 41, 104, 27, 90, 14, 77, 26, 89, 40, 103, 52, 115, 60, 123, 63, 126, 58, 121, 49, 112, 36, 99, 22, 85, 35, 98, 48, 111, 57, 120, 62, 125, 59, 122, 50, 113, 37, 100, 23, 86, 11, 74, 21, 84, 34, 97, 47, 110, 56, 119, 51, 114, 38, 101, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 33, 96, 46, 109, 39, 102, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 85)(15, 89)(16, 90)(17, 91)(18, 92)(19, 93)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 94)(26, 98)(27, 99)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 82)(34, 83)(35, 84)(36, 86)(37, 87)(38, 88)(39, 108)(40, 111)(41, 112)(42, 115)(43, 116)(44, 117)(45, 118)(46, 95)(47, 96)(48, 97)(49, 100)(50, 101)(51, 102)(52, 120)(53, 121)(54, 123)(55, 124)(56, 109)(57, 110)(58, 113)(59, 114)(60, 125)(61, 126)(62, 119)(63, 122)
	local type(s) :: { ( 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1424
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1434 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T1^-1 * T2^-9, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 32, 95, 46, 109, 38, 101, 24, 87, 12, 75, 4, 67, 10, 73, 20, 83, 33, 96, 47, 110, 56, 119, 51, 114, 37, 100, 23, 86, 11, 74, 21, 84, 34, 97, 48, 111, 57, 120, 62, 125, 59, 122, 50, 113, 36, 99, 22, 85, 35, 98, 49, 112, 58, 121, 63, 126, 61, 124, 53, 116, 41, 104, 27, 90, 14, 77, 26, 89, 40, 103, 52, 115, 60, 123, 55, 118, 43, 106, 29, 92, 16, 79, 6, 69, 15, 78, 28, 91, 42, 105, 54, 117, 45, 108, 31, 94, 18, 81, 8, 71, 2, 65, 7, 70, 17, 80, 30, 93, 44, 107, 39, 102, 25, 88, 13, 76, 5, 68)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 85)(15, 89)(16, 90)(17, 91)(18, 92)(19, 93)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 94)(26, 98)(27, 99)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 82)(34, 83)(35, 84)(36, 86)(37, 87)(38, 88)(39, 108)(40, 112)(41, 113)(42, 115)(43, 116)(44, 117)(45, 118)(46, 102)(47, 95)(48, 96)(49, 97)(50, 100)(51, 101)(52, 121)(53, 122)(54, 123)(55, 124)(56, 109)(57, 110)(58, 111)(59, 114)(60, 126)(61, 125)(62, 119)(63, 120)
	local type(s) :: { ( 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63, 7, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.1427
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 63 f = 10
	degree seq :: [ 126 ]

E27.1435 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-7, T2^7, T1^9 * T2^-2, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 33, 96, 39, 102, 24, 87, 12, 75)(6, 69, 15, 78, 29, 92, 45, 108, 46, 109, 30, 93, 16, 79)(11, 74, 21, 84, 34, 97, 47, 110, 53, 116, 38, 101, 23, 86)(14, 77, 27, 90, 43, 106, 56, 119, 57, 120, 44, 107, 28, 91)(22, 85, 35, 98, 48, 111, 58, 121, 61, 124, 52, 115, 37, 100)(26, 89, 41, 104, 55, 118, 63, 126, 59, 122, 50, 113, 42, 105)(36, 99, 49, 112, 40, 103, 54, 117, 62, 125, 60, 123, 51, 114)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 103)(27, 104)(28, 105)(29, 106)(30, 107)(31, 108)(32, 109)(33, 82)(34, 83)(35, 84)(36, 85)(37, 86)(38, 87)(39, 88)(40, 111)(41, 117)(42, 112)(43, 118)(44, 113)(45, 119)(46, 120)(47, 96)(48, 97)(49, 98)(50, 99)(51, 100)(52, 101)(53, 102)(54, 121)(55, 125)(56, 126)(57, 122)(58, 110)(59, 114)(60, 115)(61, 116)(62, 124)(63, 123)
	local type(s) :: { ( 63^14 ) }
Outer automorphisms :: reflexible
Dual of E27.1429
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 63 f = 2
	degree seq :: [ 14^9 ]

E27.1436 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 63, 63})
Quotient :: loop
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^7, T1^-9 * T2, (T1^-1 * T2^-1)^63 ]
Map:: non-degenerate
	R = (1, 64, 3, 66, 9, 72, 19, 82, 25, 88, 13, 76, 5, 68)(2, 65, 7, 70, 17, 80, 31, 94, 32, 95, 18, 81, 8, 71)(4, 67, 10, 73, 20, 83, 33, 96, 39, 102, 24, 87, 12, 75)(6, 69, 15, 78, 29, 92, 45, 108, 46, 109, 30, 93, 16, 79)(11, 74, 21, 84, 34, 97, 47, 110, 51, 114, 38, 101, 23, 86)(14, 77, 27, 90, 43, 106, 55, 118, 56, 119, 44, 107, 28, 91)(22, 85, 35, 98, 48, 111, 57, 120, 59, 122, 50, 113, 37, 100)(26, 89, 41, 104, 53, 116, 61, 124, 62, 125, 54, 117, 42, 105)(36, 99, 40, 103, 52, 115, 60, 123, 63, 126, 58, 121, 49, 112)
	L = (1, 65)(2, 69)(3, 70)(4, 64)(5, 71)(6, 77)(7, 78)(8, 79)(9, 80)(10, 66)(11, 67)(12, 68)(13, 81)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 95)(26, 103)(27, 104)(28, 105)(29, 106)(30, 107)(31, 108)(32, 109)(33, 82)(34, 83)(35, 84)(36, 85)(37, 86)(38, 87)(39, 88)(40, 98)(41, 115)(42, 99)(43, 116)(44, 117)(45, 118)(46, 119)(47, 96)(48, 97)(49, 100)(50, 101)(51, 102)(52, 111)(53, 123)(54, 112)(55, 124)(56, 125)(57, 110)(58, 113)(59, 114)(60, 120)(61, 126)(62, 121)(63, 122)
	local type(s) :: { ( 63^14 ) }
Outer automorphisms :: reflexible
Dual of E27.1428
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 63 f = 2
	degree seq :: [ 14^9 ]

E27.1437 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2^2 * Y3 * Y2^-2 * Y1, Y1^7, Y1^7, Y2^-9 * Y1^2, Y3 * Y2 * Y3 * Y2^2 * Y3^3 * Y2^-3 * Y1^-2, Y3^14, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 35, 98, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 27, 90, 36, 99, 23, 86, 12, 75)(9, 72, 17, 80, 28, 91, 40, 103, 49, 112, 34, 97, 20, 83)(13, 76, 18, 81, 29, 92, 41, 104, 50, 113, 37, 100, 24, 87)(19, 82, 30, 93, 42, 105, 54, 117, 58, 121, 48, 111, 33, 96)(25, 88, 31, 94, 43, 106, 55, 118, 59, 122, 51, 114, 38, 101)(32, 95, 44, 107, 56, 119, 62, 125, 61, 124, 53, 116, 47, 110)(39, 102, 45, 108, 46, 109, 57, 120, 63, 126, 60, 123, 52, 115)(127, 190, 129, 192, 135, 198, 145, 208, 158, 221, 172, 235, 169, 232, 155, 218, 142, 205, 132, 195, 141, 204, 154, 217, 168, 231, 182, 245, 189, 252, 185, 248, 176, 239, 162, 225, 148, 211, 161, 224, 175, 238, 184, 247, 187, 250, 178, 241, 164, 227, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 159, 222, 173, 236, 171, 234, 157, 220, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 156, 219, 170, 233, 183, 246, 181, 244, 167, 230, 153, 216, 140, 203, 152, 215, 166, 229, 180, 243, 188, 251, 186, 249, 177, 240, 163, 226, 149, 212, 137, 200, 147, 210, 160, 223, 174, 237, 179, 242, 165, 228, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 159)(20, 160)(21, 161)(22, 140)(23, 162)(24, 163)(25, 164)(26, 141)(27, 142)(28, 143)(29, 144)(30, 145)(31, 151)(32, 173)(33, 174)(34, 175)(35, 152)(36, 153)(37, 176)(38, 177)(39, 178)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 165)(46, 171)(47, 179)(48, 184)(49, 166)(50, 167)(51, 185)(52, 186)(53, 187)(54, 168)(55, 169)(56, 170)(57, 172)(58, 180)(59, 181)(60, 189)(61, 188)(62, 182)(63, 183)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1448
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 14^9, 126 ]

E27.1438 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y1^7, Y2^7 * Y3^-1 * Y2^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 35, 98, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 27, 90, 36, 99, 23, 86, 12, 75)(9, 72, 17, 80, 28, 91, 40, 103, 49, 112, 34, 97, 20, 83)(13, 76, 18, 81, 29, 92, 41, 104, 50, 113, 37, 100, 24, 87)(19, 82, 30, 93, 42, 105, 52, 115, 58, 121, 48, 111, 33, 96)(25, 88, 31, 94, 43, 106, 53, 116, 59, 122, 51, 114, 38, 101)(32, 95, 44, 107, 54, 117, 60, 123, 63, 126, 57, 120, 47, 110)(39, 102, 45, 108, 55, 118, 61, 124, 62, 125, 56, 119, 46, 109)(127, 190, 129, 192, 135, 198, 145, 208, 158, 221, 172, 235, 164, 227, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 159, 222, 173, 236, 182, 245, 177, 240, 163, 226, 149, 212, 137, 200, 147, 210, 160, 223, 174, 237, 183, 246, 188, 251, 185, 248, 176, 239, 162, 225, 148, 211, 161, 224, 175, 238, 184, 247, 189, 252, 187, 250, 179, 242, 167, 230, 153, 216, 140, 203, 152, 215, 166, 229, 178, 241, 186, 249, 181, 244, 169, 232, 155, 218, 142, 205, 132, 195, 141, 204, 154, 217, 168, 231, 180, 243, 171, 234, 157, 220, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 156, 219, 170, 233, 165, 228, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 159)(20, 160)(21, 161)(22, 140)(23, 162)(24, 163)(25, 164)(26, 141)(27, 142)(28, 143)(29, 144)(30, 145)(31, 151)(32, 173)(33, 174)(34, 175)(35, 152)(36, 153)(37, 176)(38, 177)(39, 172)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 165)(46, 182)(47, 183)(48, 184)(49, 166)(50, 167)(51, 185)(52, 168)(53, 169)(54, 170)(55, 171)(56, 188)(57, 189)(58, 178)(59, 179)(60, 180)(61, 181)(62, 187)(63, 186)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1450
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 14^9, 126 ]

E27.1439 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y1^7, Y2^9 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 35, 98, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 27, 90, 36, 99, 23, 86, 12, 75)(9, 72, 17, 80, 28, 91, 40, 103, 48, 111, 34, 97, 20, 83)(13, 76, 18, 81, 29, 92, 41, 104, 49, 112, 37, 100, 24, 87)(19, 82, 30, 93, 42, 105, 52, 115, 57, 120, 47, 110, 33, 96)(25, 88, 31, 94, 43, 106, 53, 116, 58, 121, 50, 113, 38, 101)(32, 95, 44, 107, 54, 117, 60, 123, 62, 125, 56, 119, 46, 109)(39, 102, 45, 108, 55, 118, 61, 124, 63, 126, 59, 122, 51, 114)(127, 190, 129, 192, 135, 198, 145, 208, 158, 221, 171, 234, 157, 220, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 156, 219, 170, 233, 181, 244, 169, 232, 155, 218, 142, 205, 132, 195, 141, 204, 154, 217, 168, 231, 180, 243, 187, 250, 179, 242, 167, 230, 153, 216, 140, 203, 152, 215, 166, 229, 178, 241, 186, 249, 189, 252, 184, 247, 175, 238, 162, 225, 148, 211, 161, 224, 174, 237, 183, 246, 188, 251, 185, 248, 176, 239, 163, 226, 149, 212, 137, 200, 147, 210, 160, 223, 173, 236, 182, 245, 177, 240, 164, 227, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 159, 222, 172, 235, 165, 228, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 159)(20, 160)(21, 161)(22, 140)(23, 162)(24, 163)(25, 164)(26, 141)(27, 142)(28, 143)(29, 144)(30, 145)(31, 151)(32, 172)(33, 173)(34, 174)(35, 152)(36, 153)(37, 175)(38, 176)(39, 177)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 165)(46, 182)(47, 183)(48, 166)(49, 167)(50, 184)(51, 185)(52, 168)(53, 169)(54, 170)(55, 171)(56, 188)(57, 178)(58, 179)(59, 189)(60, 180)(61, 181)(62, 186)(63, 187)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1447
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 14^9, 126 ]

E27.1440 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, (R * Y2)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2 * Y1^-2, Y1^-7, Y1^7, Y1 * Y2^-1 * Y1^4 * Y2^2 * Y1^2 * Y2^-1, Y2^-9 * Y1^-3, Y2^-5 * Y3 * Y2^-3 * Y3 * Y2^-1 * Y3, Y1^-2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-2 * Y2 * Y3 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 35, 98, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 27, 90, 36, 99, 23, 86, 12, 75)(9, 72, 17, 80, 28, 91, 40, 103, 49, 112, 34, 97, 20, 83)(13, 76, 18, 81, 29, 92, 41, 104, 50, 113, 37, 100, 24, 87)(19, 82, 30, 93, 42, 105, 54, 117, 63, 126, 48, 111, 33, 96)(25, 88, 31, 94, 43, 106, 55, 118, 60, 123, 51, 114, 38, 101)(32, 95, 44, 107, 56, 119, 53, 116, 59, 122, 62, 125, 47, 110)(39, 102, 45, 108, 57, 120, 61, 124, 46, 109, 58, 121, 52, 115)(127, 190, 129, 192, 135, 198, 145, 208, 158, 221, 172, 235, 186, 249, 176, 239, 162, 225, 148, 211, 161, 224, 175, 238, 189, 252, 185, 248, 171, 234, 157, 220, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 156, 219, 170, 233, 184, 247, 177, 240, 163, 226, 149, 212, 137, 200, 147, 210, 160, 223, 174, 237, 188, 251, 183, 246, 169, 232, 155, 218, 142, 205, 132, 195, 141, 204, 154, 217, 168, 231, 182, 245, 178, 241, 164, 227, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 159, 222, 173, 236, 187, 250, 181, 244, 167, 230, 153, 216, 140, 203, 152, 215, 166, 229, 180, 243, 179, 242, 165, 228, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 159)(20, 160)(21, 161)(22, 140)(23, 162)(24, 163)(25, 164)(26, 141)(27, 142)(28, 143)(29, 144)(30, 145)(31, 151)(32, 173)(33, 174)(34, 175)(35, 152)(36, 153)(37, 176)(38, 177)(39, 178)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 165)(46, 187)(47, 188)(48, 189)(49, 166)(50, 167)(51, 186)(52, 184)(53, 182)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 179)(60, 181)(61, 183)(62, 185)(63, 180)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1449
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 14^9, 126 ]

E27.1441 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y1^7, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-2, Y2^2 * Y3 * Y2 * Y3 * Y2^6 * Y1^-1, (Y1^-2 * Y3^2)^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 22, 85, 11, 74, 4, 67)(3, 66, 7, 70, 15, 78, 26, 89, 35, 98, 21, 84, 10, 73)(5, 68, 8, 71, 16, 79, 27, 90, 36, 99, 23, 86, 12, 75)(9, 72, 17, 80, 28, 91, 40, 103, 49, 112, 34, 97, 20, 83)(13, 76, 18, 81, 29, 92, 41, 104, 50, 113, 37, 100, 24, 87)(19, 82, 30, 93, 42, 105, 54, 117, 60, 123, 48, 111, 33, 96)(25, 88, 31, 94, 43, 106, 55, 118, 61, 124, 51, 114, 38, 101)(32, 95, 44, 107, 56, 119, 63, 126, 53, 116, 59, 122, 47, 110)(39, 102, 45, 108, 57, 120, 46, 109, 58, 121, 62, 125, 52, 115)(127, 190, 129, 192, 135, 198, 145, 208, 158, 221, 172, 235, 181, 244, 167, 230, 153, 216, 140, 203, 152, 215, 166, 229, 180, 243, 189, 252, 178, 241, 164, 227, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 159, 222, 173, 236, 183, 246, 169, 232, 155, 218, 142, 205, 132, 195, 141, 204, 154, 217, 168, 231, 182, 245, 188, 251, 177, 240, 163, 226, 149, 212, 137, 200, 147, 210, 160, 223, 174, 237, 185, 248, 171, 234, 157, 220, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 156, 219, 170, 233, 184, 247, 187, 250, 176, 239, 162, 225, 148, 211, 161, 224, 175, 238, 186, 249, 179, 242, 165, 228, 151, 214, 139, 202, 131, 194)
	L = (1, 130)(2, 127)(3, 136)(4, 137)(5, 138)(6, 128)(7, 129)(8, 131)(9, 146)(10, 147)(11, 148)(12, 149)(13, 150)(14, 132)(15, 133)(16, 134)(17, 135)(18, 139)(19, 159)(20, 160)(21, 161)(22, 140)(23, 162)(24, 163)(25, 164)(26, 141)(27, 142)(28, 143)(29, 144)(30, 145)(31, 151)(32, 173)(33, 174)(34, 175)(35, 152)(36, 153)(37, 176)(38, 177)(39, 178)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 165)(46, 183)(47, 185)(48, 186)(49, 166)(50, 167)(51, 187)(52, 188)(53, 189)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 179)(60, 180)(61, 181)(62, 184)(63, 182)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1446
Graph:: bipartite
	v = 10 e = 126 f = 64
	degree seq :: [ 14^9, 126 ]

E27.1442 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^-1 * Y1^2 * Y2^-1 * Y1 * Y2^-1 * Y1^3, Y2^9 * Y1 * Y2, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 34, 97, 19, 82, 31, 94, 44, 107, 55, 118, 62, 125, 61, 124, 52, 115, 41, 104, 46, 109, 49, 112, 38, 101, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 35, 98, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 54, 117, 58, 121, 47, 110, 53, 116, 57, 120, 59, 122, 50, 113, 39, 102, 24, 87, 13, 76, 18, 81, 30, 93, 36, 99, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 42, 105, 48, 111, 33, 96, 45, 108, 56, 119, 63, 126, 60, 123, 51, 114, 40, 103, 25, 88, 32, 95, 37, 100, 22, 85, 11, 74, 4, 67)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 173, 236, 178, 241, 166, 229, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 160, 223, 174, 237, 184, 247, 187, 250, 177, 240, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 152, 215, 168, 231, 180, 243, 188, 251, 186, 249, 176, 239, 164, 227, 148, 211, 162, 225, 154, 217, 140, 203, 153, 216, 169, 232, 181, 244, 189, 252, 185, 248, 175, 238, 163, 226, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 170, 233, 182, 245, 183, 246, 172, 235, 158, 221, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 157, 220, 171, 234, 179, 242, 167, 230, 151, 214, 139, 202, 131, 194)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 159)(20, 160)(21, 161)(22, 162)(23, 137)(24, 138)(25, 139)(26, 168)(27, 169)(28, 140)(29, 170)(30, 142)(31, 171)(32, 144)(33, 173)(34, 174)(35, 152)(36, 154)(37, 156)(38, 148)(39, 149)(40, 150)(41, 151)(42, 180)(43, 181)(44, 182)(45, 179)(46, 158)(47, 178)(48, 184)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 188)(55, 189)(56, 183)(57, 172)(58, 187)(59, 175)(60, 176)(61, 177)(62, 186)(63, 185)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.1445
Graph:: bipartite
	v = 2 e = 126 f = 72
	degree seq :: [ 126^2 ]

E27.1443 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y1^4 * Y2^-5, Y1^5 * Y2 * Y1 * Y2 * Y1^5, Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-3, (Y3^-1 * Y1^-1)^7, Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2 * Y1 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 42, 105, 52, 115, 59, 122, 49, 112, 39, 102, 24, 87, 13, 76, 18, 81, 30, 93, 34, 97, 19, 82, 31, 94, 45, 108, 55, 118, 62, 125, 61, 124, 51, 114, 41, 104, 36, 99, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 43, 106, 53, 116, 58, 121, 48, 111, 38, 101, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 33, 96, 46, 109, 56, 119, 63, 126, 60, 123, 50, 113, 40, 103, 25, 88, 32, 95, 35, 98, 20, 83, 9, 72, 17, 80, 29, 92, 44, 107, 54, 117, 57, 120, 47, 110, 37, 100, 22, 85, 11, 74, 4, 67)(127, 190, 129, 192, 135, 198, 145, 208, 159, 222, 152, 215, 169, 232, 180, 243, 188, 251, 186, 249, 175, 238, 164, 227, 148, 211, 162, 225, 158, 221, 144, 207, 134, 197, 128, 191, 133, 196, 143, 206, 157, 220, 172, 235, 168, 231, 179, 242, 183, 246, 187, 250, 176, 239, 165, 228, 149, 212, 137, 200, 147, 210, 161, 224, 156, 219, 142, 205, 132, 195, 141, 204, 155, 218, 171, 234, 182, 245, 178, 241, 184, 247, 173, 236, 177, 240, 166, 229, 150, 213, 138, 201, 130, 193, 136, 199, 146, 209, 160, 223, 154, 217, 140, 203, 153, 216, 170, 233, 181, 244, 189, 252, 185, 248, 174, 237, 163, 226, 167, 230, 151, 214, 139, 202, 131, 194)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 159)(20, 160)(21, 161)(22, 162)(23, 137)(24, 138)(25, 139)(26, 169)(27, 170)(28, 140)(29, 171)(30, 142)(31, 172)(32, 144)(33, 152)(34, 154)(35, 156)(36, 158)(37, 167)(38, 148)(39, 149)(40, 150)(41, 151)(42, 179)(43, 180)(44, 181)(45, 182)(46, 168)(47, 177)(48, 163)(49, 164)(50, 165)(51, 166)(52, 184)(53, 183)(54, 188)(55, 189)(56, 178)(57, 187)(58, 173)(59, 174)(60, 175)(61, 176)(62, 186)(63, 185)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.1444
Graph:: bipartite
	v = 2 e = 126 f = 72
	degree seq :: [ 126^2 ]

E27.1444 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^7, Y2^7, Y2^2 * Y3^9, Y3^3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^3 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-3 * Y2^-1 * Y3^-1, (Y3^-1 * Y1^-1)^63 ]
Map::
	R = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)(127, 190, 128, 191, 132, 195, 140, 203, 148, 211, 137, 200, 130, 193)(129, 192, 133, 196, 141, 204, 152, 215, 161, 224, 147, 210, 136, 199)(131, 194, 134, 197, 142, 205, 153, 216, 162, 225, 149, 212, 138, 201)(135, 198, 143, 206, 154, 217, 166, 229, 175, 238, 160, 223, 146, 209)(139, 202, 144, 207, 155, 218, 167, 230, 176, 239, 163, 226, 150, 213)(145, 208, 156, 219, 168, 231, 180, 243, 186, 249, 174, 237, 159, 222)(151, 214, 157, 220, 169, 232, 181, 244, 187, 250, 177, 240, 164, 227)(158, 221, 170, 233, 179, 242, 183, 246, 189, 252, 185, 248, 173, 236)(165, 228, 171, 234, 182, 245, 188, 251, 184, 247, 172, 235, 178, 241)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 152)(15, 154)(16, 132)(17, 156)(18, 134)(19, 158)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 166)(27, 140)(28, 168)(29, 142)(30, 170)(31, 144)(32, 172)(33, 173)(34, 174)(35, 175)(36, 148)(37, 149)(38, 150)(39, 151)(40, 180)(41, 153)(42, 179)(43, 155)(44, 178)(45, 157)(46, 177)(47, 184)(48, 185)(49, 186)(50, 162)(51, 163)(52, 164)(53, 165)(54, 183)(55, 167)(56, 169)(57, 171)(58, 187)(59, 188)(60, 189)(61, 176)(62, 181)(63, 182)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 126, 126 ), ( 126^14 ) }
Outer automorphisms :: reflexible
Dual of E27.1443
Graph:: simple bipartite
	v = 72 e = 126 f = 2
	degree seq :: [ 2^63, 14^9 ]

E27.1445 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-7, Y2^7, Y2^-3 * Y3^9, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^63 ]
Map::
	R = (1, 64)(2, 65)(3, 66)(4, 67)(5, 68)(6, 69)(7, 70)(8, 71)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 77)(15, 78)(16, 79)(17, 80)(18, 81)(19, 82)(20, 83)(21, 84)(22, 85)(23, 86)(24, 87)(25, 88)(26, 89)(27, 90)(28, 91)(29, 92)(30, 93)(31, 94)(32, 95)(33, 96)(34, 97)(35, 98)(36, 99)(37, 100)(38, 101)(39, 102)(40, 103)(41, 104)(42, 105)(43, 106)(44, 107)(45, 108)(46, 109)(47, 110)(48, 111)(49, 112)(50, 113)(51, 114)(52, 115)(53, 116)(54, 117)(55, 118)(56, 119)(57, 120)(58, 121)(59, 122)(60, 123)(61, 124)(62, 125)(63, 126)(127, 190, 128, 191, 132, 195, 140, 203, 148, 211, 137, 200, 130, 193)(129, 192, 133, 196, 141, 204, 152, 215, 161, 224, 147, 210, 136, 199)(131, 194, 134, 197, 142, 205, 153, 216, 162, 225, 149, 212, 138, 201)(135, 198, 143, 206, 154, 217, 166, 229, 175, 238, 160, 223, 146, 209)(139, 202, 144, 207, 155, 218, 167, 230, 176, 239, 163, 226, 150, 213)(145, 208, 156, 219, 168, 231, 180, 243, 186, 249, 174, 237, 159, 222)(151, 214, 157, 220, 169, 232, 181, 244, 187, 250, 177, 240, 164, 227)(158, 221, 170, 233, 182, 245, 189, 252, 179, 242, 185, 248, 173, 236)(165, 228, 171, 234, 183, 246, 172, 235, 184, 247, 188, 251, 178, 241)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 152)(15, 154)(16, 132)(17, 156)(18, 134)(19, 158)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 166)(27, 140)(28, 168)(29, 142)(30, 170)(31, 144)(32, 172)(33, 173)(34, 174)(35, 175)(36, 148)(37, 149)(38, 150)(39, 151)(40, 180)(41, 153)(42, 182)(43, 155)(44, 184)(45, 157)(46, 181)(47, 183)(48, 185)(49, 186)(50, 162)(51, 163)(52, 164)(53, 165)(54, 189)(55, 167)(56, 188)(57, 169)(58, 187)(59, 171)(60, 179)(61, 176)(62, 177)(63, 178)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 126, 126 ), ( 126^14 ) }
Outer automorphisms :: reflexible
Dual of E27.1442
Graph:: simple bipartite
	v = 72 e = 126 f = 2
	degree seq :: [ 2^63, 14^9 ]

E27.1446 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-7, Y3^7, Y1^9 * Y3^-2, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 40, 103, 48, 111, 34, 97, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 55, 118, 62, 125, 61, 124, 53, 116, 39, 102, 25, 88, 32, 95, 46, 109, 57, 120, 59, 122, 51, 114, 37, 100, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 42, 105, 49, 112, 35, 98, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 41, 104, 54, 117, 58, 121, 47, 110, 33, 96, 19, 82, 31, 94, 45, 108, 56, 119, 63, 126, 60, 123, 52, 115, 38, 101, 24, 87, 13, 76, 18, 81, 30, 93, 44, 107, 50, 113, 36, 99, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 151)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 167)(27, 169)(28, 140)(29, 171)(30, 142)(31, 158)(32, 144)(33, 165)(34, 173)(35, 174)(36, 175)(37, 148)(38, 149)(39, 150)(40, 180)(41, 181)(42, 152)(43, 182)(44, 154)(45, 172)(46, 156)(47, 179)(48, 184)(49, 166)(50, 168)(51, 162)(52, 163)(53, 164)(54, 188)(55, 189)(56, 183)(57, 170)(58, 187)(59, 176)(60, 177)(61, 178)(62, 186)(63, 185)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 14, 126 ), ( 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1441
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1447 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, Y3^-7, Y3^-3 * Y1^-9, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 40, 103, 54, 117, 53, 116, 39, 102, 25, 88, 32, 95, 46, 109, 60, 123, 63, 126, 49, 112, 35, 98, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 41, 104, 55, 118, 52, 115, 38, 101, 24, 87, 13, 76, 18, 81, 30, 93, 44, 107, 58, 121, 62, 125, 48, 111, 34, 97, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 57, 120, 51, 114, 37, 100, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 42, 105, 56, 119, 61, 124, 47, 110, 33, 96, 19, 82, 31, 94, 45, 108, 59, 122, 50, 113, 36, 99, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 151)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 167)(27, 169)(28, 140)(29, 171)(30, 142)(31, 158)(32, 144)(33, 165)(34, 173)(35, 174)(36, 175)(37, 148)(38, 149)(39, 150)(40, 181)(41, 183)(42, 152)(43, 185)(44, 154)(45, 172)(46, 156)(47, 179)(48, 187)(49, 188)(50, 189)(51, 162)(52, 163)(53, 164)(54, 178)(55, 177)(56, 166)(57, 176)(58, 168)(59, 186)(60, 170)(61, 180)(62, 182)(63, 184)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 14, 126 ), ( 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1439
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1448 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^7, Y3^7, Y1^-9 * Y3^3, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 40, 103, 54, 117, 47, 110, 33, 96, 19, 82, 31, 94, 45, 108, 59, 122, 61, 124, 51, 114, 37, 100, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 42, 105, 56, 119, 48, 111, 34, 97, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 57, 120, 62, 125, 52, 115, 38, 101, 24, 87, 13, 76, 18, 81, 30, 93, 44, 107, 58, 121, 49, 112, 35, 98, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 41, 104, 55, 118, 63, 126, 53, 116, 39, 102, 25, 88, 32, 95, 46, 109, 60, 123, 50, 113, 36, 99, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 151)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 167)(27, 169)(28, 140)(29, 171)(30, 142)(31, 158)(32, 144)(33, 165)(34, 173)(35, 174)(36, 175)(37, 148)(38, 149)(39, 150)(40, 181)(41, 183)(42, 152)(43, 185)(44, 154)(45, 172)(46, 156)(47, 179)(48, 180)(49, 182)(50, 184)(51, 162)(52, 163)(53, 164)(54, 189)(55, 188)(56, 166)(57, 187)(58, 168)(59, 186)(60, 170)(61, 176)(62, 177)(63, 178)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 14, 126 ), ( 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1437
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1449 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^7, Y1^-9 * Y3, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 40, 103, 35, 98, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 41, 104, 52, 115, 48, 111, 34, 97, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 53, 116, 60, 123, 57, 120, 47, 110, 33, 96, 19, 82, 31, 94, 45, 108, 55, 118, 61, 124, 63, 126, 59, 122, 51, 114, 39, 102, 25, 88, 32, 95, 46, 109, 56, 119, 62, 125, 58, 121, 50, 113, 38, 101, 24, 87, 13, 76, 18, 81, 30, 93, 44, 107, 54, 117, 49, 112, 37, 100, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 42, 105, 36, 99, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 151)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 167)(27, 169)(28, 140)(29, 171)(30, 142)(31, 158)(32, 144)(33, 165)(34, 173)(35, 174)(36, 166)(37, 148)(38, 149)(39, 150)(40, 178)(41, 179)(42, 152)(43, 181)(44, 154)(45, 172)(46, 156)(47, 177)(48, 183)(49, 162)(50, 163)(51, 164)(52, 186)(53, 187)(54, 168)(55, 182)(56, 170)(57, 185)(58, 175)(59, 176)(60, 189)(61, 188)(62, 180)(63, 184)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 14, 126 ), ( 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1440
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1450 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 63, 63})
Quotient :: dipole
Aut^+ = C63 (small group id <63, 2>)
Aut   = D126 (small group id <126, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^7, Y1^-9 * Y3^-1, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^63 ]
Map::
	R = (1, 64, 2, 65, 6, 69, 14, 77, 26, 89, 40, 103, 37, 100, 23, 86, 12, 75, 5, 68, 8, 71, 16, 79, 28, 91, 42, 105, 52, 115, 50, 113, 38, 101, 24, 87, 13, 76, 18, 81, 30, 93, 44, 107, 54, 117, 60, 123, 59, 122, 51, 114, 39, 102, 25, 88, 32, 95, 46, 109, 56, 119, 62, 125, 63, 126, 57, 120, 47, 110, 33, 96, 19, 82, 31, 94, 45, 108, 55, 118, 61, 124, 58, 121, 48, 111, 34, 97, 20, 83, 9, 72, 17, 80, 29, 92, 43, 106, 53, 116, 49, 112, 35, 98, 21, 84, 10, 73, 3, 66, 7, 70, 15, 78, 27, 90, 41, 104, 36, 99, 22, 85, 11, 74, 4, 67)(127, 190)(128, 191)(129, 192)(130, 193)(131, 194)(132, 195)(133, 196)(134, 197)(135, 198)(136, 199)(137, 200)(138, 201)(139, 202)(140, 203)(141, 204)(142, 205)(143, 206)(144, 207)(145, 208)(146, 209)(147, 210)(148, 211)(149, 212)(150, 213)(151, 214)(152, 215)(153, 216)(154, 217)(155, 218)(156, 219)(157, 220)(158, 221)(159, 222)(160, 223)(161, 224)(162, 225)(163, 226)(164, 227)(165, 228)(166, 229)(167, 230)(168, 231)(169, 232)(170, 233)(171, 234)(172, 235)(173, 236)(174, 237)(175, 238)(176, 239)(177, 240)(178, 241)(179, 242)(180, 243)(181, 244)(182, 245)(183, 246)(184, 247)(185, 248)(186, 249)(187, 250)(188, 251)(189, 252)
	L = (1, 129)(2, 133)(3, 135)(4, 136)(5, 127)(6, 141)(7, 143)(8, 128)(9, 145)(10, 146)(11, 147)(12, 130)(13, 131)(14, 153)(15, 155)(16, 132)(17, 157)(18, 134)(19, 151)(20, 159)(21, 160)(22, 161)(23, 137)(24, 138)(25, 139)(26, 167)(27, 169)(28, 140)(29, 171)(30, 142)(31, 158)(32, 144)(33, 165)(34, 173)(35, 174)(36, 175)(37, 148)(38, 149)(39, 150)(40, 162)(41, 179)(42, 152)(43, 181)(44, 154)(45, 172)(46, 156)(47, 177)(48, 183)(49, 184)(50, 163)(51, 164)(52, 166)(53, 187)(54, 168)(55, 182)(56, 170)(57, 185)(58, 189)(59, 176)(60, 178)(61, 188)(62, 180)(63, 186)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 14, 126 ), ( 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126, 14, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.1438
Graph:: bipartite
	v = 64 e = 126 f = 10
	degree seq :: [ 2^63, 126 ]

E27.1451 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-2 * Y2 * Y3, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1, Y3 * Y1 * Y3^-2 * Y1 * Y3, (Y3^2 * Y2 * Y1)^2, (Y3^-2 * Y2 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 12, 76)(5, 69, 15, 79)(6, 70, 18, 82)(7, 71, 21, 85)(8, 72, 24, 88)(10, 74, 28, 92)(11, 75, 31, 95)(13, 77, 36, 100)(14, 78, 23, 87)(16, 80, 38, 102)(17, 81, 26, 90)(19, 83, 40, 104)(20, 84, 43, 107)(22, 86, 48, 112)(25, 89, 50, 114)(27, 91, 39, 103)(29, 93, 53, 117)(30, 94, 45, 109)(32, 96, 55, 119)(33, 97, 42, 106)(34, 98, 56, 120)(35, 99, 57, 121)(37, 101, 59, 123)(41, 105, 60, 124)(44, 108, 62, 126)(46, 110, 58, 122)(47, 111, 51, 115)(49, 113, 52, 116)(54, 118, 64, 128)(61, 125, 63, 127)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 141, 205)(133, 197, 144, 208)(135, 199, 150, 214)(136, 200, 153, 217)(137, 201, 155, 219)(138, 202, 157, 221)(139, 203, 160, 224)(140, 204, 156, 220)(142, 206, 158, 222)(143, 207, 159, 223)(145, 209, 161, 225)(146, 210, 167, 231)(147, 211, 169, 233)(148, 212, 172, 236)(149, 213, 168, 232)(151, 215, 170, 234)(152, 216, 171, 235)(154, 218, 173, 237)(162, 226, 182, 246)(163, 227, 186, 250)(164, 228, 181, 245)(165, 229, 179, 243)(166, 230, 183, 247)(174, 238, 189, 253)(175, 239, 184, 248)(176, 240, 188, 252)(177, 241, 185, 249)(178, 242, 190, 254)(180, 244, 191, 255)(187, 251, 192, 256)
	L = (1, 132)(2, 135)(3, 138)(4, 142)(5, 129)(6, 147)(7, 151)(8, 130)(9, 150)(10, 158)(11, 131)(12, 162)(13, 161)(14, 160)(15, 163)(16, 146)(17, 133)(18, 141)(19, 170)(20, 134)(21, 174)(22, 173)(23, 172)(24, 175)(25, 137)(26, 136)(27, 169)(28, 179)(29, 145)(30, 144)(31, 180)(32, 167)(33, 139)(34, 183)(35, 140)(36, 182)(37, 143)(38, 186)(39, 157)(40, 185)(41, 154)(42, 153)(43, 187)(44, 155)(45, 148)(46, 190)(47, 149)(48, 189)(49, 152)(50, 184)(51, 166)(52, 156)(53, 165)(54, 159)(55, 191)(56, 176)(57, 178)(58, 164)(59, 168)(60, 177)(61, 171)(62, 192)(63, 181)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1463
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1452 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1, Y1 * Y3^2 * Y1 * Y3^-2, Y3^-2 * Y2 * Y3^2 * Y2, (Y1 * Y3^-2 * Y2)^2, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 12, 76)(5, 69, 15, 79)(6, 70, 18, 82)(7, 71, 21, 85)(8, 72, 24, 88)(10, 74, 28, 92)(11, 75, 31, 95)(13, 77, 36, 100)(14, 78, 23, 87)(16, 80, 38, 102)(17, 81, 26, 90)(19, 83, 40, 104)(20, 84, 43, 107)(22, 86, 48, 112)(25, 89, 50, 114)(27, 91, 39, 103)(29, 93, 53, 117)(30, 94, 45, 109)(32, 96, 55, 119)(33, 97, 42, 106)(34, 98, 56, 120)(35, 99, 57, 121)(37, 101, 59, 123)(41, 105, 61, 125)(44, 108, 62, 126)(46, 110, 52, 116)(47, 111, 54, 118)(49, 113, 58, 122)(51, 115, 63, 127)(60, 124, 64, 128)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 141, 205)(133, 197, 144, 208)(135, 199, 150, 214)(136, 200, 153, 217)(137, 201, 155, 219)(138, 202, 157, 221)(139, 203, 160, 224)(140, 204, 156, 220)(142, 206, 158, 222)(143, 207, 159, 223)(145, 209, 161, 225)(146, 210, 167, 231)(147, 211, 169, 233)(148, 212, 172, 236)(149, 213, 168, 232)(151, 215, 170, 234)(152, 216, 171, 235)(154, 218, 173, 237)(162, 226, 182, 246)(163, 227, 186, 250)(164, 228, 181, 245)(165, 229, 179, 243)(166, 230, 183, 247)(174, 238, 185, 249)(175, 239, 187, 251)(176, 240, 189, 253)(177, 241, 188, 252)(178, 242, 190, 254)(180, 244, 192, 256)(184, 248, 191, 255)
	L = (1, 132)(2, 135)(3, 138)(4, 142)(5, 129)(6, 147)(7, 151)(8, 130)(9, 150)(10, 158)(11, 131)(12, 162)(13, 161)(14, 160)(15, 163)(16, 146)(17, 133)(18, 141)(19, 170)(20, 134)(21, 174)(22, 173)(23, 172)(24, 175)(25, 137)(26, 136)(27, 169)(28, 179)(29, 145)(30, 144)(31, 180)(32, 167)(33, 139)(34, 183)(35, 140)(36, 182)(37, 143)(38, 186)(39, 157)(40, 188)(41, 154)(42, 153)(43, 184)(44, 155)(45, 148)(46, 190)(47, 149)(48, 185)(49, 152)(50, 187)(51, 166)(52, 156)(53, 165)(54, 159)(55, 192)(56, 168)(57, 171)(58, 164)(59, 176)(60, 178)(61, 177)(62, 191)(63, 189)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1462
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1453 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, Y2 * Y3^4, Y1 * Y3^-2 * Y1 * Y3^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 17, 81)(8, 72, 19, 83)(9, 73, 21, 85)(10, 74, 22, 86)(12, 76, 18, 82)(14, 78, 20, 84)(15, 79, 26, 90)(16, 80, 27, 91)(23, 87, 32, 96)(24, 88, 33, 97)(25, 89, 34, 98)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(31, 95, 39, 103)(35, 99, 44, 108)(40, 104, 49, 113)(41, 105, 50, 114)(42, 106, 51, 115)(43, 107, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 63, 127)(58, 122, 64, 128)(59, 123, 61, 125)(60, 124, 62, 126)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 143, 207)(136, 200, 144, 208)(139, 203, 149, 213)(140, 204, 142, 206)(141, 205, 150, 214)(145, 209, 154, 218)(146, 210, 148, 212)(147, 211, 155, 219)(151, 215, 153, 217)(152, 216, 159, 223)(156, 220, 158, 222)(157, 221, 163, 227)(160, 224, 162, 226)(161, 225, 167, 231)(164, 228, 166, 230)(165, 229, 172, 236)(168, 232, 170, 234)(169, 233, 171, 235)(173, 237, 175, 239)(174, 238, 176, 240)(177, 241, 179, 243)(178, 242, 180, 244)(181, 245, 183, 247)(182, 246, 184, 248)(185, 249, 187, 251)(186, 250, 188, 252)(189, 253, 191, 255)(190, 254, 192, 256)
	L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 143)(7, 146)(8, 130)(9, 142)(10, 131)(11, 151)(12, 138)(13, 152)(14, 133)(15, 148)(16, 134)(17, 156)(18, 144)(19, 157)(20, 136)(21, 153)(22, 159)(23, 150)(24, 139)(25, 141)(26, 158)(27, 163)(28, 155)(29, 145)(30, 147)(31, 149)(32, 168)(33, 169)(34, 170)(35, 154)(36, 173)(37, 174)(38, 175)(39, 171)(40, 167)(41, 160)(42, 161)(43, 162)(44, 176)(45, 172)(46, 164)(47, 165)(48, 166)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 180)(58, 177)(59, 178)(60, 179)(61, 184)(62, 181)(63, 182)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1464
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1454 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2^2 * Y3 * Y2^-2 * Y3, Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1, Y2^-3 * Y3 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3)^4 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 17, 81)(8, 72, 22, 86)(10, 74, 18, 82)(11, 75, 20, 84)(12, 76, 19, 83)(13, 77, 23, 87)(15, 79, 21, 85)(16, 80, 24, 88)(25, 89, 33, 97)(26, 90, 35, 99)(27, 91, 34, 98)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 63, 127)(58, 122, 64, 128)(59, 123, 61, 125)(60, 124, 62, 126)(129, 193, 131, 195, 138, 202, 149, 213, 135, 199, 148, 212, 144, 208, 133, 197)(130, 194, 134, 198, 146, 210, 141, 205, 132, 196, 140, 204, 152, 216, 136, 200)(137, 201, 153, 217, 143, 207, 156, 220, 139, 203, 155, 219, 142, 206, 154, 218)(145, 209, 157, 221, 151, 215, 160, 224, 147, 211, 159, 223, 150, 214, 158, 222)(161, 225, 169, 233, 164, 228, 172, 236, 162, 226, 171, 235, 163, 227, 170, 234)(165, 229, 173, 237, 168, 232, 176, 240, 166, 230, 175, 239, 167, 231, 174, 238)(177, 241, 185, 249, 180, 244, 188, 252, 178, 242, 187, 251, 179, 243, 186, 250)(181, 245, 189, 253, 184, 248, 192, 256, 182, 246, 191, 255, 183, 247, 190, 254)
	L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 147)(7, 130)(8, 151)(9, 148)(10, 152)(11, 131)(12, 145)(13, 150)(14, 149)(15, 133)(16, 146)(17, 140)(18, 144)(19, 134)(20, 137)(21, 142)(22, 141)(23, 136)(24, 138)(25, 162)(26, 164)(27, 161)(28, 163)(29, 166)(30, 168)(31, 165)(32, 167)(33, 155)(34, 153)(35, 156)(36, 154)(37, 159)(38, 157)(39, 160)(40, 158)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 189)(58, 190)(59, 191)(60, 192)(61, 185)(62, 186)(63, 187)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1461
Graph:: bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1455 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^4, (Y3 * R)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y3, Y2 * Y3^-2 * Y1 * Y2^-1 * Y1, Y2^-3 * Y3^2 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y3 * Y2^-1)^2, Y3 * Y2 * Y3^-2 * Y2^-1 * Y3, (Y2^-1 * R * Y2^-1 * Y1)^2, Y3 * Y2 * Y1 * Y3 * Y2 * R * Y2 * R * Y2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y1, Y3 * Y2^-1 * Y1 * R * Y2 * R * Y2 * Y3^-1 * Y2^-1, (Y3 * Y2 * Y3^-1 * Y2)^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 18, 82)(6, 70, 8, 72)(7, 71, 24, 88)(9, 73, 31, 95)(12, 76, 25, 89)(13, 77, 26, 90)(14, 78, 27, 91)(15, 79, 28, 92)(16, 80, 29, 93)(17, 81, 30, 94)(19, 83, 32, 96)(20, 84, 33, 97)(21, 85, 34, 98)(22, 86, 35, 99)(23, 87, 36, 100)(37, 101, 48, 112)(38, 102, 47, 111)(39, 103, 51, 115)(40, 104, 52, 116)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 54, 118)(44, 108, 53, 117)(45, 109, 56, 120)(46, 110, 55, 119)(57, 121, 62, 126)(58, 122, 64, 128)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195, 140, 204, 159, 223, 144, 208, 152, 216, 148, 212, 133, 197)(130, 194, 135, 199, 153, 217, 146, 210, 157, 221, 139, 203, 161, 225, 137, 201)(132, 196, 143, 207, 165, 229, 151, 215, 134, 198, 150, 214, 166, 230, 145, 209)(136, 200, 156, 220, 175, 239, 164, 228, 138, 202, 163, 227, 176, 240, 158, 222)(141, 205, 167, 231, 149, 213, 170, 234, 142, 206, 169, 233, 147, 211, 168, 232)(154, 218, 177, 241, 162, 226, 180, 244, 155, 219, 179, 243, 160, 224, 178, 242)(171, 235, 189, 253, 174, 238, 192, 256, 172, 236, 191, 255, 173, 237, 190, 254)(181, 245, 188, 252, 184, 248, 186, 250, 182, 246, 187, 251, 183, 247, 185, 249)
	L = (1, 132)(2, 136)(3, 141)(4, 144)(5, 147)(6, 129)(7, 154)(8, 157)(9, 160)(10, 130)(11, 155)(12, 165)(13, 152)(14, 131)(15, 171)(16, 134)(17, 173)(18, 162)(19, 159)(20, 166)(21, 133)(22, 172)(23, 174)(24, 142)(25, 175)(26, 139)(27, 135)(28, 181)(29, 138)(30, 183)(31, 149)(32, 146)(33, 176)(34, 137)(35, 182)(36, 184)(37, 148)(38, 140)(39, 185)(40, 187)(41, 186)(42, 188)(43, 150)(44, 143)(45, 151)(46, 145)(47, 161)(48, 153)(49, 190)(50, 191)(51, 192)(52, 189)(53, 163)(54, 156)(55, 164)(56, 158)(57, 169)(58, 167)(59, 170)(60, 168)(61, 178)(62, 179)(63, 180)(64, 177)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1458
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1456 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, Y3^4, Y3^4, (Y3^-1 * Y1)^2, (R * Y3^-1)^2, (R * Y1)^2, Y3^2 * Y2^-1 * Y1 * Y2 * Y1, Y3^-2 * Y2^-4, Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y3^-2 * Y2 * Y3, Y2 * Y1 * Y2^-1 * Y3^-2 * Y1, Y3^-2 * Y1 * Y3^2 * Y1, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-2 * Y3^-1 * Y2 * Y3^-1, (Y2^-1 * R * Y2^-1 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y1, (Y3 * Y2^-1)^16 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 18, 82)(6, 70, 8, 72)(7, 71, 24, 88)(9, 73, 31, 95)(12, 76, 25, 89)(13, 77, 26, 90)(14, 78, 27, 91)(15, 79, 28, 92)(16, 80, 29, 93)(17, 81, 30, 94)(19, 83, 32, 96)(20, 84, 33, 97)(21, 85, 34, 98)(22, 86, 35, 99)(23, 87, 36, 100)(37, 101, 48, 112)(38, 102, 47, 111)(39, 103, 51, 115)(40, 104, 52, 116)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 54, 118)(44, 108, 53, 117)(45, 109, 56, 120)(46, 110, 55, 119)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 61, 125)(60, 124, 63, 127)(129, 193, 131, 195, 140, 204, 159, 223, 144, 208, 152, 216, 148, 212, 133, 197)(130, 194, 135, 199, 153, 217, 146, 210, 157, 221, 139, 203, 161, 225, 137, 201)(132, 196, 143, 207, 165, 229, 151, 215, 134, 198, 150, 214, 166, 230, 145, 209)(136, 200, 156, 220, 175, 239, 164, 228, 138, 202, 163, 227, 176, 240, 158, 222)(141, 205, 167, 231, 149, 213, 170, 234, 142, 206, 169, 233, 147, 211, 168, 232)(154, 218, 177, 241, 162, 226, 180, 244, 155, 219, 179, 243, 160, 224, 178, 242)(171, 235, 189, 253, 174, 238, 192, 256, 172, 236, 191, 255, 173, 237, 190, 254)(181, 245, 187, 251, 184, 248, 185, 249, 182, 246, 188, 252, 183, 247, 186, 250)
	L = (1, 132)(2, 136)(3, 141)(4, 144)(5, 147)(6, 129)(7, 154)(8, 157)(9, 160)(10, 130)(11, 155)(12, 165)(13, 152)(14, 131)(15, 171)(16, 134)(17, 173)(18, 162)(19, 159)(20, 166)(21, 133)(22, 172)(23, 174)(24, 142)(25, 175)(26, 139)(27, 135)(28, 181)(29, 138)(30, 183)(31, 149)(32, 146)(33, 176)(34, 137)(35, 182)(36, 184)(37, 148)(38, 140)(39, 185)(40, 187)(41, 186)(42, 188)(43, 150)(44, 143)(45, 151)(46, 145)(47, 161)(48, 153)(49, 192)(50, 189)(51, 190)(52, 191)(53, 163)(54, 156)(55, 164)(56, 158)(57, 169)(58, 167)(59, 170)(60, 168)(61, 180)(62, 177)(63, 178)(64, 179)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1459
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1457 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y1 * Y2^4, Y3 * Y2^-2 * Y3 * Y2^2, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 24, 88)(20, 84, 25, 89)(21, 85, 26, 90)(22, 86, 27, 91)(23, 87, 28, 92)(29, 93, 34, 98)(30, 94, 35, 99)(31, 95, 33, 97)(32, 96, 36, 100)(37, 101, 39, 103)(38, 102, 43, 107)(40, 104, 42, 106)(41, 105, 44, 108)(45, 109, 47, 111)(46, 110, 52, 116)(48, 112, 50, 114)(49, 113, 51, 115)(53, 117, 55, 119)(54, 118, 56, 120)(57, 121, 59, 123)(58, 122, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 137, 201, 136, 200, 130, 194, 134, 198, 142, 206, 133, 197)(132, 196, 139, 203, 147, 211, 145, 209, 135, 199, 144, 208, 152, 216, 140, 204)(138, 202, 148, 212, 146, 210, 154, 218, 143, 207, 153, 217, 141, 205, 149, 213)(150, 214, 159, 223, 156, 220, 164, 228, 155, 219, 161, 225, 151, 215, 160, 224)(157, 221, 165, 229, 163, 227, 171, 235, 162, 226, 167, 231, 158, 222, 166, 230)(168, 232, 176, 240, 172, 236, 179, 243, 170, 234, 178, 242, 169, 233, 177, 241)(173, 237, 181, 245, 180, 244, 184, 248, 175, 239, 183, 247, 174, 238, 182, 246)(185, 249, 191, 255, 188, 252, 190, 254, 187, 251, 189, 253, 186, 250, 192, 256)
	L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 150)(12, 151)(13, 133)(14, 152)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 139)(23, 140)(24, 142)(25, 162)(26, 163)(27, 144)(28, 145)(29, 148)(30, 149)(31, 168)(32, 169)(33, 170)(34, 153)(35, 154)(36, 172)(37, 173)(38, 174)(39, 175)(40, 159)(41, 160)(42, 161)(43, 180)(44, 164)(45, 165)(46, 166)(47, 167)(48, 185)(49, 186)(50, 187)(51, 188)(52, 171)(53, 189)(54, 190)(55, 191)(56, 192)(57, 176)(58, 177)(59, 178)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1460
Graph:: bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1458 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1^-3, Y3^-1 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y1^-3, Y2 * Y3^2 * R * Y2 * R, (Y3 * Y1^-2)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1, Y1^-3 * R * Y2 * R * Y1 * Y3^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y1^-1, Y1^5 * R * Y2 * R * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 24, 88, 51, 115, 44, 108, 62, 126, 47, 111, 16, 80, 33, 97, 56, 120, 38, 102, 59, 123, 42, 106, 20, 84, 5, 69)(3, 67, 11, 75, 34, 98, 9, 73, 32, 96, 21, 85, 25, 89, 53, 117, 39, 103, 52, 116, 36, 100, 10, 74, 35, 99, 19, 83, 43, 107, 13, 77)(4, 68, 15, 79, 30, 94, 8, 72, 28, 92, 57, 121, 26, 90, 23, 87, 6, 70, 22, 86, 50, 114, 60, 124, 49, 113, 18, 82, 27, 91, 17, 81)(12, 76, 29, 93, 54, 118, 37, 101, 58, 122, 48, 112, 64, 128, 45, 109, 14, 78, 31, 95, 55, 119, 46, 110, 63, 127, 41, 105, 61, 125, 40, 104)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 146, 210)(134, 198, 140, 204)(135, 199, 153, 217)(137, 201, 159, 223)(138, 202, 157, 221)(139, 203, 165, 229)(141, 205, 169, 233)(143, 207, 166, 230)(144, 208, 167, 231)(145, 209, 172, 236)(147, 211, 173, 237)(148, 212, 164, 228)(149, 213, 168, 232)(150, 214, 152, 216)(151, 215, 170, 234)(154, 218, 183, 247)(155, 219, 182, 246)(156, 220, 186, 250)(158, 222, 189, 253)(160, 224, 187, 251)(161, 225, 188, 252)(162, 226, 190, 254)(163, 227, 179, 243)(171, 235, 184, 248)(174, 238, 180, 244)(175, 239, 185, 249)(176, 240, 181, 245)(177, 241, 191, 255)(178, 242, 192, 256)
	L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 147)(6, 129)(7, 154)(8, 157)(9, 161)(10, 130)(11, 152)(12, 167)(13, 170)(14, 131)(15, 174)(16, 134)(17, 176)(18, 168)(19, 175)(20, 178)(21, 133)(22, 165)(23, 169)(24, 180)(25, 182)(26, 184)(27, 135)(28, 179)(29, 188)(30, 148)(31, 136)(32, 191)(33, 138)(34, 192)(35, 186)(36, 189)(37, 143)(38, 139)(39, 142)(40, 185)(41, 145)(42, 181)(43, 183)(44, 141)(45, 146)(46, 150)(47, 149)(48, 151)(49, 187)(50, 190)(51, 177)(52, 166)(53, 172)(54, 171)(55, 153)(56, 155)(57, 173)(58, 160)(59, 156)(60, 159)(61, 162)(62, 158)(63, 163)(64, 164)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1455
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1459 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y1^2 * Y3 * Y1^-1 * Y2 * Y1, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * R * Y2 * R, Y3^-1 * Y1^3 * Y2 * Y1^-1, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1^-2 * Y3 * Y2 * Y3^-1 * Y1^-2, Y1^-1 * Y3^-1 * Y1 * R * Y2 * R * Y1^-2 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 24, 88, 51, 115, 42, 106, 62, 126, 48, 112, 16, 80, 33, 97, 56, 120, 38, 102, 59, 123, 44, 108, 20, 84, 5, 69)(3, 67, 11, 75, 36, 100, 10, 74, 35, 99, 19, 83, 25, 89, 53, 117, 39, 103, 52, 116, 34, 98, 9, 73, 32, 96, 21, 85, 43, 107, 13, 77)(4, 68, 15, 79, 46, 110, 60, 124, 50, 114, 18, 82, 26, 90, 23, 87, 6, 70, 22, 86, 30, 94, 8, 72, 28, 92, 57, 121, 27, 91, 17, 81)(12, 76, 29, 93, 54, 118, 47, 111, 63, 127, 41, 105, 61, 125, 45, 109, 14, 78, 31, 95, 55, 119, 37, 101, 58, 122, 49, 113, 64, 128, 40, 104)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 146, 210)(134, 198, 140, 204)(135, 199, 153, 217)(137, 201, 159, 223)(138, 202, 157, 221)(139, 203, 165, 229)(141, 205, 169, 233)(143, 207, 152, 216)(144, 208, 167, 231)(145, 209, 172, 236)(147, 211, 173, 237)(148, 212, 162, 226)(149, 213, 168, 232)(150, 214, 166, 230)(151, 215, 170, 234)(154, 218, 183, 247)(155, 219, 182, 246)(156, 220, 186, 250)(158, 222, 189, 253)(160, 224, 179, 243)(161, 225, 188, 252)(163, 227, 187, 251)(164, 228, 190, 254)(171, 235, 184, 248)(174, 238, 192, 256)(175, 239, 180, 244)(176, 240, 185, 249)(177, 241, 181, 245)(178, 242, 191, 255)
	L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 147)(6, 129)(7, 154)(8, 157)(9, 161)(10, 130)(11, 166)(12, 167)(13, 170)(14, 131)(15, 175)(16, 134)(17, 177)(18, 168)(19, 176)(20, 158)(21, 133)(22, 165)(23, 169)(24, 139)(25, 182)(26, 184)(27, 135)(28, 187)(29, 188)(30, 190)(31, 136)(32, 191)(33, 138)(34, 192)(35, 186)(36, 189)(37, 143)(38, 180)(39, 142)(40, 185)(41, 145)(42, 181)(43, 183)(44, 141)(45, 146)(46, 148)(47, 150)(48, 149)(49, 151)(50, 179)(51, 156)(52, 152)(53, 172)(54, 171)(55, 153)(56, 155)(57, 173)(58, 160)(59, 178)(60, 159)(61, 162)(62, 174)(63, 163)(64, 164)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1456
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1460 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y2 * Y3 * Y1^-1 * Y3 * Y2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y1^-2 * Y3 * Y1^-2 * Y2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2, Y1^-2 * Y3 * Y2 * Y1^-6 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 46, 110, 28, 92, 10, 74, 21, 85, 38, 102, 56, 120, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 39, 103, 18, 82, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 54, 118, 40, 104, 19, 83, 11, 75)(7, 71, 20, 84, 15, 79, 33, 97, 51, 115, 57, 121, 36, 100, 24, 88, 8, 72, 23, 87, 14, 78, 32, 96, 50, 114, 58, 122, 37, 101, 22, 86)(26, 90, 41, 105, 30, 94, 44, 108, 60, 124, 64, 128, 61, 125, 48, 112, 27, 91, 42, 106, 29, 93, 43, 107, 59, 123, 63, 127, 62, 126, 47, 111)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 159, 223)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(153, 217, 174, 238)(160, 224, 175, 239)(161, 225, 176, 240)(162, 226, 179, 243)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 189, 253)(177, 241, 190, 254)(178, 242, 181, 245)(180, 244, 183, 247)(185, 249, 191, 255)(186, 250, 192, 256)
	L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 153)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 144)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 174)(32, 176)(33, 175)(34, 178)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 190)(46, 159)(47, 161)(48, 160)(49, 189)(50, 162)(51, 181)(52, 182)(53, 179)(54, 180)(55, 163)(56, 164)(57, 192)(58, 191)(59, 168)(60, 167)(61, 177)(62, 173)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1457
Graph:: bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1461 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1^-2 * Y3 * Y1^-2 * Y2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^8 * Y2 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 6, 70, 15, 79, 33, 97, 44, 108, 24, 88, 10, 74, 3, 67, 7, 71, 16, 80, 34, 98, 52, 116, 32, 96, 14, 78, 5, 69)(4, 68, 11, 75, 25, 89, 45, 109, 56, 120, 36, 100, 17, 81, 22, 86, 9, 73, 21, 85, 31, 95, 50, 114, 53, 117, 48, 112, 28, 92, 12, 76)(8, 72, 19, 83, 23, 87, 43, 107, 51, 115, 54, 118, 35, 99, 37, 101, 18, 82, 30, 94, 13, 77, 29, 93, 49, 113, 58, 122, 40, 104, 20, 84)(26, 90, 38, 102, 42, 106, 57, 121, 62, 126, 64, 128, 60, 124, 59, 123, 41, 105, 47, 111, 27, 91, 39, 103, 55, 119, 63, 127, 61, 125, 46, 110)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 162, 226)(145, 209, 156, 220)(147, 211, 158, 222)(148, 212, 165, 229)(153, 217, 159, 223)(154, 218, 169, 233)(155, 219, 170, 234)(157, 221, 171, 235)(160, 224, 172, 236)(161, 225, 180, 244)(163, 227, 168, 232)(164, 228, 176, 240)(166, 230, 175, 239)(167, 231, 185, 249)(173, 237, 178, 242)(174, 238, 187, 251)(177, 241, 179, 243)(181, 245, 184, 248)(182, 246, 186, 250)(183, 247, 190, 254)(188, 252, 189, 253)(191, 255, 192, 256)
	L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 159)(15, 163)(16, 156)(17, 134)(18, 135)(19, 166)(20, 167)(21, 169)(22, 170)(23, 138)(24, 153)(25, 152)(26, 139)(27, 140)(28, 144)(29, 174)(30, 175)(31, 142)(32, 179)(33, 181)(34, 168)(35, 143)(36, 183)(37, 185)(38, 147)(39, 148)(40, 162)(41, 149)(42, 150)(43, 187)(44, 177)(45, 188)(46, 157)(47, 158)(48, 190)(49, 172)(50, 189)(51, 160)(52, 184)(53, 161)(54, 191)(55, 164)(56, 180)(57, 165)(58, 192)(59, 171)(60, 173)(61, 178)(62, 176)(63, 182)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1454
Graph:: bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1462 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, (Y2^-1 * Y1)^2, Y3^2 * Y2^-2, (Y2, Y3^-1), (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^2 * Y2 * Y3 * Y1^-2, Y2^3 * Y1^-2 * Y3, Y2^-1 * Y1 * Y3 * Y2^2 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^5, Y1 * Y2 * Y1 * Y2^9 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66, 8, 72, 27, 91, 53, 117, 47, 111, 21, 85, 5, 69)(3, 67, 13, 77, 28, 92, 56, 120, 52, 116, 22, 86, 37, 101, 11, 75)(4, 68, 17, 81, 29, 93, 12, 76, 40, 104, 55, 119, 48, 112, 18, 82)(6, 70, 19, 83, 30, 94, 9, 73, 32, 96, 54, 118, 51, 115, 23, 87)(7, 71, 26, 90, 31, 95, 60, 124, 50, 114, 20, 84, 36, 100, 10, 74)(14, 78, 42, 106, 57, 121, 46, 110, 64, 128, 38, 102, 25, 89, 34, 98)(15, 79, 39, 103, 58, 122, 33, 97, 62, 126, 49, 113, 24, 88, 43, 107)(16, 80, 44, 108, 59, 123, 45, 109, 61, 125, 35, 99, 63, 127, 41, 105)(129, 193, 131, 195, 142, 206, 159, 223, 187, 251, 157, 221, 186, 250, 160, 224, 181, 245, 180, 244, 192, 256, 164, 228, 191, 255, 176, 240, 152, 216, 134, 198)(130, 194, 137, 201, 161, 225, 183, 247, 169, 233, 154, 218, 170, 234, 184, 248, 175, 239, 151, 215, 171, 235, 145, 209, 173, 237, 148, 212, 166, 230, 139, 203)(132, 196, 143, 207, 158, 222, 136, 200, 156, 220, 185, 249, 178, 242, 189, 253, 168, 232, 190, 254, 179, 243, 149, 213, 165, 229, 153, 217, 135, 199, 144, 208)(133, 197, 147, 211, 167, 231, 140, 204, 163, 227, 138, 202, 162, 226, 141, 205, 155, 219, 182, 246, 177, 241, 146, 210, 172, 236, 188, 252, 174, 238, 150, 214)
	L = (1, 132)(2, 138)(3, 143)(4, 142)(5, 148)(6, 144)(7, 129)(8, 157)(9, 162)(10, 161)(11, 163)(12, 130)(13, 169)(14, 158)(15, 159)(16, 131)(17, 133)(18, 175)(19, 166)(20, 167)(21, 176)(22, 173)(23, 174)(24, 135)(25, 134)(26, 177)(27, 154)(28, 186)(29, 185)(30, 187)(31, 136)(32, 189)(33, 141)(34, 183)(35, 137)(36, 149)(37, 152)(38, 140)(39, 139)(40, 192)(41, 182)(42, 146)(43, 150)(44, 151)(45, 147)(46, 145)(47, 188)(48, 153)(49, 184)(50, 181)(51, 191)(52, 190)(53, 168)(54, 170)(55, 155)(56, 172)(57, 160)(58, 178)(59, 156)(60, 171)(61, 180)(62, 164)(63, 165)(64, 179)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1452
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1463 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, (Y2 * Y1^-1)^2, (Y1 * Y3)^2, (R * Y3)^2, (Y2, Y3), (Y2^-1 * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y2^-3 * Y1, Y1 * Y3^5 * Y1^-1 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1^5 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66, 8, 72, 27, 91, 53, 117, 48, 112, 21, 85, 5, 69)(3, 67, 13, 77, 28, 92, 56, 120, 52, 116, 22, 86, 37, 101, 11, 75)(4, 68, 17, 81, 29, 93, 12, 76, 40, 104, 55, 119, 49, 113, 18, 82)(6, 70, 19, 83, 30, 94, 9, 73, 32, 96, 54, 118, 45, 109, 23, 87)(7, 71, 26, 90, 31, 95, 60, 124, 51, 115, 20, 84, 36, 100, 10, 74)(14, 78, 44, 108, 25, 89, 34, 98, 59, 123, 38, 102, 63, 127, 42, 106)(15, 79, 39, 103, 24, 88, 43, 107, 58, 122, 50, 114, 62, 126, 33, 97)(16, 80, 46, 110, 57, 121, 47, 111, 61, 125, 35, 99, 64, 128, 41, 105)(129, 193, 131, 195, 142, 206, 164, 228, 192, 256, 177, 241, 190, 254, 160, 224, 181, 245, 180, 244, 187, 251, 159, 223, 185, 249, 157, 221, 152, 216, 134, 198)(130, 194, 137, 201, 161, 225, 145, 209, 175, 239, 148, 212, 172, 236, 184, 248, 176, 240, 151, 215, 171, 235, 183, 247, 169, 233, 154, 218, 166, 230, 139, 203)(132, 196, 143, 207, 173, 237, 149, 213, 165, 229, 191, 255, 179, 243, 189, 253, 168, 232, 186, 250, 158, 222, 136, 200, 156, 220, 153, 217, 135, 199, 144, 208)(133, 197, 147, 211, 178, 242, 146, 210, 174, 238, 188, 252, 170, 234, 141, 205, 155, 219, 182, 246, 167, 231, 140, 204, 163, 227, 138, 202, 162, 226, 150, 214)
	L = (1, 132)(2, 138)(3, 143)(4, 142)(5, 148)(6, 144)(7, 129)(8, 157)(9, 162)(10, 161)(11, 163)(12, 130)(13, 169)(14, 173)(15, 164)(16, 131)(17, 133)(18, 176)(19, 172)(20, 178)(21, 177)(22, 175)(23, 170)(24, 135)(25, 134)(26, 167)(27, 154)(28, 152)(29, 153)(30, 185)(31, 136)(32, 189)(33, 150)(34, 145)(35, 137)(36, 149)(37, 190)(38, 140)(39, 139)(40, 187)(41, 182)(42, 183)(43, 141)(44, 146)(45, 192)(46, 151)(47, 147)(48, 188)(49, 191)(50, 184)(51, 181)(52, 186)(53, 168)(54, 166)(55, 155)(56, 174)(57, 156)(58, 159)(59, 158)(60, 171)(61, 180)(62, 179)(63, 160)(64, 165)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1451
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1464 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 40>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y2)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y3^2 * Y1^-1 * Y3 * Y2 * Y1, Y2^-1 * Y3 * Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^-7 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 8, 72, 23, 87, 16, 80, 30, 94, 20, 84, 5, 69)(3, 67, 13, 77, 24, 88, 11, 75, 4, 68, 17, 81, 25, 89, 12, 76)(6, 70, 19, 83, 26, 90, 10, 74, 7, 71, 18, 82, 27, 91, 9, 73)(14, 78, 32, 96, 41, 105, 33, 97, 15, 79, 31, 95, 42, 106, 34, 98)(21, 85, 29, 93, 43, 107, 37, 101, 22, 86, 28, 92, 44, 108, 38, 102)(35, 99, 50, 114, 55, 119, 48, 112, 36, 100, 49, 113, 56, 120, 47, 111)(39, 103, 53, 117, 57, 121, 45, 109, 40, 104, 54, 118, 58, 122, 46, 110)(51, 115, 60, 124, 63, 127, 62, 126, 52, 116, 59, 123, 64, 128, 61, 125)(129, 193, 131, 195, 142, 206, 163, 227, 179, 243, 168, 232, 150, 214, 135, 199, 144, 208, 132, 196, 143, 207, 164, 228, 180, 244, 167, 231, 149, 213, 134, 198)(130, 194, 137, 201, 156, 220, 173, 237, 187, 251, 176, 240, 160, 224, 140, 204, 158, 222, 138, 202, 157, 221, 174, 238, 188, 252, 175, 239, 159, 223, 139, 203)(133, 197, 146, 210, 165, 229, 181, 245, 190, 254, 178, 242, 162, 226, 145, 209, 151, 215, 147, 211, 166, 230, 182, 246, 189, 253, 177, 241, 161, 225, 141, 205)(136, 200, 152, 216, 169, 233, 183, 247, 191, 255, 186, 250, 172, 236, 155, 219, 148, 212, 153, 217, 170, 234, 184, 248, 192, 256, 185, 249, 171, 235, 154, 218)
	L = (1, 132)(2, 138)(3, 143)(4, 142)(5, 147)(6, 144)(7, 129)(8, 153)(9, 157)(10, 156)(11, 158)(12, 130)(13, 151)(14, 164)(15, 163)(16, 131)(17, 133)(18, 166)(19, 165)(20, 152)(21, 135)(22, 134)(23, 146)(24, 170)(25, 169)(26, 148)(27, 136)(28, 174)(29, 173)(30, 137)(31, 140)(32, 139)(33, 145)(34, 141)(35, 180)(36, 179)(37, 182)(38, 181)(39, 150)(40, 149)(41, 184)(42, 183)(43, 155)(44, 154)(45, 188)(46, 187)(47, 160)(48, 159)(49, 162)(50, 161)(51, 167)(52, 168)(53, 189)(54, 190)(55, 192)(56, 191)(57, 172)(58, 171)(59, 175)(60, 176)(61, 178)(62, 177)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1453
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1465 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y2 * Y3 * Y2 * Y3, (Y3^-1 * R * Y2)^2, Y3^-2 * Y2 * Y3^2 * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 14, 78)(7, 71, 19, 83)(8, 72, 22, 86)(9, 73, 25, 89)(10, 74, 28, 92)(12, 76, 31, 95)(13, 77, 24, 88)(15, 79, 35, 99)(16, 80, 21, 85)(17, 81, 37, 101)(18, 82, 40, 104)(20, 84, 43, 107)(23, 87, 47, 111)(26, 90, 49, 113)(27, 91, 42, 106)(29, 93, 53, 117)(30, 94, 39, 103)(32, 96, 56, 120)(33, 97, 57, 121)(34, 98, 46, 110)(36, 100, 58, 122)(38, 102, 59, 123)(41, 105, 61, 125)(44, 108, 51, 115)(45, 109, 50, 114)(48, 112, 55, 119)(52, 116, 60, 124)(54, 118, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 140, 204)(133, 197, 143, 207)(135, 199, 148, 212)(136, 200, 151, 215)(137, 201, 154, 218)(138, 202, 157, 221)(139, 203, 159, 223)(141, 205, 155, 219)(142, 206, 163, 227)(144, 208, 158, 222)(145, 209, 166, 230)(146, 210, 169, 233)(147, 211, 171, 235)(149, 213, 167, 231)(150, 214, 175, 239)(152, 216, 170, 234)(153, 217, 177, 241)(156, 220, 181, 245)(160, 224, 178, 242)(161, 225, 179, 243)(162, 226, 180, 244)(164, 228, 182, 246)(165, 229, 187, 251)(168, 232, 189, 253)(172, 236, 185, 249)(173, 237, 184, 248)(174, 238, 188, 252)(176, 240, 190, 254)(183, 247, 191, 255)(186, 250, 192, 256)
	L = (1, 132)(2, 135)(3, 137)(4, 141)(5, 129)(6, 145)(7, 149)(8, 130)(9, 155)(10, 131)(11, 160)(12, 158)(13, 157)(14, 164)(15, 162)(16, 133)(17, 167)(18, 134)(19, 172)(20, 170)(21, 169)(22, 176)(23, 174)(24, 136)(25, 178)(26, 144)(27, 143)(28, 182)(29, 180)(30, 138)(31, 183)(32, 142)(33, 139)(34, 140)(35, 179)(36, 177)(37, 185)(38, 152)(39, 151)(40, 190)(41, 188)(42, 146)(43, 186)(44, 150)(45, 147)(46, 148)(47, 184)(48, 187)(49, 191)(50, 156)(51, 153)(52, 154)(53, 161)(54, 159)(55, 163)(56, 165)(57, 168)(58, 175)(59, 192)(60, 166)(61, 173)(62, 171)(63, 181)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1473
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1466 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-2 * Y2 * Y3^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2, (Y3^-1 * Y1 * Y3^-1)^2, (Y3^-1 * R * Y2)^2, Y3 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3^-1, Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 14, 78)(7, 71, 19, 83)(8, 72, 22, 86)(9, 73, 25, 89)(10, 74, 28, 92)(12, 76, 31, 95)(13, 77, 24, 88)(15, 79, 35, 99)(16, 80, 21, 85)(17, 81, 37, 101)(18, 82, 40, 104)(20, 84, 43, 107)(23, 87, 47, 111)(26, 90, 49, 113)(27, 91, 42, 106)(29, 93, 53, 117)(30, 94, 39, 103)(32, 96, 56, 120)(33, 97, 57, 121)(34, 98, 46, 110)(36, 100, 58, 122)(38, 102, 59, 123)(41, 105, 62, 126)(44, 108, 54, 118)(45, 109, 55, 119)(48, 112, 50, 114)(51, 115, 64, 128)(52, 116, 61, 125)(60, 124, 63, 127)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 140, 204)(133, 197, 143, 207)(135, 199, 148, 212)(136, 200, 151, 215)(137, 201, 154, 218)(138, 202, 157, 221)(139, 203, 159, 223)(141, 205, 155, 219)(142, 206, 163, 227)(144, 208, 158, 222)(145, 209, 166, 230)(146, 210, 169, 233)(147, 211, 171, 235)(149, 213, 167, 231)(150, 214, 175, 239)(152, 216, 170, 234)(153, 217, 177, 241)(156, 220, 181, 245)(160, 224, 178, 242)(161, 225, 179, 243)(162, 226, 180, 244)(164, 228, 182, 246)(165, 229, 187, 251)(168, 232, 190, 254)(172, 236, 186, 250)(173, 237, 188, 252)(174, 238, 189, 253)(176, 240, 184, 248)(183, 247, 191, 255)(185, 249, 192, 256)
	L = (1, 132)(2, 135)(3, 137)(4, 141)(5, 129)(6, 145)(7, 149)(8, 130)(9, 155)(10, 131)(11, 160)(12, 158)(13, 157)(14, 164)(15, 162)(16, 133)(17, 167)(18, 134)(19, 172)(20, 170)(21, 169)(22, 176)(23, 174)(24, 136)(25, 178)(26, 144)(27, 143)(28, 182)(29, 180)(30, 138)(31, 183)(32, 142)(33, 139)(34, 140)(35, 179)(36, 177)(37, 186)(38, 152)(39, 151)(40, 184)(41, 189)(42, 146)(43, 185)(44, 150)(45, 147)(46, 148)(47, 188)(48, 187)(49, 191)(50, 156)(51, 153)(52, 154)(53, 161)(54, 159)(55, 163)(56, 171)(57, 175)(58, 168)(59, 192)(60, 165)(61, 166)(62, 173)(63, 181)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1472
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1467 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (Y1 * Y2)^2, Y2 * Y3^4, (Y1 * Y3^2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 17, 81)(8, 72, 19, 83)(9, 73, 21, 85)(10, 74, 22, 86)(12, 76, 20, 84)(14, 78, 18, 82)(15, 79, 26, 90)(16, 80, 27, 91)(23, 87, 32, 96)(24, 88, 33, 97)(25, 89, 34, 98)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(31, 95, 39, 103)(35, 99, 44, 108)(40, 104, 49, 113)(41, 105, 50, 114)(42, 106, 51, 115)(43, 107, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 143, 207)(136, 200, 144, 208)(139, 203, 149, 213)(140, 204, 142, 206)(141, 205, 150, 214)(145, 209, 154, 218)(146, 210, 148, 212)(147, 211, 155, 219)(151, 215, 159, 223)(152, 216, 153, 217)(156, 220, 163, 227)(157, 221, 158, 222)(160, 224, 167, 231)(161, 225, 162, 226)(164, 228, 172, 236)(165, 229, 166, 230)(168, 232, 171, 235)(169, 233, 170, 234)(173, 237, 176, 240)(174, 238, 175, 239)(177, 241, 180, 244)(178, 242, 179, 243)(181, 245, 184, 248)(182, 246, 183, 247)(185, 249, 188, 252)(186, 250, 187, 251)(189, 253, 192, 256)(190, 254, 191, 255)
	L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 143)(7, 146)(8, 130)(9, 142)(10, 131)(11, 151)(12, 138)(13, 153)(14, 133)(15, 148)(16, 134)(17, 156)(18, 144)(19, 158)(20, 136)(21, 159)(22, 152)(23, 141)(24, 139)(25, 149)(26, 163)(27, 157)(28, 147)(29, 145)(30, 154)(31, 150)(32, 168)(33, 170)(34, 169)(35, 155)(36, 173)(37, 175)(38, 174)(39, 171)(40, 161)(41, 160)(42, 167)(43, 162)(44, 176)(45, 165)(46, 164)(47, 172)(48, 166)(49, 185)(50, 187)(51, 186)(52, 188)(53, 189)(54, 191)(55, 190)(56, 192)(57, 178)(58, 177)(59, 180)(60, 179)(61, 182)(62, 181)(63, 184)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 32, 16, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1474
Graph:: simple bipartite
	v = 64 e = 128 f = 12
	degree seq :: [ 4^64 ]

E27.1468 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y1 * Y2 * Y1 * Y3, (R * Y2 * Y3)^2, Y2^3 * Y1 * Y3 * Y2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 17, 81)(8, 72, 22, 86)(10, 74, 24, 88)(11, 75, 20, 84)(12, 76, 19, 83)(13, 77, 23, 87)(15, 79, 21, 85)(16, 80, 18, 82)(25, 89, 33, 97)(26, 90, 35, 99)(27, 91, 34, 98)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 63, 127)(58, 122, 62, 126)(59, 123, 61, 125)(60, 124, 64, 128)(129, 193, 131, 195, 138, 202, 149, 213, 135, 199, 148, 212, 144, 208, 133, 197)(130, 194, 134, 198, 146, 210, 141, 205, 132, 196, 140, 204, 152, 216, 136, 200)(137, 201, 153, 217, 142, 206, 156, 220, 139, 203, 155, 219, 143, 207, 154, 218)(145, 209, 157, 221, 150, 214, 160, 224, 147, 211, 159, 223, 151, 215, 158, 222)(161, 225, 169, 233, 163, 227, 172, 236, 162, 226, 171, 235, 164, 228, 170, 234)(165, 229, 173, 237, 167, 231, 176, 240, 166, 230, 175, 239, 168, 232, 174, 238)(177, 241, 185, 249, 179, 243, 188, 252, 178, 242, 187, 251, 180, 244, 186, 250)(181, 245, 189, 253, 183, 247, 192, 256, 182, 246, 191, 255, 184, 248, 190, 254)
	L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 147)(7, 130)(8, 151)(9, 148)(10, 146)(11, 131)(12, 145)(13, 150)(14, 149)(15, 133)(16, 152)(17, 140)(18, 138)(19, 134)(20, 137)(21, 142)(22, 141)(23, 136)(24, 144)(25, 162)(26, 164)(27, 161)(28, 163)(29, 166)(30, 168)(31, 165)(32, 167)(33, 155)(34, 153)(35, 156)(36, 154)(37, 159)(38, 157)(39, 160)(40, 158)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 189)(58, 192)(59, 191)(60, 190)(61, 185)(62, 188)(63, 187)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1471
Graph:: bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1469 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y1 * Y2^-4, (R * Y2 * Y3)^2, (Y2 * Y3 * Y2)^2, Y1 * Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 22, 86)(20, 84, 26, 90)(21, 85, 25, 89)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 35, 99)(30, 94, 34, 98)(31, 95, 36, 100)(32, 96, 33, 97)(37, 101, 43, 107)(38, 102, 39, 103)(40, 104, 44, 108)(41, 105, 42, 106)(45, 109, 52, 116)(46, 110, 47, 111)(48, 112, 51, 115)(49, 113, 50, 114)(53, 117, 56, 120)(54, 118, 55, 119)(57, 121, 60, 124)(58, 122, 59, 123)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195, 137, 201, 136, 200, 130, 194, 134, 198, 142, 206, 133, 197)(132, 196, 139, 203, 150, 214, 145, 209, 135, 199, 144, 208, 147, 211, 140, 204)(138, 202, 148, 212, 141, 205, 153, 217, 143, 207, 154, 218, 146, 210, 149, 213)(151, 215, 159, 223, 152, 216, 161, 225, 155, 219, 164, 228, 156, 220, 160, 224)(157, 221, 165, 229, 158, 222, 167, 231, 163, 227, 171, 235, 162, 226, 166, 230)(168, 232, 176, 240, 169, 233, 178, 242, 172, 236, 179, 243, 170, 234, 177, 241)(173, 237, 181, 245, 174, 238, 183, 247, 180, 244, 184, 248, 175, 239, 182, 246)(185, 249, 192, 256, 186, 250, 191, 255, 188, 252, 189, 253, 187, 251, 190, 254)
	L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 151)(12, 152)(13, 133)(14, 150)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 142)(23, 139)(24, 140)(25, 162)(26, 163)(27, 144)(28, 145)(29, 148)(30, 149)(31, 168)(32, 169)(33, 170)(34, 153)(35, 154)(36, 172)(37, 173)(38, 174)(39, 175)(40, 159)(41, 160)(42, 161)(43, 180)(44, 164)(45, 165)(46, 166)(47, 167)(48, 185)(49, 186)(50, 187)(51, 188)(52, 171)(53, 189)(54, 190)(55, 191)(56, 192)(57, 176)(58, 177)(59, 178)(60, 179)(61, 181)(62, 182)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1470
Graph:: bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1470 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y2 * Y1^-2)^2, (Y3 * Y1^-2)^2, Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y3, Y1^-2 * Y2 * Y3 * Y1^-6 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 46, 110, 28, 92, 10, 74, 21, 85, 38, 102, 56, 120, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 40, 104, 19, 83, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 54, 118, 39, 103, 18, 82, 11, 75)(7, 71, 20, 84, 14, 78, 32, 96, 50, 114, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 15, 79, 33, 97, 51, 115, 57, 121, 36, 100, 22, 86)(26, 90, 42, 106, 29, 93, 44, 108, 59, 123, 64, 128, 62, 126, 48, 112, 27, 91, 41, 105, 30, 94, 43, 107, 60, 124, 63, 127, 61, 125, 47, 111)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 153, 217)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(159, 223, 174, 238)(160, 224, 176, 240)(161, 225, 175, 239)(162, 226, 178, 242)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 189, 253)(177, 241, 190, 254)(179, 243, 181, 245)(180, 244, 183, 247)(185, 249, 191, 255)(186, 250, 192, 256)
	L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 159)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 174)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 144)(32, 175)(33, 176)(34, 179)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 190)(46, 153)(47, 160)(48, 161)(49, 189)(50, 181)(51, 162)(52, 182)(53, 178)(54, 180)(55, 163)(56, 164)(57, 192)(58, 191)(59, 168)(60, 167)(61, 177)(62, 173)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1469
Graph:: bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1471 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y2 * Y1^8, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 43, 107, 24, 88, 10, 74, 3, 67, 7, 71, 16, 80, 31, 95, 50, 114, 29, 93, 14, 78, 5, 69)(4, 68, 11, 75, 25, 89, 44, 108, 59, 123, 54, 118, 33, 97, 22, 86, 9, 73, 21, 85, 39, 103, 57, 121, 51, 115, 34, 98, 17, 81, 12, 76)(8, 72, 19, 83, 13, 77, 28, 92, 48, 112, 61, 125, 52, 116, 36, 100, 18, 82, 35, 99, 23, 87, 42, 106, 58, 122, 53, 117, 32, 96, 20, 84)(26, 90, 45, 109, 27, 91, 47, 111, 55, 119, 64, 128, 62, 126, 49, 113, 40, 104, 37, 101, 41, 105, 38, 102, 56, 120, 63, 127, 60, 124, 46, 110)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 159, 223)(145, 209, 161, 225)(147, 211, 163, 227)(148, 212, 164, 228)(153, 217, 167, 231)(154, 218, 168, 232)(155, 219, 169, 233)(156, 220, 170, 234)(157, 221, 171, 235)(158, 222, 178, 242)(160, 224, 180, 244)(162, 226, 182, 246)(165, 229, 173, 237)(166, 230, 175, 239)(172, 236, 185, 249)(174, 238, 177, 241)(176, 240, 186, 250)(179, 243, 187, 251)(181, 245, 189, 253)(183, 247, 184, 248)(188, 252, 190, 254)(191, 255, 192, 256)
	L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 153)(15, 160)(16, 161)(17, 134)(18, 135)(19, 165)(20, 166)(21, 168)(22, 169)(23, 138)(24, 167)(25, 142)(26, 139)(27, 140)(28, 177)(29, 176)(30, 179)(31, 180)(32, 143)(33, 144)(34, 183)(35, 173)(36, 175)(37, 147)(38, 148)(39, 152)(40, 149)(41, 150)(42, 174)(43, 186)(44, 188)(45, 163)(46, 170)(47, 164)(48, 157)(49, 156)(50, 187)(51, 158)(52, 159)(53, 191)(54, 184)(55, 162)(56, 182)(57, 190)(58, 171)(59, 178)(60, 172)(61, 192)(62, 185)(63, 181)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1468
Graph:: bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1472 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3)^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-3 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3^2 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y2^-3, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^2, Y3^-1 * Y2^2 * Y1 * Y3 * Y1^-3, Y1^8, Y3 * Y2^11 * Y1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66, 8, 72, 28, 92, 54, 118, 53, 117, 22, 86, 5, 69)(3, 67, 13, 77, 43, 107, 63, 127, 51, 115, 57, 121, 29, 93, 11, 75)(4, 68, 17, 81, 50, 114, 62, 126, 46, 110, 58, 122, 30, 94, 12, 76)(6, 70, 20, 84, 45, 109, 64, 128, 49, 113, 55, 119, 31, 95, 9, 73)(7, 71, 21, 85, 47, 111, 61, 125, 48, 112, 56, 120, 32, 96, 10, 74)(14, 78, 39, 103, 25, 89, 34, 98, 19, 83, 42, 106, 26, 90, 36, 100)(15, 79, 40, 104, 27, 91, 37, 101, 18, 82, 41, 105, 24, 88, 33, 97)(16, 80, 38, 102, 59, 123, 52, 116, 23, 87, 35, 99, 60, 124, 44, 108)(129, 193, 131, 195, 142, 206, 160, 224, 188, 252, 178, 242, 155, 219, 177, 241, 182, 246, 179, 243, 147, 211, 175, 239, 187, 251, 158, 222, 152, 216, 134, 198)(130, 194, 137, 201, 161, 225, 186, 250, 180, 244, 149, 213, 170, 234, 191, 255, 181, 245, 192, 256, 165, 229, 145, 209, 172, 236, 184, 248, 167, 231, 139, 203)(132, 196, 146, 210, 173, 237, 150, 214, 171, 235, 154, 218, 135, 199, 151, 215, 174, 238, 143, 207, 159, 223, 136, 200, 157, 221, 153, 217, 176, 240, 144, 208)(133, 197, 148, 212, 169, 233, 140, 204, 166, 230, 189, 253, 162, 226, 185, 249, 156, 220, 183, 247, 168, 232, 190, 254, 163, 227, 138, 202, 164, 228, 141, 205)
	L = (1, 132)(2, 138)(3, 143)(4, 147)(5, 149)(6, 151)(7, 129)(8, 158)(9, 162)(10, 165)(11, 166)(12, 130)(13, 172)(14, 173)(15, 175)(16, 131)(17, 133)(18, 160)(19, 159)(20, 167)(21, 168)(22, 178)(23, 179)(24, 176)(25, 134)(26, 177)(27, 135)(28, 184)(29, 155)(30, 154)(31, 188)(32, 136)(33, 141)(34, 145)(35, 137)(36, 186)(37, 185)(38, 192)(39, 190)(40, 139)(41, 191)(42, 140)(43, 152)(44, 183)(45, 187)(46, 142)(47, 150)(48, 182)(49, 144)(50, 153)(51, 146)(52, 148)(53, 189)(54, 174)(55, 170)(56, 169)(57, 180)(58, 156)(59, 157)(60, 171)(61, 161)(62, 181)(63, 163)(64, 164)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1466
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1473 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, (Y1^-1 * Y3^-1)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, Y3^-2 * Y2 * Y3^2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, Y3 * Y2^2 * Y1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y2^2 * Y3 * Y1 * Y2^-1 * Y1^-1, Y1^8, Y2^16 ]
Map:: polytopal non-degenerate
	R = (1, 65, 2, 66, 8, 72, 28, 92, 54, 118, 53, 117, 22, 86, 5, 69)(3, 67, 13, 77, 43, 107, 63, 127, 51, 115, 57, 121, 29, 93, 11, 75)(4, 68, 17, 81, 50, 114, 62, 126, 46, 110, 58, 122, 30, 94, 12, 76)(6, 70, 20, 84, 47, 111, 64, 128, 49, 113, 55, 119, 31, 95, 9, 73)(7, 71, 21, 85, 45, 109, 61, 125, 48, 112, 56, 120, 32, 96, 10, 74)(14, 78, 39, 103, 26, 90, 36, 100, 19, 83, 42, 106, 25, 89, 34, 98)(15, 79, 40, 104, 24, 88, 33, 97, 18, 82, 41, 105, 27, 91, 37, 101)(16, 80, 38, 102, 59, 123, 52, 116, 23, 87, 35, 99, 60, 124, 44, 108)(129, 193, 131, 195, 142, 206, 173, 237, 187, 251, 158, 222, 155, 219, 177, 241, 182, 246, 179, 243, 147, 211, 160, 224, 188, 252, 178, 242, 152, 216, 134, 198)(130, 194, 137, 201, 161, 225, 145, 209, 172, 236, 184, 248, 170, 234, 191, 255, 181, 245, 192, 256, 165, 229, 186, 250, 180, 244, 149, 213, 167, 231, 139, 203)(132, 196, 146, 210, 159, 223, 136, 200, 157, 221, 154, 218, 135, 199, 151, 215, 174, 238, 143, 207, 175, 239, 150, 214, 171, 235, 153, 217, 176, 240, 144, 208)(133, 197, 148, 212, 168, 232, 190, 254, 163, 227, 138, 202, 164, 228, 185, 249, 156, 220, 183, 247, 169, 233, 140, 204, 166, 230, 189, 253, 162, 226, 141, 205)
	L = (1, 132)(2, 138)(3, 143)(4, 147)(5, 149)(6, 151)(7, 129)(8, 158)(9, 162)(10, 165)(11, 166)(12, 130)(13, 172)(14, 159)(15, 160)(16, 131)(17, 133)(18, 173)(19, 175)(20, 170)(21, 169)(22, 178)(23, 179)(24, 176)(25, 134)(26, 177)(27, 135)(28, 184)(29, 152)(30, 153)(31, 188)(32, 136)(33, 185)(34, 186)(35, 137)(36, 145)(37, 141)(38, 192)(39, 190)(40, 139)(41, 191)(42, 140)(43, 155)(44, 183)(45, 150)(46, 142)(47, 187)(48, 182)(49, 144)(50, 154)(51, 146)(52, 148)(53, 189)(54, 174)(55, 167)(56, 168)(57, 180)(58, 156)(59, 157)(60, 171)(61, 161)(62, 181)(63, 163)(64, 164)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1465
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1474 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 : C2) : C2 (small group id <64, 42>)
Aut   = $<128, 924>$ (small group id <128, 924>)
|r| :: 2
Presentation :: [ R^2, (Y3^-1 * Y2)^2, (Y3, Y2^-1), (R * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2^2 * Y3^-2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y3^-1 * Y1^-1 * Y2^-2 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^3 * Y2^-1, Y1^-1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3, Y1^-1 * Y2^-1 * Y3 * Y1^-3, Y3^-2 * Y2^-2 * Y3^-1 * Y2^-3 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 8, 72, 23, 87, 16, 80, 30, 94, 20, 84, 5, 69)(3, 67, 13, 77, 25, 89, 12, 76, 4, 68, 17, 81, 24, 88, 11, 75)(6, 70, 18, 82, 27, 91, 10, 74, 7, 71, 19, 83, 26, 90, 9, 73)(14, 78, 31, 95, 41, 105, 34, 98, 15, 79, 32, 96, 42, 106, 33, 97)(21, 85, 28, 92, 43, 107, 38, 102, 22, 86, 29, 93, 44, 108, 37, 101)(35, 99, 49, 113, 56, 120, 48, 112, 36, 100, 50, 114, 55, 119, 47, 111)(39, 103, 53, 117, 58, 122, 46, 110, 40, 104, 54, 118, 57, 121, 45, 109)(51, 115, 60, 124, 63, 127, 62, 126, 52, 116, 59, 123, 64, 128, 61, 125)(129, 193, 131, 195, 142, 206, 163, 227, 179, 243, 168, 232, 150, 214, 135, 199, 144, 208, 132, 196, 143, 207, 164, 228, 180, 244, 167, 231, 149, 213, 134, 198)(130, 194, 137, 201, 156, 220, 173, 237, 187, 251, 176, 240, 160, 224, 140, 204, 158, 222, 138, 202, 157, 221, 174, 238, 188, 252, 175, 239, 159, 223, 139, 203)(133, 197, 146, 210, 165, 229, 181, 245, 190, 254, 178, 242, 162, 226, 145, 209, 151, 215, 147, 211, 166, 230, 182, 246, 189, 253, 177, 241, 161, 225, 141, 205)(136, 200, 152, 216, 169, 233, 183, 247, 191, 255, 186, 250, 172, 236, 155, 219, 148, 212, 153, 217, 170, 234, 184, 248, 192, 256, 185, 249, 171, 235, 154, 218)
	L = (1, 132)(2, 138)(3, 143)(4, 142)(5, 147)(6, 144)(7, 129)(8, 153)(9, 157)(10, 156)(11, 158)(12, 130)(13, 151)(14, 164)(15, 163)(16, 131)(17, 133)(18, 166)(19, 165)(20, 152)(21, 135)(22, 134)(23, 146)(24, 170)(25, 169)(26, 148)(27, 136)(28, 174)(29, 173)(30, 137)(31, 140)(32, 139)(33, 145)(34, 141)(35, 180)(36, 179)(37, 182)(38, 181)(39, 150)(40, 149)(41, 184)(42, 183)(43, 155)(44, 154)(45, 188)(46, 187)(47, 160)(48, 159)(49, 162)(50, 161)(51, 167)(52, 168)(53, 189)(54, 190)(55, 192)(56, 191)(57, 172)(58, 171)(59, 175)(60, 176)(61, 178)(62, 177)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4^16 ), ( 4^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1467
Graph:: bipartite
	v = 12 e = 128 f = 64
	degree seq :: [ 16^8, 32^4 ]

E27.1475 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: halfedge^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-4, Y1^2 * Y2 * Y1^-2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y1^3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 66, 2, 70, 6, 78, 14, 90, 26, 106, 42, 100, 36, 113, 49, 124, 60, 119, 55, 104, 40, 114, 50, 105, 41, 89, 25, 77, 13, 69, 5, 65)(3, 73, 9, 83, 19, 97, 33, 112, 48, 96, 32, 88, 24, 103, 39, 118, 54, 125, 61, 115, 51, 121, 57, 107, 43, 91, 27, 79, 15, 71, 7, 67)(4, 75, 11, 86, 22, 101, 37, 116, 52, 126, 62, 120, 56, 123, 59, 111, 47, 95, 31, 85, 21, 99, 35, 108, 44, 92, 28, 80, 16, 72, 8, 68)(10, 81, 17, 93, 29, 109, 45, 122, 58, 128, 64, 127, 63, 117, 53, 102, 38, 87, 23, 76, 12, 82, 18, 94, 30, 110, 46, 98, 34, 84, 20, 74)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 43)(28, 46)(29, 47)(32, 50)(34, 44)(36, 51)(37, 53)(39, 55)(41, 48)(42, 57)(45, 59)(49, 61)(52, 63)(54, 60)(56, 58)(62, 64)(65, 68)(66, 72)(67, 74)(69, 75)(70, 80)(71, 81)(73, 84)(76, 88)(77, 86)(78, 92)(79, 93)(82, 96)(83, 98)(85, 100)(87, 103)(89, 101)(90, 108)(91, 109)(94, 112)(95, 113)(97, 110)(99, 106)(102, 118)(104, 120)(105, 116)(107, 122)(111, 124)(114, 126)(115, 127)(117, 125)(119, 123)(121, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1476
Transitivity :: VT+ AT
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.1476 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: halfedge^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^8, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 66, 2, 70, 6, 78, 14, 90, 26, 89, 25, 77, 13, 69, 5, 65)(3, 73, 9, 83, 19, 97, 33, 105, 41, 91, 27, 79, 15, 71, 7, 67)(4, 75, 11, 86, 22, 101, 37, 106, 42, 92, 28, 80, 16, 72, 8, 68)(10, 81, 17, 93, 29, 107, 43, 118, 54, 113, 49, 98, 34, 84, 20, 74)(12, 82, 18, 94, 30, 108, 44, 119, 55, 115, 51, 102, 38, 87, 23, 76)(21, 99, 35, 114, 50, 123, 59, 126, 62, 120, 56, 109, 45, 95, 31, 85)(24, 103, 39, 116, 52, 124, 60, 127, 63, 121, 57, 110, 46, 96, 32, 88)(36, 111, 47, 122, 58, 128, 64, 125, 61, 117, 53, 104, 40, 112, 48, 100)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 41)(28, 44)(29, 45)(32, 48)(34, 50)(36, 46)(37, 51)(39, 53)(42, 55)(43, 56)(47, 57)(49, 59)(52, 61)(54, 62)(58, 63)(60, 64)(65, 68)(66, 72)(67, 74)(69, 75)(70, 80)(71, 81)(73, 84)(76, 88)(77, 86)(78, 92)(79, 93)(82, 96)(83, 98)(85, 100)(87, 103)(89, 101)(90, 106)(91, 107)(94, 110)(95, 111)(97, 113)(99, 112)(102, 116)(104, 114)(105, 118)(108, 121)(109, 122)(115, 124)(117, 123)(119, 127)(120, 128)(125, 126)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1475
Transitivity :: VT+ AT
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.1477 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: edge^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^8, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 65, 4, 68, 12, 76, 24, 88, 40, 104, 25, 89, 13, 77, 5, 69)(2, 66, 7, 71, 17, 81, 31, 95, 48, 112, 32, 96, 18, 82, 8, 72)(3, 67, 10, 74, 22, 86, 38, 102, 53, 117, 39, 103, 23, 87, 11, 75)(6, 70, 15, 79, 29, 93, 46, 110, 58, 122, 47, 111, 30, 94, 16, 80)(9, 73, 20, 84, 36, 100, 51, 115, 61, 125, 52, 116, 37, 101, 21, 85)(14, 78, 27, 91, 44, 108, 56, 120, 64, 128, 57, 121, 45, 109, 28, 92)(19, 83, 34, 98, 50, 114, 60, 124, 62, 126, 54, 118, 41, 105, 35, 99)(26, 90, 42, 106, 55, 119, 63, 127, 59, 123, 49, 113, 33, 97, 43, 107)(129, 130)(131, 137)(132, 136)(133, 135)(134, 142)(138, 149)(139, 148)(140, 146)(141, 145)(143, 156)(144, 155)(147, 161)(150, 165)(151, 164)(152, 160)(153, 159)(154, 169)(157, 173)(158, 172)(162, 177)(163, 171)(166, 180)(167, 179)(168, 176)(170, 182)(174, 185)(175, 184)(178, 187)(181, 189)(183, 190)(186, 192)(188, 191)(193, 195)(194, 198)(196, 203)(197, 202)(199, 208)(200, 207)(201, 211)(204, 215)(205, 214)(206, 218)(209, 222)(210, 221)(212, 227)(213, 226)(216, 231)(217, 230)(219, 235)(220, 234)(223, 239)(224, 238)(225, 236)(228, 233)(229, 242)(232, 245)(237, 247)(240, 250)(241, 248)(243, 246)(244, 252)(249, 255)(251, 256)(253, 254)
	L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 64, 64 ), ( 64^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1480
Graph:: simple bipartite
	v = 72 e = 128 f = 4
	degree seq :: [ 2^64, 16^8 ]

E27.1478 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: edge^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^4 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 65, 4, 68, 12, 76, 24, 88, 40, 104, 53, 117, 33, 97, 52, 116, 60, 124, 44, 108, 26, 90, 43, 107, 41, 105, 25, 89, 13, 77, 5, 69)(2, 66, 7, 71, 17, 81, 31, 95, 49, 113, 59, 123, 42, 106, 58, 122, 54, 118, 35, 99, 19, 83, 34, 98, 50, 114, 32, 96, 18, 82, 8, 72)(3, 67, 10, 74, 22, 86, 38, 102, 46, 110, 28, 92, 14, 78, 27, 91, 45, 109, 61, 125, 51, 115, 63, 127, 56, 120, 39, 103, 23, 87, 11, 75)(6, 70, 15, 79, 29, 93, 47, 111, 37, 101, 21, 85, 9, 73, 20, 84, 36, 100, 55, 119, 57, 121, 64, 128, 62, 126, 48, 112, 30, 94, 16, 80)(129, 130)(131, 137)(132, 136)(133, 135)(134, 142)(138, 149)(139, 148)(140, 146)(141, 145)(143, 156)(144, 155)(147, 161)(150, 165)(151, 164)(152, 160)(153, 159)(154, 170)(157, 174)(158, 173)(162, 181)(163, 180)(166, 175)(167, 183)(168, 178)(169, 177)(171, 187)(172, 186)(176, 189)(179, 190)(182, 188)(184, 185)(191, 192)(193, 195)(194, 198)(196, 203)(197, 202)(199, 208)(200, 207)(201, 211)(204, 215)(205, 214)(206, 218)(209, 222)(210, 221)(212, 227)(213, 226)(216, 231)(217, 230)(219, 236)(220, 235)(223, 240)(224, 239)(225, 243)(228, 246)(229, 242)(232, 248)(233, 238)(234, 249)(237, 252)(241, 254)(244, 253)(245, 255)(247, 250)(251, 256)
	L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 32, 32 ), ( 32^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1479
Graph:: simple bipartite
	v = 68 e = 128 f = 8
	degree seq :: [ 2^64, 32^4 ]

E27.1479 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 8, 16})
Quotient :: loop^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^8, Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 65, 129, 193, 4, 68, 132, 196, 12, 76, 140, 204, 24, 88, 152, 216, 40, 104, 168, 232, 25, 89, 153, 217, 13, 77, 141, 205, 5, 69, 133, 197)(2, 66, 130, 194, 7, 71, 135, 199, 17, 81, 145, 209, 31, 95, 159, 223, 48, 112, 176, 240, 32, 96, 160, 224, 18, 82, 146, 210, 8, 72, 136, 200)(3, 67, 131, 195, 10, 74, 138, 202, 22, 86, 150, 214, 38, 102, 166, 230, 53, 117, 181, 245, 39, 103, 167, 231, 23, 87, 151, 215, 11, 75, 139, 203)(6, 70, 134, 198, 15, 79, 143, 207, 29, 93, 157, 221, 46, 110, 174, 238, 58, 122, 186, 250, 47, 111, 175, 239, 30, 94, 158, 222, 16, 80, 144, 208)(9, 73, 137, 201, 20, 84, 148, 212, 36, 100, 164, 228, 51, 115, 179, 243, 61, 125, 189, 253, 52, 116, 180, 244, 37, 101, 165, 229, 21, 85, 149, 213)(14, 78, 142, 206, 27, 91, 155, 219, 44, 108, 172, 236, 56, 120, 184, 248, 64, 128, 192, 256, 57, 121, 185, 249, 45, 109, 173, 237, 28, 92, 156, 220)(19, 83, 147, 211, 34, 98, 162, 226, 50, 114, 178, 242, 60, 124, 188, 252, 62, 126, 190, 254, 54, 118, 182, 246, 41, 105, 169, 233, 35, 99, 163, 227)(26, 90, 154, 218, 42, 106, 170, 234, 55, 119, 183, 247, 63, 127, 191, 255, 59, 123, 187, 251, 49, 113, 177, 241, 33, 97, 161, 225, 43, 107, 171, 235)
	L = (1, 66)(2, 65)(3, 73)(4, 72)(5, 71)(6, 78)(7, 69)(8, 68)(9, 67)(10, 85)(11, 84)(12, 82)(13, 81)(14, 70)(15, 92)(16, 91)(17, 77)(18, 76)(19, 97)(20, 75)(21, 74)(22, 101)(23, 100)(24, 96)(25, 95)(26, 105)(27, 80)(28, 79)(29, 109)(30, 108)(31, 89)(32, 88)(33, 83)(34, 113)(35, 107)(36, 87)(37, 86)(38, 116)(39, 115)(40, 112)(41, 90)(42, 118)(43, 99)(44, 94)(45, 93)(46, 121)(47, 120)(48, 104)(49, 98)(50, 123)(51, 103)(52, 102)(53, 125)(54, 106)(55, 126)(56, 111)(57, 110)(58, 128)(59, 114)(60, 127)(61, 117)(62, 119)(63, 124)(64, 122)(129, 195)(130, 198)(131, 193)(132, 203)(133, 202)(134, 194)(135, 208)(136, 207)(137, 211)(138, 197)(139, 196)(140, 215)(141, 214)(142, 218)(143, 200)(144, 199)(145, 222)(146, 221)(147, 201)(148, 227)(149, 226)(150, 205)(151, 204)(152, 231)(153, 230)(154, 206)(155, 235)(156, 234)(157, 210)(158, 209)(159, 239)(160, 238)(161, 236)(162, 213)(163, 212)(164, 233)(165, 242)(166, 217)(167, 216)(168, 245)(169, 228)(170, 220)(171, 219)(172, 225)(173, 247)(174, 224)(175, 223)(176, 250)(177, 248)(178, 229)(179, 246)(180, 252)(181, 232)(182, 243)(183, 237)(184, 241)(185, 255)(186, 240)(187, 256)(188, 244)(189, 254)(190, 253)(191, 249)(192, 251)
	local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1478
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 128 f = 68
	degree seq :: [ 32^8 ]

E27.1480 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 8, 16})
Quotient :: loop^2
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1)^2, Y3^4 * Y1 * Y3^-2 * Y2 * Y1 * Y2, Y3^2 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 65, 129, 193, 4, 68, 132, 196, 12, 76, 140, 204, 24, 88, 152, 216, 40, 104, 168, 232, 53, 117, 181, 245, 33, 97, 161, 225, 52, 116, 180, 244, 60, 124, 188, 252, 44, 108, 172, 236, 26, 90, 154, 218, 43, 107, 171, 235, 41, 105, 169, 233, 25, 89, 153, 217, 13, 77, 141, 205, 5, 69, 133, 197)(2, 66, 130, 194, 7, 71, 135, 199, 17, 81, 145, 209, 31, 95, 159, 223, 49, 113, 177, 241, 59, 123, 187, 251, 42, 106, 170, 234, 58, 122, 186, 250, 54, 118, 182, 246, 35, 99, 163, 227, 19, 83, 147, 211, 34, 98, 162, 226, 50, 114, 178, 242, 32, 96, 160, 224, 18, 82, 146, 210, 8, 72, 136, 200)(3, 67, 131, 195, 10, 74, 138, 202, 22, 86, 150, 214, 38, 102, 166, 230, 46, 110, 174, 238, 28, 92, 156, 220, 14, 78, 142, 206, 27, 91, 155, 219, 45, 109, 173, 237, 61, 125, 189, 253, 51, 115, 179, 243, 63, 127, 191, 255, 56, 120, 184, 248, 39, 103, 167, 231, 23, 87, 151, 215, 11, 75, 139, 203)(6, 70, 134, 198, 15, 79, 143, 207, 29, 93, 157, 221, 47, 111, 175, 239, 37, 101, 165, 229, 21, 85, 149, 213, 9, 73, 137, 201, 20, 84, 148, 212, 36, 100, 164, 228, 55, 119, 183, 247, 57, 121, 185, 249, 64, 128, 192, 256, 62, 126, 190, 254, 48, 112, 176, 240, 30, 94, 158, 222, 16, 80, 144, 208)
	L = (1, 66)(2, 65)(3, 73)(4, 72)(5, 71)(6, 78)(7, 69)(8, 68)(9, 67)(10, 85)(11, 84)(12, 82)(13, 81)(14, 70)(15, 92)(16, 91)(17, 77)(18, 76)(19, 97)(20, 75)(21, 74)(22, 101)(23, 100)(24, 96)(25, 95)(26, 106)(27, 80)(28, 79)(29, 110)(30, 109)(31, 89)(32, 88)(33, 83)(34, 117)(35, 116)(36, 87)(37, 86)(38, 111)(39, 119)(40, 114)(41, 113)(42, 90)(43, 123)(44, 122)(45, 94)(46, 93)(47, 102)(48, 125)(49, 105)(50, 104)(51, 126)(52, 99)(53, 98)(54, 124)(55, 103)(56, 121)(57, 120)(58, 108)(59, 107)(60, 118)(61, 112)(62, 115)(63, 128)(64, 127)(129, 195)(130, 198)(131, 193)(132, 203)(133, 202)(134, 194)(135, 208)(136, 207)(137, 211)(138, 197)(139, 196)(140, 215)(141, 214)(142, 218)(143, 200)(144, 199)(145, 222)(146, 221)(147, 201)(148, 227)(149, 226)(150, 205)(151, 204)(152, 231)(153, 230)(154, 206)(155, 236)(156, 235)(157, 210)(158, 209)(159, 240)(160, 239)(161, 243)(162, 213)(163, 212)(164, 246)(165, 242)(166, 217)(167, 216)(168, 248)(169, 238)(170, 249)(171, 220)(172, 219)(173, 252)(174, 233)(175, 224)(176, 223)(177, 254)(178, 229)(179, 225)(180, 253)(181, 255)(182, 228)(183, 250)(184, 232)(185, 234)(186, 247)(187, 256)(188, 237)(189, 244)(190, 241)(191, 245)(192, 251)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1477
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 128 f = 72
	degree seq :: [ 64^4 ]

E27.1481 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 2140>$ (small group id <128, 2140>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y3^4 * Y2^-2, Y2^8, Y2^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 24, 88)(12, 76, 25, 89)(13, 77, 23, 87)(14, 78, 26, 90)(15, 79, 21, 85)(16, 80, 19, 83)(17, 81, 20, 84)(18, 82, 22, 86)(27, 91, 42, 106)(28, 92, 43, 107)(29, 93, 41, 105)(30, 94, 44, 108)(31, 95, 40, 104)(32, 96, 38, 102)(33, 97, 36, 100)(34, 98, 37, 101)(35, 99, 39, 103)(45, 109, 52, 116)(46, 110, 57, 121)(47, 111, 56, 120)(48, 112, 58, 122)(49, 113, 54, 118)(50, 114, 53, 117)(51, 115, 55, 119)(59, 123, 63, 127)(60, 124, 62, 126)(61, 125, 64, 128)(129, 193, 131, 195, 139, 203, 155, 219, 173, 237, 161, 225, 144, 208, 133, 197)(130, 194, 135, 199, 147, 211, 164, 228, 180, 244, 170, 234, 152, 216, 137, 201)(132, 196, 140, 204, 156, 220, 174, 238, 187, 251, 177, 241, 160, 224, 143, 207)(134, 198, 141, 205, 157, 221, 175, 239, 188, 252, 178, 242, 162, 226, 145, 209)(136, 200, 148, 212, 165, 229, 181, 245, 190, 254, 184, 248, 169, 233, 151, 215)(138, 202, 149, 213, 166, 230, 182, 246, 191, 255, 185, 249, 171, 235, 153, 217)(142, 206, 158, 222, 176, 240, 189, 253, 179, 243, 163, 227, 146, 210, 159, 223)(150, 214, 167, 231, 183, 247, 192, 256, 186, 250, 172, 236, 154, 218, 168, 232)
	L = (1, 132)(2, 136)(3, 140)(4, 142)(5, 143)(6, 129)(7, 148)(8, 150)(9, 151)(10, 130)(11, 156)(12, 158)(13, 131)(14, 157)(15, 159)(16, 160)(17, 133)(18, 134)(19, 165)(20, 167)(21, 135)(22, 166)(23, 168)(24, 169)(25, 137)(26, 138)(27, 174)(28, 176)(29, 139)(30, 175)(31, 141)(32, 146)(33, 177)(34, 144)(35, 145)(36, 181)(37, 183)(38, 147)(39, 182)(40, 149)(41, 154)(42, 184)(43, 152)(44, 153)(45, 187)(46, 189)(47, 155)(48, 188)(49, 163)(50, 161)(51, 162)(52, 190)(53, 192)(54, 164)(55, 191)(56, 172)(57, 170)(58, 171)(59, 179)(60, 173)(61, 178)(62, 186)(63, 180)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1484
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1482 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 2140>$ (small group id <128, 2140>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^-2 * Y3^-4, Y2^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 24, 88)(12, 76, 25, 89)(13, 77, 23, 87)(14, 78, 26, 90)(15, 79, 21, 85)(16, 80, 19, 83)(17, 81, 20, 84)(18, 82, 22, 86)(27, 91, 44, 108)(28, 92, 41, 105)(29, 93, 43, 107)(30, 94, 39, 103)(31, 95, 42, 106)(32, 96, 37, 101)(33, 97, 40, 104)(34, 98, 38, 102)(35, 99, 36, 100)(45, 109, 52, 116)(46, 110, 56, 120)(47, 111, 58, 122)(48, 112, 57, 121)(49, 113, 53, 117)(50, 114, 55, 119)(51, 115, 54, 118)(59, 123, 63, 127)(60, 124, 62, 126)(61, 125, 64, 128)(129, 193, 131, 195, 139, 203, 155, 219, 173, 237, 163, 227, 144, 208, 133, 197)(130, 194, 135, 199, 147, 211, 164, 228, 180, 244, 172, 236, 152, 216, 137, 201)(132, 196, 140, 204, 156, 220, 174, 238, 187, 251, 179, 243, 162, 226, 143, 207)(134, 198, 141, 205, 157, 221, 175, 239, 188, 252, 177, 241, 160, 224, 145, 209)(136, 200, 148, 212, 165, 229, 181, 245, 190, 254, 186, 250, 171, 235, 151, 215)(138, 202, 149, 213, 166, 230, 182, 246, 191, 255, 184, 248, 169, 233, 153, 217)(142, 206, 158, 222, 146, 210, 159, 223, 176, 240, 189, 253, 178, 242, 161, 225)(150, 214, 167, 231, 154, 218, 168, 232, 183, 247, 192, 256, 185, 249, 170, 234)
	L = (1, 132)(2, 136)(3, 140)(4, 142)(5, 143)(6, 129)(7, 148)(8, 150)(9, 151)(10, 130)(11, 156)(12, 158)(13, 131)(14, 160)(15, 161)(16, 162)(17, 133)(18, 134)(19, 165)(20, 167)(21, 135)(22, 169)(23, 170)(24, 171)(25, 137)(26, 138)(27, 174)(28, 146)(29, 139)(30, 145)(31, 141)(32, 144)(33, 177)(34, 178)(35, 179)(36, 181)(37, 154)(38, 147)(39, 153)(40, 149)(41, 152)(42, 184)(43, 185)(44, 186)(45, 187)(46, 159)(47, 155)(48, 157)(49, 163)(50, 188)(51, 189)(52, 190)(53, 168)(54, 164)(55, 166)(56, 172)(57, 191)(58, 192)(59, 176)(60, 173)(61, 175)(62, 183)(63, 180)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1483
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1483 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 2140>$ (small group id <128, 2140>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-3, Y3^3 * Y1^-1 * Y3 * Y1^-3, Y3^-2 * Y1^2 * Y3^2 * Y1^-2, Y1^7 * Y3^-2 * Y1^3 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 19, 83, 39, 103, 37, 101, 18, 82, 26, 90, 46, 110, 33, 97, 14, 78, 25, 89, 45, 109, 35, 99, 16, 80, 5, 69)(3, 67, 11, 75, 27, 91, 51, 115, 62, 126, 48, 112, 31, 95, 55, 119, 61, 125, 47, 111, 30, 94, 54, 118, 58, 122, 40, 104, 20, 84, 8, 72)(4, 68, 9, 73, 21, 85, 41, 105, 36, 100, 17, 81, 6, 70, 10, 74, 22, 86, 42, 106, 32, 96, 49, 113, 38, 102, 50, 114, 34, 98, 15, 79)(12, 76, 28, 92, 52, 116, 60, 124, 44, 108, 24, 88, 13, 77, 29, 93, 53, 117, 63, 127, 56, 120, 64, 128, 57, 121, 59, 123, 43, 107, 23, 87)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 148, 212)(137, 201, 152, 216)(138, 202, 151, 215)(142, 206, 159, 223)(143, 207, 157, 221)(144, 208, 155, 219)(145, 209, 156, 220)(146, 210, 158, 222)(147, 211, 168, 232)(149, 213, 172, 236)(150, 214, 171, 235)(153, 217, 176, 240)(154, 218, 175, 239)(160, 224, 185, 249)(161, 225, 183, 247)(162, 226, 181, 245)(163, 227, 179, 243)(164, 228, 180, 244)(165, 229, 182, 246)(166, 230, 184, 248)(167, 231, 186, 250)(169, 233, 188, 252)(170, 234, 187, 251)(173, 237, 190, 254)(174, 238, 189, 253)(177, 241, 192, 256)(178, 242, 191, 255)
	L = (1, 132)(2, 137)(3, 140)(4, 142)(5, 143)(6, 129)(7, 149)(8, 151)(9, 153)(10, 130)(11, 156)(12, 158)(13, 131)(14, 160)(15, 161)(16, 162)(17, 133)(18, 134)(19, 169)(20, 171)(21, 173)(22, 135)(23, 175)(24, 136)(25, 177)(26, 138)(27, 180)(28, 182)(29, 139)(30, 184)(31, 141)(32, 167)(33, 170)(34, 174)(35, 178)(36, 144)(37, 145)(38, 146)(39, 164)(40, 187)(41, 163)(42, 147)(43, 189)(44, 148)(45, 166)(46, 150)(47, 191)(48, 152)(49, 165)(50, 154)(51, 188)(52, 186)(53, 155)(54, 192)(55, 157)(56, 190)(57, 159)(58, 185)(59, 183)(60, 168)(61, 181)(62, 172)(63, 179)(64, 176)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1482
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1484 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = C2 x D32 (small group id <64, 186>)
Aut   = $<128, 2140>$ (small group id <128, 2140>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, Y1^-1 * Y3^2 * Y1^-1, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^14, (Y1^-1 * Y3^-1)^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 16, 80, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 55, 119, 47, 111, 39, 103, 31, 95, 23, 87, 14, 78, 5, 69)(3, 67, 11, 75, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 17, 81, 8, 72)(4, 68, 9, 73, 18, 82, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 56, 120, 48, 112, 40, 104, 32, 96, 24, 88, 15, 79, 6, 70, 10, 74)(12, 76, 22, 86, 30, 94, 38, 102, 46, 110, 54, 118, 62, 126, 64, 128, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 13, 77, 19, 83)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 145, 209)(137, 201, 148, 212)(138, 202, 147, 211)(142, 206, 149, 213)(143, 207, 150, 214)(144, 208, 154, 218)(146, 210, 156, 220)(151, 215, 157, 221)(152, 216, 158, 222)(153, 217, 162, 226)(155, 219, 164, 228)(159, 223, 165, 229)(160, 224, 166, 230)(161, 225, 170, 234)(163, 227, 172, 236)(167, 231, 173, 237)(168, 232, 174, 238)(169, 233, 178, 242)(171, 235, 180, 244)(175, 239, 181, 245)(176, 240, 182, 246)(177, 241, 186, 250)(179, 243, 188, 252)(183, 247, 189, 253)(184, 248, 190, 254)(185, 249, 191, 255)(187, 251, 192, 256)
	L = (1, 132)(2, 137)(3, 140)(4, 135)(5, 138)(6, 129)(7, 146)(8, 147)(9, 144)(10, 130)(11, 150)(12, 149)(13, 131)(14, 134)(15, 133)(16, 155)(17, 141)(18, 153)(19, 139)(20, 136)(21, 158)(22, 157)(23, 143)(24, 142)(25, 163)(26, 148)(27, 161)(28, 145)(29, 166)(30, 165)(31, 152)(32, 151)(33, 171)(34, 156)(35, 169)(36, 154)(37, 174)(38, 173)(39, 160)(40, 159)(41, 179)(42, 164)(43, 177)(44, 162)(45, 182)(46, 181)(47, 168)(48, 167)(49, 187)(50, 172)(51, 185)(52, 170)(53, 190)(54, 189)(55, 176)(56, 175)(57, 184)(58, 180)(59, 183)(60, 178)(61, 192)(62, 191)(63, 188)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1481
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1485 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: halfedge^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1 * Y2)^2, Y3 * Y2 * Y3 * Y2 * Y1^-2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y1^3 * Y2 * Y1)^2, Y1^-3 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1 * Y2, Y2 * Y1^5 * Y2 * Y1^-3, (Y1^-1 * Y2 * Y3)^8 ]
Map:: non-degenerate
	R = (1, 66, 2, 70, 6, 82, 18, 102, 38, 121, 57, 115, 51, 92, 28, 108, 44, 96, 32, 110, 46, 127, 63, 120, 56, 101, 37, 81, 17, 69, 5, 65)(3, 73, 9, 91, 27, 113, 49, 124, 60, 103, 39, 87, 23, 71, 7, 85, 21, 79, 15, 99, 35, 119, 55, 122, 58, 105, 41, 83, 19, 75, 11, 67)(4, 76, 12, 94, 30, 116, 52, 126, 62, 104, 40, 90, 26, 72, 8, 88, 24, 80, 16, 100, 36, 118, 54, 123, 59, 107, 43, 84, 20, 78, 14, 68)(10, 86, 22, 77, 13, 89, 25, 106, 42, 125, 61, 117, 53, 93, 29, 109, 45, 97, 33, 111, 47, 98, 34, 112, 48, 128, 64, 114, 50, 95, 31, 74)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 33)(14, 34)(16, 22)(17, 27)(18, 39)(20, 42)(21, 44)(23, 46)(24, 47)(26, 48)(29, 52)(31, 54)(35, 51)(36, 45)(37, 55)(38, 58)(40, 61)(41, 63)(43, 64)(49, 57)(50, 62)(53, 59)(56, 60)(65, 68)(66, 72)(67, 74)(69, 80)(70, 84)(71, 86)(73, 93)(75, 97)(76, 92)(77, 83)(78, 96)(79, 95)(81, 94)(82, 104)(85, 109)(87, 111)(88, 108)(89, 103)(90, 110)(91, 114)(98, 105)(99, 117)(100, 115)(101, 118)(102, 123)(106, 122)(107, 127)(112, 124)(113, 125)(116, 121)(119, 128)(120, 126)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1486
Transitivity :: VT+ AT
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.1486 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: halfedge^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, (Y2 * Y1)^4, Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2, (Y2 * Y3 * Y1^-1)^16 ]
Map:: non-degenerate
	R = (1, 66, 2, 70, 6, 82, 18, 100, 36, 94, 30, 81, 17, 69, 5, 65)(3, 73, 9, 87, 23, 71, 7, 85, 21, 79, 15, 83, 19, 75, 11, 67)(4, 76, 12, 90, 26, 72, 8, 88, 24, 80, 16, 84, 20, 78, 14, 68)(10, 86, 22, 101, 37, 91, 27, 103, 39, 95, 31, 105, 41, 93, 29, 74)(13, 89, 25, 102, 38, 96, 32, 106, 42, 99, 35, 108, 44, 98, 34, 77)(28, 109, 45, 121, 57, 104, 40, 119, 55, 112, 48, 117, 53, 111, 47, 92)(33, 113, 49, 124, 60, 107, 43, 122, 58, 116, 52, 118, 54, 115, 51, 97)(46, 120, 56, 114, 50, 123, 59, 127, 63, 126, 62, 128, 64, 125, 61, 110)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 18)(10, 28)(11, 30)(12, 32)(14, 35)(16, 34)(17, 23)(20, 38)(21, 36)(22, 40)(24, 42)(26, 44)(27, 45)(29, 48)(31, 47)(33, 50)(37, 53)(39, 55)(41, 57)(43, 59)(46, 60)(49, 62)(51, 61)(52, 56)(54, 63)(58, 64)(65, 68)(66, 72)(67, 74)(69, 80)(70, 84)(71, 86)(73, 91)(75, 95)(76, 82)(77, 97)(78, 94)(79, 93)(81, 90)(83, 101)(85, 103)(87, 105)(88, 100)(89, 107)(92, 110)(96, 113)(98, 116)(99, 115)(102, 118)(104, 120)(106, 122)(108, 124)(109, 123)(111, 126)(112, 125)(114, 117)(119, 127)(121, 128)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1485
Transitivity :: VT+ AT
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.1487 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: edge^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3^-2, (Y3^2 * Y1)^2, (Y3^-2 * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2 ]
Map::
	R = (1, 65, 4, 68, 14, 78, 21, 85, 43, 107, 24, 88, 17, 81, 5, 69)(2, 66, 7, 71, 23, 87, 12, 76, 34, 98, 15, 79, 26, 90, 8, 72)(3, 67, 10, 74, 31, 95, 13, 77, 35, 99, 16, 80, 33, 97, 11, 75)(6, 70, 19, 83, 40, 104, 22, 86, 44, 108, 25, 89, 42, 106, 20, 84)(9, 73, 28, 92, 49, 113, 30, 94, 52, 116, 32, 96, 51, 115, 29, 93)(18, 82, 37, 101, 57, 121, 39, 103, 60, 124, 41, 105, 59, 123, 38, 102)(27, 91, 46, 110, 61, 125, 48, 112, 62, 126, 50, 114, 53, 117, 47, 111)(36, 100, 54, 118, 63, 127, 56, 120, 64, 128, 58, 122, 45, 109, 55, 119)(129, 130)(131, 137)(132, 140)(133, 143)(134, 146)(135, 149)(136, 152)(138, 158)(139, 160)(141, 156)(142, 154)(144, 157)(145, 151)(147, 167)(148, 169)(150, 165)(153, 166)(155, 173)(159, 179)(161, 177)(162, 171)(163, 180)(164, 181)(168, 187)(170, 185)(172, 188)(174, 182)(175, 184)(176, 183)(178, 186)(189, 192)(190, 191)(193, 195)(194, 198)(196, 205)(197, 208)(199, 214)(200, 217)(201, 219)(202, 213)(203, 216)(204, 211)(206, 225)(207, 212)(209, 223)(210, 228)(215, 234)(218, 232)(220, 240)(221, 242)(222, 238)(224, 239)(226, 236)(227, 235)(229, 248)(230, 250)(231, 246)(233, 247)(237, 249)(241, 245)(243, 253)(244, 254)(251, 255)(252, 256)
	L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 64, 64 ), ( 64^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1490
Graph:: simple bipartite
	v = 72 e = 128 f = 4
	degree seq :: [ 2^64, 16^8 ]

E27.1488 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 8, 16})
Quotient :: edge^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, Y3^2 * Y2 * Y1 * Y2 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y1, (Y3^-2 * Y1)^2, (Y3 * Y2 * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y3^7 * Y1 * Y3^-1, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1 ]
Map::
	R = (1, 65, 4, 68, 14, 78, 34, 98, 54, 118, 61, 125, 42, 106, 21, 85, 41, 105, 24, 88, 46, 110, 57, 121, 56, 120, 37, 101, 17, 81, 5, 69)(2, 66, 7, 71, 23, 87, 45, 109, 62, 126, 53, 117, 31, 95, 12, 76, 30, 94, 15, 79, 35, 99, 49, 113, 64, 128, 48, 112, 26, 90, 8, 72)(3, 67, 10, 74, 29, 93, 52, 116, 59, 123, 39, 103, 33, 97, 13, 77, 32, 96, 16, 80, 36, 100, 55, 119, 58, 122, 38, 102, 18, 82, 11, 75)(6, 70, 19, 83, 40, 104, 60, 124, 51, 115, 28, 92, 44, 108, 22, 86, 43, 107, 25, 89, 47, 111, 63, 127, 50, 114, 27, 91, 9, 73, 20, 84)(129, 130)(131, 137)(132, 140)(133, 143)(134, 146)(135, 149)(136, 152)(138, 156)(139, 150)(141, 148)(142, 154)(144, 155)(145, 151)(147, 167)(153, 166)(157, 178)(158, 169)(159, 174)(160, 172)(161, 171)(162, 181)(163, 170)(164, 179)(165, 177)(168, 186)(173, 189)(175, 187)(176, 185)(180, 188)(182, 192)(183, 191)(184, 190)(193, 195)(194, 198)(196, 205)(197, 208)(199, 214)(200, 217)(201, 215)(202, 213)(203, 216)(204, 211)(206, 210)(207, 212)(209, 221)(218, 232)(219, 241)(220, 237)(222, 235)(223, 239)(224, 233)(225, 238)(226, 231)(227, 236)(228, 234)(229, 247)(230, 249)(240, 255)(242, 254)(243, 256)(244, 253)(245, 252)(246, 250)(248, 251)
	L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 32, 32 ), ( 32^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1489
Graph:: simple bipartite
	v = 68 e = 128 f = 8
	degree seq :: [ 2^64, 32^4 ]

E27.1489 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 8, 16})
Quotient :: loop^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3^-2, (Y3^2 * Y1)^2, (Y3^-2 * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2 ]
Map::
	R = (1, 65, 129, 193, 4, 68, 132, 196, 14, 78, 142, 206, 21, 85, 149, 213, 43, 107, 171, 235, 24, 88, 152, 216, 17, 81, 145, 209, 5, 69, 133, 197)(2, 66, 130, 194, 7, 71, 135, 199, 23, 87, 151, 215, 12, 76, 140, 204, 34, 98, 162, 226, 15, 79, 143, 207, 26, 90, 154, 218, 8, 72, 136, 200)(3, 67, 131, 195, 10, 74, 138, 202, 31, 95, 159, 223, 13, 77, 141, 205, 35, 99, 163, 227, 16, 80, 144, 208, 33, 97, 161, 225, 11, 75, 139, 203)(6, 70, 134, 198, 19, 83, 147, 211, 40, 104, 168, 232, 22, 86, 150, 214, 44, 108, 172, 236, 25, 89, 153, 217, 42, 106, 170, 234, 20, 84, 148, 212)(9, 73, 137, 201, 28, 92, 156, 220, 49, 113, 177, 241, 30, 94, 158, 222, 52, 116, 180, 244, 32, 96, 160, 224, 51, 115, 179, 243, 29, 93, 157, 221)(18, 82, 146, 210, 37, 101, 165, 229, 57, 121, 185, 249, 39, 103, 167, 231, 60, 124, 188, 252, 41, 105, 169, 233, 59, 123, 187, 251, 38, 102, 166, 230)(27, 91, 155, 219, 46, 110, 174, 238, 61, 125, 189, 253, 48, 112, 176, 240, 62, 126, 190, 254, 50, 114, 178, 242, 53, 117, 181, 245, 47, 111, 175, 239)(36, 100, 164, 228, 54, 118, 182, 246, 63, 127, 191, 255, 56, 120, 184, 248, 64, 128, 192, 256, 58, 122, 186, 250, 45, 109, 173, 237, 55, 119, 183, 247)
	L = (1, 66)(2, 65)(3, 73)(4, 76)(5, 79)(6, 82)(7, 85)(8, 88)(9, 67)(10, 94)(11, 96)(12, 68)(13, 92)(14, 90)(15, 69)(16, 93)(17, 87)(18, 70)(19, 103)(20, 105)(21, 71)(22, 101)(23, 81)(24, 72)(25, 102)(26, 78)(27, 109)(28, 77)(29, 80)(30, 74)(31, 115)(32, 75)(33, 113)(34, 107)(35, 116)(36, 117)(37, 86)(38, 89)(39, 83)(40, 123)(41, 84)(42, 121)(43, 98)(44, 124)(45, 91)(46, 118)(47, 120)(48, 119)(49, 97)(50, 122)(51, 95)(52, 99)(53, 100)(54, 110)(55, 112)(56, 111)(57, 106)(58, 114)(59, 104)(60, 108)(61, 128)(62, 127)(63, 126)(64, 125)(129, 195)(130, 198)(131, 193)(132, 205)(133, 208)(134, 194)(135, 214)(136, 217)(137, 219)(138, 213)(139, 216)(140, 211)(141, 196)(142, 225)(143, 212)(144, 197)(145, 223)(146, 228)(147, 204)(148, 207)(149, 202)(150, 199)(151, 234)(152, 203)(153, 200)(154, 232)(155, 201)(156, 240)(157, 242)(158, 238)(159, 209)(160, 239)(161, 206)(162, 236)(163, 235)(164, 210)(165, 248)(166, 250)(167, 246)(168, 218)(169, 247)(170, 215)(171, 227)(172, 226)(173, 249)(174, 222)(175, 224)(176, 220)(177, 245)(178, 221)(179, 253)(180, 254)(181, 241)(182, 231)(183, 233)(184, 229)(185, 237)(186, 230)(187, 255)(188, 256)(189, 243)(190, 244)(191, 251)(192, 252)
	local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1488
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 128 f = 68
	degree seq :: [ 32^8 ]

E27.1490 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 8, 16})
Quotient :: loop^2
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^2 * Y2 * Y1, Y3^2 * Y2 * Y1 * Y2 * Y1, (Y3^-1 * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y1, (Y3^-2 * Y1)^2, (Y3 * Y2 * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, Y1 * Y3^7 * Y1 * Y3^-1, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1 ]
Map::
	R = (1, 65, 129, 193, 4, 68, 132, 196, 14, 78, 142, 206, 34, 98, 162, 226, 54, 118, 182, 246, 61, 125, 189, 253, 42, 106, 170, 234, 21, 85, 149, 213, 41, 105, 169, 233, 24, 88, 152, 216, 46, 110, 174, 238, 57, 121, 185, 249, 56, 120, 184, 248, 37, 101, 165, 229, 17, 81, 145, 209, 5, 69, 133, 197)(2, 66, 130, 194, 7, 71, 135, 199, 23, 87, 151, 215, 45, 109, 173, 237, 62, 126, 190, 254, 53, 117, 181, 245, 31, 95, 159, 223, 12, 76, 140, 204, 30, 94, 158, 222, 15, 79, 143, 207, 35, 99, 163, 227, 49, 113, 177, 241, 64, 128, 192, 256, 48, 112, 176, 240, 26, 90, 154, 218, 8, 72, 136, 200)(3, 67, 131, 195, 10, 74, 138, 202, 29, 93, 157, 221, 52, 116, 180, 244, 59, 123, 187, 251, 39, 103, 167, 231, 33, 97, 161, 225, 13, 77, 141, 205, 32, 96, 160, 224, 16, 80, 144, 208, 36, 100, 164, 228, 55, 119, 183, 247, 58, 122, 186, 250, 38, 102, 166, 230, 18, 82, 146, 210, 11, 75, 139, 203)(6, 70, 134, 198, 19, 83, 147, 211, 40, 104, 168, 232, 60, 124, 188, 252, 51, 115, 179, 243, 28, 92, 156, 220, 44, 108, 172, 236, 22, 86, 150, 214, 43, 107, 171, 235, 25, 89, 153, 217, 47, 111, 175, 239, 63, 127, 191, 255, 50, 114, 178, 242, 27, 91, 155, 219, 9, 73, 137, 201, 20, 84, 148, 212)
	L = (1, 66)(2, 65)(3, 73)(4, 76)(5, 79)(6, 82)(7, 85)(8, 88)(9, 67)(10, 92)(11, 86)(12, 68)(13, 84)(14, 90)(15, 69)(16, 91)(17, 87)(18, 70)(19, 103)(20, 77)(21, 71)(22, 75)(23, 81)(24, 72)(25, 102)(26, 78)(27, 80)(28, 74)(29, 114)(30, 105)(31, 110)(32, 108)(33, 107)(34, 117)(35, 106)(36, 115)(37, 113)(38, 89)(39, 83)(40, 122)(41, 94)(42, 99)(43, 97)(44, 96)(45, 125)(46, 95)(47, 123)(48, 121)(49, 101)(50, 93)(51, 100)(52, 124)(53, 98)(54, 128)(55, 127)(56, 126)(57, 112)(58, 104)(59, 111)(60, 116)(61, 109)(62, 120)(63, 119)(64, 118)(129, 195)(130, 198)(131, 193)(132, 205)(133, 208)(134, 194)(135, 214)(136, 217)(137, 215)(138, 213)(139, 216)(140, 211)(141, 196)(142, 210)(143, 212)(144, 197)(145, 221)(146, 206)(147, 204)(148, 207)(149, 202)(150, 199)(151, 201)(152, 203)(153, 200)(154, 232)(155, 241)(156, 237)(157, 209)(158, 235)(159, 239)(160, 233)(161, 238)(162, 231)(163, 236)(164, 234)(165, 247)(166, 249)(167, 226)(168, 218)(169, 224)(170, 228)(171, 222)(172, 227)(173, 220)(174, 225)(175, 223)(176, 255)(177, 219)(178, 254)(179, 256)(180, 253)(181, 252)(182, 250)(183, 229)(184, 251)(185, 230)(186, 246)(187, 248)(188, 245)(189, 244)(190, 242)(191, 240)(192, 243)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1487
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 128 f = 72
	degree seq :: [ 64^4 ]

E27.1491 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-2 * Y3^4, Y2^-1 * Y1 * Y2^3 * Y1, Y2^8, (Y1 * Y2)^4, Y2^-1 * Y3^-2 * Y1 * Y3^2 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 17, 81)(6, 70, 8, 72)(7, 71, 21, 85)(9, 73, 27, 91)(12, 76, 28, 92)(13, 77, 33, 97)(14, 78, 32, 96)(15, 79, 30, 94)(16, 80, 38, 102)(18, 82, 22, 86)(19, 83, 40, 104)(20, 84, 25, 89)(23, 87, 45, 109)(24, 88, 44, 108)(26, 90, 50, 114)(29, 93, 52, 116)(31, 95, 43, 107)(34, 98, 53, 117)(35, 99, 51, 115)(36, 100, 48, 112)(37, 101, 57, 121)(39, 103, 47, 111)(41, 105, 46, 110)(42, 106, 54, 118)(49, 113, 62, 126)(55, 119, 61, 125)(56, 120, 60, 124)(58, 122, 64, 128)(59, 123, 63, 127)(129, 193, 131, 195, 140, 204, 149, 213, 171, 235, 155, 219, 146, 210, 133, 197)(130, 194, 135, 199, 150, 214, 139, 203, 159, 223, 145, 209, 156, 220, 137, 201)(132, 196, 141, 205, 162, 226, 172, 236, 188, 252, 180, 244, 167, 231, 144, 208)(134, 198, 142, 206, 163, 227, 173, 237, 189, 253, 178, 242, 169, 233, 147, 211)(136, 200, 151, 215, 174, 238, 160, 224, 183, 247, 168, 232, 179, 243, 154, 218)(138, 202, 152, 216, 175, 239, 161, 225, 184, 248, 166, 230, 181, 245, 157, 221)(143, 207, 164, 228, 186, 250, 190, 254, 187, 251, 170, 234, 148, 212, 165, 229)(153, 217, 176, 240, 191, 255, 185, 249, 192, 256, 182, 246, 158, 222, 177, 241)
	L = (1, 132)(2, 136)(3, 141)(4, 143)(5, 144)(6, 129)(7, 151)(8, 153)(9, 154)(10, 130)(11, 160)(12, 162)(13, 164)(14, 131)(15, 163)(16, 165)(17, 168)(18, 167)(19, 133)(20, 134)(21, 172)(22, 174)(23, 176)(24, 135)(25, 175)(26, 177)(27, 180)(28, 179)(29, 137)(30, 138)(31, 183)(32, 185)(33, 139)(34, 186)(35, 140)(36, 173)(37, 142)(38, 145)(39, 148)(40, 182)(41, 146)(42, 147)(43, 188)(44, 190)(45, 149)(46, 191)(47, 150)(48, 161)(49, 152)(50, 155)(51, 158)(52, 170)(53, 156)(54, 157)(55, 192)(56, 159)(57, 166)(58, 189)(59, 169)(60, 187)(61, 171)(62, 178)(63, 184)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1493
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1492 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y2 * Y1 * Y2^-3 * Y1, (Y2^2 * Y1)^2, Y3^2 * Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-3 * Y3 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 17, 81)(6, 70, 8, 72)(7, 71, 21, 85)(9, 73, 27, 91)(12, 76, 28, 92)(13, 77, 33, 97)(14, 78, 32, 96)(15, 79, 30, 94)(16, 80, 40, 104)(18, 82, 22, 86)(19, 83, 42, 106)(20, 84, 25, 89)(23, 87, 45, 109)(24, 88, 44, 108)(26, 90, 52, 116)(29, 93, 54, 118)(31, 95, 43, 107)(34, 98, 50, 114)(35, 99, 53, 117)(36, 100, 57, 121)(37, 101, 49, 113)(38, 102, 46, 110)(39, 103, 51, 115)(41, 105, 47, 111)(48, 112, 62, 126)(55, 119, 61, 125)(56, 120, 60, 124)(58, 122, 64, 128)(59, 123, 63, 127)(129, 193, 131, 195, 140, 204, 149, 213, 171, 235, 155, 219, 146, 210, 133, 197)(130, 194, 135, 199, 150, 214, 139, 203, 159, 223, 145, 209, 156, 220, 137, 201)(132, 196, 141, 205, 162, 226, 172, 236, 188, 252, 182, 246, 169, 233, 144, 208)(134, 198, 142, 206, 163, 227, 173, 237, 189, 253, 180, 244, 166, 230, 147, 211)(136, 200, 151, 215, 174, 238, 160, 224, 183, 247, 170, 234, 181, 245, 154, 218)(138, 202, 152, 216, 175, 239, 161, 225, 184, 248, 168, 232, 178, 242, 157, 221)(143, 207, 164, 228, 148, 212, 165, 229, 186, 250, 190, 254, 187, 251, 167, 231)(153, 217, 176, 240, 158, 222, 177, 241, 191, 255, 185, 249, 192, 256, 179, 243)
	L = (1, 132)(2, 136)(3, 141)(4, 143)(5, 144)(6, 129)(7, 151)(8, 153)(9, 154)(10, 130)(11, 160)(12, 162)(13, 164)(14, 131)(15, 166)(16, 167)(17, 170)(18, 169)(19, 133)(20, 134)(21, 172)(22, 174)(23, 176)(24, 135)(25, 178)(26, 179)(27, 182)(28, 181)(29, 137)(30, 138)(31, 183)(32, 177)(33, 139)(34, 148)(35, 140)(36, 147)(37, 142)(38, 146)(39, 180)(40, 145)(41, 187)(42, 185)(43, 188)(44, 165)(45, 149)(46, 158)(47, 150)(48, 157)(49, 152)(50, 156)(51, 168)(52, 155)(53, 192)(54, 190)(55, 191)(56, 159)(57, 161)(58, 163)(59, 189)(60, 186)(61, 171)(62, 173)(63, 175)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1494
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1493 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1 * Y3)^2, (Y3, Y1^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y1^-1)^4, Y2 * Y3 * Y1^2 * Y3 * Y1^3 * Y2 * Y1^-1, Y1^2 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^3, Y2 * Y3 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y2 * Y3^-1 * Y1, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 18, 82, 35, 99, 55, 119, 48, 112, 26, 90, 40, 104, 29, 93, 43, 107, 60, 124, 53, 117, 33, 97, 16, 80, 5, 69)(3, 67, 11, 75, 25, 89, 45, 109, 58, 122, 36, 100, 23, 87, 8, 72, 21, 85, 15, 79, 31, 95, 51, 115, 56, 120, 38, 102, 19, 83, 13, 77)(4, 68, 9, 73, 20, 84, 37, 101, 57, 121, 49, 113, 63, 127, 47, 111, 62, 126, 50, 114, 64, 128, 54, 118, 34, 98, 17, 81, 6, 70, 10, 74)(12, 76, 27, 91, 46, 110, 59, 123, 44, 108, 24, 88, 42, 106, 22, 86, 41, 105, 32, 96, 52, 116, 61, 125, 39, 103, 30, 94, 14, 78, 28, 92)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 143, 207)(134, 198, 140, 204)(135, 199, 147, 211)(137, 201, 152, 216)(138, 202, 150, 214)(139, 203, 154, 218)(141, 205, 157, 221)(144, 208, 153, 217)(145, 209, 160, 224)(146, 210, 164, 228)(148, 212, 167, 231)(149, 213, 168, 232)(151, 215, 171, 235)(155, 219, 177, 241)(156, 220, 175, 239)(158, 222, 178, 242)(159, 223, 176, 240)(161, 225, 179, 243)(162, 226, 174, 238)(163, 227, 184, 248)(165, 229, 187, 251)(166, 230, 188, 252)(169, 233, 191, 255)(170, 234, 190, 254)(172, 236, 192, 256)(173, 237, 183, 247)(180, 244, 185, 249)(181, 245, 186, 250)(182, 246, 189, 253)
	L = (1, 132)(2, 137)(3, 140)(4, 135)(5, 138)(6, 129)(7, 148)(8, 150)(9, 146)(10, 130)(11, 155)(12, 153)(13, 156)(14, 131)(15, 160)(16, 134)(17, 133)(18, 165)(19, 142)(20, 163)(21, 169)(22, 143)(23, 170)(24, 136)(25, 174)(26, 175)(27, 173)(28, 139)(29, 178)(30, 141)(31, 180)(32, 179)(33, 145)(34, 144)(35, 185)(36, 152)(37, 183)(38, 158)(39, 147)(40, 190)(41, 159)(42, 149)(43, 192)(44, 151)(45, 187)(46, 186)(47, 157)(48, 191)(49, 154)(50, 188)(51, 189)(52, 184)(53, 162)(54, 161)(55, 177)(56, 167)(57, 176)(58, 172)(59, 164)(60, 182)(61, 166)(62, 171)(63, 168)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1491
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1494 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C16 x C2) : C2 (small group id <64, 189>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * R)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3^-2 * Y2 * Y1^-1 * Y2 * Y1, R * Y2 * R * Y1 * Y2 * Y1^-1, (Y2 * R * Y3)^2, (Y2 * Y1^-2)^2, R * Y2 * Y3^-2 * R * Y2, Y1^-1 * Y3 * Y1^-2 * Y3^3 * Y1^-1, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2, Y1^7 * Y3^-2 * Y1^3 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 21, 85, 44, 108, 42, 106, 20, 84, 30, 94, 52, 116, 35, 99, 15, 79, 29, 93, 51, 115, 40, 104, 18, 82, 5, 69)(3, 67, 11, 75, 31, 95, 57, 121, 62, 126, 45, 109, 27, 91, 8, 72, 25, 89, 17, 81, 33, 97, 59, 123, 61, 125, 49, 113, 22, 86, 13, 77)(4, 68, 9, 73, 23, 87, 46, 110, 41, 105, 19, 83, 6, 70, 10, 74, 24, 88, 47, 111, 37, 101, 55, 119, 43, 107, 56, 120, 38, 102, 16, 80)(12, 76, 32, 96, 58, 122, 64, 128, 50, 114, 36, 100, 14, 78, 26, 90, 53, 117, 39, 103, 60, 124, 63, 127, 54, 118, 28, 92, 48, 112, 34, 98)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 150, 214)(137, 201, 156, 220)(138, 202, 154, 218)(139, 203, 158, 222)(141, 205, 163, 227)(143, 207, 155, 219)(144, 208, 162, 226)(146, 210, 159, 223)(147, 211, 167, 231)(148, 212, 161, 225)(149, 213, 173, 237)(151, 215, 178, 242)(152, 216, 176, 240)(153, 217, 180, 244)(157, 221, 177, 241)(160, 224, 184, 248)(164, 228, 175, 239)(165, 229, 182, 246)(166, 230, 181, 245)(168, 232, 187, 251)(169, 233, 186, 250)(170, 234, 185, 249)(171, 235, 188, 252)(172, 236, 189, 253)(174, 238, 191, 255)(179, 243, 190, 254)(183, 247, 192, 256)
	L = (1, 132)(2, 137)(3, 140)(4, 143)(5, 144)(6, 129)(7, 151)(8, 154)(9, 157)(10, 130)(11, 160)(12, 161)(13, 162)(14, 131)(15, 165)(16, 163)(17, 167)(18, 166)(19, 133)(20, 134)(21, 174)(22, 176)(23, 179)(24, 135)(25, 181)(26, 139)(27, 142)(28, 136)(29, 183)(30, 138)(31, 186)(32, 187)(33, 188)(34, 145)(35, 175)(36, 141)(37, 172)(38, 180)(39, 185)(40, 184)(41, 146)(42, 147)(43, 148)(44, 169)(45, 164)(46, 168)(47, 149)(48, 153)(49, 156)(50, 150)(51, 171)(52, 152)(53, 159)(54, 155)(55, 170)(56, 158)(57, 192)(58, 189)(59, 191)(60, 190)(61, 182)(62, 178)(63, 173)(64, 177)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1492
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1495 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2^2 * Y3^-1 * Y2^-2 * Y3, (Y3^-2 * Y1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-2, Y2 * Y3 * Y2 * Y3^-1 * Y2^2, Y3^-2 * Y2^2 * Y3^-2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y2 * R * Y1 * Y2^-2 * R * Y2^-1 * Y1, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2, (Y3^2 * Y2^2)^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 30, 94)(12, 76, 31, 95)(13, 77, 29, 93)(14, 78, 33, 97)(15, 79, 34, 98)(16, 80, 32, 96)(17, 81, 25, 89)(18, 82, 23, 87)(19, 83, 24, 88)(20, 84, 28, 92)(21, 85, 26, 90)(22, 86, 27, 91)(35, 99, 57, 121)(36, 100, 53, 117)(37, 101, 50, 114)(38, 102, 49, 113)(39, 103, 56, 120)(40, 104, 54, 118)(41, 105, 48, 112)(42, 106, 52, 116)(43, 107, 55, 119)(44, 108, 51, 115)(45, 109, 47, 111)(46, 110, 58, 122)(59, 123, 62, 126)(60, 124, 64, 128)(61, 125, 63, 127)(129, 193, 131, 195, 139, 203, 163, 227, 187, 251, 173, 237, 146, 210, 133, 197)(130, 194, 135, 199, 151, 215, 175, 239, 190, 254, 185, 249, 158, 222, 137, 201)(132, 196, 142, 206, 164, 228, 145, 209, 168, 232, 140, 204, 166, 230, 144, 208)(134, 198, 148, 212, 165, 229, 147, 211, 170, 234, 141, 205, 169, 233, 149, 213)(136, 200, 154, 218, 176, 240, 157, 221, 180, 244, 152, 216, 178, 242, 156, 220)(138, 202, 160, 224, 177, 241, 159, 223, 182, 246, 153, 217, 181, 245, 161, 225)(143, 207, 167, 231, 188, 252, 174, 238, 189, 253, 172, 236, 150, 214, 171, 235)(155, 219, 179, 243, 191, 255, 186, 250, 192, 256, 184, 248, 162, 226, 183, 247)
	L = (1, 132)(2, 136)(3, 140)(4, 143)(5, 145)(6, 129)(7, 152)(8, 155)(9, 157)(10, 130)(11, 164)(12, 167)(13, 131)(14, 172)(15, 165)(16, 174)(17, 171)(18, 166)(19, 133)(20, 173)(21, 163)(22, 134)(23, 176)(24, 179)(25, 135)(26, 184)(27, 177)(28, 186)(29, 183)(30, 178)(31, 137)(32, 185)(33, 175)(34, 138)(35, 144)(36, 188)(37, 139)(38, 150)(39, 149)(40, 189)(41, 146)(42, 187)(43, 141)(44, 147)(45, 142)(46, 148)(47, 156)(48, 191)(49, 151)(50, 162)(51, 161)(52, 192)(53, 158)(54, 190)(55, 153)(56, 159)(57, 154)(58, 160)(59, 168)(60, 170)(61, 169)(62, 180)(63, 182)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1500
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1496 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2144>$ (small group id <128, 2144>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2^3, Y3^-2 * Y2^-1 * Y3^2 * Y2, Y2 * Y3 * Y2^3 * Y3^-1, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1, Y3^-2 * Y2^2 * Y3^-2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2^-1)^2, (Y2^-2 * Y1)^2, (Y2^-1 * Y3^-1 * Y2 * Y1)^2, (Y2^-1 * Y3^-1 * Y2 * Y3^-1)^8 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 18, 82)(6, 70, 8, 72)(7, 71, 25, 89)(9, 73, 32, 96)(12, 76, 34, 98)(13, 77, 37, 101)(14, 78, 31, 95)(15, 79, 35, 99)(16, 80, 38, 102)(17, 81, 28, 92)(19, 83, 36, 100)(20, 84, 26, 90)(21, 85, 29, 93)(22, 86, 33, 97)(23, 87, 27, 91)(24, 88, 30, 94)(39, 103, 50, 114)(40, 104, 56, 120)(41, 105, 53, 117)(42, 106, 52, 116)(43, 107, 54, 118)(44, 108, 57, 121)(45, 109, 51, 115)(46, 110, 55, 119)(47, 111, 60, 124)(48, 112, 59, 123)(49, 113, 58, 122)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195, 140, 204, 153, 217, 178, 242, 160, 224, 148, 212, 133, 197)(130, 194, 135, 199, 154, 218, 139, 203, 167, 231, 146, 210, 162, 226, 137, 201)(132, 196, 143, 207, 168, 232, 147, 211, 172, 236, 141, 205, 170, 234, 145, 209)(134, 198, 150, 214, 169, 233, 149, 213, 174, 238, 142, 206, 173, 237, 151, 215)(136, 200, 157, 221, 179, 243, 161, 225, 183, 247, 155, 219, 181, 245, 159, 223)(138, 202, 164, 228, 180, 244, 163, 227, 185, 249, 156, 220, 184, 248, 165, 229)(144, 208, 171, 235, 189, 253, 177, 241, 190, 254, 176, 240, 152, 216, 175, 239)(158, 222, 182, 246, 191, 255, 188, 252, 192, 256, 187, 251, 166, 230, 186, 250)
	L = (1, 132)(2, 136)(3, 141)(4, 144)(5, 147)(6, 129)(7, 155)(8, 158)(9, 161)(10, 130)(11, 159)(12, 168)(13, 171)(14, 131)(15, 176)(16, 169)(17, 177)(18, 157)(19, 175)(20, 170)(21, 133)(22, 160)(23, 153)(24, 134)(25, 145)(26, 179)(27, 182)(28, 135)(29, 187)(30, 180)(31, 188)(32, 143)(33, 186)(34, 181)(35, 137)(36, 146)(37, 139)(38, 138)(39, 183)(40, 189)(41, 140)(42, 152)(43, 151)(44, 190)(45, 148)(46, 178)(47, 142)(48, 149)(49, 150)(50, 172)(51, 191)(52, 154)(53, 166)(54, 165)(55, 192)(56, 162)(57, 167)(58, 156)(59, 163)(60, 164)(61, 174)(62, 173)(63, 185)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1502
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1497 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y3^-1 * Y2^-2 * Y3 * Y2^2, Y3^-1 * Y2 * Y3^-3 * Y2, Y3^-1 * Y2^3 * Y3 * Y2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2, Y3^2 * Y1 * Y2^-1 * Y3^2 * Y2 * Y1, Y2 * R * Y1 * Y2^-2 * R * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 30, 94)(12, 76, 31, 95)(13, 77, 29, 93)(14, 78, 33, 97)(15, 79, 34, 98)(16, 80, 32, 96)(17, 81, 25, 89)(18, 82, 23, 87)(19, 83, 24, 88)(20, 84, 28, 92)(21, 85, 26, 90)(22, 86, 27, 91)(35, 99, 57, 121)(36, 100, 53, 117)(37, 101, 50, 114)(38, 102, 49, 113)(39, 103, 51, 115)(40, 104, 54, 118)(41, 105, 48, 112)(42, 106, 52, 116)(43, 107, 58, 122)(44, 108, 56, 120)(45, 109, 47, 111)(46, 110, 55, 119)(59, 123, 62, 126)(60, 124, 64, 128)(61, 125, 63, 127)(129, 193, 131, 195, 139, 203, 163, 227, 187, 251, 173, 237, 146, 210, 133, 197)(130, 194, 135, 199, 151, 215, 175, 239, 190, 254, 185, 249, 158, 222, 137, 201)(132, 196, 142, 206, 164, 228, 145, 209, 168, 232, 140, 204, 166, 230, 144, 208)(134, 198, 148, 212, 165, 229, 147, 211, 170, 234, 141, 205, 169, 233, 149, 213)(136, 200, 154, 218, 176, 240, 157, 221, 180, 244, 152, 216, 178, 242, 156, 220)(138, 202, 160, 224, 177, 241, 159, 223, 182, 246, 153, 217, 181, 245, 161, 225)(143, 207, 167, 231, 150, 214, 171, 235, 188, 252, 172, 236, 189, 253, 174, 238)(155, 219, 179, 243, 162, 226, 183, 247, 191, 255, 184, 248, 192, 256, 186, 250)
	L = (1, 132)(2, 136)(3, 140)(4, 143)(5, 145)(6, 129)(7, 152)(8, 155)(9, 157)(10, 130)(11, 164)(12, 167)(13, 131)(14, 172)(15, 169)(16, 171)(17, 174)(18, 166)(19, 133)(20, 173)(21, 163)(22, 134)(23, 176)(24, 179)(25, 135)(26, 184)(27, 181)(28, 183)(29, 186)(30, 178)(31, 137)(32, 185)(33, 175)(34, 138)(35, 144)(36, 150)(37, 139)(38, 189)(39, 147)(40, 188)(41, 146)(42, 187)(43, 141)(44, 149)(45, 142)(46, 148)(47, 156)(48, 162)(49, 151)(50, 192)(51, 159)(52, 191)(53, 158)(54, 190)(55, 153)(56, 161)(57, 154)(58, 160)(59, 168)(60, 165)(61, 170)(62, 180)(63, 177)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1499
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1498 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2144>$ (small group id <128, 2144>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^2 * Y3 * Y2^-2, Y3^3 * Y2^2 * Y3, (Y2 * Y3^-1 * Y1)^2, Y2^3 * Y1 * Y2^-1 * Y1, Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-2, Y3^-1 * Y2^-3 * Y3 * Y2^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, (Y2 * Y3 * Y1)^2, (Y2^-2 * Y1)^2, (Y2^-1 * Y3 * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 18, 82)(6, 70, 8, 72)(7, 71, 25, 89)(9, 73, 32, 96)(12, 76, 34, 98)(13, 77, 37, 101)(14, 78, 31, 95)(15, 79, 35, 99)(16, 80, 38, 102)(17, 81, 28, 92)(19, 83, 36, 100)(20, 84, 26, 90)(21, 85, 29, 93)(22, 86, 33, 97)(23, 87, 27, 91)(24, 88, 30, 94)(39, 103, 50, 114)(40, 104, 56, 120)(41, 105, 53, 117)(42, 106, 52, 116)(43, 107, 59, 123)(44, 108, 57, 121)(45, 109, 51, 115)(46, 110, 55, 119)(47, 111, 58, 122)(48, 112, 54, 118)(49, 113, 60, 124)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195, 140, 204, 153, 217, 178, 242, 160, 224, 148, 212, 133, 197)(130, 194, 135, 199, 154, 218, 139, 203, 167, 231, 146, 210, 162, 226, 137, 201)(132, 196, 143, 207, 168, 232, 147, 211, 172, 236, 141, 205, 170, 234, 145, 209)(134, 198, 150, 214, 169, 233, 149, 213, 174, 238, 142, 206, 173, 237, 151, 215)(136, 200, 157, 221, 179, 243, 161, 225, 183, 247, 155, 219, 181, 245, 159, 223)(138, 202, 164, 228, 180, 244, 163, 227, 185, 249, 156, 220, 184, 248, 165, 229)(144, 208, 171, 235, 152, 216, 175, 239, 189, 253, 176, 240, 190, 254, 177, 241)(158, 222, 182, 246, 166, 230, 186, 250, 191, 255, 187, 251, 192, 256, 188, 252)
	L = (1, 132)(2, 136)(3, 141)(4, 144)(5, 147)(6, 129)(7, 155)(8, 158)(9, 161)(10, 130)(11, 159)(12, 168)(13, 171)(14, 131)(15, 176)(16, 173)(17, 175)(18, 157)(19, 177)(20, 170)(21, 133)(22, 160)(23, 153)(24, 134)(25, 145)(26, 179)(27, 182)(28, 135)(29, 187)(30, 184)(31, 186)(32, 143)(33, 188)(34, 181)(35, 137)(36, 146)(37, 139)(38, 138)(39, 183)(40, 152)(41, 140)(42, 190)(43, 149)(44, 189)(45, 148)(46, 178)(47, 142)(48, 151)(49, 150)(50, 172)(51, 166)(52, 154)(53, 192)(54, 163)(55, 191)(56, 162)(57, 167)(58, 156)(59, 165)(60, 164)(61, 169)(62, 174)(63, 180)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1501
Graph:: simple bipartite
	v = 40 e = 128 f = 36
	degree seq :: [ 4^32, 16^8 ]

E27.1499 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1^-2 * Y3^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3^5 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 19, 83, 39, 103, 38, 102, 50, 114, 34, 98, 49, 113, 33, 97, 48, 112, 32, 96, 47, 111, 35, 99, 16, 80, 5, 69)(3, 67, 11, 75, 27, 91, 51, 115, 64, 128, 57, 121, 63, 127, 56, 120, 62, 126, 55, 119, 61, 125, 54, 118, 58, 122, 40, 104, 20, 84, 8, 72)(4, 68, 14, 78, 21, 85, 43, 107, 37, 101, 17, 81, 26, 90, 10, 74, 25, 89, 9, 73, 24, 88, 41, 105, 36, 100, 18, 82, 6, 70, 15, 79)(12, 76, 29, 93, 52, 116, 59, 123, 46, 110, 23, 87, 45, 109, 22, 86, 44, 108, 28, 92, 53, 117, 60, 124, 42, 106, 31, 95, 13, 77, 30, 94)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 148, 212)(137, 201, 151, 215)(138, 202, 150, 214)(142, 206, 159, 223)(143, 207, 158, 222)(144, 208, 155, 219)(145, 209, 156, 220)(146, 210, 157, 221)(147, 211, 168, 232)(149, 213, 170, 234)(152, 216, 174, 238)(153, 217, 173, 237)(154, 218, 172, 236)(160, 224, 185, 249)(161, 225, 184, 248)(162, 226, 183, 247)(163, 227, 179, 243)(164, 228, 180, 244)(165, 229, 181, 245)(166, 230, 182, 246)(167, 231, 186, 250)(169, 233, 187, 251)(171, 235, 188, 252)(175, 239, 192, 256)(176, 240, 191, 255)(177, 241, 190, 254)(178, 242, 189, 253)
	L = (1, 132)(2, 137)(3, 140)(4, 135)(5, 138)(6, 129)(7, 149)(8, 150)(9, 147)(10, 130)(11, 156)(12, 155)(13, 131)(14, 160)(15, 161)(16, 134)(17, 133)(18, 162)(19, 169)(20, 141)(21, 167)(22, 139)(23, 136)(24, 175)(25, 176)(26, 177)(27, 180)(28, 179)(29, 182)(30, 183)(31, 184)(32, 171)(33, 142)(34, 143)(35, 145)(36, 144)(37, 178)(38, 146)(39, 165)(40, 151)(41, 166)(42, 148)(43, 163)(44, 189)(45, 190)(46, 191)(47, 164)(48, 152)(49, 153)(50, 154)(51, 188)(52, 192)(53, 186)(54, 187)(55, 157)(56, 158)(57, 159)(58, 170)(59, 168)(60, 185)(61, 181)(62, 172)(63, 173)(64, 174)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1497
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1500 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2147>$ (small group id <128, 2147>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3^-1 * Y1^-1 * Y3^-3 * Y1^-3, Y1^16 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 21, 85, 43, 107, 42, 106, 20, 84, 30, 94, 50, 114, 38, 102, 15, 79, 28, 92, 49, 113, 39, 103, 17, 81, 5, 69)(3, 67, 11, 75, 31, 95, 55, 119, 64, 128, 54, 118, 37, 101, 59, 123, 62, 126, 52, 116, 35, 99, 58, 122, 60, 124, 44, 108, 22, 86, 8, 72)(4, 68, 14, 78, 23, 87, 48, 112, 40, 104, 19, 83, 6, 70, 16, 80, 24, 88, 9, 73, 27, 91, 45, 109, 41, 105, 18, 82, 29, 93, 10, 74)(12, 76, 34, 98, 56, 120, 63, 127, 47, 111, 36, 100, 13, 77, 25, 89, 51, 115, 32, 96, 57, 121, 61, 125, 53, 117, 26, 90, 46, 110, 33, 97)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 150, 214)(137, 201, 154, 218)(138, 202, 153, 217)(142, 206, 164, 228)(143, 207, 165, 229)(144, 208, 161, 225)(145, 209, 159, 223)(146, 210, 160, 224)(147, 211, 162, 226)(148, 212, 163, 227)(149, 213, 172, 236)(151, 215, 175, 239)(152, 216, 174, 238)(155, 219, 181, 245)(156, 220, 182, 246)(157, 221, 179, 243)(158, 222, 180, 244)(166, 230, 187, 251)(167, 231, 183, 247)(168, 232, 184, 248)(169, 233, 185, 249)(170, 234, 186, 250)(171, 235, 188, 252)(173, 237, 189, 253)(176, 240, 191, 255)(177, 241, 192, 256)(178, 242, 190, 254)
	L = (1, 132)(2, 137)(3, 140)(4, 143)(5, 144)(6, 129)(7, 151)(8, 153)(9, 156)(10, 130)(11, 160)(12, 163)(13, 131)(14, 149)(15, 155)(16, 166)(17, 157)(18, 133)(19, 158)(20, 134)(21, 173)(22, 174)(23, 177)(24, 135)(25, 180)(26, 136)(27, 171)(28, 176)(29, 178)(30, 138)(31, 184)(32, 186)(33, 139)(34, 183)(35, 185)(36, 187)(37, 141)(38, 142)(39, 147)(40, 145)(41, 148)(42, 146)(43, 168)(44, 164)(45, 167)(46, 190)(47, 150)(48, 170)(49, 169)(50, 152)(51, 159)(52, 162)(53, 165)(54, 154)(55, 189)(56, 188)(57, 192)(58, 191)(59, 161)(60, 181)(61, 172)(62, 179)(63, 182)(64, 175)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1495
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1501 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2144>$ (small group id <128, 2144>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1 * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y3^-1 * Y2 * Y1 * Y2 * R * Y3^-1 * Y1^-1, Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y2 * Y1^-2 * Y3^-1 * Y1 * Y3 * Y2 * Y1^-1, (Y3^-3 * Y1^-1)^2, Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1, (Y3, Y1)^2 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 21, 85, 44, 108, 43, 107, 56, 120, 32, 96, 50, 114, 36, 100, 53, 117, 38, 102, 55, 119, 40, 104, 18, 82, 5, 69)(3, 67, 11, 75, 31, 95, 57, 121, 62, 126, 45, 109, 26, 90, 8, 72, 24, 88, 17, 81, 39, 103, 60, 124, 61, 125, 47, 111, 22, 86, 13, 77)(4, 68, 15, 79, 23, 87, 49, 113, 42, 106, 19, 83, 30, 94, 10, 74, 29, 93, 9, 73, 28, 92, 46, 110, 41, 105, 20, 84, 6, 70, 16, 80)(12, 76, 35, 99, 58, 122, 64, 128, 54, 118, 37, 101, 52, 116, 34, 98, 51, 115, 33, 97, 59, 123, 63, 127, 48, 112, 27, 91, 14, 78, 25, 89)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 150, 214)(137, 201, 155, 219)(138, 202, 153, 217)(139, 203, 160, 224)(141, 205, 164, 228)(143, 207, 165, 229)(144, 208, 162, 226)(146, 210, 159, 223)(147, 211, 163, 227)(148, 212, 161, 225)(149, 213, 173, 237)(151, 215, 176, 240)(152, 216, 178, 242)(154, 218, 181, 245)(156, 220, 182, 246)(157, 221, 180, 244)(158, 222, 179, 243)(166, 230, 175, 239)(167, 231, 184, 248)(168, 232, 188, 252)(169, 233, 186, 250)(170, 234, 187, 251)(171, 235, 185, 249)(172, 236, 189, 253)(174, 238, 191, 255)(177, 241, 192, 256)(183, 247, 190, 254)
	L = (1, 132)(2, 137)(3, 140)(4, 135)(5, 138)(6, 129)(7, 151)(8, 153)(9, 149)(10, 130)(11, 161)(12, 159)(13, 162)(14, 131)(15, 166)(16, 164)(17, 163)(18, 134)(19, 133)(20, 160)(21, 174)(22, 142)(23, 172)(24, 179)(25, 145)(26, 180)(27, 136)(28, 183)(29, 181)(30, 178)(31, 186)(32, 144)(33, 185)(34, 139)(35, 188)(36, 143)(37, 141)(38, 177)(39, 187)(40, 147)(41, 146)(42, 184)(43, 148)(44, 170)(45, 155)(46, 171)(47, 165)(48, 150)(49, 168)(50, 157)(51, 167)(52, 152)(53, 156)(54, 154)(55, 169)(56, 158)(57, 191)(58, 190)(59, 189)(60, 192)(61, 176)(62, 182)(63, 173)(64, 175)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1498
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1502 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 8, 16})
Quotient :: dipole
Aut^+ = (C2 x D16) : C2 (small group id <64, 190>)
Aut   = $<128, 2144>$ (small group id <128, 2144>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2 * Y1^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y2 * Y1^-2)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^3, (Y1^-1 * R * Y2)^2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^2 * Y3^4, Y1^-1 * Y3^-2 * Y1^-5 ]
Map:: non-degenerate
	R = (1, 65, 2, 66, 7, 71, 23, 87, 46, 110, 45, 109, 22, 86, 34, 98, 54, 118, 39, 103, 16, 80, 32, 96, 53, 117, 42, 106, 19, 83, 5, 69)(3, 67, 11, 75, 35, 99, 57, 121, 62, 126, 47, 111, 29, 93, 8, 72, 27, 91, 17, 81, 38, 102, 60, 124, 61, 125, 50, 114, 24, 88, 13, 77)(4, 68, 15, 79, 25, 89, 52, 116, 43, 107, 21, 85, 6, 70, 18, 82, 26, 90, 9, 73, 31, 95, 48, 112, 44, 108, 20, 84, 33, 97, 10, 74)(12, 76, 37, 101, 58, 122, 63, 127, 51, 115, 30, 94, 14, 78, 40, 104, 55, 119, 36, 100, 59, 123, 64, 128, 56, 120, 41, 105, 49, 113, 28, 92)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 152, 216)(137, 201, 158, 222)(138, 202, 156, 220)(139, 203, 162, 226)(141, 205, 167, 231)(143, 207, 169, 233)(144, 208, 157, 221)(146, 210, 168, 232)(147, 211, 163, 227)(148, 212, 165, 229)(149, 213, 164, 228)(150, 214, 166, 230)(151, 215, 175, 239)(153, 217, 179, 243)(154, 218, 177, 241)(155, 219, 182, 246)(159, 223, 184, 248)(160, 224, 178, 242)(161, 225, 183, 247)(170, 234, 188, 252)(171, 235, 186, 250)(172, 236, 187, 251)(173, 237, 185, 249)(174, 238, 189, 253)(176, 240, 191, 255)(180, 244, 192, 256)(181, 245, 190, 254)
	L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 146)(6, 129)(7, 153)(8, 156)(9, 160)(10, 130)(11, 164)(12, 166)(13, 168)(14, 131)(15, 151)(16, 159)(17, 165)(18, 167)(19, 161)(20, 133)(21, 162)(22, 134)(23, 176)(24, 177)(25, 181)(26, 135)(27, 183)(28, 139)(29, 142)(30, 136)(31, 174)(32, 180)(33, 182)(34, 138)(35, 186)(36, 188)(37, 185)(38, 187)(39, 143)(40, 145)(41, 141)(42, 149)(43, 147)(44, 150)(45, 148)(46, 171)(47, 169)(48, 170)(49, 155)(50, 158)(51, 152)(52, 173)(53, 172)(54, 154)(55, 163)(56, 157)(57, 192)(58, 189)(59, 190)(60, 191)(61, 184)(62, 179)(63, 175)(64, 178)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1496
Graph:: simple bipartite
	v = 36 e = 128 f = 40
	degree seq :: [ 4^32, 32^4 ]

E27.1503 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-8, T2^8 * T1^-2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 46, 30, 16, 6, 15, 29, 45, 58, 63, 55, 42, 26, 41, 54, 62, 61, 52, 38, 23, 11, 21, 35, 49, 40, 25, 13, 5)(2, 7, 17, 31, 47, 57, 44, 28, 14, 27, 43, 56, 64, 60, 51, 37, 22, 36, 50, 59, 53, 39, 24, 12, 4, 10, 20, 34, 48, 32, 18, 8)(65, 66, 70, 78, 90, 86, 75, 68)(67, 71, 79, 91, 105, 100, 85, 74)(69, 72, 80, 92, 106, 101, 87, 76)(73, 81, 93, 107, 118, 114, 99, 84)(77, 82, 94, 108, 119, 115, 102, 88)(83, 95, 109, 120, 126, 123, 113, 98)(89, 96, 110, 121, 127, 124, 116, 103)(97, 111, 122, 128, 125, 117, 104, 112)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1507
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.1504 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^-8, T1^-2 * T2^-8 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 49, 38, 23, 11, 21, 35, 51, 60, 63, 55, 42, 26, 41, 54, 62, 58, 46, 30, 16, 6, 15, 29, 45, 40, 25, 13, 5)(2, 7, 17, 31, 47, 39, 24, 12, 4, 10, 20, 34, 50, 59, 53, 37, 22, 36, 52, 61, 64, 57, 44, 28, 14, 27, 43, 56, 48, 32, 18, 8)(65, 66, 70, 78, 90, 86, 75, 68)(67, 71, 79, 91, 105, 100, 85, 74)(69, 72, 80, 92, 106, 101, 87, 76)(73, 81, 93, 107, 118, 116, 99, 84)(77, 82, 94, 108, 119, 117, 102, 88)(83, 95, 109, 120, 126, 125, 115, 98)(89, 96, 110, 121, 127, 123, 113, 103)(97, 111, 104, 112, 122, 128, 124, 114)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1506
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.1505 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T1^-2 * T2 * T1^-1 * T2 * T1^-3, T1 * T2 * T1 * T2^9, (T1^-1 * T2^-1)^8 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 45, 57, 48, 36, 23, 11, 21, 26, 39, 51, 60, 64, 62, 54, 42, 30, 16, 6, 15, 29, 41, 53, 50, 38, 25, 13, 5)(2, 7, 17, 31, 43, 55, 49, 37, 24, 12, 4, 10, 20, 34, 46, 58, 63, 59, 47, 35, 22, 28, 14, 27, 40, 52, 61, 56, 44, 32, 18, 8)(65, 66, 70, 78, 90, 84, 73, 81, 93, 104, 115, 110, 97, 107, 117, 125, 128, 127, 121, 113, 102, 108, 118, 111, 100, 88, 77, 82, 94, 86, 75, 68)(67, 71, 79, 91, 103, 98, 83, 95, 105, 116, 124, 122, 109, 119, 114, 120, 126, 123, 112, 101, 89, 96, 106, 99, 87, 76, 69, 72, 80, 92, 85, 74)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1508
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.1506 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T1^-8, T2^8 * T1^-2 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 9, 73, 19, 83, 33, 97, 46, 110, 30, 94, 16, 80, 6, 70, 15, 79, 29, 93, 45, 109, 58, 122, 63, 127, 55, 119, 42, 106, 26, 90, 41, 105, 54, 118, 62, 126, 61, 125, 52, 116, 38, 102, 23, 87, 11, 75, 21, 85, 35, 99, 49, 113, 40, 104, 25, 89, 13, 77, 5, 69)(2, 66, 7, 71, 17, 81, 31, 95, 47, 111, 57, 121, 44, 108, 28, 92, 14, 78, 27, 91, 43, 107, 56, 120, 64, 128, 60, 124, 51, 115, 37, 101, 22, 86, 36, 100, 50, 114, 59, 123, 53, 117, 39, 103, 24, 88, 12, 76, 4, 68, 10, 74, 20, 84, 34, 98, 48, 112, 32, 96, 18, 82, 8, 72)
	L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 78)(7, 79)(8, 80)(9, 81)(10, 67)(11, 68)(12, 69)(13, 82)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 73)(21, 74)(22, 75)(23, 76)(24, 77)(25, 96)(26, 86)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 83)(35, 84)(36, 85)(37, 87)(38, 88)(39, 89)(40, 112)(41, 100)(42, 101)(43, 118)(44, 119)(45, 120)(46, 121)(47, 122)(48, 97)(49, 98)(50, 99)(51, 102)(52, 103)(53, 104)(54, 114)(55, 115)(56, 126)(57, 127)(58, 128)(59, 113)(60, 116)(61, 117)(62, 123)(63, 124)(64, 125)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1504
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.1507 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^-8, T1^-2 * T2^-8 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 9, 73, 19, 83, 33, 97, 49, 113, 38, 102, 23, 87, 11, 75, 21, 85, 35, 99, 51, 115, 60, 124, 63, 127, 55, 119, 42, 106, 26, 90, 41, 105, 54, 118, 62, 126, 58, 122, 46, 110, 30, 94, 16, 80, 6, 70, 15, 79, 29, 93, 45, 109, 40, 104, 25, 89, 13, 77, 5, 69)(2, 66, 7, 71, 17, 81, 31, 95, 47, 111, 39, 103, 24, 88, 12, 76, 4, 68, 10, 74, 20, 84, 34, 98, 50, 114, 59, 123, 53, 117, 37, 101, 22, 86, 36, 100, 52, 116, 61, 125, 64, 128, 57, 121, 44, 108, 28, 92, 14, 78, 27, 91, 43, 107, 56, 120, 48, 112, 32, 96, 18, 82, 8, 72)
	L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 78)(7, 79)(8, 80)(9, 81)(10, 67)(11, 68)(12, 69)(13, 82)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 73)(21, 74)(22, 75)(23, 76)(24, 77)(25, 96)(26, 86)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 83)(35, 84)(36, 85)(37, 87)(38, 88)(39, 89)(40, 112)(41, 100)(42, 101)(43, 118)(44, 119)(45, 120)(46, 121)(47, 104)(48, 122)(49, 103)(50, 97)(51, 98)(52, 99)(53, 102)(54, 116)(55, 117)(56, 126)(57, 127)(58, 128)(59, 113)(60, 114)(61, 115)(62, 125)(63, 123)(64, 124)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1503
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.1508 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), (F * T2)^2, (F * T1)^2, T2^-8, T2^2 * T1^-8 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 9, 73, 19, 83, 33, 97, 25, 89, 13, 77, 5, 69)(2, 66, 7, 71, 17, 81, 31, 95, 48, 112, 32, 96, 18, 82, 8, 72)(4, 68, 10, 74, 20, 84, 34, 98, 49, 113, 40, 104, 24, 88, 12, 76)(6, 70, 15, 79, 29, 93, 46, 110, 58, 122, 47, 111, 30, 94, 16, 80)(11, 75, 21, 85, 35, 99, 50, 114, 59, 123, 53, 117, 39, 103, 23, 87)(14, 78, 27, 91, 44, 108, 56, 120, 64, 128, 57, 121, 45, 109, 28, 92)(22, 86, 36, 100, 41, 105, 54, 118, 62, 126, 61, 125, 52, 116, 38, 102)(26, 90, 42, 106, 55, 119, 63, 127, 60, 124, 51, 115, 37, 101, 43, 107)
	L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 78)(7, 79)(8, 80)(9, 81)(10, 67)(11, 68)(12, 69)(13, 82)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 73)(21, 74)(22, 75)(23, 76)(24, 77)(25, 96)(26, 105)(27, 106)(28, 107)(29, 108)(30, 109)(31, 110)(32, 111)(33, 112)(34, 83)(35, 84)(36, 85)(37, 86)(38, 87)(39, 88)(40, 89)(41, 99)(42, 118)(43, 100)(44, 119)(45, 101)(46, 120)(47, 121)(48, 122)(49, 97)(50, 98)(51, 102)(52, 103)(53, 104)(54, 114)(55, 126)(56, 127)(57, 115)(58, 128)(59, 113)(60, 116)(61, 117)(62, 123)(63, 125)(64, 124)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1505
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.1509 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y3 * Y2^3 * Y3^-1 * Y2^-3, Y1^8, Y2^2 * Y3 * Y2^6 * Y1^-1, Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 22, 86, 11, 75, 4, 68)(3, 67, 7, 71, 15, 79, 27, 91, 41, 105, 36, 100, 21, 85, 10, 74)(5, 69, 8, 72, 16, 80, 28, 92, 42, 106, 37, 101, 23, 87, 12, 76)(9, 73, 17, 81, 29, 93, 43, 107, 54, 118, 50, 114, 35, 99, 20, 84)(13, 77, 18, 82, 30, 94, 44, 108, 55, 119, 51, 115, 38, 102, 24, 88)(19, 83, 31, 95, 45, 109, 56, 120, 62, 126, 59, 123, 49, 113, 34, 98)(25, 89, 32, 96, 46, 110, 57, 121, 63, 127, 60, 124, 52, 116, 39, 103)(33, 97, 47, 111, 58, 122, 64, 128, 61, 125, 53, 117, 40, 104, 48, 112)(129, 193, 131, 195, 137, 201, 147, 211, 161, 225, 174, 238, 158, 222, 144, 208, 134, 198, 143, 207, 157, 221, 173, 237, 186, 250, 191, 255, 183, 247, 170, 234, 154, 218, 169, 233, 182, 246, 190, 254, 189, 253, 180, 244, 166, 230, 151, 215, 139, 203, 149, 213, 163, 227, 177, 241, 168, 232, 153, 217, 141, 205, 133, 197)(130, 194, 135, 199, 145, 209, 159, 223, 175, 239, 185, 249, 172, 236, 156, 220, 142, 206, 155, 219, 171, 235, 184, 248, 192, 256, 188, 252, 179, 243, 165, 229, 150, 214, 164, 228, 178, 242, 187, 251, 181, 245, 167, 231, 152, 216, 140, 204, 132, 196, 138, 202, 148, 212, 162, 226, 176, 240, 160, 224, 146, 210, 136, 200)
	L = (1, 132)(2, 129)(3, 138)(4, 139)(5, 140)(6, 130)(7, 131)(8, 133)(9, 148)(10, 149)(11, 150)(12, 151)(13, 152)(14, 134)(15, 135)(16, 136)(17, 137)(18, 141)(19, 162)(20, 163)(21, 164)(22, 154)(23, 165)(24, 166)(25, 167)(26, 142)(27, 143)(28, 144)(29, 145)(30, 146)(31, 147)(32, 153)(33, 176)(34, 177)(35, 178)(36, 169)(37, 170)(38, 179)(39, 180)(40, 181)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 168)(49, 187)(50, 182)(51, 183)(52, 188)(53, 189)(54, 171)(55, 172)(56, 173)(57, 174)(58, 175)(59, 190)(60, 191)(61, 192)(62, 184)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1514
Graph:: bipartite
	v = 10 e = 128 f = 66
	degree seq :: [ 16^8, 64^2 ]

E27.1510 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y2)^2, (R * Y1)^2, Y3 * Y2^-1 * Y1 * Y2, (R * Y3)^2, Y3 * Y2^2 * Y1 * Y2^-2, Y1^8, Y2^-3 * Y3^2 * Y2^-5, Y3^-2 * Y2^3 * Y1^-2 * Y2^-3, Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 22, 86, 11, 75, 4, 68)(3, 67, 7, 71, 15, 79, 27, 91, 41, 105, 36, 100, 21, 85, 10, 74)(5, 69, 8, 72, 16, 80, 28, 92, 42, 106, 37, 101, 23, 87, 12, 76)(9, 73, 17, 81, 29, 93, 43, 107, 54, 118, 52, 116, 35, 99, 20, 84)(13, 77, 18, 82, 30, 94, 44, 108, 55, 119, 53, 117, 38, 102, 24, 88)(19, 83, 31, 95, 45, 109, 56, 120, 62, 126, 61, 125, 51, 115, 34, 98)(25, 89, 32, 96, 46, 110, 57, 121, 63, 127, 59, 123, 49, 113, 39, 103)(33, 97, 47, 111, 40, 104, 48, 112, 58, 122, 64, 128, 60, 124, 50, 114)(129, 193, 131, 195, 137, 201, 147, 211, 161, 225, 177, 241, 166, 230, 151, 215, 139, 203, 149, 213, 163, 227, 179, 243, 188, 252, 191, 255, 183, 247, 170, 234, 154, 218, 169, 233, 182, 246, 190, 254, 186, 250, 174, 238, 158, 222, 144, 208, 134, 198, 143, 207, 157, 221, 173, 237, 168, 232, 153, 217, 141, 205, 133, 197)(130, 194, 135, 199, 145, 209, 159, 223, 175, 239, 167, 231, 152, 216, 140, 204, 132, 196, 138, 202, 148, 212, 162, 226, 178, 242, 187, 251, 181, 245, 165, 229, 150, 214, 164, 228, 180, 244, 189, 253, 192, 256, 185, 249, 172, 236, 156, 220, 142, 206, 155, 219, 171, 235, 184, 248, 176, 240, 160, 224, 146, 210, 136, 200)
	L = (1, 132)(2, 129)(3, 138)(4, 139)(5, 140)(6, 130)(7, 131)(8, 133)(9, 148)(10, 149)(11, 150)(12, 151)(13, 152)(14, 134)(15, 135)(16, 136)(17, 137)(18, 141)(19, 162)(20, 163)(21, 164)(22, 154)(23, 165)(24, 166)(25, 167)(26, 142)(27, 143)(28, 144)(29, 145)(30, 146)(31, 147)(32, 153)(33, 178)(34, 179)(35, 180)(36, 169)(37, 170)(38, 181)(39, 177)(40, 175)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 168)(49, 187)(50, 188)(51, 189)(52, 182)(53, 183)(54, 171)(55, 172)(56, 173)(57, 174)(58, 176)(59, 191)(60, 192)(61, 190)(62, 184)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1513
Graph:: bipartite
	v = 10 e = 128 f = 66
	degree seq :: [ 16^8, 64^2 ]

E27.1511 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^-4 * Y2^2 * Y1^-2, Y1 * Y2 * Y1 * Y2^9, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 20, 84, 9, 73, 17, 81, 29, 93, 40, 104, 51, 115, 46, 110, 33, 97, 43, 107, 53, 117, 61, 125, 64, 128, 63, 127, 57, 121, 49, 113, 38, 102, 44, 108, 54, 118, 47, 111, 36, 100, 24, 88, 13, 77, 18, 82, 30, 94, 22, 86, 11, 75, 4, 68)(3, 67, 7, 71, 15, 79, 27, 91, 39, 103, 34, 98, 19, 83, 31, 95, 41, 105, 52, 116, 60, 124, 58, 122, 45, 109, 55, 119, 50, 114, 56, 120, 62, 126, 59, 123, 48, 112, 37, 101, 25, 89, 32, 96, 42, 106, 35, 99, 23, 87, 12, 76, 5, 69, 8, 72, 16, 80, 28, 92, 21, 85, 10, 74)(129, 193, 131, 195, 137, 201, 147, 211, 161, 225, 173, 237, 185, 249, 176, 240, 164, 228, 151, 215, 139, 203, 149, 213, 154, 218, 167, 231, 179, 243, 188, 252, 192, 256, 190, 254, 182, 246, 170, 234, 158, 222, 144, 208, 134, 198, 143, 207, 157, 221, 169, 233, 181, 245, 178, 242, 166, 230, 153, 217, 141, 205, 133, 197)(130, 194, 135, 199, 145, 209, 159, 223, 171, 235, 183, 247, 177, 241, 165, 229, 152, 216, 140, 204, 132, 196, 138, 202, 148, 212, 162, 226, 174, 238, 186, 250, 191, 255, 187, 251, 175, 239, 163, 227, 150, 214, 156, 220, 142, 206, 155, 219, 168, 232, 180, 244, 189, 253, 184, 248, 172, 236, 160, 224, 146, 210, 136, 200)
	L = (1, 131)(2, 135)(3, 137)(4, 138)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 148)(11, 149)(12, 132)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 162)(21, 154)(22, 156)(23, 139)(24, 140)(25, 141)(26, 167)(27, 168)(28, 142)(29, 169)(30, 144)(31, 171)(32, 146)(33, 173)(34, 174)(35, 150)(36, 151)(37, 152)(38, 153)(39, 179)(40, 180)(41, 181)(42, 158)(43, 183)(44, 160)(45, 185)(46, 186)(47, 163)(48, 164)(49, 165)(50, 166)(51, 188)(52, 189)(53, 178)(54, 170)(55, 177)(56, 172)(57, 176)(58, 191)(59, 175)(60, 192)(61, 184)(62, 182)(63, 187)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1512
Graph:: bipartite
	v = 4 e = 128 f = 72
	degree seq :: [ 64^4 ]

E27.1512 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (R * Y2)^2, Y2^8, Y2^8, Y3^8 * Y2^-2, (Y3^-1 * Y1^-1)^32 ]
Map::
	R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194, 134, 198, 142, 206, 154, 218, 150, 214, 139, 203, 132, 196)(131, 195, 135, 199, 143, 207, 155, 219, 169, 233, 164, 228, 149, 213, 138, 202)(133, 197, 136, 200, 144, 208, 156, 220, 170, 234, 165, 229, 151, 215, 140, 204)(137, 201, 145, 209, 157, 221, 171, 235, 182, 246, 178, 242, 163, 227, 148, 212)(141, 205, 146, 210, 158, 222, 172, 236, 183, 247, 179, 243, 166, 230, 152, 216)(147, 211, 159, 223, 173, 237, 184, 248, 190, 254, 187, 251, 177, 241, 162, 226)(153, 217, 160, 224, 174, 238, 185, 249, 191, 255, 188, 252, 180, 244, 167, 231)(161, 225, 175, 239, 186, 250, 192, 256, 189, 253, 181, 245, 168, 232, 176, 240)
	L = (1, 131)(2, 135)(3, 137)(4, 138)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 148)(11, 149)(12, 132)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 162)(21, 163)(22, 164)(23, 139)(24, 140)(25, 141)(26, 169)(27, 171)(28, 142)(29, 173)(30, 144)(31, 175)(32, 146)(33, 174)(34, 176)(35, 177)(36, 178)(37, 150)(38, 151)(39, 152)(40, 153)(41, 182)(42, 154)(43, 184)(44, 156)(45, 186)(46, 158)(47, 185)(48, 160)(49, 168)(50, 187)(51, 165)(52, 166)(53, 167)(54, 190)(55, 170)(56, 192)(57, 172)(58, 191)(59, 181)(60, 179)(61, 180)(62, 189)(63, 183)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 64, 64 ), ( 64^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1511
Graph:: simple bipartite
	v = 72 e = 128 f = 4
	degree seq :: [ 2^64, 16^8 ]

E27.1513 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-8, Y3^2 * Y1^-8, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 41, 105, 35, 99, 20, 84, 9, 73, 17, 81, 29, 93, 44, 108, 55, 119, 62, 126, 59, 123, 49, 113, 33, 97, 48, 112, 58, 122, 64, 128, 60, 124, 52, 116, 39, 103, 24, 88, 13, 77, 18, 82, 30, 94, 45, 109, 37, 101, 22, 86, 11, 75, 4, 68)(3, 67, 7, 71, 15, 79, 27, 91, 42, 106, 54, 118, 50, 114, 34, 98, 19, 83, 31, 95, 46, 110, 56, 120, 63, 127, 61, 125, 53, 117, 40, 104, 25, 89, 32, 96, 47, 111, 57, 121, 51, 115, 38, 102, 23, 87, 12, 76, 5, 69, 8, 72, 16, 80, 28, 92, 43, 107, 36, 100, 21, 85, 10, 74)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256)
	L = (1, 131)(2, 135)(3, 137)(4, 138)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 148)(11, 149)(12, 132)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 162)(21, 163)(22, 164)(23, 139)(24, 140)(25, 141)(26, 170)(27, 172)(28, 142)(29, 174)(30, 144)(31, 176)(32, 146)(33, 153)(34, 177)(35, 178)(36, 169)(37, 171)(38, 150)(39, 151)(40, 152)(41, 182)(42, 183)(43, 154)(44, 184)(45, 156)(46, 186)(47, 158)(48, 160)(49, 168)(50, 187)(51, 165)(52, 166)(53, 167)(54, 190)(55, 191)(56, 192)(57, 173)(58, 175)(59, 181)(60, 179)(61, 180)(62, 189)(63, 188)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1510
Graph:: simple bipartite
	v = 66 e = 128 f = 10
	degree seq :: [ 2^64, 64^2 ]

E27.1514 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 x C2 (small group id <64, 50>)
Aut   = $<128, 991>$ (small group id <128, 991>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-8, Y3^-2 * Y1^-8, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 41, 105, 39, 103, 24, 88, 13, 77, 18, 82, 30, 94, 45, 109, 55, 119, 62, 126, 59, 123, 49, 113, 33, 97, 48, 112, 58, 122, 64, 128, 61, 125, 51, 115, 35, 99, 20, 84, 9, 73, 17, 81, 29, 93, 44, 108, 37, 101, 22, 86, 11, 75, 4, 68)(3, 67, 7, 71, 15, 79, 27, 91, 42, 106, 38, 102, 23, 87, 12, 76, 5, 69, 8, 72, 16, 80, 28, 92, 43, 107, 54, 118, 53, 117, 40, 104, 25, 89, 32, 96, 47, 111, 57, 121, 63, 127, 60, 124, 50, 114, 34, 98, 19, 83, 31, 95, 46, 110, 56, 120, 52, 116, 36, 100, 21, 85, 10, 74)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256)
	L = (1, 131)(2, 135)(3, 137)(4, 138)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 148)(11, 149)(12, 132)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 162)(21, 163)(22, 164)(23, 139)(24, 140)(25, 141)(26, 170)(27, 172)(28, 142)(29, 174)(30, 144)(31, 176)(32, 146)(33, 153)(34, 177)(35, 178)(36, 179)(37, 180)(38, 150)(39, 151)(40, 152)(41, 166)(42, 165)(43, 154)(44, 184)(45, 156)(46, 186)(47, 158)(48, 160)(49, 168)(50, 187)(51, 188)(52, 189)(53, 167)(54, 169)(55, 171)(56, 192)(57, 173)(58, 175)(59, 181)(60, 190)(61, 191)(62, 182)(63, 183)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1509
Graph:: simple bipartite
	v = 66 e = 128 f = 10
	degree seq :: [ 2^64, 64^2 ]

E27.1515 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-2 * T2, T2 * T1^3 * T2^-1 * T1, T2 * T1^-1 * T2^-2 * T1 * T2, T1^-1 * T2^-1 * T1^-3 * T2, T2^7 * T1 * T2 * T1, (T2^-1 * T1 * T2^-3)^2, (T2^-2 * T1^2)^16 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 46, 54, 38, 20, 6, 19, 37, 53, 63, 59, 43, 25, 36, 23, 41, 57, 64, 58, 42, 24, 13, 21, 39, 55, 52, 35, 17, 5)(2, 7, 22, 40, 56, 51, 34, 16, 18, 11, 31, 47, 62, 50, 33, 15, 28, 9, 27, 45, 61, 49, 32, 14, 4, 12, 30, 48, 60, 44, 26, 8)(65, 66, 70, 82, 100, 92, 77, 68)(67, 73, 83, 76, 87, 71, 85, 75)(69, 79, 84, 78, 89, 72, 88, 80)(74, 86, 101, 95, 105, 91, 103, 94)(81, 90, 102, 98, 107, 97, 106, 96)(93, 109, 117, 112, 121, 104, 119, 111)(99, 114, 118, 113, 123, 108, 122, 115)(110, 120, 127, 126, 128, 125, 116, 124)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1519
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.1516 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^-1 * T2^-1 * T1^-1, T1^-2 * T2^-1 * T1^-1 * T2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T1^-1 * T2^-6 * T1^-1 * T2^-2, (T2^-2 * T1^2)^16 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 46, 58, 42, 24, 13, 21, 39, 55, 64, 59, 43, 25, 36, 23, 41, 57, 63, 54, 38, 20, 6, 19, 37, 53, 52, 35, 17, 5)(2, 7, 22, 40, 56, 49, 32, 14, 4, 12, 30, 48, 62, 50, 33, 15, 28, 9, 27, 45, 61, 51, 34, 16, 18, 11, 31, 47, 60, 44, 26, 8)(65, 66, 70, 82, 100, 92, 77, 68)(67, 73, 83, 76, 87, 71, 85, 75)(69, 79, 84, 78, 89, 72, 88, 80)(74, 86, 101, 95, 105, 91, 103, 94)(81, 90, 102, 98, 107, 97, 106, 96)(93, 109, 117, 112, 121, 104, 119, 111)(99, 114, 118, 113, 123, 108, 122, 115)(110, 120, 116, 124, 127, 125, 128, 126)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 64^8 ), ( 64^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1518
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 64 f = 2
	degree seq :: [ 8^8, 32^2 ]

E27.1517 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 32, 32})
Quotient :: edge
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-2 * T2 * T1^2, T2^-1 * T1^2 * T2 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1, T2^5 * T1^-1 * T2 * T1^-1, (T2, T1^-1)^2, T1^-1 * T2 * T1^-2 * T2 * T1^-3, T2^-1 * T1^-1 * T2^-1 * T1^-3 * T2^-2, (T2^2 * T1^2)^4 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 54, 24, 50, 21, 49, 36, 13, 32, 42, 61, 55, 25, 53, 23, 52, 64, 48, 20, 6, 19, 46, 37, 60, 34, 59, 41, 17, 5)(2, 7, 22, 51, 63, 47, 62, 45, 38, 14, 4, 12, 30, 58, 39, 15, 28, 9, 27, 57, 35, 44, 18, 43, 40, 16, 33, 11, 31, 56, 26, 8)(65, 66, 70, 82, 106, 94, 74, 86, 110, 104, 119, 103, 118, 127, 124, 97, 117, 92, 114, 126, 123, 95, 116, 91, 113, 102, 81, 90, 112, 99, 77, 68)(67, 73, 83, 109, 125, 120, 93, 121, 101, 78, 89, 72, 88, 108, 98, 76, 87, 71, 85, 107, 105, 122, 128, 115, 100, 80, 69, 79, 84, 111, 96, 75)
	L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 16^32 ) }
Outer automorphisms :: reflexible
Dual of E27.1520
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 64 f = 8
	degree seq :: [ 32^4 ]

E27.1518 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-2 * T2, T2 * T1^3 * T2^-1 * T1, T2 * T1^-1 * T2^-2 * T1 * T2, T1^-1 * T2^-1 * T1^-3 * T2, T2^7 * T1 * T2 * T1, (T2^-1 * T1 * T2^-3)^2, (T2^-2 * T1^2)^16 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 10, 74, 29, 93, 46, 110, 54, 118, 38, 102, 20, 84, 6, 70, 19, 83, 37, 101, 53, 117, 63, 127, 59, 123, 43, 107, 25, 89, 36, 100, 23, 87, 41, 105, 57, 121, 64, 128, 58, 122, 42, 106, 24, 88, 13, 77, 21, 85, 39, 103, 55, 119, 52, 116, 35, 99, 17, 81, 5, 69)(2, 66, 7, 71, 22, 86, 40, 104, 56, 120, 51, 115, 34, 98, 16, 80, 18, 82, 11, 75, 31, 95, 47, 111, 62, 126, 50, 114, 33, 97, 15, 79, 28, 92, 9, 73, 27, 91, 45, 109, 61, 125, 49, 113, 32, 96, 14, 78, 4, 68, 12, 76, 30, 94, 48, 112, 60, 124, 44, 108, 26, 90, 8, 72)
	L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 83)(10, 86)(11, 67)(12, 87)(13, 68)(14, 89)(15, 84)(16, 69)(17, 90)(18, 100)(19, 76)(20, 78)(21, 75)(22, 101)(23, 71)(24, 80)(25, 72)(26, 102)(27, 103)(28, 77)(29, 109)(30, 74)(31, 105)(32, 81)(33, 106)(34, 107)(35, 114)(36, 92)(37, 95)(38, 98)(39, 94)(40, 119)(41, 91)(42, 96)(43, 97)(44, 122)(45, 117)(46, 120)(47, 93)(48, 121)(49, 123)(50, 118)(51, 99)(52, 124)(53, 112)(54, 113)(55, 111)(56, 127)(57, 104)(58, 115)(59, 108)(60, 110)(61, 116)(62, 128)(63, 126)(64, 125)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1516
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.1519 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^-1 * T2^-1 * T1^-1, T1^-2 * T2^-1 * T1^-1 * T2 * T1^-1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T1^-1 * T2^-6 * T1^-1 * T2^-2, (T2^-2 * T1^2)^16 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 10, 74, 29, 93, 46, 110, 58, 122, 42, 106, 24, 88, 13, 77, 21, 85, 39, 103, 55, 119, 64, 128, 59, 123, 43, 107, 25, 89, 36, 100, 23, 87, 41, 105, 57, 121, 63, 127, 54, 118, 38, 102, 20, 84, 6, 70, 19, 83, 37, 101, 53, 117, 52, 116, 35, 99, 17, 81, 5, 69)(2, 66, 7, 71, 22, 86, 40, 104, 56, 120, 49, 113, 32, 96, 14, 78, 4, 68, 12, 76, 30, 94, 48, 112, 62, 126, 50, 114, 33, 97, 15, 79, 28, 92, 9, 73, 27, 91, 45, 109, 61, 125, 51, 115, 34, 98, 16, 80, 18, 82, 11, 75, 31, 95, 47, 111, 60, 124, 44, 108, 26, 90, 8, 72)
	L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 83)(10, 86)(11, 67)(12, 87)(13, 68)(14, 89)(15, 84)(16, 69)(17, 90)(18, 100)(19, 76)(20, 78)(21, 75)(22, 101)(23, 71)(24, 80)(25, 72)(26, 102)(27, 103)(28, 77)(29, 109)(30, 74)(31, 105)(32, 81)(33, 106)(34, 107)(35, 114)(36, 92)(37, 95)(38, 98)(39, 94)(40, 119)(41, 91)(42, 96)(43, 97)(44, 122)(45, 117)(46, 120)(47, 93)(48, 121)(49, 123)(50, 118)(51, 99)(52, 124)(53, 112)(54, 113)(55, 111)(56, 116)(57, 104)(58, 115)(59, 108)(60, 127)(61, 128)(62, 110)(63, 125)(64, 126)
	local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E27.1515
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 64 f = 10
	degree seq :: [ 64^2 ]

E27.1520 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 32, 32})
Quotient :: loop
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1 * T2 * T1^-1, T2^-2 * T1^-1 * T2^-1 * T1 * T2^-1, T1 * T2^-1 * T1^-2 * T2 * T1, T2^2 * T1 * T2^-2 * T1^-1, T1^-3 * T2^-1 * T1^-2 * T2^-1 * T1^-3, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 65, 3, 67, 10, 74, 25, 89, 44, 108, 23, 87, 17, 81, 5, 69)(2, 66, 7, 71, 22, 86, 15, 79, 27, 91, 9, 73, 26, 90, 8, 72)(4, 68, 12, 76, 28, 92, 16, 80, 31, 95, 11, 75, 29, 93, 14, 78)(6, 70, 19, 83, 40, 104, 24, 88, 43, 107, 21, 85, 42, 106, 20, 84)(13, 77, 30, 94, 45, 109, 35, 99, 48, 112, 32, 96, 46, 110, 34, 98)(18, 82, 37, 101, 57, 121, 41, 105, 60, 124, 39, 103, 59, 123, 38, 102)(33, 97, 49, 113, 61, 125, 52, 116, 62, 126, 47, 111, 53, 117, 51, 115)(36, 100, 54, 118, 50, 114, 58, 122, 64, 128, 56, 120, 63, 127, 55, 119)
	L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 83)(10, 86)(11, 67)(12, 87)(13, 68)(14, 89)(15, 84)(16, 69)(17, 90)(18, 100)(19, 103)(20, 105)(21, 101)(22, 104)(23, 71)(24, 102)(25, 72)(26, 106)(27, 107)(28, 74)(29, 81)(30, 75)(31, 108)(32, 76)(33, 77)(34, 80)(35, 78)(36, 117)(37, 120)(38, 122)(39, 118)(40, 121)(41, 119)(42, 123)(43, 124)(44, 91)(45, 92)(46, 93)(47, 94)(48, 95)(49, 96)(50, 97)(51, 99)(52, 98)(53, 110)(54, 116)(55, 113)(56, 115)(57, 114)(58, 111)(59, 127)(60, 128)(61, 109)(62, 112)(63, 126)(64, 125)
	local type(s) :: { ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1517
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 64 f = 4
	degree seq :: [ 16^8 ]

E27.1521 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y1^-1 * Y3^-1, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^2 * Y1^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y1^2 * Y2^-1, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y1^2 * Y2 * Y3^-1 * Y2^-1 * Y1, Y2^-1 * Y3^2 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y3, Y2 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y2^2 * Y1^-1 * Y2^-2 * Y1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-4 * Y3 * Y2^-1 * Y1^-1 * Y2^-3, (Y3 * Y2^-1)^32 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 18, 82, 36, 100, 28, 92, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 12, 76, 23, 87, 7, 71, 21, 85, 11, 75)(5, 69, 15, 79, 20, 84, 14, 78, 25, 89, 8, 72, 24, 88, 16, 80)(10, 74, 22, 86, 37, 101, 31, 95, 41, 105, 27, 91, 39, 103, 30, 94)(17, 81, 26, 90, 38, 102, 34, 98, 43, 107, 33, 97, 42, 106, 32, 96)(29, 93, 45, 109, 53, 117, 48, 112, 57, 121, 40, 104, 55, 119, 47, 111)(35, 99, 50, 114, 54, 118, 49, 113, 59, 123, 44, 108, 58, 122, 51, 115)(46, 110, 56, 120, 63, 127, 62, 126, 64, 128, 61, 125, 52, 116, 60, 124)(129, 193, 131, 195, 138, 202, 157, 221, 174, 238, 182, 246, 166, 230, 148, 212, 134, 198, 147, 211, 165, 229, 181, 245, 191, 255, 187, 251, 171, 235, 153, 217, 164, 228, 151, 215, 169, 233, 185, 249, 192, 256, 186, 250, 170, 234, 152, 216, 141, 205, 149, 213, 167, 231, 183, 247, 180, 244, 163, 227, 145, 209, 133, 197)(130, 194, 135, 199, 150, 214, 168, 232, 184, 248, 179, 243, 162, 226, 144, 208, 146, 210, 139, 203, 159, 223, 175, 239, 190, 254, 178, 242, 161, 225, 143, 207, 156, 220, 137, 201, 155, 219, 173, 237, 189, 253, 177, 241, 160, 224, 142, 206, 132, 196, 140, 204, 158, 222, 176, 240, 188, 252, 172, 236, 154, 218, 136, 200)
	L = (1, 132)(2, 129)(3, 139)(4, 141)(5, 144)(6, 130)(7, 151)(8, 153)(9, 131)(10, 158)(11, 149)(12, 147)(13, 156)(14, 148)(15, 133)(16, 152)(17, 160)(18, 134)(19, 137)(20, 143)(21, 135)(22, 138)(23, 140)(24, 136)(25, 142)(26, 145)(27, 169)(28, 164)(29, 175)(30, 167)(31, 165)(32, 170)(33, 171)(34, 166)(35, 179)(36, 146)(37, 150)(38, 154)(39, 155)(40, 185)(41, 159)(42, 161)(43, 162)(44, 187)(45, 157)(46, 188)(47, 183)(48, 181)(49, 182)(50, 163)(51, 186)(52, 189)(53, 173)(54, 178)(55, 168)(56, 174)(57, 176)(58, 172)(59, 177)(60, 180)(61, 192)(62, 191)(63, 184)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1525
Graph:: bipartite
	v = 10 e = 128 f = 66
	degree seq :: [ 16^8, 64^2 ]

E27.1522 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y1^-1 * Y2^-1 * Y1^-2 * Y3 * Y2, Y2^-1 * Y3 * Y2 * Y1^-3, Y1^-1 * Y2 * Y3 * Y2^-1 * Y1^-2, Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-2 * Y1^-1 * Y2^2 * Y1, Y2 * Y1^2 * Y3^-1 * Y2^-1 * Y1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y1^-1 * Y3)^4, Y2^-2 * Y3 * Y2^-6 * Y1^-1, (Y3 * Y2^-1)^32 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 18, 82, 36, 100, 28, 92, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 12, 76, 23, 87, 7, 71, 21, 85, 11, 75)(5, 69, 15, 79, 20, 84, 14, 78, 25, 89, 8, 72, 24, 88, 16, 80)(10, 74, 22, 86, 37, 101, 31, 95, 41, 105, 27, 91, 39, 103, 30, 94)(17, 81, 26, 90, 38, 102, 34, 98, 43, 107, 33, 97, 42, 106, 32, 96)(29, 93, 45, 109, 53, 117, 48, 112, 57, 121, 40, 104, 55, 119, 47, 111)(35, 99, 50, 114, 54, 118, 49, 113, 59, 123, 44, 108, 58, 122, 51, 115)(46, 110, 56, 120, 52, 116, 60, 124, 63, 127, 61, 125, 64, 128, 62, 126)(129, 193, 131, 195, 138, 202, 157, 221, 174, 238, 186, 250, 170, 234, 152, 216, 141, 205, 149, 213, 167, 231, 183, 247, 192, 256, 187, 251, 171, 235, 153, 217, 164, 228, 151, 215, 169, 233, 185, 249, 191, 255, 182, 246, 166, 230, 148, 212, 134, 198, 147, 211, 165, 229, 181, 245, 180, 244, 163, 227, 145, 209, 133, 197)(130, 194, 135, 199, 150, 214, 168, 232, 184, 248, 177, 241, 160, 224, 142, 206, 132, 196, 140, 204, 158, 222, 176, 240, 190, 254, 178, 242, 161, 225, 143, 207, 156, 220, 137, 201, 155, 219, 173, 237, 189, 253, 179, 243, 162, 226, 144, 208, 146, 210, 139, 203, 159, 223, 175, 239, 188, 252, 172, 236, 154, 218, 136, 200)
	L = (1, 132)(2, 129)(3, 139)(4, 141)(5, 144)(6, 130)(7, 151)(8, 153)(9, 131)(10, 158)(11, 149)(12, 147)(13, 156)(14, 148)(15, 133)(16, 152)(17, 160)(18, 134)(19, 137)(20, 143)(21, 135)(22, 138)(23, 140)(24, 136)(25, 142)(26, 145)(27, 169)(28, 164)(29, 175)(30, 167)(31, 165)(32, 170)(33, 171)(34, 166)(35, 179)(36, 146)(37, 150)(38, 154)(39, 155)(40, 185)(41, 159)(42, 161)(43, 162)(44, 187)(45, 157)(46, 190)(47, 183)(48, 181)(49, 182)(50, 163)(51, 186)(52, 184)(53, 173)(54, 178)(55, 168)(56, 174)(57, 176)(58, 172)(59, 177)(60, 180)(61, 191)(62, 192)(63, 188)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ), ( 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64, 2, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1526
Graph:: bipartite
	v = 10 e = 128 f = 66
	degree seq :: [ 16^8, 64^2 ]

E27.1523 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2^2 * Y1^-1 * Y2^-2 * Y1, (Y2^3 * Y1^-1)^2, (Y1^-1, Y2^-1, Y1^-1), Y2^-1 * Y1^-1 * Y2^-3 * Y1^-3, Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-3, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 18, 82, 42, 106, 30, 94, 10, 74, 22, 86, 46, 110, 40, 104, 55, 119, 39, 103, 54, 118, 63, 127, 60, 124, 33, 97, 53, 117, 28, 92, 50, 114, 62, 126, 59, 123, 31, 95, 52, 116, 27, 91, 49, 113, 38, 102, 17, 81, 26, 90, 48, 112, 35, 99, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 45, 109, 61, 125, 56, 120, 29, 93, 57, 121, 37, 101, 14, 78, 25, 89, 8, 72, 24, 88, 44, 108, 34, 98, 12, 76, 23, 87, 7, 71, 21, 85, 43, 107, 41, 105, 58, 122, 64, 128, 51, 115, 36, 100, 16, 80, 5, 69, 15, 79, 20, 84, 47, 111, 32, 96, 11, 75)(129, 193, 131, 195, 138, 202, 157, 221, 182, 246, 152, 216, 178, 242, 149, 213, 177, 241, 164, 228, 141, 205, 160, 224, 170, 234, 189, 253, 183, 247, 153, 217, 181, 245, 151, 215, 180, 244, 192, 256, 176, 240, 148, 212, 134, 198, 147, 211, 174, 238, 165, 229, 188, 252, 162, 226, 187, 251, 169, 233, 145, 209, 133, 197)(130, 194, 135, 199, 150, 214, 179, 243, 191, 255, 175, 239, 190, 254, 173, 237, 166, 230, 142, 206, 132, 196, 140, 204, 158, 222, 186, 250, 167, 231, 143, 207, 156, 220, 137, 201, 155, 219, 185, 249, 163, 227, 172, 236, 146, 210, 171, 235, 168, 232, 144, 208, 161, 225, 139, 203, 159, 223, 184, 248, 154, 218, 136, 200)
	L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 155)(10, 157)(11, 159)(12, 158)(13, 160)(14, 132)(15, 156)(16, 161)(17, 133)(18, 171)(19, 174)(20, 134)(21, 177)(22, 179)(23, 180)(24, 178)(25, 181)(26, 136)(27, 185)(28, 137)(29, 182)(30, 186)(31, 184)(32, 170)(33, 139)(34, 187)(35, 172)(36, 141)(37, 188)(38, 142)(39, 143)(40, 144)(41, 145)(42, 189)(43, 168)(44, 146)(45, 166)(46, 165)(47, 190)(48, 148)(49, 164)(50, 149)(51, 191)(52, 192)(53, 151)(54, 152)(55, 153)(56, 154)(57, 163)(58, 167)(59, 169)(60, 162)(61, 183)(62, 173)(63, 175)(64, 176)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1524
Graph:: bipartite
	v = 4 e = 128 f = 72
	degree seq :: [ 64^4 ]

E27.1524 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-3 * Y3^-1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-2, Y3^2 * Y2^-1 * Y3^-2 * Y2, (Y3^-1, Y2^-1)^2, Y3^4 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2, (Y3^2 * Y2^2)^16, (Y3^-1 * Y1^-1)^32 ]
Map::
	R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194, 134, 198, 146, 210, 164, 228, 156, 220, 141, 205, 132, 196)(131, 195, 137, 201, 147, 211, 140, 204, 151, 215, 135, 199, 149, 213, 139, 203)(133, 197, 143, 207, 148, 212, 142, 206, 153, 217, 136, 200, 152, 216, 144, 208)(138, 202, 150, 214, 165, 229, 159, 223, 169, 233, 155, 219, 167, 231, 158, 222)(145, 209, 154, 218, 166, 230, 162, 226, 171, 235, 161, 225, 170, 234, 160, 224)(157, 221, 173, 237, 181, 245, 176, 240, 185, 249, 168, 232, 183, 247, 175, 239)(163, 227, 178, 242, 182, 246, 177, 241, 187, 251, 172, 236, 186, 250, 179, 243)(174, 238, 184, 248, 191, 255, 190, 254, 192, 256, 189, 253, 180, 244, 188, 252)
	L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 155)(10, 157)(11, 159)(12, 158)(13, 149)(14, 132)(15, 156)(16, 146)(17, 133)(18, 139)(19, 165)(20, 134)(21, 167)(22, 168)(23, 169)(24, 141)(25, 164)(26, 136)(27, 173)(28, 137)(29, 174)(30, 176)(31, 175)(32, 142)(33, 143)(34, 144)(35, 145)(36, 151)(37, 181)(38, 148)(39, 183)(40, 184)(41, 185)(42, 152)(43, 153)(44, 154)(45, 189)(46, 182)(47, 190)(48, 188)(49, 160)(50, 161)(51, 162)(52, 163)(53, 191)(54, 166)(55, 180)(56, 179)(57, 192)(58, 170)(59, 171)(60, 172)(61, 177)(62, 178)(63, 187)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 64, 64 ), ( 64^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1523
Graph:: simple bipartite
	v = 72 e = 128 f = 4
	degree seq :: [ 2^64, 16^8 ]

E27.1525 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-3 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1 * Y3, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y1, Y3^-1)^2, Y1^-3 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-3, (Y3 * Y2^-1)^8, (Y3^2 * Y1^-2)^16 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 18, 82, 36, 100, 53, 117, 46, 110, 29, 93, 17, 81, 26, 90, 42, 106, 59, 123, 63, 127, 62, 126, 48, 112, 31, 95, 44, 108, 27, 91, 43, 107, 60, 124, 64, 128, 61, 125, 45, 109, 28, 92, 10, 74, 22, 86, 40, 104, 57, 121, 50, 114, 33, 97, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 39, 103, 54, 118, 52, 116, 34, 98, 16, 80, 5, 69, 15, 79, 20, 84, 41, 105, 55, 119, 49, 113, 32, 96, 12, 76, 23, 87, 7, 71, 21, 85, 37, 101, 56, 120, 51, 115, 35, 99, 14, 78, 25, 89, 8, 72, 24, 88, 38, 102, 58, 122, 47, 111, 30, 94, 11, 75)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256)
	L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 154)(10, 153)(11, 157)(12, 156)(13, 158)(14, 132)(15, 155)(16, 159)(17, 133)(18, 165)(19, 168)(20, 134)(21, 170)(22, 143)(23, 145)(24, 171)(25, 172)(26, 136)(27, 137)(28, 144)(29, 142)(30, 173)(31, 139)(32, 174)(33, 177)(34, 141)(35, 176)(36, 182)(37, 185)(38, 146)(39, 187)(40, 152)(41, 188)(42, 148)(43, 149)(44, 151)(45, 163)(46, 162)(47, 181)(48, 160)(49, 189)(50, 186)(51, 161)(52, 190)(53, 179)(54, 178)(55, 164)(56, 191)(57, 169)(58, 192)(59, 166)(60, 167)(61, 180)(62, 175)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1521
Graph:: simple bipartite
	v = 66 e = 128 f = 10
	degree seq :: [ 2^64, 64^2 ]

E27.1526 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 32, 32})
Quotient :: dipole
Aut^+ = C32 : C2 (small group id <64, 51>)
Aut   = $<128, 995>$ (small group id <128, 995>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-2 * Y1 * Y3^2, Y1^-1 * Y3^3 * Y1 * Y3, Y3^-1 * Y1 * Y3^-3 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5 * Y3^-1 * Y1^-3, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-4, (Y3 * Y2^-1)^8, (Y3^2 * Y1^-2)^16 ]
Map::
	R = (1, 65, 2, 66, 6, 70, 18, 82, 36, 100, 53, 117, 45, 109, 28, 92, 10, 74, 22, 86, 40, 104, 57, 121, 63, 127, 62, 126, 48, 112, 31, 95, 44, 108, 27, 91, 43, 107, 60, 124, 64, 128, 61, 125, 46, 110, 29, 93, 17, 81, 26, 90, 42, 106, 59, 123, 50, 114, 33, 97, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 39, 103, 54, 118, 51, 115, 35, 99, 14, 78, 25, 89, 8, 72, 24, 88, 38, 102, 58, 122, 49, 113, 32, 96, 12, 76, 23, 87, 7, 71, 21, 85, 37, 101, 56, 120, 52, 116, 34, 98, 16, 80, 5, 69, 15, 79, 20, 84, 41, 105, 55, 119, 47, 111, 30, 94, 11, 75)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256)
	L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 154)(10, 153)(11, 157)(12, 156)(13, 158)(14, 132)(15, 155)(16, 159)(17, 133)(18, 165)(19, 168)(20, 134)(21, 170)(22, 143)(23, 145)(24, 171)(25, 172)(26, 136)(27, 137)(28, 144)(29, 142)(30, 173)(31, 139)(32, 174)(33, 177)(34, 141)(35, 176)(36, 182)(37, 185)(38, 146)(39, 187)(40, 152)(41, 188)(42, 148)(43, 149)(44, 151)(45, 163)(46, 162)(47, 189)(48, 160)(49, 181)(50, 183)(51, 161)(52, 190)(53, 180)(54, 191)(55, 164)(56, 178)(57, 169)(58, 192)(59, 166)(60, 167)(61, 179)(62, 175)(63, 186)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)
	local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64, 16, 64 ) }
Outer automorphisms :: reflexible
Dual of E27.1522
Graph:: simple bipartite
	v = 66 e = 128 f = 10
	degree seq :: [ 2^64, 64^2 ]

E27.1527 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 33, 66})
Quotient :: edge
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^6, T1^-2 * T2^11 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 31, 43, 55, 52, 40, 28, 16, 6, 15, 27, 39, 51, 63, 65, 58, 46, 34, 22, 11, 21, 33, 45, 57, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 64, 62, 50, 38, 26, 14, 25, 37, 49, 61, 66, 59, 47, 35, 23, 12, 4, 10, 20, 32, 44, 56, 54, 42, 30, 18, 8)(67, 68, 72, 80, 77, 70)(69, 73, 81, 91, 87, 76)(71, 74, 82, 92, 88, 78)(75, 83, 93, 103, 99, 86)(79, 84, 94, 104, 100, 89)(85, 95, 105, 115, 111, 98)(90, 96, 106, 116, 112, 101)(97, 107, 117, 127, 123, 110)(102, 108, 118, 128, 124, 113)(109, 119, 129, 132, 126, 122)(114, 120, 121, 130, 131, 125)
	L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 132^6 ), ( 132^33 ) }
Outer automorphisms :: reflexible
Dual of E27.1531
Transitivity :: ET+
Graph:: bipartite
	v = 13 e = 66 f = 1
	degree seq :: [ 6^11, 33^2 ]

E27.1528 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 33, 66})
Quotient :: edge
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^2 * T2^2 * T1^-2 * T2^-2, T2^-10 * T1, T1^5 * T2^-1 * T1 * T2^-3 * T1, (T1^-1 * T2^-1)^6 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 51, 50, 32, 18, 8, 2, 7, 17, 31, 49, 66, 56, 48, 30, 16, 6, 15, 29, 47, 65, 57, 37, 55, 46, 28, 14, 27, 45, 64, 58, 38, 22, 36, 54, 44, 26, 43, 63, 59, 39, 23, 11, 21, 35, 53, 42, 62, 60, 40, 24, 12, 4, 10, 20, 34, 52, 61, 41, 25, 13, 5)(67, 68, 72, 80, 92, 108, 118, 99, 115, 131, 124, 105, 90, 79, 84, 96, 112, 120, 101, 86, 75, 83, 95, 111, 129, 126, 107, 116, 122, 103, 88, 77, 70)(69, 73, 81, 93, 109, 128, 127, 117, 132, 123, 104, 89, 78, 71, 74, 82, 94, 110, 119, 100, 85, 97, 113, 130, 125, 106, 91, 98, 114, 121, 102, 87, 76)
	L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 12^33 ), ( 12^66 ) }
Outer automorphisms :: reflexible
Dual of E27.1532
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 66 f = 11
	degree seq :: [ 33^2, 66 ]

E27.1529 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 33, 66})
Quotient :: edge
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^6, T1^-11 * T2^-1, T1^3 * T2^-1 * T1^4 * T2^-1 * T1^3 * T2^3 * T1, T2^2 * T1^-1 * T2 * T1^-4 * T2^3 * T1^5, (T1^-1 * T2^-1)^33 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 13, 5)(2, 7, 17, 30, 18, 8)(4, 10, 20, 31, 24, 12)(6, 15, 28, 42, 29, 16)(11, 21, 32, 43, 36, 23)(14, 26, 40, 54, 41, 27)(22, 33, 44, 55, 48, 35)(25, 38, 52, 62, 53, 39)(34, 45, 56, 63, 58, 47)(37, 50, 60, 66, 61, 51)(46, 57, 64, 65, 59, 49)(67, 68, 72, 80, 91, 103, 115, 113, 101, 89, 78, 71, 74, 82, 93, 105, 117, 125, 124, 114, 102, 90, 79, 84, 95, 107, 119, 127, 131, 129, 121, 109, 97, 85, 96, 108, 120, 128, 132, 130, 122, 110, 98, 86, 75, 83, 94, 106, 118, 126, 123, 111, 99, 87, 76, 69, 73, 81, 92, 104, 116, 112, 100, 88, 77, 70)
	L = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)
	local type(s) :: { ( 66^6 ), ( 66^66 ) }
Outer automorphisms :: reflexible
Dual of E27.1530
Transitivity :: ET+
Graph:: bipartite
	v = 12 e = 66 f = 2
	degree seq :: [ 6^11, 66 ]

E27.1530 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 33, 66})
Quotient :: loop
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^6, T1^-2 * T2^11 ]
Map:: non-degenerate
	R = (1, 67, 3, 69, 9, 75, 19, 85, 31, 97, 43, 109, 55, 121, 52, 118, 40, 106, 28, 94, 16, 82, 6, 72, 15, 81, 27, 93, 39, 105, 51, 117, 63, 129, 65, 131, 58, 124, 46, 112, 34, 100, 22, 88, 11, 77, 21, 87, 33, 99, 45, 111, 57, 123, 60, 126, 48, 114, 36, 102, 24, 90, 13, 79, 5, 71)(2, 68, 7, 73, 17, 83, 29, 95, 41, 107, 53, 119, 64, 130, 62, 128, 50, 116, 38, 104, 26, 92, 14, 80, 25, 91, 37, 103, 49, 115, 61, 127, 66, 132, 59, 125, 47, 113, 35, 101, 23, 89, 12, 78, 4, 70, 10, 76, 20, 86, 32, 98, 44, 110, 56, 122, 54, 120, 42, 108, 30, 96, 18, 84, 8, 74)
	L = (1, 68)(2, 72)(3, 73)(4, 67)(5, 74)(6, 80)(7, 81)(8, 82)(9, 83)(10, 69)(11, 70)(12, 71)(13, 84)(14, 77)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 75)(21, 76)(22, 78)(23, 79)(24, 96)(25, 87)(26, 88)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 85)(33, 86)(34, 89)(35, 90)(36, 108)(37, 99)(38, 100)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 97)(45, 98)(46, 101)(47, 102)(48, 120)(49, 111)(50, 112)(51, 127)(52, 128)(53, 129)(54, 121)(55, 130)(56, 109)(57, 110)(58, 113)(59, 114)(60, 122)(61, 123)(62, 124)(63, 132)(64, 131)(65, 125)(66, 126)
	local type(s) :: { ( 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66, 6, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.1529
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 66 f = 12
	degree seq :: [ 66^2 ]

E27.1531 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 33, 66})
Quotient :: loop
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^2 * T2^2 * T1^-2 * T2^-2, T2^-10 * T1, T1^5 * T2^-1 * T1 * T2^-3 * T1, (T1^-1 * T2^-1)^6 ]
Map:: non-degenerate
	R = (1, 67, 3, 69, 9, 75, 19, 85, 33, 99, 51, 117, 50, 116, 32, 98, 18, 84, 8, 74, 2, 68, 7, 73, 17, 83, 31, 97, 49, 115, 66, 132, 56, 122, 48, 114, 30, 96, 16, 82, 6, 72, 15, 81, 29, 95, 47, 113, 65, 131, 57, 123, 37, 103, 55, 121, 46, 112, 28, 94, 14, 80, 27, 93, 45, 111, 64, 130, 58, 124, 38, 104, 22, 88, 36, 102, 54, 120, 44, 110, 26, 92, 43, 109, 63, 129, 59, 125, 39, 105, 23, 89, 11, 77, 21, 87, 35, 101, 53, 119, 42, 108, 62, 128, 60, 126, 40, 106, 24, 90, 12, 78, 4, 70, 10, 76, 20, 86, 34, 100, 52, 118, 61, 127, 41, 107, 25, 91, 13, 79, 5, 71)
	L = (1, 68)(2, 72)(3, 73)(4, 67)(5, 74)(6, 80)(7, 81)(8, 82)(9, 83)(10, 69)(11, 70)(12, 71)(13, 84)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 98)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 115)(34, 85)(35, 86)(36, 87)(37, 88)(38, 89)(39, 90)(40, 91)(41, 116)(42, 118)(43, 128)(44, 119)(45, 129)(46, 120)(47, 130)(48, 121)(49, 131)(50, 122)(51, 132)(52, 99)(53, 100)(54, 101)(55, 102)(56, 103)(57, 104)(58, 105)(59, 106)(60, 107)(61, 117)(62, 127)(63, 126)(64, 125)(65, 124)(66, 123)
	local type(s) :: { ( 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33, 6, 33 ) }
Outer automorphisms :: reflexible
Dual of E27.1527
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 66 f = 13
	degree seq :: [ 132 ]

E27.1532 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 33, 66})
Quotient :: loop
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^6, T1^-11 * T2^-1, T1^3 * T2^-1 * T1^4 * T2^-1 * T1^3 * T2^3 * T1, T2^2 * T1^-1 * T2 * T1^-4 * T2^3 * T1^5, (T1^-1 * T2^-1)^33 ]
Map:: non-degenerate
	R = (1, 67, 3, 69, 9, 75, 19, 85, 13, 79, 5, 71)(2, 68, 7, 73, 17, 83, 30, 96, 18, 84, 8, 74)(4, 70, 10, 76, 20, 86, 31, 97, 24, 90, 12, 78)(6, 72, 15, 81, 28, 94, 42, 108, 29, 95, 16, 82)(11, 77, 21, 87, 32, 98, 43, 109, 36, 102, 23, 89)(14, 80, 26, 92, 40, 106, 54, 120, 41, 107, 27, 93)(22, 88, 33, 99, 44, 110, 55, 121, 48, 114, 35, 101)(25, 91, 38, 104, 52, 118, 62, 128, 53, 119, 39, 105)(34, 100, 45, 111, 56, 122, 63, 129, 58, 124, 47, 113)(37, 103, 50, 116, 60, 126, 66, 132, 61, 127, 51, 117)(46, 112, 57, 123, 64, 130, 65, 131, 59, 125, 49, 115)
	L = (1, 68)(2, 72)(3, 73)(4, 67)(5, 74)(6, 80)(7, 81)(8, 82)(9, 83)(10, 69)(11, 70)(12, 71)(13, 84)(14, 91)(15, 92)(16, 93)(17, 94)(18, 95)(19, 96)(20, 75)(21, 76)(22, 77)(23, 78)(24, 79)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 97)(44, 98)(45, 99)(46, 100)(47, 101)(48, 102)(49, 113)(50, 112)(51, 125)(52, 126)(53, 127)(54, 128)(55, 109)(56, 110)(57, 111)(58, 114)(59, 124)(60, 123)(61, 131)(62, 132)(63, 121)(64, 122)(65, 129)(66, 130)
	local type(s) :: { ( 33, 66, 33, 66, 33, 66, 33, 66, 33, 66, 33, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.1528
Transitivity :: ET+ VT+ AT
Graph::
	v = 11 e = 66 f = 3
	degree seq :: [ 12^11 ]

E27.1533 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^6, Y3^6, Y2^-11 * Y1^2 ]
Map::
	R = (1, 67, 2, 68, 6, 72, 14, 80, 11, 77, 4, 70)(3, 69, 7, 73, 15, 81, 25, 91, 21, 87, 10, 76)(5, 71, 8, 74, 16, 82, 26, 92, 22, 88, 12, 78)(9, 75, 17, 83, 27, 93, 37, 103, 33, 99, 20, 86)(13, 79, 18, 84, 28, 94, 38, 104, 34, 100, 23, 89)(19, 85, 29, 95, 39, 105, 49, 115, 45, 111, 32, 98)(24, 90, 30, 96, 40, 106, 50, 116, 46, 112, 35, 101)(31, 97, 41, 107, 51, 117, 61, 127, 57, 123, 44, 110)(36, 102, 42, 108, 52, 118, 62, 128, 58, 124, 47, 113)(43, 109, 53, 119, 63, 129, 66, 132, 60, 126, 56, 122)(48, 114, 54, 120, 55, 121, 64, 130, 65, 131, 59, 125)(133, 199, 135, 201, 141, 207, 151, 217, 163, 229, 175, 241, 187, 253, 184, 250, 172, 238, 160, 226, 148, 214, 138, 204, 147, 213, 159, 225, 171, 237, 183, 249, 195, 261, 197, 263, 190, 256, 178, 244, 166, 232, 154, 220, 143, 209, 153, 219, 165, 231, 177, 243, 189, 255, 192, 258, 180, 246, 168, 234, 156, 222, 145, 211, 137, 203)(134, 200, 139, 205, 149, 215, 161, 227, 173, 239, 185, 251, 196, 262, 194, 260, 182, 248, 170, 236, 158, 224, 146, 212, 157, 223, 169, 235, 181, 247, 193, 259, 198, 264, 191, 257, 179, 245, 167, 233, 155, 221, 144, 210, 136, 202, 142, 208, 152, 218, 164, 230, 176, 242, 188, 254, 186, 252, 174, 240, 162, 228, 150, 216, 140, 206)
	L = (1, 136)(2, 133)(3, 142)(4, 143)(5, 144)(6, 134)(7, 135)(8, 137)(9, 152)(10, 153)(11, 146)(12, 154)(13, 155)(14, 138)(15, 139)(16, 140)(17, 141)(18, 145)(19, 164)(20, 165)(21, 157)(22, 158)(23, 166)(24, 167)(25, 147)(26, 148)(27, 149)(28, 150)(29, 151)(30, 156)(31, 176)(32, 177)(33, 169)(34, 170)(35, 178)(36, 179)(37, 159)(38, 160)(39, 161)(40, 162)(41, 163)(42, 168)(43, 188)(44, 189)(45, 181)(46, 182)(47, 190)(48, 191)(49, 171)(50, 172)(51, 173)(52, 174)(53, 175)(54, 180)(55, 186)(56, 192)(57, 193)(58, 194)(59, 197)(60, 198)(61, 183)(62, 184)(63, 185)(64, 187)(65, 196)(66, 195)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132 ), ( 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132, 2, 132 ) }
Outer automorphisms :: reflexible
Dual of E27.1536
Graph:: bipartite
	v = 13 e = 132 f = 67
	degree seq :: [ 12^11, 66^2 ]

E27.1534 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), Y1 * Y2^-10, Y1^4 * Y2^-1 * Y1^3 * Y2^-3, (Y3^-1 * Y1^-1)^6, Y1^33 ]
Map::
	R = (1, 67, 2, 68, 6, 72, 14, 80, 26, 92, 42, 108, 52, 118, 33, 99, 49, 115, 65, 131, 58, 124, 39, 105, 24, 90, 13, 79, 18, 84, 30, 96, 46, 112, 54, 120, 35, 101, 20, 86, 9, 75, 17, 83, 29, 95, 45, 111, 63, 129, 60, 126, 41, 107, 50, 116, 56, 122, 37, 103, 22, 88, 11, 77, 4, 70)(3, 69, 7, 73, 15, 81, 27, 93, 43, 109, 62, 128, 61, 127, 51, 117, 66, 132, 57, 123, 38, 104, 23, 89, 12, 78, 5, 71, 8, 74, 16, 82, 28, 94, 44, 110, 53, 119, 34, 100, 19, 85, 31, 97, 47, 113, 64, 130, 59, 125, 40, 106, 25, 91, 32, 98, 48, 114, 55, 121, 36, 102, 21, 87, 10, 76)(133, 199, 135, 201, 141, 207, 151, 217, 165, 231, 183, 249, 182, 248, 164, 230, 150, 216, 140, 206, 134, 200, 139, 205, 149, 215, 163, 229, 181, 247, 198, 264, 188, 254, 180, 246, 162, 228, 148, 214, 138, 204, 147, 213, 161, 227, 179, 245, 197, 263, 189, 255, 169, 235, 187, 253, 178, 244, 160, 226, 146, 212, 159, 225, 177, 243, 196, 262, 190, 256, 170, 236, 154, 220, 168, 234, 186, 252, 176, 242, 158, 224, 175, 241, 195, 261, 191, 257, 171, 237, 155, 221, 143, 209, 153, 219, 167, 233, 185, 251, 174, 240, 194, 260, 192, 258, 172, 238, 156, 222, 144, 210, 136, 202, 142, 208, 152, 218, 166, 232, 184, 250, 193, 259, 173, 239, 157, 223, 145, 211, 137, 203)
	L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 152)(11, 153)(12, 136)(13, 137)(14, 159)(15, 161)(16, 138)(17, 163)(18, 140)(19, 165)(20, 166)(21, 167)(22, 168)(23, 143)(24, 144)(25, 145)(26, 175)(27, 177)(28, 146)(29, 179)(30, 148)(31, 181)(32, 150)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 154)(39, 155)(40, 156)(41, 157)(42, 194)(43, 195)(44, 158)(45, 196)(46, 160)(47, 197)(48, 162)(49, 198)(50, 164)(51, 182)(52, 193)(53, 174)(54, 176)(55, 178)(56, 180)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 192)(63, 191)(64, 190)(65, 189)(66, 188)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1535
Graph:: bipartite
	v = 3 e = 132 f = 77
	degree seq :: [ 66^2, 132 ]

E27.1535 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^6, Y2^-1 * Y3^11, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^66 ]
Map::
	R = (1, 67)(2, 68)(3, 69)(4, 70)(5, 71)(6, 72)(7, 73)(8, 74)(9, 75)(10, 76)(11, 77)(12, 78)(13, 79)(14, 80)(15, 81)(16, 82)(17, 83)(18, 84)(19, 85)(20, 86)(21, 87)(22, 88)(23, 89)(24, 90)(25, 91)(26, 92)(27, 93)(28, 94)(29, 95)(30, 96)(31, 97)(32, 98)(33, 99)(34, 100)(35, 101)(36, 102)(37, 103)(38, 104)(39, 105)(40, 106)(41, 107)(42, 108)(43, 109)(44, 110)(45, 111)(46, 112)(47, 113)(48, 114)(49, 115)(50, 116)(51, 117)(52, 118)(53, 119)(54, 120)(55, 121)(56, 122)(57, 123)(58, 124)(59, 125)(60, 126)(61, 127)(62, 128)(63, 129)(64, 130)(65, 131)(66, 132)(133, 199, 134, 200, 138, 204, 146, 212, 143, 209, 136, 202)(135, 201, 139, 205, 147, 213, 157, 223, 153, 219, 142, 208)(137, 203, 140, 206, 148, 214, 158, 224, 154, 220, 144, 210)(141, 207, 149, 215, 159, 225, 169, 235, 165, 231, 152, 218)(145, 211, 150, 216, 160, 226, 170, 236, 166, 232, 155, 221)(151, 217, 161, 227, 171, 237, 181, 247, 177, 243, 164, 230)(156, 222, 162, 228, 172, 238, 182, 248, 178, 244, 167, 233)(163, 229, 173, 239, 183, 249, 191, 257, 188, 254, 176, 242)(168, 234, 174, 240, 184, 250, 192, 258, 189, 255, 179, 245)(175, 241, 185, 251, 193, 259, 197, 263, 195, 261, 187, 253)(180, 246, 186, 252, 194, 260, 198, 264, 196, 262, 190, 256)
	L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 152)(11, 153)(12, 136)(13, 137)(14, 157)(15, 159)(16, 138)(17, 161)(18, 140)(19, 163)(20, 164)(21, 165)(22, 143)(23, 144)(24, 145)(25, 169)(26, 146)(27, 171)(28, 148)(29, 173)(30, 150)(31, 175)(32, 176)(33, 177)(34, 154)(35, 155)(36, 156)(37, 181)(38, 158)(39, 183)(40, 160)(41, 185)(42, 162)(43, 186)(44, 187)(45, 188)(46, 166)(47, 167)(48, 168)(49, 191)(50, 170)(51, 193)(52, 172)(53, 194)(54, 174)(55, 180)(56, 195)(57, 178)(58, 179)(59, 197)(60, 182)(61, 198)(62, 184)(63, 190)(64, 189)(65, 196)(66, 192)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 66, 132 ), ( 66, 132, 66, 132, 66, 132, 66, 132, 66, 132, 66, 132 ) }
Outer automorphisms :: reflexible
Dual of E27.1534
Graph:: simple bipartite
	v = 77 e = 132 f = 3
	degree seq :: [ 2^66, 12^11 ]

E27.1536 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3 * Y1^3 * Y3^-1 * Y1^-3, Y1^-3 * Y3^-1 * Y1^-8, (Y3 * Y2^-1)^6, Y1^3 * Y3^-1 * Y1^4 * Y3^-1 * Y1^3 * Y3^-3 * Y1, (Y1^-1 * Y3^-1)^33 ]
Map::
	R = (1, 67, 2, 68, 6, 72, 14, 80, 25, 91, 37, 103, 49, 115, 47, 113, 35, 101, 23, 89, 12, 78, 5, 71, 8, 74, 16, 82, 27, 93, 39, 105, 51, 117, 59, 125, 58, 124, 48, 114, 36, 102, 24, 90, 13, 79, 18, 84, 29, 95, 41, 107, 53, 119, 61, 127, 65, 131, 63, 129, 55, 121, 43, 109, 31, 97, 19, 85, 30, 96, 42, 108, 54, 120, 62, 128, 66, 132, 64, 130, 56, 122, 44, 110, 32, 98, 20, 86, 9, 75, 17, 83, 28, 94, 40, 106, 52, 118, 60, 126, 57, 123, 45, 111, 33, 99, 21, 87, 10, 76, 3, 69, 7, 73, 15, 81, 26, 92, 38, 104, 50, 116, 46, 112, 34, 100, 22, 88, 11, 77, 4, 70)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264)
	L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 152)(11, 153)(12, 136)(13, 137)(14, 158)(15, 160)(16, 138)(17, 162)(18, 140)(19, 145)(20, 163)(21, 164)(22, 165)(23, 143)(24, 144)(25, 170)(26, 172)(27, 146)(28, 174)(29, 148)(30, 150)(31, 156)(32, 175)(33, 176)(34, 177)(35, 154)(36, 155)(37, 182)(38, 184)(39, 157)(40, 186)(41, 159)(42, 161)(43, 168)(44, 187)(45, 188)(46, 189)(47, 166)(48, 167)(49, 178)(50, 192)(51, 169)(52, 194)(53, 171)(54, 173)(55, 180)(56, 195)(57, 196)(58, 179)(59, 181)(60, 198)(61, 183)(62, 185)(63, 190)(64, 197)(65, 191)(66, 193)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 12, 66 ), ( 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66, 12, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.1533
Graph:: bipartite
	v = 67 e = 132 f = 13
	degree seq :: [ 2^66, 132 ]

E27.1537 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y1^6, Y3 * Y2^-3 * Y3^-1 * Y1 * Y2^3 * Y3, Y2^-11 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 67, 2, 68, 6, 72, 14, 80, 11, 77, 4, 70)(3, 69, 7, 73, 15, 81, 25, 91, 21, 87, 10, 76)(5, 71, 8, 74, 16, 82, 26, 92, 22, 88, 12, 78)(9, 75, 17, 83, 27, 93, 37, 103, 33, 99, 20, 86)(13, 79, 18, 84, 28, 94, 38, 104, 34, 100, 23, 89)(19, 85, 29, 95, 39, 105, 49, 115, 45, 111, 32, 98)(24, 90, 30, 96, 40, 106, 50, 116, 46, 112, 35, 101)(31, 97, 41, 107, 51, 117, 59, 125, 57, 123, 44, 110)(36, 102, 42, 108, 52, 118, 60, 126, 58, 124, 47, 113)(43, 109, 53, 119, 61, 127, 65, 131, 64, 130, 56, 122)(48, 114, 54, 120, 62, 128, 66, 132, 63, 129, 55, 121)(133, 199, 135, 201, 141, 207, 151, 217, 163, 229, 175, 241, 187, 253, 179, 245, 167, 233, 155, 221, 144, 210, 136, 202, 142, 208, 152, 218, 164, 230, 176, 242, 188, 254, 195, 261, 190, 256, 178, 244, 166, 232, 154, 220, 143, 209, 153, 219, 165, 231, 177, 243, 189, 255, 196, 262, 198, 264, 192, 258, 182, 248, 170, 236, 158, 224, 146, 212, 157, 223, 169, 235, 181, 247, 191, 257, 197, 263, 194, 260, 184, 250, 172, 238, 160, 226, 148, 214, 138, 204, 147, 213, 159, 225, 171, 237, 183, 249, 193, 259, 186, 252, 174, 240, 162, 228, 150, 216, 140, 206, 134, 200, 139, 205, 149, 215, 161, 227, 173, 239, 185, 251, 180, 246, 168, 234, 156, 222, 145, 211, 137, 203)
	L = (1, 136)(2, 133)(3, 142)(4, 143)(5, 144)(6, 134)(7, 135)(8, 137)(9, 152)(10, 153)(11, 146)(12, 154)(13, 155)(14, 138)(15, 139)(16, 140)(17, 141)(18, 145)(19, 164)(20, 165)(21, 157)(22, 158)(23, 166)(24, 167)(25, 147)(26, 148)(27, 149)(28, 150)(29, 151)(30, 156)(31, 176)(32, 177)(33, 169)(34, 170)(35, 178)(36, 179)(37, 159)(38, 160)(39, 161)(40, 162)(41, 163)(42, 168)(43, 188)(44, 189)(45, 181)(46, 182)(47, 190)(48, 187)(49, 171)(50, 172)(51, 173)(52, 174)(53, 175)(54, 180)(55, 195)(56, 196)(57, 191)(58, 192)(59, 183)(60, 184)(61, 185)(62, 186)(63, 198)(64, 197)(65, 193)(66, 194)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ), ( 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66, 2, 66 ) }
Outer automorphisms :: reflexible
Dual of E27.1538
Graph:: bipartite
	v = 12 e = 132 f = 68
	degree seq :: [ 12^11, 132 ]

E27.1538 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 33, 66})
Quotient :: dipole
Aut^+ = C66 (small group id <66, 4>)
Aut   = D132 (small group id <132, 9>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^7 * Y3^-4, Y3^-10 * Y1, (Y1^-1 * Y3^-1)^6, (Y3 * Y2^-1)^66 ]
Map::
	R = (1, 67, 2, 68, 6, 72, 14, 80, 26, 92, 42, 108, 52, 118, 33, 99, 49, 115, 65, 131, 58, 124, 39, 105, 24, 90, 13, 79, 18, 84, 30, 96, 46, 112, 54, 120, 35, 101, 20, 86, 9, 75, 17, 83, 29, 95, 45, 111, 63, 129, 60, 126, 41, 107, 50, 116, 56, 122, 37, 103, 22, 88, 11, 77, 4, 70)(3, 69, 7, 73, 15, 81, 27, 93, 43, 109, 62, 128, 61, 127, 51, 117, 66, 132, 57, 123, 38, 104, 23, 89, 12, 78, 5, 71, 8, 74, 16, 82, 28, 94, 44, 110, 53, 119, 34, 100, 19, 85, 31, 97, 47, 113, 64, 130, 59, 125, 40, 106, 25, 91, 32, 98, 48, 114, 55, 121, 36, 102, 21, 87, 10, 76)(133, 199)(134, 200)(135, 201)(136, 202)(137, 203)(138, 204)(139, 205)(140, 206)(141, 207)(142, 208)(143, 209)(144, 210)(145, 211)(146, 212)(147, 213)(148, 214)(149, 215)(150, 216)(151, 217)(152, 218)(153, 219)(154, 220)(155, 221)(156, 222)(157, 223)(158, 224)(159, 225)(160, 226)(161, 227)(162, 228)(163, 229)(164, 230)(165, 231)(166, 232)(167, 233)(168, 234)(169, 235)(170, 236)(171, 237)(172, 238)(173, 239)(174, 240)(175, 241)(176, 242)(177, 243)(178, 244)(179, 245)(180, 246)(181, 247)(182, 248)(183, 249)(184, 250)(185, 251)(186, 252)(187, 253)(188, 254)(189, 255)(190, 256)(191, 257)(192, 258)(193, 259)(194, 260)(195, 261)(196, 262)(197, 263)(198, 264)
	L = (1, 135)(2, 139)(3, 141)(4, 142)(5, 133)(6, 147)(7, 149)(8, 134)(9, 151)(10, 152)(11, 153)(12, 136)(13, 137)(14, 159)(15, 161)(16, 138)(17, 163)(18, 140)(19, 165)(20, 166)(21, 167)(22, 168)(23, 143)(24, 144)(25, 145)(26, 175)(27, 177)(28, 146)(29, 179)(30, 148)(31, 181)(32, 150)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 154)(39, 155)(40, 156)(41, 157)(42, 194)(43, 195)(44, 158)(45, 196)(46, 160)(47, 197)(48, 162)(49, 198)(50, 164)(51, 182)(52, 193)(53, 174)(54, 176)(55, 178)(56, 180)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 192)(63, 191)(64, 190)(65, 189)(66, 188)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264)
	local type(s) :: { ( 12, 132 ), ( 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132, 12, 132 ) }
Outer automorphisms :: reflexible
Dual of E27.1537
Graph:: simple bipartite
	v = 68 e = 132 f = 12
	degree seq :: [ 2^66, 66^2 ]

E27.1539 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 10, 70})
Quotient :: edge
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T2^10 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 32, 46, 39, 25, 13, 5)(2, 7, 17, 30, 44, 57, 45, 31, 18, 8)(4, 10, 20, 33, 47, 58, 52, 38, 24, 12)(6, 15, 28, 42, 55, 65, 56, 43, 29, 16)(11, 21, 34, 48, 59, 66, 62, 51, 37, 23)(14, 26, 40, 53, 63, 69, 64, 54, 41, 27)(22, 35, 49, 60, 67, 70, 68, 61, 50, 36)(71, 72, 76, 84, 92, 81, 74)(73, 77, 85, 96, 105, 91, 80)(75, 78, 86, 97, 106, 93, 82)(79, 87, 98, 110, 119, 104, 90)(83, 88, 99, 111, 120, 107, 94)(89, 100, 112, 123, 130, 118, 103)(95, 101, 113, 124, 131, 121, 108)(102, 114, 125, 133, 137, 129, 117)(109, 115, 126, 134, 138, 132, 122)(116, 127, 135, 139, 140, 136, 128)
	L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 140^7 ), ( 140^10 ) }
Outer automorphisms :: reflexible
Dual of E27.1543
Transitivity :: ET+
Graph:: simple bipartite
	v = 17 e = 70 f = 1
	degree seq :: [ 7^10, 10^7 ]

E27.1540 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 10, 70})
Quotient :: edge
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^7 * T1^-3, T1^10, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 46, 28, 14, 27, 45, 61, 70, 64, 53, 37, 52, 63, 56, 40, 24, 12, 4, 10, 20, 34, 48, 30, 16, 6, 15, 29, 47, 62, 68, 58, 42, 57, 67, 66, 55, 39, 23, 11, 21, 35, 50, 32, 18, 8, 2, 7, 17, 31, 49, 60, 44, 26, 43, 59, 69, 65, 54, 38, 22, 36, 51, 41, 25, 13, 5)(71, 72, 76, 84, 96, 112, 107, 92, 81, 74)(73, 77, 85, 97, 113, 127, 122, 106, 91, 80)(75, 78, 86, 98, 114, 128, 123, 108, 93, 82)(79, 87, 99, 115, 129, 137, 133, 121, 105, 90)(83, 88, 100, 116, 130, 138, 134, 124, 109, 94)(89, 101, 117, 131, 139, 136, 126, 111, 120, 104)(95, 102, 118, 103, 119, 132, 140, 135, 125, 110)
	L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 14^10 ), ( 14^70 ) }
Outer automorphisms :: reflexible
Dual of E27.1544
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 70 f = 10
	degree seq :: [ 10^7, 70 ]

E27.1541 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 10, 70})
Quotient :: edge
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^7, T2^7, T1^10 * T2^3, T1^-1 * T2^-1 * T1^-1 * T2 * T1^5 * T2 * T1^-3 * T2^-1, T2 * T1^-1 * T2 * T1^-4 * T2^2 * T1^-5, (T1^-1 * T2^-1)^10 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 25, 13, 5)(2, 7, 17, 31, 32, 18, 8)(4, 10, 20, 33, 39, 24, 12)(6, 15, 29, 45, 46, 30, 16)(11, 21, 34, 47, 53, 38, 23)(14, 27, 43, 59, 60, 44, 28)(22, 35, 48, 61, 67, 52, 37)(26, 41, 57, 64, 70, 58, 42)(36, 49, 62, 68, 54, 66, 51)(40, 55, 65, 50, 63, 69, 56)(71, 72, 76, 84, 96, 110, 124, 137, 123, 109, 95, 102, 116, 130, 140, 133, 119, 105, 91, 80, 73, 77, 85, 97, 111, 125, 136, 122, 108, 94, 83, 88, 100, 114, 128, 139, 132, 118, 104, 90, 79, 87, 99, 113, 127, 135, 121, 107, 93, 82, 75, 78, 86, 98, 112, 126, 138, 131, 117, 103, 89, 101, 115, 129, 134, 120, 106, 92, 81, 74)
	L = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)
	local type(s) :: { ( 20^7 ), ( 20^70 ) }
Outer automorphisms :: reflexible
Dual of E27.1542
Transitivity :: ET+
Graph:: bipartite
	v = 11 e = 70 f = 7
	degree seq :: [ 7^10, 70 ]

E27.1542 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 10, 70})
Quotient :: loop
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^7, T2^10 ]
Map:: non-degenerate
	R = (1, 71, 3, 73, 9, 79, 19, 89, 32, 102, 46, 116, 39, 109, 25, 95, 13, 83, 5, 75)(2, 72, 7, 77, 17, 87, 30, 100, 44, 114, 57, 127, 45, 115, 31, 101, 18, 88, 8, 78)(4, 74, 10, 80, 20, 90, 33, 103, 47, 117, 58, 128, 52, 122, 38, 108, 24, 94, 12, 82)(6, 76, 15, 85, 28, 98, 42, 112, 55, 125, 65, 135, 56, 126, 43, 113, 29, 99, 16, 86)(11, 81, 21, 91, 34, 104, 48, 118, 59, 129, 66, 136, 62, 132, 51, 121, 37, 107, 23, 93)(14, 84, 26, 96, 40, 110, 53, 123, 63, 133, 69, 139, 64, 134, 54, 124, 41, 111, 27, 97)(22, 92, 35, 105, 49, 119, 60, 130, 67, 137, 70, 140, 68, 138, 61, 131, 50, 120, 36, 106)
	L = (1, 72)(2, 76)(3, 77)(4, 71)(5, 78)(6, 84)(7, 85)(8, 86)(9, 87)(10, 73)(11, 74)(12, 75)(13, 88)(14, 92)(15, 96)(16, 97)(17, 98)(18, 99)(19, 100)(20, 79)(21, 80)(22, 81)(23, 82)(24, 83)(25, 101)(26, 105)(27, 106)(28, 110)(29, 111)(30, 112)(31, 113)(32, 114)(33, 89)(34, 90)(35, 91)(36, 93)(37, 94)(38, 95)(39, 115)(40, 119)(41, 120)(42, 123)(43, 124)(44, 125)(45, 126)(46, 127)(47, 102)(48, 103)(49, 104)(50, 107)(51, 108)(52, 109)(53, 130)(54, 131)(55, 133)(56, 134)(57, 135)(58, 116)(59, 117)(60, 118)(61, 121)(62, 122)(63, 137)(64, 138)(65, 139)(66, 128)(67, 129)(68, 132)(69, 140)(70, 136)
	local type(s) :: { ( 7, 70, 7, 70, 7, 70, 7, 70, 7, 70, 7, 70, 7, 70, 7, 70, 7, 70, 7, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.1541
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 70 f = 11
	degree seq :: [ 20^7 ]

E27.1543 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 10, 70})
Quotient :: loop
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T2^7 * T1^-3, T1^10, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 71, 3, 73, 9, 79, 19, 89, 33, 103, 46, 116, 28, 98, 14, 84, 27, 97, 45, 115, 61, 131, 70, 140, 64, 134, 53, 123, 37, 107, 52, 122, 63, 133, 56, 126, 40, 110, 24, 94, 12, 82, 4, 74, 10, 80, 20, 90, 34, 104, 48, 118, 30, 100, 16, 86, 6, 76, 15, 85, 29, 99, 47, 117, 62, 132, 68, 138, 58, 128, 42, 112, 57, 127, 67, 137, 66, 136, 55, 125, 39, 109, 23, 93, 11, 81, 21, 91, 35, 105, 50, 120, 32, 102, 18, 88, 8, 78, 2, 72, 7, 77, 17, 87, 31, 101, 49, 119, 60, 130, 44, 114, 26, 96, 43, 113, 59, 129, 69, 139, 65, 135, 54, 124, 38, 108, 22, 92, 36, 106, 51, 121, 41, 111, 25, 95, 13, 83, 5, 75)
	L = (1, 72)(2, 76)(3, 77)(4, 71)(5, 78)(6, 84)(7, 85)(8, 86)(9, 87)(10, 73)(11, 74)(12, 75)(13, 88)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 79)(21, 80)(22, 81)(23, 82)(24, 83)(25, 102)(26, 112)(27, 113)(28, 114)(29, 115)(30, 116)(31, 117)(32, 118)(33, 119)(34, 89)(35, 90)(36, 91)(37, 92)(38, 93)(39, 94)(40, 95)(41, 120)(42, 107)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 103)(49, 132)(50, 104)(51, 105)(52, 106)(53, 108)(54, 109)(55, 110)(56, 111)(57, 122)(58, 123)(59, 137)(60, 138)(61, 139)(62, 140)(63, 121)(64, 124)(65, 125)(66, 126)(67, 133)(68, 134)(69, 136)(70, 135)
	local type(s) :: { ( 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10, 7, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.1539
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 70 f = 17
	degree seq :: [ 140 ]

E27.1544 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 10, 70})
Quotient :: loop
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^7, T2^7, T1^10 * T2^3, T1^-1 * T2^-1 * T1^-1 * T2 * T1^5 * T2 * T1^-3 * T2^-1, T2 * T1^-1 * T2 * T1^-4 * T2^2 * T1^-5, (T1^-1 * T2^-1)^10 ]
Map:: non-degenerate
	R = (1, 71, 3, 73, 9, 79, 19, 89, 25, 95, 13, 83, 5, 75)(2, 72, 7, 77, 17, 87, 31, 101, 32, 102, 18, 88, 8, 78)(4, 74, 10, 80, 20, 90, 33, 103, 39, 109, 24, 94, 12, 82)(6, 76, 15, 85, 29, 99, 45, 115, 46, 116, 30, 100, 16, 86)(11, 81, 21, 91, 34, 104, 47, 117, 53, 123, 38, 108, 23, 93)(14, 84, 27, 97, 43, 113, 59, 129, 60, 130, 44, 114, 28, 98)(22, 92, 35, 105, 48, 118, 61, 131, 67, 137, 52, 122, 37, 107)(26, 96, 41, 111, 57, 127, 64, 134, 70, 140, 58, 128, 42, 112)(36, 106, 49, 119, 62, 132, 68, 138, 54, 124, 66, 136, 51, 121)(40, 110, 55, 125, 65, 135, 50, 120, 63, 133, 69, 139, 56, 126)
	L = (1, 72)(2, 76)(3, 77)(4, 71)(5, 78)(6, 84)(7, 85)(8, 86)(9, 87)(10, 73)(11, 74)(12, 75)(13, 88)(14, 96)(15, 97)(16, 98)(17, 99)(18, 100)(19, 101)(20, 79)(21, 80)(22, 81)(23, 82)(24, 83)(25, 102)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 137)(55, 136)(56, 138)(57, 135)(58, 139)(59, 134)(60, 140)(61, 117)(62, 118)(63, 119)(64, 120)(65, 121)(66, 122)(67, 123)(68, 131)(69, 132)(70, 133)
	local type(s) :: { ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) }
Outer automorphisms :: reflexible
Dual of E27.1540
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 10 e = 70 f = 8
	degree seq :: [ 14^10 ]

E27.1545 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^7, Y2^10, Y3^70 ]
Map::
	R = (1, 71, 2, 72, 6, 76, 14, 84, 22, 92, 11, 81, 4, 74)(3, 73, 7, 77, 15, 85, 26, 96, 35, 105, 21, 91, 10, 80)(5, 75, 8, 78, 16, 86, 27, 97, 36, 106, 23, 93, 12, 82)(9, 79, 17, 87, 28, 98, 40, 110, 49, 119, 34, 104, 20, 90)(13, 83, 18, 88, 29, 99, 41, 111, 50, 120, 37, 107, 24, 94)(19, 89, 30, 100, 42, 112, 53, 123, 60, 130, 48, 118, 33, 103)(25, 95, 31, 101, 43, 113, 54, 124, 61, 131, 51, 121, 38, 108)(32, 102, 44, 114, 55, 125, 63, 133, 67, 137, 59, 129, 47, 117)(39, 109, 45, 115, 56, 126, 64, 134, 68, 138, 62, 132, 52, 122)(46, 116, 57, 127, 65, 135, 69, 139, 70, 140, 66, 136, 58, 128)(141, 211, 143, 213, 149, 219, 159, 229, 172, 242, 186, 256, 179, 249, 165, 235, 153, 223, 145, 215)(142, 212, 147, 217, 157, 227, 170, 240, 184, 254, 197, 267, 185, 255, 171, 241, 158, 228, 148, 218)(144, 214, 150, 220, 160, 230, 173, 243, 187, 257, 198, 268, 192, 262, 178, 248, 164, 234, 152, 222)(146, 216, 155, 225, 168, 238, 182, 252, 195, 265, 205, 275, 196, 266, 183, 253, 169, 239, 156, 226)(151, 221, 161, 231, 174, 244, 188, 258, 199, 269, 206, 276, 202, 272, 191, 261, 177, 247, 163, 233)(154, 224, 166, 236, 180, 250, 193, 263, 203, 273, 209, 279, 204, 274, 194, 264, 181, 251, 167, 237)(162, 232, 175, 245, 189, 259, 200, 270, 207, 277, 210, 280, 208, 278, 201, 271, 190, 260, 176, 246)
	L = (1, 144)(2, 141)(3, 150)(4, 151)(5, 152)(6, 142)(7, 143)(8, 145)(9, 160)(10, 161)(11, 162)(12, 163)(13, 164)(14, 146)(15, 147)(16, 148)(17, 149)(18, 153)(19, 173)(20, 174)(21, 175)(22, 154)(23, 176)(24, 177)(25, 178)(26, 155)(27, 156)(28, 157)(29, 158)(30, 159)(31, 165)(32, 187)(33, 188)(34, 189)(35, 166)(36, 167)(37, 190)(38, 191)(39, 192)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 179)(46, 198)(47, 199)(48, 200)(49, 180)(50, 181)(51, 201)(52, 202)(53, 182)(54, 183)(55, 184)(56, 185)(57, 186)(58, 206)(59, 207)(60, 193)(61, 194)(62, 208)(63, 195)(64, 196)(65, 197)(66, 210)(67, 203)(68, 204)(69, 205)(70, 209)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140 ), ( 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140, 2, 140 ) }
Outer automorphisms :: reflexible
Dual of E27.1548
Graph:: bipartite
	v = 17 e = 140 f = 71
	degree seq :: [ 14^10, 20^7 ]

E27.1546 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (Y2^-1, Y1), (R * Y1)^2, Y2^7 * Y1^-3, Y1^10, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 71, 2, 72, 6, 76, 14, 84, 26, 96, 42, 112, 37, 107, 22, 92, 11, 81, 4, 74)(3, 73, 7, 77, 15, 85, 27, 97, 43, 113, 57, 127, 52, 122, 36, 106, 21, 91, 10, 80)(5, 75, 8, 78, 16, 86, 28, 98, 44, 114, 58, 128, 53, 123, 38, 108, 23, 93, 12, 82)(9, 79, 17, 87, 29, 99, 45, 115, 59, 129, 67, 137, 63, 133, 51, 121, 35, 105, 20, 90)(13, 83, 18, 88, 30, 100, 46, 116, 60, 130, 68, 138, 64, 134, 54, 124, 39, 109, 24, 94)(19, 89, 31, 101, 47, 117, 61, 131, 69, 139, 66, 136, 56, 126, 41, 111, 50, 120, 34, 104)(25, 95, 32, 102, 48, 118, 33, 103, 49, 119, 62, 132, 70, 140, 65, 135, 55, 125, 40, 110)(141, 211, 143, 213, 149, 219, 159, 229, 173, 243, 186, 256, 168, 238, 154, 224, 167, 237, 185, 255, 201, 271, 210, 280, 204, 274, 193, 263, 177, 247, 192, 262, 203, 273, 196, 266, 180, 250, 164, 234, 152, 222, 144, 214, 150, 220, 160, 230, 174, 244, 188, 258, 170, 240, 156, 226, 146, 216, 155, 225, 169, 239, 187, 257, 202, 272, 208, 278, 198, 268, 182, 252, 197, 267, 207, 277, 206, 276, 195, 265, 179, 249, 163, 233, 151, 221, 161, 231, 175, 245, 190, 260, 172, 242, 158, 228, 148, 218, 142, 212, 147, 217, 157, 227, 171, 241, 189, 259, 200, 270, 184, 254, 166, 236, 183, 253, 199, 269, 209, 279, 205, 275, 194, 264, 178, 248, 162, 232, 176, 246, 191, 261, 181, 251, 165, 235, 153, 223, 145, 215)
	L = (1, 143)(2, 147)(3, 149)(4, 150)(5, 141)(6, 155)(7, 157)(8, 142)(9, 159)(10, 160)(11, 161)(12, 144)(13, 145)(14, 167)(15, 169)(16, 146)(17, 171)(18, 148)(19, 173)(20, 174)(21, 175)(22, 176)(23, 151)(24, 152)(25, 153)(26, 183)(27, 185)(28, 154)(29, 187)(30, 156)(31, 189)(32, 158)(33, 186)(34, 188)(35, 190)(36, 191)(37, 192)(38, 162)(39, 163)(40, 164)(41, 165)(42, 197)(43, 199)(44, 166)(45, 201)(46, 168)(47, 202)(48, 170)(49, 200)(50, 172)(51, 181)(52, 203)(53, 177)(54, 178)(55, 179)(56, 180)(57, 207)(58, 182)(59, 209)(60, 184)(61, 210)(62, 208)(63, 196)(64, 193)(65, 194)(66, 195)(67, 206)(68, 198)(69, 205)(70, 204)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.1547
Graph:: bipartite
	v = 8 e = 140 f = 80
	degree seq :: [ 20^7, 140 ]

E27.1547 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^7, Y2^7, Y2^3 * Y3^-10, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^70 ]
Map::
	R = (1, 71)(2, 72)(3, 73)(4, 74)(5, 75)(6, 76)(7, 77)(8, 78)(9, 79)(10, 80)(11, 81)(12, 82)(13, 83)(14, 84)(15, 85)(16, 86)(17, 87)(18, 88)(19, 89)(20, 90)(21, 91)(22, 92)(23, 93)(24, 94)(25, 95)(26, 96)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 104)(35, 105)(36, 106)(37, 107)(38, 108)(39, 109)(40, 110)(41, 111)(42, 112)(43, 113)(44, 114)(45, 115)(46, 116)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 127)(58, 128)(59, 129)(60, 130)(61, 131)(62, 132)(63, 133)(64, 134)(65, 135)(66, 136)(67, 137)(68, 138)(69, 139)(70, 140)(141, 211, 142, 212, 146, 216, 154, 224, 162, 232, 151, 221, 144, 214)(143, 213, 147, 217, 155, 225, 166, 236, 175, 245, 161, 231, 150, 220)(145, 215, 148, 218, 156, 226, 167, 237, 176, 246, 163, 233, 152, 222)(149, 219, 157, 227, 168, 238, 180, 250, 189, 259, 174, 244, 160, 230)(153, 223, 158, 228, 169, 239, 181, 251, 190, 260, 177, 247, 164, 234)(159, 229, 170, 240, 182, 252, 194, 264, 203, 273, 188, 258, 173, 243)(165, 235, 171, 241, 183, 253, 195, 265, 204, 274, 191, 261, 178, 248)(172, 242, 184, 254, 196, 266, 208, 278, 207, 277, 202, 272, 187, 257)(179, 249, 185, 255, 197, 267, 200, 270, 210, 280, 205, 275, 192, 262)(186, 256, 198, 268, 209, 279, 206, 276, 193, 263, 199, 269, 201, 271)
	L = (1, 143)(2, 147)(3, 149)(4, 150)(5, 141)(6, 155)(7, 157)(8, 142)(9, 159)(10, 160)(11, 161)(12, 144)(13, 145)(14, 166)(15, 168)(16, 146)(17, 170)(18, 148)(19, 172)(20, 173)(21, 174)(22, 175)(23, 151)(24, 152)(25, 153)(26, 180)(27, 154)(28, 182)(29, 156)(30, 184)(31, 158)(32, 186)(33, 187)(34, 188)(35, 189)(36, 162)(37, 163)(38, 164)(39, 165)(40, 194)(41, 167)(42, 196)(43, 169)(44, 198)(45, 171)(46, 200)(47, 201)(48, 202)(49, 203)(50, 176)(51, 177)(52, 178)(53, 179)(54, 208)(55, 181)(56, 209)(57, 183)(58, 210)(59, 185)(60, 195)(61, 197)(62, 199)(63, 207)(64, 190)(65, 191)(66, 192)(67, 193)(68, 206)(69, 205)(70, 204)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 20, 140 ), ( 20, 140, 20, 140, 20, 140, 20, 140, 20, 140, 20, 140, 20, 140 ) }
Outer automorphisms :: reflexible
Dual of E27.1546
Graph:: simple bipartite
	v = 80 e = 140 f = 8
	degree seq :: [ 2^70, 14^10 ]

E27.1548 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-4 * Y1^2 * Y3^-2, Y1^6 * Y3 * Y1 * Y3^2 * Y1^3, Y3^2 * Y1^-1 * Y3 * Y1^-3 * Y3 * Y1^-6, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^10 ]
Map::
	R = (1, 71, 2, 72, 6, 76, 14, 84, 26, 96, 40, 110, 54, 124, 67, 137, 53, 123, 39, 109, 25, 95, 32, 102, 46, 116, 60, 130, 70, 140, 63, 133, 49, 119, 35, 105, 21, 91, 10, 80, 3, 73, 7, 77, 15, 85, 27, 97, 41, 111, 55, 125, 66, 136, 52, 122, 38, 108, 24, 94, 13, 83, 18, 88, 30, 100, 44, 114, 58, 128, 69, 139, 62, 132, 48, 118, 34, 104, 20, 90, 9, 79, 17, 87, 29, 99, 43, 113, 57, 127, 65, 135, 51, 121, 37, 107, 23, 93, 12, 82, 5, 75, 8, 78, 16, 86, 28, 98, 42, 112, 56, 126, 68, 138, 61, 131, 47, 117, 33, 103, 19, 89, 31, 101, 45, 115, 59, 129, 64, 134, 50, 120, 36, 106, 22, 92, 11, 81, 4, 74)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280)
	L = (1, 143)(2, 147)(3, 149)(4, 150)(5, 141)(6, 155)(7, 157)(8, 142)(9, 159)(10, 160)(11, 161)(12, 144)(13, 145)(14, 167)(15, 169)(16, 146)(17, 171)(18, 148)(19, 165)(20, 173)(21, 174)(22, 175)(23, 151)(24, 152)(25, 153)(26, 181)(27, 183)(28, 154)(29, 185)(30, 156)(31, 172)(32, 158)(33, 179)(34, 187)(35, 188)(36, 189)(37, 162)(38, 163)(39, 164)(40, 195)(41, 197)(42, 166)(43, 199)(44, 168)(45, 186)(46, 170)(47, 193)(48, 201)(49, 202)(50, 203)(51, 176)(52, 177)(53, 178)(54, 206)(55, 205)(56, 180)(57, 204)(58, 182)(59, 200)(60, 184)(61, 207)(62, 208)(63, 209)(64, 210)(65, 190)(66, 191)(67, 192)(68, 194)(69, 196)(70, 198)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 14, 20 ), ( 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20, 14, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1545
Graph:: bipartite
	v = 71 e = 140 f = 17
	degree seq :: [ 2^70, 140 ]

E27.1549 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y1^7, Y1^7, Y2^10 * Y1^3, Y2^3 * Y3 * Y2 * Y3 * Y2^6 * Y1^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 71, 2, 72, 6, 76, 14, 84, 22, 92, 11, 81, 4, 74)(3, 73, 7, 77, 15, 85, 26, 96, 35, 105, 21, 91, 10, 80)(5, 75, 8, 78, 16, 86, 27, 97, 36, 106, 23, 93, 12, 82)(9, 79, 17, 87, 28, 98, 40, 110, 49, 119, 34, 104, 20, 90)(13, 83, 18, 88, 29, 99, 41, 111, 50, 120, 37, 107, 24, 94)(19, 89, 30, 100, 42, 112, 54, 124, 63, 133, 48, 118, 33, 103)(25, 95, 31, 101, 43, 113, 55, 125, 64, 134, 51, 121, 38, 108)(32, 102, 44, 114, 56, 126, 67, 137, 70, 140, 62, 132, 47, 117)(39, 109, 45, 115, 57, 127, 68, 138, 60, 130, 65, 135, 52, 122)(46, 116, 58, 128, 66, 136, 53, 123, 59, 129, 69, 139, 61, 131)(141, 211, 143, 213, 149, 219, 159, 229, 172, 242, 186, 256, 200, 270, 204, 274, 190, 260, 176, 246, 162, 232, 175, 245, 189, 259, 203, 273, 210, 280, 199, 269, 185, 255, 171, 241, 158, 228, 148, 218, 142, 212, 147, 217, 157, 227, 170, 240, 184, 254, 198, 268, 205, 275, 191, 261, 177, 247, 163, 233, 151, 221, 161, 231, 174, 244, 188, 258, 202, 272, 209, 279, 197, 267, 183, 253, 169, 239, 156, 226, 146, 216, 155, 225, 168, 238, 182, 252, 196, 266, 206, 276, 192, 262, 178, 248, 164, 234, 152, 222, 144, 214, 150, 220, 160, 230, 173, 243, 187, 257, 201, 271, 208, 278, 195, 265, 181, 251, 167, 237, 154, 224, 166, 236, 180, 250, 194, 264, 207, 277, 193, 263, 179, 249, 165, 235, 153, 223, 145, 215)
	L = (1, 144)(2, 141)(3, 150)(4, 151)(5, 152)(6, 142)(7, 143)(8, 145)(9, 160)(10, 161)(11, 162)(12, 163)(13, 164)(14, 146)(15, 147)(16, 148)(17, 149)(18, 153)(19, 173)(20, 174)(21, 175)(22, 154)(23, 176)(24, 177)(25, 178)(26, 155)(27, 156)(28, 157)(29, 158)(30, 159)(31, 165)(32, 187)(33, 188)(34, 189)(35, 166)(36, 167)(37, 190)(38, 191)(39, 192)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 179)(46, 201)(47, 202)(48, 203)(49, 180)(50, 181)(51, 204)(52, 205)(53, 206)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 193)(60, 208)(61, 209)(62, 210)(63, 194)(64, 195)(65, 200)(66, 198)(67, 196)(68, 197)(69, 199)(70, 207)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1550
Graph:: bipartite
	v = 11 e = 140 f = 77
	degree seq :: [ 14^10, 140 ]

E27.1550 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 10, 70})
Quotient :: dipole
Aut^+ = C70 (small group id <70, 4>)
Aut   = D140 (small group id <140, 10>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^7 * Y1^-3, Y1^10, Y1^-1 * Y3^-4 * Y1^-2 * Y3^-2 * Y1^-3 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^70 ]
Map::
	R = (1, 71, 2, 72, 6, 76, 14, 84, 26, 96, 42, 112, 37, 107, 22, 92, 11, 81, 4, 74)(3, 73, 7, 77, 15, 85, 27, 97, 43, 113, 57, 127, 52, 122, 36, 106, 21, 91, 10, 80)(5, 75, 8, 78, 16, 86, 28, 98, 44, 114, 58, 128, 53, 123, 38, 108, 23, 93, 12, 82)(9, 79, 17, 87, 29, 99, 45, 115, 59, 129, 67, 137, 63, 133, 51, 121, 35, 105, 20, 90)(13, 83, 18, 88, 30, 100, 46, 116, 60, 130, 68, 138, 64, 134, 54, 124, 39, 109, 24, 94)(19, 89, 31, 101, 47, 117, 61, 131, 69, 139, 66, 136, 56, 126, 41, 111, 50, 120, 34, 104)(25, 95, 32, 102, 48, 118, 33, 103, 49, 119, 62, 132, 70, 140, 65, 135, 55, 125, 40, 110)(141, 211)(142, 212)(143, 213)(144, 214)(145, 215)(146, 216)(147, 217)(148, 218)(149, 219)(150, 220)(151, 221)(152, 222)(153, 223)(154, 224)(155, 225)(156, 226)(157, 227)(158, 228)(159, 229)(160, 230)(161, 231)(162, 232)(163, 233)(164, 234)(165, 235)(166, 236)(167, 237)(168, 238)(169, 239)(170, 240)(171, 241)(172, 242)(173, 243)(174, 244)(175, 245)(176, 246)(177, 247)(178, 248)(179, 249)(180, 250)(181, 251)(182, 252)(183, 253)(184, 254)(185, 255)(186, 256)(187, 257)(188, 258)(189, 259)(190, 260)(191, 261)(192, 262)(193, 263)(194, 264)(195, 265)(196, 266)(197, 267)(198, 268)(199, 269)(200, 270)(201, 271)(202, 272)(203, 273)(204, 274)(205, 275)(206, 276)(207, 277)(208, 278)(209, 279)(210, 280)
	L = (1, 143)(2, 147)(3, 149)(4, 150)(5, 141)(6, 155)(7, 157)(8, 142)(9, 159)(10, 160)(11, 161)(12, 144)(13, 145)(14, 167)(15, 169)(16, 146)(17, 171)(18, 148)(19, 173)(20, 174)(21, 175)(22, 176)(23, 151)(24, 152)(25, 153)(26, 183)(27, 185)(28, 154)(29, 187)(30, 156)(31, 189)(32, 158)(33, 186)(34, 188)(35, 190)(36, 191)(37, 192)(38, 162)(39, 163)(40, 164)(41, 165)(42, 197)(43, 199)(44, 166)(45, 201)(46, 168)(47, 202)(48, 170)(49, 200)(50, 172)(51, 181)(52, 203)(53, 177)(54, 178)(55, 179)(56, 180)(57, 207)(58, 182)(59, 209)(60, 184)(61, 210)(62, 208)(63, 196)(64, 193)(65, 194)(66, 195)(67, 206)(68, 198)(69, 205)(70, 204)(71, 211)(72, 212)(73, 213)(74, 214)(75, 215)(76, 216)(77, 217)(78, 218)(79, 219)(80, 220)(81, 221)(82, 222)(83, 223)(84, 224)(85, 225)(86, 226)(87, 227)(88, 228)(89, 229)(90, 230)(91, 231)(92, 232)(93, 233)(94, 234)(95, 235)(96, 236)(97, 237)(98, 238)(99, 239)(100, 240)(101, 241)(102, 242)(103, 243)(104, 244)(105, 245)(106, 246)(107, 247)(108, 248)(109, 249)(110, 250)(111, 251)(112, 252)(113, 253)(114, 254)(115, 255)(116, 256)(117, 257)(118, 258)(119, 259)(120, 260)(121, 261)(122, 262)(123, 263)(124, 264)(125, 265)(126, 266)(127, 267)(128, 268)(129, 269)(130, 270)(131, 271)(132, 272)(133, 273)(134, 274)(135, 275)(136, 276)(137, 277)(138, 278)(139, 279)(140, 280)
	local type(s) :: { ( 14, 140 ), ( 14, 140, 14, 140, 14, 140, 14, 140, 14, 140, 14, 140, 14, 140, 14, 140, 14, 140, 14, 140 ) }
Outer automorphisms :: reflexible
Dual of E27.1549
Graph:: simple bipartite
	v = 77 e = 140 f = 11
	degree seq :: [ 2^70, 20^7 ]

E27.1551 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 6, 9})
Quotient :: halfedge^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-1 * Y2 * Y1^2 * Y3 * Y1^-1, Y1^2 * Y2 * Y3 * Y1^-1 * Y2 * Y3, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2, Y1^3 * Y2 * Y1^-1 * Y3 * Y1, Y2 * Y1 * Y3 * Y2 * Y1^-2 * Y3, (Y1^-1 * Y2)^4, (Y3 * Y1 * Y3 * Y2)^2, (Y3 * Y1^-1)^4, (Y1 * Y2 * Y3 * Y2)^2, Y3 * Y1^-3 * Y2 * Y3 * Y2 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 74, 2, 78, 6, 90, 18, 108, 36, 105, 33, 122, 50, 89, 17, 77, 5, 73)(3, 81, 9, 92, 20, 125, 53, 120, 48, 88, 16, 118, 46, 106, 34, 83, 11, 75)(4, 84, 12, 107, 35, 95, 23, 79, 7, 93, 21, 123, 51, 115, 43, 86, 14, 76)(8, 96, 24, 130, 58, 121, 49, 91, 19, 124, 52, 117, 45, 87, 15, 98, 26, 80)(10, 101, 29, 97, 25, 132, 60, 99, 27, 136, 64, 143, 71, 135, 63, 103, 31, 82)(13, 110, 38, 134, 62, 139, 67, 131, 59, 114, 42, 129, 57, 116, 44, 112, 40, 85)(22, 113, 41, 126, 54, 109, 37, 127, 55, 104, 32, 137, 65, 100, 28, 119, 47, 94)(30, 138, 66, 133, 61, 111, 39, 142, 70, 140, 68, 144, 72, 141, 69, 128, 56, 102)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 27)(10, 30)(11, 32)(12, 36)(14, 41)(16, 47)(17, 43)(18, 46)(20, 54)(21, 55)(22, 56)(23, 57)(24, 33)(26, 62)(28, 35)(29, 48)(31, 49)(34, 63)(37, 68)(38, 69)(39, 71)(40, 58)(42, 52)(44, 66)(45, 64)(50, 53)(51, 67)(59, 70)(60, 72)(61, 65)(73, 76)(74, 80)(75, 82)(77, 88)(78, 92)(79, 94)(81, 100)(83, 105)(84, 109)(85, 111)(86, 114)(87, 116)(89, 121)(90, 123)(91, 110)(93, 112)(95, 122)(96, 131)(97, 133)(98, 135)(99, 130)(101, 124)(102, 139)(103, 140)(104, 141)(106, 113)(107, 134)(108, 117)(115, 137)(118, 132)(119, 142)(120, 127)(125, 143)(126, 138)(128, 136)(129, 144)
	local type(s) :: { ( 12^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1552
Transitivity :: VT+ AT
Graph:: bipartite
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.1552 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 6, 9})
Quotient :: halfedge^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y1^6, Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y3, Y1 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y2, (Y2 * Y1)^4, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 74, 2, 78, 6, 90, 18, 89, 17, 77, 5, 73)(3, 81, 9, 99, 27, 122, 50, 91, 19, 83, 11, 75)(4, 84, 12, 107, 35, 124, 52, 92, 20, 86, 14, 76)(7, 93, 21, 87, 15, 115, 43, 119, 47, 95, 23, 79)(8, 96, 24, 88, 16, 117, 45, 120, 48, 98, 26, 80)(10, 102, 30, 121, 49, 126, 54, 133, 61, 104, 32, 82)(13, 110, 38, 123, 51, 129, 57, 139, 67, 112, 40, 85)(22, 101, 29, 134, 62, 106, 34, 116, 44, 128, 56, 94)(25, 108, 36, 140, 68, 113, 41, 118, 46, 132, 60, 97)(28, 125, 53, 105, 33, 109, 37, 130, 58, 114, 42, 100)(31, 131, 59, 111, 39, 142, 70, 144, 72, 127, 55, 103)(63, 136, 64, 143, 71, 137, 65, 138, 66, 141, 69, 135)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 31)(11, 33)(12, 36)(14, 41)(16, 46)(17, 27)(18, 47)(20, 51)(21, 53)(22, 55)(23, 37)(24, 57)(26, 40)(29, 63)(30, 64)(32, 65)(34, 66)(35, 67)(38, 45)(39, 61)(42, 43)(44, 59)(48, 68)(49, 72)(50, 58)(52, 60)(54, 69)(56, 71)(62, 70)(73, 76)(74, 80)(75, 82)(77, 88)(78, 92)(79, 94)(81, 101)(83, 106)(84, 109)(85, 111)(86, 114)(87, 116)(89, 107)(90, 120)(91, 121)(93, 126)(95, 104)(96, 130)(97, 131)(98, 100)(99, 133)(102, 115)(103, 123)(105, 117)(108, 141)(110, 135)(112, 143)(113, 137)(118, 142)(119, 134)(122, 128)(124, 125)(127, 140)(129, 138)(132, 136)(139, 144)
	local type(s) :: { ( 18^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1551
Transitivity :: VT+ AT
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 12^12 ]

E27.1553 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 9})
Quotient :: edge^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y3^-2)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^6, Y3^-1 * Y2 * Y3 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y2 * Y3, Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 ]
Map::
	R = (1, 73, 4, 76, 14, 86, 42, 114, 17, 89, 5, 77)(2, 74, 7, 79, 23, 95, 57, 129, 26, 98, 8, 80)(3, 75, 10, 82, 32, 104, 65, 137, 35, 107, 11, 83)(6, 78, 19, 91, 51, 123, 67, 139, 53, 125, 20, 92)(9, 81, 28, 100, 47, 119, 70, 142, 61, 133, 29, 101)(12, 84, 37, 109, 15, 87, 44, 116, 68, 140, 38, 110)(13, 85, 40, 112, 16, 88, 46, 118, 71, 143, 41, 113)(18, 90, 48, 120, 27, 99, 59, 131, 72, 144, 49, 121)(21, 93, 54, 126, 24, 96, 31, 103, 64, 136, 34, 106)(22, 94, 56, 128, 25, 97, 43, 115, 66, 138, 36, 108)(30, 102, 63, 135, 33, 105, 45, 117, 69, 141, 39, 111)(50, 122, 60, 132, 52, 124, 58, 130, 62, 134, 55, 127)(145, 146)(147, 153)(148, 156)(149, 159)(150, 162)(151, 165)(152, 168)(154, 174)(155, 177)(157, 183)(158, 170)(160, 189)(161, 167)(163, 194)(164, 196)(166, 199)(169, 202)(171, 197)(172, 190)(173, 185)(175, 182)(176, 205)(178, 188)(179, 191)(180, 193)(181, 198)(184, 214)(186, 212)(187, 192)(195, 216)(200, 203)(201, 208)(204, 210)(206, 211)(207, 215)(209, 213)(217, 219)(218, 222)(220, 229)(221, 232)(223, 238)(224, 241)(225, 243)(226, 247)(227, 250)(228, 252)(230, 251)(231, 259)(233, 248)(234, 263)(235, 260)(236, 254)(237, 257)(239, 269)(240, 262)(242, 267)(244, 271)(245, 276)(246, 278)(249, 268)(253, 283)(255, 264)(256, 280)(258, 287)(261, 275)(265, 279)(266, 285)(270, 281)(272, 284)(273, 282)(274, 286)(277, 288)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 36, 36 ), ( 36^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1556
Graph:: simple bipartite
	v = 84 e = 144 f = 8
	degree seq :: [ 2^72, 12^12 ]

E27.1554 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 9})
Quotient :: edge^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y2 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^2, Y1 * Y3 * Y2 * Y3^-4, (Y2 * Y3^-1)^4, (Y3 * Y1 * Y2 * Y1)^2, (Y2 * Y3^-1 * Y2 * Y1)^2, (Y3 * Y1)^4 ]
Map::
	R = (1, 73, 4, 76, 14, 86, 43, 115, 22, 94, 33, 105, 50, 122, 17, 89, 5, 77)(2, 74, 7, 79, 23, 95, 41, 113, 13, 85, 40, 112, 64, 136, 26, 98, 8, 80)(3, 75, 10, 82, 32, 104, 71, 143, 46, 118, 15, 87, 45, 117, 35, 107, 11, 83)(6, 78, 19, 91, 55, 127, 65, 137, 62, 134, 24, 96, 61, 133, 47, 119, 20, 92)(9, 81, 28, 100, 36, 108, 70, 142, 31, 103, 69, 141, 51, 123, 68, 140, 29, 101)(12, 84, 37, 109, 56, 128, 49, 121, 42, 114, 60, 132, 48, 120, 16, 88, 38, 110)(18, 90, 52, 124, 57, 129, 72, 144, 54, 126, 67, 139, 27, 99, 66, 138, 53, 125)(21, 93, 58, 130, 34, 106, 63, 135, 30, 102, 44, 116, 39, 111, 25, 97, 59, 131)(145, 146)(147, 153)(148, 156)(149, 159)(150, 162)(151, 165)(152, 168)(154, 174)(155, 177)(157, 183)(158, 176)(160, 191)(161, 193)(163, 186)(164, 184)(166, 192)(167, 199)(169, 179)(170, 207)(171, 209)(172, 204)(173, 201)(175, 200)(178, 198)(180, 197)(181, 206)(182, 212)(185, 194)(187, 208)(188, 196)(189, 214)(190, 202)(195, 215)(203, 210)(205, 216)(211, 213)(217, 219)(218, 222)(220, 229)(221, 232)(223, 238)(224, 241)(225, 243)(226, 247)(227, 250)(228, 252)(230, 258)(231, 260)(233, 242)(234, 267)(235, 270)(236, 272)(237, 273)(239, 246)(240, 276)(244, 262)(245, 265)(248, 275)(249, 253)(251, 284)(254, 271)(255, 283)(256, 274)(257, 277)(259, 261)(263, 282)(264, 285)(266, 287)(268, 278)(269, 279)(280, 281)(286, 288)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 24, 24 ), ( 24^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1555
Graph:: simple bipartite
	v = 80 e = 144 f = 12
	degree seq :: [ 2^72, 18^8 ]

E27.1555 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 9})
Quotient :: loop^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y3^-2)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^6, Y3^-1 * Y2 * Y3 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y2 * Y3, Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 ]
Map::
	R = (1, 73, 145, 217, 4, 76, 148, 220, 14, 86, 158, 230, 42, 114, 186, 258, 17, 89, 161, 233, 5, 77, 149, 221)(2, 74, 146, 218, 7, 79, 151, 223, 23, 95, 167, 239, 57, 129, 201, 273, 26, 98, 170, 242, 8, 80, 152, 224)(3, 75, 147, 219, 10, 82, 154, 226, 32, 104, 176, 248, 65, 137, 209, 281, 35, 107, 179, 251, 11, 83, 155, 227)(6, 78, 150, 222, 19, 91, 163, 235, 51, 123, 195, 267, 67, 139, 211, 283, 53, 125, 197, 269, 20, 92, 164, 236)(9, 81, 153, 225, 28, 100, 172, 244, 47, 119, 191, 263, 70, 142, 214, 286, 61, 133, 205, 277, 29, 101, 173, 245)(12, 84, 156, 228, 37, 109, 181, 253, 15, 87, 159, 231, 44, 116, 188, 260, 68, 140, 212, 284, 38, 110, 182, 254)(13, 85, 157, 229, 40, 112, 184, 256, 16, 88, 160, 232, 46, 118, 190, 262, 71, 143, 215, 287, 41, 113, 185, 257)(18, 90, 162, 234, 48, 120, 192, 264, 27, 99, 171, 243, 59, 131, 203, 275, 72, 144, 216, 288, 49, 121, 193, 265)(21, 93, 165, 237, 54, 126, 198, 270, 24, 96, 168, 240, 31, 103, 175, 247, 64, 136, 208, 280, 34, 106, 178, 250)(22, 94, 166, 238, 56, 128, 200, 272, 25, 97, 169, 241, 43, 115, 187, 259, 66, 138, 210, 282, 36, 108, 180, 252)(30, 102, 174, 246, 63, 135, 207, 279, 33, 105, 177, 249, 45, 117, 189, 261, 69, 141, 213, 285, 39, 111, 183, 255)(50, 122, 194, 266, 60, 132, 204, 276, 52, 124, 196, 268, 58, 130, 202, 274, 62, 134, 206, 278, 55, 127, 199, 271)
	L = (1, 74)(2, 73)(3, 81)(4, 84)(5, 87)(6, 90)(7, 93)(8, 96)(9, 75)(10, 102)(11, 105)(12, 76)(13, 111)(14, 98)(15, 77)(16, 117)(17, 95)(18, 78)(19, 122)(20, 124)(21, 79)(22, 127)(23, 89)(24, 80)(25, 130)(26, 86)(27, 125)(28, 118)(29, 113)(30, 82)(31, 110)(32, 133)(33, 83)(34, 116)(35, 119)(36, 121)(37, 126)(38, 103)(39, 85)(40, 142)(41, 101)(42, 140)(43, 120)(44, 106)(45, 88)(46, 100)(47, 107)(48, 115)(49, 108)(50, 91)(51, 144)(52, 92)(53, 99)(54, 109)(55, 94)(56, 131)(57, 136)(58, 97)(59, 128)(60, 138)(61, 104)(62, 139)(63, 143)(64, 129)(65, 141)(66, 132)(67, 134)(68, 114)(69, 137)(70, 112)(71, 135)(72, 123)(145, 219)(146, 222)(147, 217)(148, 229)(149, 232)(150, 218)(151, 238)(152, 241)(153, 243)(154, 247)(155, 250)(156, 252)(157, 220)(158, 251)(159, 259)(160, 221)(161, 248)(162, 263)(163, 260)(164, 254)(165, 257)(166, 223)(167, 269)(168, 262)(169, 224)(170, 267)(171, 225)(172, 271)(173, 276)(174, 278)(175, 226)(176, 233)(177, 268)(178, 227)(179, 230)(180, 228)(181, 283)(182, 236)(183, 264)(184, 280)(185, 237)(186, 287)(187, 231)(188, 235)(189, 275)(190, 240)(191, 234)(192, 255)(193, 279)(194, 285)(195, 242)(196, 249)(197, 239)(198, 281)(199, 244)(200, 284)(201, 282)(202, 286)(203, 261)(204, 245)(205, 288)(206, 246)(207, 265)(208, 256)(209, 270)(210, 273)(211, 253)(212, 272)(213, 266)(214, 274)(215, 258)(216, 277)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1554
Transitivity :: VT+
Graph:: bipartite
	v = 12 e = 144 f = 80
	degree seq :: [ 24^12 ]

E27.1556 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 9})
Quotient :: loop^2
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y2 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3, Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^2, Y1 * Y3 * Y2 * Y3^-4, (Y2 * Y3^-1)^4, (Y3 * Y1 * Y2 * Y1)^2, (Y2 * Y3^-1 * Y2 * Y1)^2, (Y3 * Y1)^4 ]
Map::
	R = (1, 73, 145, 217, 4, 76, 148, 220, 14, 86, 158, 230, 43, 115, 187, 259, 22, 94, 166, 238, 33, 105, 177, 249, 50, 122, 194, 266, 17, 89, 161, 233, 5, 77, 149, 221)(2, 74, 146, 218, 7, 79, 151, 223, 23, 95, 167, 239, 41, 113, 185, 257, 13, 85, 157, 229, 40, 112, 184, 256, 64, 136, 208, 280, 26, 98, 170, 242, 8, 80, 152, 224)(3, 75, 147, 219, 10, 82, 154, 226, 32, 104, 176, 248, 71, 143, 215, 287, 46, 118, 190, 262, 15, 87, 159, 231, 45, 117, 189, 261, 35, 107, 179, 251, 11, 83, 155, 227)(6, 78, 150, 222, 19, 91, 163, 235, 55, 127, 199, 271, 65, 137, 209, 281, 62, 134, 206, 278, 24, 96, 168, 240, 61, 133, 205, 277, 47, 119, 191, 263, 20, 92, 164, 236)(9, 81, 153, 225, 28, 100, 172, 244, 36, 108, 180, 252, 70, 142, 214, 286, 31, 103, 175, 247, 69, 141, 213, 285, 51, 123, 195, 267, 68, 140, 212, 284, 29, 101, 173, 245)(12, 84, 156, 228, 37, 109, 181, 253, 56, 128, 200, 272, 49, 121, 193, 265, 42, 114, 186, 258, 60, 132, 204, 276, 48, 120, 192, 264, 16, 88, 160, 232, 38, 110, 182, 254)(18, 90, 162, 234, 52, 124, 196, 268, 57, 129, 201, 273, 72, 144, 216, 288, 54, 126, 198, 270, 67, 139, 211, 283, 27, 99, 171, 243, 66, 138, 210, 282, 53, 125, 197, 269)(21, 93, 165, 237, 58, 130, 202, 274, 34, 106, 178, 250, 63, 135, 207, 279, 30, 102, 174, 246, 44, 116, 188, 260, 39, 111, 183, 255, 25, 97, 169, 241, 59, 131, 203, 275)
	L = (1, 74)(2, 73)(3, 81)(4, 84)(5, 87)(6, 90)(7, 93)(8, 96)(9, 75)(10, 102)(11, 105)(12, 76)(13, 111)(14, 104)(15, 77)(16, 119)(17, 121)(18, 78)(19, 114)(20, 112)(21, 79)(22, 120)(23, 127)(24, 80)(25, 107)(26, 135)(27, 137)(28, 132)(29, 129)(30, 82)(31, 128)(32, 86)(33, 83)(34, 126)(35, 97)(36, 125)(37, 134)(38, 140)(39, 85)(40, 92)(41, 122)(42, 91)(43, 136)(44, 124)(45, 142)(46, 130)(47, 88)(48, 94)(49, 89)(50, 113)(51, 143)(52, 116)(53, 108)(54, 106)(55, 95)(56, 103)(57, 101)(58, 118)(59, 138)(60, 100)(61, 144)(62, 109)(63, 98)(64, 115)(65, 99)(66, 131)(67, 141)(68, 110)(69, 139)(70, 117)(71, 123)(72, 133)(145, 219)(146, 222)(147, 217)(148, 229)(149, 232)(150, 218)(151, 238)(152, 241)(153, 243)(154, 247)(155, 250)(156, 252)(157, 220)(158, 258)(159, 260)(160, 221)(161, 242)(162, 267)(163, 270)(164, 272)(165, 273)(166, 223)(167, 246)(168, 276)(169, 224)(170, 233)(171, 225)(172, 262)(173, 265)(174, 239)(175, 226)(176, 275)(177, 253)(178, 227)(179, 284)(180, 228)(181, 249)(182, 271)(183, 283)(184, 274)(185, 277)(186, 230)(187, 261)(188, 231)(189, 259)(190, 244)(191, 282)(192, 285)(193, 245)(194, 287)(195, 234)(196, 278)(197, 279)(198, 235)(199, 254)(200, 236)(201, 237)(202, 256)(203, 248)(204, 240)(205, 257)(206, 268)(207, 269)(208, 281)(209, 280)(210, 263)(211, 255)(212, 251)(213, 264)(214, 288)(215, 266)(216, 286)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1553
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 144 f = 84
	degree seq :: [ 36^8 ]

E27.1557 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-3 * Y2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y2^-1, (Y1 * Y2^-1 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2 * Y3^-1 * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, Y2^-1 * Y1 * Y2 * Y3 * Y1 * Y2^-1 * Y3, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^2 * Y2, Y2^-1 * Y3^-2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 18, 90)(6, 78, 8, 80)(7, 79, 25, 97)(9, 81, 32, 104)(12, 84, 34, 106)(13, 85, 41, 113)(14, 86, 31, 103)(15, 87, 35, 107)(16, 88, 38, 110)(17, 89, 28, 100)(19, 91, 52, 124)(20, 92, 26, 98)(21, 93, 29, 101)(22, 94, 56, 128)(23, 95, 58, 130)(24, 96, 30, 102)(27, 99, 47, 119)(33, 105, 50, 122)(36, 108, 44, 116)(37, 109, 53, 125)(39, 111, 61, 133)(40, 112, 59, 131)(42, 114, 71, 143)(43, 115, 68, 140)(45, 117, 70, 142)(46, 118, 67, 139)(48, 120, 69, 141)(49, 121, 65, 137)(51, 123, 57, 129)(54, 126, 63, 135)(55, 127, 66, 138)(60, 132, 64, 136)(62, 134, 72, 144)(145, 217, 147, 219, 156, 228, 186, 258, 164, 236, 149, 221)(146, 218, 151, 223, 170, 242, 206, 278, 178, 250, 153, 225)(148, 220, 159, 231, 187, 259, 204, 276, 168, 240, 161, 233)(150, 222, 166, 238, 160, 232, 193, 265, 198, 270, 167, 239)(152, 224, 173, 245, 207, 279, 214, 286, 182, 254, 175, 247)(154, 226, 180, 252, 174, 246, 211, 283, 212, 284, 181, 253)(155, 227, 183, 255, 162, 234, 195, 267, 215, 287, 184, 256)(157, 229, 188, 260, 199, 271, 197, 269, 163, 235, 190, 262)(158, 230, 191, 263, 189, 261, 194, 266, 165, 237, 192, 264)(169, 241, 205, 277, 176, 248, 203, 275, 216, 288, 201, 273)(171, 243, 200, 272, 213, 285, 202, 274, 177, 249, 209, 281)(172, 244, 185, 257, 208, 280, 196, 268, 179, 251, 210, 282)
	L = (1, 148)(2, 152)(3, 157)(4, 160)(5, 163)(6, 145)(7, 171)(8, 174)(9, 177)(10, 146)(11, 175)(12, 187)(13, 189)(14, 147)(15, 192)(16, 156)(17, 194)(18, 173)(19, 158)(20, 168)(21, 149)(22, 201)(23, 203)(24, 150)(25, 161)(26, 207)(27, 208)(28, 151)(29, 210)(30, 170)(31, 196)(32, 159)(33, 172)(34, 182)(35, 153)(36, 184)(37, 195)(38, 154)(39, 209)(40, 202)(41, 155)(42, 199)(43, 198)(44, 166)(45, 186)(46, 167)(47, 169)(48, 216)(49, 205)(50, 176)(51, 200)(52, 162)(53, 193)(54, 164)(55, 165)(56, 180)(57, 197)(58, 211)(59, 188)(60, 191)(61, 190)(62, 213)(63, 212)(64, 206)(65, 181)(66, 215)(67, 183)(68, 178)(69, 179)(70, 185)(71, 214)(72, 204)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1560
Graph:: simple bipartite
	v = 48 e = 144 f = 44
	degree seq :: [ 4^36, 12^12 ]

E27.1558 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y2^2 * Y3, (Y2^2 * Y1)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^6, Y2^-2 * Y3 * Y2^-2 * Y3^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y1, Y1 * Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 11, 83)(4, 76, 10, 82)(5, 77, 18, 90)(6, 78, 8, 80)(7, 79, 25, 97)(9, 81, 32, 104)(12, 84, 34, 106)(13, 85, 41, 113)(14, 86, 31, 103)(15, 87, 35, 107)(16, 88, 38, 110)(17, 89, 28, 100)(19, 91, 52, 124)(20, 92, 26, 98)(21, 93, 29, 101)(22, 94, 56, 128)(23, 95, 58, 130)(24, 96, 30, 102)(27, 99, 46, 118)(33, 105, 55, 127)(36, 108, 44, 116)(37, 109, 54, 126)(39, 111, 61, 133)(40, 112, 59, 131)(42, 114, 71, 143)(43, 115, 68, 140)(45, 117, 67, 139)(47, 119, 66, 138)(48, 120, 65, 137)(49, 121, 64, 136)(50, 122, 63, 135)(51, 123, 57, 129)(53, 125, 70, 142)(60, 132, 69, 141)(62, 134, 72, 144)(145, 217, 147, 219, 156, 228, 186, 258, 164, 236, 149, 221)(146, 218, 151, 223, 170, 242, 206, 278, 178, 250, 153, 225)(148, 220, 159, 231, 168, 240, 204, 276, 194, 266, 161, 233)(150, 222, 166, 238, 187, 259, 193, 265, 160, 232, 167, 239)(152, 224, 173, 245, 182, 254, 214, 286, 212, 284, 175, 247)(154, 226, 180, 252, 207, 279, 211, 283, 174, 246, 181, 253)(155, 227, 183, 255, 162, 234, 195, 267, 215, 287, 184, 256)(157, 229, 188, 260, 192, 264, 198, 270, 163, 235, 189, 261)(158, 230, 190, 262, 197, 269, 199, 271, 165, 237, 191, 263)(169, 241, 205, 277, 176, 248, 203, 275, 216, 288, 201, 273)(171, 243, 200, 272, 210, 282, 202, 274, 177, 249, 208, 280)(172, 244, 185, 257, 213, 285, 196, 268, 179, 251, 209, 281)
	L = (1, 148)(2, 152)(3, 157)(4, 160)(5, 163)(6, 145)(7, 171)(8, 174)(9, 177)(10, 146)(11, 175)(12, 168)(13, 165)(14, 147)(15, 190)(16, 164)(17, 191)(18, 173)(19, 197)(20, 194)(21, 149)(22, 201)(23, 203)(24, 150)(25, 161)(26, 182)(27, 179)(28, 151)(29, 185)(30, 178)(31, 209)(32, 159)(33, 213)(34, 212)(35, 153)(36, 184)(37, 195)(38, 154)(39, 208)(40, 202)(41, 155)(42, 192)(43, 156)(44, 193)(45, 166)(46, 169)(47, 216)(48, 158)(49, 205)(50, 187)(51, 200)(52, 162)(53, 186)(54, 167)(55, 176)(56, 211)(57, 198)(58, 181)(59, 188)(60, 199)(61, 189)(62, 210)(63, 170)(64, 180)(65, 215)(66, 172)(67, 183)(68, 207)(69, 206)(70, 196)(71, 214)(72, 204)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1559
Graph:: simple bipartite
	v = 48 e = 144 f = 44
	degree seq :: [ 4^36, 12^12 ]

E27.1559 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^-2 * Y3 * Y1, (Y2 * Y1^-1 * Y3)^2, (Y2 * Y1 * Y3)^2, Y1 * Y3^3 * Y1^2, (Y3^2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y3^2 * Y1, Y3 * Y2 * Y1^2 * Y2 * Y1 * Y3, Y2 * Y3^3 * Y2 * Y1^-3, (Y3 * Y1 * Y3^-1 * Y2)^2 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 25, 97, 64, 136, 71, 143, 53, 125, 20, 92, 5, 77)(3, 75, 11, 83, 36, 108, 69, 141, 29, 101, 54, 126, 65, 137, 45, 117, 13, 85)(4, 76, 15, 87, 49, 121, 24, 96, 60, 132, 43, 115, 63, 135, 21, 93, 17, 89)(6, 78, 22, 94, 9, 81, 32, 104, 56, 128, 35, 107, 16, 88, 52, 124, 23, 95)(8, 80, 28, 100, 67, 139, 62, 134, 50, 122, 44, 116, 39, 111, 58, 130, 30, 102)(10, 82, 34, 106, 27, 99, 37, 109, 55, 127, 51, 123, 33, 105, 61, 133, 19, 91)(12, 84, 40, 112, 26, 98, 48, 120, 59, 131, 18, 90, 57, 129, 46, 118, 42, 114)(14, 86, 47, 119, 38, 110, 70, 142, 72, 144, 68, 140, 41, 113, 66, 138, 31, 103)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 162, 234)(150, 222, 156, 228)(151, 223, 170, 242)(153, 225, 175, 247)(154, 226, 173, 245)(155, 227, 181, 253)(157, 229, 187, 259)(159, 231, 194, 266)(160, 232, 192, 264)(161, 233, 198, 270)(163, 235, 191, 263)(164, 236, 206, 278)(165, 237, 202, 274)(166, 238, 188, 260)(167, 239, 182, 254)(168, 240, 185, 257)(169, 241, 209, 281)(171, 243, 210, 282)(172, 244, 204, 276)(174, 246, 196, 268)(176, 248, 201, 273)(177, 249, 189, 261)(178, 250, 190, 262)(179, 251, 212, 284)(180, 252, 193, 265)(183, 255, 208, 280)(184, 256, 205, 277)(186, 258, 215, 287)(195, 267, 216, 288)(197, 269, 213, 285)(199, 271, 203, 275)(200, 272, 211, 283)(207, 279, 214, 286)
	L = (1, 148)(2, 153)(3, 156)(4, 160)(5, 163)(6, 145)(7, 171)(8, 173)(9, 177)(10, 146)(11, 182)(12, 185)(13, 188)(14, 147)(15, 151)(16, 197)(17, 199)(18, 202)(19, 204)(20, 167)(21, 149)(22, 187)(23, 181)(24, 150)(25, 168)(26, 194)(27, 165)(28, 191)(29, 212)(30, 190)(31, 152)(32, 169)(33, 164)(34, 196)(35, 154)(36, 174)(37, 208)(38, 206)(39, 155)(40, 180)(41, 209)(42, 172)(43, 178)(44, 203)(45, 175)(46, 157)(47, 162)(48, 158)(49, 205)(50, 216)(51, 159)(52, 193)(53, 207)(54, 211)(55, 166)(56, 161)(57, 214)(58, 210)(59, 198)(60, 215)(61, 200)(62, 189)(63, 176)(64, 179)(65, 201)(66, 170)(67, 184)(68, 183)(69, 192)(70, 213)(71, 195)(72, 186)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1558
Graph:: simple bipartite
	v = 44 e = 144 f = 48
	degree seq :: [ 4^36, 18^8 ]

E27.1560 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2, Y1 * Y3 * Y1 * Y3^-2, (Y1 * Y3 * Y2)^2, (Y1^-2 * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^2)^2, Y1^-2 * Y3^-3 * Y1^-1, Y1 * Y2 * Y1^-2 * Y2 * Y1^-1 * Y3^-1, Y1^2 * Y2 * Y1^-1 * Y3 * Y1 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^5, Y1^9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 25, 97, 58, 130, 47, 119, 49, 121, 20, 92, 5, 77)(3, 75, 11, 83, 36, 108, 67, 139, 66, 138, 65, 137, 59, 131, 41, 113, 13, 85)(4, 76, 15, 87, 45, 117, 24, 96, 21, 93, 56, 128, 63, 135, 28, 100, 17, 89)(6, 78, 22, 94, 55, 127, 60, 132, 33, 105, 9, 81, 16, 88, 48, 120, 23, 95)(8, 80, 29, 101, 40, 112, 54, 126, 51, 123, 68, 140, 69, 141, 46, 118, 30, 102)(10, 82, 34, 106, 19, 91, 53, 125, 50, 122, 27, 99, 32, 104, 57, 129, 35, 107)(12, 84, 38, 110, 70, 142, 44, 116, 42, 114, 26, 98, 61, 133, 52, 124, 18, 90)(14, 86, 43, 115, 71, 143, 72, 144, 64, 136, 37, 109, 39, 111, 62, 134, 31, 103)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 162, 234)(150, 222, 156, 228)(151, 223, 170, 242)(153, 225, 175, 247)(154, 226, 155, 227)(157, 229, 161, 233)(159, 231, 190, 262)(160, 232, 188, 260)(163, 235, 187, 259)(164, 236, 198, 270)(165, 237, 195, 267)(166, 238, 184, 256)(167, 239, 181, 253)(168, 240, 183, 255)(169, 241, 203, 275)(171, 243, 206, 278)(172, 244, 173, 245)(174, 246, 177, 249)(176, 248, 210, 282)(178, 250, 196, 268)(179, 251, 208, 280)(180, 252, 200, 272)(182, 254, 201, 273)(185, 257, 197, 269)(186, 258, 194, 266)(189, 261, 209, 281)(191, 263, 214, 286)(192, 264, 212, 284)(193, 265, 211, 283)(199, 271, 215, 287)(202, 274, 213, 285)(204, 276, 205, 277)(207, 279, 216, 288)
	L = (1, 148)(2, 153)(3, 156)(4, 160)(5, 163)(6, 145)(7, 171)(8, 155)(9, 176)(10, 146)(11, 181)(12, 183)(13, 184)(14, 147)(15, 191)(16, 193)(17, 194)(18, 195)(19, 159)(20, 199)(21, 149)(22, 161)(23, 154)(24, 150)(25, 168)(26, 173)(27, 165)(28, 151)(29, 208)(30, 196)(31, 152)(32, 164)(33, 189)(34, 177)(35, 172)(36, 212)(37, 213)(38, 209)(39, 203)(40, 182)(41, 215)(42, 157)(43, 162)(44, 158)(45, 201)(46, 187)(47, 179)(48, 200)(49, 207)(50, 192)(51, 206)(52, 180)(53, 202)(54, 210)(55, 197)(56, 178)(57, 166)(58, 167)(59, 205)(60, 169)(61, 216)(62, 170)(63, 204)(64, 214)(65, 174)(66, 175)(67, 188)(68, 186)(69, 185)(70, 190)(71, 198)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1557
Graph:: simple bipartite
	v = 44 e = 144 f = 48
	degree seq :: [ 4^36, 18^8 ]

E27.1561 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 9, 18})
Quotient :: edge
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2^-3, T1 * T2 * T1^-1 * T2^2 * T1^-1 * T2, T1^-3 * T2^-6 ]
Map:: non-degenerate
	R = (1, 3, 10, 18, 49, 69, 37, 17, 5)(2, 7, 22, 48, 70, 38, 13, 26, 8)(4, 12, 20, 6, 19, 50, 68, 41, 14)(9, 28, 61, 53, 21, 35, 33, 62, 29)(11, 32, 39, 27, 60, 52, 47, 67, 34)(15, 42, 64, 30, 59, 71, 45, 23, 43)(16, 44, 65, 31, 25, 40, 63, 55, 46)(24, 56, 72, 54, 36, 66, 58, 51, 57)(73, 74, 78, 90, 120, 140, 109, 85, 76)(75, 81, 99, 121, 125, 119, 89, 105, 83)(77, 87, 103, 82, 102, 135, 141, 117, 88)(79, 93, 114, 142, 134, 131, 98, 100, 95)(80, 96, 127, 94, 126, 116, 110, 130, 97)(84, 107, 123, 91, 101, 128, 113, 133, 108)(86, 111, 118, 92, 124, 137, 122, 106, 112)(104, 115, 129, 132, 136, 144, 139, 143, 138)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 36^9 ) }
Outer automorphisms :: reflexible
Dual of E27.1568
Transitivity :: ET+
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 9^16 ]

E27.1562 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 9, 18})
Quotient :: edge
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^2 * T1 * T2^-1 * T1^-1, T2 * T1^-2 * T2^-1 * T1 * T2, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^4, T1 * T2 * T1^4 * T2 * T1 * T2, T1 * T2^3 * T1 * T2^3 * T1, T1^9 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 58, 62, 35, 59, 34, 54, 24, 44, 18, 43, 68, 41, 17, 5)(2, 7, 22, 51, 64, 36, 13, 33, 11, 31, 47, 69, 42, 67, 72, 56, 26, 8)(4, 12, 23, 52, 70, 57, 61, 71, 60, 39, 15, 20, 6, 19, 46, 66, 38, 14)(9, 27, 45, 63, 40, 16, 32, 48, 30, 50, 21, 49, 65, 37, 55, 25, 53, 28)(73, 74, 78, 90, 114, 133, 107, 85, 76)(75, 81, 94, 115, 137, 144, 131, 104, 83)(77, 87, 100, 116, 142, 121, 134, 110, 88)(79, 93, 118, 139, 112, 132, 105, 125, 95)(80, 96, 122, 141, 130, 135, 108, 89, 97)(82, 91, 117, 140, 143, 127, 106, 84, 102)(86, 98, 120, 92, 119, 99, 129, 136, 109)(101, 123, 138, 113, 128, 111, 126, 103, 124)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18^9 ), ( 18^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1566
Transitivity :: ET+
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 9^8, 18^4 ]

E27.1563 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 9, 18})
Quotient :: edge
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^-2 * T1^2 * T2 * T1, T1 * T2^-1 * T1 * T2^-4, T1 * T2^-1 * T1^-1 * T2^2 * T1 * T2, T1 * T2 * T1 * T2^2 * T1^-1 * T2^-1, T2^-1 * T1 * T2^2 * T1^4, T2 * T1^3 * T2^-1 * T1^-3 ]
Map:: non-degenerate
	R = (1, 3, 10, 31, 24, 66, 40, 61, 58, 72, 67, 56, 18, 55, 38, 53, 17, 5)(2, 7, 22, 62, 59, 41, 13, 39, 27, 69, 42, 52, 54, 35, 11, 33, 26, 8)(4, 12, 37, 47, 15, 46, 70, 30, 23, 63, 49, 20, 6, 19, 57, 71, 44, 14)(9, 28, 36, 65, 64, 45, 34, 60, 68, 25, 50, 16, 48, 43, 32, 51, 21, 29)(73, 74, 78, 90, 126, 142, 112, 85, 76)(75, 81, 99, 127, 120, 94, 133, 106, 83)(77, 87, 117, 128, 116, 101, 138, 121, 88)(79, 93, 109, 107, 122, 129, 111, 136, 95)(80, 96, 137, 124, 89, 123, 113, 139, 97)(82, 102, 140, 110, 84, 108, 130, 91, 104)(86, 114, 132, 92, 131, 100, 118, 98, 115)(103, 134, 143, 125, 105, 135, 144, 141, 119)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18^9 ), ( 18^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1567
Transitivity :: ET+
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 9^8, 18^4 ]

E27.1564 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 9, 18})
Quotient :: edge
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1 * T2, T2^2 * T1^-1 * T2 * T1 * T2 * T1^-1, T1^3 * T2^-1 * T1^-3 * T2, T2^-1 * T1^-1 * T2^-1 * T1^-4 * T2^-1 * T1^-1, T1^9, T2^18 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 54, 63, 34, 60, 69, 72, 68, 46, 18, 45, 48, 43, 17, 5)(2, 7, 11, 29, 36, 35, 13, 33, 61, 71, 65, 67, 44, 56, 25, 55, 24, 8)(4, 12, 32, 58, 40, 57, 62, 59, 51, 70, 50, 20, 6, 19, 22, 39, 15, 14)(9, 26, 28, 23, 21, 52, 30, 49, 47, 64, 53, 38, 66, 37, 31, 42, 41, 16)(73, 74, 78, 90, 116, 134, 106, 85, 76)(75, 81, 97, 117, 138, 133, 132, 102, 83)(77, 87, 110, 118, 122, 124, 135, 112, 88)(79, 93, 123, 128, 113, 104, 105, 125, 94)(80, 89, 114, 139, 140, 136, 107, 126, 95)(82, 84, 103, 120, 91, 119, 141, 131, 100)(86, 108, 121, 92, 96, 98, 129, 137, 109)(99, 101, 111, 115, 127, 142, 144, 143, 130)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18^9 ), ( 18^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1565
Transitivity :: ET+
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 9^8, 18^4 ]

E27.1565 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 9, 18})
Quotient :: loop
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1^-3 * T2, (T2 * T1^-1)^4, T2^2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1, T1^9, T2 * T1^3 * T2 * T1^3 * T2, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^2 * T2^2 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 18, 90, 43, 115, 62, 134, 35, 107, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 42, 114, 64, 136, 36, 108, 13, 85, 26, 98, 8, 80)(4, 76, 12, 84, 20, 92, 6, 78, 19, 91, 45, 117, 61, 133, 38, 110, 14, 86)(9, 81, 21, 93, 44, 116, 68, 140, 72, 144, 59, 131, 32, 104, 53, 125, 28, 100)(11, 83, 31, 103, 47, 119, 27, 99, 57, 129, 65, 137, 41, 113, 60, 132, 33, 105)(15, 87, 23, 95, 52, 124, 29, 101, 49, 121, 67, 139, 40, 112, 56, 128, 39, 111)(16, 88, 25, 97, 48, 120, 30, 102, 51, 123, 69, 141, 58, 130, 63, 135, 37, 109)(24, 96, 46, 118, 70, 142, 50, 122, 66, 138, 71, 143, 55, 127, 34, 106, 54, 126)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 101)(11, 75)(12, 100)(13, 76)(14, 105)(15, 102)(16, 77)(17, 104)(18, 114)(19, 116)(20, 119)(21, 121)(22, 122)(23, 79)(24, 123)(25, 80)(26, 125)(27, 115)(28, 118)(29, 130)(30, 82)(31, 124)(32, 83)(33, 120)(34, 84)(35, 85)(36, 127)(37, 86)(38, 131)(39, 126)(40, 88)(41, 89)(42, 133)(43, 140)(44, 138)(45, 137)(46, 91)(47, 141)(48, 92)(49, 136)(50, 135)(51, 94)(52, 142)(53, 95)(54, 103)(55, 97)(56, 98)(57, 139)(58, 134)(59, 106)(60, 111)(61, 107)(62, 112)(63, 108)(64, 144)(65, 109)(66, 110)(67, 143)(68, 113)(69, 117)(70, 129)(71, 132)(72, 128)
	local type(s) :: { ( 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1564
Transitivity :: ET+ VT+ AT
Graph::
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.1566 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 9, 18})
Quotient :: loop
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2^-3, T1 * T2 * T1^-1 * T2^2 * T1^-1 * T2, T1^-3 * T2^-6 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 18, 90, 49, 121, 69, 141, 37, 109, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 48, 120, 70, 142, 38, 110, 13, 85, 26, 98, 8, 80)(4, 76, 12, 84, 20, 92, 6, 78, 19, 91, 50, 122, 68, 140, 41, 113, 14, 86)(9, 81, 28, 100, 61, 133, 53, 125, 21, 93, 35, 107, 33, 105, 62, 134, 29, 101)(11, 83, 32, 104, 39, 111, 27, 99, 60, 132, 52, 124, 47, 119, 67, 139, 34, 106)(15, 87, 42, 114, 64, 136, 30, 102, 59, 131, 71, 143, 45, 117, 23, 95, 43, 115)(16, 88, 44, 116, 65, 137, 31, 103, 25, 97, 40, 112, 63, 135, 55, 127, 46, 118)(24, 96, 56, 128, 72, 144, 54, 126, 36, 108, 66, 138, 58, 130, 51, 123, 57, 129)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 102)(11, 75)(12, 107)(13, 76)(14, 111)(15, 103)(16, 77)(17, 105)(18, 120)(19, 101)(20, 124)(21, 114)(22, 126)(23, 79)(24, 127)(25, 80)(26, 100)(27, 121)(28, 95)(29, 128)(30, 135)(31, 82)(32, 115)(33, 83)(34, 112)(35, 123)(36, 84)(37, 85)(38, 130)(39, 118)(40, 86)(41, 133)(42, 142)(43, 129)(44, 110)(45, 88)(46, 92)(47, 89)(48, 140)(49, 125)(50, 106)(51, 91)(52, 137)(53, 119)(54, 116)(55, 94)(56, 113)(57, 132)(58, 97)(59, 98)(60, 136)(61, 108)(62, 131)(63, 141)(64, 144)(65, 122)(66, 104)(67, 143)(68, 109)(69, 117)(70, 134)(71, 138)(72, 139)
	local type(s) :: { ( 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1562
Transitivity :: ET+ VT+ AT
Graph::
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.1567 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 9, 18})
Quotient :: loop
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^3 * T1^-3, T2 * T1 * T2^-1 * T1^2 * T2^-1 * T1, T2^9, T1^9 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 18, 90, 49, 121, 70, 142, 37, 109, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 48, 120, 63, 135, 38, 110, 13, 85, 26, 98, 8, 80)(4, 76, 12, 84, 20, 92, 6, 78, 19, 91, 51, 123, 69, 141, 41, 113, 14, 86)(9, 81, 28, 100, 35, 107, 68, 140, 57, 129, 50, 122, 33, 105, 21, 93, 29, 101)(11, 83, 32, 104, 62, 134, 27, 99, 61, 133, 39, 111, 47, 119, 67, 139, 34, 106)(15, 87, 42, 114, 64, 136, 30, 102, 23, 95, 56, 128, 45, 117, 54, 126, 43, 115)(16, 88, 44, 116, 40, 112, 31, 103, 65, 137, 53, 125, 60, 132, 25, 97, 46, 118)(24, 96, 36, 108, 66, 138, 55, 127, 52, 124, 72, 144, 59, 131, 71, 143, 58, 130)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 102)(11, 75)(12, 107)(13, 76)(14, 111)(15, 103)(16, 77)(17, 105)(18, 120)(19, 122)(20, 106)(21, 126)(22, 127)(23, 79)(24, 116)(25, 80)(26, 129)(27, 121)(28, 114)(29, 108)(30, 132)(31, 82)(32, 128)(33, 83)(34, 118)(35, 124)(36, 84)(37, 85)(38, 131)(39, 125)(40, 86)(41, 101)(42, 98)(43, 130)(44, 94)(45, 88)(46, 123)(47, 89)(48, 141)(49, 140)(50, 143)(51, 134)(52, 91)(53, 92)(54, 135)(55, 137)(56, 144)(57, 95)(58, 139)(59, 97)(60, 142)(61, 115)(62, 112)(63, 100)(64, 138)(65, 110)(66, 104)(67, 136)(68, 119)(69, 109)(70, 117)(71, 113)(72, 133)
	local type(s) :: { ( 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18, 9, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1563
Transitivity :: ET+ VT+ AT
Graph::
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.1568 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 9, 18})
Quotient :: loop
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^2 * T1 * T2^-1 * T1^-1, T2 * T1^-2 * T2^-1 * T1 * T2, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^4, T1 * T2 * T1^4 * T2 * T1 * T2, T1 * T2^3 * T1 * T2^3 * T1, T1^9 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 29, 101, 58, 130, 62, 134, 35, 107, 59, 131, 34, 106, 54, 126, 24, 96, 44, 116, 18, 90, 43, 115, 68, 140, 41, 113, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 51, 123, 64, 136, 36, 108, 13, 85, 33, 105, 11, 83, 31, 103, 47, 119, 69, 141, 42, 114, 67, 139, 72, 144, 56, 128, 26, 98, 8, 80)(4, 76, 12, 84, 23, 95, 52, 124, 70, 142, 57, 129, 61, 133, 71, 143, 60, 132, 39, 111, 15, 87, 20, 92, 6, 78, 19, 91, 46, 118, 66, 138, 38, 110, 14, 86)(9, 81, 27, 99, 45, 117, 63, 135, 40, 112, 16, 88, 32, 104, 48, 120, 30, 102, 50, 122, 21, 93, 49, 121, 65, 137, 37, 109, 55, 127, 25, 97, 53, 125, 28, 100)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 94)(10, 91)(11, 75)(12, 102)(13, 76)(14, 98)(15, 100)(16, 77)(17, 97)(18, 114)(19, 117)(20, 119)(21, 118)(22, 115)(23, 79)(24, 122)(25, 80)(26, 120)(27, 129)(28, 116)(29, 123)(30, 82)(31, 124)(32, 83)(33, 125)(34, 84)(35, 85)(36, 89)(37, 86)(38, 88)(39, 126)(40, 132)(41, 128)(42, 133)(43, 137)(44, 142)(45, 140)(46, 139)(47, 99)(48, 92)(49, 134)(50, 141)(51, 138)(52, 101)(53, 95)(54, 103)(55, 106)(56, 111)(57, 136)(58, 135)(59, 104)(60, 105)(61, 107)(62, 110)(63, 108)(64, 109)(65, 144)(66, 113)(67, 112)(68, 143)(69, 130)(70, 121)(71, 127)(72, 131)
	local type(s) :: { ( 9^36 ) }
Outer automorphisms :: reflexible
Dual of E27.1561
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.1569 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1^2 * Y3^-1 * Y2^-1, Y3 * Y2^3 * Y1^-2, Y1 * Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^2, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y1 * Y2^-1 * R * Y2^-2 * R * Y2, Y3^2 * Y2^-1 * Y1 * Y3^-2 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^6, (Y3^-1 * Y1 * Y3^-1)^3, Y3^9 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 48, 120, 69, 141, 37, 109, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 49, 121, 68, 140, 47, 119, 17, 89, 33, 105, 11, 83)(5, 77, 15, 87, 31, 103, 10, 82, 30, 102, 60, 132, 70, 142, 45, 117, 16, 88)(7, 79, 21, 93, 54, 126, 63, 135, 28, 100, 42, 114, 26, 98, 57, 129, 23, 95)(8, 80, 24, 96, 44, 116, 22, 94, 55, 127, 65, 137, 38, 110, 59, 131, 25, 97)(12, 84, 35, 107, 52, 124, 19, 91, 50, 122, 71, 143, 41, 113, 29, 101, 36, 108)(14, 86, 39, 111, 53, 125, 20, 92, 34, 106, 46, 118, 51, 123, 62, 134, 40, 112)(32, 104, 56, 128, 72, 144, 61, 133, 43, 115, 58, 130, 67, 139, 64, 136, 66, 138)(145, 217, 147, 219, 154, 226, 162, 234, 193, 265, 214, 286, 181, 253, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 192, 264, 207, 279, 182, 254, 157, 229, 170, 242, 152, 224)(148, 220, 156, 228, 164, 236, 150, 222, 163, 235, 195, 267, 213, 285, 185, 257, 158, 230)(153, 225, 172, 244, 179, 251, 212, 284, 201, 273, 194, 266, 177, 249, 165, 237, 173, 245)(155, 227, 176, 248, 206, 278, 171, 243, 205, 277, 183, 255, 191, 263, 211, 283, 178, 250)(159, 231, 186, 258, 208, 280, 174, 246, 167, 239, 200, 272, 189, 261, 198, 270, 187, 259)(160, 232, 188, 260, 184, 256, 175, 247, 209, 281, 197, 269, 204, 276, 169, 241, 190, 262)(168, 240, 180, 252, 210, 282, 199, 271, 196, 268, 216, 288, 203, 275, 215, 287, 202, 274)
	L = (1, 148)(2, 145)(3, 155)(4, 157)(5, 160)(6, 146)(7, 167)(8, 169)(9, 147)(10, 175)(11, 177)(12, 180)(13, 181)(14, 184)(15, 149)(16, 189)(17, 191)(18, 150)(19, 196)(20, 197)(21, 151)(22, 188)(23, 201)(24, 152)(25, 203)(26, 186)(27, 153)(28, 207)(29, 185)(30, 154)(31, 159)(32, 210)(33, 161)(34, 164)(35, 156)(36, 173)(37, 213)(38, 209)(39, 158)(40, 206)(41, 215)(42, 172)(43, 205)(44, 168)(45, 214)(46, 178)(47, 212)(48, 162)(49, 171)(50, 163)(51, 190)(52, 179)(53, 183)(54, 165)(55, 166)(56, 176)(57, 170)(58, 187)(59, 182)(60, 174)(61, 216)(62, 195)(63, 198)(64, 211)(65, 199)(66, 208)(67, 202)(68, 193)(69, 192)(70, 204)(71, 194)(72, 200)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1576
Graph:: bipartite
	v = 16 e = 144 f = 76
	degree seq :: [ 18^16 ]

E27.1570 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^2 * Y2^-2 * Y1^-1, Y1^-1 * Y2^2 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1^-2, (Y2 * Y1^-1)^4, Y1^9, Y1^2 * Y2^3 * Y1 * Y2^3, (Y3^-1 * Y1^-1)^9 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 42, 114, 61, 133, 35, 107, 13, 85, 4, 76)(3, 75, 9, 81, 22, 94, 43, 115, 65, 137, 72, 144, 59, 131, 32, 104, 11, 83)(5, 77, 15, 87, 28, 100, 44, 116, 70, 142, 49, 121, 62, 134, 38, 110, 16, 88)(7, 79, 21, 93, 46, 118, 67, 139, 40, 112, 60, 132, 33, 105, 53, 125, 23, 95)(8, 80, 24, 96, 50, 122, 69, 141, 58, 130, 63, 135, 36, 108, 17, 89, 25, 97)(10, 82, 19, 91, 45, 117, 68, 140, 71, 143, 55, 127, 34, 106, 12, 84, 30, 102)(14, 86, 26, 98, 48, 120, 20, 92, 47, 119, 27, 99, 57, 129, 64, 136, 37, 109)(29, 101, 51, 123, 66, 138, 41, 113, 56, 128, 39, 111, 54, 126, 31, 103, 52, 124)(145, 217, 147, 219, 154, 226, 173, 245, 202, 274, 206, 278, 179, 251, 203, 275, 178, 250, 198, 270, 168, 240, 188, 260, 162, 234, 187, 259, 212, 284, 185, 257, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 195, 267, 208, 280, 180, 252, 157, 229, 177, 249, 155, 227, 175, 247, 191, 263, 213, 285, 186, 258, 211, 283, 216, 288, 200, 272, 170, 242, 152, 224)(148, 220, 156, 228, 167, 239, 196, 268, 214, 286, 201, 273, 205, 277, 215, 287, 204, 276, 183, 255, 159, 231, 164, 236, 150, 222, 163, 235, 190, 262, 210, 282, 182, 254, 158, 230)(153, 225, 171, 243, 189, 261, 207, 279, 184, 256, 160, 232, 176, 248, 192, 264, 174, 246, 194, 266, 165, 237, 193, 265, 209, 281, 181, 253, 199, 271, 169, 241, 197, 269, 172, 244)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 175)(12, 167)(13, 177)(14, 148)(15, 164)(16, 176)(17, 149)(18, 187)(19, 190)(20, 150)(21, 193)(22, 195)(23, 196)(24, 188)(25, 197)(26, 152)(27, 189)(28, 153)(29, 202)(30, 194)(31, 191)(32, 192)(33, 155)(34, 198)(35, 203)(36, 157)(37, 199)(38, 158)(39, 159)(40, 160)(41, 161)(42, 211)(43, 212)(44, 162)(45, 207)(46, 210)(47, 213)(48, 174)(49, 209)(50, 165)(51, 208)(52, 214)(53, 172)(54, 168)(55, 169)(56, 170)(57, 205)(58, 206)(59, 178)(60, 183)(61, 215)(62, 179)(63, 184)(64, 180)(65, 181)(66, 182)(67, 216)(68, 185)(69, 186)(70, 201)(71, 204)(72, 200)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1574
Graph:: bipartite
	v = 12 e = 144 f = 80
	degree seq :: [ 18^8, 36^4 ]

E27.1571 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2, Y1 * Y2^2 * Y1^-1 * Y2^-1 * Y1 * Y2, Y1 * Y2^-1 * Y1 * Y2^-4, Y1^2 * Y2 * Y1^2 * Y2^-2, Y2 * Y1 * Y2 * Y1^-2 * Y2 * Y1^-2, Y1^9, (Y3^-1 * Y1^-1)^9 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 54, 126, 70, 142, 40, 112, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 55, 127, 48, 120, 22, 94, 61, 133, 34, 106, 11, 83)(5, 77, 15, 87, 45, 117, 56, 128, 44, 116, 29, 101, 66, 138, 49, 121, 16, 88)(7, 79, 21, 93, 37, 109, 35, 107, 50, 122, 57, 129, 39, 111, 64, 136, 23, 95)(8, 80, 24, 96, 65, 137, 52, 124, 17, 89, 51, 123, 41, 113, 67, 139, 25, 97)(10, 82, 30, 102, 68, 140, 38, 110, 12, 84, 36, 108, 58, 130, 19, 91, 32, 104)(14, 86, 42, 114, 60, 132, 20, 92, 59, 131, 28, 100, 46, 118, 26, 98, 43, 115)(31, 103, 62, 134, 71, 143, 53, 125, 33, 105, 63, 135, 72, 144, 69, 141, 47, 119)(145, 217, 147, 219, 154, 226, 175, 247, 168, 240, 210, 282, 184, 256, 205, 277, 202, 274, 216, 288, 211, 283, 200, 272, 162, 234, 199, 271, 182, 254, 197, 269, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 206, 278, 203, 275, 185, 257, 157, 229, 183, 255, 171, 243, 213, 285, 186, 258, 196, 268, 198, 270, 179, 251, 155, 227, 177, 249, 170, 242, 152, 224)(148, 220, 156, 228, 181, 253, 191, 263, 159, 231, 190, 262, 214, 286, 174, 246, 167, 239, 207, 279, 193, 265, 164, 236, 150, 222, 163, 235, 201, 273, 215, 287, 188, 260, 158, 230)(153, 225, 172, 244, 180, 252, 209, 281, 208, 280, 189, 261, 178, 250, 204, 276, 212, 284, 169, 241, 194, 266, 160, 232, 192, 264, 187, 259, 176, 248, 195, 267, 165, 237, 173, 245)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 175)(11, 177)(12, 181)(13, 183)(14, 148)(15, 190)(16, 192)(17, 149)(18, 199)(19, 201)(20, 150)(21, 173)(22, 206)(23, 207)(24, 210)(25, 194)(26, 152)(27, 213)(28, 180)(29, 153)(30, 167)(31, 168)(32, 195)(33, 170)(34, 204)(35, 155)(36, 209)(37, 191)(38, 197)(39, 171)(40, 205)(41, 157)(42, 196)(43, 176)(44, 158)(45, 178)(46, 214)(47, 159)(48, 187)(49, 164)(50, 160)(51, 165)(52, 198)(53, 161)(54, 179)(55, 182)(56, 162)(57, 215)(58, 216)(59, 185)(60, 212)(61, 202)(62, 203)(63, 193)(64, 189)(65, 208)(66, 184)(67, 200)(68, 169)(69, 186)(70, 174)(71, 188)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1573
Graph:: bipartite
	v = 12 e = 144 f = 80
	degree seq :: [ 18^8, 36^4 ]

E27.1572 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^2 * Y1 * Y2^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1^-3 * Y2 * Y1^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-4 * Y2^-1 * Y1^-1, Y1^9, (Y3^-1 * Y1^-1)^9, Y2^18 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 44, 116, 62, 134, 34, 106, 13, 85, 4, 76)(3, 75, 9, 81, 25, 97, 45, 117, 66, 138, 61, 133, 60, 132, 30, 102, 11, 83)(5, 77, 15, 87, 38, 110, 46, 118, 50, 122, 52, 124, 63, 135, 40, 112, 16, 88)(7, 79, 21, 93, 51, 123, 56, 128, 41, 113, 32, 104, 33, 105, 53, 125, 22, 94)(8, 80, 17, 89, 42, 114, 67, 139, 68, 140, 64, 136, 35, 107, 54, 126, 23, 95)(10, 82, 12, 84, 31, 103, 48, 120, 19, 91, 47, 119, 69, 141, 59, 131, 28, 100)(14, 86, 36, 108, 49, 121, 20, 92, 24, 96, 26, 98, 57, 129, 65, 137, 37, 109)(27, 99, 29, 101, 39, 111, 43, 115, 55, 127, 70, 142, 72, 144, 71, 143, 58, 130)(145, 217, 147, 219, 154, 226, 171, 243, 198, 270, 207, 279, 178, 250, 204, 276, 213, 285, 216, 288, 212, 284, 190, 262, 162, 234, 189, 261, 192, 264, 187, 259, 161, 233, 149, 221)(146, 218, 151, 223, 155, 227, 173, 245, 180, 252, 179, 251, 157, 229, 177, 249, 205, 277, 215, 287, 209, 281, 211, 283, 188, 260, 200, 272, 169, 241, 199, 271, 168, 240, 152, 224)(148, 220, 156, 228, 176, 248, 202, 274, 184, 256, 201, 273, 206, 278, 203, 275, 195, 267, 214, 286, 194, 266, 164, 236, 150, 222, 163, 235, 166, 238, 183, 255, 159, 231, 158, 230)(153, 225, 170, 242, 172, 244, 167, 239, 165, 237, 196, 268, 174, 246, 193, 265, 191, 263, 208, 280, 197, 269, 182, 254, 210, 282, 181, 253, 175, 247, 186, 258, 185, 257, 160, 232)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 155)(8, 146)(9, 170)(10, 171)(11, 173)(12, 176)(13, 177)(14, 148)(15, 158)(16, 153)(17, 149)(18, 189)(19, 166)(20, 150)(21, 196)(22, 183)(23, 165)(24, 152)(25, 199)(26, 172)(27, 198)(28, 167)(29, 180)(30, 193)(31, 186)(32, 202)(33, 205)(34, 204)(35, 157)(36, 179)(37, 175)(38, 210)(39, 159)(40, 201)(41, 160)(42, 185)(43, 161)(44, 200)(45, 192)(46, 162)(47, 208)(48, 187)(49, 191)(50, 164)(51, 214)(52, 174)(53, 182)(54, 207)(55, 168)(56, 169)(57, 206)(58, 184)(59, 195)(60, 213)(61, 215)(62, 203)(63, 178)(64, 197)(65, 211)(66, 181)(67, 188)(68, 190)(69, 216)(70, 194)(71, 209)(72, 212)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1575
Graph:: bipartite
	v = 12 e = 144 f = 80
	degree seq :: [ 18^8, 36^4 ]

E27.1573 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3^-1)^2, (R * Y1)^2, Y3^-2 * Y2 * Y3 * Y2^-2, R * Y3 * Y2^-1 * Y3^-1 * R * Y2^-1, Y2^-1 * Y3^-1 * Y2^2 * Y3^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-1, Y3 * Y2^3 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y2^-1)^4, Y2 * Y3^-2 * Y2 * Y3^-5, Y2 * Y3^-2 * Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2^9, (Y3^-1 * Y1^-1)^18 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 186, 258, 210, 282, 179, 251, 157, 229, 148, 220)(147, 219, 153, 225, 171, 243, 187, 259, 214, 286, 198, 270, 207, 279, 176, 248, 155, 227)(149, 221, 159, 231, 170, 242, 188, 260, 209, 281, 215, 287, 208, 280, 177, 249, 160, 232)(151, 223, 165, 237, 193, 265, 213, 285, 212, 284, 205, 277, 174, 246, 154, 226, 167, 239)(152, 224, 168, 240, 192, 264, 206, 278, 175, 247, 201, 273, 180, 252, 197, 269, 169, 241)(156, 228, 166, 238, 190, 262, 163, 235, 189, 261, 183, 255, 211, 283, 204, 276, 178, 250)(158, 230, 181, 253, 161, 233, 164, 236, 191, 263, 202, 274, 216, 288, 196, 268, 182, 254)(172, 244, 194, 266, 184, 256, 199, 271, 185, 257, 200, 272, 203, 275, 173, 245, 195, 267)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 173)(11, 175)(12, 176)(13, 174)(14, 148)(15, 171)(16, 180)(17, 149)(18, 187)(19, 153)(20, 150)(21, 194)(22, 195)(23, 196)(24, 193)(25, 158)(26, 152)(27, 197)(28, 201)(29, 202)(30, 204)(31, 205)(32, 203)(33, 155)(34, 209)(35, 207)(36, 157)(37, 190)(38, 208)(39, 159)(40, 160)(41, 161)(42, 213)(43, 165)(44, 162)(45, 184)(46, 177)(47, 183)(48, 164)(49, 181)(50, 182)(51, 215)(52, 178)(53, 167)(54, 168)(55, 169)(56, 170)(57, 216)(58, 188)(59, 192)(60, 200)(61, 191)(62, 186)(63, 212)(64, 179)(65, 198)(66, 211)(67, 214)(68, 185)(69, 189)(70, 199)(71, 206)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1571
Graph:: simple bipartite
	v = 80 e = 144 f = 12
	degree seq :: [ 2^72, 18^8 ]

E27.1574 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * R * Y3^-1 * Y2^-2 * R * Y2, Y2 * Y3 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y2 * Y3^-1 * Y2^2 * Y3^2 * Y2, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * Y3 * Y2 * Y3^4, Y3 * Y2 * Y3^-2 * Y2^4, Y3 * Y2^4 * Y3^-2 * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-4 * Y3, (Y3^-1 * Y1^-1)^18 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 198, 270, 214, 286, 184, 256, 157, 229, 148, 220)(147, 219, 153, 225, 171, 243, 199, 271, 181, 253, 190, 262, 206, 278, 178, 250, 155, 227)(149, 221, 159, 231, 189, 261, 200, 272, 179, 251, 170, 242, 211, 283, 193, 265, 160, 232)(151, 223, 165, 237, 205, 277, 176, 248, 154, 226, 174, 246, 183, 255, 208, 280, 167, 239)(152, 224, 168, 240, 188, 260, 192, 264, 177, 249, 204, 276, 185, 257, 209, 281, 169, 241)(156, 228, 180, 252, 202, 274, 163, 235, 201, 273, 191, 263, 173, 245, 166, 238, 182, 254)(158, 230, 186, 258, 203, 275, 164, 236, 196, 268, 161, 233, 195, 267, 207, 279, 187, 259)(172, 244, 197, 269, 212, 284, 215, 287, 175, 247, 194, 266, 210, 282, 216, 288, 213, 285)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 175)(11, 177)(12, 181)(13, 183)(14, 148)(15, 190)(16, 192)(17, 149)(18, 199)(19, 178)(20, 150)(21, 197)(22, 194)(23, 207)(24, 174)(25, 195)(26, 152)(27, 209)(28, 188)(29, 153)(30, 196)(31, 187)(32, 180)(33, 167)(34, 210)(35, 155)(36, 213)(37, 215)(38, 179)(39, 201)(40, 206)(41, 157)(42, 191)(43, 200)(44, 158)(45, 185)(46, 168)(47, 159)(48, 198)(49, 171)(50, 160)(51, 214)(52, 182)(53, 161)(54, 176)(55, 208)(56, 162)(57, 212)(58, 193)(59, 211)(60, 164)(61, 186)(62, 165)(63, 202)(64, 216)(65, 205)(66, 169)(67, 184)(68, 170)(69, 189)(70, 173)(71, 204)(72, 203)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1570
Graph:: simple bipartite
	v = 80 e = 144 f = 12
	degree seq :: [ 2^72, 18^8 ]

E27.1575 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3^-2 * Y2 * Y3, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^2, Y2^2 * Y3^-1 * Y2^-3 * Y3 * Y2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^3, Y2^9, (Y3^-1 * Y1^-1)^18 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 188, 260, 208, 280, 178, 250, 157, 229, 148, 220)(147, 219, 153, 225, 169, 241, 189, 261, 191, 263, 198, 270, 204, 276, 174, 246, 155, 227)(149, 221, 159, 231, 182, 254, 190, 262, 200, 272, 210, 282, 209, 281, 184, 256, 160, 232)(151, 223, 154, 226, 171, 243, 201, 273, 212, 284, 207, 279, 177, 249, 196, 268, 166, 238)(152, 224, 167, 239, 197, 269, 202, 274, 173, 245, 181, 253, 179, 251, 199, 271, 168, 240)(156, 228, 175, 247, 192, 264, 163, 235, 165, 237, 183, 255, 205, 277, 206, 278, 176, 248)(158, 230, 180, 252, 194, 266, 164, 236, 193, 265, 214, 286, 211, 283, 186, 258, 161, 233)(170, 242, 172, 244, 195, 267, 213, 285, 216, 288, 215, 287, 203, 275, 187, 259, 185, 257)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 165)(8, 146)(9, 170)(10, 172)(11, 173)(12, 153)(13, 177)(14, 148)(15, 155)(16, 152)(17, 149)(18, 189)(19, 191)(20, 150)(21, 195)(22, 186)(23, 166)(24, 164)(25, 199)(26, 168)(27, 180)(28, 194)(29, 171)(30, 203)(31, 185)(32, 200)(33, 175)(34, 204)(35, 157)(36, 176)(37, 158)(38, 202)(39, 159)(40, 198)(41, 160)(42, 183)(43, 161)(44, 201)(45, 212)(46, 162)(47, 213)(48, 184)(49, 192)(50, 190)(51, 182)(52, 187)(53, 211)(54, 167)(55, 207)(56, 169)(57, 206)(58, 188)(59, 181)(60, 196)(61, 174)(62, 215)(63, 193)(64, 205)(65, 178)(66, 179)(67, 208)(68, 216)(69, 197)(70, 209)(71, 210)(72, 214)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 18, 36 ), ( 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36, 18, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1572
Graph:: simple bipartite
	v = 80 e = 144 f = 12
	degree seq :: [ 2^72, 18^8 ]

E27.1576 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 18})
Quotient :: dipole
Aut^+ = Q8 : C9 (small group id <72, 3>)
Aut   = (Q8 : C9) : C2 (small group id <144, 32>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^2 * Y1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-1, Y3^9, Y3 * Y1 * Y3^2 * Y1^2 * Y3^2 * Y1, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 42, 114, 66, 138, 41, 113, 56, 128, 39, 111, 54, 126, 31, 103, 52, 124, 29, 101, 51, 123, 61, 133, 35, 107, 13, 85, 4, 76)(3, 75, 9, 81, 22, 94, 43, 115, 63, 135, 36, 108, 17, 89, 25, 97, 8, 80, 24, 96, 50, 122, 69, 141, 58, 130, 65, 137, 72, 144, 59, 131, 32, 104, 11, 83)(5, 77, 15, 87, 28, 100, 44, 116, 70, 142, 49, 121, 68, 140, 71, 143, 55, 127, 34, 106, 12, 84, 30, 102, 10, 82, 19, 91, 45, 117, 62, 134, 38, 110, 16, 88)(7, 79, 21, 93, 46, 118, 64, 136, 37, 109, 14, 86, 26, 98, 48, 120, 20, 92, 47, 119, 27, 99, 57, 129, 67, 139, 40, 112, 60, 132, 33, 105, 53, 125, 23, 95)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 175)(12, 167)(13, 177)(14, 148)(15, 164)(16, 176)(17, 149)(18, 187)(19, 190)(20, 150)(21, 193)(22, 195)(23, 196)(24, 188)(25, 197)(26, 152)(27, 189)(28, 153)(29, 202)(30, 194)(31, 191)(32, 192)(33, 155)(34, 198)(35, 203)(36, 157)(37, 199)(38, 158)(39, 159)(40, 160)(41, 161)(42, 208)(43, 206)(44, 162)(45, 209)(46, 205)(47, 213)(48, 174)(49, 207)(50, 165)(51, 211)(52, 214)(53, 172)(54, 168)(55, 169)(56, 170)(57, 210)(58, 212)(59, 178)(60, 183)(61, 215)(62, 179)(63, 184)(64, 180)(65, 181)(66, 182)(67, 216)(68, 185)(69, 186)(70, 201)(71, 204)(72, 200)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 18, 18 ), ( 18^36 ) }
Outer automorphisms :: reflexible
Dual of E27.1569
Graph:: simple bipartite
	v = 76 e = 144 f = 16
	degree seq :: [ 2^72, 36^4 ]

E27.1577 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 18, 18})
Quotient :: edge
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-2 * T2 * T1^2 * T2^-1, T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1 * T2^-2, (T2^-1, T1)^2, (T2 * T1 * T2^2)^2 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 64, 37, 13, 33, 67, 72, 52, 20, 6, 19, 50, 46, 17, 5)(2, 7, 22, 53, 39, 14, 4, 12, 35, 65, 69, 48, 18, 47, 62, 60, 26, 8)(9, 27, 61, 45, 24, 34, 11, 32, 68, 58, 25, 57, 49, 54, 71, 44, 38, 28)(15, 40, 36, 29, 63, 43, 16, 42, 21, 31, 66, 59, 51, 56, 23, 55, 70, 41)(73, 74, 78, 90, 85, 76)(75, 81, 91, 121, 105, 83)(77, 87, 92, 123, 109, 88)(79, 93, 119, 108, 84, 95)(80, 96, 120, 110, 86, 97)(82, 101, 122, 127, 139, 103)(89, 116, 124, 130, 136, 117)(94, 104, 134, 99, 107, 126)(98, 115, 141, 113, 111, 131)(100, 114, 129, 112, 106, 128)(102, 125, 118, 132, 144, 137)(133, 138, 143, 135, 140, 142)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 36^6 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1581
Transitivity :: ET+
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.1578 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 18, 18})
Quotient :: edge
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T2 * T1^2 * T2^-1 * T1^-2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2, (T2 * T1^-1 * T2^2)^2 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 52, 20, 6, 19, 50, 72, 67, 37, 13, 33, 65, 46, 17, 5)(2, 7, 22, 53, 69, 48, 18, 47, 62, 68, 39, 14, 4, 12, 35, 60, 26, 8)(9, 27, 61, 58, 25, 57, 49, 54, 71, 45, 24, 34, 11, 32, 66, 44, 38, 28)(15, 40, 36, 29, 63, 59, 51, 56, 23, 55, 70, 43, 16, 42, 21, 31, 64, 41)(73, 74, 78, 90, 85, 76)(75, 81, 91, 121, 105, 83)(77, 87, 92, 123, 109, 88)(79, 93, 119, 108, 84, 95)(80, 96, 120, 110, 86, 97)(82, 101, 122, 127, 137, 103)(89, 116, 124, 130, 139, 117)(94, 104, 134, 99, 107, 126)(98, 115, 141, 113, 111, 131)(100, 114, 129, 112, 106, 128)(102, 125, 144, 140, 118, 132)(133, 136, 143, 135, 138, 142)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 36^6 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1580
Transitivity :: ET+
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 6^12, 18^4 ]

E27.1579 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {6, 18, 18})
Quotient :: edge
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-3 * T2^-1, (T2 * T1^-1 * T2)^2, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1, T2 * T1^-2 * T2^2 * T1 * T2 * T1^-1, (T2^-1, T1^-1)^2, (T2^-1 * T1^-1)^6, T2^-1 * T1^11 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 31, 54, 21, 53, 70, 57, 72, 50, 71, 67, 40, 46, 18, 17, 5)(2, 7, 22, 13, 38, 47, 69, 66, 35, 63, 41, 64, 44, 16, 43, 45, 26, 8)(4, 12, 36, 65, 29, 9, 28, 59, 33, 62, 25, 61, 68, 51, 20, 6, 19, 14)(11, 32, 15, 42, 48, 30, 49, 37, 52, 39, 58, 23, 56, 24, 60, 27, 55, 34)(73, 74, 78, 90, 117, 140, 139, 116, 134, 144, 135, 100, 125, 141, 137, 103, 85, 76)(75, 81, 99, 89, 108, 128, 112, 86, 111, 122, 92, 121, 142, 133, 114, 126, 105, 83)(77, 87, 113, 118, 106, 138, 143, 132, 110, 129, 95, 79, 93, 124, 98, 82, 102, 88)(80, 96, 131, 115, 130, 101, 136, 109, 84, 107, 120, 91, 119, 104, 123, 94, 127, 97)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 12^18 ) }
Outer automorphisms :: reflexible
Dual of E27.1582
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 72 f = 12
	degree seq :: [ 18^8 ]

E27.1580 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 18, 18})
Quotient :: loop
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-2 * T2 * T1^2 * T2^-1, T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1 * T2^-2, (T2^-1, T1)^2, (T2 * T1 * T2^2)^2 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 30, 102, 64, 136, 37, 109, 13, 85, 33, 105, 67, 139, 72, 144, 52, 124, 20, 92, 6, 78, 19, 91, 50, 122, 46, 118, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 53, 125, 39, 111, 14, 86, 4, 76, 12, 84, 35, 107, 65, 137, 69, 141, 48, 120, 18, 90, 47, 119, 62, 134, 60, 132, 26, 98, 8, 80)(9, 81, 27, 99, 61, 133, 45, 117, 24, 96, 34, 106, 11, 83, 32, 104, 68, 140, 58, 130, 25, 97, 57, 129, 49, 121, 54, 126, 71, 143, 44, 116, 38, 110, 28, 100)(15, 87, 40, 112, 36, 108, 29, 101, 63, 135, 43, 115, 16, 88, 42, 114, 21, 93, 31, 103, 66, 138, 59, 131, 51, 123, 56, 128, 23, 95, 55, 127, 70, 142, 41, 113)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 91)(10, 101)(11, 75)(12, 95)(13, 76)(14, 97)(15, 92)(16, 77)(17, 116)(18, 85)(19, 121)(20, 123)(21, 119)(22, 104)(23, 79)(24, 120)(25, 80)(26, 115)(27, 107)(28, 114)(29, 122)(30, 125)(31, 82)(32, 134)(33, 83)(34, 128)(35, 126)(36, 84)(37, 88)(38, 86)(39, 131)(40, 106)(41, 111)(42, 129)(43, 141)(44, 124)(45, 89)(46, 132)(47, 108)(48, 110)(49, 105)(50, 127)(51, 109)(52, 130)(53, 118)(54, 94)(55, 139)(56, 100)(57, 112)(58, 136)(59, 98)(60, 144)(61, 138)(62, 99)(63, 140)(64, 117)(65, 102)(66, 143)(67, 103)(68, 142)(69, 113)(70, 133)(71, 135)(72, 137)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1578
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.1581 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 18, 18})
Quotient :: loop
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T2 * T1^2 * T2^-1 * T1^-2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2, (T2 * T1^-1 * T2^2)^2 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 30, 102, 52, 124, 20, 92, 6, 78, 19, 91, 50, 122, 72, 144, 67, 139, 37, 109, 13, 85, 33, 105, 65, 137, 46, 118, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 53, 125, 69, 141, 48, 120, 18, 90, 47, 119, 62, 134, 68, 140, 39, 111, 14, 86, 4, 76, 12, 84, 35, 107, 60, 132, 26, 98, 8, 80)(9, 81, 27, 99, 61, 133, 58, 130, 25, 97, 57, 129, 49, 121, 54, 126, 71, 143, 45, 117, 24, 96, 34, 106, 11, 83, 32, 104, 66, 138, 44, 116, 38, 110, 28, 100)(15, 87, 40, 112, 36, 108, 29, 101, 63, 135, 59, 131, 51, 123, 56, 128, 23, 95, 55, 127, 70, 142, 43, 115, 16, 88, 42, 114, 21, 93, 31, 103, 64, 136, 41, 113)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 91)(10, 101)(11, 75)(12, 95)(13, 76)(14, 97)(15, 92)(16, 77)(17, 116)(18, 85)(19, 121)(20, 123)(21, 119)(22, 104)(23, 79)(24, 120)(25, 80)(26, 115)(27, 107)(28, 114)(29, 122)(30, 125)(31, 82)(32, 134)(33, 83)(34, 128)(35, 126)(36, 84)(37, 88)(38, 86)(39, 131)(40, 106)(41, 111)(42, 129)(43, 141)(44, 124)(45, 89)(46, 132)(47, 108)(48, 110)(49, 105)(50, 127)(51, 109)(52, 130)(53, 144)(54, 94)(55, 137)(56, 100)(57, 112)(58, 139)(59, 98)(60, 102)(61, 136)(62, 99)(63, 138)(64, 143)(65, 103)(66, 142)(67, 117)(68, 118)(69, 113)(70, 133)(71, 135)(72, 140)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.1577
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.1582 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {6, 18, 18})
Quotient :: loop
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^6, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-2, T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1, (T1, T2)^2, (T1^2 * T2 * T1)^2 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 10, 82, 30, 102, 17, 89, 5, 77)(2, 74, 7, 79, 22, 94, 56, 128, 26, 98, 8, 80)(4, 76, 12, 84, 31, 103, 63, 135, 42, 114, 14, 86)(6, 78, 19, 91, 51, 123, 61, 133, 53, 125, 20, 92)(9, 81, 28, 100, 60, 132, 44, 116, 15, 87, 29, 101)(11, 83, 32, 104, 62, 134, 46, 118, 16, 88, 34, 106)(13, 85, 37, 109, 64, 136, 68, 140, 47, 119, 39, 111)(18, 90, 48, 120, 38, 110, 65, 137, 72, 144, 49, 121)(21, 93, 43, 115, 59, 131, 27, 99, 24, 96, 55, 127)(23, 95, 40, 112, 67, 139, 35, 107, 25, 97, 57, 129)(33, 105, 41, 113, 70, 142, 36, 108, 45, 117, 66, 138)(50, 122, 58, 130, 69, 141, 54, 126, 52, 124, 71, 143)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 87)(6, 90)(7, 93)(8, 96)(9, 99)(10, 94)(11, 75)(12, 107)(13, 76)(14, 112)(15, 115)(16, 77)(17, 98)(18, 119)(19, 122)(20, 124)(21, 126)(22, 123)(23, 79)(24, 130)(25, 80)(26, 125)(27, 120)(28, 92)(29, 133)(30, 132)(31, 82)(32, 97)(33, 83)(34, 139)(35, 116)(36, 84)(37, 118)(38, 85)(39, 104)(40, 100)(41, 86)(42, 89)(43, 121)(44, 91)(45, 88)(46, 95)(47, 114)(48, 117)(49, 142)(50, 113)(51, 110)(52, 138)(53, 144)(54, 111)(55, 137)(56, 131)(57, 101)(58, 140)(59, 143)(60, 127)(61, 141)(62, 102)(63, 129)(64, 103)(65, 105)(66, 135)(67, 128)(68, 106)(69, 108)(70, 134)(71, 109)(72, 136)
	local type(s) :: { ( 18^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1579
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 72 f = 8
	degree seq :: [ 12^12 ]

E27.1583 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3^-1 * Y2, Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^6, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^2, Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y2^-2, Y2^-1 * Y1 * Y2^-3 * Y3^-1 * Y2^-2, Y1 * Y2 * R * Y2^-4 * R * Y2, Y1 * Y2^2 * R * Y2^-2 * R * Y2^2, (Y3 * Y2^-1)^18 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 49, 121, 33, 105, 11, 83)(5, 77, 15, 87, 20, 92, 51, 123, 37, 109, 16, 88)(7, 79, 21, 93, 47, 119, 36, 108, 12, 84, 23, 95)(8, 80, 24, 96, 48, 120, 38, 110, 14, 86, 25, 97)(10, 82, 29, 101, 50, 122, 55, 127, 65, 137, 31, 103)(17, 89, 44, 116, 52, 124, 58, 130, 67, 139, 45, 117)(22, 94, 32, 104, 62, 134, 27, 99, 35, 107, 54, 126)(26, 98, 43, 115, 69, 141, 41, 113, 39, 111, 59, 131)(28, 100, 42, 114, 57, 129, 40, 112, 34, 106, 56, 128)(30, 102, 53, 125, 72, 144, 68, 140, 46, 118, 60, 132)(61, 133, 64, 136, 71, 143, 63, 135, 66, 138, 70, 142)(145, 217, 147, 219, 154, 226, 174, 246, 196, 268, 164, 236, 150, 222, 163, 235, 194, 266, 216, 288, 211, 283, 181, 253, 157, 229, 177, 249, 209, 281, 190, 262, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 197, 269, 213, 285, 192, 264, 162, 234, 191, 263, 206, 278, 212, 284, 183, 255, 158, 230, 148, 220, 156, 228, 179, 251, 204, 276, 170, 242, 152, 224)(153, 225, 171, 243, 205, 277, 202, 274, 169, 241, 201, 273, 193, 265, 198, 270, 215, 287, 189, 261, 168, 240, 178, 250, 155, 227, 176, 248, 210, 282, 188, 260, 182, 254, 172, 244)(159, 231, 184, 256, 180, 252, 173, 245, 207, 279, 203, 275, 195, 267, 200, 272, 167, 239, 199, 271, 214, 286, 187, 259, 160, 232, 186, 258, 165, 237, 175, 247, 208, 280, 185, 257)
	L = (1, 148)(2, 145)(3, 155)(4, 157)(5, 160)(6, 146)(7, 167)(8, 169)(9, 147)(10, 175)(11, 177)(12, 180)(13, 162)(14, 182)(15, 149)(16, 181)(17, 189)(18, 150)(19, 153)(20, 159)(21, 151)(22, 198)(23, 156)(24, 152)(25, 158)(26, 203)(27, 206)(28, 200)(29, 154)(30, 204)(31, 209)(32, 166)(33, 193)(34, 184)(35, 171)(36, 191)(37, 195)(38, 192)(39, 185)(40, 201)(41, 213)(42, 172)(43, 170)(44, 161)(45, 211)(46, 212)(47, 165)(48, 168)(49, 163)(50, 173)(51, 164)(52, 188)(53, 174)(54, 179)(55, 194)(56, 178)(57, 186)(58, 196)(59, 183)(60, 190)(61, 214)(62, 176)(63, 215)(64, 205)(65, 199)(66, 207)(67, 202)(68, 216)(69, 187)(70, 210)(71, 208)(72, 197)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1587
Graph:: bipartite
	v = 16 e = 144 f = 76
	degree seq :: [ 12^12, 36^4 ]

E27.1584 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y3^6, Y1^6, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y3 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^2, Y2 * Y1 * Y2 * Y1 * Y2^-2 * Y3^-1, Y3^2 * Y2^-6, (Y2^2 * Y1 * Y2)^2, Y1 * Y2^-1 * R * Y3^2 * Y2^-2 * R * Y2^-1, Y1 * Y2^-2 * R * Y2^2 * R * Y2^-2, (Y3 * Y2^-1)^18 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 49, 121, 33, 105, 11, 83)(5, 77, 15, 87, 20, 92, 51, 123, 37, 109, 16, 88)(7, 79, 21, 93, 47, 119, 36, 108, 12, 84, 23, 95)(8, 80, 24, 96, 48, 120, 38, 110, 14, 86, 25, 97)(10, 82, 29, 101, 50, 122, 55, 127, 67, 139, 31, 103)(17, 89, 44, 116, 52, 124, 58, 130, 64, 136, 45, 117)(22, 94, 32, 104, 62, 134, 27, 99, 35, 107, 54, 126)(26, 98, 43, 115, 69, 141, 41, 113, 39, 111, 59, 131)(28, 100, 42, 114, 57, 129, 40, 112, 34, 106, 56, 128)(30, 102, 53, 125, 46, 118, 60, 132, 72, 144, 65, 137)(61, 133, 66, 138, 71, 143, 63, 135, 68, 140, 70, 142)(145, 217, 147, 219, 154, 226, 174, 246, 208, 280, 181, 253, 157, 229, 177, 249, 211, 283, 216, 288, 196, 268, 164, 236, 150, 222, 163, 235, 194, 266, 190, 262, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 197, 269, 183, 255, 158, 230, 148, 220, 156, 228, 179, 251, 209, 281, 213, 285, 192, 264, 162, 234, 191, 263, 206, 278, 204, 276, 170, 242, 152, 224)(153, 225, 171, 243, 205, 277, 189, 261, 168, 240, 178, 250, 155, 227, 176, 248, 212, 284, 202, 274, 169, 241, 201, 273, 193, 265, 198, 270, 215, 287, 188, 260, 182, 254, 172, 244)(159, 231, 184, 256, 180, 252, 173, 245, 207, 279, 187, 259, 160, 232, 186, 258, 165, 237, 175, 247, 210, 282, 203, 275, 195, 267, 200, 272, 167, 239, 199, 271, 214, 286, 185, 257)
	L = (1, 148)(2, 145)(3, 155)(4, 157)(5, 160)(6, 146)(7, 167)(8, 169)(9, 147)(10, 175)(11, 177)(12, 180)(13, 162)(14, 182)(15, 149)(16, 181)(17, 189)(18, 150)(19, 153)(20, 159)(21, 151)(22, 198)(23, 156)(24, 152)(25, 158)(26, 203)(27, 206)(28, 200)(29, 154)(30, 209)(31, 211)(32, 166)(33, 193)(34, 184)(35, 171)(36, 191)(37, 195)(38, 192)(39, 185)(40, 201)(41, 213)(42, 172)(43, 170)(44, 161)(45, 208)(46, 197)(47, 165)(48, 168)(49, 163)(50, 173)(51, 164)(52, 188)(53, 174)(54, 179)(55, 194)(56, 178)(57, 186)(58, 196)(59, 183)(60, 190)(61, 214)(62, 176)(63, 215)(64, 202)(65, 216)(66, 205)(67, 199)(68, 207)(69, 187)(70, 212)(71, 210)(72, 204)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1588
Graph:: bipartite
	v = 16 e = 144 f = 76
	degree seq :: [ 12^12, 36^4 ]

E27.1585 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1^-3 * Y2^-1, (Y2 * Y1^-2)^2, (Y2^-1, Y1^-1)^2, Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, (Y3^-1 * Y1^-1)^6, Y1^18 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 45, 117, 28, 100, 52, 124, 69, 141, 64, 136, 71, 143, 65, 137, 72, 144, 67, 139, 43, 115, 61, 133, 31, 103, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 17, 89, 44, 116, 59, 131, 68, 140, 60, 132, 40, 112, 53, 125, 36, 108, 56, 128, 39, 111, 14, 86, 38, 110, 49, 121, 20, 92, 11, 83)(5, 77, 15, 87, 37, 109, 46, 118, 23, 95, 7, 79, 21, 93, 51, 123, 26, 98, 62, 134, 34, 106, 66, 138, 70, 142, 58, 130, 32, 104, 10, 82, 30, 102, 16, 88)(8, 80, 24, 96, 12, 84, 35, 107, 48, 120, 19, 91, 47, 119, 41, 113, 50, 122, 42, 114, 57, 129, 29, 101, 63, 135, 33, 105, 55, 127, 22, 94, 54, 126, 25, 97)(145, 217, 147, 219, 154, 226, 175, 247, 193, 265, 214, 286, 211, 283, 183, 255, 206, 278, 215, 287, 197, 269, 165, 237, 196, 268, 212, 284, 190, 262, 162, 234, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 157, 229, 181, 253, 207, 279, 187, 259, 160, 232, 186, 258, 209, 281, 176, 248, 191, 263, 213, 285, 210, 282, 179, 251, 189, 261, 170, 242, 152, 224)(148, 220, 156, 228, 180, 252, 205, 277, 169, 241, 204, 276, 216, 288, 199, 271, 188, 260, 208, 280, 173, 245, 153, 225, 172, 244, 194, 266, 164, 236, 150, 222, 163, 235, 158, 230)(155, 227, 177, 249, 195, 267, 182, 254, 201, 273, 167, 239, 200, 272, 185, 257, 159, 231, 184, 256, 192, 264, 174, 246, 203, 275, 168, 240, 202, 274, 171, 243, 198, 270, 178, 250)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 175)(11, 177)(12, 180)(13, 181)(14, 148)(15, 184)(16, 186)(17, 149)(18, 161)(19, 158)(20, 150)(21, 196)(22, 157)(23, 200)(24, 202)(25, 204)(26, 152)(27, 198)(28, 194)(29, 153)(30, 203)(31, 193)(32, 191)(33, 195)(34, 155)(35, 189)(36, 205)(37, 207)(38, 201)(39, 206)(40, 192)(41, 159)(42, 209)(43, 160)(44, 208)(45, 170)(46, 162)(47, 213)(48, 174)(49, 214)(50, 164)(51, 182)(52, 212)(53, 165)(54, 178)(55, 188)(56, 185)(57, 167)(58, 171)(59, 168)(60, 216)(61, 169)(62, 215)(63, 187)(64, 173)(65, 176)(66, 179)(67, 183)(68, 190)(69, 210)(70, 211)(71, 197)(72, 199)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1586
Graph:: bipartite
	v = 8 e = 144 f = 84
	degree seq :: [ 36^8 ]

E27.1586 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y2^-2 * Y3 * Y2^2 * Y3^-1, Y2^-1 * Y3^-2 * Y2^-1 * Y3 * Y2^-1 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, (Y3^-1, Y2)^2, (Y3 * Y2 * Y3^2)^2, (Y3^-1 * Y1^-1)^18 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 157, 229, 148, 220)(147, 219, 153, 225, 163, 235, 193, 265, 177, 249, 155, 227)(149, 221, 159, 231, 164, 236, 195, 267, 181, 253, 160, 232)(151, 223, 165, 237, 191, 263, 180, 252, 156, 228, 167, 239)(152, 224, 168, 240, 192, 264, 182, 254, 158, 230, 169, 241)(154, 226, 173, 245, 194, 266, 199, 271, 211, 283, 175, 247)(161, 233, 188, 260, 196, 268, 202, 274, 208, 280, 189, 261)(166, 238, 176, 248, 206, 278, 171, 243, 179, 251, 198, 270)(170, 242, 187, 259, 213, 285, 185, 257, 183, 255, 203, 275)(172, 244, 186, 258, 201, 273, 184, 256, 178, 250, 200, 272)(174, 246, 197, 269, 190, 262, 204, 276, 216, 288, 209, 281)(205, 277, 210, 282, 215, 287, 207, 279, 212, 284, 214, 286)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 174)(11, 176)(12, 179)(13, 177)(14, 148)(15, 184)(16, 186)(17, 149)(18, 191)(19, 194)(20, 150)(21, 175)(22, 197)(23, 199)(24, 178)(25, 201)(26, 152)(27, 205)(28, 153)(29, 207)(30, 208)(31, 210)(32, 212)(33, 211)(34, 155)(35, 209)(36, 173)(37, 157)(38, 172)(39, 158)(40, 180)(41, 159)(42, 165)(43, 160)(44, 182)(45, 168)(46, 161)(47, 206)(48, 162)(49, 198)(50, 190)(51, 200)(52, 164)(53, 183)(54, 215)(55, 214)(56, 167)(57, 193)(58, 169)(59, 195)(60, 170)(61, 189)(62, 204)(63, 187)(64, 181)(65, 213)(66, 203)(67, 216)(68, 202)(69, 192)(70, 185)(71, 188)(72, 196)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 36, 36 ), ( 36^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1585
Graph:: simple bipartite
	v = 84 e = 144 f = 8
	degree seq :: [ 2^72, 12^12 ]

E27.1587 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-2 * Y1^-1 * Y3^2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, (Y1, Y3)^2, (Y1^2 * Y3 * Y1)^2, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 47, 119, 42, 114, 17, 89, 26, 98, 53, 125, 72, 144, 64, 136, 31, 103, 10, 82, 22, 94, 51, 123, 38, 110, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 48, 120, 45, 117, 16, 88, 5, 77, 15, 87, 43, 115, 49, 121, 70, 142, 62, 134, 30, 102, 60, 132, 55, 127, 65, 137, 33, 105, 11, 83)(7, 79, 21, 93, 54, 126, 39, 111, 32, 104, 25, 97, 8, 80, 24, 96, 58, 130, 68, 140, 34, 106, 67, 139, 56, 128, 59, 131, 71, 143, 37, 109, 46, 118, 23, 95)(12, 84, 35, 107, 44, 116, 19, 91, 50, 122, 41, 113, 14, 86, 40, 112, 28, 100, 20, 92, 52, 124, 66, 138, 63, 135, 57, 129, 29, 101, 61, 133, 69, 141, 36, 108)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 174)(11, 176)(12, 175)(13, 181)(14, 148)(15, 173)(16, 178)(17, 149)(18, 192)(19, 195)(20, 150)(21, 187)(22, 200)(23, 184)(24, 199)(25, 201)(26, 152)(27, 168)(28, 204)(29, 153)(30, 161)(31, 207)(32, 206)(33, 185)(34, 155)(35, 169)(36, 189)(37, 208)(38, 209)(39, 157)(40, 211)(41, 214)(42, 158)(43, 203)(44, 159)(45, 210)(46, 160)(47, 183)(48, 182)(49, 162)(50, 202)(51, 205)(52, 215)(53, 164)(54, 196)(55, 165)(56, 170)(57, 167)(58, 213)(59, 171)(60, 188)(61, 197)(62, 190)(63, 186)(64, 212)(65, 216)(66, 177)(67, 179)(68, 191)(69, 198)(70, 180)(71, 194)(72, 193)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1583
Graph:: simple bipartite
	v = 76 e = 144 f = 16
	degree seq :: [ 2^72, 36^4 ]

E27.1588 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {6, 18, 18})
Quotient :: dipole
Aut^+ = C2 x ((C2 x C2) : C9) (small group id <72, 16>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-2 * Y1^-1 * Y3^2 * Y1, Y3^-1 * Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3, Y3^-2 * Y1^6, (Y3, Y1^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1^4, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 47, 119, 31, 103, 10, 82, 22, 94, 51, 123, 72, 144, 70, 142, 42, 114, 17, 89, 26, 98, 53, 125, 38, 110, 13, 85, 4, 76)(3, 75, 9, 81, 27, 99, 48, 120, 67, 139, 62, 134, 30, 102, 60, 132, 55, 127, 68, 140, 45, 117, 16, 88, 5, 77, 15, 87, 43, 115, 49, 121, 33, 105, 11, 83)(7, 79, 21, 93, 54, 126, 66, 138, 34, 106, 65, 137, 56, 128, 59, 131, 69, 141, 39, 111, 32, 104, 25, 97, 8, 80, 24, 96, 58, 130, 37, 109, 46, 118, 23, 95)(12, 84, 35, 107, 44, 116, 19, 91, 50, 122, 64, 136, 63, 135, 57, 129, 29, 101, 61, 133, 71, 143, 41, 113, 14, 86, 40, 112, 28, 100, 20, 92, 52, 124, 36, 108)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 172)(10, 174)(11, 176)(12, 175)(13, 181)(14, 148)(15, 173)(16, 178)(17, 149)(18, 192)(19, 195)(20, 150)(21, 187)(22, 200)(23, 184)(24, 199)(25, 201)(26, 152)(27, 168)(28, 204)(29, 153)(30, 161)(31, 207)(32, 206)(33, 185)(34, 155)(35, 169)(36, 189)(37, 191)(38, 193)(39, 157)(40, 209)(41, 211)(42, 158)(43, 203)(44, 159)(45, 208)(46, 160)(47, 210)(48, 216)(49, 162)(50, 202)(51, 205)(52, 213)(53, 164)(54, 196)(55, 165)(56, 170)(57, 167)(58, 215)(59, 171)(60, 188)(61, 197)(62, 190)(63, 186)(64, 177)(65, 179)(66, 214)(67, 180)(68, 182)(69, 194)(70, 183)(71, 198)(72, 212)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 12, 36 ), ( 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36, 12, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1584
Graph:: simple bipartite
	v = 76 e = 144 f = 16
	degree seq :: [ 2^72, 36^4 ]

E27.1589 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 6, 78)(4, 76, 9, 81)(5, 77, 10, 82)(7, 79, 11, 83)(8, 80, 12, 84)(13, 85, 17, 89)(14, 86, 18, 90)(15, 87, 19, 91)(16, 88, 20, 92)(21, 93, 25, 97)(22, 94, 26, 98)(23, 95, 27, 99)(24, 96, 28, 100)(29, 101, 33, 105)(30, 102, 34, 106)(31, 103, 51, 123)(32, 104, 52, 124)(35, 107, 55, 127)(36, 108, 56, 128)(37, 109, 57, 129)(38, 110, 58, 130)(39, 111, 59, 131)(40, 112, 60, 132)(41, 113, 61, 133)(42, 114, 62, 134)(43, 115, 63, 135)(44, 116, 64, 136)(45, 117, 65, 137)(46, 118, 66, 138)(47, 119, 67, 139)(48, 120, 68, 140)(49, 121, 69, 141)(50, 122, 70, 142)(53, 125, 71, 143)(54, 126, 72, 144)(145, 217, 147, 219)(146, 218, 150, 222)(148, 220, 149, 221)(151, 223, 152, 224)(153, 225, 154, 226)(155, 227, 156, 228)(157, 229, 158, 230)(159, 231, 160, 232)(161, 233, 162, 234)(163, 235, 164, 236)(165, 237, 166, 238)(167, 239, 168, 240)(169, 241, 170, 242)(171, 243, 172, 244)(173, 245, 174, 246)(175, 247, 176, 248)(177, 249, 178, 250)(179, 251, 181, 253)(180, 252, 182, 254)(183, 255, 184, 256)(185, 257, 186, 258)(187, 259, 188, 260)(189, 261, 190, 262)(191, 263, 192, 264)(193, 265, 194, 266)(195, 267, 196, 268)(197, 269, 198, 270)(199, 271, 201, 273)(200, 272, 202, 274)(203, 275, 204, 276)(205, 277, 206, 278)(207, 279, 208, 280)(209, 281, 210, 282)(211, 283, 212, 284)(213, 285, 214, 286)(215, 287, 216, 288)
	L = (1, 148)(2, 151)(3, 149)(4, 147)(5, 145)(6, 152)(7, 150)(8, 146)(9, 157)(10, 158)(11, 159)(12, 160)(13, 154)(14, 153)(15, 156)(16, 155)(17, 165)(18, 166)(19, 167)(20, 168)(21, 162)(22, 161)(23, 164)(24, 163)(25, 173)(26, 174)(27, 175)(28, 176)(29, 170)(30, 169)(31, 172)(32, 171)(33, 181)(34, 179)(35, 177)(36, 195)(37, 178)(38, 196)(39, 201)(40, 199)(41, 202)(42, 200)(43, 204)(44, 203)(45, 206)(46, 205)(47, 208)(48, 207)(49, 210)(50, 209)(51, 182)(52, 180)(53, 212)(54, 211)(55, 183)(56, 185)(57, 184)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 197)(68, 198)(69, 215)(70, 216)(71, 214)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1598
Graph:: simple bipartite
	v = 72 e = 144 f = 20
	degree seq :: [ 4^72 ]

E27.1590 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y3^9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 10, 82)(5, 77, 9, 81)(6, 78, 8, 80)(11, 83, 18, 90)(12, 84, 20, 92)(13, 85, 19, 91)(14, 86, 24, 96)(15, 87, 23, 95)(16, 88, 22, 94)(17, 89, 21, 93)(25, 97, 34, 106)(26, 98, 33, 105)(27, 99, 36, 108)(28, 100, 35, 107)(29, 101, 40, 112)(30, 102, 39, 111)(31, 103, 38, 110)(32, 104, 37, 109)(41, 113, 50, 122)(42, 114, 49, 121)(43, 115, 52, 124)(44, 116, 51, 123)(45, 117, 56, 128)(46, 118, 55, 127)(47, 119, 54, 126)(48, 120, 53, 125)(57, 129, 64, 136)(58, 130, 63, 135)(59, 131, 66, 138)(60, 132, 65, 137)(61, 133, 68, 140)(62, 134, 67, 139)(69, 141, 72, 144)(70, 142, 71, 143)(145, 217, 147, 219, 155, 227, 149, 221)(146, 218, 151, 223, 162, 234, 153, 225)(148, 220, 156, 228, 169, 241, 159, 231)(150, 222, 157, 229, 170, 242, 160, 232)(152, 224, 163, 235, 177, 249, 166, 238)(154, 226, 164, 236, 178, 250, 167, 239)(158, 230, 171, 243, 185, 257, 174, 246)(161, 233, 172, 244, 186, 258, 175, 247)(165, 237, 179, 251, 193, 265, 182, 254)(168, 240, 180, 252, 194, 266, 183, 255)(173, 245, 187, 259, 201, 273, 190, 262)(176, 248, 188, 260, 202, 274, 191, 263)(181, 253, 195, 267, 207, 279, 198, 270)(184, 256, 196, 268, 208, 280, 199, 271)(189, 261, 203, 275, 213, 285, 205, 277)(192, 264, 204, 276, 214, 286, 206, 278)(197, 269, 209, 281, 215, 287, 211, 283)(200, 272, 210, 282, 216, 288, 212, 284)
	L = (1, 148)(2, 152)(3, 156)(4, 158)(5, 159)(6, 145)(7, 163)(8, 165)(9, 166)(10, 146)(11, 169)(12, 171)(13, 147)(14, 173)(15, 174)(16, 149)(17, 150)(18, 177)(19, 179)(20, 151)(21, 181)(22, 182)(23, 153)(24, 154)(25, 185)(26, 155)(27, 187)(28, 157)(29, 189)(30, 190)(31, 160)(32, 161)(33, 193)(34, 162)(35, 195)(36, 164)(37, 197)(38, 198)(39, 167)(40, 168)(41, 201)(42, 170)(43, 203)(44, 172)(45, 192)(46, 205)(47, 175)(48, 176)(49, 207)(50, 178)(51, 209)(52, 180)(53, 200)(54, 211)(55, 183)(56, 184)(57, 213)(58, 186)(59, 204)(60, 188)(61, 206)(62, 191)(63, 215)(64, 194)(65, 210)(66, 196)(67, 212)(68, 199)(69, 214)(70, 202)(71, 216)(72, 208)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1596
Graph:: simple bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1591 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^4, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^2 * Y3^-9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 10, 82)(5, 77, 9, 81)(6, 78, 8, 80)(11, 83, 18, 90)(12, 84, 20, 92)(13, 85, 19, 91)(14, 86, 24, 96)(15, 87, 23, 95)(16, 88, 22, 94)(17, 89, 21, 93)(25, 97, 34, 106)(26, 98, 33, 105)(27, 99, 36, 108)(28, 100, 35, 107)(29, 101, 40, 112)(30, 102, 39, 111)(31, 103, 38, 110)(32, 104, 37, 109)(41, 113, 50, 122)(42, 114, 49, 121)(43, 115, 52, 124)(44, 116, 51, 123)(45, 117, 56, 128)(46, 118, 55, 127)(47, 119, 54, 126)(48, 120, 53, 125)(57, 129, 66, 138)(58, 130, 65, 137)(59, 131, 68, 140)(60, 132, 67, 139)(61, 133, 72, 144)(62, 134, 71, 143)(63, 135, 70, 142)(64, 136, 69, 141)(145, 217, 147, 219, 155, 227, 149, 221)(146, 218, 151, 223, 162, 234, 153, 225)(148, 220, 156, 228, 169, 241, 159, 231)(150, 222, 157, 229, 170, 242, 160, 232)(152, 224, 163, 235, 177, 249, 166, 238)(154, 226, 164, 236, 178, 250, 167, 239)(158, 230, 171, 243, 185, 257, 174, 246)(161, 233, 172, 244, 186, 258, 175, 247)(165, 237, 179, 251, 193, 265, 182, 254)(168, 240, 180, 252, 194, 266, 183, 255)(173, 245, 187, 259, 201, 273, 190, 262)(176, 248, 188, 260, 202, 274, 191, 263)(181, 253, 195, 267, 209, 281, 198, 270)(184, 256, 196, 268, 210, 282, 199, 271)(189, 261, 203, 275, 208, 280, 206, 278)(192, 264, 204, 276, 205, 277, 207, 279)(197, 269, 211, 283, 216, 288, 214, 286)(200, 272, 212, 284, 213, 285, 215, 287)
	L = (1, 148)(2, 152)(3, 156)(4, 158)(5, 159)(6, 145)(7, 163)(8, 165)(9, 166)(10, 146)(11, 169)(12, 171)(13, 147)(14, 173)(15, 174)(16, 149)(17, 150)(18, 177)(19, 179)(20, 151)(21, 181)(22, 182)(23, 153)(24, 154)(25, 185)(26, 155)(27, 187)(28, 157)(29, 189)(30, 190)(31, 160)(32, 161)(33, 193)(34, 162)(35, 195)(36, 164)(37, 197)(38, 198)(39, 167)(40, 168)(41, 201)(42, 170)(43, 203)(44, 172)(45, 205)(46, 206)(47, 175)(48, 176)(49, 209)(50, 178)(51, 211)(52, 180)(53, 213)(54, 214)(55, 183)(56, 184)(57, 208)(58, 186)(59, 207)(60, 188)(61, 202)(62, 204)(63, 191)(64, 192)(65, 216)(66, 194)(67, 215)(68, 196)(69, 210)(70, 212)(71, 199)(72, 200)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1597
Graph:: simple bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1592 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2 * Y1 * Y2, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 5, 77)(4, 76, 6, 78)(7, 79, 10, 82)(8, 80, 9, 81)(11, 83, 12, 84)(13, 85, 14, 86)(15, 87, 16, 88)(17, 89, 18, 90)(19, 91, 20, 92)(21, 93, 22, 94)(23, 95, 24, 96)(25, 97, 26, 98)(27, 99, 28, 100)(29, 101, 30, 102)(31, 103, 32, 104)(33, 105, 34, 106)(35, 107, 36, 108)(37, 109, 38, 110)(39, 111, 40, 112)(41, 113, 42, 114)(43, 115, 44, 116)(45, 117, 46, 118)(47, 119, 48, 120)(49, 121, 50, 122)(51, 123, 52, 124)(53, 125, 54, 126)(55, 127, 56, 128)(57, 129, 58, 130)(59, 131, 60, 132)(61, 133, 62, 134)(63, 135, 64, 136)(65, 137, 66, 138)(67, 139, 68, 140)(69, 141, 70, 142)(71, 143, 72, 144)(145, 217, 147, 219, 146, 218, 149, 221)(148, 220, 152, 224, 150, 222, 153, 225)(151, 223, 155, 227, 154, 226, 156, 228)(157, 229, 161, 233, 158, 230, 162, 234)(159, 231, 163, 235, 160, 232, 164, 236)(165, 237, 169, 241, 166, 238, 170, 242)(167, 239, 171, 243, 168, 240, 172, 244)(173, 245, 177, 249, 174, 246, 178, 250)(175, 247, 180, 252, 176, 248, 179, 251)(181, 253, 197, 269, 182, 254, 198, 270)(183, 255, 200, 272, 184, 256, 199, 271)(185, 257, 202, 274, 186, 258, 201, 273)(187, 259, 204, 276, 188, 260, 203, 275)(189, 261, 206, 278, 190, 262, 205, 277)(191, 263, 208, 280, 192, 264, 207, 279)(193, 265, 210, 282, 194, 266, 209, 281)(195, 267, 212, 284, 196, 268, 211, 283)(213, 285, 215, 287, 214, 286, 216, 288)
	L = (1, 148)(2, 150)(3, 151)(4, 145)(5, 154)(6, 146)(7, 147)(8, 157)(9, 158)(10, 149)(11, 159)(12, 160)(13, 152)(14, 153)(15, 155)(16, 156)(17, 165)(18, 166)(19, 167)(20, 168)(21, 161)(22, 162)(23, 163)(24, 164)(25, 173)(26, 174)(27, 175)(28, 176)(29, 169)(30, 170)(31, 171)(32, 172)(33, 197)(34, 198)(35, 199)(36, 200)(37, 201)(38, 202)(39, 203)(40, 204)(41, 205)(42, 206)(43, 207)(44, 208)(45, 209)(46, 210)(47, 211)(48, 212)(49, 213)(50, 214)(51, 215)(52, 216)(53, 177)(54, 178)(55, 179)(56, 180)(57, 181)(58, 182)(59, 183)(60, 184)(61, 185)(62, 186)(63, 187)(64, 188)(65, 189)(66, 190)(67, 191)(68, 192)(69, 193)(70, 194)(71, 195)(72, 196)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1595
Graph:: bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1593 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^-2 * Y3 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, (R * Y2 * Y3)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 7, 79)(5, 77, 10, 82)(6, 78, 11, 83)(8, 80, 12, 84)(13, 85, 17, 89)(14, 86, 18, 90)(15, 87, 19, 91)(16, 88, 20, 92)(21, 93, 25, 97)(22, 94, 26, 98)(23, 95, 27, 99)(24, 96, 28, 100)(29, 101, 33, 105)(30, 102, 34, 106)(31, 103, 39, 111)(32, 104, 37, 109)(35, 107, 53, 125)(36, 108, 60, 132)(38, 110, 62, 134)(40, 112, 55, 127)(41, 113, 57, 129)(42, 114, 59, 131)(43, 115, 61, 133)(44, 116, 64, 136)(45, 117, 69, 141)(46, 118, 71, 143)(47, 119, 70, 142)(48, 120, 72, 144)(49, 121, 66, 138)(50, 122, 63, 135)(51, 123, 68, 140)(52, 124, 58, 130)(54, 126, 67, 139)(56, 128, 65, 137)(145, 217, 147, 219, 151, 223, 149, 221)(146, 218, 150, 222, 148, 220, 152, 224)(153, 225, 157, 229, 154, 226, 158, 230)(155, 227, 159, 231, 156, 228, 160, 232)(161, 233, 165, 237, 162, 234, 166, 238)(163, 235, 167, 239, 164, 236, 168, 240)(169, 241, 173, 245, 170, 242, 174, 246)(171, 243, 175, 247, 172, 244, 176, 248)(177, 249, 197, 269, 178, 250, 199, 271)(179, 251, 201, 273, 184, 256, 203, 275)(180, 252, 205, 277, 182, 254, 208, 280)(181, 253, 206, 278, 183, 255, 204, 276)(185, 257, 213, 285, 186, 258, 215, 287)(187, 259, 214, 286, 188, 260, 216, 288)(189, 261, 210, 282, 190, 262, 207, 279)(191, 263, 212, 284, 192, 264, 202, 274)(193, 265, 211, 283, 194, 266, 209, 281)(195, 267, 198, 270, 196, 268, 200, 272)
	L = (1, 148)(2, 151)(3, 154)(4, 145)(5, 153)(6, 156)(7, 146)(8, 155)(9, 149)(10, 147)(11, 152)(12, 150)(13, 162)(14, 161)(15, 164)(16, 163)(17, 158)(18, 157)(19, 160)(20, 159)(21, 170)(22, 169)(23, 172)(24, 171)(25, 166)(26, 165)(27, 168)(28, 167)(29, 178)(30, 177)(31, 181)(32, 183)(33, 174)(34, 173)(35, 199)(36, 206)(37, 175)(38, 204)(39, 176)(40, 197)(41, 203)(42, 201)(43, 208)(44, 205)(45, 215)(46, 213)(47, 216)(48, 214)(49, 207)(50, 210)(51, 202)(52, 212)(53, 184)(54, 209)(55, 179)(56, 211)(57, 186)(58, 195)(59, 185)(60, 182)(61, 188)(62, 180)(63, 193)(64, 187)(65, 198)(66, 194)(67, 200)(68, 196)(69, 190)(70, 192)(71, 189)(72, 191)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1594
Graph:: bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1594 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y1 * Y3 * Y1, Y1^18 * Y2, Y3 * Y1^9 * Y3 * Y1^-9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 6, 78, 15, 87, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 19, 91, 10, 82, 3, 75, 7, 79, 16, 88, 24, 96, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 70, 142, 62, 134, 54, 126, 46, 118, 38, 110, 30, 102, 22, 94, 14, 86, 5, 77)(4, 76, 11, 83, 20, 92, 28, 100, 36, 108, 44, 116, 52, 124, 60, 132, 68, 140, 71, 143, 66, 138, 57, 129, 50, 122, 41, 113, 34, 106, 25, 97, 18, 90, 8, 80, 9, 81, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 72, 144, 65, 137, 58, 130, 49, 121, 42, 114, 33, 105, 26, 98, 17, 89, 12, 84)(145, 217, 147, 219)(146, 218, 151, 223)(148, 220, 153, 225)(149, 221, 154, 226)(150, 222, 160, 232)(152, 224, 156, 228)(155, 227, 157, 229)(158, 230, 163, 235)(159, 231, 168, 240)(161, 233, 162, 234)(164, 236, 165, 237)(166, 238, 171, 243)(167, 239, 176, 248)(169, 241, 170, 242)(172, 244, 173, 245)(174, 246, 179, 251)(175, 247, 184, 256)(177, 249, 178, 250)(180, 252, 181, 253)(182, 254, 187, 259)(183, 255, 192, 264)(185, 257, 186, 258)(188, 260, 189, 261)(190, 262, 195, 267)(191, 263, 200, 272)(193, 265, 194, 266)(196, 268, 197, 269)(198, 270, 203, 275)(199, 271, 208, 280)(201, 273, 202, 274)(204, 276, 205, 277)(206, 278, 211, 283)(207, 279, 214, 286)(209, 281, 210, 282)(212, 284, 213, 285)(215, 287, 216, 288)
	L = (1, 148)(2, 152)(3, 153)(4, 145)(5, 157)(6, 161)(7, 156)(8, 146)(9, 147)(10, 155)(11, 154)(12, 151)(13, 149)(14, 164)(15, 169)(16, 162)(17, 150)(18, 160)(19, 165)(20, 158)(21, 163)(22, 173)(23, 177)(24, 170)(25, 159)(26, 168)(27, 172)(28, 171)(29, 166)(30, 180)(31, 185)(32, 178)(33, 167)(34, 176)(35, 181)(36, 174)(37, 179)(38, 189)(39, 193)(40, 186)(41, 175)(42, 184)(43, 188)(44, 187)(45, 182)(46, 196)(47, 201)(48, 194)(49, 183)(50, 192)(51, 197)(52, 190)(53, 195)(54, 205)(55, 209)(56, 202)(57, 191)(58, 200)(59, 204)(60, 203)(61, 198)(62, 212)(63, 215)(64, 210)(65, 199)(66, 208)(67, 213)(68, 206)(69, 211)(70, 216)(71, 207)(72, 214)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1593
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1595 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1^-1 * Y2, Y3 * Y2 * Y1^18, Y1^-1 * Y3 * Y1^8 * Y2 * Y1^-9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 6, 78, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 66, 138, 58, 130, 50, 122, 42, 114, 34, 106, 26, 98, 18, 90, 10, 82, 16, 88, 24, 96, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 72, 144, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92, 12, 84, 5, 77)(3, 75, 9, 81, 17, 89, 25, 97, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 70, 142, 63, 135, 54, 126, 47, 119, 38, 110, 31, 103, 22, 94, 15, 87, 7, 79, 4, 76, 11, 83, 19, 91, 27, 99, 35, 107, 43, 115, 51, 123, 59, 131, 67, 139, 71, 143, 62, 134, 55, 127, 46, 118, 39, 111, 30, 102, 23, 95, 14, 86, 8, 80)(145, 217, 147, 219)(146, 218, 151, 223)(148, 220, 154, 226)(149, 221, 155, 227)(150, 222, 158, 230)(152, 224, 160, 232)(153, 225, 162, 234)(156, 228, 161, 233)(157, 229, 166, 238)(159, 231, 168, 240)(163, 235, 170, 242)(164, 236, 171, 243)(165, 237, 174, 246)(167, 239, 176, 248)(169, 241, 178, 250)(172, 244, 177, 249)(173, 245, 182, 254)(175, 247, 184, 256)(179, 251, 186, 258)(180, 252, 187, 259)(181, 253, 190, 262)(183, 255, 192, 264)(185, 257, 194, 266)(188, 260, 193, 265)(189, 261, 198, 270)(191, 263, 200, 272)(195, 267, 202, 274)(196, 268, 203, 275)(197, 269, 206, 278)(199, 271, 208, 280)(201, 273, 210, 282)(204, 276, 209, 281)(205, 277, 214, 286)(207, 279, 216, 288)(211, 283, 213, 285)(212, 284, 215, 287)
	L = (1, 148)(2, 152)(3, 154)(4, 145)(5, 153)(6, 159)(7, 160)(8, 146)(9, 149)(10, 147)(11, 162)(12, 163)(13, 167)(14, 168)(15, 150)(16, 151)(17, 170)(18, 155)(19, 156)(20, 169)(21, 175)(22, 176)(23, 157)(24, 158)(25, 164)(26, 161)(27, 178)(28, 179)(29, 183)(30, 184)(31, 165)(32, 166)(33, 186)(34, 171)(35, 172)(36, 185)(37, 191)(38, 192)(39, 173)(40, 174)(41, 180)(42, 177)(43, 194)(44, 195)(45, 199)(46, 200)(47, 181)(48, 182)(49, 202)(50, 187)(51, 188)(52, 201)(53, 207)(54, 208)(55, 189)(56, 190)(57, 196)(58, 193)(59, 210)(60, 211)(61, 215)(62, 216)(63, 197)(64, 198)(65, 213)(66, 203)(67, 204)(68, 214)(69, 209)(70, 212)(71, 205)(72, 206)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1592
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1596 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1, Y3), (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, (Y2 * Y1^-2)^2, (R * Y2 * Y3^-1)^2, Y1^6 * Y3^-1 * Y1^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-3 * Y1 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 21, 93, 44, 116, 64, 136, 40, 112, 16, 88, 4, 76, 9, 81, 23, 95, 46, 118, 43, 115, 56, 128, 63, 135, 38, 110, 15, 87, 29, 101, 51, 123, 34, 106, 20, 92, 30, 102, 52, 124, 62, 134, 37, 109, 55, 127, 42, 114, 19, 91, 6, 78, 10, 82, 24, 96, 47, 119, 61, 133, 41, 113, 18, 90, 5, 77)(3, 75, 11, 83, 31, 103, 57, 129, 69, 141, 68, 140, 48, 120, 33, 105, 12, 84, 28, 100, 53, 125, 39, 111, 60, 132, 72, 144, 67, 139, 45, 117, 27, 99, 8, 80, 25, 97, 17, 89, 36, 108, 59, 131, 71, 143, 66, 138, 54, 126, 26, 98, 50, 122, 35, 107, 14, 86, 32, 104, 58, 130, 70, 142, 65, 137, 49, 121, 22, 94, 13, 85)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 161, 233)(150, 222, 156, 228)(151, 223, 166, 238)(153, 225, 172, 244)(154, 226, 170, 242)(155, 227, 173, 245)(157, 229, 178, 250)(159, 231, 180, 252)(160, 232, 183, 255)(162, 234, 175, 247)(163, 235, 179, 251)(164, 236, 171, 243)(165, 237, 189, 261)(167, 239, 194, 266)(168, 240, 192, 264)(169, 241, 195, 267)(174, 246, 193, 265)(176, 248, 199, 271)(177, 249, 190, 262)(181, 253, 204, 276)(182, 254, 201, 273)(184, 256, 202, 274)(185, 257, 203, 275)(186, 258, 197, 269)(187, 259, 198, 270)(188, 260, 209, 281)(191, 263, 210, 282)(196, 268, 211, 283)(200, 272, 212, 284)(205, 277, 213, 285)(206, 278, 214, 286)(207, 279, 215, 287)(208, 280, 216, 288)
	L = (1, 148)(2, 153)(3, 156)(4, 159)(5, 160)(6, 145)(7, 167)(8, 170)(9, 173)(10, 146)(11, 172)(12, 171)(13, 177)(14, 147)(15, 181)(16, 182)(17, 179)(18, 184)(19, 149)(20, 150)(21, 190)(22, 192)(23, 195)(24, 151)(25, 194)(26, 193)(27, 198)(28, 152)(29, 199)(30, 154)(31, 197)(32, 155)(33, 189)(34, 163)(35, 157)(36, 158)(37, 205)(38, 206)(39, 161)(40, 207)(41, 208)(42, 162)(43, 164)(44, 187)(45, 210)(46, 178)(47, 165)(48, 211)(49, 212)(50, 166)(51, 186)(52, 168)(53, 169)(54, 209)(55, 185)(56, 174)(57, 183)(58, 175)(59, 176)(60, 180)(61, 188)(62, 191)(63, 196)(64, 200)(65, 213)(66, 214)(67, 215)(68, 216)(69, 204)(70, 201)(71, 202)(72, 203)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1590
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1597 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, (Y2 * Y1^-2)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-3 * Y1^6, Y3^18 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 21, 93, 44, 116, 62, 134, 37, 109, 55, 127, 42, 114, 19, 91, 6, 78, 10, 82, 24, 96, 47, 119, 63, 135, 38, 110, 15, 87, 29, 101, 51, 123, 34, 106, 20, 92, 30, 102, 52, 124, 64, 136, 40, 112, 16, 88, 4, 76, 9, 81, 23, 95, 46, 118, 43, 115, 56, 128, 61, 133, 41, 113, 18, 90, 5, 77)(3, 75, 11, 83, 31, 103, 57, 129, 69, 141, 66, 138, 54, 126, 26, 98, 50, 122, 35, 107, 14, 86, 32, 104, 58, 130, 70, 142, 67, 139, 45, 117, 27, 99, 8, 80, 25, 97, 17, 89, 36, 108, 59, 131, 71, 143, 68, 140, 48, 120, 33, 105, 12, 84, 28, 100, 53, 125, 39, 111, 60, 132, 72, 144, 65, 137, 49, 121, 22, 94, 13, 85)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 158, 230)(149, 221, 161, 233)(150, 222, 156, 228)(151, 223, 166, 238)(153, 225, 172, 244)(154, 226, 170, 242)(155, 227, 173, 245)(157, 229, 178, 250)(159, 231, 180, 252)(160, 232, 183, 255)(162, 234, 175, 247)(163, 235, 179, 251)(164, 236, 171, 243)(165, 237, 189, 261)(167, 239, 194, 266)(168, 240, 192, 264)(169, 241, 195, 267)(174, 246, 193, 265)(176, 248, 199, 271)(177, 249, 190, 262)(181, 253, 204, 276)(182, 254, 201, 273)(184, 256, 202, 274)(185, 257, 203, 275)(186, 258, 197, 269)(187, 259, 198, 270)(188, 260, 209, 281)(191, 263, 210, 282)(196, 268, 211, 283)(200, 272, 212, 284)(205, 277, 213, 285)(206, 278, 214, 286)(207, 279, 215, 287)(208, 280, 216, 288)
	L = (1, 148)(2, 153)(3, 156)(4, 159)(5, 160)(6, 145)(7, 167)(8, 170)(9, 173)(10, 146)(11, 172)(12, 171)(13, 177)(14, 147)(15, 181)(16, 182)(17, 179)(18, 184)(19, 149)(20, 150)(21, 190)(22, 192)(23, 195)(24, 151)(25, 194)(26, 193)(27, 198)(28, 152)(29, 199)(30, 154)(31, 197)(32, 155)(33, 189)(34, 163)(35, 157)(36, 158)(37, 205)(38, 206)(39, 161)(40, 207)(41, 208)(42, 162)(43, 164)(44, 187)(45, 210)(46, 178)(47, 165)(48, 211)(49, 212)(50, 166)(51, 186)(52, 168)(53, 169)(54, 209)(55, 185)(56, 174)(57, 183)(58, 175)(59, 176)(60, 180)(61, 196)(62, 200)(63, 188)(64, 191)(65, 215)(66, 216)(67, 213)(68, 214)(69, 204)(70, 201)(71, 202)(72, 203)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1591
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1598 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = C4 x D18 (small group id <72, 5>)
Aut   = D8 x D18 (small group id <144, 41>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-18 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 13, 85, 8, 80)(5, 77, 11, 83, 14, 86, 7, 79)(10, 82, 16, 88, 21, 93, 17, 89)(12, 84, 15, 87, 22, 94, 19, 91)(18, 90, 25, 97, 29, 101, 24, 96)(20, 92, 27, 99, 30, 102, 23, 95)(26, 98, 32, 104, 37, 109, 33, 105)(28, 100, 31, 103, 38, 110, 35, 107)(34, 106, 41, 113, 45, 117, 40, 112)(36, 108, 43, 115, 46, 118, 39, 111)(42, 114, 48, 120, 53, 125, 49, 121)(44, 116, 47, 119, 54, 126, 51, 123)(50, 122, 57, 129, 61, 133, 56, 128)(52, 124, 59, 131, 62, 134, 55, 127)(58, 130, 64, 136, 69, 141, 65, 137)(60, 132, 63, 135, 70, 142, 67, 139)(66, 138, 71, 143, 68, 140, 72, 144)(145, 217, 147, 219, 154, 226, 162, 234, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 214, 286, 206, 278, 198, 270, 190, 262, 182, 254, 174, 246, 166, 238, 158, 230, 150, 222, 157, 229, 165, 237, 173, 245, 181, 253, 189, 261, 197, 269, 205, 277, 213, 285, 212, 284, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 164, 236, 156, 228, 149, 221)(146, 218, 151, 223, 159, 231, 167, 239, 175, 247, 183, 255, 191, 263, 199, 271, 207, 279, 215, 287, 209, 281, 201, 273, 193, 265, 185, 257, 177, 249, 169, 241, 161, 233, 153, 225, 148, 220, 155, 227, 163, 235, 171, 243, 179, 251, 187, 259, 195, 267, 203, 275, 211, 283, 216, 288, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 160, 232, 152, 224)
	L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 155)(6, 148)(7, 149)(8, 147)(9, 157)(10, 160)(11, 158)(12, 159)(13, 152)(14, 151)(15, 166)(16, 165)(17, 154)(18, 169)(19, 156)(20, 171)(21, 161)(22, 163)(23, 164)(24, 162)(25, 173)(26, 176)(27, 174)(28, 175)(29, 168)(30, 167)(31, 182)(32, 181)(33, 170)(34, 185)(35, 172)(36, 187)(37, 177)(38, 179)(39, 180)(40, 178)(41, 189)(42, 192)(43, 190)(44, 191)(45, 184)(46, 183)(47, 198)(48, 197)(49, 186)(50, 201)(51, 188)(52, 203)(53, 193)(54, 195)(55, 196)(56, 194)(57, 205)(58, 208)(59, 206)(60, 207)(61, 200)(62, 199)(63, 214)(64, 213)(65, 202)(66, 215)(67, 204)(68, 216)(69, 209)(70, 211)(71, 212)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4^8 ), ( 4^72 ) }
Outer automorphisms :: reflexible
Dual of E27.1589
Graph:: bipartite
	v = 20 e = 144 f = 72
	degree seq :: [ 8^18, 72^2 ]

E27.1599 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 36})
Quotient :: halfedge^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y1^-1)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, Y1^-4 * Y3 * Y1 * Y2 * Y1^-3, Y1^2 * Y3 * Y1^-2 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 74, 2, 78, 6, 86, 14, 98, 26, 114, 42, 110, 38, 95, 23, 84, 12, 90, 18, 102, 30, 118, 46, 132, 60, 142, 70, 140, 68, 129, 57, 112, 40, 122, 50, 136, 64, 126, 54, 108, 36, 121, 49, 135, 63, 143, 71, 139, 67, 124, 52, 106, 34, 92, 20, 82, 10, 89, 17, 101, 29, 117, 45, 113, 41, 97, 25, 85, 13, 77, 5, 73)(3, 81, 9, 91, 19, 105, 33, 123, 51, 133, 61, 119, 47, 103, 31, 93, 21, 107, 35, 125, 53, 138, 66, 130, 58, 141, 69, 144, 72, 137, 65, 127, 55, 134, 62, 120, 48, 104, 32, 96, 24, 111, 39, 128, 56, 131, 59, 116, 44, 100, 28, 88, 16, 80, 8, 76, 4, 83, 11, 94, 22, 109, 37, 115, 43, 99, 27, 87, 15, 79, 7, 75)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 27)(16, 30)(17, 31)(20, 35)(22, 38)(24, 40)(25, 33)(26, 43)(28, 46)(29, 47)(32, 50)(34, 53)(36, 55)(37, 42)(39, 57)(41, 51)(44, 60)(45, 61)(48, 64)(49, 65)(52, 66)(54, 62)(56, 68)(58, 67)(59, 70)(63, 72)(69, 71)(73, 76)(74, 80)(75, 82)(77, 83)(78, 88)(79, 89)(81, 92)(84, 96)(85, 94)(86, 100)(87, 101)(90, 104)(91, 106)(93, 108)(95, 111)(97, 109)(98, 116)(99, 117)(102, 120)(103, 121)(105, 124)(107, 126)(110, 128)(112, 130)(113, 115)(114, 131)(118, 134)(119, 135)(122, 138)(123, 139)(125, 136)(127, 132)(129, 141)(133, 143)(137, 142)(140, 144)
	local type(s) :: { ( 8^72 ) }
Outer automorphisms :: reflexible
Dual of E27.1600
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 72 f = 18
	degree seq :: [ 72^2 ]

E27.1600 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 36})
Quotient :: halfedge^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, Y1^4, (Y2 * Y1)^2, (Y3 * Y2)^9, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 74, 2, 78, 6, 77, 5, 73)(3, 81, 9, 85, 13, 79, 7, 75)(4, 83, 11, 86, 14, 80, 8, 76)(10, 87, 15, 93, 21, 89, 17, 82)(12, 88, 16, 94, 22, 91, 19, 84)(18, 97, 25, 101, 29, 95, 23, 90)(20, 99, 27, 102, 30, 96, 24, 92)(26, 103, 31, 109, 37, 105, 33, 98)(28, 104, 32, 110, 38, 107, 35, 100)(34, 113, 41, 117, 45, 111, 39, 106)(36, 115, 43, 118, 46, 112, 40, 108)(42, 119, 47, 125, 53, 121, 49, 114)(44, 120, 48, 126, 54, 123, 51, 116)(50, 129, 57, 133, 61, 127, 55, 122)(52, 131, 59, 134, 62, 128, 56, 124)(58, 135, 63, 140, 68, 137, 65, 130)(60, 136, 64, 141, 69, 139, 67, 132)(66, 143, 71, 144, 72, 142, 70, 138)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 13)(8, 16)(10, 18)(11, 19)(14, 22)(15, 23)(17, 25)(20, 28)(21, 29)(24, 32)(26, 34)(27, 35)(30, 38)(31, 39)(33, 41)(36, 44)(37, 45)(40, 48)(42, 50)(43, 51)(46, 54)(47, 55)(49, 57)(52, 60)(53, 61)(56, 64)(58, 66)(59, 67)(62, 69)(63, 70)(65, 71)(68, 72)(73, 76)(74, 80)(75, 82)(77, 83)(78, 86)(79, 87)(81, 89)(84, 92)(85, 93)(88, 96)(90, 98)(91, 99)(94, 102)(95, 103)(97, 105)(100, 108)(101, 109)(104, 112)(106, 114)(107, 115)(110, 118)(111, 119)(113, 121)(116, 124)(117, 125)(120, 128)(122, 130)(123, 131)(126, 134)(127, 135)(129, 137)(132, 138)(133, 140)(136, 142)(139, 143)(141, 144)
	local type(s) :: { ( 72^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1599
Transitivity :: VT+ AT
Graph:: bipartite
	v = 18 e = 72 f = 2
	degree seq :: [ 8^18 ]

E27.1601 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 36})
Quotient :: edge^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y1)^2, Y3^4, (Y2 * Y1)^9, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 73, 4, 76, 12, 84, 5, 77)(2, 74, 7, 79, 16, 88, 8, 80)(3, 75, 10, 82, 20, 92, 11, 83)(6, 78, 14, 86, 24, 96, 15, 87)(9, 81, 18, 90, 28, 100, 19, 91)(13, 85, 22, 94, 32, 104, 23, 95)(17, 89, 26, 98, 36, 108, 27, 99)(21, 93, 30, 102, 40, 112, 31, 103)(25, 97, 34, 106, 44, 116, 35, 107)(29, 101, 38, 110, 48, 120, 39, 111)(33, 105, 42, 114, 52, 124, 43, 115)(37, 109, 46, 118, 56, 128, 47, 119)(41, 113, 50, 122, 60, 132, 51, 123)(45, 117, 54, 126, 64, 136, 55, 127)(49, 121, 58, 130, 67, 139, 59, 131)(53, 125, 62, 134, 70, 142, 63, 135)(57, 129, 65, 137, 71, 143, 66, 138)(61, 133, 68, 140, 72, 144, 69, 141)(145, 146)(147, 153)(148, 152)(149, 151)(150, 157)(154, 163)(155, 162)(156, 160)(158, 167)(159, 166)(161, 169)(164, 172)(165, 173)(168, 176)(170, 179)(171, 178)(174, 183)(175, 182)(177, 185)(180, 188)(181, 189)(184, 192)(186, 195)(187, 194)(190, 199)(191, 198)(193, 201)(196, 204)(197, 205)(200, 208)(202, 210)(203, 209)(206, 213)(207, 212)(211, 215)(214, 216)(217, 219)(218, 222)(220, 227)(221, 226)(223, 231)(224, 230)(225, 233)(228, 236)(229, 237)(232, 240)(234, 243)(235, 242)(238, 247)(239, 246)(241, 249)(244, 252)(245, 253)(248, 256)(250, 259)(251, 258)(254, 263)(255, 262)(257, 265)(260, 268)(261, 269)(264, 272)(266, 275)(267, 274)(270, 279)(271, 278)(273, 277)(276, 283)(280, 286)(281, 285)(282, 284)(287, 288)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 144, 144 ), ( 144^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1604
Graph:: simple bipartite
	v = 90 e = 144 f = 2
	degree seq :: [ 2^72, 8^18 ]

E27.1602 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 36})
Quotient :: edge^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-7 * Y1 * Y3 * Y2, Y3^2 * Y1 * Y3^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 73, 4, 76, 12, 84, 24, 96, 40, 112, 48, 120, 30, 102, 16, 88, 6, 78, 15, 87, 29, 101, 47, 119, 66, 138, 72, 144, 63, 135, 44, 116, 26, 98, 43, 115, 62, 134, 53, 125, 33, 105, 52, 124, 68, 140, 70, 142, 59, 131, 57, 129, 37, 109, 21, 93, 9, 81, 20, 92, 36, 108, 56, 128, 41, 113, 25, 97, 13, 85, 5, 77)(2, 74, 7, 79, 17, 89, 31, 103, 49, 121, 39, 111, 23, 95, 11, 83, 3, 75, 10, 82, 22, 94, 38, 110, 58, 130, 69, 141, 55, 127, 35, 107, 19, 91, 34, 106, 54, 126, 61, 133, 42, 114, 60, 132, 71, 143, 67, 139, 51, 123, 65, 137, 46, 118, 28, 100, 14, 86, 27, 99, 45, 117, 64, 136, 50, 122, 32, 104, 18, 90, 8, 80)(145, 146)(147, 153)(148, 152)(149, 151)(150, 158)(154, 165)(155, 164)(156, 162)(157, 161)(159, 172)(160, 171)(163, 177)(166, 181)(167, 180)(168, 176)(169, 175)(170, 186)(173, 190)(174, 189)(178, 197)(179, 196)(182, 201)(183, 200)(184, 194)(185, 193)(187, 205)(188, 204)(191, 209)(192, 208)(195, 210)(198, 206)(199, 212)(202, 203)(207, 215)(211, 216)(213, 214)(217, 219)(218, 222)(220, 227)(221, 226)(223, 232)(224, 231)(225, 235)(228, 239)(229, 238)(230, 242)(233, 246)(234, 245)(236, 251)(237, 250)(240, 255)(241, 254)(243, 260)(244, 259)(247, 264)(248, 263)(249, 267)(252, 271)(253, 270)(256, 265)(257, 274)(258, 275)(261, 279)(262, 278)(266, 282)(268, 283)(269, 281)(272, 285)(273, 277)(276, 286)(280, 288)(284, 287)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 16, 16 ), ( 16^72 ) }
Outer automorphisms :: reflexible
Dual of E27.1603
Graph:: simple bipartite
	v = 74 e = 144 f = 18
	degree seq :: [ 2^72, 72^2 ]

E27.1603 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 36})
Quotient :: loop^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y1)^2, Y3^4, (Y2 * Y1)^9, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 73, 145, 217, 4, 76, 148, 220, 12, 84, 156, 228, 5, 77, 149, 221)(2, 74, 146, 218, 7, 79, 151, 223, 16, 88, 160, 232, 8, 80, 152, 224)(3, 75, 147, 219, 10, 82, 154, 226, 20, 92, 164, 236, 11, 83, 155, 227)(6, 78, 150, 222, 14, 86, 158, 230, 24, 96, 168, 240, 15, 87, 159, 231)(9, 81, 153, 225, 18, 90, 162, 234, 28, 100, 172, 244, 19, 91, 163, 235)(13, 85, 157, 229, 22, 94, 166, 238, 32, 104, 176, 248, 23, 95, 167, 239)(17, 89, 161, 233, 26, 98, 170, 242, 36, 108, 180, 252, 27, 99, 171, 243)(21, 93, 165, 237, 30, 102, 174, 246, 40, 112, 184, 256, 31, 103, 175, 247)(25, 97, 169, 241, 34, 106, 178, 250, 44, 116, 188, 260, 35, 107, 179, 251)(29, 101, 173, 245, 38, 110, 182, 254, 48, 120, 192, 264, 39, 111, 183, 255)(33, 105, 177, 249, 42, 114, 186, 258, 52, 124, 196, 268, 43, 115, 187, 259)(37, 109, 181, 253, 46, 118, 190, 262, 56, 128, 200, 272, 47, 119, 191, 263)(41, 113, 185, 257, 50, 122, 194, 266, 60, 132, 204, 276, 51, 123, 195, 267)(45, 117, 189, 261, 54, 126, 198, 270, 64, 136, 208, 280, 55, 127, 199, 271)(49, 121, 193, 265, 58, 130, 202, 274, 67, 139, 211, 283, 59, 131, 203, 275)(53, 125, 197, 269, 62, 134, 206, 278, 70, 142, 214, 286, 63, 135, 207, 279)(57, 129, 201, 273, 65, 137, 209, 281, 71, 143, 215, 287, 66, 138, 210, 282)(61, 133, 205, 277, 68, 140, 212, 284, 72, 144, 216, 288, 69, 141, 213, 285)
	L = (1, 74)(2, 73)(3, 81)(4, 80)(5, 79)(6, 85)(7, 77)(8, 76)(9, 75)(10, 91)(11, 90)(12, 88)(13, 78)(14, 95)(15, 94)(16, 84)(17, 97)(18, 83)(19, 82)(20, 100)(21, 101)(22, 87)(23, 86)(24, 104)(25, 89)(26, 107)(27, 106)(28, 92)(29, 93)(30, 111)(31, 110)(32, 96)(33, 113)(34, 99)(35, 98)(36, 116)(37, 117)(38, 103)(39, 102)(40, 120)(41, 105)(42, 123)(43, 122)(44, 108)(45, 109)(46, 127)(47, 126)(48, 112)(49, 129)(50, 115)(51, 114)(52, 132)(53, 133)(54, 119)(55, 118)(56, 136)(57, 121)(58, 138)(59, 137)(60, 124)(61, 125)(62, 141)(63, 140)(64, 128)(65, 131)(66, 130)(67, 143)(68, 135)(69, 134)(70, 144)(71, 139)(72, 142)(145, 219)(146, 222)(147, 217)(148, 227)(149, 226)(150, 218)(151, 231)(152, 230)(153, 233)(154, 221)(155, 220)(156, 236)(157, 237)(158, 224)(159, 223)(160, 240)(161, 225)(162, 243)(163, 242)(164, 228)(165, 229)(166, 247)(167, 246)(168, 232)(169, 249)(170, 235)(171, 234)(172, 252)(173, 253)(174, 239)(175, 238)(176, 256)(177, 241)(178, 259)(179, 258)(180, 244)(181, 245)(182, 263)(183, 262)(184, 248)(185, 265)(186, 251)(187, 250)(188, 268)(189, 269)(190, 255)(191, 254)(192, 272)(193, 257)(194, 275)(195, 274)(196, 260)(197, 261)(198, 279)(199, 278)(200, 264)(201, 277)(202, 267)(203, 266)(204, 283)(205, 273)(206, 271)(207, 270)(208, 286)(209, 285)(210, 284)(211, 276)(212, 282)(213, 281)(214, 280)(215, 288)(216, 287)
	local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1602
Transitivity :: VT+
Graph:: bipartite
	v = 18 e = 144 f = 74
	degree seq :: [ 16^18 ]

E27.1604 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 36})
Quotient :: loop^2
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-7 * Y1 * Y3 * Y2, Y3^2 * Y1 * Y3^-2 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ]
Map::
	R = (1, 73, 145, 217, 4, 76, 148, 220, 12, 84, 156, 228, 24, 96, 168, 240, 40, 112, 184, 256, 48, 120, 192, 264, 30, 102, 174, 246, 16, 88, 160, 232, 6, 78, 150, 222, 15, 87, 159, 231, 29, 101, 173, 245, 47, 119, 191, 263, 66, 138, 210, 282, 72, 144, 216, 288, 63, 135, 207, 279, 44, 116, 188, 260, 26, 98, 170, 242, 43, 115, 187, 259, 62, 134, 206, 278, 53, 125, 197, 269, 33, 105, 177, 249, 52, 124, 196, 268, 68, 140, 212, 284, 70, 142, 214, 286, 59, 131, 203, 275, 57, 129, 201, 273, 37, 109, 181, 253, 21, 93, 165, 237, 9, 81, 153, 225, 20, 92, 164, 236, 36, 108, 180, 252, 56, 128, 200, 272, 41, 113, 185, 257, 25, 97, 169, 241, 13, 85, 157, 229, 5, 77, 149, 221)(2, 74, 146, 218, 7, 79, 151, 223, 17, 89, 161, 233, 31, 103, 175, 247, 49, 121, 193, 265, 39, 111, 183, 255, 23, 95, 167, 239, 11, 83, 155, 227, 3, 75, 147, 219, 10, 82, 154, 226, 22, 94, 166, 238, 38, 110, 182, 254, 58, 130, 202, 274, 69, 141, 213, 285, 55, 127, 199, 271, 35, 107, 179, 251, 19, 91, 163, 235, 34, 106, 178, 250, 54, 126, 198, 270, 61, 133, 205, 277, 42, 114, 186, 258, 60, 132, 204, 276, 71, 143, 215, 287, 67, 139, 211, 283, 51, 123, 195, 267, 65, 137, 209, 281, 46, 118, 190, 262, 28, 100, 172, 244, 14, 86, 158, 230, 27, 99, 171, 243, 45, 117, 189, 261, 64, 136, 208, 280, 50, 122, 194, 266, 32, 104, 176, 248, 18, 90, 162, 234, 8, 80, 152, 224)
	L = (1, 74)(2, 73)(3, 81)(4, 80)(5, 79)(6, 86)(7, 77)(8, 76)(9, 75)(10, 93)(11, 92)(12, 90)(13, 89)(14, 78)(15, 100)(16, 99)(17, 85)(18, 84)(19, 105)(20, 83)(21, 82)(22, 109)(23, 108)(24, 104)(25, 103)(26, 114)(27, 88)(28, 87)(29, 118)(30, 117)(31, 97)(32, 96)(33, 91)(34, 125)(35, 124)(36, 95)(37, 94)(38, 129)(39, 128)(40, 122)(41, 121)(42, 98)(43, 133)(44, 132)(45, 102)(46, 101)(47, 137)(48, 136)(49, 113)(50, 112)(51, 138)(52, 107)(53, 106)(54, 134)(55, 140)(56, 111)(57, 110)(58, 131)(59, 130)(60, 116)(61, 115)(62, 126)(63, 143)(64, 120)(65, 119)(66, 123)(67, 144)(68, 127)(69, 142)(70, 141)(71, 135)(72, 139)(145, 219)(146, 222)(147, 217)(148, 227)(149, 226)(150, 218)(151, 232)(152, 231)(153, 235)(154, 221)(155, 220)(156, 239)(157, 238)(158, 242)(159, 224)(160, 223)(161, 246)(162, 245)(163, 225)(164, 251)(165, 250)(166, 229)(167, 228)(168, 255)(169, 254)(170, 230)(171, 260)(172, 259)(173, 234)(174, 233)(175, 264)(176, 263)(177, 267)(178, 237)(179, 236)(180, 271)(181, 270)(182, 241)(183, 240)(184, 265)(185, 274)(186, 275)(187, 244)(188, 243)(189, 279)(190, 278)(191, 248)(192, 247)(193, 256)(194, 282)(195, 249)(196, 283)(197, 281)(198, 253)(199, 252)(200, 285)(201, 277)(202, 257)(203, 258)(204, 286)(205, 273)(206, 262)(207, 261)(208, 288)(209, 269)(210, 266)(211, 268)(212, 287)(213, 272)(214, 276)(215, 284)(216, 280)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1601
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 144 f = 90
	degree seq :: [ 144^2 ]

E27.1605 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2)^2, Y2^4, Y3^9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 10, 82)(5, 77, 7, 79)(6, 78, 8, 80)(11, 83, 18, 90)(12, 84, 23, 95)(13, 85, 22, 94)(14, 86, 24, 96)(15, 87, 20, 92)(16, 88, 19, 91)(17, 89, 21, 93)(25, 97, 34, 106)(26, 98, 33, 105)(27, 99, 39, 111)(28, 100, 38, 110)(29, 101, 40, 112)(30, 102, 36, 108)(31, 103, 35, 107)(32, 104, 37, 109)(41, 113, 50, 122)(42, 114, 49, 121)(43, 115, 55, 127)(44, 116, 54, 126)(45, 117, 56, 128)(46, 118, 52, 124)(47, 119, 51, 123)(48, 120, 53, 125)(57, 129, 64, 136)(58, 130, 63, 135)(59, 131, 68, 140)(60, 132, 67, 139)(61, 133, 66, 138)(62, 134, 65, 137)(69, 141, 72, 144)(70, 142, 71, 143)(145, 217, 147, 219, 155, 227, 149, 221)(146, 218, 151, 223, 162, 234, 153, 225)(148, 220, 156, 228, 169, 241, 159, 231)(150, 222, 157, 229, 170, 242, 160, 232)(152, 224, 163, 235, 177, 249, 166, 238)(154, 226, 164, 236, 178, 250, 167, 239)(158, 230, 171, 243, 185, 257, 174, 246)(161, 233, 172, 244, 186, 258, 175, 247)(165, 237, 179, 251, 193, 265, 182, 254)(168, 240, 180, 252, 194, 266, 183, 255)(173, 245, 187, 259, 201, 273, 190, 262)(176, 248, 188, 260, 202, 274, 191, 263)(181, 253, 195, 267, 207, 279, 198, 270)(184, 256, 196, 268, 208, 280, 199, 271)(189, 261, 203, 275, 213, 285, 205, 277)(192, 264, 204, 276, 214, 286, 206, 278)(197, 269, 209, 281, 215, 287, 211, 283)(200, 272, 210, 282, 216, 288, 212, 284)
	L = (1, 148)(2, 152)(3, 156)(4, 158)(5, 159)(6, 145)(7, 163)(8, 165)(9, 166)(10, 146)(11, 169)(12, 171)(13, 147)(14, 173)(15, 174)(16, 149)(17, 150)(18, 177)(19, 179)(20, 151)(21, 181)(22, 182)(23, 153)(24, 154)(25, 185)(26, 155)(27, 187)(28, 157)(29, 189)(30, 190)(31, 160)(32, 161)(33, 193)(34, 162)(35, 195)(36, 164)(37, 197)(38, 198)(39, 167)(40, 168)(41, 201)(42, 170)(43, 203)(44, 172)(45, 192)(46, 205)(47, 175)(48, 176)(49, 207)(50, 178)(51, 209)(52, 180)(53, 200)(54, 211)(55, 183)(56, 184)(57, 213)(58, 186)(59, 204)(60, 188)(61, 206)(62, 191)(63, 215)(64, 194)(65, 210)(66, 196)(67, 212)(68, 199)(69, 214)(70, 202)(71, 216)(72, 208)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1607
Graph:: simple bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1606 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^4, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^2 * Y3^9 ]
Map:: non-degenerate
	R = (1, 73, 2, 74)(3, 75, 9, 81)(4, 76, 10, 82)(5, 77, 7, 79)(6, 78, 8, 80)(11, 83, 18, 90)(12, 84, 23, 95)(13, 85, 22, 94)(14, 86, 24, 96)(15, 87, 20, 92)(16, 88, 19, 91)(17, 89, 21, 93)(25, 97, 34, 106)(26, 98, 33, 105)(27, 99, 39, 111)(28, 100, 38, 110)(29, 101, 40, 112)(30, 102, 36, 108)(31, 103, 35, 107)(32, 104, 37, 109)(41, 113, 50, 122)(42, 114, 49, 121)(43, 115, 55, 127)(44, 116, 54, 126)(45, 117, 56, 128)(46, 118, 52, 124)(47, 119, 51, 123)(48, 120, 53, 125)(57, 129, 66, 138)(58, 130, 65, 137)(59, 131, 71, 143)(60, 132, 70, 142)(61, 133, 72, 144)(62, 134, 68, 140)(63, 135, 67, 139)(64, 136, 69, 141)(145, 217, 147, 219, 155, 227, 149, 221)(146, 218, 151, 223, 162, 234, 153, 225)(148, 220, 156, 228, 169, 241, 159, 231)(150, 222, 157, 229, 170, 242, 160, 232)(152, 224, 163, 235, 177, 249, 166, 238)(154, 226, 164, 236, 178, 250, 167, 239)(158, 230, 171, 243, 185, 257, 174, 246)(161, 233, 172, 244, 186, 258, 175, 247)(165, 237, 179, 251, 193, 265, 182, 254)(168, 240, 180, 252, 194, 266, 183, 255)(173, 245, 187, 259, 201, 273, 190, 262)(176, 248, 188, 260, 202, 274, 191, 263)(181, 253, 195, 267, 209, 281, 198, 270)(184, 256, 196, 268, 210, 282, 199, 271)(189, 261, 203, 275, 208, 280, 206, 278)(192, 264, 204, 276, 205, 277, 207, 279)(197, 269, 211, 283, 216, 288, 214, 286)(200, 272, 212, 284, 213, 285, 215, 287)
	L = (1, 148)(2, 152)(3, 156)(4, 158)(5, 159)(6, 145)(7, 163)(8, 165)(9, 166)(10, 146)(11, 169)(12, 171)(13, 147)(14, 173)(15, 174)(16, 149)(17, 150)(18, 177)(19, 179)(20, 151)(21, 181)(22, 182)(23, 153)(24, 154)(25, 185)(26, 155)(27, 187)(28, 157)(29, 189)(30, 190)(31, 160)(32, 161)(33, 193)(34, 162)(35, 195)(36, 164)(37, 197)(38, 198)(39, 167)(40, 168)(41, 201)(42, 170)(43, 203)(44, 172)(45, 205)(46, 206)(47, 175)(48, 176)(49, 209)(50, 178)(51, 211)(52, 180)(53, 213)(54, 214)(55, 183)(56, 184)(57, 208)(58, 186)(59, 207)(60, 188)(61, 202)(62, 204)(63, 191)(64, 192)(65, 216)(66, 194)(67, 215)(68, 196)(69, 210)(70, 212)(71, 199)(72, 200)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 72, 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1608
Graph:: simple bipartite
	v = 54 e = 144 f = 38
	degree seq :: [ 4^36, 8^18 ]

E27.1607 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^-1 * Y3^-1 * Y1^-3, Y1^7 * Y3^-1 * Y1, Y1 * Y3^-1 * Y1 * Y3^-2 * Y1^2 * Y3^-2 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 19, 91, 39, 111, 61, 133, 34, 106, 15, 87, 4, 76, 9, 81, 21, 93, 41, 113, 38, 110, 50, 122, 60, 132, 33, 105, 14, 86, 25, 97, 45, 117, 37, 109, 18, 90, 26, 98, 46, 118, 59, 131, 32, 104, 49, 121, 36, 108, 17, 89, 6, 78, 10, 82, 22, 94, 42, 114, 58, 130, 35, 107, 16, 88, 5, 77)(3, 75, 11, 83, 27, 99, 51, 123, 69, 141, 63, 135, 43, 115, 23, 95, 12, 84, 28, 100, 52, 124, 68, 140, 57, 129, 72, 144, 65, 137, 47, 119, 30, 102, 54, 126, 66, 138, 48, 120, 31, 103, 55, 127, 71, 143, 67, 139, 56, 128, 64, 136, 44, 116, 24, 96, 13, 85, 29, 101, 53, 125, 70, 142, 62, 134, 40, 112, 20, 92, 8, 80)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 157, 229)(149, 221, 155, 227)(150, 222, 156, 228)(151, 223, 164, 236)(153, 225, 168, 240)(154, 226, 167, 239)(158, 230, 175, 247)(159, 231, 173, 245)(160, 232, 171, 243)(161, 233, 172, 244)(162, 234, 174, 246)(163, 235, 184, 256)(165, 237, 188, 260)(166, 238, 187, 259)(169, 241, 192, 264)(170, 242, 191, 263)(176, 248, 201, 273)(177, 249, 199, 271)(178, 250, 197, 269)(179, 251, 195, 267)(180, 252, 196, 268)(181, 253, 198, 270)(182, 254, 200, 272)(183, 255, 206, 278)(185, 257, 208, 280)(186, 258, 207, 279)(189, 261, 210, 282)(190, 262, 209, 281)(193, 265, 212, 284)(194, 266, 211, 283)(202, 274, 213, 285)(203, 275, 216, 288)(204, 276, 215, 287)(205, 277, 214, 286)
	L = (1, 148)(2, 153)(3, 156)(4, 158)(5, 159)(6, 145)(7, 165)(8, 167)(9, 169)(10, 146)(11, 172)(12, 174)(13, 147)(14, 176)(15, 177)(16, 178)(17, 149)(18, 150)(19, 185)(20, 187)(21, 189)(22, 151)(23, 191)(24, 152)(25, 193)(26, 154)(27, 196)(28, 198)(29, 155)(30, 200)(31, 157)(32, 202)(33, 203)(34, 204)(35, 205)(36, 160)(37, 161)(38, 162)(39, 182)(40, 207)(41, 181)(42, 163)(43, 209)(44, 164)(45, 180)(46, 166)(47, 211)(48, 168)(49, 179)(50, 170)(51, 212)(52, 210)(53, 171)(54, 208)(55, 173)(56, 206)(57, 175)(58, 183)(59, 186)(60, 190)(61, 194)(62, 213)(63, 216)(64, 184)(65, 215)(66, 188)(67, 214)(68, 192)(69, 201)(70, 195)(71, 197)(72, 199)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1605
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1608 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 36})
Quotient :: dipole
Aut^+ = D72 (small group id <72, 6>)
Aut   = C2 x D72 (small group id <144, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^-4, Y3^-3 * Y1^6, Y3^18 ]
Map:: non-degenerate
	R = (1, 73, 2, 74, 7, 79, 19, 91, 39, 111, 59, 131, 32, 104, 49, 121, 36, 108, 17, 89, 6, 78, 10, 82, 22, 94, 42, 114, 60, 132, 33, 105, 14, 86, 25, 97, 45, 117, 37, 109, 18, 90, 26, 98, 46, 118, 61, 133, 34, 106, 15, 87, 4, 76, 9, 81, 21, 93, 41, 113, 38, 110, 50, 122, 58, 130, 35, 107, 16, 88, 5, 77)(3, 75, 11, 83, 27, 99, 51, 123, 69, 141, 67, 139, 56, 128, 64, 136, 44, 116, 24, 96, 13, 85, 29, 101, 53, 125, 70, 142, 65, 137, 47, 119, 30, 102, 54, 126, 66, 138, 48, 120, 31, 103, 55, 127, 71, 143, 63, 135, 43, 115, 23, 95, 12, 84, 28, 100, 52, 124, 68, 140, 57, 129, 72, 144, 62, 134, 40, 112, 20, 92, 8, 80)(145, 217, 147, 219)(146, 218, 152, 224)(148, 220, 157, 229)(149, 221, 155, 227)(150, 222, 156, 228)(151, 223, 164, 236)(153, 225, 168, 240)(154, 226, 167, 239)(158, 230, 175, 247)(159, 231, 173, 245)(160, 232, 171, 243)(161, 233, 172, 244)(162, 234, 174, 246)(163, 235, 184, 256)(165, 237, 188, 260)(166, 238, 187, 259)(169, 241, 192, 264)(170, 242, 191, 263)(176, 248, 201, 273)(177, 249, 199, 271)(178, 250, 197, 269)(179, 251, 195, 267)(180, 252, 196, 268)(181, 253, 198, 270)(182, 254, 200, 272)(183, 255, 206, 278)(185, 257, 208, 280)(186, 258, 207, 279)(189, 261, 210, 282)(190, 262, 209, 281)(193, 265, 212, 284)(194, 266, 211, 283)(202, 274, 213, 285)(203, 275, 216, 288)(204, 276, 215, 287)(205, 277, 214, 286)
	L = (1, 148)(2, 153)(3, 156)(4, 158)(5, 159)(6, 145)(7, 165)(8, 167)(9, 169)(10, 146)(11, 172)(12, 174)(13, 147)(14, 176)(15, 177)(16, 178)(17, 149)(18, 150)(19, 185)(20, 187)(21, 189)(22, 151)(23, 191)(24, 152)(25, 193)(26, 154)(27, 196)(28, 198)(29, 155)(30, 200)(31, 157)(32, 202)(33, 203)(34, 204)(35, 205)(36, 160)(37, 161)(38, 162)(39, 182)(40, 207)(41, 181)(42, 163)(43, 209)(44, 164)(45, 180)(46, 166)(47, 211)(48, 168)(49, 179)(50, 170)(51, 212)(52, 210)(53, 171)(54, 208)(55, 173)(56, 206)(57, 175)(58, 190)(59, 194)(60, 183)(61, 186)(62, 215)(63, 214)(64, 184)(65, 213)(66, 188)(67, 216)(68, 192)(69, 201)(70, 195)(71, 197)(72, 199)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1606
Graph:: bipartite
	v = 38 e = 144 f = 54
	degree seq :: [ 4^36, 72^2 ]

E27.1609 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 8, 36})
Quotient :: edge
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-2 * T2, T2^-1 * T1^3 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-3, T1^-1 * T2^-9 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 46, 62, 55, 39, 21, 13, 24, 42, 58, 71, 70, 57, 41, 23, 36, 25, 43, 59, 72, 69, 54, 38, 20, 6, 19, 37, 53, 68, 52, 35, 17, 5)(2, 7, 22, 40, 56, 63, 48, 30, 14, 4, 12, 32, 49, 65, 61, 45, 28, 9, 27, 15, 33, 50, 66, 64, 47, 31, 11, 18, 16, 34, 51, 67, 60, 44, 26, 8)(73, 74, 78, 90, 108, 99, 85, 76)(75, 81, 91, 86, 97, 80, 96, 83)(77, 87, 92, 84, 95, 79, 93, 88)(82, 98, 109, 103, 115, 100, 114, 102)(89, 94, 110, 106, 113, 105, 111, 104)(101, 117, 125, 120, 131, 116, 130, 119)(107, 122, 126, 121, 129, 112, 127, 123)(118, 132, 140, 136, 144, 133, 143, 135)(124, 128, 141, 139, 142, 138, 134, 137)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 16^8 ), ( 16^36 ) }
Outer automorphisms :: reflexible
Dual of E27.1611
Transitivity :: ET+
Graph:: bipartite
	v = 11 e = 72 f = 9
	degree seq :: [ 8^9, 36^2 ]

E27.1610 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 8, 36})
Quotient :: edge
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-1 * T1^-3, T1 * T2^-2 * T1^-1 * T2^-2, (T2 * T1 * T2 * T1^-1)^2, T2^-2 * T1 * T2^4 * T1 * T2^-3, T1^-2 * T2^3 * T1^-2 * T2^3 * T1^-2 * T2^3 * T1^-2 * T2^3 * T1^-1 * T2^2 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 46, 62, 54, 38, 20, 6, 19, 37, 53, 69, 71, 57, 41, 23, 36, 25, 43, 59, 72, 70, 55, 39, 21, 13, 24, 42, 58, 68, 52, 35, 17, 5)(2, 7, 22, 40, 56, 64, 47, 31, 11, 18, 16, 34, 51, 67, 61, 45, 28, 9, 27, 15, 33, 50, 66, 63, 48, 30, 14, 4, 12, 32, 49, 65, 60, 44, 26, 8)(73, 74, 78, 90, 108, 99, 85, 76)(75, 81, 91, 86, 97, 80, 96, 83)(77, 87, 92, 84, 95, 79, 93, 88)(82, 98, 109, 103, 115, 100, 114, 102)(89, 94, 110, 106, 113, 105, 111, 104)(101, 117, 125, 120, 131, 116, 130, 119)(107, 122, 126, 121, 129, 112, 127, 123)(118, 132, 141, 136, 144, 133, 140, 135)(124, 128, 134, 139, 143, 138, 142, 137)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 16^8 ), ( 16^36 ) }
Outer automorphisms :: reflexible
Dual of E27.1612
Transitivity :: ET+
Graph:: bipartite
	v = 11 e = 72 f = 9
	degree seq :: [ 8^9, 36^2 ]

E27.1611 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 8, 36})
Quotient :: loop
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T2)^2, (F * T1)^2, T1^2 * T2^6, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^36 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 6, 78, 15, 87, 26, 98, 23, 95, 11, 83, 5, 77)(2, 74, 7, 79, 14, 86, 27, 99, 22, 94, 12, 84, 4, 76, 8, 80)(9, 81, 19, 91, 28, 100, 25, 97, 13, 85, 21, 93, 10, 82, 20, 92)(16, 88, 29, 101, 24, 96, 32, 104, 18, 90, 31, 103, 17, 89, 30, 102)(33, 105, 41, 113, 36, 108, 44, 116, 35, 107, 43, 115, 34, 106, 42, 114)(37, 109, 45, 117, 40, 112, 48, 120, 39, 111, 47, 119, 38, 110, 46, 118)(49, 121, 57, 129, 52, 124, 60, 132, 51, 123, 59, 131, 50, 122, 58, 130)(53, 125, 61, 133, 56, 128, 64, 136, 55, 127, 63, 135, 54, 126, 62, 134)(65, 137, 69, 141, 68, 140, 72, 144, 67, 139, 71, 143, 66, 138, 70, 142)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 82)(6, 86)(7, 88)(8, 89)(9, 87)(10, 75)(11, 76)(12, 90)(13, 77)(14, 98)(15, 100)(16, 99)(17, 79)(18, 80)(19, 105)(20, 106)(21, 107)(22, 83)(23, 85)(24, 84)(25, 108)(26, 94)(27, 96)(28, 95)(29, 109)(30, 110)(31, 111)(32, 112)(33, 97)(34, 91)(35, 92)(36, 93)(37, 104)(38, 101)(39, 102)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 116)(50, 113)(51, 114)(52, 115)(53, 120)(54, 117)(55, 118)(56, 119)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 132)(66, 129)(67, 130)(68, 131)(69, 136)(70, 133)(71, 134)(72, 135)
	local type(s) :: { ( 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1609
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 72 f = 11
	degree seq :: [ 16^9 ]

E27.1612 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 8, 36})
Quotient :: loop
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-1, T1^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 6, 78, 15, 87, 26, 98, 23, 95, 11, 83, 5, 77)(2, 74, 7, 79, 14, 86, 27, 99, 22, 94, 12, 84, 4, 76, 8, 80)(9, 81, 19, 91, 28, 100, 25, 97, 13, 85, 21, 93, 10, 82, 20, 92)(16, 88, 29, 101, 24, 96, 32, 104, 18, 90, 31, 103, 17, 89, 30, 102)(33, 105, 41, 113, 36, 108, 44, 116, 35, 107, 43, 115, 34, 106, 42, 114)(37, 109, 45, 117, 40, 112, 48, 120, 39, 111, 47, 119, 38, 110, 46, 118)(49, 121, 57, 129, 52, 124, 60, 132, 51, 123, 59, 131, 50, 122, 58, 130)(53, 125, 61, 133, 56, 128, 64, 136, 55, 127, 63, 135, 54, 126, 62, 134)(65, 137, 71, 143, 68, 140, 70, 142, 67, 139, 69, 141, 66, 138, 72, 144)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 82)(6, 86)(7, 88)(8, 89)(9, 87)(10, 75)(11, 76)(12, 90)(13, 77)(14, 98)(15, 100)(16, 99)(17, 79)(18, 80)(19, 105)(20, 106)(21, 107)(22, 83)(23, 85)(24, 84)(25, 108)(26, 94)(27, 96)(28, 95)(29, 109)(30, 110)(31, 111)(32, 112)(33, 97)(34, 91)(35, 92)(36, 93)(37, 104)(38, 101)(39, 102)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 116)(50, 113)(51, 114)(52, 115)(53, 120)(54, 117)(55, 118)(56, 119)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 132)(66, 129)(67, 130)(68, 131)(69, 136)(70, 133)(71, 134)(72, 135)
	local type(s) :: { ( 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36, 8, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.1610
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 72 f = 11
	degree seq :: [ 16^9 ]

E27.1613 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 36})
Quotient :: dipole
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-2 * Y1 * Y2^-1, Y2^-1 * Y1^3 * Y2^-1 * Y1, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, Y2^-9 * Y1^-2, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 36, 108, 27, 99, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 14, 86, 25, 97, 8, 80, 24, 96, 11, 83)(5, 77, 15, 87, 20, 92, 12, 84, 23, 95, 7, 79, 21, 93, 16, 88)(10, 82, 26, 98, 37, 109, 31, 103, 43, 115, 28, 100, 42, 114, 30, 102)(17, 89, 22, 94, 38, 110, 34, 106, 41, 113, 33, 105, 39, 111, 32, 104)(29, 101, 45, 117, 53, 125, 48, 120, 59, 131, 44, 116, 58, 130, 47, 119)(35, 107, 50, 122, 54, 126, 49, 121, 57, 129, 40, 112, 55, 127, 51, 123)(46, 118, 60, 132, 68, 140, 64, 136, 72, 144, 61, 133, 71, 143, 63, 135)(52, 124, 56, 128, 69, 141, 67, 139, 70, 142, 66, 138, 62, 134, 65, 137)(145, 217, 147, 219, 154, 226, 173, 245, 190, 262, 206, 278, 199, 271, 183, 255, 165, 237, 157, 229, 168, 240, 186, 258, 202, 274, 215, 287, 214, 286, 201, 273, 185, 257, 167, 239, 180, 252, 169, 241, 187, 259, 203, 275, 216, 288, 213, 285, 198, 270, 182, 254, 164, 236, 150, 222, 163, 235, 181, 253, 197, 269, 212, 284, 196, 268, 179, 251, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 184, 256, 200, 272, 207, 279, 192, 264, 174, 246, 158, 230, 148, 220, 156, 228, 176, 248, 193, 265, 209, 281, 205, 277, 189, 261, 172, 244, 153, 225, 171, 243, 159, 231, 177, 249, 194, 266, 210, 282, 208, 280, 191, 263, 175, 247, 155, 227, 162, 234, 160, 232, 178, 250, 195, 267, 211, 283, 204, 276, 188, 260, 170, 242, 152, 224)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 162)(12, 176)(13, 168)(14, 148)(15, 177)(16, 178)(17, 149)(18, 160)(19, 181)(20, 150)(21, 157)(22, 184)(23, 180)(24, 186)(25, 187)(26, 152)(27, 159)(28, 153)(29, 190)(30, 158)(31, 155)(32, 193)(33, 194)(34, 195)(35, 161)(36, 169)(37, 197)(38, 164)(39, 165)(40, 200)(41, 167)(42, 202)(43, 203)(44, 170)(45, 172)(46, 206)(47, 175)(48, 174)(49, 209)(50, 210)(51, 211)(52, 179)(53, 212)(54, 182)(55, 183)(56, 207)(57, 185)(58, 215)(59, 216)(60, 188)(61, 189)(62, 199)(63, 192)(64, 191)(65, 205)(66, 208)(67, 204)(68, 196)(69, 198)(70, 201)(71, 214)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1616
Graph:: bipartite
	v = 11 e = 144 f = 81
	degree seq :: [ 16^9, 72^2 ]

E27.1614 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 36})
Quotient :: dipole
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^3, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1 * Y2^2 * Y1^-1 * Y2^2, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y2^-6 * Y1^2 * Y2^-3, (Y3^-1 * Y1^-1)^8, Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 18, 90, 36, 108, 27, 99, 13, 85, 4, 76)(3, 75, 9, 81, 19, 91, 14, 86, 25, 97, 8, 80, 24, 96, 11, 83)(5, 77, 15, 87, 20, 92, 12, 84, 23, 95, 7, 79, 21, 93, 16, 88)(10, 82, 26, 98, 37, 109, 31, 103, 43, 115, 28, 100, 42, 114, 30, 102)(17, 89, 22, 94, 38, 110, 34, 106, 41, 113, 33, 105, 39, 111, 32, 104)(29, 101, 45, 117, 53, 125, 48, 120, 59, 131, 44, 116, 58, 130, 47, 119)(35, 107, 50, 122, 54, 126, 49, 121, 57, 129, 40, 112, 55, 127, 51, 123)(46, 118, 60, 132, 69, 141, 64, 136, 72, 144, 61, 133, 68, 140, 63, 135)(52, 124, 56, 128, 62, 134, 67, 139, 71, 143, 66, 138, 70, 142, 65, 137)(145, 217, 147, 219, 154, 226, 173, 245, 190, 262, 206, 278, 198, 270, 182, 254, 164, 236, 150, 222, 163, 235, 181, 253, 197, 269, 213, 285, 215, 287, 201, 273, 185, 257, 167, 239, 180, 252, 169, 241, 187, 259, 203, 275, 216, 288, 214, 286, 199, 271, 183, 255, 165, 237, 157, 229, 168, 240, 186, 258, 202, 274, 212, 284, 196, 268, 179, 251, 161, 233, 149, 221)(146, 218, 151, 223, 166, 238, 184, 256, 200, 272, 208, 280, 191, 263, 175, 247, 155, 227, 162, 234, 160, 232, 178, 250, 195, 267, 211, 283, 205, 277, 189, 261, 172, 244, 153, 225, 171, 243, 159, 231, 177, 249, 194, 266, 210, 282, 207, 279, 192, 264, 174, 246, 158, 230, 148, 220, 156, 228, 176, 248, 193, 265, 209, 281, 204, 276, 188, 260, 170, 242, 152, 224)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 162)(12, 176)(13, 168)(14, 148)(15, 177)(16, 178)(17, 149)(18, 160)(19, 181)(20, 150)(21, 157)(22, 184)(23, 180)(24, 186)(25, 187)(26, 152)(27, 159)(28, 153)(29, 190)(30, 158)(31, 155)(32, 193)(33, 194)(34, 195)(35, 161)(36, 169)(37, 197)(38, 164)(39, 165)(40, 200)(41, 167)(42, 202)(43, 203)(44, 170)(45, 172)(46, 206)(47, 175)(48, 174)(49, 209)(50, 210)(51, 211)(52, 179)(53, 213)(54, 182)(55, 183)(56, 208)(57, 185)(58, 212)(59, 216)(60, 188)(61, 189)(62, 198)(63, 192)(64, 191)(65, 204)(66, 207)(67, 205)(68, 196)(69, 215)(70, 199)(71, 201)(72, 214)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1615
Graph:: bipartite
	v = 11 e = 144 f = 81
	degree seq :: [ 16^9, 72^2 ]

E27.1615 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 36})
Quotient :: dipole
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3^-1 * Y2^-2 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^3 * Y3^-1 * Y2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y2^-2 * Y3^-9, (Y3^-1 * Y1^-1)^36 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 180, 252, 171, 243, 157, 229, 148, 220)(147, 219, 153, 225, 163, 235, 158, 230, 169, 241, 152, 224, 168, 240, 155, 227)(149, 221, 159, 231, 164, 236, 156, 228, 167, 239, 151, 223, 165, 237, 160, 232)(154, 226, 170, 242, 181, 253, 175, 247, 187, 259, 172, 244, 186, 258, 174, 246)(161, 233, 166, 238, 182, 254, 178, 250, 185, 257, 177, 249, 183, 255, 176, 248)(173, 245, 189, 261, 197, 269, 192, 264, 203, 275, 188, 260, 202, 274, 191, 263)(179, 251, 194, 266, 198, 270, 193, 265, 201, 273, 184, 256, 199, 271, 195, 267)(190, 262, 204, 276, 212, 284, 208, 280, 216, 288, 205, 277, 215, 287, 207, 279)(196, 268, 200, 272, 213, 285, 211, 283, 214, 286, 210, 282, 206, 278, 209, 281)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 162)(12, 176)(13, 168)(14, 148)(15, 177)(16, 178)(17, 149)(18, 160)(19, 181)(20, 150)(21, 157)(22, 184)(23, 180)(24, 186)(25, 187)(26, 152)(27, 159)(28, 153)(29, 190)(30, 158)(31, 155)(32, 193)(33, 194)(34, 195)(35, 161)(36, 169)(37, 197)(38, 164)(39, 165)(40, 200)(41, 167)(42, 202)(43, 203)(44, 170)(45, 172)(46, 206)(47, 175)(48, 174)(49, 209)(50, 210)(51, 211)(52, 179)(53, 212)(54, 182)(55, 183)(56, 207)(57, 185)(58, 215)(59, 216)(60, 188)(61, 189)(62, 199)(63, 192)(64, 191)(65, 205)(66, 208)(67, 204)(68, 196)(69, 198)(70, 201)(71, 214)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 16, 72 ), ( 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1614
Graph:: simple bipartite
	v = 81 e = 144 f = 11
	degree seq :: [ 2^72, 16^9 ]

E27.1616 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 36})
Quotient :: dipole
Aut^+ = C9 : C8 (small group id <72, 1>)
Aut   = (C9 x D8) : C2 (small group id <144, 16>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2 * Y3 * Y2^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3 * Y2^-3, Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-1, Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3^2 * Y2 * Y3^-1 * Y2 * Y3^6, (Y3^-1 * Y1^-1)^36 ]
Map::
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218, 150, 222, 162, 234, 180, 252, 171, 243, 157, 229, 148, 220)(147, 219, 153, 225, 163, 235, 158, 230, 169, 241, 152, 224, 168, 240, 155, 227)(149, 221, 159, 231, 164, 236, 156, 228, 167, 239, 151, 223, 165, 237, 160, 232)(154, 226, 170, 242, 181, 253, 175, 247, 187, 259, 172, 244, 186, 258, 174, 246)(161, 233, 166, 238, 182, 254, 178, 250, 185, 257, 177, 249, 183, 255, 176, 248)(173, 245, 189, 261, 197, 269, 192, 264, 203, 275, 188, 260, 202, 274, 191, 263)(179, 251, 194, 266, 198, 270, 193, 265, 201, 273, 184, 256, 199, 271, 195, 267)(190, 262, 204, 276, 213, 285, 208, 280, 216, 288, 205, 277, 212, 284, 207, 279)(196, 268, 200, 272, 206, 278, 211, 283, 215, 287, 210, 282, 214, 286, 209, 281)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 163)(7, 166)(8, 146)(9, 171)(10, 173)(11, 162)(12, 176)(13, 168)(14, 148)(15, 177)(16, 178)(17, 149)(18, 160)(19, 181)(20, 150)(21, 157)(22, 184)(23, 180)(24, 186)(25, 187)(26, 152)(27, 159)(28, 153)(29, 190)(30, 158)(31, 155)(32, 193)(33, 194)(34, 195)(35, 161)(36, 169)(37, 197)(38, 164)(39, 165)(40, 200)(41, 167)(42, 202)(43, 203)(44, 170)(45, 172)(46, 206)(47, 175)(48, 174)(49, 209)(50, 210)(51, 211)(52, 179)(53, 213)(54, 182)(55, 183)(56, 208)(57, 185)(58, 212)(59, 216)(60, 188)(61, 189)(62, 198)(63, 192)(64, 191)(65, 204)(66, 207)(67, 205)(68, 196)(69, 215)(70, 199)(71, 201)(72, 214)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 16, 72 ), ( 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72, 16, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1613
Graph:: simple bipartite
	v = 81 e = 144 f = 11
	degree seq :: [ 2^72, 16^9 ]

E27.1617 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 72, 72})
Quotient :: edge
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^18 * T1^-1, (T1^-1 * T2^-1)^72 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 64, 56, 48, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 72, 67, 59, 51, 43, 35, 27, 19, 11, 4, 10, 18, 26, 34, 42, 50, 58, 66, 68, 60, 52, 44, 36, 28, 20, 12, 5)(73, 74, 78, 76)(75, 79, 85, 82)(77, 80, 86, 83)(81, 87, 93, 90)(84, 88, 94, 91)(89, 95, 101, 98)(92, 96, 102, 99)(97, 103, 109, 106)(100, 104, 110, 107)(105, 111, 117, 114)(108, 112, 118, 115)(113, 119, 125, 122)(116, 120, 126, 123)(121, 127, 133, 130)(124, 128, 134, 131)(129, 135, 141, 138)(132, 136, 142, 139)(137, 143, 144, 140)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 144^4 ), ( 144^72 ) }
Outer automorphisms :: reflexible
Dual of E27.1619
Transitivity :: ET+
Graph:: bipartite
	v = 19 e = 72 f = 1
	degree seq :: [ 4^18, 72 ]

E27.1618 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 72, 72})
Quotient :: edge
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^18 * T1, (T1^-1 * T2^-1)^72 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 67, 59, 51, 43, 35, 27, 19, 11, 4, 10, 18, 26, 34, 42, 50, 58, 66, 72, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 71, 64, 56, 48, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 47, 55, 63, 68, 60, 52, 44, 36, 28, 20, 12, 5)(73, 74, 78, 76)(75, 79, 85, 82)(77, 80, 86, 83)(81, 87, 93, 90)(84, 88, 94, 91)(89, 95, 101, 98)(92, 96, 102, 99)(97, 103, 109, 106)(100, 104, 110, 107)(105, 111, 117, 114)(108, 112, 118, 115)(113, 119, 125, 122)(116, 120, 126, 123)(121, 127, 133, 130)(124, 128, 134, 131)(129, 135, 141, 138)(132, 136, 142, 139)(137, 140, 143, 144)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 144^4 ), ( 144^72 ) }
Outer automorphisms :: reflexible
Dual of E27.1620
Transitivity :: ET+
Graph:: bipartite
	v = 19 e = 72 f = 1
	degree seq :: [ 4^18, 72 ]

E27.1619 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 72, 72})
Quotient :: loop
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^18 * T1^-1, (T1^-1 * T2^-1)^72 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 9, 81, 17, 89, 25, 97, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 64, 136, 56, 128, 48, 120, 40, 112, 32, 104, 24, 96, 16, 88, 8, 80, 2, 74, 7, 79, 15, 87, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 71, 143, 70, 142, 62, 134, 54, 126, 46, 118, 38, 110, 30, 102, 22, 94, 14, 86, 6, 78, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 72, 144, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 19, 91, 11, 83, 4, 76, 10, 82, 18, 90, 26, 98, 34, 106, 42, 114, 50, 122, 58, 130, 66, 138, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92, 12, 84, 5, 77)
	L = (1, 74)(2, 78)(3, 79)(4, 73)(5, 80)(6, 76)(7, 85)(8, 86)(9, 87)(10, 75)(11, 77)(12, 88)(13, 82)(14, 83)(15, 93)(16, 94)(17, 95)(18, 81)(19, 84)(20, 96)(21, 90)(22, 91)(23, 101)(24, 102)(25, 103)(26, 89)(27, 92)(28, 104)(29, 98)(30, 99)(31, 109)(32, 110)(33, 111)(34, 97)(35, 100)(36, 112)(37, 106)(38, 107)(39, 117)(40, 118)(41, 119)(42, 105)(43, 108)(44, 120)(45, 114)(46, 115)(47, 125)(48, 126)(49, 127)(50, 113)(51, 116)(52, 128)(53, 122)(54, 123)(55, 133)(56, 134)(57, 135)(58, 121)(59, 124)(60, 136)(61, 130)(62, 131)(63, 141)(64, 142)(65, 143)(66, 129)(67, 132)(68, 137)(69, 138)(70, 139)(71, 144)(72, 140)
	local type(s) :: { ( 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1617
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 72 f = 19
	degree seq :: [ 144 ]

E27.1620 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 72, 72})
Quotient :: loop
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^18 * T1, (T1^-1 * T2^-1)^72 ]
Map:: non-degenerate
	R = (1, 73, 3, 75, 9, 81, 17, 89, 25, 97, 33, 105, 41, 113, 49, 121, 57, 129, 65, 137, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 19, 91, 11, 83, 4, 76, 10, 82, 18, 90, 26, 98, 34, 106, 42, 114, 50, 122, 58, 130, 66, 138, 72, 144, 70, 142, 62, 134, 54, 126, 46, 118, 38, 110, 30, 102, 22, 94, 14, 86, 6, 78, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 69, 141, 71, 143, 64, 136, 56, 128, 48, 120, 40, 112, 32, 104, 24, 96, 16, 88, 8, 80, 2, 74, 7, 79, 15, 87, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92, 12, 84, 5, 77)
	L = (1, 74)(2, 78)(3, 79)(4, 73)(5, 80)(6, 76)(7, 85)(8, 86)(9, 87)(10, 75)(11, 77)(12, 88)(13, 82)(14, 83)(15, 93)(16, 94)(17, 95)(18, 81)(19, 84)(20, 96)(21, 90)(22, 91)(23, 101)(24, 102)(25, 103)(26, 89)(27, 92)(28, 104)(29, 98)(30, 99)(31, 109)(32, 110)(33, 111)(34, 97)(35, 100)(36, 112)(37, 106)(38, 107)(39, 117)(40, 118)(41, 119)(42, 105)(43, 108)(44, 120)(45, 114)(46, 115)(47, 125)(48, 126)(49, 127)(50, 113)(51, 116)(52, 128)(53, 122)(54, 123)(55, 133)(56, 134)(57, 135)(58, 121)(59, 124)(60, 136)(61, 130)(62, 131)(63, 141)(64, 142)(65, 140)(66, 129)(67, 132)(68, 143)(69, 138)(70, 139)(71, 144)(72, 137)
	local type(s) :: { ( 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.1618
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 72 f = 19
	degree seq :: [ 144 ]

E27.1621 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 72, 72})
Quotient :: dipole
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y2^18 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 7, 79, 13, 85, 10, 82)(5, 77, 8, 80, 14, 86, 11, 83)(9, 81, 15, 87, 21, 93, 18, 90)(12, 84, 16, 88, 22, 94, 19, 91)(17, 89, 23, 95, 29, 101, 26, 98)(20, 92, 24, 96, 30, 102, 27, 99)(25, 97, 31, 103, 37, 109, 34, 106)(28, 100, 32, 104, 38, 110, 35, 107)(33, 105, 39, 111, 45, 117, 42, 114)(36, 108, 40, 112, 46, 118, 43, 115)(41, 113, 47, 119, 53, 125, 50, 122)(44, 116, 48, 120, 54, 126, 51, 123)(49, 121, 55, 127, 61, 133, 58, 130)(52, 124, 56, 128, 62, 134, 59, 131)(57, 129, 63, 135, 69, 141, 66, 138)(60, 132, 64, 136, 70, 142, 67, 139)(65, 137, 68, 140, 71, 143, 72, 144)(145, 217, 147, 219, 153, 225, 161, 233, 169, 241, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 211, 283, 203, 275, 195, 267, 187, 259, 179, 251, 171, 243, 163, 235, 155, 227, 148, 220, 154, 226, 162, 234, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 216, 288, 214, 286, 206, 278, 198, 270, 190, 262, 182, 254, 174, 246, 166, 238, 158, 230, 150, 222, 157, 229, 165, 237, 173, 245, 181, 253, 189, 261, 197, 269, 205, 277, 213, 285, 215, 287, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 160, 232, 152, 224, 146, 218, 151, 223, 159, 231, 167, 239, 175, 247, 183, 255, 191, 263, 199, 271, 207, 279, 212, 284, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 164, 236, 156, 228, 149, 221)
	L = (1, 148)(2, 145)(3, 154)(4, 150)(5, 155)(6, 146)(7, 147)(8, 149)(9, 162)(10, 157)(11, 158)(12, 163)(13, 151)(14, 152)(15, 153)(16, 156)(17, 170)(18, 165)(19, 166)(20, 171)(21, 159)(22, 160)(23, 161)(24, 164)(25, 178)(26, 173)(27, 174)(28, 179)(29, 167)(30, 168)(31, 169)(32, 172)(33, 186)(34, 181)(35, 182)(36, 187)(37, 175)(38, 176)(39, 177)(40, 180)(41, 194)(42, 189)(43, 190)(44, 195)(45, 183)(46, 184)(47, 185)(48, 188)(49, 202)(50, 197)(51, 198)(52, 203)(53, 191)(54, 192)(55, 193)(56, 196)(57, 210)(58, 205)(59, 206)(60, 211)(61, 199)(62, 200)(63, 201)(64, 204)(65, 216)(66, 213)(67, 214)(68, 209)(69, 207)(70, 208)(71, 212)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 144, 2, 144, 2, 144, 2, 144 ), ( 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.1624
Graph:: bipartite
	v = 19 e = 144 f = 73
	degree seq :: [ 8^18, 144 ]

E27.1622 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 72, 72})
Quotient :: dipole
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y3^4, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3 * Y2^18, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 7, 79, 13, 85, 10, 82)(5, 77, 8, 80, 14, 86, 11, 83)(9, 81, 15, 87, 21, 93, 18, 90)(12, 84, 16, 88, 22, 94, 19, 91)(17, 89, 23, 95, 29, 101, 26, 98)(20, 92, 24, 96, 30, 102, 27, 99)(25, 97, 31, 103, 37, 109, 34, 106)(28, 100, 32, 104, 38, 110, 35, 107)(33, 105, 39, 111, 45, 117, 42, 114)(36, 108, 40, 112, 46, 118, 43, 115)(41, 113, 47, 119, 53, 125, 50, 122)(44, 116, 48, 120, 54, 126, 51, 123)(49, 121, 55, 127, 61, 133, 58, 130)(52, 124, 56, 128, 62, 134, 59, 131)(57, 129, 63, 135, 69, 141, 66, 138)(60, 132, 64, 136, 70, 142, 67, 139)(65, 137, 71, 143, 72, 144, 68, 140)(145, 217, 147, 219, 153, 225, 161, 233, 169, 241, 177, 249, 185, 257, 193, 265, 201, 273, 209, 281, 208, 280, 200, 272, 192, 264, 184, 256, 176, 248, 168, 240, 160, 232, 152, 224, 146, 218, 151, 223, 159, 231, 167, 239, 175, 247, 183, 255, 191, 263, 199, 271, 207, 279, 215, 287, 214, 286, 206, 278, 198, 270, 190, 262, 182, 254, 174, 246, 166, 238, 158, 230, 150, 222, 157, 229, 165, 237, 173, 245, 181, 253, 189, 261, 197, 269, 205, 277, 213, 285, 216, 288, 211, 283, 203, 275, 195, 267, 187, 259, 179, 251, 171, 243, 163, 235, 155, 227, 148, 220, 154, 226, 162, 234, 170, 242, 178, 250, 186, 258, 194, 266, 202, 274, 210, 282, 212, 284, 204, 276, 196, 268, 188, 260, 180, 252, 172, 244, 164, 236, 156, 228, 149, 221)
	L = (1, 148)(2, 145)(3, 154)(4, 150)(5, 155)(6, 146)(7, 147)(8, 149)(9, 162)(10, 157)(11, 158)(12, 163)(13, 151)(14, 152)(15, 153)(16, 156)(17, 170)(18, 165)(19, 166)(20, 171)(21, 159)(22, 160)(23, 161)(24, 164)(25, 178)(26, 173)(27, 174)(28, 179)(29, 167)(30, 168)(31, 169)(32, 172)(33, 186)(34, 181)(35, 182)(36, 187)(37, 175)(38, 176)(39, 177)(40, 180)(41, 194)(42, 189)(43, 190)(44, 195)(45, 183)(46, 184)(47, 185)(48, 188)(49, 202)(50, 197)(51, 198)(52, 203)(53, 191)(54, 192)(55, 193)(56, 196)(57, 210)(58, 205)(59, 206)(60, 211)(61, 199)(62, 200)(63, 201)(64, 204)(65, 212)(66, 213)(67, 214)(68, 216)(69, 207)(70, 208)(71, 209)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 144, 2, 144, 2, 144, 2, 144 ), ( 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.1623
Graph:: bipartite
	v = 19 e = 144 f = 73
	degree seq :: [ 8^18, 144 ]

E27.1623 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 72, 72})
Quotient :: dipole
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^18 * Y3^-1, (Y1^-1 * Y3^-1)^72 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 66, 138, 58, 130, 50, 122, 42, 114, 34, 106, 26, 98, 18, 90, 10, 82, 3, 75, 7, 79, 14, 86, 22, 94, 30, 102, 38, 110, 46, 118, 54, 126, 62, 134, 69, 141, 71, 143, 65, 137, 57, 129, 49, 121, 41, 113, 33, 105, 25, 97, 17, 89, 9, 81, 16, 88, 24, 96, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 70, 142, 72, 144, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92, 12, 84, 5, 77, 8, 80, 15, 87, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 19, 91, 11, 83, 4, 76)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 153)(4, 154)(5, 145)(6, 158)(7, 160)(8, 146)(9, 149)(10, 161)(11, 162)(12, 148)(13, 166)(14, 168)(15, 150)(16, 152)(17, 156)(18, 169)(19, 170)(20, 155)(21, 174)(22, 176)(23, 157)(24, 159)(25, 164)(26, 177)(27, 178)(28, 163)(29, 182)(30, 184)(31, 165)(32, 167)(33, 172)(34, 185)(35, 186)(36, 171)(37, 190)(38, 192)(39, 173)(40, 175)(41, 180)(42, 193)(43, 194)(44, 179)(45, 198)(46, 200)(47, 181)(48, 183)(49, 188)(50, 201)(51, 202)(52, 187)(53, 206)(54, 208)(55, 189)(56, 191)(57, 196)(58, 209)(59, 210)(60, 195)(61, 213)(62, 214)(63, 197)(64, 199)(65, 204)(66, 215)(67, 205)(68, 203)(69, 216)(70, 207)(71, 212)(72, 211)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 8, 144 ), ( 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.1622
Graph:: bipartite
	v = 73 e = 144 f = 19
	degree seq :: [ 2^72, 144 ]

E27.1624 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 72, 72})
Quotient :: dipole
Aut^+ = C72 (small group id <72, 2>)
Aut   = D144 (small group id <144, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^18 * Y3, Y1^7 * Y3^-2 * Y1^-8 * Y3^-2 * Y1, (Y1^-1 * Y3^-1)^72 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 13, 85, 21, 93, 29, 101, 37, 109, 45, 117, 53, 125, 61, 133, 68, 140, 60, 132, 52, 124, 44, 116, 36, 108, 28, 100, 20, 92, 12, 84, 5, 77, 8, 80, 15, 87, 23, 95, 31, 103, 39, 111, 47, 119, 55, 127, 63, 135, 69, 141, 71, 143, 65, 137, 57, 129, 49, 121, 41, 113, 33, 105, 25, 97, 17, 89, 9, 81, 16, 88, 24, 96, 32, 104, 40, 112, 48, 120, 56, 128, 64, 136, 70, 142, 72, 144, 66, 138, 58, 130, 50, 122, 42, 114, 34, 106, 26, 98, 18, 90, 10, 82, 3, 75, 7, 79, 14, 86, 22, 94, 30, 102, 38, 110, 46, 118, 54, 126, 62, 134, 67, 139, 59, 131, 51, 123, 43, 115, 35, 107, 27, 99, 19, 91, 11, 83, 4, 76)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 153)(4, 154)(5, 145)(6, 158)(7, 160)(8, 146)(9, 149)(10, 161)(11, 162)(12, 148)(13, 166)(14, 168)(15, 150)(16, 152)(17, 156)(18, 169)(19, 170)(20, 155)(21, 174)(22, 176)(23, 157)(24, 159)(25, 164)(26, 177)(27, 178)(28, 163)(29, 182)(30, 184)(31, 165)(32, 167)(33, 172)(34, 185)(35, 186)(36, 171)(37, 190)(38, 192)(39, 173)(40, 175)(41, 180)(42, 193)(43, 194)(44, 179)(45, 198)(46, 200)(47, 181)(48, 183)(49, 188)(50, 201)(51, 202)(52, 187)(53, 206)(54, 208)(55, 189)(56, 191)(57, 196)(58, 209)(59, 210)(60, 195)(61, 211)(62, 214)(63, 197)(64, 199)(65, 204)(66, 215)(67, 216)(68, 203)(69, 205)(70, 207)(71, 212)(72, 213)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 8, 144 ), ( 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144, 8, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.1621
Graph:: bipartite
	v = 73 e = 144 f = 19
	degree seq :: [ 2^72, 144 ]

E27.1625 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 19, 76})
Quotient :: edge
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 10, 18, 26, 34, 42, 50, 58, 66, 73, 74, 67, 59, 51, 43, 35, 27, 19, 11)(6, 13, 21, 29, 37, 45, 53, 61, 69, 75, 76, 70, 62, 54, 46, 38, 30, 22, 14)(77, 78, 82, 80)(79, 83, 89, 86)(81, 84, 90, 87)(85, 91, 97, 94)(88, 92, 98, 95)(93, 99, 105, 102)(96, 100, 106, 103)(101, 107, 113, 110)(104, 108, 114, 111)(109, 115, 121, 118)(112, 116, 122, 119)(117, 123, 129, 126)(120, 124, 130, 127)(125, 131, 137, 134)(128, 132, 138, 135)(133, 139, 145, 142)(136, 140, 146, 143)(141, 147, 151, 149)(144, 148, 152, 150)
	L = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 85)(10, 86)(11, 87)(12, 88)(13, 89)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 96)(21, 97)(22, 98)(23, 99)(24, 100)(25, 101)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 110)(35, 111)(36, 112)(37, 113)(38, 114)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 152^4 ), ( 152^19 ) }
Outer automorphisms :: reflexible
Dual of E27.1629
Transitivity :: ET+
Graph:: simple bipartite
	v = 23 e = 76 f = 1
	degree seq :: [ 4^19, 19^4 ]

E27.1626 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 19, 76})
Quotient :: edge
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-4 * T2^-4, (T1^-1 * T2^-1)^4, T2^-16 * T1^3, T1^7 * T2^-1 * T1^3 * T2^-7 * T1, T1^19, T2^76 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 41, 49, 57, 65, 73, 71, 62, 53, 48, 39, 28, 14, 27, 24, 12, 4, 10, 20, 34, 42, 50, 58, 66, 74, 72, 63, 54, 45, 40, 30, 16, 6, 15, 29, 23, 11, 21, 35, 43, 51, 59, 67, 75, 69, 64, 55, 46, 37, 32, 18, 8, 2, 7, 17, 31, 22, 36, 44, 52, 60, 68, 76, 70, 61, 56, 47, 38, 26, 25, 13, 5)(77, 78, 82, 90, 102, 113, 121, 129, 137, 145, 150, 141, 136, 127, 118, 109, 98, 87, 80)(79, 83, 91, 103, 101, 108, 116, 124, 132, 140, 148, 149, 144, 135, 126, 117, 112, 97, 86)(81, 84, 92, 104, 114, 122, 130, 138, 146, 151, 142, 133, 128, 119, 110, 95, 107, 99, 88)(85, 93, 105, 100, 89, 94, 106, 115, 123, 131, 139, 147, 152, 143, 134, 125, 120, 111, 96)
	L = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 85)(10, 86)(11, 87)(12, 88)(13, 89)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 96)(21, 97)(22, 98)(23, 99)(24, 100)(25, 101)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 110)(35, 111)(36, 112)(37, 113)(38, 114)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 8^19 ), ( 8^76 ) }
Outer automorphisms :: reflexible
Dual of E27.1630
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 76 f = 19
	degree seq :: [ 19^4, 76 ]

E27.1627 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 19, 76})
Quotient :: edge
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, T2^4, (F * T1)^2, (T1, T2^-1), T1^-19 * T2, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 24, 15)(11, 18, 25, 20)(13, 22, 32, 23)(19, 26, 33, 28)(21, 30, 40, 31)(27, 34, 41, 36)(29, 38, 48, 39)(35, 42, 49, 44)(37, 46, 56, 47)(43, 50, 57, 52)(45, 54, 64, 55)(51, 58, 65, 60)(53, 62, 72, 63)(59, 66, 73, 68)(61, 70, 76, 71)(67, 69, 75, 74)(77, 78, 82, 89, 97, 105, 113, 121, 129, 137, 145, 142, 134, 126, 118, 110, 102, 94, 86, 79, 83, 90, 98, 106, 114, 122, 130, 138, 146, 151, 149, 141, 133, 125, 117, 109, 101, 93, 85, 92, 100, 108, 116, 124, 132, 140, 148, 152, 150, 144, 136, 128, 120, 112, 104, 96, 88, 81, 84, 91, 99, 107, 115, 123, 131, 139, 147, 143, 135, 127, 119, 111, 103, 95, 87, 80)
	L = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 85)(10, 86)(11, 87)(12, 88)(13, 89)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 96)(21, 97)(22, 98)(23, 99)(24, 100)(25, 101)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 110)(35, 111)(36, 112)(37, 113)(38, 114)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)
	local type(s) :: { ( 38^4 ), ( 38^76 ) }
Outer automorphisms :: reflexible
Dual of E27.1628
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 76 f = 4
	degree seq :: [ 4^19, 76 ]

E27.1628 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 19, 76})
Quotient :: loop
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^19 ]
Map:: non-degenerate
	R = (1, 77, 3, 79, 9, 85, 17, 93, 25, 101, 33, 109, 41, 117, 49, 125, 57, 133, 65, 141, 68, 144, 60, 136, 52, 128, 44, 120, 36, 112, 28, 104, 20, 96, 12, 88, 5, 81)(2, 78, 7, 83, 15, 91, 23, 99, 31, 107, 39, 115, 47, 123, 55, 131, 63, 139, 71, 147, 72, 148, 64, 140, 56, 132, 48, 124, 40, 116, 32, 108, 24, 100, 16, 92, 8, 84)(4, 80, 10, 86, 18, 94, 26, 102, 34, 110, 42, 118, 50, 126, 58, 134, 66, 142, 73, 149, 74, 150, 67, 143, 59, 135, 51, 127, 43, 119, 35, 111, 27, 103, 19, 95, 11, 87)(6, 82, 13, 89, 21, 97, 29, 105, 37, 113, 45, 121, 53, 129, 61, 137, 69, 145, 75, 151, 76, 152, 70, 146, 62, 138, 54, 130, 46, 122, 38, 114, 30, 106, 22, 98, 14, 90)
	L = (1, 78)(2, 82)(3, 83)(4, 77)(5, 84)(6, 80)(7, 89)(8, 90)(9, 91)(10, 79)(11, 81)(12, 92)(13, 86)(14, 87)(15, 97)(16, 98)(17, 99)(18, 85)(19, 88)(20, 100)(21, 94)(22, 95)(23, 105)(24, 106)(25, 107)(26, 93)(27, 96)(28, 108)(29, 102)(30, 103)(31, 113)(32, 114)(33, 115)(34, 101)(35, 104)(36, 116)(37, 110)(38, 111)(39, 121)(40, 122)(41, 123)(42, 109)(43, 112)(44, 124)(45, 118)(46, 119)(47, 129)(48, 130)(49, 131)(50, 117)(51, 120)(52, 132)(53, 126)(54, 127)(55, 137)(56, 138)(57, 139)(58, 125)(59, 128)(60, 140)(61, 134)(62, 135)(63, 145)(64, 146)(65, 147)(66, 133)(67, 136)(68, 148)(69, 142)(70, 143)(71, 151)(72, 152)(73, 141)(74, 144)(75, 149)(76, 150)
	local type(s) :: { ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.1627
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 76 f = 20
	degree seq :: [ 38^4 ]

E27.1629 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 19, 76})
Quotient :: loop
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-4 * T2^-4, (T1^-1 * T2^-1)^4, T2^-16 * T1^3, T1^7 * T2^-1 * T1^3 * T2^-7 * T1, T1^19, T2^76 ]
Map:: non-degenerate
	R = (1, 77, 3, 79, 9, 85, 19, 95, 33, 109, 41, 117, 49, 125, 57, 133, 65, 141, 73, 149, 71, 147, 62, 138, 53, 129, 48, 124, 39, 115, 28, 104, 14, 90, 27, 103, 24, 100, 12, 88, 4, 80, 10, 86, 20, 96, 34, 110, 42, 118, 50, 126, 58, 134, 66, 142, 74, 150, 72, 148, 63, 139, 54, 130, 45, 121, 40, 116, 30, 106, 16, 92, 6, 82, 15, 91, 29, 105, 23, 99, 11, 87, 21, 97, 35, 111, 43, 119, 51, 127, 59, 135, 67, 143, 75, 151, 69, 145, 64, 140, 55, 131, 46, 122, 37, 113, 32, 108, 18, 94, 8, 84, 2, 78, 7, 83, 17, 93, 31, 107, 22, 98, 36, 112, 44, 120, 52, 128, 60, 136, 68, 144, 76, 152, 70, 146, 61, 137, 56, 132, 47, 123, 38, 114, 26, 102, 25, 101, 13, 89, 5, 81)
	L = (1, 78)(2, 82)(3, 83)(4, 77)(5, 84)(6, 90)(7, 91)(8, 92)(9, 93)(10, 79)(11, 80)(12, 81)(13, 94)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 85)(21, 86)(22, 87)(23, 88)(24, 89)(25, 108)(26, 113)(27, 101)(28, 114)(29, 100)(30, 115)(31, 99)(32, 116)(33, 98)(34, 95)(35, 96)(36, 97)(37, 121)(38, 122)(39, 123)(40, 124)(41, 112)(42, 109)(43, 110)(44, 111)(45, 129)(46, 130)(47, 131)(48, 132)(49, 120)(50, 117)(51, 118)(52, 119)(53, 137)(54, 138)(55, 139)(56, 140)(57, 128)(58, 125)(59, 126)(60, 127)(61, 145)(62, 146)(63, 147)(64, 148)(65, 136)(66, 133)(67, 134)(68, 135)(69, 150)(70, 151)(71, 152)(72, 149)(73, 144)(74, 141)(75, 142)(76, 143)
	local type(s) :: { ( 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19, 4, 19 ) }
Outer automorphisms :: reflexible
Dual of E27.1625
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 76 f = 23
	degree seq :: [ 152 ]

E27.1630 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 19, 76})
Quotient :: loop
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, T2^4, (F * T1)^2, (T1, T2^-1), T1^-19 * T2, (T1^-1 * T2^-1)^19 ]
Map:: non-degenerate
	R = (1, 77, 3, 79, 9, 85, 5, 81)(2, 78, 7, 83, 16, 92, 8, 84)(4, 80, 10, 86, 17, 93, 12, 88)(6, 82, 14, 90, 24, 100, 15, 91)(11, 87, 18, 94, 25, 101, 20, 96)(13, 89, 22, 98, 32, 108, 23, 99)(19, 95, 26, 102, 33, 109, 28, 104)(21, 97, 30, 106, 40, 116, 31, 107)(27, 103, 34, 110, 41, 117, 36, 112)(29, 105, 38, 114, 48, 124, 39, 115)(35, 111, 42, 118, 49, 125, 44, 120)(37, 113, 46, 122, 56, 132, 47, 123)(43, 119, 50, 126, 57, 133, 52, 128)(45, 121, 54, 130, 64, 140, 55, 131)(51, 127, 58, 134, 65, 141, 60, 136)(53, 129, 62, 138, 72, 148, 63, 139)(59, 135, 66, 142, 73, 149, 68, 144)(61, 137, 70, 146, 76, 152, 71, 147)(67, 143, 69, 145, 75, 151, 74, 150)
	L = (1, 78)(2, 82)(3, 83)(4, 77)(5, 84)(6, 89)(7, 90)(8, 91)(9, 92)(10, 79)(11, 80)(12, 81)(13, 97)(14, 98)(15, 99)(16, 100)(17, 85)(18, 86)(19, 87)(20, 88)(21, 105)(22, 106)(23, 107)(24, 108)(25, 93)(26, 94)(27, 95)(28, 96)(29, 113)(30, 114)(31, 115)(32, 116)(33, 101)(34, 102)(35, 103)(36, 104)(37, 121)(38, 122)(39, 123)(40, 124)(41, 109)(42, 110)(43, 111)(44, 112)(45, 129)(46, 130)(47, 131)(48, 132)(49, 117)(50, 118)(51, 119)(52, 120)(53, 137)(54, 138)(55, 139)(56, 140)(57, 125)(58, 126)(59, 127)(60, 128)(61, 145)(62, 146)(63, 147)(64, 148)(65, 133)(66, 134)(67, 135)(68, 136)(69, 142)(70, 151)(71, 143)(72, 152)(73, 141)(74, 144)(75, 149)(76, 150)
	local type(s) :: { ( 19, 76, 19, 76, 19, 76, 19, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.1626
Transitivity :: ET+ VT+ AT
Graph::
	v = 19 e = 76 f = 5
	degree seq :: [ 8^19 ]

E27.1631 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y2^19, Y3^76 ]
Map::
	R = (1, 77, 2, 78, 6, 82, 4, 80)(3, 79, 7, 83, 13, 89, 10, 86)(5, 81, 8, 84, 14, 90, 11, 87)(9, 85, 15, 91, 21, 97, 18, 94)(12, 88, 16, 92, 22, 98, 19, 95)(17, 93, 23, 99, 29, 105, 26, 102)(20, 96, 24, 100, 30, 106, 27, 103)(25, 101, 31, 107, 37, 113, 34, 110)(28, 104, 32, 108, 38, 114, 35, 111)(33, 109, 39, 115, 45, 121, 42, 118)(36, 112, 40, 116, 46, 122, 43, 119)(41, 117, 47, 123, 53, 129, 50, 126)(44, 120, 48, 124, 54, 130, 51, 127)(49, 125, 55, 131, 61, 137, 58, 134)(52, 128, 56, 132, 62, 138, 59, 135)(57, 133, 63, 139, 69, 145, 66, 142)(60, 136, 64, 140, 70, 146, 67, 143)(65, 141, 71, 147, 75, 151, 73, 149)(68, 144, 72, 148, 76, 152, 74, 150)(153, 229, 155, 231, 161, 237, 169, 245, 177, 253, 185, 261, 193, 269, 201, 277, 209, 285, 217, 293, 220, 296, 212, 288, 204, 280, 196, 272, 188, 264, 180, 256, 172, 248, 164, 240, 157, 233)(154, 230, 159, 235, 167, 243, 175, 251, 183, 259, 191, 267, 199, 275, 207, 283, 215, 291, 223, 299, 224, 300, 216, 292, 208, 284, 200, 276, 192, 268, 184, 260, 176, 252, 168, 244, 160, 236)(156, 232, 162, 238, 170, 246, 178, 254, 186, 262, 194, 270, 202, 278, 210, 286, 218, 294, 225, 301, 226, 302, 219, 295, 211, 287, 203, 279, 195, 271, 187, 263, 179, 255, 171, 247, 163, 239)(158, 234, 165, 241, 173, 249, 181, 257, 189, 265, 197, 273, 205, 281, 213, 289, 221, 297, 227, 303, 228, 304, 222, 298, 214, 290, 206, 282, 198, 274, 190, 266, 182, 258, 174, 250, 166, 242)
	L = (1, 156)(2, 153)(3, 162)(4, 158)(5, 163)(6, 154)(7, 155)(8, 157)(9, 170)(10, 165)(11, 166)(12, 171)(13, 159)(14, 160)(15, 161)(16, 164)(17, 178)(18, 173)(19, 174)(20, 179)(21, 167)(22, 168)(23, 169)(24, 172)(25, 186)(26, 181)(27, 182)(28, 187)(29, 175)(30, 176)(31, 177)(32, 180)(33, 194)(34, 189)(35, 190)(36, 195)(37, 183)(38, 184)(39, 185)(40, 188)(41, 202)(42, 197)(43, 198)(44, 203)(45, 191)(46, 192)(47, 193)(48, 196)(49, 210)(50, 205)(51, 206)(52, 211)(53, 199)(54, 200)(55, 201)(56, 204)(57, 218)(58, 213)(59, 214)(60, 219)(61, 207)(62, 208)(63, 209)(64, 212)(65, 225)(66, 221)(67, 222)(68, 226)(69, 215)(70, 216)(71, 217)(72, 220)(73, 227)(74, 228)(75, 223)(76, 224)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 2, 152, 2, 152, 2, 152, 2, 152 ), ( 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152, 2, 152 ) }
Outer automorphisms :: reflexible
Dual of E27.1634
Graph:: bipartite
	v = 23 e = 152 f = 77
	degree seq :: [ 8^19, 38^4 ]

E27.1632 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^4 * Y1^4, (Y3^-1 * Y1^-1)^4, Y2^16 * Y1^-3, Y1^6 * Y2^-1 * Y1 * Y2^-11, Y1^19 ]
Map::
	R = (1, 77, 2, 78, 6, 82, 14, 90, 26, 102, 37, 113, 45, 121, 53, 129, 61, 137, 69, 145, 74, 150, 65, 141, 60, 136, 51, 127, 42, 118, 33, 109, 22, 98, 11, 87, 4, 80)(3, 79, 7, 83, 15, 91, 27, 103, 25, 101, 32, 108, 40, 116, 48, 124, 56, 132, 64, 140, 72, 148, 73, 149, 68, 144, 59, 135, 50, 126, 41, 117, 36, 112, 21, 97, 10, 86)(5, 81, 8, 84, 16, 92, 28, 104, 38, 114, 46, 122, 54, 130, 62, 138, 70, 146, 75, 151, 66, 142, 57, 133, 52, 128, 43, 119, 34, 110, 19, 95, 31, 107, 23, 99, 12, 88)(9, 85, 17, 93, 29, 105, 24, 100, 13, 89, 18, 94, 30, 106, 39, 115, 47, 123, 55, 131, 63, 139, 71, 147, 76, 152, 67, 143, 58, 134, 49, 125, 44, 120, 35, 111, 20, 96)(153, 229, 155, 231, 161, 237, 171, 247, 185, 261, 193, 269, 201, 277, 209, 285, 217, 293, 225, 301, 223, 299, 214, 290, 205, 281, 200, 276, 191, 267, 180, 256, 166, 242, 179, 255, 176, 252, 164, 240, 156, 232, 162, 238, 172, 248, 186, 262, 194, 270, 202, 278, 210, 286, 218, 294, 226, 302, 224, 300, 215, 291, 206, 282, 197, 273, 192, 268, 182, 258, 168, 244, 158, 234, 167, 243, 181, 257, 175, 251, 163, 239, 173, 249, 187, 263, 195, 271, 203, 279, 211, 287, 219, 295, 227, 303, 221, 297, 216, 292, 207, 283, 198, 274, 189, 265, 184, 260, 170, 246, 160, 236, 154, 230, 159, 235, 169, 245, 183, 259, 174, 250, 188, 264, 196, 272, 204, 280, 212, 288, 220, 296, 228, 304, 222, 298, 213, 289, 208, 284, 199, 275, 190, 266, 178, 254, 177, 253, 165, 241, 157, 233)
	L = (1, 155)(2, 159)(3, 161)(4, 162)(5, 153)(6, 167)(7, 169)(8, 154)(9, 171)(10, 172)(11, 173)(12, 156)(13, 157)(14, 179)(15, 181)(16, 158)(17, 183)(18, 160)(19, 185)(20, 186)(21, 187)(22, 188)(23, 163)(24, 164)(25, 165)(26, 177)(27, 176)(28, 166)(29, 175)(30, 168)(31, 174)(32, 170)(33, 193)(34, 194)(35, 195)(36, 196)(37, 184)(38, 178)(39, 180)(40, 182)(41, 201)(42, 202)(43, 203)(44, 204)(45, 192)(46, 189)(47, 190)(48, 191)(49, 209)(50, 210)(51, 211)(52, 212)(53, 200)(54, 197)(55, 198)(56, 199)(57, 217)(58, 218)(59, 219)(60, 220)(61, 208)(62, 205)(63, 206)(64, 207)(65, 225)(66, 226)(67, 227)(68, 228)(69, 216)(70, 213)(71, 214)(72, 215)(73, 223)(74, 224)(75, 221)(76, 222)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1633
Graph:: bipartite
	v = 5 e = 152 f = 95
	degree seq :: [ 38^4, 152 ]

E27.1633 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2, Y3^-1), Y2^-1 * Y3^-19, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^76 ]
Map::
	R = (1, 77)(2, 78)(3, 79)(4, 80)(5, 81)(6, 82)(7, 83)(8, 84)(9, 85)(10, 86)(11, 87)(12, 88)(13, 89)(14, 90)(15, 91)(16, 92)(17, 93)(18, 94)(19, 95)(20, 96)(21, 97)(22, 98)(23, 99)(24, 100)(25, 101)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 107)(32, 108)(33, 109)(34, 110)(35, 111)(36, 112)(37, 113)(38, 114)(39, 115)(40, 116)(41, 117)(42, 118)(43, 119)(44, 120)(45, 121)(46, 122)(47, 123)(48, 124)(49, 125)(50, 126)(51, 127)(52, 128)(53, 129)(54, 130)(55, 131)(56, 132)(57, 133)(58, 134)(59, 135)(60, 136)(61, 137)(62, 138)(63, 139)(64, 140)(65, 141)(66, 142)(67, 143)(68, 144)(69, 145)(70, 146)(71, 147)(72, 148)(73, 149)(74, 150)(75, 151)(76, 152)(153, 229, 154, 230, 158, 234, 156, 232)(155, 231, 159, 235, 165, 241, 162, 238)(157, 233, 160, 236, 166, 242, 163, 239)(161, 237, 167, 243, 173, 249, 170, 246)(164, 240, 168, 244, 174, 250, 171, 247)(169, 245, 175, 251, 181, 257, 178, 254)(172, 248, 176, 252, 182, 258, 179, 255)(177, 253, 183, 259, 189, 265, 186, 262)(180, 256, 184, 260, 190, 266, 187, 263)(185, 261, 191, 267, 197, 273, 194, 270)(188, 264, 192, 268, 198, 274, 195, 271)(193, 269, 199, 275, 205, 281, 202, 278)(196, 272, 200, 276, 206, 282, 203, 279)(201, 277, 207, 283, 213, 289, 210, 286)(204, 280, 208, 284, 214, 290, 211, 287)(209, 285, 215, 291, 221, 297, 218, 294)(212, 288, 216, 292, 222, 298, 219, 295)(217, 293, 223, 299, 227, 303, 226, 302)(220, 296, 224, 300, 228, 304, 225, 301)
	L = (1, 155)(2, 159)(3, 161)(4, 162)(5, 153)(6, 165)(7, 167)(8, 154)(9, 169)(10, 170)(11, 156)(12, 157)(13, 173)(14, 158)(15, 175)(16, 160)(17, 177)(18, 178)(19, 163)(20, 164)(21, 181)(22, 166)(23, 183)(24, 168)(25, 185)(26, 186)(27, 171)(28, 172)(29, 189)(30, 174)(31, 191)(32, 176)(33, 193)(34, 194)(35, 179)(36, 180)(37, 197)(38, 182)(39, 199)(40, 184)(41, 201)(42, 202)(43, 187)(44, 188)(45, 205)(46, 190)(47, 207)(48, 192)(49, 209)(50, 210)(51, 195)(52, 196)(53, 213)(54, 198)(55, 215)(56, 200)(57, 217)(58, 218)(59, 203)(60, 204)(61, 221)(62, 206)(63, 223)(64, 208)(65, 225)(66, 226)(67, 211)(68, 212)(69, 227)(70, 214)(71, 220)(72, 216)(73, 219)(74, 228)(75, 224)(76, 222)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 38, 152 ), ( 38, 152, 38, 152, 38, 152, 38, 152 ) }
Outer automorphisms :: reflexible
Dual of E27.1632
Graph:: simple bipartite
	v = 95 e = 152 f = 5
	degree seq :: [ 2^76, 8^19 ]

E27.1634 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-19 * Y3, (Y1^-1 * Y3^-1)^19 ]
Map::
	R = (1, 77, 2, 78, 6, 82, 13, 89, 21, 97, 29, 105, 37, 113, 45, 121, 53, 129, 61, 137, 69, 145, 66, 142, 58, 134, 50, 126, 42, 118, 34, 110, 26, 102, 18, 94, 10, 86, 3, 79, 7, 83, 14, 90, 22, 98, 30, 106, 38, 114, 46, 122, 54, 130, 62, 138, 70, 146, 75, 151, 73, 149, 65, 141, 57, 133, 49, 125, 41, 117, 33, 109, 25, 101, 17, 93, 9, 85, 16, 92, 24, 100, 32, 108, 40, 116, 48, 124, 56, 132, 64, 140, 72, 148, 76, 152, 74, 150, 68, 144, 60, 136, 52, 128, 44, 120, 36, 112, 28, 104, 20, 96, 12, 88, 5, 81, 8, 84, 15, 91, 23, 99, 31, 107, 39, 115, 47, 123, 55, 131, 63, 139, 71, 147, 67, 143, 59, 135, 51, 127, 43, 119, 35, 111, 27, 103, 19, 95, 11, 87, 4, 80)(153, 229)(154, 230)(155, 231)(156, 232)(157, 233)(158, 234)(159, 235)(160, 236)(161, 237)(162, 238)(163, 239)(164, 240)(165, 241)(166, 242)(167, 243)(168, 244)(169, 245)(170, 246)(171, 247)(172, 248)(173, 249)(174, 250)(175, 251)(176, 252)(177, 253)(178, 254)(179, 255)(180, 256)(181, 257)(182, 258)(183, 259)(184, 260)(185, 261)(186, 262)(187, 263)(188, 264)(189, 265)(190, 266)(191, 267)(192, 268)(193, 269)(194, 270)(195, 271)(196, 272)(197, 273)(198, 274)(199, 275)(200, 276)(201, 277)(202, 278)(203, 279)(204, 280)(205, 281)(206, 282)(207, 283)(208, 284)(209, 285)(210, 286)(211, 287)(212, 288)(213, 289)(214, 290)(215, 291)(216, 292)(217, 293)(218, 294)(219, 295)(220, 296)(221, 297)(222, 298)(223, 299)(224, 300)(225, 301)(226, 302)(227, 303)(228, 304)
	L = (1, 155)(2, 159)(3, 161)(4, 162)(5, 153)(6, 166)(7, 168)(8, 154)(9, 157)(10, 169)(11, 170)(12, 156)(13, 174)(14, 176)(15, 158)(16, 160)(17, 164)(18, 177)(19, 178)(20, 163)(21, 182)(22, 184)(23, 165)(24, 167)(25, 172)(26, 185)(27, 186)(28, 171)(29, 190)(30, 192)(31, 173)(32, 175)(33, 180)(34, 193)(35, 194)(36, 179)(37, 198)(38, 200)(39, 181)(40, 183)(41, 188)(42, 201)(43, 202)(44, 187)(45, 206)(46, 208)(47, 189)(48, 191)(49, 196)(50, 209)(51, 210)(52, 195)(53, 214)(54, 216)(55, 197)(56, 199)(57, 204)(58, 217)(59, 218)(60, 203)(61, 222)(62, 224)(63, 205)(64, 207)(65, 212)(66, 225)(67, 221)(68, 211)(69, 227)(70, 228)(71, 213)(72, 215)(73, 220)(74, 219)(75, 226)(76, 223)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 8, 38 ), ( 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38, 8, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1631
Graph:: bipartite
	v = 77 e = 152 f = 23
	degree seq :: [ 2^76, 152 ]

E27.1635 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^19 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 77, 2, 78, 6, 82, 4, 80)(3, 79, 7, 83, 13, 89, 10, 86)(5, 81, 8, 84, 14, 90, 11, 87)(9, 85, 15, 91, 21, 97, 18, 94)(12, 88, 16, 92, 22, 98, 19, 95)(17, 93, 23, 99, 29, 105, 26, 102)(20, 96, 24, 100, 30, 106, 27, 103)(25, 101, 31, 107, 37, 113, 34, 110)(28, 104, 32, 108, 38, 114, 35, 111)(33, 109, 39, 115, 45, 121, 42, 118)(36, 112, 40, 116, 46, 122, 43, 119)(41, 117, 47, 123, 53, 129, 50, 126)(44, 120, 48, 124, 54, 130, 51, 127)(49, 125, 55, 131, 61, 137, 58, 134)(52, 128, 56, 132, 62, 138, 59, 135)(57, 133, 63, 139, 69, 145, 66, 142)(60, 136, 64, 140, 70, 146, 67, 143)(65, 141, 71, 147, 75, 151, 73, 149)(68, 144, 72, 148, 76, 152, 74, 150)(153, 229, 155, 231, 161, 237, 169, 245, 177, 253, 185, 261, 193, 269, 201, 277, 209, 285, 217, 293, 224, 300, 216, 292, 208, 284, 200, 276, 192, 268, 184, 260, 176, 252, 168, 244, 160, 236, 154, 230, 159, 235, 167, 243, 175, 251, 183, 259, 191, 267, 199, 275, 207, 283, 215, 291, 223, 299, 228, 304, 222, 298, 214, 290, 206, 282, 198, 274, 190, 266, 182, 258, 174, 250, 166, 242, 158, 234, 165, 241, 173, 249, 181, 257, 189, 265, 197, 273, 205, 281, 213, 289, 221, 297, 227, 303, 226, 302, 219, 295, 211, 287, 203, 279, 195, 271, 187, 263, 179, 255, 171, 247, 163, 239, 156, 232, 162, 238, 170, 246, 178, 254, 186, 262, 194, 270, 202, 278, 210, 286, 218, 294, 225, 301, 220, 296, 212, 288, 204, 280, 196, 272, 188, 264, 180, 256, 172, 248, 164, 240, 157, 233)
	L = (1, 156)(2, 153)(3, 162)(4, 158)(5, 163)(6, 154)(7, 155)(8, 157)(9, 170)(10, 165)(11, 166)(12, 171)(13, 159)(14, 160)(15, 161)(16, 164)(17, 178)(18, 173)(19, 174)(20, 179)(21, 167)(22, 168)(23, 169)(24, 172)(25, 186)(26, 181)(27, 182)(28, 187)(29, 175)(30, 176)(31, 177)(32, 180)(33, 194)(34, 189)(35, 190)(36, 195)(37, 183)(38, 184)(39, 185)(40, 188)(41, 202)(42, 197)(43, 198)(44, 203)(45, 191)(46, 192)(47, 193)(48, 196)(49, 210)(50, 205)(51, 206)(52, 211)(53, 199)(54, 200)(55, 201)(56, 204)(57, 218)(58, 213)(59, 214)(60, 219)(61, 207)(62, 208)(63, 209)(64, 212)(65, 225)(66, 221)(67, 222)(68, 226)(69, 215)(70, 216)(71, 217)(72, 220)(73, 227)(74, 228)(75, 223)(76, 224)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38 ), ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.1636
Graph:: bipartite
	v = 20 e = 152 f = 80
	degree seq :: [ 8^19, 152 ]

E27.1636 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 19, 76})
Quotient :: dipole
Aut^+ = C76 (small group id <76, 2>)
Aut   = D152 (small group id <152, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^-4 * Y3^-4, (Y1^-1 * Y3^-1)^4, Y3^-16 * Y1^3, Y1^7 * Y3^-1 * Y1^3 * Y3^-7 * Y1, Y1^19, (Y3 * Y2^-1)^76 ]
Map::
	R = (1, 77, 2, 78, 6, 82, 14, 90, 26, 102, 37, 113, 45, 121, 53, 129, 61, 137, 69, 145, 74, 150, 65, 141, 60, 136, 51, 127, 42, 118, 33, 109, 22, 98, 11, 87, 4, 80)(3, 79, 7, 83, 15, 91, 27, 103, 25, 101, 32, 108, 40, 116, 48, 124, 56, 132, 64, 140, 72, 148, 73, 149, 68, 144, 59, 135, 50, 126, 41, 117, 36, 112, 21, 97, 10, 86)(5, 81, 8, 84, 16, 92, 28, 104, 38, 114, 46, 122, 54, 130, 62, 138, 70, 146, 75, 151, 66, 142, 57, 133, 52, 128, 43, 119, 34, 110, 19, 95, 31, 107, 23, 99, 12, 88)(9, 85, 17, 93, 29, 105, 24, 100, 13, 89, 18, 94, 30, 106, 39, 115, 47, 123, 55, 131, 63, 139, 71, 147, 76, 152, 67, 143, 58, 134, 49, 125, 44, 120, 35, 111, 20, 96)(153, 229)(154, 230)(155, 231)(156, 232)(157, 233)(158, 234)(159, 235)(160, 236)(161, 237)(162, 238)(163, 239)(164, 240)(165, 241)(166, 242)(167, 243)(168, 244)(169, 245)(170, 246)(171, 247)(172, 248)(173, 249)(174, 250)(175, 251)(176, 252)(177, 253)(178, 254)(179, 255)(180, 256)(181, 257)(182, 258)(183, 259)(184, 260)(185, 261)(186, 262)(187, 263)(188, 264)(189, 265)(190, 266)(191, 267)(192, 268)(193, 269)(194, 270)(195, 271)(196, 272)(197, 273)(198, 274)(199, 275)(200, 276)(201, 277)(202, 278)(203, 279)(204, 280)(205, 281)(206, 282)(207, 283)(208, 284)(209, 285)(210, 286)(211, 287)(212, 288)(213, 289)(214, 290)(215, 291)(216, 292)(217, 293)(218, 294)(219, 295)(220, 296)(221, 297)(222, 298)(223, 299)(224, 300)(225, 301)(226, 302)(227, 303)(228, 304)
	L = (1, 155)(2, 159)(3, 161)(4, 162)(5, 153)(6, 167)(7, 169)(8, 154)(9, 171)(10, 172)(11, 173)(12, 156)(13, 157)(14, 179)(15, 181)(16, 158)(17, 183)(18, 160)(19, 185)(20, 186)(21, 187)(22, 188)(23, 163)(24, 164)(25, 165)(26, 177)(27, 176)(28, 166)(29, 175)(30, 168)(31, 174)(32, 170)(33, 193)(34, 194)(35, 195)(36, 196)(37, 184)(38, 178)(39, 180)(40, 182)(41, 201)(42, 202)(43, 203)(44, 204)(45, 192)(46, 189)(47, 190)(48, 191)(49, 209)(50, 210)(51, 211)(52, 212)(53, 200)(54, 197)(55, 198)(56, 199)(57, 217)(58, 218)(59, 219)(60, 220)(61, 208)(62, 205)(63, 206)(64, 207)(65, 225)(66, 226)(67, 227)(68, 228)(69, 216)(70, 213)(71, 214)(72, 215)(73, 223)(74, 224)(75, 221)(76, 222)(77, 229)(78, 230)(79, 231)(80, 232)(81, 233)(82, 234)(83, 235)(84, 236)(85, 237)(86, 238)(87, 239)(88, 240)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 249)(98, 250)(99, 251)(100, 252)(101, 253)(102, 254)(103, 255)(104, 256)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 265)(114, 266)(115, 267)(116, 268)(117, 269)(118, 270)(119, 271)(120, 272)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 281)(130, 282)(131, 283)(132, 284)(133, 285)(134, 286)(135, 287)(136, 288)(137, 289)(138, 290)(139, 291)(140, 292)(141, 293)(142, 294)(143, 295)(144, 296)(145, 297)(146, 298)(147, 299)(148, 300)(149, 301)(150, 302)(151, 303)(152, 304)
	local type(s) :: { ( 8, 152 ), ( 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152, 8, 152 ) }
Outer automorphisms :: reflexible
Dual of E27.1635
Graph:: simple bipartite
	v = 80 e = 152 f = 20
	degree seq :: [ 2^76, 38^4 ]

E27.1637 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 6})
Quotient :: edge^2
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^6, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^3 * Y1^-3, Y3 * Y2^3 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-3, Y2^2 * Y3 * Y2^3 * Y3 * Y2^-2 * Y3 * Y1^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y2 * Y1^-2 * Y3 * Y2^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2^3 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-2 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 79, 4, 82)(2, 80, 6, 84)(3, 81, 8, 86)(5, 83, 12, 90)(7, 85, 15, 93)(9, 87, 17, 95)(10, 88, 13, 91)(11, 89, 20, 98)(14, 92, 21, 99)(16, 94, 26, 104)(18, 96, 30, 108)(19, 97, 31, 109)(22, 100, 32, 110)(23, 101, 37, 115)(24, 102, 38, 116)(25, 103, 33, 111)(27, 105, 42, 120)(28, 106, 43, 121)(29, 107, 44, 122)(34, 112, 50, 128)(35, 113, 51, 129)(36, 114, 52, 130)(39, 117, 56, 134)(40, 118, 57, 135)(41, 119, 58, 136)(45, 123, 61, 139)(46, 124, 62, 140)(47, 125, 66, 144)(48, 126, 67, 145)(49, 127, 68, 146)(53, 131, 71, 149)(54, 132, 72, 150)(55, 133, 73, 151)(59, 137, 69, 147)(60, 138, 74, 152)(63, 141, 65, 143)(64, 142, 75, 153)(70, 148, 78, 156)(76, 154, 77, 155)(157, 158, 161, 167, 163, 159)(160, 165, 174, 185, 175, 166)(162, 169, 179, 192, 180, 170)(164, 172, 183, 197, 184, 173)(168, 177, 190, 205, 191, 178)(171, 181, 195, 211, 196, 182)(176, 188, 203, 221, 204, 189)(186, 199, 216, 232, 219, 201)(187, 202, 220, 229, 209, 193)(194, 210, 230, 214, 225, 206)(198, 213, 231, 234, 224, 215)(200, 217, 222, 207, 226, 218)(208, 227, 212, 223, 233, 228)(235, 237, 241, 245, 239, 236)(238, 244, 253, 263, 252, 243)(240, 248, 258, 270, 257, 247)(242, 251, 262, 275, 261, 250)(246, 256, 269, 283, 268, 255)(249, 260, 274, 289, 273, 259)(254, 267, 282, 299, 281, 266)(264, 279, 297, 310, 294, 277)(265, 271, 287, 307, 298, 280)(272, 284, 303, 292, 308, 288)(276, 293, 302, 312, 309, 291)(278, 296, 304, 285, 300, 295)(286, 306, 311, 301, 290, 305)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^4 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1640
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 4^39, 6^26 ]

E27.1638 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 6})
Quotient :: edge^2
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y1^-1 * Y2^-1, Y2^2 * Y1^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^4 * Y1^-2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^6, Y3 * Y1^3 * Y3 * Y1 * Y2^-2 * Y3 * Y1^-2 * Y3 * Y1 * Y2^-1, Y2 * Y3 * Y2^2 * Y3 * Y1^2 * Y3 * Y1^3 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 79, 4, 82)(2, 80, 6, 84)(3, 81, 8, 86)(5, 83, 12, 90)(7, 85, 15, 93)(9, 87, 17, 95)(10, 88, 13, 91)(11, 89, 20, 98)(14, 92, 21, 99)(16, 94, 26, 104)(18, 96, 30, 108)(19, 97, 31, 109)(22, 100, 32, 110)(23, 101, 37, 115)(24, 102, 38, 116)(25, 103, 33, 111)(27, 105, 42, 120)(28, 106, 43, 121)(29, 107, 44, 122)(34, 112, 50, 128)(35, 113, 51, 129)(36, 114, 52, 130)(39, 117, 56, 134)(40, 118, 57, 135)(41, 119, 58, 136)(45, 123, 61, 139)(46, 124, 62, 140)(47, 125, 66, 144)(48, 126, 67, 145)(49, 127, 68, 146)(53, 131, 71, 149)(54, 132, 72, 150)(55, 133, 74, 152)(59, 137, 76, 154)(60, 138, 70, 148)(63, 141, 69, 147)(64, 142, 65, 143)(73, 151, 77, 155)(75, 153, 78, 156)(157, 158, 161, 167, 163, 159)(160, 165, 174, 185, 175, 166)(162, 169, 179, 192, 180, 170)(164, 172, 183, 197, 184, 173)(168, 177, 190, 205, 191, 178)(171, 181, 195, 211, 196, 182)(176, 188, 203, 221, 204, 189)(186, 199, 216, 224, 219, 201)(187, 202, 220, 229, 209, 193)(194, 210, 230, 234, 225, 206)(198, 213, 228, 208, 227, 215)(200, 217, 231, 212, 223, 218)(207, 226, 214, 232, 233, 222)(235, 237, 241, 245, 239, 236)(238, 244, 253, 263, 252, 243)(240, 248, 258, 270, 257, 247)(242, 251, 262, 275, 261, 250)(246, 256, 269, 283, 268, 255)(249, 260, 274, 289, 273, 259)(254, 267, 282, 299, 281, 266)(264, 279, 297, 302, 294, 277)(265, 271, 287, 307, 298, 280)(272, 284, 303, 312, 308, 288)(276, 293, 305, 286, 306, 291)(278, 296, 301, 290, 309, 295)(285, 300, 311, 310, 292, 304)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^4 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1639
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 4^39, 6^26 ]

E27.1639 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 6})
Quotient :: loop^2
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, Y1^6, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^3 * Y1^-3, Y3 * Y2^3 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-3, Y2^2 * Y3 * Y2^3 * Y3 * Y2^-2 * Y3 * Y1^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y2 * Y1^-2 * Y3 * Y2^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2^3 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-2 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 79, 157, 235, 4, 82, 160, 238)(2, 80, 158, 236, 6, 84, 162, 240)(3, 81, 159, 237, 8, 86, 164, 242)(5, 83, 161, 239, 12, 90, 168, 246)(7, 85, 163, 241, 15, 93, 171, 249)(9, 87, 165, 243, 17, 95, 173, 251)(10, 88, 166, 244, 13, 91, 169, 247)(11, 89, 167, 245, 20, 98, 176, 254)(14, 92, 170, 248, 21, 99, 177, 255)(16, 94, 172, 250, 26, 104, 182, 260)(18, 96, 174, 252, 30, 108, 186, 264)(19, 97, 175, 253, 31, 109, 187, 265)(22, 100, 178, 256, 32, 110, 188, 266)(23, 101, 179, 257, 37, 115, 193, 271)(24, 102, 180, 258, 38, 116, 194, 272)(25, 103, 181, 259, 33, 111, 189, 267)(27, 105, 183, 261, 42, 120, 198, 276)(28, 106, 184, 262, 43, 121, 199, 277)(29, 107, 185, 263, 44, 122, 200, 278)(34, 112, 190, 268, 50, 128, 206, 284)(35, 113, 191, 269, 51, 129, 207, 285)(36, 114, 192, 270, 52, 130, 208, 286)(39, 117, 195, 273, 56, 134, 212, 290)(40, 118, 196, 274, 57, 135, 213, 291)(41, 119, 197, 275, 58, 136, 214, 292)(45, 123, 201, 279, 61, 139, 217, 295)(46, 124, 202, 280, 62, 140, 218, 296)(47, 125, 203, 281, 66, 144, 222, 300)(48, 126, 204, 282, 67, 145, 223, 301)(49, 127, 205, 283, 68, 146, 224, 302)(53, 131, 209, 287, 71, 149, 227, 305)(54, 132, 210, 288, 72, 150, 228, 306)(55, 133, 211, 289, 73, 151, 229, 307)(59, 137, 215, 293, 69, 147, 225, 303)(60, 138, 216, 294, 74, 152, 230, 308)(63, 141, 219, 297, 65, 143, 221, 299)(64, 142, 220, 298, 75, 153, 231, 309)(70, 148, 226, 304, 78, 156, 234, 312)(76, 154, 232, 310, 77, 155, 233, 311)
	L = (1, 80)(2, 83)(3, 79)(4, 87)(5, 89)(6, 91)(7, 81)(8, 94)(9, 96)(10, 82)(11, 85)(12, 99)(13, 101)(14, 84)(15, 103)(16, 105)(17, 86)(18, 107)(19, 88)(20, 110)(21, 112)(22, 90)(23, 114)(24, 92)(25, 117)(26, 93)(27, 119)(28, 95)(29, 97)(30, 121)(31, 124)(32, 125)(33, 98)(34, 127)(35, 100)(36, 102)(37, 109)(38, 132)(39, 133)(40, 104)(41, 106)(42, 135)(43, 138)(44, 139)(45, 108)(46, 142)(47, 143)(48, 111)(49, 113)(50, 116)(51, 148)(52, 149)(53, 115)(54, 152)(55, 118)(56, 145)(57, 153)(58, 147)(59, 120)(60, 154)(61, 144)(62, 122)(63, 123)(64, 151)(65, 126)(66, 129)(67, 155)(68, 137)(69, 128)(70, 140)(71, 134)(72, 130)(73, 131)(74, 136)(75, 156)(76, 141)(77, 150)(78, 146)(157, 237)(158, 235)(159, 241)(160, 244)(161, 236)(162, 248)(163, 245)(164, 251)(165, 238)(166, 253)(167, 239)(168, 256)(169, 240)(170, 258)(171, 260)(172, 242)(173, 262)(174, 243)(175, 263)(176, 267)(177, 246)(178, 269)(179, 247)(180, 270)(181, 249)(182, 274)(183, 250)(184, 275)(185, 252)(186, 279)(187, 271)(188, 254)(189, 282)(190, 255)(191, 283)(192, 257)(193, 287)(194, 284)(195, 259)(196, 289)(197, 261)(198, 293)(199, 264)(200, 296)(201, 297)(202, 265)(203, 266)(204, 299)(205, 268)(206, 303)(207, 300)(208, 306)(209, 307)(210, 272)(211, 273)(212, 305)(213, 276)(214, 308)(215, 302)(216, 277)(217, 278)(218, 304)(219, 310)(220, 280)(221, 281)(222, 295)(223, 290)(224, 312)(225, 292)(226, 285)(227, 286)(228, 311)(229, 298)(230, 288)(231, 291)(232, 294)(233, 301)(234, 309)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1638
Transitivity :: VT+
Graph::
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.1640 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 6})
Quotient :: loop^2
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y1^-1 * Y2^-1, Y2^2 * Y1^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^4 * Y1^-2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^6, Y3 * Y1^3 * Y3 * Y1 * Y2^-2 * Y3 * Y1^-2 * Y3 * Y1 * Y2^-1, Y2 * Y3 * Y2^2 * Y3 * Y1^2 * Y3 * Y1^3 * Y3 * Y1^-2 ]
Map:: non-degenerate
	R = (1, 79, 157, 235, 4, 82, 160, 238)(2, 80, 158, 236, 6, 84, 162, 240)(3, 81, 159, 237, 8, 86, 164, 242)(5, 83, 161, 239, 12, 90, 168, 246)(7, 85, 163, 241, 15, 93, 171, 249)(9, 87, 165, 243, 17, 95, 173, 251)(10, 88, 166, 244, 13, 91, 169, 247)(11, 89, 167, 245, 20, 98, 176, 254)(14, 92, 170, 248, 21, 99, 177, 255)(16, 94, 172, 250, 26, 104, 182, 260)(18, 96, 174, 252, 30, 108, 186, 264)(19, 97, 175, 253, 31, 109, 187, 265)(22, 100, 178, 256, 32, 110, 188, 266)(23, 101, 179, 257, 37, 115, 193, 271)(24, 102, 180, 258, 38, 116, 194, 272)(25, 103, 181, 259, 33, 111, 189, 267)(27, 105, 183, 261, 42, 120, 198, 276)(28, 106, 184, 262, 43, 121, 199, 277)(29, 107, 185, 263, 44, 122, 200, 278)(34, 112, 190, 268, 50, 128, 206, 284)(35, 113, 191, 269, 51, 129, 207, 285)(36, 114, 192, 270, 52, 130, 208, 286)(39, 117, 195, 273, 56, 134, 212, 290)(40, 118, 196, 274, 57, 135, 213, 291)(41, 119, 197, 275, 58, 136, 214, 292)(45, 123, 201, 279, 61, 139, 217, 295)(46, 124, 202, 280, 62, 140, 218, 296)(47, 125, 203, 281, 66, 144, 222, 300)(48, 126, 204, 282, 67, 145, 223, 301)(49, 127, 205, 283, 68, 146, 224, 302)(53, 131, 209, 287, 71, 149, 227, 305)(54, 132, 210, 288, 72, 150, 228, 306)(55, 133, 211, 289, 74, 152, 230, 308)(59, 137, 215, 293, 76, 154, 232, 310)(60, 138, 216, 294, 70, 148, 226, 304)(63, 141, 219, 297, 69, 147, 225, 303)(64, 142, 220, 298, 65, 143, 221, 299)(73, 151, 229, 307, 77, 155, 233, 311)(75, 153, 231, 309, 78, 156, 234, 312)
	L = (1, 80)(2, 83)(3, 79)(4, 87)(5, 89)(6, 91)(7, 81)(8, 94)(9, 96)(10, 82)(11, 85)(12, 99)(13, 101)(14, 84)(15, 103)(16, 105)(17, 86)(18, 107)(19, 88)(20, 110)(21, 112)(22, 90)(23, 114)(24, 92)(25, 117)(26, 93)(27, 119)(28, 95)(29, 97)(30, 121)(31, 124)(32, 125)(33, 98)(34, 127)(35, 100)(36, 102)(37, 109)(38, 132)(39, 133)(40, 104)(41, 106)(42, 135)(43, 138)(44, 139)(45, 108)(46, 142)(47, 143)(48, 111)(49, 113)(50, 116)(51, 148)(52, 149)(53, 115)(54, 152)(55, 118)(56, 145)(57, 150)(58, 154)(59, 120)(60, 146)(61, 153)(62, 122)(63, 123)(64, 151)(65, 126)(66, 129)(67, 140)(68, 141)(69, 128)(70, 136)(71, 137)(72, 130)(73, 131)(74, 156)(75, 134)(76, 155)(77, 144)(78, 147)(157, 237)(158, 235)(159, 241)(160, 244)(161, 236)(162, 248)(163, 245)(164, 251)(165, 238)(166, 253)(167, 239)(168, 256)(169, 240)(170, 258)(171, 260)(172, 242)(173, 262)(174, 243)(175, 263)(176, 267)(177, 246)(178, 269)(179, 247)(180, 270)(181, 249)(182, 274)(183, 250)(184, 275)(185, 252)(186, 279)(187, 271)(188, 254)(189, 282)(190, 255)(191, 283)(192, 257)(193, 287)(194, 284)(195, 259)(196, 289)(197, 261)(198, 293)(199, 264)(200, 296)(201, 297)(202, 265)(203, 266)(204, 299)(205, 268)(206, 303)(207, 300)(208, 306)(209, 307)(210, 272)(211, 273)(212, 309)(213, 276)(214, 304)(215, 305)(216, 277)(217, 278)(218, 301)(219, 302)(220, 280)(221, 281)(222, 311)(223, 290)(224, 294)(225, 312)(226, 285)(227, 286)(228, 291)(229, 298)(230, 288)(231, 295)(232, 292)(233, 310)(234, 308)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1637
Transitivity :: VT+
Graph::
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.1641 :: Family: { 5P } :: Oriented family(ies): { E5b }
Signature :: (0; {2, 2, 6, 6})
Quotient :: dipole
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 6
Presentation :: [ Y1^2, Y2^2, R^-1 * Y3 * R^-1, Y3^3, Y1 * R * Y2 * R^-1, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1, (R^-1 * Y2 * Y1 * Y3^-1)^2, Y1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, R * Y2 * Y1 * Y2 * R * Y2 * Y1 * Y3^-1 * Y2, Y1 * Y2 * Y3 * Y1 * R^-1 * Y1 * Y2 * Y1 * R^-1 ]
Map:: polytopal non-degenerate
	R = (1, 79, 2, 80)(3, 81, 9, 87)(4, 82, 12, 90)(5, 83, 14, 92)(6, 84, 16, 94)(7, 85, 19, 97)(8, 86, 21, 99)(10, 88, 26, 104)(11, 89, 28, 106)(13, 91, 33, 111)(15, 93, 39, 117)(17, 95, 45, 123)(18, 96, 47, 125)(20, 98, 50, 128)(22, 100, 54, 132)(23, 101, 57, 135)(24, 102, 41, 119)(25, 103, 59, 137)(27, 105, 38, 116)(29, 107, 66, 144)(30, 108, 67, 145)(31, 109, 70, 148)(32, 110, 63, 141)(34, 112, 64, 142)(35, 113, 71, 149)(36, 114, 58, 136)(37, 115, 55, 133)(40, 118, 52, 130)(42, 120, 74, 152)(43, 121, 56, 134)(44, 122, 62, 140)(46, 124, 53, 131)(48, 126, 72, 150)(49, 127, 75, 153)(51, 129, 78, 156)(60, 138, 68, 146)(61, 139, 73, 151)(65, 143, 77, 155)(69, 147, 76, 154)(157, 235, 159, 237)(158, 236, 162, 240)(160, 238, 169, 247)(161, 239, 171, 249)(163, 241, 176, 254)(164, 242, 178, 256)(165, 243, 179, 257)(166, 244, 183, 261)(167, 245, 185, 263)(168, 246, 186, 264)(170, 248, 192, 270)(172, 250, 198, 276)(173, 251, 202, 280)(174, 252, 187, 265)(175, 253, 204, 282)(177, 255, 190, 268)(180, 258, 206, 284)(181, 259, 216, 294)(182, 260, 217, 295)(184, 262, 203, 281)(188, 266, 205, 283)(189, 267, 199, 277)(191, 269, 213, 291)(193, 271, 225, 303)(194, 272, 228, 306)(195, 273, 222, 300)(196, 274, 219, 297)(197, 275, 212, 290)(200, 278, 224, 302)(201, 279, 229, 307)(207, 285, 230, 308)(208, 286, 233, 311)(209, 287, 223, 301)(210, 288, 226, 304)(211, 289, 231, 309)(214, 292, 218, 296)(215, 293, 220, 298)(221, 299, 234, 312)(227, 305, 232, 310)
	L = (1, 160)(2, 163)(3, 166)(4, 161)(5, 157)(6, 173)(7, 164)(8, 158)(9, 180)(10, 167)(11, 159)(12, 187)(13, 190)(14, 193)(15, 196)(16, 199)(17, 174)(18, 162)(19, 185)(20, 192)(21, 208)(22, 211)(23, 202)(24, 181)(25, 165)(26, 218)(27, 220)(28, 221)(29, 205)(30, 224)(31, 188)(32, 168)(33, 184)(34, 191)(35, 169)(36, 207)(37, 194)(38, 170)(39, 227)(40, 197)(41, 171)(42, 183)(43, 200)(44, 172)(45, 215)(46, 214)(47, 232)(48, 216)(49, 175)(50, 203)(51, 176)(52, 209)(53, 177)(54, 234)(55, 212)(56, 178)(57, 228)(58, 179)(59, 231)(60, 233)(61, 210)(62, 219)(63, 182)(64, 198)(65, 189)(66, 230)(67, 222)(68, 225)(69, 186)(70, 213)(71, 229)(72, 226)(73, 195)(74, 223)(75, 201)(76, 206)(77, 204)(78, 217)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1642
Transitivity :: VT
Graph:: simple bipartite
	v = 78 e = 156 f = 26
	degree seq :: [ 4^78 ]

E27.1642 :: Family: { 5P } :: Oriented family(ies): { E5b }
Signature :: (0; {2, 2, 6, 6})
Quotient :: dipole
Aut^+ = (C13 : C3) : C2 (small group id <78, 1>)
Aut   = C2 x ((C13 : C3) : C2) (small group id <156, 8>)
|r| :: 6
Presentation :: [ Y3^3, Y3^3, R * Y3^-1 * R, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y2 * R^-1 * Y1 * R, R * Y1 * R^-1 * Y3^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-2, Y3 * Y1^-1 * Y2^2 * Y1, Y2^6, Y1^6, Y3^-1 * Y2^2 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y3^-1 * Y1^2 * Y3^-1, Y1 * Y2^2 * Y3 * Y2 * Y1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 79, 2, 80, 8, 86, 32, 110, 23, 101, 5, 83)(3, 81, 13, 91, 47, 125, 57, 135, 33, 111, 16, 94)(4, 82, 18, 96, 56, 134, 48, 126, 44, 122, 20, 98)(6, 84, 25, 103, 17, 95, 55, 133, 31, 109, 27, 105)(7, 85, 30, 108, 54, 132, 72, 150, 28, 106, 10, 88)(9, 87, 35, 113, 69, 147, 26, 104, 68, 146, 38, 116)(11, 89, 40, 118, 21, 99, 62, 140, 46, 124, 42, 120)(12, 90, 45, 123, 75, 153, 70, 148, 43, 121, 14, 92)(15, 93, 51, 129, 61, 139, 41, 119, 64, 142, 53, 131)(19, 97, 59, 137, 77, 155, 73, 151, 36, 114, 34, 112)(22, 100, 63, 141, 50, 128, 49, 127, 29, 107, 60, 138)(24, 102, 65, 143, 37, 115, 74, 152, 58, 136, 66, 144)(39, 117, 76, 154, 67, 145, 78, 156, 52, 130, 71, 149)(157, 235, 159, 237, 170, 248, 206, 284, 184, 262, 162, 240)(158, 236, 165, 243, 192, 270, 212, 290, 199, 277, 167, 245)(160, 238, 175, 253, 216, 294, 220, 298, 179, 257, 173, 251)(161, 239, 177, 255, 166, 244, 195, 273, 176, 254, 180, 258)(163, 241, 182, 260, 207, 285, 231, 309, 200, 278, 187, 265)(164, 242, 171, 249, 208, 286, 186, 264, 229, 307, 189, 267)(168, 246, 197, 275, 230, 308, 215, 293, 228, 306, 202, 280)(169, 247, 204, 282, 223, 301, 217, 295, 219, 297, 198, 276)(172, 250, 196, 274, 181, 259, 221, 299, 209, 287, 194, 272)(174, 252, 213, 291, 191, 269, 210, 288, 185, 263, 214, 292)(178, 256, 201, 279, 234, 312, 224, 302, 188, 266, 193, 271)(183, 261, 218, 296, 205, 283, 233, 311, 225, 303, 227, 305)(190, 268, 222, 300, 211, 289, 232, 310, 226, 304, 203, 281)
	L = (1, 160)(2, 166)(3, 171)(4, 163)(5, 178)(6, 182)(7, 157)(8, 170)(9, 193)(10, 168)(11, 197)(12, 158)(13, 181)(14, 190)(15, 173)(16, 210)(17, 159)(18, 161)(19, 199)(20, 217)(21, 165)(22, 174)(23, 208)(24, 213)(25, 205)(26, 185)(27, 226)(28, 214)(29, 162)(30, 176)(31, 175)(32, 192)(33, 222)(34, 164)(35, 196)(36, 227)(37, 177)(38, 231)(39, 229)(40, 204)(41, 200)(42, 233)(43, 187)(44, 167)(45, 184)(46, 195)(47, 206)(48, 191)(49, 169)(50, 234)(51, 172)(52, 219)(53, 215)(54, 207)(55, 209)(56, 216)(57, 223)(58, 201)(59, 211)(60, 225)(61, 186)(62, 221)(63, 179)(64, 198)(65, 232)(66, 228)(67, 180)(68, 183)(69, 212)(70, 224)(71, 188)(72, 189)(73, 202)(74, 194)(75, 230)(76, 218)(77, 220)(78, 203)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1641
Transitivity :: VT
Graph:: bipartite
	v = 26 e = 156 f = 78
	degree seq :: [ 12^26 ]

E27.1643 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 6, 6})
Quotient :: halfedge^2
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = S3 x D26 (small group id <156, 11>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 ]
Map::
	R = (1, 80, 2, 83, 5, 89, 11, 88, 10, 82, 4, 79)(3, 85, 7, 90, 12, 98, 20, 95, 17, 86, 8, 81)(6, 91, 13, 97, 19, 96, 18, 87, 9, 92, 14, 84)(15, 101, 23, 105, 27, 103, 25, 94, 16, 102, 24, 93)(21, 106, 28, 104, 26, 108, 30, 100, 22, 107, 29, 99)(31, 115, 37, 111, 33, 117, 39, 110, 32, 116, 38, 109)(34, 118, 40, 114, 36, 120, 42, 113, 35, 119, 41, 112)(43, 127, 49, 123, 45, 129, 51, 122, 44, 128, 50, 121)(46, 130, 52, 126, 48, 132, 54, 125, 47, 131, 53, 124)(55, 139, 61, 135, 57, 141, 63, 134, 56, 140, 62, 133)(58, 142, 64, 138, 60, 144, 66, 137, 59, 143, 65, 136)(67, 151, 73, 147, 69, 153, 75, 146, 68, 152, 74, 145)(70, 154, 76, 150, 72, 156, 78, 149, 71, 155, 77, 148)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 67)(62, 68)(63, 69)(64, 70)(65, 71)(66, 72)(73, 78)(74, 76)(75, 77)(79, 81)(80, 84)(82, 87)(83, 90)(85, 93)(86, 94)(88, 95)(89, 97)(91, 99)(92, 100)(96, 104)(98, 105)(101, 109)(102, 110)(103, 111)(106, 112)(107, 113)(108, 114)(115, 121)(116, 122)(117, 123)(118, 124)(119, 125)(120, 126)(127, 133)(128, 134)(129, 135)(130, 136)(131, 137)(132, 138)(139, 145)(140, 146)(141, 147)(142, 148)(143, 149)(144, 150)(151, 156)(152, 154)(153, 155)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph::
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.1644 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 6})
Quotient :: edge^2
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = S3 x D26 (small group id <156, 11>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ]
Map::
	R = (1, 79, 3, 81, 8, 86, 17, 95, 10, 88, 4, 82)(2, 80, 5, 83, 12, 90, 21, 99, 14, 92, 6, 84)(7, 85, 15, 93, 24, 102, 18, 96, 9, 87, 16, 94)(11, 89, 19, 97, 28, 106, 22, 100, 13, 91, 20, 98)(23, 101, 31, 109, 26, 104, 33, 111, 25, 103, 32, 110)(27, 105, 34, 112, 30, 108, 36, 114, 29, 107, 35, 113)(37, 115, 43, 121, 39, 117, 45, 123, 38, 116, 44, 122)(40, 118, 46, 124, 42, 120, 48, 126, 41, 119, 47, 125)(49, 127, 55, 133, 51, 129, 57, 135, 50, 128, 56, 134)(52, 130, 58, 136, 54, 132, 60, 138, 53, 131, 59, 137)(61, 139, 67, 145, 63, 141, 69, 147, 62, 140, 68, 146)(64, 142, 70, 148, 66, 144, 72, 150, 65, 143, 71, 149)(73, 151, 77, 155, 75, 153, 76, 154, 74, 152, 78, 156)(157, 158)(159, 163)(160, 165)(161, 167)(162, 169)(164, 168)(166, 170)(171, 179)(172, 181)(173, 180)(174, 182)(175, 183)(176, 185)(177, 184)(178, 186)(187, 193)(188, 194)(189, 195)(190, 196)(191, 197)(192, 198)(199, 205)(200, 206)(201, 207)(202, 208)(203, 209)(204, 210)(211, 217)(212, 218)(213, 219)(214, 220)(215, 221)(216, 222)(223, 229)(224, 230)(225, 231)(226, 232)(227, 233)(228, 234)(235, 236)(237, 241)(238, 243)(239, 245)(240, 247)(242, 246)(244, 248)(249, 257)(250, 259)(251, 258)(252, 260)(253, 261)(254, 263)(255, 262)(256, 264)(265, 271)(266, 272)(267, 273)(268, 274)(269, 275)(270, 276)(277, 283)(278, 284)(279, 285)(280, 286)(281, 287)(282, 288)(289, 295)(290, 296)(291, 297)(292, 298)(293, 299)(294, 300)(301, 307)(302, 308)(303, 309)(304, 310)(305, 311)(306, 312)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24, 24 ), ( 24^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1646
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 2^78, 12^13 ]

E27.1645 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 6, 6})
Quotient :: edge^2
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = C6 x D26 (small group id <156, 15>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^-2 * Y2 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y2^6, Y3 * Y2^2 * Y3 * Y2^-2, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 79, 4, 82)(2, 80, 6, 84)(3, 81, 8, 86)(5, 83, 12, 90)(7, 85, 15, 93)(9, 87, 17, 95)(10, 88, 18, 96)(11, 89, 19, 97)(13, 91, 21, 99)(14, 92, 22, 100)(16, 94, 23, 101)(20, 98, 27, 105)(24, 102, 31, 109)(25, 103, 32, 110)(26, 104, 33, 111)(28, 106, 34, 112)(29, 107, 35, 113)(30, 108, 36, 114)(37, 115, 43, 121)(38, 116, 44, 122)(39, 117, 45, 123)(40, 118, 46, 124)(41, 119, 47, 125)(42, 120, 48, 126)(49, 127, 55, 133)(50, 128, 56, 134)(51, 129, 57, 135)(52, 130, 58, 136)(53, 131, 59, 137)(54, 132, 60, 138)(61, 139, 67, 145)(62, 140, 68, 146)(63, 141, 69, 147)(64, 142, 70, 148)(65, 143, 71, 149)(66, 144, 72, 150)(73, 151, 78, 156)(74, 152, 76, 154)(75, 153, 77, 155)(157, 158, 161, 167, 163, 159)(160, 165, 168, 176, 171, 166)(162, 169, 175, 172, 164, 170)(173, 180, 183, 182, 174, 181)(177, 184, 179, 186, 178, 185)(187, 193, 189, 195, 188, 194)(190, 196, 192, 198, 191, 197)(199, 205, 201, 207, 200, 206)(202, 208, 204, 210, 203, 209)(211, 217, 213, 219, 212, 218)(214, 220, 216, 222, 215, 221)(223, 229, 225, 231, 224, 230)(226, 232, 228, 234, 227, 233)(235, 237, 241, 245, 239, 236)(238, 244, 249, 254, 246, 243)(240, 248, 242, 250, 253, 247)(251, 259, 252, 260, 261, 258)(255, 263, 256, 264, 257, 262)(265, 272, 266, 273, 267, 271)(268, 275, 269, 276, 270, 274)(277, 284, 278, 285, 279, 283)(280, 287, 281, 288, 282, 286)(289, 296, 290, 297, 291, 295)(292, 299, 293, 300, 294, 298)(301, 308, 302, 309, 303, 307)(304, 311, 305, 312, 306, 310)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^4 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1647
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 4^39, 6^26 ]

E27.1646 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 6})
Quotient :: loop^2
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = S3 x D26 (small group id <156, 11>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ]
Map::
	R = (1, 79, 157, 235, 3, 81, 159, 237, 8, 86, 164, 242, 17, 95, 173, 251, 10, 88, 166, 244, 4, 82, 160, 238)(2, 80, 158, 236, 5, 83, 161, 239, 12, 90, 168, 246, 21, 99, 177, 255, 14, 92, 170, 248, 6, 84, 162, 240)(7, 85, 163, 241, 15, 93, 171, 249, 24, 102, 180, 258, 18, 96, 174, 252, 9, 87, 165, 243, 16, 94, 172, 250)(11, 89, 167, 245, 19, 97, 175, 253, 28, 106, 184, 262, 22, 100, 178, 256, 13, 91, 169, 247, 20, 98, 176, 254)(23, 101, 179, 257, 31, 109, 187, 265, 26, 104, 182, 260, 33, 111, 189, 267, 25, 103, 181, 259, 32, 110, 188, 266)(27, 105, 183, 261, 34, 112, 190, 268, 30, 108, 186, 264, 36, 114, 192, 270, 29, 107, 185, 263, 35, 113, 191, 269)(37, 115, 193, 271, 43, 121, 199, 277, 39, 117, 195, 273, 45, 123, 201, 279, 38, 116, 194, 272, 44, 122, 200, 278)(40, 118, 196, 274, 46, 124, 202, 280, 42, 120, 198, 276, 48, 126, 204, 282, 41, 119, 197, 275, 47, 125, 203, 281)(49, 127, 205, 283, 55, 133, 211, 289, 51, 129, 207, 285, 57, 135, 213, 291, 50, 128, 206, 284, 56, 134, 212, 290)(52, 130, 208, 286, 58, 136, 214, 292, 54, 132, 210, 288, 60, 138, 216, 294, 53, 131, 209, 287, 59, 137, 215, 293)(61, 139, 217, 295, 67, 145, 223, 301, 63, 141, 219, 297, 69, 147, 225, 303, 62, 140, 218, 296, 68, 146, 224, 302)(64, 142, 220, 298, 70, 148, 226, 304, 66, 144, 222, 300, 72, 150, 228, 306, 65, 143, 221, 299, 71, 149, 227, 305)(73, 151, 229, 307, 77, 155, 233, 311, 75, 153, 231, 309, 76, 154, 232, 310, 74, 152, 230, 308, 78, 156, 234, 312)
	L = (1, 80)(2, 79)(3, 85)(4, 87)(5, 89)(6, 91)(7, 81)(8, 90)(9, 82)(10, 92)(11, 83)(12, 86)(13, 84)(14, 88)(15, 101)(16, 103)(17, 102)(18, 104)(19, 105)(20, 107)(21, 106)(22, 108)(23, 93)(24, 95)(25, 94)(26, 96)(27, 97)(28, 99)(29, 98)(30, 100)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 145)(74, 146)(75, 147)(76, 148)(77, 149)(78, 150)(157, 236)(158, 235)(159, 241)(160, 243)(161, 245)(162, 247)(163, 237)(164, 246)(165, 238)(166, 248)(167, 239)(168, 242)(169, 240)(170, 244)(171, 257)(172, 259)(173, 258)(174, 260)(175, 261)(176, 263)(177, 262)(178, 264)(179, 249)(180, 251)(181, 250)(182, 252)(183, 253)(184, 255)(185, 254)(186, 256)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 289)(218, 290)(219, 291)(220, 292)(221, 293)(222, 294)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 301)(230, 302)(231, 303)(232, 304)(233, 305)(234, 306)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1644
Transitivity :: VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.1647 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 6, 6})
Quotient :: loop^2
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = C6 x D26 (small group id <156, 15>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^-2 * Y2 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y2^6, Y3 * Y2^2 * Y3 * Y2^-2, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 79, 157, 235, 4, 82, 160, 238)(2, 80, 158, 236, 6, 84, 162, 240)(3, 81, 159, 237, 8, 86, 164, 242)(5, 83, 161, 239, 12, 90, 168, 246)(7, 85, 163, 241, 15, 93, 171, 249)(9, 87, 165, 243, 17, 95, 173, 251)(10, 88, 166, 244, 18, 96, 174, 252)(11, 89, 167, 245, 19, 97, 175, 253)(13, 91, 169, 247, 21, 99, 177, 255)(14, 92, 170, 248, 22, 100, 178, 256)(16, 94, 172, 250, 23, 101, 179, 257)(20, 98, 176, 254, 27, 105, 183, 261)(24, 102, 180, 258, 31, 109, 187, 265)(25, 103, 181, 259, 32, 110, 188, 266)(26, 104, 182, 260, 33, 111, 189, 267)(28, 106, 184, 262, 34, 112, 190, 268)(29, 107, 185, 263, 35, 113, 191, 269)(30, 108, 186, 264, 36, 114, 192, 270)(37, 115, 193, 271, 43, 121, 199, 277)(38, 116, 194, 272, 44, 122, 200, 278)(39, 117, 195, 273, 45, 123, 201, 279)(40, 118, 196, 274, 46, 124, 202, 280)(41, 119, 197, 275, 47, 125, 203, 281)(42, 120, 198, 276, 48, 126, 204, 282)(49, 127, 205, 283, 55, 133, 211, 289)(50, 128, 206, 284, 56, 134, 212, 290)(51, 129, 207, 285, 57, 135, 213, 291)(52, 130, 208, 286, 58, 136, 214, 292)(53, 131, 209, 287, 59, 137, 215, 293)(54, 132, 210, 288, 60, 138, 216, 294)(61, 139, 217, 295, 67, 145, 223, 301)(62, 140, 218, 296, 68, 146, 224, 302)(63, 141, 219, 297, 69, 147, 225, 303)(64, 142, 220, 298, 70, 148, 226, 304)(65, 143, 221, 299, 71, 149, 227, 305)(66, 144, 222, 300, 72, 150, 228, 306)(73, 151, 229, 307, 78, 156, 234, 312)(74, 152, 230, 308, 76, 154, 232, 310)(75, 153, 231, 309, 77, 155, 233, 311)
	L = (1, 80)(2, 83)(3, 79)(4, 87)(5, 89)(6, 91)(7, 81)(8, 92)(9, 90)(10, 82)(11, 85)(12, 98)(13, 97)(14, 84)(15, 88)(16, 86)(17, 102)(18, 103)(19, 94)(20, 93)(21, 106)(22, 107)(23, 108)(24, 105)(25, 95)(26, 96)(27, 104)(28, 101)(29, 99)(30, 100)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 111)(38, 109)(39, 110)(40, 114)(41, 112)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 123)(50, 121)(51, 122)(52, 126)(53, 124)(54, 125)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 135)(62, 133)(63, 134)(64, 138)(65, 136)(66, 137)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 147)(74, 145)(75, 146)(76, 150)(77, 148)(78, 149)(157, 237)(158, 235)(159, 241)(160, 244)(161, 236)(162, 248)(163, 245)(164, 250)(165, 238)(166, 249)(167, 239)(168, 243)(169, 240)(170, 242)(171, 254)(172, 253)(173, 259)(174, 260)(175, 247)(176, 246)(177, 263)(178, 264)(179, 262)(180, 251)(181, 252)(182, 261)(183, 258)(184, 255)(185, 256)(186, 257)(187, 272)(188, 273)(189, 271)(190, 275)(191, 276)(192, 274)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 284)(200, 285)(201, 283)(202, 287)(203, 288)(204, 286)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 296)(212, 297)(213, 295)(214, 299)(215, 300)(216, 298)(217, 289)(218, 290)(219, 291)(220, 292)(221, 293)(222, 294)(223, 308)(224, 309)(225, 307)(226, 311)(227, 312)(228, 310)(229, 301)(230, 302)(231, 303)(232, 304)(233, 305)(234, 306)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1645
Transitivity :: VT+
Graph::
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.1648 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 6})
Quotient :: dipole
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = S3 x D26 (small group id <156, 11>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2^6, (Y3 * Y2^-1)^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 ]
Map::
	R = (1, 79, 2, 80)(3, 81, 7, 85)(4, 82, 9, 87)(5, 83, 11, 89)(6, 84, 13, 91)(8, 86, 12, 90)(10, 88, 14, 92)(15, 93, 23, 101)(16, 94, 25, 103)(17, 95, 24, 102)(18, 96, 26, 104)(19, 97, 27, 105)(20, 98, 29, 107)(21, 99, 28, 106)(22, 100, 30, 108)(31, 109, 37, 115)(32, 110, 38, 116)(33, 111, 39, 117)(34, 112, 40, 118)(35, 113, 41, 119)(36, 114, 42, 120)(43, 121, 49, 127)(44, 122, 50, 128)(45, 123, 51, 129)(46, 124, 52, 130)(47, 125, 53, 131)(48, 126, 54, 132)(55, 133, 61, 139)(56, 134, 62, 140)(57, 135, 63, 141)(58, 136, 64, 142)(59, 137, 65, 143)(60, 138, 66, 144)(67, 145, 73, 151)(68, 146, 74, 152)(69, 147, 75, 153)(70, 148, 76, 154)(71, 149, 77, 155)(72, 150, 78, 156)(157, 235, 159, 237, 164, 242, 173, 251, 166, 244, 160, 238)(158, 236, 161, 239, 168, 246, 177, 255, 170, 248, 162, 240)(163, 241, 171, 249, 180, 258, 174, 252, 165, 243, 172, 250)(167, 245, 175, 253, 184, 262, 178, 256, 169, 247, 176, 254)(179, 257, 187, 265, 182, 260, 189, 267, 181, 259, 188, 266)(183, 261, 190, 268, 186, 264, 192, 270, 185, 263, 191, 269)(193, 271, 199, 277, 195, 273, 201, 279, 194, 272, 200, 278)(196, 274, 202, 280, 198, 276, 204, 282, 197, 275, 203, 281)(205, 283, 211, 289, 207, 285, 213, 291, 206, 284, 212, 290)(208, 286, 214, 292, 210, 288, 216, 294, 209, 287, 215, 293)(217, 295, 223, 301, 219, 297, 225, 303, 218, 296, 224, 302)(220, 298, 226, 304, 222, 300, 228, 306, 221, 299, 227, 305)(229, 307, 233, 311, 231, 309, 232, 310, 230, 308, 234, 312)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 4^39, 12^13 ]

E27.1649 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 6, 6})
Quotient :: dipole
Aut^+ = C3 x D26 (small group id <78, 4>)
Aut   = S3 x D26 (small group id <156, 11>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^13, Y3^6 * Y1 * Y2 * Y3^5 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 79, 2, 80)(3, 81, 11, 89)(4, 82, 10, 88)(5, 83, 17, 95)(6, 84, 8, 86)(7, 85, 21, 99)(9, 87, 24, 102)(12, 90, 16, 94)(13, 91, 27, 105)(14, 92, 19, 97)(15, 93, 26, 104)(18, 96, 30, 108)(20, 98, 23, 101)(22, 100, 33, 111)(25, 103, 36, 114)(28, 106, 39, 117)(29, 107, 38, 116)(31, 109, 42, 120)(32, 110, 35, 113)(34, 112, 45, 123)(37, 115, 48, 126)(40, 118, 51, 129)(41, 119, 50, 128)(43, 121, 54, 132)(44, 122, 47, 125)(46, 124, 57, 135)(49, 127, 60, 138)(52, 130, 63, 141)(53, 131, 62, 140)(55, 133, 66, 144)(56, 134, 59, 137)(58, 136, 69, 147)(61, 139, 72, 150)(64, 142, 75, 153)(65, 143, 74, 152)(67, 145, 77, 155)(68, 146, 71, 149)(70, 148, 76, 154)(73, 151, 78, 156)(157, 235, 159, 237, 168, 246, 164, 242, 175, 253, 161, 239)(158, 236, 163, 241, 172, 250, 160, 238, 170, 248, 165, 243)(162, 240, 169, 247, 173, 251, 179, 257, 167, 245, 174, 252)(166, 244, 178, 256, 180, 258, 171, 249, 177, 255, 181, 259)(176, 254, 184, 262, 186, 264, 191, 269, 183, 261, 187, 265)(182, 260, 190, 268, 192, 270, 185, 263, 189, 267, 193, 271)(188, 266, 196, 274, 198, 276, 203, 281, 195, 273, 199, 277)(194, 272, 202, 280, 204, 282, 197, 275, 201, 279, 205, 283)(200, 278, 208, 286, 210, 288, 215, 293, 207, 285, 211, 289)(206, 284, 214, 292, 216, 294, 209, 287, 213, 291, 217, 295)(212, 290, 220, 298, 222, 300, 227, 305, 219, 297, 223, 301)(218, 296, 226, 304, 228, 306, 221, 299, 225, 303, 229, 307)(224, 302, 232, 310, 233, 311, 230, 308, 231, 309, 234, 312)
	L = (1, 160)(2, 164)(3, 169)(4, 171)(5, 174)(6, 157)(7, 178)(8, 179)(9, 181)(10, 158)(11, 175)(12, 165)(13, 184)(14, 159)(15, 185)(16, 161)(17, 168)(18, 187)(19, 163)(20, 162)(21, 170)(22, 190)(23, 191)(24, 172)(25, 193)(26, 166)(27, 167)(28, 196)(29, 197)(30, 173)(31, 199)(32, 176)(33, 177)(34, 202)(35, 203)(36, 180)(37, 205)(38, 182)(39, 183)(40, 208)(41, 209)(42, 186)(43, 211)(44, 188)(45, 189)(46, 214)(47, 215)(48, 192)(49, 217)(50, 194)(51, 195)(52, 220)(53, 221)(54, 198)(55, 223)(56, 200)(57, 201)(58, 226)(59, 227)(60, 204)(61, 229)(62, 206)(63, 207)(64, 232)(65, 224)(66, 210)(67, 234)(68, 212)(69, 213)(70, 231)(71, 230)(72, 216)(73, 233)(74, 218)(75, 219)(76, 225)(77, 222)(78, 228)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 4^39, 12^13 ]

E27.1650 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1 * Y3^-1)^2, (Y3 * Y1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 6, 86)(4, 84, 11, 91)(5, 85, 13, 93)(7, 87, 16, 96)(8, 88, 18, 98)(9, 89, 19, 99)(10, 90, 21, 101)(12, 92, 17, 97)(14, 94, 24, 104)(15, 95, 26, 106)(20, 100, 25, 105)(22, 102, 31, 111)(23, 103, 32, 112)(27, 107, 35, 115)(28, 108, 36, 116)(29, 109, 37, 117)(30, 110, 38, 118)(33, 113, 41, 121)(34, 114, 42, 122)(39, 119, 47, 127)(40, 120, 48, 128)(43, 123, 51, 131)(44, 124, 52, 132)(45, 125, 53, 133)(46, 126, 54, 134)(49, 129, 57, 137)(50, 130, 58, 138)(55, 135, 63, 143)(56, 136, 64, 144)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(65, 145, 73, 153)(66, 146, 74, 154)(71, 151, 76, 156)(72, 152, 75, 155)(77, 157, 80, 160)(78, 158, 79, 159)(161, 241, 163, 243)(162, 242, 166, 246)(164, 244, 169, 249)(165, 245, 170, 250)(167, 247, 174, 254)(168, 248, 175, 255)(171, 251, 179, 259)(172, 252, 180, 260)(173, 253, 181, 261)(176, 256, 184, 264)(177, 257, 185, 265)(178, 258, 186, 266)(182, 262, 189, 269)(183, 263, 190, 270)(187, 267, 193, 273)(188, 268, 194, 274)(191, 271, 197, 277)(192, 272, 198, 278)(195, 275, 201, 281)(196, 276, 202, 282)(199, 279, 205, 285)(200, 280, 206, 286)(203, 283, 209, 289)(204, 284, 210, 290)(207, 287, 213, 293)(208, 288, 214, 294)(211, 291, 217, 297)(212, 292, 218, 298)(215, 295, 221, 301)(216, 296, 222, 302)(219, 299, 225, 305)(220, 300, 226, 306)(223, 303, 229, 309)(224, 304, 230, 310)(227, 307, 233, 313)(228, 308, 234, 314)(231, 311, 237, 317)(232, 312, 238, 318)(235, 315, 239, 319)(236, 316, 240, 320)
	L = (1, 164)(2, 167)(3, 169)(4, 172)(5, 161)(6, 174)(7, 177)(8, 162)(9, 180)(10, 163)(11, 182)(12, 165)(13, 183)(14, 185)(15, 166)(16, 187)(17, 168)(18, 188)(19, 189)(20, 170)(21, 190)(22, 173)(23, 171)(24, 193)(25, 175)(26, 194)(27, 178)(28, 176)(29, 181)(30, 179)(31, 199)(32, 200)(33, 186)(34, 184)(35, 203)(36, 204)(37, 205)(38, 206)(39, 192)(40, 191)(41, 209)(42, 210)(43, 196)(44, 195)(45, 198)(46, 197)(47, 215)(48, 216)(49, 202)(50, 201)(51, 219)(52, 220)(53, 221)(54, 222)(55, 208)(56, 207)(57, 225)(58, 226)(59, 212)(60, 211)(61, 214)(62, 213)(63, 231)(64, 232)(65, 218)(66, 217)(67, 235)(68, 236)(69, 237)(70, 238)(71, 224)(72, 223)(73, 239)(74, 240)(75, 228)(76, 227)(77, 230)(78, 229)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1675
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1651 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y1 * Y3 * Y2)^2, (Y3 * Y2)^4, (Y3 * Y1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 5, 85)(4, 84, 8, 88)(6, 86, 11, 91)(7, 87, 13, 93)(9, 89, 15, 95)(10, 90, 18, 98)(12, 92, 20, 100)(14, 94, 23, 103)(16, 96, 27, 107)(17, 97, 22, 102)(19, 99, 28, 108)(21, 101, 32, 112)(24, 104, 34, 114)(25, 105, 30, 110)(26, 106, 35, 115)(29, 109, 38, 118)(31, 111, 39, 119)(33, 113, 41, 121)(36, 116, 44, 124)(37, 117, 45, 125)(40, 120, 48, 128)(42, 122, 50, 130)(43, 123, 51, 131)(46, 126, 54, 134)(47, 127, 55, 135)(49, 129, 57, 137)(52, 132, 60, 140)(53, 133, 61, 141)(56, 136, 64, 144)(58, 138, 66, 146)(59, 139, 67, 147)(62, 142, 70, 150)(63, 143, 71, 151)(65, 145, 73, 153)(68, 148, 72, 152)(69, 149, 76, 156)(74, 154, 77, 157)(75, 155, 78, 158)(79, 159, 80, 160)(161, 241, 163, 243)(162, 242, 165, 245)(164, 244, 169, 249)(166, 246, 172, 252)(167, 247, 174, 254)(168, 248, 175, 255)(170, 250, 179, 259)(171, 251, 180, 260)(173, 253, 183, 263)(176, 256, 184, 264)(177, 257, 185, 265)(178, 258, 188, 268)(181, 261, 189, 269)(182, 262, 190, 270)(186, 266, 193, 273)(187, 267, 194, 274)(191, 271, 197, 277)(192, 272, 198, 278)(195, 275, 201, 281)(196, 276, 203, 283)(199, 279, 205, 285)(200, 280, 207, 287)(202, 282, 209, 289)(204, 284, 211, 291)(206, 286, 213, 293)(208, 288, 215, 295)(210, 290, 217, 297)(212, 292, 218, 298)(214, 294, 221, 301)(216, 296, 222, 302)(219, 299, 225, 305)(220, 300, 226, 306)(223, 303, 229, 309)(224, 304, 230, 310)(227, 307, 233, 313)(228, 308, 235, 315)(231, 311, 236, 316)(232, 312, 238, 318)(234, 314, 239, 319)(237, 317, 240, 320)
	L = (1, 164)(2, 166)(3, 167)(4, 161)(5, 170)(6, 162)(7, 163)(8, 176)(9, 177)(10, 165)(11, 181)(12, 182)(13, 184)(14, 185)(15, 186)(16, 168)(17, 169)(18, 189)(19, 190)(20, 191)(21, 171)(22, 172)(23, 193)(24, 173)(25, 174)(26, 175)(27, 196)(28, 197)(29, 178)(30, 179)(31, 180)(32, 200)(33, 183)(34, 202)(35, 203)(36, 187)(37, 188)(38, 206)(39, 207)(40, 192)(41, 209)(42, 194)(43, 195)(44, 212)(45, 213)(46, 198)(47, 199)(48, 216)(49, 201)(50, 218)(51, 219)(52, 204)(53, 205)(54, 222)(55, 223)(56, 208)(57, 225)(58, 210)(59, 211)(60, 228)(61, 229)(62, 214)(63, 215)(64, 232)(65, 217)(66, 234)(67, 235)(68, 220)(69, 221)(70, 237)(71, 238)(72, 224)(73, 239)(74, 226)(75, 227)(76, 240)(77, 230)(78, 231)(79, 233)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1674
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1652 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2, (Y3 * Y2)^4, (Y3 * Y1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 16, 96)(10, 90, 19, 99)(12, 92, 21, 101)(14, 94, 24, 104)(15, 95, 20, 100)(17, 97, 26, 106)(18, 98, 27, 107)(22, 102, 30, 110)(23, 103, 31, 111)(25, 105, 33, 113)(28, 108, 36, 116)(29, 109, 37, 117)(32, 112, 40, 120)(34, 114, 42, 122)(35, 115, 43, 123)(38, 118, 46, 126)(39, 119, 47, 127)(41, 121, 49, 129)(44, 124, 52, 132)(45, 125, 53, 133)(48, 128, 56, 136)(50, 130, 58, 138)(51, 131, 59, 139)(54, 134, 62, 142)(55, 135, 63, 143)(57, 137, 65, 145)(60, 140, 68, 148)(61, 141, 69, 149)(64, 144, 72, 152)(66, 146, 74, 154)(67, 147, 71, 151)(70, 150, 77, 157)(73, 153, 78, 158)(75, 155, 76, 156)(79, 159, 80, 160)(161, 241, 163, 243)(162, 242, 165, 245)(164, 244, 170, 250)(166, 246, 174, 254)(167, 247, 175, 255)(168, 248, 177, 257)(169, 249, 176, 256)(171, 251, 180, 260)(172, 252, 182, 262)(173, 253, 181, 261)(178, 258, 188, 268)(179, 259, 186, 266)(183, 263, 192, 272)(184, 264, 190, 270)(185, 265, 194, 274)(187, 267, 193, 273)(189, 269, 198, 278)(191, 271, 197, 277)(195, 275, 204, 284)(196, 276, 202, 282)(199, 279, 208, 288)(200, 280, 206, 286)(201, 281, 210, 290)(203, 283, 209, 289)(205, 285, 214, 294)(207, 287, 213, 293)(211, 291, 220, 300)(212, 292, 218, 298)(215, 295, 224, 304)(216, 296, 222, 302)(217, 297, 226, 306)(219, 299, 225, 305)(221, 301, 230, 310)(223, 303, 229, 309)(227, 307, 235, 315)(228, 308, 234, 314)(231, 311, 238, 318)(232, 312, 237, 317)(233, 313, 239, 319)(236, 316, 240, 320)
	L = (1, 164)(2, 166)(3, 168)(4, 161)(5, 172)(6, 162)(7, 174)(8, 163)(9, 178)(10, 171)(11, 170)(12, 165)(13, 183)(14, 167)(15, 182)(16, 185)(17, 180)(18, 169)(19, 188)(20, 177)(21, 189)(22, 175)(23, 173)(24, 192)(25, 176)(26, 194)(27, 195)(28, 179)(29, 181)(30, 198)(31, 199)(32, 184)(33, 201)(34, 186)(35, 187)(36, 204)(37, 205)(38, 190)(39, 191)(40, 208)(41, 193)(42, 210)(43, 211)(44, 196)(45, 197)(46, 214)(47, 215)(48, 200)(49, 217)(50, 202)(51, 203)(52, 220)(53, 221)(54, 206)(55, 207)(56, 224)(57, 209)(58, 226)(59, 227)(60, 212)(61, 213)(62, 230)(63, 231)(64, 216)(65, 233)(66, 218)(67, 219)(68, 235)(69, 236)(70, 222)(71, 223)(72, 238)(73, 225)(74, 239)(75, 228)(76, 229)(77, 240)(78, 232)(79, 234)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1672
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1653 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-1 * Y2 * Y3 * Y2, Y3^4, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, Y2 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 12, 92)(5, 85, 14, 94)(6, 86, 15, 95)(7, 87, 18, 98)(8, 88, 20, 100)(10, 90, 17, 97)(11, 91, 16, 96)(13, 93, 19, 99)(21, 101, 31, 111)(22, 102, 32, 112)(23, 103, 34, 114)(24, 104, 33, 113)(25, 105, 35, 115)(26, 106, 36, 116)(27, 107, 37, 117)(28, 108, 39, 119)(29, 109, 38, 118)(30, 110, 40, 120)(41, 121, 49, 129)(42, 122, 50, 130)(43, 123, 51, 131)(44, 124, 52, 132)(45, 125, 53, 133)(46, 126, 54, 134)(47, 127, 55, 135)(48, 128, 56, 136)(57, 137, 65, 145)(58, 138, 66, 146)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(63, 143, 71, 151)(64, 144, 72, 152)(73, 153, 77, 157)(74, 154, 79, 159)(75, 155, 78, 158)(76, 156, 80, 160)(161, 241, 163, 243)(162, 242, 166, 246)(164, 244, 170, 250)(165, 245, 171, 251)(167, 247, 176, 256)(168, 248, 177, 257)(169, 249, 181, 261)(172, 252, 183, 263)(173, 253, 184, 264)(174, 254, 182, 262)(175, 255, 186, 266)(178, 258, 188, 268)(179, 259, 189, 269)(180, 260, 187, 267)(185, 265, 193, 273)(190, 270, 198, 278)(191, 271, 201, 281)(192, 272, 203, 283)(194, 274, 202, 282)(195, 275, 204, 284)(196, 276, 205, 285)(197, 277, 207, 287)(199, 279, 206, 286)(200, 280, 208, 288)(209, 289, 217, 297)(210, 290, 219, 299)(211, 291, 218, 298)(212, 292, 220, 300)(213, 293, 221, 301)(214, 294, 223, 303)(215, 295, 222, 302)(216, 296, 224, 304)(225, 305, 233, 313)(226, 306, 235, 315)(227, 307, 234, 314)(228, 308, 236, 316)(229, 309, 237, 317)(230, 310, 239, 319)(231, 311, 238, 318)(232, 312, 240, 320)
	L = (1, 164)(2, 167)(3, 170)(4, 173)(5, 161)(6, 176)(7, 179)(8, 162)(9, 182)(10, 184)(11, 163)(12, 181)(13, 165)(14, 185)(15, 187)(16, 189)(17, 166)(18, 186)(19, 168)(20, 190)(21, 174)(22, 193)(23, 169)(24, 171)(25, 172)(26, 180)(27, 198)(28, 175)(29, 177)(30, 178)(31, 202)(32, 201)(33, 183)(34, 204)(35, 203)(36, 206)(37, 205)(38, 188)(39, 208)(40, 207)(41, 194)(42, 195)(43, 191)(44, 192)(45, 199)(46, 200)(47, 196)(48, 197)(49, 218)(50, 217)(51, 220)(52, 219)(53, 222)(54, 221)(55, 224)(56, 223)(57, 211)(58, 212)(59, 209)(60, 210)(61, 215)(62, 216)(63, 213)(64, 214)(65, 234)(66, 233)(67, 236)(68, 235)(69, 238)(70, 237)(71, 240)(72, 239)(73, 227)(74, 228)(75, 225)(76, 226)(77, 231)(78, 232)(79, 229)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1673
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1654 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x D40 (small group id <80, 37>)
Aut   = C2 x C2 x D40 (small group id <160, 215>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^4, Y2^2 * Y3^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 10, 90)(5, 85, 7, 87)(6, 86, 8, 88)(11, 91, 18, 98)(12, 92, 23, 103)(13, 93, 22, 102)(14, 94, 24, 104)(15, 95, 20, 100)(16, 96, 19, 99)(17, 97, 21, 101)(25, 105, 34, 114)(26, 106, 33, 113)(27, 107, 39, 119)(28, 108, 38, 118)(29, 109, 40, 120)(30, 110, 36, 116)(31, 111, 35, 115)(32, 112, 37, 117)(41, 121, 50, 130)(42, 122, 49, 129)(43, 123, 55, 135)(44, 124, 54, 134)(45, 125, 56, 136)(46, 126, 52, 132)(47, 127, 51, 131)(48, 128, 53, 133)(57, 137, 66, 146)(58, 138, 65, 145)(59, 139, 71, 151)(60, 140, 70, 150)(61, 141, 72, 152)(62, 142, 68, 148)(63, 143, 67, 147)(64, 144, 69, 149)(73, 153, 78, 158)(74, 154, 77, 157)(75, 155, 79, 159)(76, 156, 80, 160)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 178, 258, 169, 249)(164, 244, 172, 252, 185, 265, 175, 255)(166, 246, 173, 253, 186, 266, 176, 256)(168, 248, 179, 259, 193, 273, 182, 262)(170, 250, 180, 260, 194, 274, 183, 263)(174, 254, 187, 267, 201, 281, 190, 270)(177, 257, 188, 268, 202, 282, 191, 271)(181, 261, 195, 275, 209, 289, 198, 278)(184, 264, 196, 276, 210, 290, 199, 279)(189, 269, 203, 283, 217, 297, 206, 286)(192, 272, 204, 284, 218, 298, 207, 287)(197, 277, 211, 291, 225, 305, 214, 294)(200, 280, 212, 292, 226, 306, 215, 295)(205, 285, 219, 299, 233, 313, 222, 302)(208, 288, 220, 300, 234, 314, 223, 303)(213, 293, 227, 307, 237, 317, 230, 310)(216, 296, 228, 308, 238, 318, 231, 311)(221, 301, 235, 315, 224, 304, 236, 316)(229, 309, 239, 319, 232, 312, 240, 320)
	L = (1, 164)(2, 168)(3, 172)(4, 174)(5, 175)(6, 161)(7, 179)(8, 181)(9, 182)(10, 162)(11, 185)(12, 187)(13, 163)(14, 189)(15, 190)(16, 165)(17, 166)(18, 193)(19, 195)(20, 167)(21, 197)(22, 198)(23, 169)(24, 170)(25, 201)(26, 171)(27, 203)(28, 173)(29, 205)(30, 206)(31, 176)(32, 177)(33, 209)(34, 178)(35, 211)(36, 180)(37, 213)(38, 214)(39, 183)(40, 184)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 222)(47, 191)(48, 192)(49, 225)(50, 194)(51, 227)(52, 196)(53, 229)(54, 230)(55, 199)(56, 200)(57, 233)(58, 202)(59, 235)(60, 204)(61, 234)(62, 236)(63, 207)(64, 208)(65, 237)(66, 210)(67, 239)(68, 212)(69, 238)(70, 240)(71, 215)(72, 216)(73, 224)(74, 218)(75, 223)(76, 220)(77, 232)(78, 226)(79, 231)(80, 228)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1663
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1655 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, Y2^4, Y3^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 10, 90)(5, 85, 9, 89)(6, 86, 8, 88)(11, 91, 18, 98)(12, 92, 20, 100)(13, 93, 19, 99)(14, 94, 23, 103)(15, 95, 24, 104)(16, 96, 21, 101)(17, 97, 22, 102)(25, 105, 34, 114)(26, 106, 33, 113)(27, 107, 36, 116)(28, 108, 35, 115)(29, 109, 39, 119)(30, 110, 40, 120)(31, 111, 37, 117)(32, 112, 38, 118)(41, 121, 50, 130)(42, 122, 49, 129)(43, 123, 52, 132)(44, 124, 51, 131)(45, 125, 55, 135)(46, 126, 56, 136)(47, 127, 53, 133)(48, 128, 54, 134)(57, 137, 65, 145)(58, 138, 64, 144)(59, 139, 67, 147)(60, 140, 66, 146)(61, 141, 70, 150)(62, 142, 69, 149)(63, 143, 68, 148)(71, 151, 76, 156)(72, 152, 75, 155)(73, 153, 77, 157)(74, 154, 78, 158)(79, 159, 80, 160)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 178, 258, 169, 249)(164, 244, 174, 254, 185, 265, 172, 252)(166, 246, 176, 256, 186, 266, 173, 253)(168, 248, 181, 261, 193, 273, 179, 259)(170, 250, 183, 263, 194, 274, 180, 260)(175, 255, 187, 267, 201, 281, 189, 269)(177, 257, 188, 268, 202, 282, 191, 271)(182, 262, 195, 275, 209, 289, 197, 277)(184, 264, 196, 276, 210, 290, 199, 279)(190, 270, 205, 285, 217, 297, 203, 283)(192, 272, 207, 287, 218, 298, 204, 284)(198, 278, 213, 293, 224, 304, 211, 291)(200, 280, 215, 295, 225, 305, 212, 292)(206, 286, 219, 299, 231, 311, 221, 301)(208, 288, 220, 300, 232, 312, 223, 303)(214, 294, 226, 306, 235, 315, 228, 308)(216, 296, 227, 307, 236, 316, 230, 310)(222, 302, 234, 314, 239, 319, 233, 313)(229, 309, 238, 318, 240, 320, 237, 317)
	L = (1, 164)(2, 168)(3, 172)(4, 175)(5, 174)(6, 161)(7, 179)(8, 182)(9, 181)(10, 162)(11, 185)(12, 187)(13, 163)(14, 189)(15, 190)(16, 165)(17, 166)(18, 193)(19, 195)(20, 167)(21, 197)(22, 198)(23, 169)(24, 170)(25, 201)(26, 171)(27, 203)(28, 173)(29, 205)(30, 206)(31, 176)(32, 177)(33, 209)(34, 178)(35, 211)(36, 180)(37, 213)(38, 214)(39, 183)(40, 184)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 222)(47, 191)(48, 192)(49, 224)(50, 194)(51, 226)(52, 196)(53, 228)(54, 229)(55, 199)(56, 200)(57, 231)(58, 202)(59, 233)(60, 204)(61, 234)(62, 208)(63, 207)(64, 235)(65, 210)(66, 237)(67, 212)(68, 238)(69, 216)(70, 215)(71, 239)(72, 218)(73, 220)(74, 223)(75, 240)(76, 225)(77, 227)(78, 230)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1670
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1656 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y2^4, Y3^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 10, 90)(5, 85, 7, 87)(6, 86, 8, 88)(11, 91, 18, 98)(12, 92, 23, 103)(13, 93, 21, 101)(14, 94, 20, 100)(15, 95, 24, 104)(16, 96, 19, 99)(17, 97, 22, 102)(25, 105, 34, 114)(26, 106, 33, 113)(27, 107, 39, 119)(28, 108, 37, 117)(29, 109, 36, 116)(30, 110, 40, 120)(31, 111, 35, 115)(32, 112, 38, 118)(41, 121, 50, 130)(42, 122, 49, 129)(43, 123, 55, 135)(44, 124, 53, 133)(45, 125, 52, 132)(46, 126, 56, 136)(47, 127, 51, 131)(48, 128, 54, 134)(57, 137, 65, 145)(58, 138, 64, 144)(59, 139, 70, 150)(60, 140, 68, 148)(61, 141, 67, 147)(62, 142, 69, 149)(63, 143, 66, 146)(71, 151, 76, 156)(72, 152, 75, 155)(73, 153, 78, 158)(74, 154, 77, 157)(79, 159, 80, 160)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 178, 258, 169, 249)(164, 244, 174, 254, 185, 265, 172, 252)(166, 246, 176, 256, 186, 266, 173, 253)(168, 248, 181, 261, 193, 273, 179, 259)(170, 250, 183, 263, 194, 274, 180, 260)(175, 255, 187, 267, 201, 281, 189, 269)(177, 257, 188, 268, 202, 282, 191, 271)(182, 262, 195, 275, 209, 289, 197, 277)(184, 264, 196, 276, 210, 290, 199, 279)(190, 270, 205, 285, 217, 297, 203, 283)(192, 272, 207, 287, 218, 298, 204, 284)(198, 278, 213, 293, 224, 304, 211, 291)(200, 280, 215, 295, 225, 305, 212, 292)(206, 286, 219, 299, 231, 311, 221, 301)(208, 288, 220, 300, 232, 312, 223, 303)(214, 294, 226, 306, 235, 315, 228, 308)(216, 296, 227, 307, 236, 316, 230, 310)(222, 302, 234, 314, 239, 319, 233, 313)(229, 309, 238, 318, 240, 320, 237, 317)
	L = (1, 164)(2, 168)(3, 172)(4, 175)(5, 174)(6, 161)(7, 179)(8, 182)(9, 181)(10, 162)(11, 185)(12, 187)(13, 163)(14, 189)(15, 190)(16, 165)(17, 166)(18, 193)(19, 195)(20, 167)(21, 197)(22, 198)(23, 169)(24, 170)(25, 201)(26, 171)(27, 203)(28, 173)(29, 205)(30, 206)(31, 176)(32, 177)(33, 209)(34, 178)(35, 211)(36, 180)(37, 213)(38, 214)(39, 183)(40, 184)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 222)(47, 191)(48, 192)(49, 224)(50, 194)(51, 226)(52, 196)(53, 228)(54, 229)(55, 199)(56, 200)(57, 231)(58, 202)(59, 233)(60, 204)(61, 234)(62, 208)(63, 207)(64, 235)(65, 210)(66, 237)(67, 212)(68, 238)(69, 216)(70, 215)(71, 239)(72, 218)(73, 220)(74, 223)(75, 240)(76, 225)(77, 227)(78, 230)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1667
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1657 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, Y2^4, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (Y2^-1 * Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 6, 86)(4, 84, 7, 87)(5, 85, 8, 88)(9, 89, 14, 94)(10, 90, 15, 95)(11, 91, 16, 96)(12, 92, 17, 97)(13, 93, 18, 98)(19, 99, 24, 104)(20, 100, 25, 105)(21, 101, 26, 106)(22, 102, 27, 107)(23, 103, 28, 108)(29, 109, 33, 113)(30, 110, 34, 114)(31, 111, 35, 115)(32, 112, 36, 116)(37, 117, 41, 121)(38, 118, 42, 122)(39, 119, 43, 123)(40, 120, 44, 124)(45, 125, 49, 129)(46, 126, 50, 130)(47, 127, 51, 131)(48, 128, 52, 132)(53, 133, 57, 137)(54, 134, 58, 138)(55, 135, 59, 139)(56, 136, 60, 140)(61, 141, 65, 145)(62, 142, 66, 146)(63, 143, 67, 147)(64, 144, 68, 148)(69, 149, 73, 153)(70, 150, 74, 154)(71, 151, 75, 155)(72, 152, 76, 156)(77, 157, 79, 159)(78, 158, 80, 160)(161, 241, 163, 243, 169, 249, 165, 245)(162, 242, 166, 246, 174, 254, 168, 248)(164, 244, 171, 251, 179, 259, 172, 252)(167, 247, 176, 256, 184, 264, 177, 257)(170, 250, 180, 260, 173, 253, 181, 261)(175, 255, 185, 265, 178, 258, 186, 266)(182, 262, 191, 271, 183, 263, 192, 272)(187, 267, 195, 275, 188, 268, 196, 276)(189, 269, 197, 277, 190, 270, 198, 278)(193, 273, 201, 281, 194, 274, 202, 282)(199, 279, 207, 287, 200, 280, 208, 288)(203, 283, 211, 291, 204, 284, 212, 292)(205, 285, 213, 293, 206, 286, 214, 294)(209, 289, 217, 297, 210, 290, 218, 298)(215, 295, 223, 303, 216, 296, 224, 304)(219, 299, 227, 307, 220, 300, 228, 308)(221, 301, 229, 309, 222, 302, 230, 310)(225, 305, 233, 313, 226, 306, 234, 314)(231, 311, 238, 318, 232, 312, 237, 317)(235, 315, 240, 320, 236, 316, 239, 319)
	L = (1, 164)(2, 167)(3, 170)(4, 161)(5, 173)(6, 175)(7, 162)(8, 178)(9, 179)(10, 163)(11, 182)(12, 183)(13, 165)(14, 184)(15, 166)(16, 187)(17, 188)(18, 168)(19, 169)(20, 189)(21, 190)(22, 171)(23, 172)(24, 174)(25, 193)(26, 194)(27, 176)(28, 177)(29, 180)(30, 181)(31, 199)(32, 200)(33, 185)(34, 186)(35, 203)(36, 204)(37, 205)(38, 206)(39, 191)(40, 192)(41, 209)(42, 210)(43, 195)(44, 196)(45, 197)(46, 198)(47, 215)(48, 216)(49, 201)(50, 202)(51, 219)(52, 220)(53, 221)(54, 222)(55, 207)(56, 208)(57, 225)(58, 226)(59, 211)(60, 212)(61, 213)(62, 214)(63, 231)(64, 232)(65, 217)(66, 218)(67, 235)(68, 236)(69, 237)(70, 238)(71, 223)(72, 224)(73, 239)(74, 240)(75, 227)(76, 228)(77, 229)(78, 230)(79, 233)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1668
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1658 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y2^4, Y1 * Y2 * Y3 * Y1 * Y3 * Y2, Y1 * Y2^-1 * Y3 * Y1 * Y3 * Y2^-1, (Y2^-1 * Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 8, 88)(4, 84, 7, 87)(5, 85, 6, 86)(9, 89, 14, 94)(10, 90, 18, 98)(11, 91, 17, 97)(12, 92, 16, 96)(13, 93, 15, 95)(19, 99, 24, 104)(20, 100, 25, 105)(21, 101, 26, 106)(22, 102, 28, 108)(23, 103, 27, 107)(29, 109, 33, 113)(30, 110, 34, 114)(31, 111, 35, 115)(32, 112, 36, 116)(37, 117, 42, 122)(38, 118, 41, 121)(39, 119, 43, 123)(40, 120, 44, 124)(45, 125, 50, 130)(46, 126, 49, 129)(47, 127, 52, 132)(48, 128, 51, 131)(53, 133, 57, 137)(54, 134, 58, 138)(55, 135, 60, 140)(56, 136, 59, 139)(61, 141, 65, 145)(62, 142, 66, 146)(63, 143, 67, 147)(64, 144, 68, 148)(69, 149, 74, 154)(70, 150, 73, 153)(71, 151, 75, 155)(72, 152, 76, 156)(77, 157, 80, 160)(78, 158, 79, 159)(161, 241, 163, 243, 169, 249, 165, 245)(162, 242, 166, 246, 174, 254, 168, 248)(164, 244, 171, 251, 179, 259, 172, 252)(167, 247, 176, 256, 184, 264, 177, 257)(170, 250, 180, 260, 173, 253, 181, 261)(175, 255, 185, 265, 178, 258, 186, 266)(182, 262, 191, 271, 183, 263, 192, 272)(187, 267, 195, 275, 188, 268, 196, 276)(189, 269, 197, 277, 190, 270, 198, 278)(193, 273, 201, 281, 194, 274, 202, 282)(199, 279, 207, 287, 200, 280, 208, 288)(203, 283, 211, 291, 204, 284, 212, 292)(205, 285, 213, 293, 206, 286, 214, 294)(209, 289, 217, 297, 210, 290, 218, 298)(215, 295, 223, 303, 216, 296, 224, 304)(219, 299, 227, 307, 220, 300, 228, 308)(221, 301, 229, 309, 222, 302, 230, 310)(225, 305, 233, 313, 226, 306, 234, 314)(231, 311, 238, 318, 232, 312, 237, 317)(235, 315, 240, 320, 236, 316, 239, 319)
	L = (1, 164)(2, 167)(3, 170)(4, 161)(5, 173)(6, 175)(7, 162)(8, 178)(9, 179)(10, 163)(11, 182)(12, 183)(13, 165)(14, 184)(15, 166)(16, 187)(17, 188)(18, 168)(19, 169)(20, 189)(21, 190)(22, 171)(23, 172)(24, 174)(25, 193)(26, 194)(27, 176)(28, 177)(29, 180)(30, 181)(31, 199)(32, 200)(33, 185)(34, 186)(35, 203)(36, 204)(37, 205)(38, 206)(39, 191)(40, 192)(41, 209)(42, 210)(43, 195)(44, 196)(45, 197)(46, 198)(47, 215)(48, 216)(49, 201)(50, 202)(51, 219)(52, 220)(53, 221)(54, 222)(55, 207)(56, 208)(57, 225)(58, 226)(59, 211)(60, 212)(61, 213)(62, 214)(63, 231)(64, 232)(65, 217)(66, 218)(67, 235)(68, 236)(69, 237)(70, 238)(71, 223)(72, 224)(73, 239)(74, 240)(75, 227)(76, 228)(77, 229)(78, 230)(79, 233)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1666
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1659 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, (Y3 * Y2^-2)^2, (Y2^-1 * Y1 * Y2^-1)^2, (R * Y2 * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 7, 87)(5, 85, 14, 94)(6, 86, 16, 96)(8, 88, 21, 101)(10, 90, 17, 97)(11, 91, 20, 100)(12, 92, 22, 102)(13, 93, 18, 98)(15, 95, 19, 99)(23, 103, 33, 113)(24, 104, 35, 115)(25, 105, 30, 110)(26, 106, 36, 116)(27, 107, 34, 114)(28, 108, 37, 117)(29, 109, 39, 119)(31, 111, 40, 120)(32, 112, 38, 118)(41, 121, 49, 129)(42, 122, 51, 131)(43, 123, 52, 132)(44, 124, 50, 130)(45, 125, 53, 133)(46, 126, 55, 135)(47, 127, 56, 136)(48, 128, 54, 134)(57, 137, 65, 145)(58, 138, 67, 147)(59, 139, 68, 148)(60, 140, 66, 146)(61, 141, 69, 149)(62, 142, 71, 151)(63, 143, 72, 152)(64, 144, 70, 150)(73, 153, 77, 157)(74, 154, 78, 158)(75, 155, 79, 159)(76, 156, 80, 160)(161, 241, 163, 243, 170, 250, 165, 245)(162, 242, 166, 246, 177, 257, 168, 248)(164, 244, 172, 252, 185, 265, 173, 253)(167, 247, 179, 259, 190, 270, 180, 260)(169, 249, 183, 263, 174, 254, 184, 264)(171, 251, 186, 266, 175, 255, 187, 267)(176, 256, 188, 268, 181, 261, 189, 269)(178, 258, 191, 271, 182, 262, 192, 272)(193, 273, 201, 281, 195, 275, 202, 282)(194, 274, 203, 283, 196, 276, 204, 284)(197, 277, 205, 285, 199, 279, 206, 286)(198, 278, 207, 287, 200, 280, 208, 288)(209, 289, 217, 297, 211, 291, 218, 298)(210, 290, 219, 299, 212, 292, 220, 300)(213, 293, 221, 301, 215, 295, 222, 302)(214, 294, 223, 303, 216, 296, 224, 304)(225, 305, 233, 313, 227, 307, 234, 314)(226, 306, 235, 315, 228, 308, 236, 316)(229, 309, 237, 317, 231, 311, 238, 318)(230, 310, 239, 319, 232, 312, 240, 320)
	L = (1, 164)(2, 167)(3, 171)(4, 161)(5, 175)(6, 178)(7, 162)(8, 182)(9, 180)(10, 185)(11, 163)(12, 181)(13, 176)(14, 179)(15, 165)(16, 173)(17, 190)(18, 166)(19, 174)(20, 169)(21, 172)(22, 168)(23, 194)(24, 196)(25, 170)(26, 195)(27, 193)(28, 198)(29, 200)(30, 177)(31, 199)(32, 197)(33, 187)(34, 183)(35, 186)(36, 184)(37, 192)(38, 188)(39, 191)(40, 189)(41, 210)(42, 212)(43, 211)(44, 209)(45, 214)(46, 216)(47, 215)(48, 213)(49, 204)(50, 201)(51, 203)(52, 202)(53, 208)(54, 205)(55, 207)(56, 206)(57, 226)(58, 228)(59, 227)(60, 225)(61, 230)(62, 232)(63, 231)(64, 229)(65, 220)(66, 217)(67, 219)(68, 218)(69, 224)(70, 221)(71, 223)(72, 222)(73, 240)(74, 239)(75, 238)(76, 237)(77, 236)(78, 235)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1665
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1660 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, (Y3 * Y2^-2)^2, (Y3 * Y2)^10, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 7, 87)(5, 85, 14, 94)(6, 86, 16, 96)(8, 88, 21, 101)(10, 90, 17, 97)(11, 91, 19, 99)(12, 92, 18, 98)(13, 93, 22, 102)(15, 95, 20, 100)(23, 103, 33, 113)(24, 104, 35, 115)(25, 105, 30, 110)(26, 106, 34, 114)(27, 107, 36, 116)(28, 108, 37, 117)(29, 109, 39, 119)(31, 111, 38, 118)(32, 112, 40, 120)(41, 121, 49, 129)(42, 122, 51, 131)(43, 123, 50, 130)(44, 124, 52, 132)(45, 125, 53, 133)(46, 126, 55, 135)(47, 127, 54, 134)(48, 128, 56, 136)(57, 137, 65, 145)(58, 138, 67, 147)(59, 139, 66, 146)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 71, 151)(63, 143, 70, 150)(64, 144, 72, 152)(73, 153, 78, 158)(74, 154, 77, 157)(75, 155, 80, 160)(76, 156, 79, 159)(161, 241, 163, 243, 170, 250, 165, 245)(162, 242, 166, 246, 177, 257, 168, 248)(164, 244, 172, 252, 185, 265, 173, 253)(167, 247, 179, 259, 190, 270, 180, 260)(169, 249, 183, 263, 174, 254, 184, 264)(171, 251, 186, 266, 175, 255, 187, 267)(176, 256, 188, 268, 181, 261, 189, 269)(178, 258, 191, 271, 182, 262, 192, 272)(193, 273, 201, 281, 195, 275, 202, 282)(194, 274, 203, 283, 196, 276, 204, 284)(197, 277, 205, 285, 199, 279, 206, 286)(198, 278, 207, 287, 200, 280, 208, 288)(209, 289, 217, 297, 211, 291, 218, 298)(210, 290, 219, 299, 212, 292, 220, 300)(213, 293, 221, 301, 215, 295, 222, 302)(214, 294, 223, 303, 216, 296, 224, 304)(225, 305, 233, 313, 227, 307, 234, 314)(226, 306, 235, 315, 228, 308, 236, 316)(229, 309, 237, 317, 231, 311, 238, 318)(230, 310, 239, 319, 232, 312, 240, 320)
	L = (1, 164)(2, 167)(3, 171)(4, 161)(5, 175)(6, 178)(7, 162)(8, 182)(9, 179)(10, 185)(11, 163)(12, 176)(13, 181)(14, 180)(15, 165)(16, 172)(17, 190)(18, 166)(19, 169)(20, 174)(21, 173)(22, 168)(23, 194)(24, 196)(25, 170)(26, 193)(27, 195)(28, 198)(29, 200)(30, 177)(31, 197)(32, 199)(33, 186)(34, 183)(35, 187)(36, 184)(37, 191)(38, 188)(39, 192)(40, 189)(41, 210)(42, 212)(43, 209)(44, 211)(45, 214)(46, 216)(47, 213)(48, 215)(49, 203)(50, 201)(51, 204)(52, 202)(53, 207)(54, 205)(55, 208)(56, 206)(57, 226)(58, 228)(59, 225)(60, 227)(61, 230)(62, 232)(63, 229)(64, 231)(65, 219)(66, 217)(67, 220)(68, 218)(69, 223)(70, 221)(71, 224)(72, 222)(73, 240)(74, 239)(75, 238)(76, 237)(77, 236)(78, 235)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1664
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1661 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-2, Y3^4, Y3^-1 * Y2^2 * Y3^-1, (Y3^-1 * Y1)^2, Y2^4, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 10, 90)(5, 85, 7, 87)(6, 86, 8, 88)(11, 91, 16, 96)(12, 92, 17, 97)(13, 93, 18, 98)(14, 94, 19, 99)(15, 95, 20, 100)(21, 101, 26, 106)(22, 102, 25, 105)(23, 103, 28, 108)(24, 104, 27, 107)(29, 109, 33, 113)(30, 110, 34, 114)(31, 111, 35, 115)(32, 112, 36, 116)(37, 117, 42, 122)(38, 118, 41, 121)(39, 119, 44, 124)(40, 120, 43, 123)(45, 125, 49, 129)(46, 126, 50, 130)(47, 127, 51, 131)(48, 128, 52, 132)(53, 133, 58, 138)(54, 134, 57, 137)(55, 135, 60, 140)(56, 136, 59, 139)(61, 141, 65, 145)(62, 142, 66, 146)(63, 143, 67, 147)(64, 144, 68, 148)(69, 149, 74, 154)(70, 150, 73, 153)(71, 151, 76, 156)(72, 152, 75, 155)(77, 157, 79, 159)(78, 158, 80, 160)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 176, 256, 169, 249)(164, 244, 174, 254, 166, 246, 175, 255)(168, 248, 179, 259, 170, 250, 180, 260)(172, 252, 181, 261, 173, 253, 182, 262)(177, 257, 185, 265, 178, 258, 186, 266)(183, 263, 191, 271, 184, 264, 192, 272)(187, 267, 195, 275, 188, 268, 196, 276)(189, 269, 197, 277, 190, 270, 198, 278)(193, 273, 201, 281, 194, 274, 202, 282)(199, 279, 207, 287, 200, 280, 208, 288)(203, 283, 211, 291, 204, 284, 212, 292)(205, 285, 213, 293, 206, 286, 214, 294)(209, 289, 217, 297, 210, 290, 218, 298)(215, 295, 223, 303, 216, 296, 224, 304)(219, 299, 227, 307, 220, 300, 228, 308)(221, 301, 229, 309, 222, 302, 230, 310)(225, 305, 233, 313, 226, 306, 234, 314)(231, 311, 237, 317, 232, 312, 238, 318)(235, 315, 239, 319, 236, 316, 240, 320)
	L = (1, 164)(2, 168)(3, 172)(4, 171)(5, 173)(6, 161)(7, 177)(8, 176)(9, 178)(10, 162)(11, 166)(12, 165)(13, 163)(14, 183)(15, 184)(16, 170)(17, 169)(18, 167)(19, 187)(20, 188)(21, 189)(22, 190)(23, 175)(24, 174)(25, 193)(26, 194)(27, 180)(28, 179)(29, 182)(30, 181)(31, 199)(32, 200)(33, 186)(34, 185)(35, 203)(36, 204)(37, 205)(38, 206)(39, 192)(40, 191)(41, 209)(42, 210)(43, 196)(44, 195)(45, 198)(46, 197)(47, 215)(48, 216)(49, 202)(50, 201)(51, 219)(52, 220)(53, 221)(54, 222)(55, 208)(56, 207)(57, 225)(58, 226)(59, 212)(60, 211)(61, 214)(62, 213)(63, 231)(64, 232)(65, 218)(66, 217)(67, 235)(68, 236)(69, 237)(70, 238)(71, 224)(72, 223)(73, 239)(74, 240)(75, 228)(76, 227)(77, 230)(78, 229)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1669
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1662 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C20 x C2) : C2 (small group id <80, 38>)
Aut   = (D8 x D10) : C2 (small group id <160, 224>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y2^2 * Y3^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 10, 90)(5, 85, 9, 89)(6, 86, 8, 88)(11, 91, 18, 98)(12, 92, 20, 100)(13, 93, 19, 99)(14, 94, 24, 104)(15, 95, 23, 103)(16, 96, 22, 102)(17, 97, 21, 101)(25, 105, 34, 114)(26, 106, 33, 113)(27, 107, 36, 116)(28, 108, 35, 115)(29, 109, 40, 120)(30, 110, 39, 119)(31, 111, 38, 118)(32, 112, 37, 117)(41, 121, 50, 130)(42, 122, 49, 129)(43, 123, 52, 132)(44, 124, 51, 131)(45, 125, 56, 136)(46, 126, 55, 135)(47, 127, 54, 134)(48, 128, 53, 133)(57, 137, 66, 146)(58, 138, 65, 145)(59, 139, 68, 148)(60, 140, 67, 147)(61, 141, 72, 152)(62, 142, 71, 151)(63, 143, 70, 150)(64, 144, 69, 149)(73, 153, 78, 158)(74, 154, 77, 157)(75, 155, 80, 160)(76, 156, 79, 159)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 178, 258, 169, 249)(164, 244, 172, 252, 185, 265, 175, 255)(166, 246, 173, 253, 186, 266, 176, 256)(168, 248, 179, 259, 193, 273, 182, 262)(170, 250, 180, 260, 194, 274, 183, 263)(174, 254, 187, 267, 201, 281, 190, 270)(177, 257, 188, 268, 202, 282, 191, 271)(181, 261, 195, 275, 209, 289, 198, 278)(184, 264, 196, 276, 210, 290, 199, 279)(189, 269, 203, 283, 217, 297, 206, 286)(192, 272, 204, 284, 218, 298, 207, 287)(197, 277, 211, 291, 225, 305, 214, 294)(200, 280, 212, 292, 226, 306, 215, 295)(205, 285, 219, 299, 233, 313, 222, 302)(208, 288, 220, 300, 234, 314, 223, 303)(213, 293, 227, 307, 237, 317, 230, 310)(216, 296, 228, 308, 238, 318, 231, 311)(221, 301, 235, 315, 224, 304, 236, 316)(229, 309, 239, 319, 232, 312, 240, 320)
	L = (1, 164)(2, 168)(3, 172)(4, 174)(5, 175)(6, 161)(7, 179)(8, 181)(9, 182)(10, 162)(11, 185)(12, 187)(13, 163)(14, 189)(15, 190)(16, 165)(17, 166)(18, 193)(19, 195)(20, 167)(21, 197)(22, 198)(23, 169)(24, 170)(25, 201)(26, 171)(27, 203)(28, 173)(29, 205)(30, 206)(31, 176)(32, 177)(33, 209)(34, 178)(35, 211)(36, 180)(37, 213)(38, 214)(39, 183)(40, 184)(41, 217)(42, 186)(43, 219)(44, 188)(45, 221)(46, 222)(47, 191)(48, 192)(49, 225)(50, 194)(51, 227)(52, 196)(53, 229)(54, 230)(55, 199)(56, 200)(57, 233)(58, 202)(59, 235)(60, 204)(61, 234)(62, 236)(63, 207)(64, 208)(65, 237)(66, 210)(67, 239)(68, 212)(69, 238)(70, 240)(71, 215)(72, 216)(73, 224)(74, 218)(75, 223)(76, 220)(77, 232)(78, 226)(79, 231)(80, 228)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1671
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1663 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x D40 (small group id <80, 37>)
Aut   = C2 x C2 x D40 (small group id <160, 215>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^-4, Y3^8 * Y1^-2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 19, 99, 39, 119, 62, 142, 58, 138, 35, 115, 16, 96, 5, 85)(3, 83, 11, 91, 27, 107, 51, 131, 73, 153, 77, 157, 63, 143, 40, 120, 20, 100, 8, 88)(4, 84, 9, 89, 21, 101, 41, 121, 38, 118, 50, 130, 70, 150, 61, 141, 34, 114, 15, 95)(6, 86, 10, 90, 22, 102, 42, 122, 64, 144, 59, 139, 32, 112, 49, 129, 36, 116, 17, 97)(12, 92, 28, 108, 52, 132, 72, 152, 57, 137, 76, 156, 78, 158, 65, 145, 43, 123, 23, 103)(13, 93, 29, 109, 53, 133, 74, 154, 80, 160, 71, 151, 56, 136, 66, 146, 44, 124, 24, 104)(14, 94, 25, 105, 45, 125, 37, 117, 18, 98, 26, 106, 46, 126, 67, 147, 60, 140, 33, 113)(30, 110, 54, 134, 69, 149, 48, 128, 31, 111, 55, 135, 75, 155, 79, 159, 68, 148, 47, 127)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 173, 253)(165, 245, 171, 251)(166, 246, 172, 252)(167, 247, 180, 260)(169, 249, 184, 264)(170, 250, 183, 263)(174, 254, 191, 271)(175, 255, 189, 269)(176, 256, 187, 267)(177, 257, 188, 268)(178, 258, 190, 270)(179, 259, 200, 280)(181, 261, 204, 284)(182, 262, 203, 283)(185, 265, 208, 288)(186, 266, 207, 287)(192, 272, 217, 297)(193, 273, 215, 295)(194, 274, 213, 293)(195, 275, 211, 291)(196, 276, 212, 292)(197, 277, 214, 294)(198, 278, 216, 296)(199, 279, 223, 303)(201, 281, 226, 306)(202, 282, 225, 305)(205, 285, 229, 309)(206, 286, 228, 308)(209, 289, 232, 312)(210, 290, 231, 311)(218, 298, 233, 313)(219, 299, 236, 316)(220, 300, 235, 315)(221, 301, 234, 314)(222, 302, 237, 317)(224, 304, 238, 318)(227, 307, 239, 319)(230, 310, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 174)(5, 175)(6, 161)(7, 181)(8, 183)(9, 185)(10, 162)(11, 188)(12, 190)(13, 163)(14, 192)(15, 193)(16, 194)(17, 165)(18, 166)(19, 201)(20, 203)(21, 205)(22, 167)(23, 207)(24, 168)(25, 209)(26, 170)(27, 212)(28, 214)(29, 171)(30, 216)(31, 173)(32, 218)(33, 219)(34, 220)(35, 221)(36, 176)(37, 177)(38, 178)(39, 198)(40, 225)(41, 197)(42, 179)(43, 228)(44, 180)(45, 196)(46, 182)(47, 231)(48, 184)(49, 195)(50, 186)(51, 232)(52, 229)(53, 187)(54, 226)(55, 189)(56, 223)(57, 191)(58, 230)(59, 222)(60, 224)(61, 227)(62, 210)(63, 238)(64, 199)(65, 239)(66, 200)(67, 202)(68, 240)(69, 204)(70, 206)(71, 237)(72, 208)(73, 217)(74, 211)(75, 213)(76, 215)(77, 236)(78, 235)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1654
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1664 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y3)^4, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 6, 86, 15, 95, 30, 110, 48, 128, 47, 127, 29, 109, 14, 94, 5, 85)(3, 83, 7, 87, 16, 96, 31, 111, 49, 129, 64, 144, 60, 140, 43, 123, 24, 104, 10, 90)(4, 84, 11, 91, 25, 105, 44, 124, 61, 141, 67, 147, 50, 130, 34, 114, 17, 97, 12, 92)(8, 88, 19, 99, 13, 93, 28, 108, 46, 126, 63, 143, 65, 145, 52, 132, 32, 112, 20, 100)(9, 89, 21, 101, 39, 119, 57, 137, 71, 151, 76, 156, 66, 146, 53, 133, 33, 113, 22, 102)(18, 98, 35, 115, 23, 103, 42, 122, 59, 139, 73, 153, 75, 155, 68, 148, 51, 131, 36, 116)(26, 106, 37, 117, 27, 107, 38, 118, 54, 134, 69, 149, 77, 157, 74, 154, 62, 142, 45, 125)(40, 120, 55, 135, 41, 121, 56, 136, 70, 150, 78, 158, 80, 160, 79, 159, 72, 152, 58, 138)(161, 241, 163, 243)(162, 242, 167, 247)(164, 244, 169, 249)(165, 245, 170, 250)(166, 246, 176, 256)(168, 248, 178, 258)(171, 251, 181, 261)(172, 252, 182, 262)(173, 253, 183, 263)(174, 254, 184, 264)(175, 255, 191, 271)(177, 257, 193, 273)(179, 259, 195, 275)(180, 260, 196, 276)(185, 265, 199, 279)(186, 266, 200, 280)(187, 267, 201, 281)(188, 268, 202, 282)(189, 269, 203, 283)(190, 270, 209, 289)(192, 272, 211, 291)(194, 274, 213, 293)(197, 277, 215, 295)(198, 278, 216, 296)(204, 284, 217, 297)(205, 285, 218, 298)(206, 286, 219, 299)(207, 287, 220, 300)(208, 288, 224, 304)(210, 290, 226, 306)(212, 292, 228, 308)(214, 294, 230, 310)(221, 301, 231, 311)(222, 302, 232, 312)(223, 303, 233, 313)(225, 305, 235, 315)(227, 307, 236, 316)(229, 309, 238, 318)(234, 314, 239, 319)(237, 317, 240, 320)
	L = (1, 164)(2, 168)(3, 169)(4, 161)(5, 173)(6, 177)(7, 178)(8, 162)(9, 163)(10, 183)(11, 186)(12, 187)(13, 165)(14, 185)(15, 192)(16, 193)(17, 166)(18, 167)(19, 197)(20, 198)(21, 200)(22, 201)(23, 170)(24, 199)(25, 174)(26, 171)(27, 172)(28, 205)(29, 206)(30, 210)(31, 211)(32, 175)(33, 176)(34, 214)(35, 215)(36, 216)(37, 179)(38, 180)(39, 184)(40, 181)(41, 182)(42, 218)(43, 219)(44, 222)(45, 188)(46, 189)(47, 221)(48, 225)(49, 226)(50, 190)(51, 191)(52, 229)(53, 230)(54, 194)(55, 195)(56, 196)(57, 232)(58, 202)(59, 203)(60, 231)(61, 207)(62, 204)(63, 234)(64, 235)(65, 208)(66, 209)(67, 237)(68, 238)(69, 212)(70, 213)(71, 220)(72, 217)(73, 239)(74, 223)(75, 224)(76, 240)(77, 227)(78, 228)(79, 233)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1660
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1665 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1 * Y2)^2, (Y1^-2 * Y3)^2, Y1^-2 * Y2 * Y1^2 * Y2, (Y3 * Y1)^4, (Y1 * Y2 * Y1^-1 * Y2)^2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 6, 86, 17, 97, 35, 115, 53, 133, 52, 132, 34, 114, 16, 96, 5, 85)(3, 83, 9, 89, 18, 98, 38, 118, 54, 134, 70, 150, 64, 144, 48, 128, 30, 110, 11, 91)(4, 84, 12, 92, 31, 111, 49, 129, 65, 145, 72, 152, 55, 135, 40, 120, 19, 99, 13, 93)(7, 87, 20, 100, 36, 116, 56, 136, 68, 148, 66, 146, 50, 130, 32, 112, 14, 94, 22, 102)(8, 88, 23, 103, 15, 95, 33, 113, 51, 131, 67, 147, 69, 149, 58, 138, 37, 117, 24, 104)(10, 90, 27, 107, 45, 125, 61, 141, 75, 155, 78, 158, 71, 151, 57, 137, 39, 119, 21, 101)(25, 105, 41, 121, 59, 139, 73, 153, 79, 159, 76, 156, 62, 142, 46, 126, 28, 108, 43, 123)(26, 106, 44, 124, 29, 109, 47, 127, 63, 143, 77, 157, 80, 160, 74, 154, 60, 140, 42, 122)(161, 241, 163, 243)(162, 242, 167, 247)(164, 244, 170, 250)(165, 245, 174, 254)(166, 246, 178, 258)(168, 248, 181, 261)(169, 249, 185, 265)(171, 251, 188, 268)(172, 252, 189, 269)(173, 253, 186, 266)(175, 255, 187, 267)(176, 256, 190, 270)(177, 257, 196, 276)(179, 259, 199, 279)(180, 260, 201, 281)(182, 262, 203, 283)(183, 263, 204, 284)(184, 264, 202, 282)(191, 271, 205, 285)(192, 272, 206, 286)(193, 273, 207, 287)(194, 274, 210, 290)(195, 275, 214, 294)(197, 277, 217, 297)(198, 278, 219, 299)(200, 280, 220, 300)(208, 288, 222, 302)(209, 289, 223, 303)(211, 291, 221, 301)(212, 292, 224, 304)(213, 293, 228, 308)(215, 295, 231, 311)(216, 296, 233, 313)(218, 298, 234, 314)(225, 305, 235, 315)(226, 306, 236, 316)(227, 307, 237, 317)(229, 309, 238, 318)(230, 310, 239, 319)(232, 312, 240, 320)
	L = (1, 164)(2, 168)(3, 170)(4, 161)(5, 175)(6, 179)(7, 181)(8, 162)(9, 186)(10, 163)(11, 189)(12, 188)(13, 185)(14, 187)(15, 165)(16, 191)(17, 197)(18, 199)(19, 166)(20, 202)(21, 167)(22, 204)(23, 203)(24, 201)(25, 173)(26, 169)(27, 174)(28, 172)(29, 171)(30, 205)(31, 176)(32, 207)(33, 206)(34, 211)(35, 215)(36, 217)(37, 177)(38, 220)(39, 178)(40, 219)(41, 184)(42, 180)(43, 183)(44, 182)(45, 190)(46, 193)(47, 192)(48, 223)(49, 222)(50, 221)(51, 194)(52, 225)(53, 229)(54, 231)(55, 195)(56, 234)(57, 196)(58, 233)(59, 200)(60, 198)(61, 210)(62, 209)(63, 208)(64, 235)(65, 212)(66, 237)(67, 236)(68, 238)(69, 213)(70, 240)(71, 214)(72, 239)(73, 218)(74, 216)(75, 224)(76, 227)(77, 226)(78, 228)(79, 232)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1659
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1666 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y3)^4, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 6, 86, 15, 95, 30, 110, 48, 128, 47, 127, 29, 109, 14, 94, 5, 85)(3, 83, 9, 89, 21, 101, 39, 119, 57, 137, 64, 144, 49, 129, 31, 111, 16, 96, 7, 87)(4, 84, 11, 91, 25, 105, 44, 124, 61, 141, 67, 147, 50, 130, 34, 114, 17, 97, 12, 92)(8, 88, 19, 99, 13, 93, 28, 108, 46, 126, 63, 143, 65, 145, 52, 132, 32, 112, 20, 100)(10, 90, 23, 103, 33, 113, 53, 133, 66, 146, 76, 156, 71, 151, 59, 139, 40, 120, 24, 104)(18, 98, 35, 115, 51, 131, 68, 148, 75, 155, 72, 152, 58, 138, 41, 121, 22, 102, 36, 116)(26, 106, 37, 117, 27, 107, 38, 118, 54, 134, 69, 149, 77, 157, 74, 154, 62, 142, 45, 125)(42, 122, 56, 136, 43, 123, 60, 140, 73, 153, 79, 159, 80, 160, 78, 158, 70, 150, 55, 135)(161, 241, 163, 243)(162, 242, 167, 247)(164, 244, 170, 250)(165, 245, 169, 249)(166, 246, 176, 256)(168, 248, 178, 258)(171, 251, 184, 264)(172, 252, 183, 263)(173, 253, 182, 262)(174, 254, 181, 261)(175, 255, 191, 271)(177, 257, 193, 273)(179, 259, 196, 276)(180, 260, 195, 275)(185, 265, 200, 280)(186, 266, 203, 283)(187, 267, 202, 282)(188, 268, 201, 281)(189, 269, 199, 279)(190, 270, 209, 289)(192, 272, 211, 291)(194, 274, 213, 293)(197, 277, 216, 296)(198, 278, 215, 295)(204, 284, 219, 299)(205, 285, 220, 300)(206, 286, 218, 298)(207, 287, 217, 297)(208, 288, 224, 304)(210, 290, 226, 306)(212, 292, 228, 308)(214, 294, 230, 310)(221, 301, 231, 311)(222, 302, 233, 313)(223, 303, 232, 312)(225, 305, 235, 315)(227, 307, 236, 316)(229, 309, 238, 318)(234, 314, 239, 319)(237, 317, 240, 320)
	L = (1, 164)(2, 168)(3, 170)(4, 161)(5, 173)(6, 177)(7, 178)(8, 162)(9, 182)(10, 163)(11, 186)(12, 187)(13, 165)(14, 185)(15, 192)(16, 193)(17, 166)(18, 167)(19, 197)(20, 198)(21, 200)(22, 169)(23, 202)(24, 203)(25, 174)(26, 171)(27, 172)(28, 205)(29, 206)(30, 210)(31, 211)(32, 175)(33, 176)(34, 214)(35, 215)(36, 216)(37, 179)(38, 180)(39, 218)(40, 181)(41, 220)(42, 183)(43, 184)(44, 222)(45, 188)(46, 189)(47, 221)(48, 225)(49, 226)(50, 190)(51, 191)(52, 229)(53, 230)(54, 194)(55, 195)(56, 196)(57, 231)(58, 199)(59, 233)(60, 201)(61, 207)(62, 204)(63, 234)(64, 235)(65, 208)(66, 209)(67, 237)(68, 238)(69, 212)(70, 213)(71, 217)(72, 239)(73, 219)(74, 223)(75, 224)(76, 240)(77, 227)(78, 228)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1658
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1667 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-1 * Y1^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3 * Y1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 19, 99, 39, 119, 62, 142, 58, 138, 35, 115, 15, 95, 5, 85)(3, 83, 11, 91, 27, 107, 51, 131, 73, 153, 77, 157, 63, 143, 40, 120, 20, 100, 8, 88)(4, 84, 14, 94, 6, 86, 18, 98, 21, 101, 43, 123, 64, 144, 59, 139, 34, 114, 16, 96)(9, 89, 24, 104, 10, 90, 26, 106, 41, 121, 66, 146, 60, 140, 37, 117, 17, 97, 25, 105)(12, 92, 29, 109, 13, 93, 31, 111, 52, 132, 75, 155, 78, 158, 67, 147, 42, 122, 30, 110)(22, 102, 44, 124, 23, 103, 46, 126, 28, 108, 53, 133, 74, 154, 79, 159, 65, 145, 45, 125)(32, 112, 47, 127, 33, 113, 48, 128, 38, 118, 50, 130, 68, 148, 61, 141, 36, 116, 49, 129)(54, 134, 70, 150, 55, 135, 72, 152, 57, 137, 76, 156, 80, 160, 71, 151, 56, 136, 69, 149)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 173, 253)(165, 245, 171, 251)(166, 246, 172, 252)(167, 247, 180, 260)(169, 249, 183, 263)(170, 250, 182, 262)(174, 254, 189, 269)(175, 255, 187, 267)(176, 256, 191, 271)(177, 257, 188, 268)(178, 258, 190, 270)(179, 259, 200, 280)(181, 261, 202, 282)(184, 264, 204, 284)(185, 265, 206, 286)(186, 266, 205, 285)(192, 272, 215, 295)(193, 273, 214, 294)(194, 274, 212, 292)(195, 275, 211, 291)(196, 276, 217, 297)(197, 277, 213, 293)(198, 278, 216, 296)(199, 279, 223, 303)(201, 281, 225, 305)(203, 283, 227, 307)(207, 287, 230, 310)(208, 288, 229, 309)(209, 289, 232, 312)(210, 290, 231, 311)(218, 298, 233, 313)(219, 299, 235, 315)(220, 300, 234, 314)(221, 301, 236, 316)(222, 302, 237, 317)(224, 304, 238, 318)(226, 306, 239, 319)(228, 308, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 175)(5, 177)(6, 161)(7, 166)(8, 182)(9, 165)(10, 162)(11, 183)(12, 180)(13, 163)(14, 192)(15, 194)(16, 196)(17, 195)(18, 193)(19, 170)(20, 202)(21, 167)(22, 200)(23, 168)(24, 207)(25, 209)(26, 208)(27, 173)(28, 171)(29, 214)(30, 216)(31, 215)(32, 176)(33, 174)(34, 218)(35, 220)(36, 219)(37, 221)(38, 178)(39, 181)(40, 225)(41, 179)(42, 223)(43, 198)(44, 229)(45, 231)(46, 230)(47, 185)(48, 184)(49, 197)(50, 186)(51, 188)(52, 187)(53, 232)(54, 190)(55, 189)(56, 227)(57, 191)(58, 224)(59, 228)(60, 222)(61, 226)(62, 201)(63, 238)(64, 199)(65, 237)(66, 210)(67, 240)(68, 203)(69, 205)(70, 204)(71, 239)(72, 206)(73, 212)(74, 211)(75, 217)(76, 213)(77, 234)(78, 233)(79, 236)(80, 235)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1656
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1668 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2, (Y2 * Y1^-2)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, (Y2 * Y1)^4, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 6, 86, 17, 97, 35, 115, 53, 133, 52, 132, 34, 114, 16, 96, 5, 85)(3, 83, 9, 89, 25, 105, 45, 125, 61, 141, 71, 151, 54, 134, 39, 119, 18, 98, 11, 91)(4, 84, 12, 92, 31, 111, 49, 129, 65, 145, 72, 152, 55, 135, 40, 120, 19, 99, 13, 93)(7, 87, 20, 100, 14, 94, 32, 112, 50, 130, 66, 146, 68, 148, 57, 137, 36, 116, 22, 102)(8, 88, 23, 103, 15, 95, 33, 113, 51, 131, 67, 147, 69, 149, 58, 138, 37, 117, 24, 104)(10, 90, 21, 101, 38, 118, 56, 136, 70, 150, 78, 158, 75, 155, 64, 144, 46, 126, 28, 108)(26, 106, 41, 121, 29, 109, 43, 123, 59, 139, 73, 153, 79, 159, 76, 156, 62, 142, 47, 127)(27, 107, 42, 122, 30, 110, 44, 124, 60, 140, 74, 154, 80, 160, 77, 157, 63, 143, 48, 128)(161, 241, 163, 243)(162, 242, 167, 247)(164, 244, 170, 250)(165, 245, 174, 254)(166, 246, 178, 258)(168, 248, 181, 261)(169, 249, 186, 266)(171, 251, 189, 269)(172, 252, 187, 267)(173, 253, 190, 270)(175, 255, 188, 268)(176, 256, 185, 265)(177, 257, 196, 276)(179, 259, 198, 278)(180, 260, 201, 281)(182, 262, 203, 283)(183, 263, 202, 282)(184, 264, 204, 284)(191, 271, 206, 286)(192, 272, 207, 287)(193, 273, 208, 288)(194, 274, 210, 290)(195, 275, 214, 294)(197, 277, 216, 296)(199, 279, 219, 299)(200, 280, 220, 300)(205, 285, 222, 302)(209, 289, 223, 303)(211, 291, 224, 304)(212, 292, 221, 301)(213, 293, 228, 308)(215, 295, 230, 310)(217, 297, 233, 313)(218, 298, 234, 314)(225, 305, 235, 315)(226, 306, 236, 316)(227, 307, 237, 317)(229, 309, 238, 318)(231, 311, 239, 319)(232, 312, 240, 320)
	L = (1, 164)(2, 168)(3, 170)(4, 161)(5, 175)(6, 179)(7, 181)(8, 162)(9, 187)(10, 163)(11, 190)(12, 186)(13, 189)(14, 188)(15, 165)(16, 191)(17, 197)(18, 198)(19, 166)(20, 202)(21, 167)(22, 204)(23, 201)(24, 203)(25, 206)(26, 172)(27, 169)(28, 174)(29, 173)(30, 171)(31, 176)(32, 208)(33, 207)(34, 211)(35, 215)(36, 216)(37, 177)(38, 178)(39, 220)(40, 219)(41, 183)(42, 180)(43, 184)(44, 182)(45, 223)(46, 185)(47, 193)(48, 192)(49, 222)(50, 224)(51, 194)(52, 225)(53, 229)(54, 230)(55, 195)(56, 196)(57, 234)(58, 233)(59, 200)(60, 199)(61, 235)(62, 209)(63, 205)(64, 210)(65, 212)(66, 237)(67, 236)(68, 238)(69, 213)(70, 214)(71, 240)(72, 239)(73, 218)(74, 217)(75, 221)(76, 227)(77, 226)(78, 228)(79, 232)(80, 231)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1657
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1669 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y1)^2, (Y1^-1 * Y2)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 18, 98, 33, 113, 49, 129, 47, 127, 31, 111, 16, 96, 5, 85)(3, 83, 11, 91, 25, 105, 41, 121, 57, 137, 64, 144, 50, 130, 34, 114, 19, 99, 8, 88)(4, 84, 14, 94, 29, 109, 45, 125, 61, 141, 65, 145, 51, 131, 35, 115, 20, 100, 9, 89)(6, 86, 17, 97, 32, 112, 48, 128, 63, 143, 66, 146, 52, 132, 36, 116, 21, 101, 10, 90)(12, 92, 22, 102, 37, 117, 53, 133, 67, 147, 75, 155, 71, 151, 58, 138, 42, 122, 26, 106)(13, 93, 23, 103, 38, 118, 54, 134, 68, 148, 76, 156, 72, 152, 59, 139, 43, 123, 27, 107)(15, 95, 24, 104, 39, 119, 55, 135, 69, 149, 77, 157, 74, 154, 62, 142, 46, 126, 30, 110)(28, 108, 44, 124, 60, 140, 73, 153, 79, 159, 80, 160, 78, 158, 70, 150, 56, 136, 40, 120)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 173, 253)(165, 245, 171, 251)(166, 246, 172, 252)(167, 247, 179, 259)(169, 249, 183, 263)(170, 250, 182, 262)(174, 254, 187, 267)(175, 255, 188, 268)(176, 256, 185, 265)(177, 257, 186, 266)(178, 258, 194, 274)(180, 260, 198, 278)(181, 261, 197, 277)(184, 264, 200, 280)(189, 269, 203, 283)(190, 270, 204, 284)(191, 271, 201, 281)(192, 272, 202, 282)(193, 273, 210, 290)(195, 275, 214, 294)(196, 276, 213, 293)(199, 279, 216, 296)(205, 285, 219, 299)(206, 286, 220, 300)(207, 287, 217, 297)(208, 288, 218, 298)(209, 289, 224, 304)(211, 291, 228, 308)(212, 292, 227, 307)(215, 295, 230, 310)(221, 301, 232, 312)(222, 302, 233, 313)(223, 303, 231, 311)(225, 305, 236, 316)(226, 306, 235, 315)(229, 309, 238, 318)(234, 314, 239, 319)(237, 317, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 175)(5, 174)(6, 161)(7, 180)(8, 182)(9, 184)(10, 162)(11, 186)(12, 188)(13, 163)(14, 190)(15, 166)(16, 189)(17, 165)(18, 195)(19, 197)(20, 199)(21, 167)(22, 200)(23, 168)(24, 170)(25, 202)(26, 204)(27, 171)(28, 173)(29, 206)(30, 177)(31, 205)(32, 176)(33, 211)(34, 213)(35, 215)(36, 178)(37, 216)(38, 179)(39, 181)(40, 183)(41, 218)(42, 220)(43, 185)(44, 187)(45, 222)(46, 192)(47, 221)(48, 191)(49, 225)(50, 227)(51, 229)(52, 193)(53, 230)(54, 194)(55, 196)(56, 198)(57, 231)(58, 233)(59, 201)(60, 203)(61, 234)(62, 208)(63, 207)(64, 235)(65, 237)(66, 209)(67, 238)(68, 210)(69, 212)(70, 214)(71, 239)(72, 217)(73, 219)(74, 223)(75, 240)(76, 224)(77, 226)(78, 228)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1661
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1670 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3)^2, (R * Y3)^2, Y1 * Y3^2 * Y1, (R * Y1)^2, Y1 * Y2 * Y3^-2 * Y2 * Y1, Y1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y2 * Y1^-1 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^10, Y3^10, (Y1^-2 * Y3 * Y1^-2)^2 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 21, 101, 44, 124, 65, 145, 61, 141, 39, 119, 16, 96, 5, 85)(3, 83, 11, 91, 31, 111, 57, 137, 73, 153, 79, 159, 66, 146, 48, 128, 22, 102, 13, 93)(4, 84, 15, 95, 6, 86, 20, 100, 23, 103, 49, 129, 67, 147, 62, 142, 38, 118, 17, 97)(8, 88, 24, 104, 18, 98, 41, 121, 60, 140, 76, 156, 77, 157, 69, 149, 45, 125, 26, 106)(9, 89, 28, 108, 10, 90, 30, 110, 46, 126, 70, 150, 63, 143, 42, 122, 19, 99, 29, 109)(12, 92, 27, 107, 14, 94, 37, 117, 58, 138, 75, 155, 78, 158, 68, 148, 47, 127, 25, 105)(32, 112, 50, 130, 35, 115, 53, 133, 43, 123, 56, 136, 72, 152, 64, 144, 40, 120, 55, 135)(33, 113, 52, 132, 34, 114, 59, 139, 74, 154, 80, 160, 71, 151, 54, 134, 36, 116, 51, 131)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 174, 254)(165, 245, 178, 258)(166, 246, 172, 252)(167, 247, 182, 262)(169, 249, 187, 267)(170, 250, 185, 265)(171, 251, 192, 272)(173, 253, 195, 275)(175, 255, 193, 273)(176, 256, 191, 271)(177, 257, 194, 274)(179, 259, 197, 277)(180, 260, 196, 276)(181, 261, 205, 285)(183, 263, 207, 287)(184, 264, 210, 290)(186, 266, 213, 293)(188, 268, 211, 291)(189, 269, 212, 292)(190, 270, 214, 294)(198, 278, 218, 298)(199, 279, 220, 300)(200, 280, 217, 297)(201, 281, 215, 295)(202, 282, 219, 299)(203, 283, 208, 288)(204, 284, 226, 306)(206, 286, 228, 308)(209, 289, 231, 311)(216, 296, 229, 309)(221, 301, 233, 313)(222, 302, 234, 314)(223, 303, 235, 315)(224, 304, 236, 316)(225, 305, 237, 317)(227, 307, 238, 318)(230, 310, 240, 320)(232, 312, 239, 319)
	L = (1, 164)(2, 169)(3, 172)(4, 176)(5, 179)(6, 161)(7, 166)(8, 185)(9, 165)(10, 162)(11, 193)(12, 182)(13, 196)(14, 163)(15, 192)(16, 198)(17, 200)(18, 187)(19, 199)(20, 195)(21, 170)(22, 207)(23, 167)(24, 211)(25, 205)(26, 214)(27, 168)(28, 210)(29, 215)(30, 213)(31, 174)(32, 177)(33, 173)(34, 171)(35, 175)(36, 208)(37, 178)(38, 221)(39, 223)(40, 222)(41, 212)(42, 224)(43, 180)(44, 183)(45, 228)(46, 181)(47, 226)(48, 231)(49, 203)(50, 189)(51, 186)(52, 184)(53, 188)(54, 229)(55, 202)(56, 190)(57, 194)(58, 191)(59, 201)(60, 197)(61, 227)(62, 232)(63, 225)(64, 230)(65, 206)(66, 238)(67, 204)(68, 237)(69, 240)(70, 216)(71, 239)(72, 209)(73, 218)(74, 217)(75, 220)(76, 219)(77, 235)(78, 233)(79, 234)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1655
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1671 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C20 x C2) : C2 (small group id <80, 38>)
Aut   = (D8 x D10) : C2 (small group id <160, 224>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, (Y2 * Y1^-2)^2, Y1^4 * Y3^4, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 21, 101, 44, 124, 65, 145, 61, 141, 41, 121, 18, 98, 5, 85)(3, 83, 11, 91, 31, 111, 57, 137, 73, 153, 79, 159, 66, 146, 49, 129, 22, 102, 13, 93)(4, 84, 9, 89, 23, 103, 46, 126, 43, 123, 56, 136, 72, 152, 64, 144, 40, 120, 16, 96)(6, 86, 10, 90, 24, 104, 47, 127, 67, 147, 62, 142, 37, 117, 55, 135, 42, 122, 19, 99)(8, 88, 25, 105, 17, 97, 36, 116, 59, 139, 75, 155, 77, 157, 69, 149, 45, 125, 27, 107)(12, 92, 28, 108, 53, 133, 39, 119, 60, 140, 76, 156, 78, 158, 71, 151, 48, 128, 33, 113)(14, 94, 32, 112, 58, 138, 74, 154, 80, 160, 68, 148, 54, 134, 26, 106, 50, 130, 35, 115)(15, 95, 29, 109, 51, 131, 34, 114, 20, 100, 30, 110, 52, 132, 70, 150, 63, 143, 38, 118)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 174, 254)(165, 245, 177, 257)(166, 246, 172, 252)(167, 247, 182, 262)(169, 249, 188, 268)(170, 250, 186, 266)(171, 251, 189, 269)(173, 253, 194, 274)(175, 255, 196, 276)(176, 256, 199, 279)(178, 258, 191, 271)(179, 259, 195, 275)(180, 260, 187, 267)(181, 261, 205, 285)(183, 263, 210, 290)(184, 264, 208, 288)(185, 265, 211, 291)(190, 270, 209, 289)(192, 272, 215, 295)(193, 273, 206, 286)(197, 277, 220, 300)(198, 278, 217, 297)(200, 280, 218, 298)(201, 281, 219, 299)(202, 282, 213, 293)(203, 283, 214, 294)(204, 284, 226, 306)(207, 287, 228, 308)(212, 292, 229, 309)(216, 296, 231, 311)(221, 301, 233, 313)(222, 302, 234, 314)(223, 303, 235, 315)(224, 304, 236, 316)(225, 305, 237, 317)(227, 307, 238, 318)(230, 310, 239, 319)(232, 312, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 175)(5, 176)(6, 161)(7, 183)(8, 186)(9, 189)(10, 162)(11, 188)(12, 187)(13, 193)(14, 163)(15, 197)(16, 198)(17, 195)(18, 200)(19, 165)(20, 166)(21, 206)(22, 208)(23, 211)(24, 167)(25, 210)(26, 209)(27, 214)(28, 168)(29, 215)(30, 170)(31, 213)(32, 171)(33, 205)(34, 179)(35, 173)(36, 174)(37, 221)(38, 222)(39, 177)(40, 223)(41, 224)(42, 178)(43, 180)(44, 203)(45, 228)(46, 194)(47, 181)(48, 229)(49, 231)(50, 182)(51, 202)(52, 184)(53, 185)(54, 226)(55, 201)(56, 190)(57, 199)(58, 191)(59, 192)(60, 196)(61, 232)(62, 225)(63, 227)(64, 230)(65, 216)(66, 238)(67, 204)(68, 239)(69, 240)(70, 207)(71, 237)(72, 212)(73, 220)(74, 217)(75, 218)(76, 219)(77, 234)(78, 235)(79, 236)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1662
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1672 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, (Y1^-1 * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^4, Y2^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 5, 85)(3, 83, 10, 90, 18, 98, 13, 93)(4, 84, 14, 94, 19, 99, 9, 89)(6, 86, 8, 88, 20, 100, 16, 96)(11, 91, 24, 104, 33, 113, 27, 107)(12, 92, 28, 108, 34, 114, 23, 103)(15, 95, 29, 109, 35, 115, 22, 102)(17, 97, 21, 101, 36, 116, 31, 111)(25, 105, 40, 120, 49, 129, 43, 123)(26, 106, 44, 124, 50, 130, 39, 119)(30, 110, 45, 125, 51, 131, 38, 118)(32, 112, 37, 117, 52, 132, 47, 127)(41, 121, 56, 136, 64, 144, 59, 139)(42, 122, 60, 140, 65, 145, 55, 135)(46, 126, 61, 141, 66, 146, 54, 134)(48, 128, 53, 133, 67, 147, 63, 143)(57, 137, 68, 148, 75, 155, 72, 152)(58, 138, 73, 153, 76, 156, 70, 150)(62, 142, 74, 154, 77, 157, 69, 149)(71, 151, 79, 159, 80, 160, 78, 158)(161, 241, 163, 243, 171, 251, 185, 265, 201, 281, 217, 297, 208, 288, 192, 272, 177, 257, 166, 246)(162, 242, 168, 248, 181, 261, 197, 277, 213, 293, 228, 308, 216, 296, 200, 280, 184, 264, 170, 250)(164, 244, 175, 255, 190, 270, 206, 286, 222, 302, 231, 311, 218, 298, 202, 282, 186, 266, 172, 252)(165, 245, 176, 256, 191, 271, 207, 287, 223, 303, 232, 312, 219, 299, 203, 283, 187, 267, 173, 253)(167, 247, 178, 258, 193, 273, 209, 289, 224, 304, 235, 315, 227, 307, 212, 292, 196, 276, 180, 260)(169, 249, 183, 263, 199, 279, 215, 295, 230, 310, 238, 318, 229, 309, 214, 294, 198, 278, 182, 262)(174, 254, 188, 268, 204, 284, 220, 300, 233, 313, 239, 319, 234, 314, 221, 301, 205, 285, 189, 269)(179, 259, 195, 275, 211, 291, 226, 306, 237, 317, 240, 320, 236, 316, 225, 305, 210, 290, 194, 274)
	L = (1, 164)(2, 169)(3, 172)(4, 161)(5, 174)(6, 175)(7, 179)(8, 182)(9, 162)(10, 183)(11, 186)(12, 163)(13, 188)(14, 165)(15, 166)(16, 189)(17, 190)(18, 194)(19, 167)(20, 195)(21, 198)(22, 168)(23, 170)(24, 199)(25, 202)(26, 171)(27, 204)(28, 173)(29, 176)(30, 177)(31, 205)(32, 206)(33, 210)(34, 178)(35, 180)(36, 211)(37, 214)(38, 181)(39, 184)(40, 215)(41, 218)(42, 185)(43, 220)(44, 187)(45, 191)(46, 192)(47, 221)(48, 222)(49, 225)(50, 193)(51, 196)(52, 226)(53, 229)(54, 197)(55, 200)(56, 230)(57, 231)(58, 201)(59, 233)(60, 203)(61, 207)(62, 208)(63, 234)(64, 236)(65, 209)(66, 212)(67, 237)(68, 238)(69, 213)(70, 216)(71, 217)(72, 239)(73, 219)(74, 223)(75, 240)(76, 224)(77, 227)(78, 228)(79, 232)(80, 235)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1652
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1673 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 5, 85)(3, 83, 11, 91, 18, 98, 8, 88)(4, 84, 14, 94, 19, 99, 9, 89)(6, 86, 16, 96, 20, 100, 10, 90)(12, 92, 21, 101, 33, 113, 25, 105)(13, 93, 22, 102, 34, 114, 26, 106)(15, 95, 23, 103, 35, 115, 29, 109)(17, 97, 24, 104, 36, 116, 31, 111)(27, 107, 41, 121, 49, 129, 37, 117)(28, 108, 42, 122, 50, 130, 38, 118)(30, 110, 45, 125, 51, 131, 39, 119)(32, 112, 47, 127, 52, 132, 40, 120)(43, 123, 53, 133, 64, 144, 57, 137)(44, 124, 54, 134, 65, 145, 58, 138)(46, 126, 55, 135, 66, 146, 61, 141)(48, 128, 56, 136, 67, 147, 63, 143)(59, 139, 71, 151, 75, 155, 68, 148)(60, 140, 72, 152, 76, 156, 69, 149)(62, 142, 74, 154, 77, 157, 70, 150)(73, 153, 78, 158, 80, 160, 79, 159)(161, 241, 163, 243, 172, 252, 187, 267, 203, 283, 219, 299, 208, 288, 192, 272, 177, 257, 166, 246)(162, 242, 168, 248, 181, 261, 197, 277, 213, 293, 228, 308, 216, 296, 200, 280, 184, 264, 170, 250)(164, 244, 175, 255, 190, 270, 206, 286, 222, 302, 233, 313, 220, 300, 204, 284, 188, 268, 173, 253)(165, 245, 171, 251, 185, 265, 201, 281, 217, 297, 231, 311, 223, 303, 207, 287, 191, 271, 176, 256)(167, 247, 178, 258, 193, 273, 209, 289, 224, 304, 235, 315, 227, 307, 212, 292, 196, 276, 180, 260)(169, 249, 183, 263, 199, 279, 215, 295, 230, 310, 238, 318, 229, 309, 214, 294, 198, 278, 182, 262)(174, 254, 189, 269, 205, 285, 221, 301, 234, 314, 239, 319, 232, 312, 218, 298, 202, 282, 186, 266)(179, 259, 195, 275, 211, 291, 226, 306, 237, 317, 240, 320, 236, 316, 225, 305, 210, 290, 194, 274)
	L = (1, 164)(2, 169)(3, 173)(4, 161)(5, 174)(6, 175)(7, 179)(8, 182)(9, 162)(10, 183)(11, 186)(12, 188)(13, 163)(14, 165)(15, 166)(16, 189)(17, 190)(18, 194)(19, 167)(20, 195)(21, 198)(22, 168)(23, 170)(24, 199)(25, 202)(26, 171)(27, 204)(28, 172)(29, 176)(30, 177)(31, 205)(32, 206)(33, 210)(34, 178)(35, 180)(36, 211)(37, 214)(38, 181)(39, 184)(40, 215)(41, 218)(42, 185)(43, 220)(44, 187)(45, 191)(46, 192)(47, 221)(48, 222)(49, 225)(50, 193)(51, 196)(52, 226)(53, 229)(54, 197)(55, 200)(56, 230)(57, 232)(58, 201)(59, 233)(60, 203)(61, 207)(62, 208)(63, 234)(64, 236)(65, 209)(66, 212)(67, 237)(68, 238)(69, 213)(70, 216)(71, 239)(72, 217)(73, 219)(74, 223)(75, 240)(76, 224)(77, 227)(78, 228)(79, 231)(80, 235)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1653
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1674 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = D8 x D10 (small group id <80, 39>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (Y1^-1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, (Y2^-1 * Y1)^2, Y1^4, (Y2^-1 * Y1^-1)^2, Y2^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 5, 85)(3, 83, 11, 91, 18, 98, 10, 90)(4, 84, 14, 94, 19, 99, 9, 89)(6, 86, 16, 96, 20, 100, 8, 88)(12, 92, 24, 104, 33, 113, 26, 106)(13, 93, 23, 103, 34, 114, 25, 105)(15, 95, 22, 102, 35, 115, 29, 109)(17, 97, 21, 101, 36, 116, 31, 111)(27, 107, 42, 122, 49, 129, 40, 120)(28, 108, 41, 121, 50, 130, 39, 119)(30, 110, 45, 125, 51, 131, 38, 118)(32, 112, 47, 127, 52, 132, 37, 117)(43, 123, 56, 136, 64, 144, 58, 138)(44, 124, 55, 135, 65, 145, 57, 137)(46, 126, 54, 134, 66, 146, 61, 141)(48, 128, 53, 133, 67, 147, 63, 143)(59, 139, 72, 152, 75, 155, 68, 148)(60, 140, 71, 151, 76, 156, 70, 150)(62, 142, 74, 154, 77, 157, 69, 149)(73, 153, 78, 158, 80, 160, 79, 159)(161, 241, 163, 243, 172, 252, 187, 267, 203, 283, 219, 299, 208, 288, 192, 272, 177, 257, 166, 246)(162, 242, 168, 248, 181, 261, 197, 277, 213, 293, 228, 308, 216, 296, 200, 280, 184, 264, 170, 250)(164, 244, 175, 255, 190, 270, 206, 286, 222, 302, 233, 313, 220, 300, 204, 284, 188, 268, 173, 253)(165, 245, 176, 256, 191, 271, 207, 287, 223, 303, 232, 312, 218, 298, 202, 282, 186, 266, 171, 251)(167, 247, 178, 258, 193, 273, 209, 289, 224, 304, 235, 315, 227, 307, 212, 292, 196, 276, 180, 260)(169, 249, 183, 263, 199, 279, 215, 295, 230, 310, 238, 318, 229, 309, 214, 294, 198, 278, 182, 262)(174, 254, 185, 265, 201, 281, 217, 297, 231, 311, 239, 319, 234, 314, 221, 301, 205, 285, 189, 269)(179, 259, 195, 275, 211, 291, 226, 306, 237, 317, 240, 320, 236, 316, 225, 305, 210, 290, 194, 274)
	L = (1, 164)(2, 169)(3, 173)(4, 161)(5, 174)(6, 175)(7, 179)(8, 182)(9, 162)(10, 183)(11, 185)(12, 188)(13, 163)(14, 165)(15, 166)(16, 189)(17, 190)(18, 194)(19, 167)(20, 195)(21, 198)(22, 168)(23, 170)(24, 199)(25, 171)(26, 201)(27, 204)(28, 172)(29, 176)(30, 177)(31, 205)(32, 206)(33, 210)(34, 178)(35, 180)(36, 211)(37, 214)(38, 181)(39, 184)(40, 215)(41, 186)(42, 217)(43, 220)(44, 187)(45, 191)(46, 192)(47, 221)(48, 222)(49, 225)(50, 193)(51, 196)(52, 226)(53, 229)(54, 197)(55, 200)(56, 230)(57, 202)(58, 231)(59, 233)(60, 203)(61, 207)(62, 208)(63, 234)(64, 236)(65, 209)(66, 212)(67, 237)(68, 238)(69, 213)(70, 216)(71, 218)(72, 239)(73, 219)(74, 223)(75, 240)(76, 224)(77, 227)(78, 228)(79, 232)(80, 235)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1651
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1675 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x D8 x D10 (small group id <160, 217>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, Y1^4, (Y3 * Y2^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 8, 88, 5, 85)(3, 83, 13, 93, 21, 101, 11, 91)(4, 84, 10, 90, 7, 87, 12, 92)(6, 86, 18, 98, 22, 102, 9, 89)(14, 94, 28, 108, 37, 117, 29, 109)(15, 95, 26, 106, 16, 96, 27, 107)(17, 97, 24, 104, 19, 99, 25, 105)(20, 100, 23, 103, 38, 118, 34, 114)(30, 110, 45, 125, 53, 133, 44, 124)(31, 111, 42, 122, 32, 112, 43, 123)(33, 113, 40, 120, 35, 115, 41, 121)(36, 116, 50, 130, 54, 134, 39, 119)(46, 126, 60, 140, 68, 148, 61, 141)(47, 127, 58, 138, 48, 128, 59, 139)(49, 129, 56, 136, 51, 131, 57, 137)(52, 132, 55, 135, 69, 149, 66, 146)(62, 142, 75, 155, 78, 158, 70, 150)(63, 143, 73, 153, 64, 144, 74, 154)(65, 145, 71, 151, 67, 147, 72, 152)(76, 156, 80, 160, 77, 157, 79, 159)(161, 241, 163, 243, 174, 254, 190, 270, 206, 286, 222, 302, 212, 292, 196, 276, 180, 260, 166, 246)(162, 242, 169, 249, 183, 263, 199, 279, 215, 295, 230, 310, 220, 300, 204, 284, 188, 268, 171, 251)(164, 244, 177, 257, 193, 273, 209, 289, 225, 305, 237, 317, 223, 303, 208, 288, 191, 271, 176, 256)(165, 245, 178, 258, 194, 274, 210, 290, 226, 306, 235, 315, 221, 301, 205, 285, 189, 269, 173, 253)(167, 247, 179, 259, 195, 275, 211, 291, 227, 307, 236, 316, 224, 304, 207, 287, 192, 272, 175, 255)(168, 248, 181, 261, 197, 277, 213, 293, 228, 308, 238, 318, 229, 309, 214, 294, 198, 278, 182, 262)(170, 250, 186, 266, 202, 282, 218, 298, 233, 313, 240, 320, 231, 311, 217, 297, 200, 280, 185, 265)(172, 252, 187, 267, 203, 283, 219, 299, 234, 314, 239, 319, 232, 312, 216, 296, 201, 281, 184, 264)
	L = (1, 164)(2, 170)(3, 175)(4, 168)(5, 172)(6, 179)(7, 161)(8, 167)(9, 184)(10, 165)(11, 187)(12, 162)(13, 186)(14, 191)(15, 181)(16, 163)(17, 166)(18, 185)(19, 182)(20, 193)(21, 176)(22, 177)(23, 200)(24, 178)(25, 169)(26, 171)(27, 173)(28, 202)(29, 203)(30, 207)(31, 197)(32, 174)(33, 198)(34, 201)(35, 180)(36, 211)(37, 192)(38, 195)(39, 216)(40, 194)(41, 183)(42, 189)(43, 188)(44, 219)(45, 218)(46, 223)(47, 213)(48, 190)(49, 196)(50, 217)(51, 214)(52, 225)(53, 208)(54, 209)(55, 231)(56, 210)(57, 199)(58, 204)(59, 205)(60, 233)(61, 234)(62, 236)(63, 228)(64, 206)(65, 229)(66, 232)(67, 212)(68, 224)(69, 227)(70, 239)(71, 226)(72, 215)(73, 221)(74, 220)(75, 240)(76, 238)(77, 222)(78, 237)(79, 235)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1650
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1676 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^4, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y1 * Y2 * Y1 * Y3^2 * Y2, (Y3^-1 * Y1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 9, 89)(4, 84, 12, 92)(5, 85, 14, 94)(6, 86, 15, 95)(7, 87, 18, 98)(8, 88, 20, 100)(10, 90, 21, 101)(11, 91, 22, 102)(13, 93, 19, 99)(16, 96, 25, 105)(17, 97, 26, 106)(23, 103, 31, 111)(24, 104, 32, 112)(27, 107, 35, 115)(28, 108, 36, 116)(29, 109, 37, 117)(30, 110, 38, 118)(33, 113, 41, 121)(34, 114, 42, 122)(39, 119, 47, 127)(40, 120, 48, 128)(43, 123, 51, 131)(44, 124, 52, 132)(45, 125, 53, 133)(46, 126, 54, 134)(49, 129, 57, 137)(50, 130, 58, 138)(55, 135, 63, 143)(56, 136, 64, 144)(59, 139, 67, 147)(60, 140, 68, 148)(61, 141, 69, 149)(62, 142, 70, 150)(65, 145, 73, 153)(66, 146, 74, 154)(71, 151, 76, 156)(72, 152, 75, 155)(77, 157, 79, 159)(78, 158, 80, 160)(161, 241, 163, 243)(162, 242, 166, 246)(164, 244, 170, 250)(165, 245, 171, 251)(167, 247, 176, 256)(168, 248, 177, 257)(169, 249, 179, 259)(172, 252, 182, 262)(173, 253, 175, 255)(174, 254, 181, 261)(178, 258, 186, 266)(180, 260, 185, 265)(183, 263, 190, 270)(184, 264, 189, 269)(187, 267, 194, 274)(188, 268, 193, 273)(191, 271, 197, 277)(192, 272, 198, 278)(195, 275, 201, 281)(196, 276, 202, 282)(199, 279, 205, 285)(200, 280, 206, 286)(203, 283, 209, 289)(204, 284, 210, 290)(207, 287, 214, 294)(208, 288, 213, 293)(211, 291, 218, 298)(212, 292, 217, 297)(215, 295, 222, 302)(216, 296, 221, 301)(219, 299, 226, 306)(220, 300, 225, 305)(223, 303, 229, 309)(224, 304, 230, 310)(227, 307, 233, 313)(228, 308, 234, 314)(231, 311, 237, 317)(232, 312, 238, 318)(235, 315, 239, 319)(236, 316, 240, 320)
	L = (1, 164)(2, 167)(3, 170)(4, 173)(5, 161)(6, 176)(7, 179)(8, 162)(9, 177)(10, 175)(11, 163)(12, 183)(13, 165)(14, 184)(15, 171)(16, 169)(17, 166)(18, 187)(19, 168)(20, 188)(21, 189)(22, 190)(23, 174)(24, 172)(25, 193)(26, 194)(27, 180)(28, 178)(29, 182)(30, 181)(31, 199)(32, 200)(33, 186)(34, 185)(35, 203)(36, 204)(37, 205)(38, 206)(39, 192)(40, 191)(41, 209)(42, 210)(43, 196)(44, 195)(45, 198)(46, 197)(47, 215)(48, 216)(49, 202)(50, 201)(51, 219)(52, 220)(53, 221)(54, 222)(55, 208)(56, 207)(57, 225)(58, 226)(59, 212)(60, 211)(61, 214)(62, 213)(63, 231)(64, 232)(65, 218)(66, 217)(67, 235)(68, 236)(69, 237)(70, 238)(71, 224)(72, 223)(73, 239)(74, 240)(75, 228)(76, 227)(77, 230)(78, 229)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1681
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1677 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^4, Y3^4, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^2, Y2 * Y1 * Y3^-2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 10, 90)(5, 85, 9, 89)(6, 86, 8, 88)(11, 91, 16, 96)(12, 92, 18, 98)(13, 93, 17, 97)(14, 94, 20, 100)(15, 95, 19, 99)(21, 101, 26, 106)(22, 102, 25, 105)(23, 103, 27, 107)(24, 104, 28, 108)(29, 109, 33, 113)(30, 110, 34, 114)(31, 111, 35, 115)(32, 112, 36, 116)(37, 117, 41, 121)(38, 118, 42, 122)(39, 119, 44, 124)(40, 120, 43, 123)(45, 125, 50, 130)(46, 126, 49, 129)(47, 127, 52, 132)(48, 128, 51, 131)(53, 133, 58, 138)(54, 134, 57, 137)(55, 135, 59, 139)(56, 136, 60, 140)(61, 141, 65, 145)(62, 142, 66, 146)(63, 143, 67, 147)(64, 144, 68, 148)(69, 149, 73, 153)(70, 150, 74, 154)(71, 151, 76, 156)(72, 152, 75, 155)(77, 157, 80, 160)(78, 158, 79, 159)(161, 241, 163, 243, 171, 251, 165, 245)(162, 242, 167, 247, 176, 256, 169, 249)(164, 244, 174, 254, 166, 246, 175, 255)(168, 248, 179, 259, 170, 250, 180, 260)(172, 252, 181, 261, 173, 253, 182, 262)(177, 257, 185, 265, 178, 258, 186, 266)(183, 263, 191, 271, 184, 264, 192, 272)(187, 267, 195, 275, 188, 268, 196, 276)(189, 269, 197, 277, 190, 270, 198, 278)(193, 273, 201, 281, 194, 274, 202, 282)(199, 279, 207, 287, 200, 280, 208, 288)(203, 283, 211, 291, 204, 284, 212, 292)(205, 285, 213, 293, 206, 286, 214, 294)(209, 289, 217, 297, 210, 290, 218, 298)(215, 295, 223, 303, 216, 296, 224, 304)(219, 299, 227, 307, 220, 300, 228, 308)(221, 301, 229, 309, 222, 302, 230, 310)(225, 305, 233, 313, 226, 306, 234, 314)(231, 311, 237, 317, 232, 312, 238, 318)(235, 315, 239, 319, 236, 316, 240, 320)
	L = (1, 164)(2, 168)(3, 172)(4, 171)(5, 173)(6, 161)(7, 177)(8, 176)(9, 178)(10, 162)(11, 166)(12, 165)(13, 163)(14, 183)(15, 184)(16, 170)(17, 169)(18, 167)(19, 187)(20, 188)(21, 189)(22, 190)(23, 175)(24, 174)(25, 193)(26, 194)(27, 180)(28, 179)(29, 182)(30, 181)(31, 199)(32, 200)(33, 186)(34, 185)(35, 203)(36, 204)(37, 205)(38, 206)(39, 192)(40, 191)(41, 209)(42, 210)(43, 196)(44, 195)(45, 198)(46, 197)(47, 215)(48, 216)(49, 202)(50, 201)(51, 219)(52, 220)(53, 221)(54, 222)(55, 208)(56, 207)(57, 225)(58, 226)(59, 212)(60, 211)(61, 214)(62, 213)(63, 231)(64, 232)(65, 218)(66, 217)(67, 235)(68, 236)(69, 237)(70, 238)(71, 224)(72, 223)(73, 239)(74, 240)(75, 228)(76, 227)(77, 230)(78, 229)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1680
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1678 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^4, Y3^-2 * Y2^2, Y3^-1 * Y2^-2 * Y3^-1, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y3^-2 * Y1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 11, 91)(4, 84, 10, 90)(5, 85, 17, 97)(6, 86, 8, 88)(7, 87, 18, 98)(9, 89, 24, 104)(12, 92, 19, 99)(13, 93, 23, 103)(14, 94, 22, 102)(15, 95, 21, 101)(16, 96, 20, 100)(25, 105, 33, 113)(26, 106, 36, 116)(27, 107, 35, 115)(28, 108, 34, 114)(29, 109, 37, 117)(30, 110, 40, 120)(31, 111, 39, 119)(32, 112, 38, 118)(41, 121, 49, 129)(42, 122, 52, 132)(43, 123, 51, 131)(44, 124, 50, 130)(45, 125, 53, 133)(46, 126, 56, 136)(47, 127, 55, 135)(48, 128, 54, 134)(57, 137, 65, 145)(58, 138, 68, 148)(59, 139, 67, 147)(60, 140, 66, 146)(61, 141, 69, 149)(62, 142, 72, 152)(63, 143, 71, 151)(64, 144, 70, 150)(73, 153, 77, 157)(74, 154, 78, 158)(75, 155, 80, 160)(76, 156, 79, 159)(161, 241, 163, 243, 172, 252, 165, 245)(162, 242, 167, 247, 179, 259, 169, 249)(164, 244, 175, 255, 166, 246, 176, 256)(168, 248, 182, 262, 170, 250, 183, 263)(171, 251, 185, 265, 177, 257, 186, 266)(173, 253, 187, 267, 174, 254, 188, 268)(178, 258, 189, 269, 184, 264, 190, 270)(180, 260, 191, 271, 181, 261, 192, 272)(193, 273, 201, 281, 196, 276, 202, 282)(194, 274, 203, 283, 195, 275, 204, 284)(197, 277, 205, 285, 200, 280, 206, 286)(198, 278, 207, 287, 199, 279, 208, 288)(209, 289, 217, 297, 212, 292, 218, 298)(210, 290, 219, 299, 211, 291, 220, 300)(213, 293, 221, 301, 216, 296, 222, 302)(214, 294, 223, 303, 215, 295, 224, 304)(225, 305, 233, 313, 228, 308, 234, 314)(226, 306, 235, 315, 227, 307, 236, 316)(229, 309, 237, 317, 232, 312, 238, 318)(230, 310, 239, 319, 231, 311, 240, 320)
	L = (1, 164)(2, 168)(3, 173)(4, 172)(5, 174)(6, 161)(7, 180)(8, 179)(9, 181)(10, 162)(11, 182)(12, 166)(13, 165)(14, 163)(15, 184)(16, 178)(17, 183)(18, 175)(19, 170)(20, 169)(21, 167)(22, 177)(23, 171)(24, 176)(25, 194)(26, 195)(27, 196)(28, 193)(29, 198)(30, 199)(31, 200)(32, 197)(33, 187)(34, 186)(35, 185)(36, 188)(37, 191)(38, 190)(39, 189)(40, 192)(41, 210)(42, 211)(43, 212)(44, 209)(45, 214)(46, 215)(47, 216)(48, 213)(49, 203)(50, 202)(51, 201)(52, 204)(53, 207)(54, 206)(55, 205)(56, 208)(57, 226)(58, 227)(59, 228)(60, 225)(61, 230)(62, 231)(63, 232)(64, 229)(65, 219)(66, 218)(67, 217)(68, 220)(69, 223)(70, 222)(71, 221)(72, 224)(73, 239)(74, 240)(75, 238)(76, 237)(77, 235)(78, 236)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1679
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1679 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y3^4, Y3^-2 * Y1 * Y2 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1 * Y3^2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 20, 100, 37, 117, 53, 133, 51, 131, 35, 115, 18, 98, 5, 85)(3, 83, 11, 91, 21, 101, 41, 121, 54, 134, 71, 151, 63, 143, 47, 127, 31, 111, 13, 93)(4, 84, 15, 95, 33, 113, 49, 129, 65, 145, 69, 149, 55, 135, 39, 119, 22, 102, 9, 89)(6, 86, 19, 99, 36, 116, 52, 132, 67, 147, 70, 150, 56, 136, 40, 120, 23, 103, 10, 90)(8, 88, 24, 104, 38, 118, 57, 137, 68, 148, 66, 146, 50, 130, 34, 114, 17, 97, 26, 106)(12, 92, 29, 109, 45, 125, 61, 141, 75, 155, 79, 159, 72, 152, 59, 139, 42, 122, 27, 107)(14, 94, 32, 112, 48, 128, 64, 144, 77, 157, 78, 158, 73, 153, 58, 138, 43, 123, 25, 105)(16, 96, 28, 108, 44, 124, 60, 140, 74, 154, 80, 160, 76, 156, 62, 142, 46, 126, 30, 110)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 174, 254)(165, 245, 177, 257)(166, 246, 172, 252)(167, 247, 181, 261)(169, 249, 187, 267)(170, 250, 185, 265)(171, 251, 188, 268)(173, 253, 190, 270)(175, 255, 189, 269)(176, 256, 186, 266)(178, 258, 191, 271)(179, 259, 192, 272)(180, 260, 198, 278)(182, 262, 203, 283)(183, 263, 202, 282)(184, 264, 204, 284)(193, 273, 208, 288)(194, 274, 206, 286)(195, 275, 210, 290)(196, 276, 205, 285)(197, 277, 214, 294)(199, 279, 219, 299)(200, 280, 218, 298)(201, 281, 220, 300)(207, 287, 222, 302)(209, 289, 221, 301)(211, 291, 223, 303)(212, 292, 224, 304)(213, 293, 228, 308)(215, 295, 233, 313)(216, 296, 232, 312)(217, 297, 234, 314)(225, 305, 237, 317)(226, 306, 236, 316)(227, 307, 235, 315)(229, 309, 239, 319)(230, 310, 238, 318)(231, 311, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 176)(5, 175)(6, 161)(7, 182)(8, 185)(9, 188)(10, 162)(11, 187)(12, 186)(13, 189)(14, 163)(15, 190)(16, 166)(17, 192)(18, 193)(19, 165)(20, 199)(21, 202)(22, 204)(23, 167)(24, 203)(25, 171)(26, 174)(27, 168)(28, 170)(29, 177)(30, 179)(31, 205)(32, 173)(33, 206)(34, 208)(35, 209)(36, 178)(37, 215)(38, 218)(39, 220)(40, 180)(41, 219)(42, 184)(43, 181)(44, 183)(45, 194)(46, 196)(47, 221)(48, 191)(49, 222)(50, 224)(51, 225)(52, 195)(53, 229)(54, 232)(55, 234)(56, 197)(57, 233)(58, 201)(59, 198)(60, 200)(61, 210)(62, 212)(63, 235)(64, 207)(65, 236)(66, 237)(67, 211)(68, 238)(69, 240)(70, 213)(71, 239)(72, 217)(73, 214)(74, 216)(75, 226)(76, 227)(77, 223)(78, 231)(79, 228)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1678
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1680 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y1 * Y3 * Y1 * Y3^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1 * Y2 * Y1 * Y2 * Y3^2, Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * R * Y2 * R * Y1, (Y2 * Y1^-2)^2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 20, 100, 37, 117, 53, 133, 51, 131, 35, 115, 18, 98, 5, 85)(3, 83, 11, 91, 29, 109, 45, 125, 61, 141, 72, 152, 54, 134, 42, 122, 21, 101, 13, 93)(4, 84, 15, 95, 33, 113, 49, 129, 65, 145, 69, 149, 55, 135, 39, 119, 22, 102, 9, 89)(6, 86, 19, 99, 36, 116, 52, 132, 67, 147, 70, 150, 56, 136, 40, 120, 23, 103, 10, 90)(8, 88, 24, 104, 17, 97, 34, 114, 50, 130, 66, 146, 68, 148, 58, 138, 38, 118, 26, 106)(12, 92, 27, 107, 41, 121, 59, 139, 71, 151, 79, 159, 75, 155, 63, 143, 46, 126, 31, 111)(14, 94, 25, 105, 43, 123, 57, 137, 73, 153, 78, 158, 76, 156, 64, 144, 47, 127, 32, 112)(16, 96, 28, 108, 44, 124, 60, 140, 74, 154, 80, 160, 77, 157, 62, 142, 48, 128, 30, 110)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 174, 254)(165, 245, 177, 257)(166, 246, 172, 252)(167, 247, 181, 261)(169, 249, 187, 267)(170, 250, 185, 265)(171, 251, 190, 270)(173, 253, 188, 268)(175, 255, 191, 271)(176, 256, 184, 264)(178, 258, 189, 269)(179, 259, 192, 272)(180, 260, 198, 278)(182, 262, 203, 283)(183, 263, 201, 281)(186, 266, 204, 284)(193, 273, 207, 287)(194, 274, 208, 288)(195, 275, 210, 290)(196, 276, 206, 286)(197, 277, 214, 294)(199, 279, 219, 299)(200, 280, 217, 297)(202, 282, 220, 300)(205, 285, 222, 302)(209, 289, 223, 303)(211, 291, 221, 301)(212, 292, 224, 304)(213, 293, 228, 308)(215, 295, 233, 313)(216, 296, 231, 311)(218, 298, 234, 314)(225, 305, 236, 316)(226, 306, 237, 317)(227, 307, 235, 315)(229, 309, 239, 319)(230, 310, 238, 318)(232, 312, 240, 320)
	L = (1, 164)(2, 169)(3, 172)(4, 176)(5, 175)(6, 161)(7, 182)(8, 185)(9, 188)(10, 162)(11, 191)(12, 184)(13, 187)(14, 163)(15, 190)(16, 166)(17, 192)(18, 193)(19, 165)(20, 199)(21, 201)(22, 204)(23, 167)(24, 174)(25, 173)(26, 203)(27, 168)(28, 170)(29, 206)(30, 179)(31, 177)(32, 171)(33, 208)(34, 207)(35, 209)(36, 178)(37, 215)(38, 217)(39, 220)(40, 180)(41, 186)(42, 219)(43, 181)(44, 183)(45, 223)(46, 194)(47, 189)(48, 196)(49, 222)(50, 224)(51, 225)(52, 195)(53, 229)(54, 231)(55, 234)(56, 197)(57, 202)(58, 233)(59, 198)(60, 200)(61, 235)(62, 212)(63, 210)(64, 205)(65, 237)(66, 236)(67, 211)(68, 238)(69, 240)(70, 213)(71, 218)(72, 239)(73, 214)(74, 216)(75, 226)(76, 221)(77, 227)(78, 232)(79, 228)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1677
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1681 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C4)) : C2 (small group id <80, 40>)
Aut   = (C10 x D8) : C2 (small group id <160, 219>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^2, Y1^2 * Y3^-2, Y1^4, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y3^-1), Y2^-1 * Y1^-1 * Y2^-1 * Y1, (Y2^-1 * Y3^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, R * Y1^-1 * Y2^2 * R * Y2^-1 * Y1^-1 * Y2, Y2^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 8, 88, 5, 85)(3, 83, 11, 91, 21, 101, 15, 95)(4, 84, 10, 90, 7, 87, 12, 92)(6, 86, 9, 89, 22, 102, 18, 98)(13, 93, 28, 108, 37, 117, 31, 111)(14, 94, 27, 107, 16, 96, 26, 106)(17, 97, 25, 105, 19, 99, 24, 104)(20, 100, 23, 103, 38, 118, 34, 114)(29, 109, 44, 124, 53, 133, 47, 127)(30, 110, 42, 122, 32, 112, 43, 123)(33, 113, 40, 120, 35, 115, 41, 121)(36, 116, 39, 119, 54, 134, 50, 130)(45, 125, 60, 140, 68, 148, 63, 143)(46, 126, 59, 139, 48, 128, 58, 138)(49, 129, 57, 137, 51, 131, 56, 136)(52, 132, 55, 135, 69, 149, 66, 146)(61, 141, 70, 150, 78, 158, 76, 156)(62, 142, 73, 153, 64, 144, 74, 154)(65, 145, 71, 151, 67, 147, 72, 152)(75, 155, 79, 159, 77, 157, 80, 160)(161, 241, 163, 243, 173, 253, 189, 269, 205, 285, 221, 301, 212, 292, 196, 276, 180, 260, 166, 246)(162, 242, 169, 249, 183, 263, 199, 279, 215, 295, 230, 310, 220, 300, 204, 284, 188, 268, 171, 251)(164, 244, 177, 257, 193, 273, 209, 289, 225, 305, 237, 317, 222, 302, 208, 288, 190, 270, 176, 256)(165, 245, 178, 258, 194, 274, 210, 290, 226, 306, 236, 316, 223, 303, 207, 287, 191, 271, 175, 255)(167, 247, 179, 259, 195, 275, 211, 291, 227, 307, 235, 315, 224, 304, 206, 286, 192, 272, 174, 254)(168, 248, 181, 261, 197, 277, 213, 293, 228, 308, 238, 318, 229, 309, 214, 294, 198, 278, 182, 262)(170, 250, 186, 266, 202, 282, 218, 298, 233, 313, 240, 320, 231, 311, 217, 297, 200, 280, 185, 265)(172, 252, 187, 267, 203, 283, 219, 299, 234, 314, 239, 319, 232, 312, 216, 296, 201, 281, 184, 264)
	L = (1, 164)(2, 170)(3, 174)(4, 168)(5, 172)(6, 179)(7, 161)(8, 167)(9, 184)(10, 165)(11, 187)(12, 162)(13, 190)(14, 181)(15, 186)(16, 163)(17, 166)(18, 185)(19, 182)(20, 193)(21, 176)(22, 177)(23, 200)(24, 178)(25, 169)(26, 171)(27, 175)(28, 202)(29, 206)(30, 197)(31, 203)(32, 173)(33, 198)(34, 201)(35, 180)(36, 211)(37, 192)(38, 195)(39, 216)(40, 194)(41, 183)(42, 191)(43, 188)(44, 219)(45, 222)(46, 213)(47, 218)(48, 189)(49, 196)(50, 217)(51, 214)(52, 225)(53, 208)(54, 209)(55, 231)(56, 210)(57, 199)(58, 204)(59, 207)(60, 233)(61, 235)(62, 228)(63, 234)(64, 205)(65, 229)(66, 232)(67, 212)(68, 224)(69, 227)(70, 239)(71, 226)(72, 215)(73, 223)(74, 220)(75, 238)(76, 240)(77, 221)(78, 237)(79, 236)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1676
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1682 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x C2 x ((C10 x C2) : C2) (small group id <160, 227>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^4, Y2^4, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y3^2 * Y1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1, Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2, Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82)(3, 83, 11, 91)(4, 84, 10, 90)(5, 85, 17, 97)(6, 86, 8, 88)(7, 87, 18, 98)(9, 89, 24, 104)(12, 92, 19, 99)(13, 93, 22, 102)(14, 94, 23, 103)(15, 95, 20, 100)(16, 96, 21, 101)(25, 105, 33, 113)(26, 106, 36, 116)(27, 107, 34, 114)(28, 108, 35, 115)(29, 109, 37, 117)(30, 110, 40, 120)(31, 111, 38, 118)(32, 112, 39, 119)(41, 121, 49, 129)(42, 122, 52, 132)(43, 123, 50, 130)(44, 124, 51, 131)(45, 125, 53, 133)(46, 126, 56, 136)(47, 127, 54, 134)(48, 128, 55, 135)(57, 137, 65, 145)(58, 138, 68, 148)(59, 139, 66, 146)(60, 140, 67, 147)(61, 141, 69, 149)(62, 142, 72, 152)(63, 143, 70, 150)(64, 144, 71, 151)(73, 153, 78, 158)(74, 154, 77, 157)(75, 155, 79, 159)(76, 156, 80, 160)(161, 241, 163, 243, 172, 252, 165, 245)(162, 242, 167, 247, 179, 259, 169, 249)(164, 244, 175, 255, 166, 246, 176, 256)(168, 248, 182, 262, 170, 250, 183, 263)(171, 251, 185, 265, 177, 257, 186, 266)(173, 253, 187, 267, 174, 254, 188, 268)(178, 258, 189, 269, 184, 264, 190, 270)(180, 260, 191, 271, 181, 261, 192, 272)(193, 273, 201, 281, 196, 276, 202, 282)(194, 274, 203, 283, 195, 275, 204, 284)(197, 277, 205, 285, 200, 280, 206, 286)(198, 278, 207, 287, 199, 279, 208, 288)(209, 289, 217, 297, 212, 292, 218, 298)(210, 290, 219, 299, 211, 291, 220, 300)(213, 293, 221, 301, 216, 296, 222, 302)(214, 294, 223, 303, 215, 295, 224, 304)(225, 305, 233, 313, 228, 308, 234, 314)(226, 306, 235, 315, 227, 307, 236, 316)(229, 309, 237, 317, 232, 312, 238, 318)(230, 310, 239, 319, 231, 311, 240, 320)
	L = (1, 164)(2, 168)(3, 173)(4, 172)(5, 174)(6, 161)(7, 180)(8, 179)(9, 181)(10, 162)(11, 183)(12, 166)(13, 165)(14, 163)(15, 178)(16, 184)(17, 182)(18, 176)(19, 170)(20, 169)(21, 167)(22, 171)(23, 177)(24, 175)(25, 194)(26, 195)(27, 193)(28, 196)(29, 198)(30, 199)(31, 197)(32, 200)(33, 188)(34, 186)(35, 185)(36, 187)(37, 192)(38, 190)(39, 189)(40, 191)(41, 210)(42, 211)(43, 209)(44, 212)(45, 214)(46, 215)(47, 213)(48, 216)(49, 204)(50, 202)(51, 201)(52, 203)(53, 208)(54, 206)(55, 205)(56, 207)(57, 226)(58, 227)(59, 225)(60, 228)(61, 230)(62, 231)(63, 229)(64, 232)(65, 220)(66, 218)(67, 217)(68, 219)(69, 224)(70, 222)(71, 221)(72, 223)(73, 239)(74, 240)(75, 238)(76, 237)(77, 235)(78, 236)(79, 234)(80, 233)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1683
Graph:: simple bipartite
	v = 60 e = 160 f = 48
	degree seq :: [ 4^40, 8^20 ]

E27.1683 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 10})
Quotient :: dipole
Aut^+ = C2 x ((C10 x C2) : C2) (small group id <80, 44>)
Aut   = C2 x C2 x ((C10 x C2) : C2) (small group id <160, 227>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, Y3^-1 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y3^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 2, 82, 7, 87, 18, 98, 33, 113, 49, 129, 47, 127, 31, 111, 16, 96, 5, 85)(3, 83, 8, 88, 19, 99, 34, 114, 50, 130, 64, 144, 59, 139, 43, 123, 27, 107, 12, 92)(4, 84, 14, 94, 29, 109, 45, 125, 61, 141, 65, 145, 51, 131, 35, 115, 20, 100, 9, 89)(6, 86, 17, 97, 32, 112, 48, 128, 63, 143, 66, 146, 52, 132, 36, 116, 21, 101, 10, 90)(11, 91, 25, 105, 41, 121, 57, 137, 71, 151, 75, 155, 67, 147, 53, 133, 37, 117, 22, 102)(13, 93, 28, 108, 44, 124, 60, 140, 73, 153, 76, 156, 68, 148, 54, 134, 38, 118, 23, 103)(15, 95, 24, 104, 39, 119, 55, 135, 69, 149, 77, 157, 74, 154, 62, 142, 46, 126, 30, 110)(26, 106, 40, 120, 56, 136, 70, 150, 78, 158, 80, 160, 79, 159, 72, 152, 58, 138, 42, 122)(161, 241, 163, 243)(162, 242, 168, 248)(164, 244, 173, 253)(165, 245, 172, 252)(166, 246, 171, 251)(167, 247, 179, 259)(169, 249, 183, 263)(170, 250, 182, 262)(174, 254, 188, 268)(175, 255, 186, 266)(176, 256, 187, 267)(177, 257, 185, 265)(178, 258, 194, 274)(180, 260, 198, 278)(181, 261, 197, 277)(184, 264, 200, 280)(189, 269, 204, 284)(190, 270, 202, 282)(191, 271, 203, 283)(192, 272, 201, 281)(193, 273, 210, 290)(195, 275, 214, 294)(196, 276, 213, 293)(199, 279, 216, 296)(205, 285, 220, 300)(206, 286, 218, 298)(207, 287, 219, 299)(208, 288, 217, 297)(209, 289, 224, 304)(211, 291, 228, 308)(212, 292, 227, 307)(215, 295, 230, 310)(221, 301, 233, 313)(222, 302, 232, 312)(223, 303, 231, 311)(225, 305, 236, 316)(226, 306, 235, 315)(229, 309, 238, 318)(234, 314, 239, 319)(237, 317, 240, 320)
	L = (1, 164)(2, 169)(3, 171)(4, 175)(5, 174)(6, 161)(7, 180)(8, 182)(9, 184)(10, 162)(11, 186)(12, 185)(13, 163)(14, 190)(15, 166)(16, 189)(17, 165)(18, 195)(19, 197)(20, 199)(21, 167)(22, 200)(23, 168)(24, 170)(25, 202)(26, 173)(27, 201)(28, 172)(29, 206)(30, 177)(31, 205)(32, 176)(33, 211)(34, 213)(35, 215)(36, 178)(37, 216)(38, 179)(39, 181)(40, 183)(41, 218)(42, 188)(43, 217)(44, 187)(45, 222)(46, 192)(47, 221)(48, 191)(49, 225)(50, 227)(51, 229)(52, 193)(53, 230)(54, 194)(55, 196)(56, 198)(57, 232)(58, 204)(59, 231)(60, 203)(61, 234)(62, 208)(63, 207)(64, 235)(65, 237)(66, 209)(67, 238)(68, 210)(69, 212)(70, 214)(71, 239)(72, 220)(73, 219)(74, 223)(75, 240)(76, 224)(77, 226)(78, 228)(79, 233)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1682
Graph:: simple bipartite
	v = 48 e = 160 f = 60
	degree seq :: [ 4^40, 20^8 ]

E27.1684 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = C2 x (C5 : C8) (small group id <80, 9>)
Aut   = C2 x ((C5 x D8) : C2) (small group id <160, 152>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^8, T2^10 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 33, 49, 40, 25, 13, 5)(2, 7, 17, 31, 47, 62, 48, 32, 18, 8)(4, 11, 22, 37, 53, 63, 50, 34, 20, 10)(6, 15, 29, 45, 60, 72, 61, 46, 30, 16)(12, 21, 35, 51, 64, 73, 66, 54, 38, 23)(14, 27, 43, 58, 70, 78, 71, 59, 44, 28)(24, 39, 55, 67, 75, 79, 74, 65, 52, 36)(26, 41, 56, 68, 76, 80, 77, 69, 57, 42)(81, 82, 86, 94, 106, 104, 92, 84)(83, 88, 95, 108, 121, 116, 101, 90)(85, 87, 96, 107, 122, 119, 103, 91)(89, 98, 109, 124, 136, 132, 115, 100)(93, 97, 110, 123, 137, 135, 118, 102)(99, 112, 125, 139, 148, 145, 131, 114)(105, 111, 126, 138, 149, 147, 134, 117)(113, 128, 140, 151, 156, 154, 144, 130)(120, 127, 141, 150, 157, 155, 146, 133)(129, 142, 152, 158, 160, 159, 153, 143)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.1685
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.1685 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = C2 x (C5 : C8) (small group id <80, 9>)
Aut   = C2 x ((C5 x D8) : C2) (small group id <160, 152>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-2 * T1^-1, T2 * T1^-4 * T2 * T1^-2, (T2 * T1)^10 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 10, 90, 21, 101, 26, 106, 15, 95, 6, 86, 5, 85)(2, 82, 7, 87, 4, 84, 12, 92, 22, 102, 27, 107, 14, 94, 8, 88)(9, 89, 19, 99, 11, 91, 23, 103, 28, 108, 25, 105, 13, 93, 20, 100)(16, 96, 29, 109, 17, 97, 31, 111, 24, 104, 32, 112, 18, 98, 30, 110)(33, 113, 41, 121, 34, 114, 43, 123, 36, 116, 44, 124, 35, 115, 42, 122)(37, 117, 45, 125, 38, 118, 47, 127, 40, 120, 48, 128, 39, 119, 46, 126)(49, 129, 57, 137, 50, 130, 59, 139, 52, 132, 60, 140, 51, 131, 58, 138)(53, 133, 61, 141, 54, 134, 63, 143, 56, 136, 64, 144, 55, 135, 62, 142)(65, 145, 73, 153, 66, 146, 75, 155, 68, 148, 76, 156, 67, 147, 74, 154)(69, 149, 77, 157, 70, 150, 79, 159, 72, 152, 80, 160, 71, 151, 78, 158)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 93)(6, 94)(7, 96)(8, 98)(9, 85)(10, 84)(11, 83)(12, 97)(13, 95)(14, 106)(15, 108)(16, 88)(17, 87)(18, 107)(19, 113)(20, 115)(21, 91)(22, 90)(23, 114)(24, 92)(25, 116)(26, 102)(27, 104)(28, 101)(29, 117)(30, 119)(31, 118)(32, 120)(33, 100)(34, 99)(35, 105)(36, 103)(37, 110)(38, 109)(39, 112)(40, 111)(41, 129)(42, 131)(43, 130)(44, 132)(45, 133)(46, 135)(47, 134)(48, 136)(49, 122)(50, 121)(51, 124)(52, 123)(53, 126)(54, 125)(55, 128)(56, 127)(57, 145)(58, 147)(59, 146)(60, 148)(61, 149)(62, 151)(63, 150)(64, 152)(65, 138)(66, 137)(67, 140)(68, 139)(69, 142)(70, 141)(71, 144)(72, 143)(73, 157)(74, 158)(75, 159)(76, 160)(77, 154)(78, 156)(79, 153)(80, 155)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.1684
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.1686 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C8) (small group id <80, 9>)
Aut   = C2 x ((C5 x D8) : C2) (small group id <160, 152>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^8, Y2^10, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 14, 94, 26, 106, 24, 104, 12, 92, 4, 84)(3, 83, 8, 88, 15, 95, 28, 108, 41, 121, 36, 116, 21, 101, 10, 90)(5, 85, 7, 87, 16, 96, 27, 107, 42, 122, 39, 119, 23, 103, 11, 91)(9, 89, 18, 98, 29, 109, 44, 124, 56, 136, 52, 132, 35, 115, 20, 100)(13, 93, 17, 97, 30, 110, 43, 123, 57, 137, 55, 135, 38, 118, 22, 102)(19, 99, 32, 112, 45, 125, 59, 139, 68, 148, 65, 145, 51, 131, 34, 114)(25, 105, 31, 111, 46, 126, 58, 138, 69, 149, 67, 147, 54, 134, 37, 117)(33, 113, 48, 128, 60, 140, 71, 151, 76, 156, 74, 154, 64, 144, 50, 130)(40, 120, 47, 127, 61, 141, 70, 150, 77, 157, 75, 155, 66, 146, 53, 133)(49, 129, 62, 142, 72, 152, 78, 158, 80, 160, 79, 159, 73, 153, 63, 143)(161, 241, 163, 243, 169, 249, 179, 259, 193, 273, 209, 289, 200, 280, 185, 265, 173, 253, 165, 245)(162, 242, 167, 247, 177, 257, 191, 271, 207, 287, 222, 302, 208, 288, 192, 272, 178, 258, 168, 248)(164, 244, 171, 251, 182, 262, 197, 277, 213, 293, 223, 303, 210, 290, 194, 274, 180, 260, 170, 250)(166, 246, 175, 255, 189, 269, 205, 285, 220, 300, 232, 312, 221, 301, 206, 286, 190, 270, 176, 256)(172, 252, 181, 261, 195, 275, 211, 291, 224, 304, 233, 313, 226, 306, 214, 294, 198, 278, 183, 263)(174, 254, 187, 267, 203, 283, 218, 298, 230, 310, 238, 318, 231, 311, 219, 299, 204, 284, 188, 268)(184, 264, 199, 279, 215, 295, 227, 307, 235, 315, 239, 319, 234, 314, 225, 305, 212, 292, 196, 276)(186, 266, 201, 281, 216, 296, 228, 308, 236, 316, 240, 320, 237, 317, 229, 309, 217, 297, 202, 282)
	L = (1, 163)(2, 167)(3, 169)(4, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 179)(10, 164)(11, 182)(12, 181)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 193)(20, 170)(21, 195)(22, 197)(23, 172)(24, 199)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 209)(34, 180)(35, 211)(36, 184)(37, 213)(38, 183)(39, 215)(40, 185)(41, 216)(42, 186)(43, 218)(44, 188)(45, 220)(46, 190)(47, 222)(48, 192)(49, 200)(50, 194)(51, 224)(52, 196)(53, 223)(54, 198)(55, 227)(56, 228)(57, 202)(58, 230)(59, 204)(60, 232)(61, 206)(62, 208)(63, 210)(64, 233)(65, 212)(66, 214)(67, 235)(68, 236)(69, 217)(70, 238)(71, 219)(72, 221)(73, 226)(74, 225)(75, 239)(76, 240)(77, 229)(78, 231)(79, 234)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1687
Graph:: bipartite
	v = 18 e = 160 f = 90
	degree seq :: [ 16^10, 20^8 ]

E27.1687 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 10})
Quotient :: dipole
Aut^+ = C2 x (C5 : C8) (small group id <80, 9>)
Aut   = C2 x ((C5 x D8) : C2) (small group id <160, 152>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^8, Y3^4 * Y2 * Y3^-6 * Y2^-1, (Y3^-1 * Y1^-1)^10 ]
Map::
	R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242, 166, 246, 174, 254, 186, 266, 184, 264, 172, 252, 164, 244)(163, 243, 168, 248, 175, 255, 188, 268, 201, 281, 196, 276, 181, 261, 170, 250)(165, 245, 167, 247, 176, 256, 187, 267, 202, 282, 199, 279, 183, 263, 171, 251)(169, 249, 178, 258, 189, 269, 204, 284, 216, 296, 212, 292, 195, 275, 180, 260)(173, 253, 177, 257, 190, 270, 203, 283, 217, 297, 215, 295, 198, 278, 182, 262)(179, 259, 192, 272, 205, 285, 219, 299, 228, 308, 225, 305, 211, 291, 194, 274)(185, 265, 191, 271, 206, 286, 218, 298, 229, 309, 227, 307, 214, 294, 197, 277)(193, 273, 208, 288, 220, 300, 231, 311, 236, 316, 234, 314, 224, 304, 210, 290)(200, 280, 207, 287, 221, 301, 230, 310, 237, 317, 235, 315, 226, 306, 213, 293)(209, 289, 222, 302, 232, 312, 238, 318, 240, 320, 239, 319, 233, 313, 223, 303)
	L = (1, 163)(2, 167)(3, 169)(4, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 179)(10, 164)(11, 182)(12, 181)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 193)(20, 170)(21, 195)(22, 197)(23, 172)(24, 199)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 209)(34, 180)(35, 211)(36, 184)(37, 213)(38, 183)(39, 215)(40, 185)(41, 216)(42, 186)(43, 218)(44, 188)(45, 220)(46, 190)(47, 222)(48, 192)(49, 200)(50, 194)(51, 224)(52, 196)(53, 223)(54, 198)(55, 227)(56, 228)(57, 202)(58, 230)(59, 204)(60, 232)(61, 206)(62, 208)(63, 210)(64, 233)(65, 212)(66, 214)(67, 235)(68, 236)(69, 217)(70, 238)(71, 219)(72, 221)(73, 226)(74, 225)(75, 239)(76, 240)(77, 229)(78, 231)(79, 234)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 16, 20 ), ( 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1686
Graph:: simple bipartite
	v = 90 e = 160 f = 18
	degree seq :: [ 2^80, 16^10 ]

E27.1688 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = (C5 : C8) : C2 (small group id <80, 10>)
Aut   = (C2 x D40) : C2 (small group id <160, 170>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2, T2 * T1^-3 * T2 * T1^-1, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^10 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 46, 62, 52, 35, 17, 5)(2, 7, 22, 40, 56, 71, 60, 44, 26, 8)(4, 12, 32, 49, 65, 77, 63, 48, 30, 14)(6, 19, 37, 53, 68, 78, 69, 54, 38, 20)(9, 27, 15, 33, 50, 66, 75, 61, 45, 28)(11, 18, 16, 34, 51, 67, 76, 64, 47, 31)(13, 24, 42, 58, 73, 79, 70, 55, 39, 21)(23, 36, 25, 43, 59, 74, 80, 72, 57, 41)(81, 82, 86, 98, 116, 107, 93, 84)(83, 89, 99, 94, 105, 88, 104, 91)(85, 95, 100, 92, 103, 87, 101, 96)(90, 106, 117, 111, 123, 108, 122, 110)(97, 102, 118, 114, 121, 113, 119, 112)(109, 125, 133, 128, 139, 124, 138, 127)(115, 130, 134, 129, 137, 120, 135, 131)(126, 140, 148, 144, 154, 141, 153, 143)(132, 136, 149, 147, 152, 146, 150, 145)(142, 155, 158, 157, 160, 151, 159, 156)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: reflexible
Dual of E27.1689
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.1689 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = (C5 : C8) : C2 (small group id <80, 10>)
Aut   = (C2 x D40) : C2 (small group id <160, 170>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T2)^2, (F * T1)^2, T1^8, (T2^-1 * T1^-1)^10 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 6, 86, 15, 95, 26, 106, 23, 103, 11, 91, 5, 85)(2, 82, 7, 87, 14, 94, 27, 107, 22, 102, 12, 92, 4, 84, 8, 88)(9, 89, 19, 99, 28, 108, 25, 105, 13, 93, 21, 101, 10, 90, 20, 100)(16, 96, 29, 109, 24, 104, 32, 112, 18, 98, 31, 111, 17, 97, 30, 110)(33, 113, 41, 121, 36, 116, 44, 124, 35, 115, 43, 123, 34, 114, 42, 122)(37, 117, 45, 125, 40, 120, 48, 128, 39, 119, 47, 127, 38, 118, 46, 126)(49, 129, 57, 137, 52, 132, 60, 140, 51, 131, 59, 139, 50, 130, 58, 138)(53, 133, 61, 141, 56, 136, 64, 144, 55, 135, 63, 143, 54, 134, 62, 142)(65, 145, 73, 153, 68, 148, 76, 156, 67, 147, 75, 155, 66, 146, 74, 154)(69, 149, 77, 157, 72, 152, 80, 160, 71, 151, 79, 159, 70, 150, 78, 158)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 90)(6, 94)(7, 96)(8, 97)(9, 95)(10, 83)(11, 84)(12, 98)(13, 85)(14, 106)(15, 108)(16, 107)(17, 87)(18, 88)(19, 113)(20, 114)(21, 115)(22, 91)(23, 93)(24, 92)(25, 116)(26, 102)(27, 104)(28, 103)(29, 117)(30, 118)(31, 119)(32, 120)(33, 105)(34, 99)(35, 100)(36, 101)(37, 112)(38, 109)(39, 110)(40, 111)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 124)(50, 121)(51, 122)(52, 123)(53, 128)(54, 125)(55, 126)(56, 127)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 140)(66, 137)(67, 138)(68, 139)(69, 144)(70, 141)(71, 142)(72, 143)(73, 159)(74, 160)(75, 157)(76, 158)(77, 154)(78, 155)(79, 156)(80, 153)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.1688
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.1690 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 10})
Quotient :: dipole
Aut^+ = (C5 : C8) : C2 (small group id <80, 10>)
Aut   = (C2 x D40) : C2 (small group id <160, 170>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^5, Y2^10, Y2 * Y1^-1 * Y2^-4 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-3 * Y1^-1, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 18, 98, 36, 116, 27, 107, 13, 93, 4, 84)(3, 83, 9, 89, 19, 99, 14, 94, 25, 105, 8, 88, 24, 104, 11, 91)(5, 85, 15, 95, 20, 100, 12, 92, 23, 103, 7, 87, 21, 101, 16, 96)(10, 90, 26, 106, 37, 117, 31, 111, 43, 123, 28, 108, 42, 122, 30, 110)(17, 97, 22, 102, 38, 118, 34, 114, 41, 121, 33, 113, 39, 119, 32, 112)(29, 109, 45, 125, 53, 133, 48, 128, 59, 139, 44, 124, 58, 138, 47, 127)(35, 115, 50, 130, 54, 134, 49, 129, 57, 137, 40, 120, 55, 135, 51, 131)(46, 126, 60, 140, 68, 148, 64, 144, 74, 154, 61, 141, 73, 153, 63, 143)(52, 132, 56, 136, 69, 149, 67, 147, 72, 152, 66, 146, 70, 150, 65, 145)(62, 142, 75, 155, 78, 158, 77, 157, 80, 160, 71, 151, 79, 159, 76, 156)(161, 241, 163, 243, 170, 250, 189, 269, 206, 286, 222, 302, 212, 292, 195, 275, 177, 257, 165, 245)(162, 242, 167, 247, 182, 262, 200, 280, 216, 296, 231, 311, 220, 300, 204, 284, 186, 266, 168, 248)(164, 244, 172, 252, 192, 272, 209, 289, 225, 305, 237, 317, 223, 303, 208, 288, 190, 270, 174, 254)(166, 246, 179, 259, 197, 277, 213, 293, 228, 308, 238, 318, 229, 309, 214, 294, 198, 278, 180, 260)(169, 249, 187, 267, 175, 255, 193, 273, 210, 290, 226, 306, 235, 315, 221, 301, 205, 285, 188, 268)(171, 251, 178, 258, 176, 256, 194, 274, 211, 291, 227, 307, 236, 316, 224, 304, 207, 287, 191, 271)(173, 253, 184, 264, 202, 282, 218, 298, 233, 313, 239, 319, 230, 310, 215, 295, 199, 279, 181, 261)(183, 263, 196, 276, 185, 265, 203, 283, 219, 299, 234, 314, 240, 320, 232, 312, 217, 297, 201, 281)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 179)(7, 182)(8, 162)(9, 187)(10, 189)(11, 178)(12, 192)(13, 184)(14, 164)(15, 193)(16, 194)(17, 165)(18, 176)(19, 197)(20, 166)(21, 173)(22, 200)(23, 196)(24, 202)(25, 203)(26, 168)(27, 175)(28, 169)(29, 206)(30, 174)(31, 171)(32, 209)(33, 210)(34, 211)(35, 177)(36, 185)(37, 213)(38, 180)(39, 181)(40, 216)(41, 183)(42, 218)(43, 219)(44, 186)(45, 188)(46, 222)(47, 191)(48, 190)(49, 225)(50, 226)(51, 227)(52, 195)(53, 228)(54, 198)(55, 199)(56, 231)(57, 201)(58, 233)(59, 234)(60, 204)(61, 205)(62, 212)(63, 208)(64, 207)(65, 237)(66, 235)(67, 236)(68, 238)(69, 214)(70, 215)(71, 220)(72, 217)(73, 239)(74, 240)(75, 221)(76, 224)(77, 223)(78, 229)(79, 230)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1691
Graph:: bipartite
	v = 18 e = 160 f = 90
	degree seq :: [ 16^10, 20^8 ]

E27.1691 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {8, 8, 10})
Quotient :: dipole
Aut^+ = (C5 : C8) : C2 (small group id <80, 10>)
Aut   = (C2 x D40) : C2 (small group id <160, 170>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y3^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, (Y3^-1 * Y2 * Y3^-1 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-4 * Y2^-1 * Y3^2 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^10 ]
Map::
	R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242, 166, 246, 178, 258, 196, 276, 187, 267, 173, 253, 164, 244)(163, 243, 169, 249, 179, 259, 174, 254, 185, 265, 168, 248, 184, 264, 171, 251)(165, 245, 175, 255, 180, 260, 172, 252, 183, 263, 167, 247, 181, 261, 176, 256)(170, 250, 186, 266, 197, 277, 191, 271, 203, 283, 188, 268, 202, 282, 190, 270)(177, 257, 182, 262, 198, 278, 194, 274, 201, 281, 193, 273, 199, 279, 192, 272)(189, 269, 205, 285, 213, 293, 208, 288, 219, 299, 204, 284, 218, 298, 207, 287)(195, 275, 210, 290, 214, 294, 209, 289, 217, 297, 200, 280, 215, 295, 211, 291)(206, 286, 220, 300, 228, 308, 224, 304, 234, 314, 221, 301, 233, 313, 223, 303)(212, 292, 216, 296, 229, 309, 227, 307, 232, 312, 226, 306, 230, 310, 225, 305)(222, 302, 235, 315, 238, 318, 237, 317, 240, 320, 231, 311, 239, 319, 236, 316)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 179)(7, 182)(8, 162)(9, 187)(10, 189)(11, 178)(12, 192)(13, 184)(14, 164)(15, 193)(16, 194)(17, 165)(18, 176)(19, 197)(20, 166)(21, 173)(22, 200)(23, 196)(24, 202)(25, 203)(26, 168)(27, 175)(28, 169)(29, 206)(30, 174)(31, 171)(32, 209)(33, 210)(34, 211)(35, 177)(36, 185)(37, 213)(38, 180)(39, 181)(40, 216)(41, 183)(42, 218)(43, 219)(44, 186)(45, 188)(46, 222)(47, 191)(48, 190)(49, 225)(50, 226)(51, 227)(52, 195)(53, 228)(54, 198)(55, 199)(56, 231)(57, 201)(58, 233)(59, 234)(60, 204)(61, 205)(62, 212)(63, 208)(64, 207)(65, 237)(66, 235)(67, 236)(68, 238)(69, 214)(70, 215)(71, 220)(72, 217)(73, 239)(74, 240)(75, 221)(76, 224)(77, 223)(78, 229)(79, 230)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 16, 20 ), ( 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20, 16, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1690
Graph:: simple bipartite
	v = 90 e = 160 f = 18
	degree seq :: [ 2^80, 16^10 ]

E27.1692 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = C2 x (C5 : C8) (small group id <80, 32>)
|r| :: 1
Presentation :: [ X2^-2 * X1^-1 * X2^-1 * X1 * X2^-1, X2^-1 * X1^-1 * X2^3 * X1, X1^8, (X2^2 * X1^-2)^4 ]
Map:: non-degenerate
	R = (1, 2, 6, 18, 38, 35, 13, 4)(3, 9, 20, 43, 59, 53, 31, 11)(5, 15, 19, 41, 60, 57, 34, 16)(7, 21, 40, 63, 58, 36, 14, 23)(8, 24, 39, 61, 56, 33, 12, 25)(10, 28, 44, 65, 74, 69, 50, 29)(17, 27, 42, 66, 75, 71, 52, 30)(22, 46, 64, 76, 73, 55, 37, 47)(26, 45, 62, 77, 72, 54, 32, 48)(49, 67, 78, 80, 79, 70, 51, 68)(81, 83, 90, 103, 128, 148, 127, 105, 97, 85)(82, 87, 102, 95, 108, 129, 107, 89, 106, 88)(84, 92, 112, 91, 110, 131, 109, 96, 117, 94)(86, 99, 122, 104, 126, 147, 125, 101, 124, 100)(93, 114, 132, 113, 135, 150, 134, 116, 130, 111)(98, 119, 142, 123, 146, 158, 145, 121, 144, 120)(115, 138, 153, 137, 149, 159, 151, 133, 152, 136)(118, 139, 154, 143, 157, 160, 156, 141, 155, 140)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.1693 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = C2 x (C5 : C8) (small group id <80, 32>)
|r| :: 1
Presentation :: [ X2 * X1^3 * X2 * X1^-1, X2 * X1^-1 * X2^-3 * X1^-1, X1^-2 * X2^-1 * X1 * X2^-1 * X1^-1, X1^-2 * X2^4 * X1^-2, X2^-2 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-2 ]
Map:: non-degenerate
	R = (1, 81, 2, 82, 6, 86, 18, 98, 42, 122, 32, 112, 13, 93, 4, 84)(3, 83, 9, 89, 25, 105, 8, 88, 24, 104, 54, 134, 33, 113, 11, 91)(5, 85, 15, 95, 39, 119, 61, 141, 30, 110, 12, 92, 34, 114, 16, 96)(7, 87, 21, 101, 47, 127, 20, 100, 46, 126, 70, 150, 53, 133, 23, 103)(10, 90, 29, 109, 59, 139, 28, 108, 17, 97, 41, 121, 62, 142, 31, 111)(14, 94, 19, 99, 44, 124, 67, 147, 43, 123, 36, 116, 57, 137, 37, 117)(22, 102, 51, 131, 40, 120, 50, 130, 26, 106, 56, 136, 75, 155, 52, 132)(27, 107, 45, 125, 69, 149, 55, 135, 68, 148, 48, 128, 72, 152, 58, 138)(35, 115, 63, 143, 73, 153, 49, 129, 38, 118, 65, 145, 71, 151, 64, 144)(60, 140, 74, 154, 79, 159, 77, 157, 66, 146, 76, 156, 80, 160, 78, 158)
	L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 110)(11, 112)(12, 115)(13, 116)(14, 84)(15, 118)(16, 109)(17, 85)(18, 95)(19, 125)(20, 86)(21, 129)(22, 91)(23, 93)(24, 97)(25, 131)(26, 88)(27, 137)(28, 89)(29, 140)(30, 122)(31, 134)(32, 126)(33, 136)(34, 132)(35, 123)(36, 128)(37, 143)(38, 94)(39, 130)(40, 96)(41, 146)(42, 104)(43, 98)(44, 108)(45, 103)(46, 106)(47, 149)(48, 100)(49, 114)(50, 101)(51, 154)(52, 150)(53, 152)(54, 148)(55, 105)(56, 156)(57, 111)(58, 113)(59, 117)(60, 155)(61, 121)(62, 147)(63, 158)(64, 119)(65, 157)(66, 120)(67, 145)(68, 124)(69, 159)(70, 144)(71, 127)(72, 160)(73, 133)(74, 138)(75, 141)(76, 135)(77, 139)(78, 142)(79, 153)(80, 151)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.1694 :: Family: { 2*ex } :: Oriented family(ies): { E3c }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ F^2, F * T1 * F * T2, T1 * T2^-1 * T1 * T2^3, T2 * T1^3 * T2 * T1^-1, T1^-3 * T2 * T1^-1 * T2 * T1^-2, T2 * T1^-1 * T2^5 * T1^-1, T2^2 * T1^-1 * T2^-1 * T1^2 * T2 * T1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 30, 42, 24, 17, 5)(2, 7, 22, 11, 32, 46, 26, 8)(4, 12, 35, 43, 18, 15, 38, 14)(6, 19, 45, 23, 13, 36, 48, 20)(9, 27, 57, 31, 54, 68, 44, 28)(16, 29, 60, 75, 61, 41, 66, 40)(21, 49, 34, 52, 70, 64, 39, 50)(25, 51, 74, 58, 33, 56, 76, 55)(37, 63, 78, 62, 67, 65, 77, 59)(47, 69, 79, 73, 53, 72, 80, 71)(81, 82, 86, 98, 122, 112, 93, 84)(83, 89, 105, 88, 104, 134, 113, 91)(85, 95, 119, 141, 110, 92, 114, 96)(87, 101, 127, 100, 126, 150, 133, 103)(90, 109, 139, 108, 97, 121, 142, 111)(94, 99, 124, 147, 123, 116, 137, 117)(102, 131, 120, 130, 106, 136, 155, 132)(107, 125, 149, 135, 148, 128, 152, 138)(115, 143, 153, 129, 118, 145, 151, 144)(140, 154, 159, 157, 146, 156, 160, 158)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1695
Transitivity :: ET+ VT AT
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.1695 :: Family: { 2ex } :: Oriented family(ies): { E3*c }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2^-1 * T1 * T2^-3 * T1^-1, T1 * T2^3 * T1^-1 * T2, T2 * T1^-1 * T2^-3 * T1, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, (T2^-1 * T1^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 81, 3, 83, 10, 90, 23, 103, 48, 128, 68, 148, 47, 127, 25, 105, 17, 97, 5, 85)(2, 82, 7, 87, 22, 102, 15, 95, 28, 108, 49, 129, 27, 107, 9, 89, 26, 106, 8, 88)(4, 84, 12, 92, 32, 112, 11, 91, 30, 110, 51, 131, 29, 109, 16, 96, 37, 117, 14, 94)(6, 86, 19, 99, 42, 122, 24, 104, 46, 126, 67, 147, 45, 125, 21, 101, 44, 124, 20, 100)(13, 93, 34, 114, 52, 132, 33, 113, 55, 135, 70, 150, 54, 134, 36, 116, 50, 130, 31, 111)(18, 98, 39, 119, 62, 142, 43, 123, 66, 146, 78, 158, 65, 145, 41, 121, 64, 144, 40, 120)(35, 115, 58, 138, 73, 153, 57, 137, 69, 149, 79, 159, 71, 151, 53, 133, 72, 152, 56, 136)(38, 118, 59, 139, 74, 154, 63, 143, 77, 157, 80, 160, 76, 156, 61, 141, 75, 155, 60, 140)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 95)(6, 98)(7, 101)(8, 104)(9, 100)(10, 108)(11, 83)(12, 105)(13, 84)(14, 103)(15, 99)(16, 85)(17, 107)(18, 118)(19, 121)(20, 123)(21, 120)(22, 126)(23, 87)(24, 119)(25, 88)(26, 125)(27, 122)(28, 124)(29, 90)(30, 97)(31, 91)(32, 128)(33, 92)(34, 96)(35, 93)(36, 94)(37, 127)(38, 115)(39, 141)(40, 143)(41, 140)(42, 146)(43, 139)(44, 145)(45, 142)(46, 144)(47, 102)(48, 106)(49, 147)(50, 109)(51, 148)(52, 110)(53, 111)(54, 112)(55, 117)(56, 113)(57, 114)(58, 116)(59, 133)(60, 137)(61, 136)(62, 157)(63, 138)(64, 156)(65, 154)(66, 155)(67, 158)(68, 129)(69, 130)(70, 131)(71, 132)(72, 134)(73, 135)(74, 149)(75, 151)(76, 153)(77, 152)(78, 160)(79, 150)(80, 159)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1694
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.1696 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1^-1 * Y2^-1 * Y3^2, Y2^-1 * Y3^-1 * Y2^2 * Y1, Y1 * Y3 * Y2 * Y3^-2, Y1^-2 * Y2^-1 * Y1 * Y3, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1 * Y3^-1, Y1^8, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2^8 ]
Map:: polytopal non-degenerate
	R = (1, 81, 4, 84, 17, 97, 12, 92, 42, 122, 69, 149, 41, 121, 23, 103, 31, 111, 7, 87)(2, 82, 9, 89, 35, 115, 28, 108, 19, 99, 53, 133, 27, 107, 6, 86, 25, 105, 11, 91)(3, 83, 5, 85, 21, 101, 16, 96, 18, 98, 52, 132, 51, 131, 29, 109, 30, 110, 15, 95)(8, 88, 33, 113, 61, 141, 40, 120, 36, 116, 54, 134, 26, 106, 10, 90, 38, 118, 24, 104)(13, 93, 14, 94, 47, 127, 20, 100, 22, 102, 58, 138, 56, 136, 49, 129, 50, 130, 45, 125)(32, 112, 63, 143, 60, 140, 59, 139, 65, 145, 70, 150, 39, 119, 34, 114, 67, 147, 37, 117)(43, 123, 44, 124, 57, 137, 46, 126, 48, 128, 78, 158, 77, 157, 75, 155, 76, 156, 55, 135)(62, 142, 73, 153, 72, 152, 71, 151, 74, 154, 80, 160, 68, 148, 64, 144, 79, 159, 66, 146)(161, 162, 168, 192, 222, 206, 182, 165)(163, 172, 169, 170, 197, 231, 208, 174)(164, 166, 184, 219, 233, 203, 180, 178)(167, 188, 193, 194, 226, 237, 218, 190)(171, 200, 223, 224, 217, 209, 181, 183)(173, 176, 202, 185, 186, 220, 234, 204)(175, 201, 195, 196, 227, 228, 238, 210)(177, 179, 198, 199, 232, 235, 207, 189)(187, 221, 225, 239, 215, 216, 212, 191)(205, 211, 229, 213, 214, 230, 240, 236)(241, 243, 253, 283, 302, 277, 266, 246)(242, 247, 269, 254, 286, 306, 279, 250)(244, 256, 285, 315, 313, 300, 294, 259)(245, 260, 295, 304, 272, 264, 267, 263)(248, 251, 281, 270, 262, 297, 308, 274)(249, 257, 291, 290, 288, 312, 310, 276)(252, 255, 289, 284, 311, 307, 280, 265)(258, 287, 317, 319, 299, 278, 268, 271)(261, 296, 316, 314, 303, 301, 293, 282)(273, 275, 309, 292, 298, 318, 320, 305)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1699
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1697 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 10})
Quotient :: edge^2
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y1^-3 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1^-1 * Y2^5 * Y1^-1, Y1^2 * Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1, (Y1^-1 * Y3^-1 * Y2^-1)^10 ]
Map:: polytopal
	R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 162, 166, 178, 202, 192, 173, 164)(163, 169, 185, 168, 184, 214, 193, 171)(165, 175, 199, 221, 190, 172, 194, 176)(167, 181, 207, 180, 206, 230, 213, 183)(170, 189, 219, 188, 177, 201, 222, 191)(174, 179, 204, 227, 203, 196, 217, 197)(182, 211, 200, 210, 186, 216, 235, 212)(187, 205, 229, 215, 228, 208, 232, 218)(195, 223, 233, 209, 198, 225, 231, 224)(220, 234, 239, 237, 226, 236, 240, 238)(241, 243, 250, 270, 282, 264, 257, 245)(242, 247, 262, 251, 272, 286, 266, 248)(244, 252, 275, 283, 258, 255, 278, 254)(246, 259, 285, 263, 253, 276, 288, 260)(249, 267, 297, 271, 294, 308, 284, 268)(256, 269, 300, 315, 301, 281, 306, 280)(261, 289, 274, 292, 310, 304, 279, 290)(265, 291, 314, 298, 273, 296, 316, 295)(277, 303, 318, 302, 307, 305, 317, 299)(287, 309, 319, 313, 293, 312, 320, 311)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 40, 40 ), ( 40^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1698
Graph:: simple bipartite
	v = 100 e = 160 f = 8
	degree seq :: [ 2^80, 8^20 ]

E27.1698 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1^-1 * Y2^-1 * Y3^2, Y2^-1 * Y3^-1 * Y2^2 * Y1, Y1 * Y3 * Y2 * Y3^-2, Y1^-2 * Y2^-1 * Y1 * Y3, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1 * Y3^-1, Y1^8, Y2 * Y1^-2 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2^8 ]
Map::
	R = (1, 81, 161, 241, 4, 84, 164, 244, 17, 97, 177, 257, 12, 92, 172, 252, 42, 122, 202, 282, 69, 149, 229, 309, 41, 121, 201, 281, 23, 103, 183, 263, 31, 111, 191, 271, 7, 87, 167, 247)(2, 82, 162, 242, 9, 89, 169, 249, 35, 115, 195, 275, 28, 108, 188, 268, 19, 99, 179, 259, 53, 133, 213, 293, 27, 107, 187, 267, 6, 86, 166, 246, 25, 105, 185, 265, 11, 91, 171, 251)(3, 83, 163, 243, 5, 85, 165, 245, 21, 101, 181, 261, 16, 96, 176, 256, 18, 98, 178, 258, 52, 132, 212, 292, 51, 131, 211, 291, 29, 109, 189, 269, 30, 110, 190, 270, 15, 95, 175, 255)(8, 88, 168, 248, 33, 113, 193, 273, 61, 141, 221, 301, 40, 120, 200, 280, 36, 116, 196, 276, 54, 134, 214, 294, 26, 106, 186, 266, 10, 90, 170, 250, 38, 118, 198, 278, 24, 104, 184, 264)(13, 93, 173, 253, 14, 94, 174, 254, 47, 127, 207, 287, 20, 100, 180, 260, 22, 102, 182, 262, 58, 138, 218, 298, 56, 136, 216, 296, 49, 129, 209, 289, 50, 130, 210, 290, 45, 125, 205, 285)(32, 112, 192, 272, 63, 143, 223, 303, 60, 140, 220, 300, 59, 139, 219, 299, 65, 145, 225, 305, 70, 150, 230, 310, 39, 119, 199, 279, 34, 114, 194, 274, 67, 147, 227, 307, 37, 117, 197, 277)(43, 123, 203, 283, 44, 124, 204, 284, 57, 137, 217, 297, 46, 126, 206, 286, 48, 128, 208, 288, 78, 158, 238, 318, 77, 157, 237, 317, 75, 155, 235, 315, 76, 156, 236, 316, 55, 135, 215, 295)(62, 142, 222, 302, 73, 153, 233, 313, 72, 152, 232, 312, 71, 151, 231, 311, 74, 154, 234, 314, 80, 160, 240, 320, 68, 148, 228, 308, 64, 144, 224, 304, 79, 159, 239, 319, 66, 146, 226, 306)
	L = (1, 82)(2, 88)(3, 92)(4, 86)(5, 81)(6, 104)(7, 108)(8, 112)(9, 90)(10, 117)(11, 120)(12, 89)(13, 96)(14, 83)(15, 121)(16, 122)(17, 99)(18, 84)(19, 118)(20, 98)(21, 103)(22, 85)(23, 91)(24, 139)(25, 106)(26, 140)(27, 141)(28, 113)(29, 97)(30, 87)(31, 107)(32, 142)(33, 114)(34, 146)(35, 116)(36, 147)(37, 151)(38, 119)(39, 152)(40, 143)(41, 115)(42, 105)(43, 100)(44, 93)(45, 131)(46, 102)(47, 109)(48, 94)(49, 101)(50, 95)(51, 149)(52, 111)(53, 134)(54, 150)(55, 136)(56, 132)(57, 129)(58, 110)(59, 153)(60, 154)(61, 145)(62, 126)(63, 144)(64, 137)(65, 159)(66, 157)(67, 148)(68, 158)(69, 133)(70, 160)(71, 128)(72, 155)(73, 123)(74, 124)(75, 127)(76, 125)(77, 138)(78, 130)(79, 135)(80, 156)(161, 243)(162, 247)(163, 253)(164, 256)(165, 260)(166, 241)(167, 269)(168, 251)(169, 257)(170, 242)(171, 281)(172, 255)(173, 283)(174, 286)(175, 289)(176, 285)(177, 291)(178, 287)(179, 244)(180, 295)(181, 296)(182, 297)(183, 245)(184, 267)(185, 252)(186, 246)(187, 263)(188, 271)(189, 254)(190, 262)(191, 258)(192, 264)(193, 275)(194, 248)(195, 309)(196, 249)(197, 266)(198, 268)(199, 250)(200, 265)(201, 270)(202, 261)(203, 302)(204, 311)(205, 315)(206, 306)(207, 317)(208, 312)(209, 284)(210, 288)(211, 290)(212, 298)(213, 282)(214, 259)(215, 304)(216, 316)(217, 308)(218, 318)(219, 278)(220, 294)(221, 293)(222, 277)(223, 301)(224, 272)(225, 273)(226, 279)(227, 280)(228, 274)(229, 292)(230, 276)(231, 307)(232, 310)(233, 300)(234, 303)(235, 313)(236, 314)(237, 319)(238, 320)(239, 299)(240, 305)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1697
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 160 f = 100
	degree seq :: [ 40^8 ]

E27.1699 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 10})
Quotient :: loop^2
Aut^+ = C2 x (C5 : C8) (small group id <80, 32>)
Aut   = (C2 x (C5 : C8)) : C2 (small group id <160, 78>)
|r| :: 2
Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y1^-3 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1^-1 * Y2^5 * Y1^-1, Y1^2 * Y2 * Y1 * Y2^2 * Y1^-1 * Y2^-1, (Y1^-1 * Y3^-1 * Y2^-1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 161, 241)(2, 82, 162, 242)(3, 83, 163, 243)(4, 84, 164, 244)(5, 85, 165, 245)(6, 86, 166, 246)(7, 87, 167, 247)(8, 88, 168, 248)(9, 89, 169, 249)(10, 90, 170, 250)(11, 91, 171, 251)(12, 92, 172, 252)(13, 93, 173, 253)(14, 94, 174, 254)(15, 95, 175, 255)(16, 96, 176, 256)(17, 97, 177, 257)(18, 98, 178, 258)(19, 99, 179, 259)(20, 100, 180, 260)(21, 101, 181, 261)(22, 102, 182, 262)(23, 103, 183, 263)(24, 104, 184, 264)(25, 105, 185, 265)(26, 106, 186, 266)(27, 107, 187, 267)(28, 108, 188, 268)(29, 109, 189, 269)(30, 110, 190, 270)(31, 111, 191, 271)(32, 112, 192, 272)(33, 113, 193, 273)(34, 114, 194, 274)(35, 115, 195, 275)(36, 116, 196, 276)(37, 117, 197, 277)(38, 118, 198, 278)(39, 119, 199, 279)(40, 120, 200, 280)(41, 121, 201, 281)(42, 122, 202, 282)(43, 123, 203, 283)(44, 124, 204, 284)(45, 125, 205, 285)(46, 126, 206, 286)(47, 127, 207, 287)(48, 128, 208, 288)(49, 129, 209, 289)(50, 130, 210, 290)(51, 131, 211, 291)(52, 132, 212, 292)(53, 133, 213, 293)(54, 134, 214, 294)(55, 135, 215, 295)(56, 136, 216, 296)(57, 137, 217, 297)(58, 138, 218, 298)(59, 139, 219, 299)(60, 140, 220, 300)(61, 141, 221, 301)(62, 142, 222, 302)(63, 143, 223, 303)(64, 144, 224, 304)(65, 145, 225, 305)(66, 146, 226, 306)(67, 147, 227, 307)(68, 148, 228, 308)(69, 149, 229, 309)(70, 150, 230, 310)(71, 151, 231, 311)(72, 152, 232, 312)(73, 153, 233, 313)(74, 154, 234, 314)(75, 155, 235, 315)(76, 156, 236, 316)(77, 157, 237, 317)(78, 158, 238, 318)(79, 159, 239, 319)(80, 160, 240, 320)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 95)(6, 98)(7, 101)(8, 104)(9, 105)(10, 109)(11, 83)(12, 114)(13, 84)(14, 99)(15, 119)(16, 85)(17, 121)(18, 122)(19, 124)(20, 126)(21, 127)(22, 131)(23, 87)(24, 134)(25, 88)(26, 136)(27, 125)(28, 97)(29, 139)(30, 92)(31, 90)(32, 93)(33, 91)(34, 96)(35, 143)(36, 137)(37, 94)(38, 145)(39, 141)(40, 130)(41, 142)(42, 112)(43, 116)(44, 147)(45, 149)(46, 150)(47, 100)(48, 152)(49, 118)(50, 106)(51, 120)(52, 102)(53, 103)(54, 113)(55, 148)(56, 155)(57, 117)(58, 107)(59, 108)(60, 154)(61, 110)(62, 111)(63, 153)(64, 115)(65, 151)(66, 156)(67, 123)(68, 128)(69, 135)(70, 133)(71, 144)(72, 138)(73, 129)(74, 159)(75, 132)(76, 160)(77, 146)(78, 140)(79, 157)(80, 158)(161, 243)(162, 247)(163, 250)(164, 252)(165, 241)(166, 259)(167, 262)(168, 242)(169, 267)(170, 270)(171, 272)(172, 275)(173, 276)(174, 244)(175, 278)(176, 269)(177, 245)(178, 255)(179, 285)(180, 246)(181, 289)(182, 251)(183, 253)(184, 257)(185, 291)(186, 248)(187, 297)(188, 249)(189, 300)(190, 282)(191, 294)(192, 286)(193, 296)(194, 292)(195, 283)(196, 288)(197, 303)(198, 254)(199, 290)(200, 256)(201, 306)(202, 264)(203, 258)(204, 268)(205, 263)(206, 266)(207, 309)(208, 260)(209, 274)(210, 261)(211, 314)(212, 310)(213, 312)(214, 308)(215, 265)(216, 316)(217, 271)(218, 273)(219, 277)(220, 315)(221, 281)(222, 307)(223, 318)(224, 279)(225, 317)(226, 280)(227, 305)(228, 284)(229, 319)(230, 304)(231, 287)(232, 320)(233, 293)(234, 298)(235, 301)(236, 295)(237, 299)(238, 302)(239, 313)(240, 311)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1696
Transitivity :: VT+
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1700 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = (C5 : C8) : C2 (small group id <80, 33>)
|r| :: 1
Presentation :: [ X2^-1 * X1^-2 * X2^-1 * X1^2, X1^-1 * X2^4 * X1 * X2^2, X2^-1 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-1, X1^-2 * X2 * X1^-1 * X2 * X1^-1 * X2^-2, X2 * X1^-3 * X2^3 * X1^-1, X2^2 * X1 * X2^-4 * X1^-1, X1^8 ]
Map:: non-degenerate
	R = (1, 2, 6, 18, 48, 38, 13, 4)(3, 9, 20, 53, 75, 68, 33, 11)(5, 15, 19, 51, 76, 58, 37, 16)(7, 21, 50, 30, 72, 39, 14, 23)(8, 24, 49, 47, 69, 36, 12, 25)(10, 29, 54, 44, 61, 41, 55, 31)(17, 45, 52, 32, 64, 28, 63, 46)(22, 57, 43, 65, 42, 62, 40, 59)(26, 66, 34, 60, 27, 56, 35, 67)(70, 78, 73, 80, 71, 77, 74, 79)(81, 83, 90, 110, 147, 159, 139, 127, 97, 85)(82, 87, 102, 138, 109, 151, 125, 148, 106, 88)(84, 92, 115, 133, 126, 153, 111, 131, 120, 94)(86, 99, 132, 116, 137, 158, 146, 119, 134, 100)(89, 107, 149, 118, 152, 122, 95, 121, 150, 108)(91, 112, 154, 124, 96, 123, 130, 98, 129, 114)(93, 117, 143, 104, 142, 157, 136, 101, 135, 113)(103, 140, 160, 145, 105, 144, 156, 128, 155, 141)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 16^8 ), ( 16^10 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 80 f = 10
	degree seq :: [ 8^10, 10^8 ]

E27.1701 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = (C5 : C8) : C2 (small group id <80, 33>)
|r| :: 1
Presentation :: [ X1^-2 * X2^-1 * X1 * X2^-1 * X1^-1, X2^-3 * X1^-1 * X2 * X1^-1, X2 * X1^-1 * X2^5 * X1^-1, X2 * X1 * X2^2 * X1^-1 * X2^-1 * X1^-2, X2^2 * X1^2 * X2 * X1 * X2 * X1^-3, X1^-1 * X2^-2 * X1 * X2^-2 * X1 * X2 * X1^-1 * X2^-1, X1^-1 * X2^-2 * X1^-1 * X2^-2 * X1 * X2 * X1 * X2^-1 ]
Map:: non-degenerate
	R = (1, 81, 2, 82, 6, 86, 18, 98, 42, 122, 32, 112, 13, 93, 4, 84)(3, 83, 9, 89, 25, 105, 8, 88, 24, 104, 54, 134, 33, 113, 11, 91)(5, 85, 15, 95, 39, 119, 61, 141, 30, 110, 12, 92, 34, 114, 16, 96)(7, 87, 21, 101, 47, 127, 20, 100, 46, 126, 70, 150, 53, 133, 23, 103)(10, 90, 29, 109, 58, 138, 28, 108, 17, 97, 41, 121, 62, 142, 31, 111)(14, 94, 19, 99, 44, 124, 67, 147, 43, 123, 36, 116, 59, 139, 37, 117)(22, 102, 51, 131, 74, 154, 50, 130, 26, 106, 56, 136, 40, 120, 52, 132)(27, 107, 48, 128, 72, 152, 55, 135, 69, 149, 45, 125, 68, 148, 57, 137)(35, 115, 64, 144, 71, 151, 63, 143, 38, 118, 65, 145, 73, 153, 49, 129)(60, 140, 76, 156, 79, 159, 77, 157, 66, 146, 75, 155, 80, 160, 78, 158)
	L = (1, 83)(2, 87)(3, 90)(4, 92)(5, 81)(6, 99)(7, 102)(8, 82)(9, 107)(10, 110)(11, 112)(12, 115)(13, 116)(14, 84)(15, 118)(16, 109)(17, 85)(18, 95)(19, 125)(20, 86)(21, 129)(22, 91)(23, 93)(24, 97)(25, 131)(26, 88)(27, 124)(28, 89)(29, 140)(30, 122)(31, 134)(32, 126)(33, 136)(34, 130)(35, 123)(36, 128)(37, 144)(38, 94)(39, 132)(40, 96)(41, 146)(42, 104)(43, 98)(44, 111)(45, 103)(46, 106)(47, 148)(48, 100)(49, 119)(50, 101)(51, 155)(52, 150)(53, 152)(54, 149)(55, 105)(56, 156)(57, 113)(58, 147)(59, 108)(60, 154)(61, 121)(62, 117)(63, 114)(64, 157)(65, 158)(66, 120)(67, 145)(68, 159)(69, 139)(70, 143)(71, 127)(72, 160)(73, 133)(74, 141)(75, 137)(76, 135)(77, 138)(78, 142)(79, 153)(80, 151)
	local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 10 e = 80 f = 18
	degree seq :: [ 16^10 ]

E27.1702 :: Family: { 2*ex } :: Oriented family(ies): { E3c }
Signature :: (0; {8, 8, 10})
Quotient :: loop
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ F^2, F * T1 * F * T2, T2^-1 * T1 * T2^3 * T1, T2^-1 * T1^-3 * T2^-1 * T1, T2 * T1^-1 * T2^-3 * T1^-1, T1^-1 * T2^-1 * T1^-2 * T2^2 * T1^-1 * T2^-1, T2^4 * T1^-4, T2 * T1 * T2 * T1 * T2^2 * T1^-2, T2 * T1^2 * T2 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 30, 42, 24, 17, 5)(2, 7, 22, 11, 32, 46, 26, 8)(4, 12, 35, 43, 18, 15, 38, 14)(6, 19, 45, 23, 13, 36, 48, 20)(9, 27, 44, 31, 54, 69, 59, 28)(16, 29, 60, 74, 61, 41, 66, 40)(21, 49, 39, 52, 70, 63, 34, 50)(25, 51, 75, 57, 33, 56, 76, 55)(37, 64, 77, 58, 67, 65, 78, 62)(47, 68, 79, 73, 53, 72, 80, 71)(81, 82, 86, 98, 122, 112, 93, 84)(83, 89, 105, 88, 104, 134, 113, 91)(85, 95, 119, 141, 110, 92, 114, 96)(87, 101, 127, 100, 126, 150, 133, 103)(90, 109, 138, 108, 97, 121, 142, 111)(94, 99, 124, 147, 123, 116, 139, 117)(102, 131, 154, 130, 106, 136, 120, 132)(107, 128, 152, 135, 149, 125, 148, 137)(115, 144, 151, 143, 118, 145, 153, 129)(140, 156, 159, 157, 146, 155, 160, 158)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1703
Transitivity :: ET+ VT AT
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.1703 :: Family: { 2ex } :: Oriented family(ies): { E3*c }
Signature :: (0; {8, 8, 10})
Quotient :: edge
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2^-1 * T1^2 * T2^-1 * T1^-2, T1^-2 * T2^-3 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1 * T2^2 * T1^-1 * T2^4, T1^-1 * T2^-1 * F * T1^-2 * F * T2 * T1^-1, T1^8, (T1 * T2^-2 * T1^-1 * T2)^2 ]
Map:: polytopal non-degenerate
	R = (1, 81, 3, 83, 10, 90, 30, 110, 67, 147, 79, 159, 59, 139, 47, 127, 17, 97, 5, 85)(2, 82, 7, 87, 22, 102, 58, 138, 29, 109, 71, 151, 45, 125, 68, 148, 26, 106, 8, 88)(4, 84, 12, 92, 35, 115, 53, 133, 46, 126, 73, 153, 31, 111, 51, 131, 40, 120, 14, 94)(6, 86, 19, 99, 52, 132, 36, 116, 57, 137, 78, 158, 66, 146, 39, 119, 54, 134, 20, 100)(9, 89, 27, 107, 69, 149, 38, 118, 72, 152, 42, 122, 15, 95, 41, 121, 70, 150, 28, 108)(11, 91, 32, 112, 74, 154, 44, 124, 16, 96, 43, 123, 50, 130, 18, 98, 49, 129, 34, 114)(13, 93, 37, 117, 63, 143, 24, 104, 62, 142, 77, 157, 56, 136, 21, 101, 55, 135, 33, 113)(23, 103, 60, 140, 80, 160, 65, 145, 25, 105, 64, 144, 76, 156, 48, 128, 75, 155, 61, 141)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 95)(6, 98)(7, 101)(8, 104)(9, 100)(10, 109)(11, 83)(12, 105)(13, 84)(14, 103)(15, 99)(16, 85)(17, 125)(18, 128)(19, 131)(20, 133)(21, 130)(22, 137)(23, 87)(24, 129)(25, 88)(26, 146)(27, 136)(28, 143)(29, 134)(30, 152)(31, 90)(32, 144)(33, 91)(34, 140)(35, 147)(36, 92)(37, 96)(38, 93)(39, 94)(40, 139)(41, 135)(42, 142)(43, 145)(44, 141)(45, 132)(46, 97)(47, 149)(48, 118)(49, 127)(50, 110)(51, 156)(52, 112)(53, 155)(54, 124)(55, 111)(56, 115)(57, 123)(58, 117)(59, 102)(60, 107)(61, 121)(62, 120)(63, 126)(64, 108)(65, 122)(66, 114)(67, 106)(68, 113)(69, 116)(70, 158)(71, 157)(72, 119)(73, 160)(74, 159)(75, 148)(76, 138)(77, 154)(78, 153)(79, 150)(80, 151)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1702
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.1704 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 10})
Quotient :: edge^2
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1^-1 * Y2^-2, Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1, Y1 * Y3 * Y1^-2 * Y2^-1, Y1 * Y2^-1 * Y3^-1 * Y2^2, Y2^-1 * Y1 * Y3 * Y1^-2, Y2 * Y3^-2 * Y1^-2 * Y2, Y1^2 * Y2^-2 * Y3^-2, Y2^-1 * Y1^2 * Y3^2 * Y2^-1, Y1 * Y3^-4 * Y2 * Y3^-1, Y2^8, Y1^8 ]
Map:: polytopal non-degenerate
	R = (1, 81, 4, 84, 17, 97, 55, 135, 50, 130, 80, 160, 66, 146, 75, 155, 31, 111, 7, 87)(2, 82, 9, 89, 36, 116, 45, 125, 46, 126, 64, 144, 19, 99, 62, 142, 43, 123, 11, 91)(3, 83, 5, 85, 21, 101, 40, 120, 34, 114, 56, 136, 74, 154, 69, 149, 53, 133, 15, 95)(6, 86, 25, 105, 67, 147, 71, 151, 28, 108, 70, 150, 57, 137, 47, 127, 49, 129, 27, 107)(8, 88, 33, 113, 13, 93, 14, 94, 48, 128, 68, 148, 37, 117, 65, 145, 61, 141, 24, 104)(10, 90, 39, 119, 51, 131, 52, 132, 41, 121, 58, 138, 20, 100, 22, 102, 63, 143, 26, 106)(12, 92, 44, 124, 77, 157, 76, 156, 79, 159, 42, 122, 23, 103, 60, 140, 78, 158, 35, 115)(16, 96, 18, 98, 59, 139, 38, 118, 32, 112, 72, 152, 29, 109, 30, 110, 73, 153, 54, 134)(161, 162, 168, 192, 236, 207, 182, 165)(163, 172, 169, 170, 198, 235, 209, 174)(164, 166, 184, 213, 239, 205, 180, 178)(167, 188, 193, 194, 237, 222, 223, 190)(171, 201, 232, 215, 217, 225, 181, 183)(173, 176, 204, 185, 186, 229, 191, 206)(175, 210, 196, 197, 219, 220, 187, 212)(177, 179, 221, 233, 202, 231, 218, 216)(189, 195, 230, 199, 200, 226, 203, 208)(211, 214, 240, 227, 228, 234, 238, 224)(241, 243, 253, 285, 316, 278, 266, 246)(242, 247, 269, 254, 287, 317, 280, 250)(244, 256, 273, 311, 319, 309, 303, 259)(245, 260, 276, 295, 272, 264, 267, 263)(248, 251, 282, 270, 262, 297, 257, 274)(249, 275, 312, 292, 289, 306, 261, 277)(252, 255, 291, 286, 315, 299, 308, 265)(258, 298, 307, 290, 293, 301, 304, 300)(268, 271, 314, 288, 302, 284, 294, 279)(281, 283, 320, 313, 305, 310, 318, 296)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1707
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.1705 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {8, 8, 10})
Quotient :: edge^2
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-2 * Y2^2 * Y1^-1 * Y2^-1, Y2 * Y1^-5 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^10 ]
Map:: polytopal
	R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 162, 166, 178, 202, 192, 173, 164)(163, 169, 185, 168, 184, 214, 193, 171)(165, 175, 199, 221, 190, 172, 194, 176)(167, 181, 207, 180, 206, 230, 213, 183)(170, 189, 218, 188, 177, 201, 222, 191)(174, 179, 204, 227, 203, 196, 219, 197)(182, 211, 234, 210, 186, 216, 200, 212)(187, 208, 232, 215, 229, 205, 228, 217)(195, 224, 231, 223, 198, 225, 233, 209)(220, 236, 239, 237, 226, 235, 240, 238)(241, 243, 250, 270, 282, 264, 257, 245)(242, 247, 262, 251, 272, 286, 266, 248)(244, 252, 275, 283, 258, 255, 278, 254)(246, 259, 285, 263, 253, 276, 288, 260)(249, 267, 284, 271, 294, 309, 299, 268)(256, 269, 300, 314, 301, 281, 306, 280)(261, 289, 279, 292, 310, 303, 274, 290)(265, 291, 315, 297, 273, 296, 316, 295)(277, 304, 317, 298, 307, 305, 318, 302)(287, 308, 319, 313, 293, 312, 320, 311)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 40, 40 ), ( 40^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1706
Graph:: simple bipartite
	v = 100 e = 160 f = 8
	degree seq :: [ 2^80, 8^20 ]

E27.1706 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 10})
Quotient :: loop^2
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1^-1 * Y2^-2, Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1, Y1 * Y3 * Y1^-2 * Y2^-1, Y1 * Y2^-1 * Y3^-1 * Y2^2, Y2^-1 * Y1 * Y3 * Y1^-2, Y2 * Y3^-2 * Y1^-2 * Y2, Y1^2 * Y2^-2 * Y3^-2, Y2^-1 * Y1^2 * Y3^2 * Y2^-1, Y1 * Y3^-4 * Y2 * Y3^-1, Y2^8, Y1^8 ]
Map::
	R = (1, 81, 161, 241, 4, 84, 164, 244, 17, 97, 177, 257, 55, 135, 215, 295, 50, 130, 210, 290, 80, 160, 240, 320, 66, 146, 226, 306, 75, 155, 235, 315, 31, 111, 191, 271, 7, 87, 167, 247)(2, 82, 162, 242, 9, 89, 169, 249, 36, 116, 196, 276, 45, 125, 205, 285, 46, 126, 206, 286, 64, 144, 224, 304, 19, 99, 179, 259, 62, 142, 222, 302, 43, 123, 203, 283, 11, 91, 171, 251)(3, 83, 163, 243, 5, 85, 165, 245, 21, 101, 181, 261, 40, 120, 200, 280, 34, 114, 194, 274, 56, 136, 216, 296, 74, 154, 234, 314, 69, 149, 229, 309, 53, 133, 213, 293, 15, 95, 175, 255)(6, 86, 166, 246, 25, 105, 185, 265, 67, 147, 227, 307, 71, 151, 231, 311, 28, 108, 188, 268, 70, 150, 230, 310, 57, 137, 217, 297, 47, 127, 207, 287, 49, 129, 209, 289, 27, 107, 187, 267)(8, 88, 168, 248, 33, 113, 193, 273, 13, 93, 173, 253, 14, 94, 174, 254, 48, 128, 208, 288, 68, 148, 228, 308, 37, 117, 197, 277, 65, 145, 225, 305, 61, 141, 221, 301, 24, 104, 184, 264)(10, 90, 170, 250, 39, 119, 199, 279, 51, 131, 211, 291, 52, 132, 212, 292, 41, 121, 201, 281, 58, 138, 218, 298, 20, 100, 180, 260, 22, 102, 182, 262, 63, 143, 223, 303, 26, 106, 186, 266)(12, 92, 172, 252, 44, 124, 204, 284, 77, 157, 237, 317, 76, 156, 236, 316, 79, 159, 239, 319, 42, 122, 202, 282, 23, 103, 183, 263, 60, 140, 220, 300, 78, 158, 238, 318, 35, 115, 195, 275)(16, 96, 176, 256, 18, 98, 178, 258, 59, 139, 219, 299, 38, 118, 198, 278, 32, 112, 192, 272, 72, 152, 232, 312, 29, 109, 189, 269, 30, 110, 190, 270, 73, 153, 233, 313, 54, 134, 214, 294)
	L = (1, 82)(2, 88)(3, 92)(4, 86)(5, 81)(6, 104)(7, 108)(8, 112)(9, 90)(10, 118)(11, 121)(12, 89)(13, 96)(14, 83)(15, 130)(16, 124)(17, 99)(18, 84)(19, 141)(20, 98)(21, 103)(22, 85)(23, 91)(24, 133)(25, 106)(26, 149)(27, 132)(28, 113)(29, 115)(30, 87)(31, 126)(32, 156)(33, 114)(34, 157)(35, 150)(36, 117)(37, 139)(38, 155)(39, 120)(40, 146)(41, 152)(42, 151)(43, 128)(44, 105)(45, 100)(46, 93)(47, 102)(48, 109)(49, 94)(50, 116)(51, 134)(52, 95)(53, 159)(54, 160)(55, 137)(56, 97)(57, 145)(58, 136)(59, 140)(60, 107)(61, 153)(62, 143)(63, 110)(64, 131)(65, 101)(66, 123)(67, 148)(68, 154)(69, 111)(70, 119)(71, 138)(72, 135)(73, 122)(74, 158)(75, 129)(76, 127)(77, 142)(78, 144)(79, 125)(80, 147)(161, 243)(162, 247)(163, 253)(164, 256)(165, 260)(166, 241)(167, 269)(168, 251)(169, 275)(170, 242)(171, 282)(172, 255)(173, 285)(174, 287)(175, 291)(176, 273)(177, 274)(178, 298)(179, 244)(180, 276)(181, 277)(182, 297)(183, 245)(184, 267)(185, 252)(186, 246)(187, 263)(188, 271)(189, 254)(190, 262)(191, 314)(192, 264)(193, 311)(194, 248)(195, 312)(196, 295)(197, 249)(198, 266)(199, 268)(200, 250)(201, 283)(202, 270)(203, 320)(204, 294)(205, 316)(206, 315)(207, 317)(208, 302)(209, 306)(210, 293)(211, 286)(212, 289)(213, 301)(214, 279)(215, 272)(216, 281)(217, 257)(218, 307)(219, 308)(220, 258)(221, 304)(222, 284)(223, 259)(224, 300)(225, 310)(226, 261)(227, 290)(228, 265)(229, 303)(230, 318)(231, 319)(232, 292)(233, 305)(234, 288)(235, 299)(236, 278)(237, 280)(238, 296)(239, 309)(240, 313)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1705
Transitivity :: VT+
Graph:: bipartite
	v = 8 e = 160 f = 100
	degree seq :: [ 40^8 ]

E27.1707 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {8, 8, 10})
Quotient :: loop^2
Aut^+ = (C5 : C8) : C2 (small group id <80, 33>)
Aut   = ((C5 : C8) : C2) : C2 (small group id <160, 88>)
|r| :: 2
Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-2 * Y2^2 * Y1^-1 * Y2^-1, Y2 * Y1^-5 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2^2 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^10 ]
Map:: polytopal non-degenerate
	R = (1, 81, 161, 241)(2, 82, 162, 242)(3, 83, 163, 243)(4, 84, 164, 244)(5, 85, 165, 245)(6, 86, 166, 246)(7, 87, 167, 247)(8, 88, 168, 248)(9, 89, 169, 249)(10, 90, 170, 250)(11, 91, 171, 251)(12, 92, 172, 252)(13, 93, 173, 253)(14, 94, 174, 254)(15, 95, 175, 255)(16, 96, 176, 256)(17, 97, 177, 257)(18, 98, 178, 258)(19, 99, 179, 259)(20, 100, 180, 260)(21, 101, 181, 261)(22, 102, 182, 262)(23, 103, 183, 263)(24, 104, 184, 264)(25, 105, 185, 265)(26, 106, 186, 266)(27, 107, 187, 267)(28, 108, 188, 268)(29, 109, 189, 269)(30, 110, 190, 270)(31, 111, 191, 271)(32, 112, 192, 272)(33, 113, 193, 273)(34, 114, 194, 274)(35, 115, 195, 275)(36, 116, 196, 276)(37, 117, 197, 277)(38, 118, 198, 278)(39, 119, 199, 279)(40, 120, 200, 280)(41, 121, 201, 281)(42, 122, 202, 282)(43, 123, 203, 283)(44, 124, 204, 284)(45, 125, 205, 285)(46, 126, 206, 286)(47, 127, 207, 287)(48, 128, 208, 288)(49, 129, 209, 289)(50, 130, 210, 290)(51, 131, 211, 291)(52, 132, 212, 292)(53, 133, 213, 293)(54, 134, 214, 294)(55, 135, 215, 295)(56, 136, 216, 296)(57, 137, 217, 297)(58, 138, 218, 298)(59, 139, 219, 299)(60, 140, 220, 300)(61, 141, 221, 301)(62, 142, 222, 302)(63, 143, 223, 303)(64, 144, 224, 304)(65, 145, 225, 305)(66, 146, 226, 306)(67, 147, 227, 307)(68, 148, 228, 308)(69, 149, 229, 309)(70, 150, 230, 310)(71, 151, 231, 311)(72, 152, 232, 312)(73, 153, 233, 313)(74, 154, 234, 314)(75, 155, 235, 315)(76, 156, 236, 316)(77, 157, 237, 317)(78, 158, 238, 318)(79, 159, 239, 319)(80, 160, 240, 320)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 95)(6, 98)(7, 101)(8, 104)(9, 105)(10, 109)(11, 83)(12, 114)(13, 84)(14, 99)(15, 119)(16, 85)(17, 121)(18, 122)(19, 124)(20, 126)(21, 127)(22, 131)(23, 87)(24, 134)(25, 88)(26, 136)(27, 128)(28, 97)(29, 138)(30, 92)(31, 90)(32, 93)(33, 91)(34, 96)(35, 144)(36, 139)(37, 94)(38, 145)(39, 141)(40, 132)(41, 142)(42, 112)(43, 116)(44, 147)(45, 148)(46, 150)(47, 100)(48, 152)(49, 115)(50, 106)(51, 154)(52, 102)(53, 103)(54, 113)(55, 149)(56, 120)(57, 107)(58, 108)(59, 117)(60, 156)(61, 110)(62, 111)(63, 118)(64, 151)(65, 153)(66, 155)(67, 123)(68, 137)(69, 125)(70, 133)(71, 143)(72, 135)(73, 129)(74, 130)(75, 160)(76, 159)(77, 146)(78, 140)(79, 157)(80, 158)(161, 243)(162, 247)(163, 250)(164, 252)(165, 241)(166, 259)(167, 262)(168, 242)(169, 267)(170, 270)(171, 272)(172, 275)(173, 276)(174, 244)(175, 278)(176, 269)(177, 245)(178, 255)(179, 285)(180, 246)(181, 289)(182, 251)(183, 253)(184, 257)(185, 291)(186, 248)(187, 284)(188, 249)(189, 300)(190, 282)(191, 294)(192, 286)(193, 296)(194, 290)(195, 283)(196, 288)(197, 304)(198, 254)(199, 292)(200, 256)(201, 306)(202, 264)(203, 258)(204, 271)(205, 263)(206, 266)(207, 308)(208, 260)(209, 279)(210, 261)(211, 315)(212, 310)(213, 312)(214, 309)(215, 265)(216, 316)(217, 273)(218, 307)(219, 268)(220, 314)(221, 281)(222, 277)(223, 274)(224, 317)(225, 318)(226, 280)(227, 305)(228, 319)(229, 299)(230, 303)(231, 287)(232, 320)(233, 293)(234, 301)(235, 297)(236, 295)(237, 298)(238, 302)(239, 313)(240, 311)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1704
Transitivity :: VT+
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.1708 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 20, 20})
Quotient :: edge
Aut^+ = C20 x C4 (small group id <80, 20>)
Aut   = (C20 x C4) : C2 (small group id <160, 95>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^20 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 78, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 10, 18, 26, 34, 42, 50, 58, 66, 74, 79, 75, 67, 59, 51, 43, 35, 27, 19, 11)(6, 13, 21, 29, 37, 45, 53, 61, 69, 76, 80, 77, 70, 62, 54, 46, 38, 30, 22, 14)(81, 82, 86, 84)(83, 87, 93, 90)(85, 88, 94, 91)(89, 95, 101, 98)(92, 96, 102, 99)(97, 103, 109, 106)(100, 104, 110, 107)(105, 111, 117, 114)(108, 112, 118, 115)(113, 119, 125, 122)(116, 120, 126, 123)(121, 127, 133, 130)(124, 128, 134, 131)(129, 135, 141, 138)(132, 136, 142, 139)(137, 143, 149, 146)(140, 144, 150, 147)(145, 151, 156, 154)(148, 152, 157, 155)(153, 158, 160, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1709
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.1709 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 20, 20})
Quotient :: loop
Aut^+ = C20 x C4 (small group id <80, 20>)
Aut   = (C20 x C4) : C2 (small group id <160, 95>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^20 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 9, 89, 17, 97, 25, 105, 33, 113, 41, 121, 49, 129, 57, 137, 65, 145, 73, 153, 68, 148, 60, 140, 52, 132, 44, 124, 36, 116, 28, 108, 20, 100, 12, 92, 5, 85)(2, 82, 7, 87, 15, 95, 23, 103, 31, 111, 39, 119, 47, 127, 55, 135, 63, 143, 71, 151, 78, 158, 72, 152, 64, 144, 56, 136, 48, 128, 40, 120, 32, 112, 24, 104, 16, 96, 8, 88)(4, 84, 10, 90, 18, 98, 26, 106, 34, 114, 42, 122, 50, 130, 58, 138, 66, 146, 74, 154, 79, 159, 75, 155, 67, 147, 59, 139, 51, 131, 43, 123, 35, 115, 27, 107, 19, 99, 11, 91)(6, 86, 13, 93, 21, 101, 29, 109, 37, 117, 45, 125, 53, 133, 61, 141, 69, 149, 76, 156, 80, 160, 77, 157, 70, 150, 62, 142, 54, 134, 46, 126, 38, 118, 30, 110, 22, 102, 14, 94)
	L = (1, 82)(2, 86)(3, 87)(4, 81)(5, 88)(6, 84)(7, 93)(8, 94)(9, 95)(10, 83)(11, 85)(12, 96)(13, 90)(14, 91)(15, 101)(16, 102)(17, 103)(18, 89)(19, 92)(20, 104)(21, 98)(22, 99)(23, 109)(24, 110)(25, 111)(26, 97)(27, 100)(28, 112)(29, 106)(30, 107)(31, 117)(32, 118)(33, 119)(34, 105)(35, 108)(36, 120)(37, 114)(38, 115)(39, 125)(40, 126)(41, 127)(42, 113)(43, 116)(44, 128)(45, 122)(46, 123)(47, 133)(48, 134)(49, 135)(50, 121)(51, 124)(52, 136)(53, 130)(54, 131)(55, 141)(56, 142)(57, 143)(58, 129)(59, 132)(60, 144)(61, 138)(62, 139)(63, 149)(64, 150)(65, 151)(66, 137)(67, 140)(68, 152)(69, 146)(70, 147)(71, 156)(72, 157)(73, 158)(74, 145)(75, 148)(76, 154)(77, 155)(78, 160)(79, 153)(80, 159)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1708
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.1710 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C4 (small group id <80, 20>)
Aut   = (C20 x C4) : C2 (small group id <160, 95>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3^20, Y2^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 4, 84)(3, 83, 7, 87, 13, 93, 10, 90)(5, 85, 8, 88, 14, 94, 11, 91)(9, 89, 15, 95, 21, 101, 18, 98)(12, 92, 16, 96, 22, 102, 19, 99)(17, 97, 23, 103, 29, 109, 26, 106)(20, 100, 24, 104, 30, 110, 27, 107)(25, 105, 31, 111, 37, 117, 34, 114)(28, 108, 32, 112, 38, 118, 35, 115)(33, 113, 39, 119, 45, 125, 42, 122)(36, 116, 40, 120, 46, 126, 43, 123)(41, 121, 47, 127, 53, 133, 50, 130)(44, 124, 48, 128, 54, 134, 51, 131)(49, 129, 55, 135, 61, 141, 58, 138)(52, 132, 56, 136, 62, 142, 59, 139)(57, 137, 63, 143, 69, 149, 66, 146)(60, 140, 64, 144, 70, 150, 67, 147)(65, 145, 71, 151, 76, 156, 74, 154)(68, 148, 72, 152, 77, 157, 75, 155)(73, 153, 78, 158, 80, 160, 79, 159)(161, 241, 163, 243, 169, 249, 177, 257, 185, 265, 193, 273, 201, 281, 209, 289, 217, 297, 225, 305, 233, 313, 228, 308, 220, 300, 212, 292, 204, 284, 196, 276, 188, 268, 180, 260, 172, 252, 165, 245)(162, 242, 167, 247, 175, 255, 183, 263, 191, 271, 199, 279, 207, 287, 215, 295, 223, 303, 231, 311, 238, 318, 232, 312, 224, 304, 216, 296, 208, 288, 200, 280, 192, 272, 184, 264, 176, 256, 168, 248)(164, 244, 170, 250, 178, 258, 186, 266, 194, 274, 202, 282, 210, 290, 218, 298, 226, 306, 234, 314, 239, 319, 235, 315, 227, 307, 219, 299, 211, 291, 203, 283, 195, 275, 187, 267, 179, 259, 171, 251)(166, 246, 173, 253, 181, 261, 189, 269, 197, 277, 205, 285, 213, 293, 221, 301, 229, 309, 236, 316, 240, 320, 237, 317, 230, 310, 222, 302, 214, 294, 206, 286, 198, 278, 190, 270, 182, 262, 174, 254)
	L = (1, 164)(2, 161)(3, 170)(4, 166)(5, 171)(6, 162)(7, 163)(8, 165)(9, 178)(10, 173)(11, 174)(12, 179)(13, 167)(14, 168)(15, 169)(16, 172)(17, 186)(18, 181)(19, 182)(20, 187)(21, 175)(22, 176)(23, 177)(24, 180)(25, 194)(26, 189)(27, 190)(28, 195)(29, 183)(30, 184)(31, 185)(32, 188)(33, 202)(34, 197)(35, 198)(36, 203)(37, 191)(38, 192)(39, 193)(40, 196)(41, 210)(42, 205)(43, 206)(44, 211)(45, 199)(46, 200)(47, 201)(48, 204)(49, 218)(50, 213)(51, 214)(52, 219)(53, 207)(54, 208)(55, 209)(56, 212)(57, 226)(58, 221)(59, 222)(60, 227)(61, 215)(62, 216)(63, 217)(64, 220)(65, 234)(66, 229)(67, 230)(68, 235)(69, 223)(70, 224)(71, 225)(72, 228)(73, 239)(74, 236)(75, 237)(76, 231)(77, 232)(78, 233)(79, 240)(80, 238)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1711
Graph:: bipartite
	v = 24 e = 160 f = 84
	degree seq :: [ 8^20, 40^4 ]

E27.1711 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C20 x C4 (small group id <80, 20>)
Aut   = (C20 x C4) : C2 (small group id <160, 95>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-20, Y1^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 13, 93, 21, 101, 29, 109, 37, 117, 45, 125, 53, 133, 61, 141, 69, 149, 67, 147, 59, 139, 51, 131, 43, 123, 35, 115, 27, 107, 19, 99, 11, 91, 4, 84)(3, 83, 7, 87, 14, 94, 22, 102, 30, 110, 38, 118, 46, 126, 54, 134, 62, 142, 70, 150, 76, 156, 74, 154, 66, 146, 58, 138, 50, 130, 42, 122, 34, 114, 26, 106, 18, 98, 10, 90)(5, 85, 8, 88, 15, 95, 23, 103, 31, 111, 39, 119, 47, 127, 55, 135, 63, 143, 71, 151, 77, 157, 75, 155, 68, 148, 60, 140, 52, 132, 44, 124, 36, 116, 28, 108, 20, 100, 12, 92)(9, 89, 16, 96, 24, 104, 32, 112, 40, 120, 48, 128, 56, 136, 64, 144, 72, 152, 78, 158, 80, 160, 79, 159, 73, 153, 65, 145, 57, 137, 49, 129, 41, 121, 33, 113, 25, 105, 17, 97)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320)
	L = (1, 163)(2, 167)(3, 169)(4, 170)(5, 161)(6, 174)(7, 176)(8, 162)(9, 165)(10, 177)(11, 178)(12, 164)(13, 182)(14, 184)(15, 166)(16, 168)(17, 172)(18, 185)(19, 186)(20, 171)(21, 190)(22, 192)(23, 173)(24, 175)(25, 180)(26, 193)(27, 194)(28, 179)(29, 198)(30, 200)(31, 181)(32, 183)(33, 188)(34, 201)(35, 202)(36, 187)(37, 206)(38, 208)(39, 189)(40, 191)(41, 196)(42, 209)(43, 210)(44, 195)(45, 214)(46, 216)(47, 197)(48, 199)(49, 204)(50, 217)(51, 218)(52, 203)(53, 222)(54, 224)(55, 205)(56, 207)(57, 212)(58, 225)(59, 226)(60, 211)(61, 230)(62, 232)(63, 213)(64, 215)(65, 220)(66, 233)(67, 234)(68, 219)(69, 236)(70, 238)(71, 221)(72, 223)(73, 228)(74, 239)(75, 227)(76, 240)(77, 229)(78, 231)(79, 235)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1710
Graph:: simple bipartite
	v = 84 e = 160 f = 24
	degree seq :: [ 2^80, 40^4 ]

E27.1712 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 20, 20})
Quotient :: edge
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^20 ]
Map:: non-degenerate
	R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 78, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 9, 17, 25, 33, 41, 49, 57, 65, 73, 79, 75, 67, 59, 51, 43, 35, 27, 19, 11)(6, 13, 21, 29, 37, 45, 53, 61, 69, 76, 80, 77, 70, 62, 54, 46, 38, 30, 22, 14)(81, 82, 86, 84)(83, 89, 93, 87)(85, 91, 94, 88)(90, 95, 101, 97)(92, 96, 102, 99)(98, 105, 109, 103)(100, 107, 110, 104)(106, 111, 117, 113)(108, 112, 118, 115)(114, 121, 125, 119)(116, 123, 126, 120)(122, 127, 133, 129)(124, 128, 134, 131)(130, 137, 141, 135)(132, 139, 142, 136)(138, 143, 149, 145)(140, 144, 150, 147)(146, 153, 156, 151)(148, 155, 157, 152)(154, 158, 160, 159)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1716
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.1713 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 20, 20})
Quotient :: edge
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T2^-2 * T1^-1 * T2^-3 * T1 * T2^-5, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 46, 62, 75, 59, 43, 23, 41, 21, 40, 57, 73, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 66, 50, 32, 14, 26, 9, 25, 45, 61, 76, 60, 44, 24, 8)(4, 12, 28, 48, 63, 78, 67, 51, 33, 15, 30, 11, 29, 47, 64, 77, 65, 49, 31, 13)(6, 17, 35, 53, 69, 79, 74, 58, 42, 22, 38, 19, 37, 55, 71, 80, 70, 54, 36, 18)(81, 82, 86, 84)(83, 89, 97, 91)(85, 94, 98, 95)(87, 99, 92, 101)(88, 102, 93, 103)(90, 100, 115, 108)(96, 104, 116, 111)(105, 117, 109, 120)(106, 118, 110, 121)(107, 125, 133, 127)(112, 122, 113, 123)(114, 130, 134, 131)(119, 135, 128, 137)(124, 138, 129, 139)(126, 136, 149, 143)(132, 140, 150, 145)(141, 151, 144, 153)(142, 156, 159, 157)(146, 154, 147, 155)(148, 152, 160, 158)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1718
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.1714 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 20, 20})
Quotient :: edge
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^-2 * T2 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1, (T2, T1^-1)^2, T2^6 * T1 * T2^2 * T1 * T2^2, (T2^-1 * T1)^20 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 46, 62, 70, 54, 36, 18, 6, 17, 35, 53, 69, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 65, 49, 31, 13, 4, 12, 28, 48, 63, 76, 60, 44, 24, 8)(9, 25, 45, 61, 77, 67, 51, 33, 15, 30, 11, 29, 47, 64, 78, 66, 50, 32, 14, 26)(19, 37, 55, 71, 79, 75, 59, 43, 23, 41, 21, 40, 57, 73, 80, 74, 58, 42, 22, 38)(81, 82, 86, 84)(83, 89, 97, 91)(85, 94, 98, 95)(87, 99, 92, 101)(88, 102, 93, 103)(90, 100, 115, 108)(96, 104, 116, 111)(105, 117, 109, 120)(106, 118, 110, 121)(107, 125, 133, 127)(112, 122, 113, 123)(114, 130, 134, 131)(119, 135, 128, 137)(124, 138, 129, 139)(126, 136, 149, 143)(132, 140, 150, 145)(141, 151, 144, 153)(142, 157, 148, 158)(146, 154, 147, 155)(152, 159, 156, 160)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 40^4 ), ( 40^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1717
Transitivity :: ET+
Graph:: bipartite
	v = 24 e = 80 f = 4
	degree seq :: [ 4^20, 20^4 ]

E27.1715 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 20, 20})
Quotient :: edge
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-2 * T2^-1, T2^2 * T1 * T2^-2 * T1^-1, T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^2 * T1^-1 * T2 * T1^-5 * T2, T2^3 * T1 * T2 * T1^13, T2^20 ]
Map:: non-degenerate
	R = (1, 3, 10, 29, 58, 76, 54, 24, 50, 21, 49, 37, 64, 34, 62, 68, 42, 41, 17, 5)(2, 7, 22, 51, 35, 65, 73, 47, 72, 45, 40, 16, 33, 11, 31, 59, 67, 56, 26, 8)(4, 12, 30, 60, 78, 66, 39, 15, 28, 9, 27, 57, 77, 63, 71, 44, 18, 43, 38, 14)(6, 19, 46, 36, 13, 32, 61, 70, 80, 69, 55, 25, 53, 23, 52, 75, 79, 74, 48, 20)(81, 82, 86, 98, 122, 147, 159, 157, 144, 113, 133, 108, 130, 152, 160, 158, 138, 115, 93, 84)(83, 89, 99, 125, 121, 146, 154, 145, 114, 92, 103, 87, 101, 123, 149, 136, 156, 143, 112, 91)(85, 95, 100, 127, 148, 140, 155, 131, 117, 94, 105, 88, 104, 124, 150, 139, 109, 137, 116, 96)(90, 102, 126, 118, 97, 106, 128, 151, 142, 111, 132, 107, 129, 120, 135, 119, 134, 153, 141, 110)
	L = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.1719
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.1716 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 20, 20})
Quotient :: loop
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^20 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 10, 90, 18, 98, 26, 106, 34, 114, 42, 122, 50, 130, 58, 138, 66, 146, 74, 154, 68, 148, 60, 140, 52, 132, 44, 124, 36, 116, 28, 108, 20, 100, 12, 92, 5, 85)(2, 82, 7, 87, 15, 95, 23, 103, 31, 111, 39, 119, 47, 127, 55, 135, 63, 143, 71, 151, 78, 158, 72, 152, 64, 144, 56, 136, 48, 128, 40, 120, 32, 112, 24, 104, 16, 96, 8, 88)(4, 84, 9, 89, 17, 97, 25, 105, 33, 113, 41, 121, 49, 129, 57, 137, 65, 145, 73, 153, 79, 159, 75, 155, 67, 147, 59, 139, 51, 131, 43, 123, 35, 115, 27, 107, 19, 99, 11, 91)(6, 86, 13, 93, 21, 101, 29, 109, 37, 117, 45, 125, 53, 133, 61, 141, 69, 149, 76, 156, 80, 160, 77, 157, 70, 150, 62, 142, 54, 134, 46, 126, 38, 118, 30, 110, 22, 102, 14, 94)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 91)(6, 84)(7, 83)(8, 85)(9, 93)(10, 95)(11, 94)(12, 96)(13, 87)(14, 88)(15, 101)(16, 102)(17, 90)(18, 105)(19, 92)(20, 107)(21, 97)(22, 99)(23, 98)(24, 100)(25, 109)(26, 111)(27, 110)(28, 112)(29, 103)(30, 104)(31, 117)(32, 118)(33, 106)(34, 121)(35, 108)(36, 123)(37, 113)(38, 115)(39, 114)(40, 116)(41, 125)(42, 127)(43, 126)(44, 128)(45, 119)(46, 120)(47, 133)(48, 134)(49, 122)(50, 137)(51, 124)(52, 139)(53, 129)(54, 131)(55, 130)(56, 132)(57, 141)(58, 143)(59, 142)(60, 144)(61, 135)(62, 136)(63, 149)(64, 150)(65, 138)(66, 153)(67, 140)(68, 155)(69, 145)(70, 147)(71, 146)(72, 148)(73, 156)(74, 158)(75, 157)(76, 151)(77, 152)(78, 160)(79, 154)(80, 159)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1712
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.1717 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 20, 20})
Quotient :: loop
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^2 * T1 * T2^-2 * T1^-1, (T2^-1, T1^-1)^2, T2^-2 * T1^-1 * T2^-3 * T1 * T2^-5, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 10, 90, 27, 107, 46, 126, 62, 142, 75, 155, 59, 139, 43, 123, 23, 103, 41, 121, 21, 101, 40, 120, 57, 137, 73, 153, 68, 148, 52, 132, 34, 114, 16, 96, 5, 85)(2, 82, 7, 87, 20, 100, 39, 119, 56, 136, 72, 152, 66, 146, 50, 130, 32, 112, 14, 94, 26, 106, 9, 89, 25, 105, 45, 125, 61, 141, 76, 156, 60, 140, 44, 124, 24, 104, 8, 88)(4, 84, 12, 92, 28, 108, 48, 128, 63, 143, 78, 158, 67, 147, 51, 131, 33, 113, 15, 95, 30, 110, 11, 91, 29, 109, 47, 127, 64, 144, 77, 157, 65, 145, 49, 129, 31, 111, 13, 93)(6, 86, 17, 97, 35, 115, 53, 133, 69, 149, 79, 159, 74, 154, 58, 138, 42, 122, 22, 102, 38, 118, 19, 99, 37, 117, 55, 135, 71, 151, 80, 160, 70, 150, 54, 134, 36, 116, 18, 98)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 94)(6, 84)(7, 99)(8, 102)(9, 97)(10, 100)(11, 83)(12, 101)(13, 103)(14, 98)(15, 85)(16, 104)(17, 91)(18, 95)(19, 92)(20, 115)(21, 87)(22, 93)(23, 88)(24, 116)(25, 117)(26, 118)(27, 125)(28, 90)(29, 120)(30, 121)(31, 96)(32, 122)(33, 123)(34, 130)(35, 108)(36, 111)(37, 109)(38, 110)(39, 135)(40, 105)(41, 106)(42, 113)(43, 112)(44, 138)(45, 133)(46, 136)(47, 107)(48, 137)(49, 139)(50, 134)(51, 114)(52, 140)(53, 127)(54, 131)(55, 128)(56, 149)(57, 119)(58, 129)(59, 124)(60, 150)(61, 151)(62, 156)(63, 126)(64, 153)(65, 132)(66, 154)(67, 155)(68, 152)(69, 143)(70, 145)(71, 144)(72, 160)(73, 141)(74, 147)(75, 146)(76, 159)(77, 142)(78, 148)(79, 157)(80, 158)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1714
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.1718 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 20, 20})
Quotient :: loop
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^-2 * T2 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1, (T2, T1^-1)^2, T2^6 * T1 * T2^2 * T1 * T2^2, (T2^-1 * T1)^20 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 10, 90, 27, 107, 46, 126, 62, 142, 70, 150, 54, 134, 36, 116, 18, 98, 6, 86, 17, 97, 35, 115, 53, 133, 69, 149, 68, 148, 52, 132, 34, 114, 16, 96, 5, 85)(2, 82, 7, 87, 20, 100, 39, 119, 56, 136, 72, 152, 65, 145, 49, 129, 31, 111, 13, 93, 4, 84, 12, 92, 28, 108, 48, 128, 63, 143, 76, 156, 60, 140, 44, 124, 24, 104, 8, 88)(9, 89, 25, 105, 45, 125, 61, 141, 77, 157, 67, 147, 51, 131, 33, 113, 15, 95, 30, 110, 11, 91, 29, 109, 47, 127, 64, 144, 78, 158, 66, 146, 50, 130, 32, 112, 14, 94, 26, 106)(19, 99, 37, 117, 55, 135, 71, 151, 79, 159, 75, 155, 59, 139, 43, 123, 23, 103, 41, 121, 21, 101, 40, 120, 57, 137, 73, 153, 80, 160, 74, 154, 58, 138, 42, 122, 22, 102, 38, 118)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 94)(6, 84)(7, 99)(8, 102)(9, 97)(10, 100)(11, 83)(12, 101)(13, 103)(14, 98)(15, 85)(16, 104)(17, 91)(18, 95)(19, 92)(20, 115)(21, 87)(22, 93)(23, 88)(24, 116)(25, 117)(26, 118)(27, 125)(28, 90)(29, 120)(30, 121)(31, 96)(32, 122)(33, 123)(34, 130)(35, 108)(36, 111)(37, 109)(38, 110)(39, 135)(40, 105)(41, 106)(42, 113)(43, 112)(44, 138)(45, 133)(46, 136)(47, 107)(48, 137)(49, 139)(50, 134)(51, 114)(52, 140)(53, 127)(54, 131)(55, 128)(56, 149)(57, 119)(58, 129)(59, 124)(60, 150)(61, 151)(62, 157)(63, 126)(64, 153)(65, 132)(66, 154)(67, 155)(68, 158)(69, 143)(70, 145)(71, 144)(72, 159)(73, 141)(74, 147)(75, 146)(76, 160)(77, 148)(78, 142)(79, 156)(80, 152)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.1713
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 80 f = 24
	degree seq :: [ 40^4 ]

E27.1719 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 20, 20})
Quotient :: loop
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T1 * T2^-1 * T1^-2 * T2 * T1, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1, T1)^2, T1^-2 * T2 * T1^-3 * T2^-1 * T1^-5, T2^-1 * T1^-4 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-4 ]
Map:: non-degenerate
	R = (1, 81, 3, 83, 10, 90, 5, 85)(2, 82, 7, 87, 21, 101, 8, 88)(4, 84, 12, 92, 27, 107, 14, 94)(6, 86, 18, 98, 39, 119, 19, 99)(9, 89, 25, 105, 15, 95, 26, 106)(11, 91, 28, 108, 16, 96, 30, 110)(13, 93, 29, 109, 45, 125, 33, 113)(17, 97, 36, 116, 57, 137, 37, 117)(20, 100, 41, 121, 23, 103, 42, 122)(22, 102, 43, 123, 24, 104, 44, 124)(31, 111, 46, 126, 34, 114, 48, 128)(32, 112, 49, 129, 61, 141, 51, 131)(35, 115, 54, 134, 73, 153, 55, 135)(38, 118, 59, 139, 40, 120, 60, 140)(47, 127, 62, 142, 52, 132, 64, 144)(50, 130, 63, 143, 77, 157, 67, 147)(53, 133, 70, 150, 79, 159, 71, 151)(56, 136, 75, 155, 58, 138, 76, 156)(65, 145, 78, 158, 68, 148, 69, 149)(66, 146, 72, 152, 80, 160, 74, 154)
	L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 95)(6, 97)(7, 100)(8, 103)(9, 98)(10, 101)(11, 83)(12, 102)(13, 84)(14, 104)(15, 99)(16, 85)(17, 115)(18, 118)(19, 120)(20, 116)(21, 119)(22, 87)(23, 117)(24, 88)(25, 121)(26, 122)(27, 90)(28, 123)(29, 91)(30, 124)(31, 92)(32, 93)(33, 96)(34, 94)(35, 133)(36, 136)(37, 138)(38, 134)(39, 137)(40, 135)(41, 139)(42, 140)(43, 105)(44, 106)(45, 107)(46, 108)(47, 109)(48, 110)(49, 111)(50, 112)(51, 114)(52, 113)(53, 149)(54, 152)(55, 154)(56, 150)(57, 153)(58, 151)(59, 155)(60, 156)(61, 125)(62, 126)(63, 127)(64, 128)(65, 129)(66, 130)(67, 132)(68, 131)(69, 144)(70, 143)(71, 147)(72, 145)(73, 159)(74, 148)(75, 160)(76, 146)(77, 141)(78, 142)(79, 158)(80, 157)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1715
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.1720 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y3, Y1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-1, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y2^9 * Y3^-1 * Y2, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 4, 84)(3, 83, 9, 89, 17, 97, 11, 91)(5, 85, 14, 94, 18, 98, 15, 95)(7, 87, 19, 99, 12, 92, 21, 101)(8, 88, 22, 102, 13, 93, 23, 103)(10, 90, 20, 100, 35, 115, 28, 108)(16, 96, 24, 104, 36, 116, 31, 111)(25, 105, 37, 117, 29, 109, 40, 120)(26, 106, 38, 118, 30, 110, 41, 121)(27, 107, 45, 125, 53, 133, 47, 127)(32, 112, 42, 122, 33, 113, 43, 123)(34, 114, 50, 130, 54, 134, 51, 131)(39, 119, 55, 135, 48, 128, 57, 137)(44, 124, 58, 138, 49, 129, 59, 139)(46, 126, 56, 136, 69, 149, 63, 143)(52, 132, 60, 140, 70, 150, 65, 145)(61, 141, 71, 151, 64, 144, 73, 153)(62, 142, 76, 156, 79, 159, 77, 157)(66, 146, 74, 154, 67, 147, 75, 155)(68, 148, 72, 152, 80, 160, 78, 158)(161, 241, 163, 243, 170, 250, 187, 267, 206, 286, 222, 302, 235, 315, 219, 299, 203, 283, 183, 263, 201, 281, 181, 261, 200, 280, 217, 297, 233, 313, 228, 308, 212, 292, 194, 274, 176, 256, 165, 245)(162, 242, 167, 247, 180, 260, 199, 279, 216, 296, 232, 312, 226, 306, 210, 290, 192, 272, 174, 254, 186, 266, 169, 249, 185, 265, 205, 285, 221, 301, 236, 316, 220, 300, 204, 284, 184, 264, 168, 248)(164, 244, 172, 252, 188, 268, 208, 288, 223, 303, 238, 318, 227, 307, 211, 291, 193, 273, 175, 255, 190, 270, 171, 251, 189, 269, 207, 287, 224, 304, 237, 317, 225, 305, 209, 289, 191, 271, 173, 253)(166, 246, 177, 257, 195, 275, 213, 293, 229, 309, 239, 319, 234, 314, 218, 298, 202, 282, 182, 262, 198, 278, 179, 259, 197, 277, 215, 295, 231, 311, 240, 320, 230, 310, 214, 294, 196, 276, 178, 258)
	L = (1, 164)(2, 161)(3, 171)(4, 166)(5, 175)(6, 162)(7, 181)(8, 183)(9, 163)(10, 188)(11, 177)(12, 179)(13, 182)(14, 165)(15, 178)(16, 191)(17, 169)(18, 174)(19, 167)(20, 170)(21, 172)(22, 168)(23, 173)(24, 176)(25, 200)(26, 201)(27, 207)(28, 195)(29, 197)(30, 198)(31, 196)(32, 203)(33, 202)(34, 211)(35, 180)(36, 184)(37, 185)(38, 186)(39, 217)(40, 189)(41, 190)(42, 192)(43, 193)(44, 219)(45, 187)(46, 223)(47, 213)(48, 215)(49, 218)(50, 194)(51, 214)(52, 225)(53, 205)(54, 210)(55, 199)(56, 206)(57, 208)(58, 204)(59, 209)(60, 212)(61, 233)(62, 237)(63, 229)(64, 231)(65, 230)(66, 235)(67, 234)(68, 238)(69, 216)(70, 220)(71, 221)(72, 228)(73, 224)(74, 226)(75, 227)(76, 222)(77, 239)(78, 240)(79, 236)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1726
Graph:: bipartite
	v = 24 e = 160 f = 84
	degree seq :: [ 8^20, 40^4 ]

E27.1721 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^20, (Y2^-1 * Y1)^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 4, 84)(3, 83, 9, 89, 13, 93, 7, 87)(5, 85, 11, 91, 14, 94, 8, 88)(10, 90, 15, 95, 21, 101, 17, 97)(12, 92, 16, 96, 22, 102, 19, 99)(18, 98, 25, 105, 29, 109, 23, 103)(20, 100, 27, 107, 30, 110, 24, 104)(26, 106, 31, 111, 37, 117, 33, 113)(28, 108, 32, 112, 38, 118, 35, 115)(34, 114, 41, 121, 45, 125, 39, 119)(36, 116, 43, 123, 46, 126, 40, 120)(42, 122, 47, 127, 53, 133, 49, 129)(44, 124, 48, 128, 54, 134, 51, 131)(50, 130, 57, 137, 61, 141, 55, 135)(52, 132, 59, 139, 62, 142, 56, 136)(58, 138, 63, 143, 69, 149, 65, 145)(60, 140, 64, 144, 70, 150, 67, 147)(66, 146, 73, 153, 76, 156, 71, 151)(68, 148, 75, 155, 77, 157, 72, 152)(74, 154, 78, 158, 80, 160, 79, 159)(161, 241, 163, 243, 170, 250, 178, 258, 186, 266, 194, 274, 202, 282, 210, 290, 218, 298, 226, 306, 234, 314, 228, 308, 220, 300, 212, 292, 204, 284, 196, 276, 188, 268, 180, 260, 172, 252, 165, 245)(162, 242, 167, 247, 175, 255, 183, 263, 191, 271, 199, 279, 207, 287, 215, 295, 223, 303, 231, 311, 238, 318, 232, 312, 224, 304, 216, 296, 208, 288, 200, 280, 192, 272, 184, 264, 176, 256, 168, 248)(164, 244, 169, 249, 177, 257, 185, 265, 193, 273, 201, 281, 209, 289, 217, 297, 225, 305, 233, 313, 239, 319, 235, 315, 227, 307, 219, 299, 211, 291, 203, 283, 195, 275, 187, 267, 179, 259, 171, 251)(166, 246, 173, 253, 181, 261, 189, 269, 197, 277, 205, 285, 213, 293, 221, 301, 229, 309, 236, 316, 240, 320, 237, 317, 230, 310, 222, 302, 214, 294, 206, 286, 198, 278, 190, 270, 182, 262, 174, 254)
	L = (1, 164)(2, 161)(3, 167)(4, 166)(5, 168)(6, 162)(7, 173)(8, 174)(9, 163)(10, 177)(11, 165)(12, 179)(13, 169)(14, 171)(15, 170)(16, 172)(17, 181)(18, 183)(19, 182)(20, 184)(21, 175)(22, 176)(23, 189)(24, 190)(25, 178)(26, 193)(27, 180)(28, 195)(29, 185)(30, 187)(31, 186)(32, 188)(33, 197)(34, 199)(35, 198)(36, 200)(37, 191)(38, 192)(39, 205)(40, 206)(41, 194)(42, 209)(43, 196)(44, 211)(45, 201)(46, 203)(47, 202)(48, 204)(49, 213)(50, 215)(51, 214)(52, 216)(53, 207)(54, 208)(55, 221)(56, 222)(57, 210)(58, 225)(59, 212)(60, 227)(61, 217)(62, 219)(63, 218)(64, 220)(65, 229)(66, 231)(67, 230)(68, 232)(69, 223)(70, 224)(71, 236)(72, 237)(73, 226)(74, 239)(75, 228)(76, 233)(77, 235)(78, 234)(79, 240)(80, 238)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1725
Graph:: bipartite
	v = 24 e = 160 f = 84
	degree seq :: [ 8^20, 40^4 ]

E27.1722 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, Y3^-1 * Y1^2 * Y3^-1, Y1^4, (R * Y3)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y2^2 * Y3 * Y2^8 * Y1^-1, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 4, 84)(3, 83, 9, 89, 17, 97, 11, 91)(5, 85, 14, 94, 18, 98, 15, 95)(7, 87, 19, 99, 12, 92, 21, 101)(8, 88, 22, 102, 13, 93, 23, 103)(10, 90, 20, 100, 35, 115, 28, 108)(16, 96, 24, 104, 36, 116, 31, 111)(25, 105, 37, 117, 29, 109, 40, 120)(26, 106, 38, 118, 30, 110, 41, 121)(27, 107, 45, 125, 53, 133, 47, 127)(32, 112, 42, 122, 33, 113, 43, 123)(34, 114, 50, 130, 54, 134, 51, 131)(39, 119, 55, 135, 48, 128, 57, 137)(44, 124, 58, 138, 49, 129, 59, 139)(46, 126, 56, 136, 69, 149, 63, 143)(52, 132, 60, 140, 70, 150, 65, 145)(61, 141, 71, 151, 64, 144, 73, 153)(62, 142, 77, 157, 68, 148, 78, 158)(66, 146, 74, 154, 67, 147, 75, 155)(72, 152, 79, 159, 76, 156, 80, 160)(161, 241, 163, 243, 170, 250, 187, 267, 206, 286, 222, 302, 230, 310, 214, 294, 196, 276, 178, 258, 166, 246, 177, 257, 195, 275, 213, 293, 229, 309, 228, 308, 212, 292, 194, 274, 176, 256, 165, 245)(162, 242, 167, 247, 180, 260, 199, 279, 216, 296, 232, 312, 225, 305, 209, 289, 191, 271, 173, 253, 164, 244, 172, 252, 188, 268, 208, 288, 223, 303, 236, 316, 220, 300, 204, 284, 184, 264, 168, 248)(169, 249, 185, 265, 205, 285, 221, 301, 237, 317, 227, 307, 211, 291, 193, 273, 175, 255, 190, 270, 171, 251, 189, 269, 207, 287, 224, 304, 238, 318, 226, 306, 210, 290, 192, 272, 174, 254, 186, 266)(179, 259, 197, 277, 215, 295, 231, 311, 239, 319, 235, 315, 219, 299, 203, 283, 183, 263, 201, 281, 181, 261, 200, 280, 217, 297, 233, 313, 240, 320, 234, 314, 218, 298, 202, 282, 182, 262, 198, 278)
	L = (1, 164)(2, 161)(3, 171)(4, 166)(5, 175)(6, 162)(7, 181)(8, 183)(9, 163)(10, 188)(11, 177)(12, 179)(13, 182)(14, 165)(15, 178)(16, 191)(17, 169)(18, 174)(19, 167)(20, 170)(21, 172)(22, 168)(23, 173)(24, 176)(25, 200)(26, 201)(27, 207)(28, 195)(29, 197)(30, 198)(31, 196)(32, 203)(33, 202)(34, 211)(35, 180)(36, 184)(37, 185)(38, 186)(39, 217)(40, 189)(41, 190)(42, 192)(43, 193)(44, 219)(45, 187)(46, 223)(47, 213)(48, 215)(49, 218)(50, 194)(51, 214)(52, 225)(53, 205)(54, 210)(55, 199)(56, 206)(57, 208)(58, 204)(59, 209)(60, 212)(61, 233)(62, 238)(63, 229)(64, 231)(65, 230)(66, 235)(67, 234)(68, 237)(69, 216)(70, 220)(71, 221)(72, 240)(73, 224)(74, 226)(75, 227)(76, 239)(77, 222)(78, 228)(79, 232)(80, 236)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1727
Graph:: bipartite
	v = 24 e = 160 f = 84
	degree seq :: [ 8^20, 40^4 ]

E27.1723 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^2 * Y1^4 * Y2^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-2, Y1 * Y2 * Y1^3 * Y2 * Y1 * Y2 * Y1^-1 * Y2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-6, Y2^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 18, 98, 42, 122, 67, 147, 62, 142, 31, 111, 52, 132, 27, 107, 49, 129, 40, 120, 55, 135, 39, 119, 54, 134, 73, 153, 58, 138, 35, 115, 13, 93, 4, 84)(3, 83, 9, 89, 19, 99, 45, 125, 41, 121, 66, 146, 74, 154, 60, 140, 75, 155, 51, 131, 37, 117, 14, 94, 25, 105, 8, 88, 24, 104, 44, 124, 70, 150, 63, 143, 32, 112, 11, 91)(5, 85, 15, 95, 20, 100, 47, 127, 68, 148, 65, 145, 34, 114, 12, 92, 23, 103, 7, 87, 21, 101, 43, 123, 69, 149, 56, 136, 76, 156, 59, 139, 29, 109, 57, 137, 36, 116, 16, 96)(10, 90, 22, 102, 46, 126, 38, 118, 17, 97, 26, 106, 48, 128, 71, 151, 79, 159, 77, 157, 64, 144, 33, 113, 53, 133, 28, 108, 50, 130, 72, 152, 80, 160, 78, 158, 61, 141, 30, 110)(161, 241, 163, 243, 170, 250, 189, 269, 218, 298, 230, 310, 240, 320, 229, 309, 215, 295, 185, 265, 213, 293, 183, 263, 212, 292, 235, 315, 239, 319, 228, 308, 202, 282, 201, 281, 177, 257, 165, 245)(162, 242, 167, 247, 182, 262, 211, 291, 195, 275, 225, 305, 238, 318, 226, 306, 199, 279, 175, 255, 188, 268, 169, 249, 187, 267, 217, 297, 237, 317, 223, 303, 227, 307, 216, 296, 186, 266, 168, 248)(164, 244, 172, 252, 190, 270, 220, 300, 233, 313, 207, 287, 232, 312, 205, 285, 200, 280, 176, 256, 193, 273, 171, 251, 191, 271, 219, 299, 231, 311, 204, 284, 178, 258, 203, 283, 198, 278, 174, 254)(166, 246, 179, 259, 206, 286, 196, 276, 173, 253, 192, 272, 221, 301, 236, 316, 214, 294, 184, 264, 210, 290, 181, 261, 209, 289, 197, 277, 224, 304, 194, 274, 222, 302, 234, 314, 208, 288, 180, 260)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 179)(7, 182)(8, 162)(9, 187)(10, 189)(11, 191)(12, 190)(13, 192)(14, 164)(15, 188)(16, 193)(17, 165)(18, 203)(19, 206)(20, 166)(21, 209)(22, 211)(23, 212)(24, 210)(25, 213)(26, 168)(27, 217)(28, 169)(29, 218)(30, 220)(31, 219)(32, 221)(33, 171)(34, 222)(35, 225)(36, 173)(37, 224)(38, 174)(39, 175)(40, 176)(41, 177)(42, 201)(43, 198)(44, 178)(45, 200)(46, 196)(47, 232)(48, 180)(49, 197)(50, 181)(51, 195)(52, 235)(53, 183)(54, 184)(55, 185)(56, 186)(57, 237)(58, 230)(59, 231)(60, 233)(61, 236)(62, 234)(63, 227)(64, 194)(65, 238)(66, 199)(67, 216)(68, 202)(69, 215)(70, 240)(71, 204)(72, 205)(73, 207)(74, 208)(75, 239)(76, 214)(77, 223)(78, 226)(79, 228)(80, 229)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1724
Graph:: bipartite
	v = 8 e = 160 f = 100
	degree seq :: [ 40^8 ]

E27.1724 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y2^-2 * Y3^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y2, Y3^-1)^2, Y3^3 * Y2 * Y3^7 * Y2^-1, (Y3 * Y2)^20, (Y3^-1 * Y1^-1)^20 ]
Map::
	R = (1, 81)(2, 82)(3, 83)(4, 84)(5, 85)(6, 86)(7, 87)(8, 88)(9, 89)(10, 90)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 103)(24, 104)(25, 105)(26, 106)(27, 107)(28, 108)(29, 109)(30, 110)(31, 111)(32, 112)(33, 113)(34, 114)(35, 115)(36, 116)(37, 117)(38, 118)(39, 119)(40, 120)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)(161, 241, 162, 242, 166, 246, 164, 244)(163, 243, 169, 249, 177, 257, 171, 251)(165, 245, 174, 254, 178, 258, 175, 255)(167, 247, 179, 259, 172, 252, 181, 261)(168, 248, 182, 262, 173, 253, 183, 263)(170, 250, 180, 260, 195, 275, 188, 268)(176, 256, 184, 264, 196, 276, 191, 271)(185, 265, 197, 277, 189, 269, 200, 280)(186, 266, 198, 278, 190, 270, 201, 281)(187, 267, 205, 285, 213, 293, 207, 287)(192, 272, 202, 282, 193, 273, 203, 283)(194, 274, 210, 290, 214, 294, 211, 291)(199, 279, 215, 295, 208, 288, 217, 297)(204, 284, 218, 298, 209, 289, 219, 299)(206, 286, 216, 296, 229, 309, 223, 303)(212, 292, 220, 300, 230, 310, 225, 305)(221, 301, 231, 311, 224, 304, 233, 313)(222, 302, 236, 316, 239, 319, 237, 317)(226, 306, 234, 314, 227, 307, 235, 315)(228, 308, 232, 312, 240, 320, 238, 318)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 177)(7, 180)(8, 162)(9, 185)(10, 187)(11, 189)(12, 188)(13, 164)(14, 186)(15, 190)(16, 165)(17, 195)(18, 166)(19, 197)(20, 199)(21, 200)(22, 198)(23, 201)(24, 168)(25, 205)(26, 169)(27, 206)(28, 208)(29, 207)(30, 171)(31, 173)(32, 174)(33, 175)(34, 176)(35, 213)(36, 178)(37, 215)(38, 179)(39, 216)(40, 217)(41, 181)(42, 182)(43, 183)(44, 184)(45, 221)(46, 222)(47, 224)(48, 223)(49, 191)(50, 192)(51, 193)(52, 194)(53, 229)(54, 196)(55, 231)(56, 232)(57, 233)(58, 202)(59, 203)(60, 204)(61, 236)(62, 235)(63, 238)(64, 237)(65, 209)(66, 210)(67, 211)(68, 212)(69, 239)(70, 214)(71, 240)(72, 226)(73, 228)(74, 218)(75, 219)(76, 220)(77, 225)(78, 227)(79, 234)(80, 230)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 40, 40 ), ( 40^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1723
Graph:: simple bipartite
	v = 100 e = 160 f = 8
	degree seq :: [ 2^80, 8^20 ]

E27.1725 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 13, 93, 21, 101, 29, 109, 37, 117, 45, 125, 53, 133, 61, 141, 69, 149, 68, 148, 60, 140, 52, 132, 44, 124, 36, 116, 28, 108, 20, 100, 12, 92, 4, 84)(3, 83, 8, 88, 14, 94, 23, 103, 30, 110, 39, 119, 46, 126, 55, 135, 62, 142, 71, 151, 76, 156, 74, 154, 66, 146, 58, 138, 50, 130, 42, 122, 34, 114, 26, 106, 18, 98, 10, 90)(5, 85, 7, 87, 15, 95, 22, 102, 31, 111, 38, 118, 47, 127, 54, 134, 63, 143, 70, 150, 77, 157, 75, 155, 67, 147, 59, 139, 51, 131, 43, 123, 35, 115, 27, 107, 19, 99, 11, 91)(9, 89, 16, 96, 24, 104, 32, 112, 40, 120, 48, 128, 56, 136, 64, 144, 72, 152, 78, 158, 80, 160, 79, 159, 73, 153, 65, 145, 57, 137, 49, 129, 41, 121, 33, 113, 25, 105, 17, 97)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320)
	L = (1, 163)(2, 167)(3, 169)(4, 171)(5, 161)(6, 174)(7, 176)(8, 162)(9, 165)(10, 164)(11, 177)(12, 178)(13, 182)(14, 184)(15, 166)(16, 168)(17, 170)(18, 185)(19, 172)(20, 187)(21, 190)(22, 192)(23, 173)(24, 175)(25, 179)(26, 180)(27, 193)(28, 194)(29, 198)(30, 200)(31, 181)(32, 183)(33, 186)(34, 201)(35, 188)(36, 203)(37, 206)(38, 208)(39, 189)(40, 191)(41, 195)(42, 196)(43, 209)(44, 210)(45, 214)(46, 216)(47, 197)(48, 199)(49, 202)(50, 217)(51, 204)(52, 219)(53, 222)(54, 224)(55, 205)(56, 207)(57, 211)(58, 212)(59, 225)(60, 226)(61, 230)(62, 232)(63, 213)(64, 215)(65, 218)(66, 233)(67, 220)(68, 235)(69, 236)(70, 238)(71, 221)(72, 223)(73, 227)(74, 228)(75, 239)(76, 240)(77, 229)(78, 231)(79, 234)(80, 237)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1721
Graph:: simple bipartite
	v = 84 e = 160 f = 24
	degree seq :: [ 2^80, 40^4 ]

E27.1726 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y3 * Y1 * Y3^-2 * Y1^-1 * Y3, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, (Y3 * Y2^-1)^4, Y3^2 * Y1^10, Y1^-2 * Y3 * Y1^-4 * Y3 * Y1^-4, (Y1^-1 * Y3^-1)^20 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 17, 97, 35, 115, 53, 133, 69, 149, 61, 141, 45, 125, 27, 107, 10, 90, 21, 101, 39, 119, 57, 137, 73, 153, 66, 146, 50, 130, 32, 112, 13, 93, 4, 84)(3, 83, 9, 89, 18, 98, 38, 118, 54, 134, 72, 152, 67, 147, 52, 132, 33, 113, 16, 96, 5, 85, 15, 95, 19, 99, 40, 120, 55, 135, 74, 154, 63, 143, 47, 127, 29, 109, 11, 91)(7, 87, 20, 100, 36, 116, 56, 136, 70, 150, 68, 148, 51, 131, 34, 114, 14, 94, 24, 104, 8, 88, 23, 103, 37, 117, 58, 138, 71, 151, 65, 145, 49, 129, 31, 111, 12, 92, 22, 102)(25, 105, 41, 121, 59, 139, 75, 155, 79, 159, 78, 158, 64, 144, 48, 128, 30, 110, 44, 124, 26, 106, 42, 122, 60, 140, 76, 156, 80, 160, 77, 157, 62, 142, 46, 126, 28, 108, 43, 123)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 178)(7, 181)(8, 162)(9, 185)(10, 165)(11, 188)(12, 187)(13, 189)(14, 164)(15, 186)(16, 190)(17, 196)(18, 199)(19, 166)(20, 201)(21, 168)(22, 203)(23, 202)(24, 204)(25, 175)(26, 169)(27, 174)(28, 176)(29, 205)(30, 171)(31, 206)(32, 209)(33, 173)(34, 208)(35, 214)(36, 217)(37, 177)(38, 219)(39, 179)(40, 220)(41, 183)(42, 180)(43, 184)(44, 182)(45, 193)(46, 194)(47, 222)(48, 191)(49, 221)(50, 223)(51, 192)(52, 224)(53, 230)(54, 233)(55, 195)(56, 235)(57, 197)(58, 236)(59, 200)(60, 198)(61, 211)(62, 212)(63, 229)(64, 207)(65, 237)(66, 231)(67, 210)(68, 238)(69, 227)(70, 226)(71, 213)(72, 239)(73, 215)(74, 240)(75, 218)(76, 216)(77, 228)(78, 225)(79, 234)(80, 232)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1720
Graph:: simple bipartite
	v = 84 e = 160 f = 24
	degree seq :: [ 2^80, 40^4 ]

E27.1727 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 20, 20})
Quotient :: dipole
Aut^+ = C5 x (C4 : C4) (small group id <80, 22>)
Aut   = (C2 x C4 x D10) : C2 (small group id <160, 116>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, (Y3 * Y2^-1)^4, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-8, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 81, 2, 82, 6, 86, 17, 97, 35, 115, 53, 133, 69, 149, 64, 144, 48, 128, 30, 110, 44, 124, 26, 106, 42, 122, 60, 140, 76, 156, 66, 146, 50, 130, 32, 112, 13, 93, 4, 84)(3, 83, 9, 89, 18, 98, 38, 118, 54, 134, 72, 152, 65, 145, 49, 129, 31, 111, 12, 92, 22, 102, 7, 87, 20, 100, 36, 116, 56, 136, 70, 150, 63, 143, 47, 127, 29, 109, 11, 91)(5, 85, 15, 95, 19, 99, 40, 120, 55, 135, 74, 154, 68, 148, 51, 131, 34, 114, 14, 94, 24, 104, 8, 88, 23, 103, 37, 117, 58, 138, 71, 151, 67, 147, 52, 132, 33, 113, 16, 96)(10, 90, 21, 101, 39, 119, 57, 137, 73, 153, 79, 159, 78, 158, 62, 142, 46, 126, 28, 108, 43, 123, 25, 105, 41, 121, 59, 139, 75, 155, 80, 160, 77, 157, 61, 141, 45, 125, 27, 107)(161, 241)(162, 242)(163, 243)(164, 244)(165, 245)(166, 246)(167, 247)(168, 248)(169, 249)(170, 250)(171, 251)(172, 252)(173, 253)(174, 254)(175, 255)(176, 256)(177, 257)(178, 258)(179, 259)(180, 260)(181, 261)(182, 262)(183, 263)(184, 264)(185, 265)(186, 266)(187, 267)(188, 268)(189, 269)(190, 270)(191, 271)(192, 272)(193, 273)(194, 274)(195, 275)(196, 276)(197, 277)(198, 278)(199, 279)(200, 280)(201, 281)(202, 282)(203, 283)(204, 284)(205, 285)(206, 286)(207, 287)(208, 288)(209, 289)(210, 290)(211, 291)(212, 292)(213, 293)(214, 294)(215, 295)(216, 296)(217, 297)(218, 298)(219, 299)(220, 300)(221, 301)(222, 302)(223, 303)(224, 304)(225, 305)(226, 306)(227, 307)(228, 308)(229, 309)(230, 310)(231, 311)(232, 312)(233, 313)(234, 314)(235, 315)(236, 316)(237, 317)(238, 318)(239, 319)(240, 320)
	L = (1, 163)(2, 167)(3, 170)(4, 172)(5, 161)(6, 178)(7, 181)(8, 162)(9, 185)(10, 165)(11, 188)(12, 187)(13, 189)(14, 164)(15, 186)(16, 190)(17, 196)(18, 199)(19, 166)(20, 201)(21, 168)(22, 203)(23, 202)(24, 204)(25, 175)(26, 169)(27, 174)(28, 176)(29, 205)(30, 171)(31, 206)(32, 209)(33, 173)(34, 208)(35, 214)(36, 217)(37, 177)(38, 219)(39, 179)(40, 220)(41, 183)(42, 180)(43, 184)(44, 182)(45, 193)(46, 194)(47, 222)(48, 191)(49, 221)(50, 223)(51, 192)(52, 224)(53, 230)(54, 233)(55, 195)(56, 235)(57, 197)(58, 236)(59, 200)(60, 198)(61, 211)(62, 212)(63, 237)(64, 207)(65, 238)(66, 232)(67, 210)(68, 229)(69, 225)(70, 239)(71, 213)(72, 240)(73, 215)(74, 226)(75, 218)(76, 216)(77, 227)(78, 228)(79, 231)(80, 234)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.1722
Graph:: simple bipartite
	v = 84 e = 160 f = 24
	degree seq :: [ 2^80, 40^4 ]

E27.1728 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 81, 81})
Quotient :: edge
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^27, (T1^-1 * T2^-1)^81 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 79, 73, 67, 61, 55, 49, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 81, 76, 70, 64, 58, 52, 46, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 80, 77, 71, 65, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(82, 83, 85)(84, 87, 90)(86, 88, 91)(89, 93, 96)(92, 94, 97)(95, 99, 102)(98, 100, 103)(101, 105, 108)(104, 106, 109)(107, 111, 114)(110, 112, 115)(113, 117, 120)(116, 118, 121)(119, 123, 126)(122, 124, 127)(125, 129, 132)(128, 130, 133)(131, 135, 138)(134, 136, 139)(137, 141, 144)(140, 142, 145)(143, 147, 150)(146, 148, 151)(149, 153, 156)(152, 154, 157)(155, 159, 161)(158, 160, 162)
	L = (1, 82)(2, 83)(3, 84)(4, 85)(5, 86)(6, 87)(7, 88)(8, 89)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 95)(15, 96)(16, 97)(17, 98)(18, 99)(19, 100)(20, 101)(21, 102)(22, 103)(23, 104)(24, 105)(25, 106)(26, 107)(27, 108)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 118)(38, 119)(39, 120)(40, 121)(41, 122)(42, 123)(43, 124)(44, 125)(45, 126)(46, 127)(47, 128)(48, 129)(49, 130)(50, 131)(51, 132)(52, 133)(53, 134)(54, 135)(55, 136)(56, 137)(57, 138)(58, 139)(59, 140)(60, 141)(61, 142)(62, 143)(63, 144)(64, 145)(65, 146)(66, 147)(67, 148)(68, 149)(69, 150)(70, 151)(71, 152)(72, 153)(73, 154)(74, 155)(75, 156)(76, 157)(77, 158)(78, 159)(79, 160)(80, 161)(81, 162)
	local type(s) :: { ( 162^3 ), ( 162^81 ) }
Outer automorphisms :: reflexible
Dual of E27.1732
Transitivity :: ET+
Graph:: bipartite
	v = 28 e = 81 f = 1
	degree seq :: [ 3^27, 81 ]

E27.1729 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 81, 81})
Quotient :: edge
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^-27, (T1^-1 * T2^-1)^81 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 76, 70, 64, 58, 52, 46, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 79, 73, 67, 61, 55, 49, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 77, 71, 65, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(82, 83, 85)(84, 87, 90)(86, 88, 91)(89, 93, 96)(92, 94, 97)(95, 99, 102)(98, 100, 103)(101, 105, 108)(104, 106, 109)(107, 111, 114)(110, 112, 115)(113, 117, 120)(116, 118, 121)(119, 123, 126)(122, 124, 127)(125, 129, 132)(128, 130, 133)(131, 135, 138)(134, 136, 139)(137, 141, 144)(140, 142, 145)(143, 147, 150)(146, 148, 151)(149, 153, 156)(152, 154, 157)(155, 159, 162)(158, 160, 161)
	L = (1, 82)(2, 83)(3, 84)(4, 85)(5, 86)(6, 87)(7, 88)(8, 89)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 95)(15, 96)(16, 97)(17, 98)(18, 99)(19, 100)(20, 101)(21, 102)(22, 103)(23, 104)(24, 105)(25, 106)(26, 107)(27, 108)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 118)(38, 119)(39, 120)(40, 121)(41, 122)(42, 123)(43, 124)(44, 125)(45, 126)(46, 127)(47, 128)(48, 129)(49, 130)(50, 131)(51, 132)(52, 133)(53, 134)(54, 135)(55, 136)(56, 137)(57, 138)(58, 139)(59, 140)(60, 141)(61, 142)(62, 143)(63, 144)(64, 145)(65, 146)(66, 147)(67, 148)(68, 149)(69, 150)(70, 151)(71, 152)(72, 153)(73, 154)(74, 155)(75, 156)(76, 157)(77, 158)(78, 159)(79, 160)(80, 161)(81, 162)
	local type(s) :: { ( 162^3 ), ( 162^81 ) }
Outer automorphisms :: reflexible
Dual of E27.1731
Transitivity :: ET+
Graph:: bipartite
	v = 28 e = 81 f = 1
	degree seq :: [ 3^27, 81 ]

E27.1730 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 81, 81})
Quotient :: edge
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^2 * T2^3 * T1, T1^2 * T2 * T1 * T2^2, T1^-2 * T2^10 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-10, T1^40 * T2^8 * T1^-1 * T2^2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 78, 71, 64, 60, 53, 46, 42, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 76, 72, 65, 58, 54, 47, 40, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 77, 70, 66, 59, 52, 48, 41, 34, 30, 23, 14, 13, 5)(82, 83, 87, 95, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 160, 156, 149, 142, 138, 131, 124, 120, 113, 106, 102, 91, 84, 88, 96, 94, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 159, 162, 155, 148, 144, 137, 130, 126, 119, 112, 108, 101, 90, 98, 93, 86, 89, 97, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 161, 154, 150, 143, 136, 132, 125, 118, 114, 107, 100, 92, 85)
	L = (1, 82)(2, 83)(3, 84)(4, 85)(5, 86)(6, 87)(7, 88)(8, 89)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 95)(15, 96)(16, 97)(17, 98)(18, 99)(19, 100)(20, 101)(21, 102)(22, 103)(23, 104)(24, 105)(25, 106)(26, 107)(27, 108)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 118)(38, 119)(39, 120)(40, 121)(41, 122)(42, 123)(43, 124)(44, 125)(45, 126)(46, 127)(47, 128)(48, 129)(49, 130)(50, 131)(51, 132)(52, 133)(53, 134)(54, 135)(55, 136)(56, 137)(57, 138)(58, 139)(59, 140)(60, 141)(61, 142)(62, 143)(63, 144)(64, 145)(65, 146)(66, 147)(67, 148)(68, 149)(69, 150)(70, 151)(71, 152)(72, 153)(73, 154)(74, 155)(75, 156)(76, 157)(77, 158)(78, 159)(79, 160)(80, 161)(81, 162)
	local type(s) :: { ( 6^81 ) }
Outer automorphisms :: reflexible
Dual of E27.1733
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 81 f = 27
	degree seq :: [ 81^2 ]

E27.1731 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 81, 81})
Quotient :: loop
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^27, (T1^-1 * T2^-1)^81 ]
Map:: non-degenerate
	R = (1, 82, 3, 84, 8, 89, 14, 95, 20, 101, 26, 107, 32, 113, 38, 119, 44, 125, 50, 131, 56, 137, 62, 143, 68, 149, 74, 155, 79, 160, 73, 154, 67, 148, 61, 142, 55, 136, 49, 130, 43, 124, 37, 118, 31, 112, 25, 106, 19, 100, 13, 94, 7, 88, 2, 83, 6, 87, 12, 93, 18, 99, 24, 105, 30, 111, 36, 117, 42, 123, 48, 129, 54, 135, 60, 141, 66, 147, 72, 153, 78, 159, 81, 162, 76, 157, 70, 151, 64, 145, 58, 139, 52, 133, 46, 127, 40, 121, 34, 115, 28, 109, 22, 103, 16, 97, 10, 91, 4, 85, 9, 90, 15, 96, 21, 102, 27, 108, 33, 114, 39, 120, 45, 126, 51, 132, 57, 138, 63, 144, 69, 150, 75, 156, 80, 161, 77, 158, 71, 152, 65, 146, 59, 140, 53, 134, 47, 128, 41, 122, 35, 116, 29, 110, 23, 104, 17, 98, 11, 92, 5, 86)
	L = (1, 83)(2, 85)(3, 87)(4, 82)(5, 88)(6, 90)(7, 91)(8, 93)(9, 84)(10, 86)(11, 94)(12, 96)(13, 97)(14, 99)(15, 89)(16, 92)(17, 100)(18, 102)(19, 103)(20, 105)(21, 95)(22, 98)(23, 106)(24, 108)(25, 109)(26, 111)(27, 101)(28, 104)(29, 112)(30, 114)(31, 115)(32, 117)(33, 107)(34, 110)(35, 118)(36, 120)(37, 121)(38, 123)(39, 113)(40, 116)(41, 124)(42, 126)(43, 127)(44, 129)(45, 119)(46, 122)(47, 130)(48, 132)(49, 133)(50, 135)(51, 125)(52, 128)(53, 136)(54, 138)(55, 139)(56, 141)(57, 131)(58, 134)(59, 142)(60, 144)(61, 145)(62, 147)(63, 137)(64, 140)(65, 148)(66, 150)(67, 151)(68, 153)(69, 143)(70, 146)(71, 154)(72, 156)(73, 157)(74, 159)(75, 149)(76, 152)(77, 160)(78, 161)(79, 162)(80, 155)(81, 158)
	local type(s) :: { ( 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81 ) }
Outer automorphisms :: reflexible
Dual of E27.1729
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 81 f = 28
	degree seq :: [ 162 ]

E27.1732 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 81, 81})
Quotient :: loop
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^-27, (T1^-1 * T2^-1)^81 ]
Map:: non-degenerate
	R = (1, 82, 3, 84, 8, 89, 14, 95, 20, 101, 26, 107, 32, 113, 38, 119, 44, 125, 50, 131, 56, 137, 62, 143, 68, 149, 74, 155, 80, 161, 76, 157, 70, 151, 64, 145, 58, 139, 52, 133, 46, 127, 40, 121, 34, 115, 28, 109, 22, 103, 16, 97, 10, 91, 4, 85, 9, 90, 15, 96, 21, 102, 27, 108, 33, 114, 39, 120, 45, 126, 51, 132, 57, 138, 63, 144, 69, 150, 75, 156, 81, 162, 79, 160, 73, 154, 67, 148, 61, 142, 55, 136, 49, 130, 43, 124, 37, 118, 31, 112, 25, 106, 19, 100, 13, 94, 7, 88, 2, 83, 6, 87, 12, 93, 18, 99, 24, 105, 30, 111, 36, 117, 42, 123, 48, 129, 54, 135, 60, 141, 66, 147, 72, 153, 78, 159, 77, 158, 71, 152, 65, 146, 59, 140, 53, 134, 47, 128, 41, 122, 35, 116, 29, 110, 23, 104, 17, 98, 11, 92, 5, 86)
	L = (1, 83)(2, 85)(3, 87)(4, 82)(5, 88)(6, 90)(7, 91)(8, 93)(9, 84)(10, 86)(11, 94)(12, 96)(13, 97)(14, 99)(15, 89)(16, 92)(17, 100)(18, 102)(19, 103)(20, 105)(21, 95)(22, 98)(23, 106)(24, 108)(25, 109)(26, 111)(27, 101)(28, 104)(29, 112)(30, 114)(31, 115)(32, 117)(33, 107)(34, 110)(35, 118)(36, 120)(37, 121)(38, 123)(39, 113)(40, 116)(41, 124)(42, 126)(43, 127)(44, 129)(45, 119)(46, 122)(47, 130)(48, 132)(49, 133)(50, 135)(51, 125)(52, 128)(53, 136)(54, 138)(55, 139)(56, 141)(57, 131)(58, 134)(59, 142)(60, 144)(61, 145)(62, 147)(63, 137)(64, 140)(65, 148)(66, 150)(67, 151)(68, 153)(69, 143)(70, 146)(71, 154)(72, 156)(73, 157)(74, 159)(75, 149)(76, 152)(77, 160)(78, 162)(79, 161)(80, 158)(81, 155)
	local type(s) :: { ( 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81, 3, 81 ) }
Outer automorphisms :: reflexible
Dual of E27.1728
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 81 f = 28
	degree seq :: [ 162 ]

E27.1733 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 81, 81})
Quotient :: loop
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2, T1), T2 * T1^-27, (T1^-1 * T2^-1)^81 ]
Map:: non-degenerate
	R = (1, 82, 3, 84, 5, 86)(2, 83, 7, 88, 8, 89)(4, 85, 9, 90, 11, 92)(6, 87, 13, 94, 14, 95)(10, 91, 15, 96, 17, 98)(12, 93, 19, 100, 20, 101)(16, 97, 21, 102, 23, 104)(18, 99, 25, 106, 26, 107)(22, 103, 27, 108, 29, 110)(24, 105, 31, 112, 32, 113)(28, 109, 33, 114, 35, 116)(30, 111, 37, 118, 38, 119)(34, 115, 39, 120, 41, 122)(36, 117, 43, 124, 44, 125)(40, 121, 45, 126, 47, 128)(42, 123, 49, 130, 50, 131)(46, 127, 51, 132, 53, 134)(48, 129, 55, 136, 56, 137)(52, 133, 57, 138, 59, 140)(54, 135, 61, 142, 62, 143)(58, 139, 63, 144, 65, 146)(60, 141, 67, 148, 68, 149)(64, 145, 69, 150, 71, 152)(66, 147, 73, 154, 74, 155)(70, 151, 75, 156, 77, 158)(72, 153, 79, 160, 80, 161)(76, 157, 78, 159, 81, 162)
	L = (1, 83)(2, 87)(3, 88)(4, 82)(5, 89)(6, 93)(7, 94)(8, 95)(9, 84)(10, 85)(11, 86)(12, 99)(13, 100)(14, 101)(15, 90)(16, 91)(17, 92)(18, 105)(19, 106)(20, 107)(21, 96)(22, 97)(23, 98)(24, 111)(25, 112)(26, 113)(27, 102)(28, 103)(29, 104)(30, 117)(31, 118)(32, 119)(33, 108)(34, 109)(35, 110)(36, 123)(37, 124)(38, 125)(39, 114)(40, 115)(41, 116)(42, 129)(43, 130)(44, 131)(45, 120)(46, 121)(47, 122)(48, 135)(49, 136)(50, 137)(51, 126)(52, 127)(53, 128)(54, 141)(55, 142)(56, 143)(57, 132)(58, 133)(59, 134)(60, 147)(61, 148)(62, 149)(63, 138)(64, 139)(65, 140)(66, 153)(67, 154)(68, 155)(69, 144)(70, 145)(71, 146)(72, 159)(73, 160)(74, 161)(75, 150)(76, 151)(77, 152)(78, 156)(79, 162)(80, 157)(81, 158)
	local type(s) :: { ( 81^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1730
Transitivity :: ET+ VT+ AT
Graph::
	v = 27 e = 81 f = 2
	degree seq :: [ 6^27 ]

E27.1734 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y3^3, Y1^3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3 * Y2^-27, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 82, 2, 83, 4, 85)(3, 84, 6, 87, 9, 90)(5, 86, 7, 88, 10, 91)(8, 89, 12, 93, 15, 96)(11, 92, 13, 94, 16, 97)(14, 95, 18, 99, 21, 102)(17, 98, 19, 100, 22, 103)(20, 101, 24, 105, 27, 108)(23, 104, 25, 106, 28, 109)(26, 107, 30, 111, 33, 114)(29, 110, 31, 112, 34, 115)(32, 113, 36, 117, 39, 120)(35, 116, 37, 118, 40, 121)(38, 119, 42, 123, 45, 126)(41, 122, 43, 124, 46, 127)(44, 125, 48, 129, 51, 132)(47, 128, 49, 130, 52, 133)(50, 131, 54, 135, 57, 138)(53, 134, 55, 136, 58, 139)(56, 137, 60, 141, 63, 144)(59, 140, 61, 142, 64, 145)(62, 143, 66, 147, 69, 150)(65, 146, 67, 148, 70, 151)(68, 149, 72, 153, 75, 156)(71, 152, 73, 154, 76, 157)(74, 155, 78, 159, 81, 162)(77, 158, 79, 160, 80, 161)(163, 244, 165, 246, 170, 251, 176, 257, 182, 263, 188, 269, 194, 275, 200, 281, 206, 287, 212, 293, 218, 299, 224, 305, 230, 311, 236, 317, 242, 323, 238, 319, 232, 313, 226, 307, 220, 301, 214, 295, 208, 289, 202, 283, 196, 277, 190, 271, 184, 265, 178, 259, 172, 253, 166, 247, 171, 252, 177, 258, 183, 264, 189, 270, 195, 276, 201, 282, 207, 288, 213, 294, 219, 300, 225, 306, 231, 312, 237, 318, 243, 324, 241, 322, 235, 316, 229, 310, 223, 304, 217, 298, 211, 292, 205, 286, 199, 280, 193, 274, 187, 268, 181, 262, 175, 256, 169, 250, 164, 245, 168, 249, 174, 255, 180, 261, 186, 267, 192, 273, 198, 279, 204, 285, 210, 291, 216, 297, 222, 303, 228, 309, 234, 315, 240, 321, 239, 320, 233, 314, 227, 308, 221, 302, 215, 296, 209, 290, 203, 284, 197, 278, 191, 272, 185, 266, 179, 260, 173, 254, 167, 248)
	L = (1, 166)(2, 163)(3, 171)(4, 164)(5, 172)(6, 165)(7, 167)(8, 177)(9, 168)(10, 169)(11, 178)(12, 170)(13, 173)(14, 183)(15, 174)(16, 175)(17, 184)(18, 176)(19, 179)(20, 189)(21, 180)(22, 181)(23, 190)(24, 182)(25, 185)(26, 195)(27, 186)(28, 187)(29, 196)(30, 188)(31, 191)(32, 201)(33, 192)(34, 193)(35, 202)(36, 194)(37, 197)(38, 207)(39, 198)(40, 199)(41, 208)(42, 200)(43, 203)(44, 213)(45, 204)(46, 205)(47, 214)(48, 206)(49, 209)(50, 219)(51, 210)(52, 211)(53, 220)(54, 212)(55, 215)(56, 225)(57, 216)(58, 217)(59, 226)(60, 218)(61, 221)(62, 231)(63, 222)(64, 223)(65, 232)(66, 224)(67, 227)(68, 237)(69, 228)(70, 229)(71, 238)(72, 230)(73, 233)(74, 243)(75, 234)(76, 235)(77, 242)(78, 236)(79, 239)(80, 241)(81, 240)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 2, 162, 2, 162, 2, 162 ), ( 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162 ) }
Outer automorphisms :: reflexible
Dual of E27.1738
Graph:: bipartite
	v = 28 e = 162 f = 82
	degree seq :: [ 6^27, 162 ]

E27.1735 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^27 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 82, 2, 83, 4, 85)(3, 84, 6, 87, 9, 90)(5, 86, 7, 88, 10, 91)(8, 89, 12, 93, 15, 96)(11, 92, 13, 94, 16, 97)(14, 95, 18, 99, 21, 102)(17, 98, 19, 100, 22, 103)(20, 101, 24, 105, 27, 108)(23, 104, 25, 106, 28, 109)(26, 107, 30, 111, 33, 114)(29, 110, 31, 112, 34, 115)(32, 113, 36, 117, 39, 120)(35, 116, 37, 118, 40, 121)(38, 119, 42, 123, 45, 126)(41, 122, 43, 124, 46, 127)(44, 125, 48, 129, 51, 132)(47, 128, 49, 130, 52, 133)(50, 131, 54, 135, 57, 138)(53, 134, 55, 136, 58, 139)(56, 137, 60, 141, 63, 144)(59, 140, 61, 142, 64, 145)(62, 143, 66, 147, 69, 150)(65, 146, 67, 148, 70, 151)(68, 149, 72, 153, 75, 156)(71, 152, 73, 154, 76, 157)(74, 155, 78, 159, 80, 161)(77, 158, 79, 160, 81, 162)(163, 244, 165, 246, 170, 251, 176, 257, 182, 263, 188, 269, 194, 275, 200, 281, 206, 287, 212, 293, 218, 299, 224, 305, 230, 311, 236, 317, 241, 322, 235, 316, 229, 310, 223, 304, 217, 298, 211, 292, 205, 286, 199, 280, 193, 274, 187, 268, 181, 262, 175, 256, 169, 250, 164, 245, 168, 249, 174, 255, 180, 261, 186, 267, 192, 273, 198, 279, 204, 285, 210, 291, 216, 297, 222, 303, 228, 309, 234, 315, 240, 321, 243, 324, 238, 319, 232, 313, 226, 307, 220, 301, 214, 295, 208, 289, 202, 283, 196, 277, 190, 271, 184, 265, 178, 259, 172, 253, 166, 247, 171, 252, 177, 258, 183, 264, 189, 270, 195, 276, 201, 282, 207, 288, 213, 294, 219, 300, 225, 306, 231, 312, 237, 318, 242, 323, 239, 320, 233, 314, 227, 308, 221, 302, 215, 296, 209, 290, 203, 284, 197, 278, 191, 272, 185, 266, 179, 260, 173, 254, 167, 248)
	L = (1, 166)(2, 163)(3, 171)(4, 164)(5, 172)(6, 165)(7, 167)(8, 177)(9, 168)(10, 169)(11, 178)(12, 170)(13, 173)(14, 183)(15, 174)(16, 175)(17, 184)(18, 176)(19, 179)(20, 189)(21, 180)(22, 181)(23, 190)(24, 182)(25, 185)(26, 195)(27, 186)(28, 187)(29, 196)(30, 188)(31, 191)(32, 201)(33, 192)(34, 193)(35, 202)(36, 194)(37, 197)(38, 207)(39, 198)(40, 199)(41, 208)(42, 200)(43, 203)(44, 213)(45, 204)(46, 205)(47, 214)(48, 206)(49, 209)(50, 219)(51, 210)(52, 211)(53, 220)(54, 212)(55, 215)(56, 225)(57, 216)(58, 217)(59, 226)(60, 218)(61, 221)(62, 231)(63, 222)(64, 223)(65, 232)(66, 224)(67, 227)(68, 237)(69, 228)(70, 229)(71, 238)(72, 230)(73, 233)(74, 242)(75, 234)(76, 235)(77, 243)(78, 236)(79, 239)(80, 240)(81, 241)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 2, 162, 2, 162, 2, 162 ), ( 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162, 2, 162 ) }
Outer automorphisms :: reflexible
Dual of E27.1739
Graph:: bipartite
	v = 28 e = 162 f = 82
	degree seq :: [ 6^27, 162 ]

E27.1736 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^3 * Y2^3, (Y3^-1 * Y1^-1)^3, Y1^13 * Y2^-14, Y2^11 * Y1^65, Y1^81, Y1^-324 ]
Map::
	R = (1, 82, 2, 83, 6, 87, 14, 95, 22, 103, 28, 109, 34, 115, 40, 121, 46, 127, 52, 133, 58, 139, 64, 145, 70, 151, 76, 157, 81, 162, 74, 155, 67, 148, 63, 144, 56, 137, 49, 130, 45, 126, 38, 119, 31, 112, 27, 108, 20, 101, 9, 90, 17, 98, 12, 93, 5, 86, 8, 89, 16, 97, 23, 104, 29, 110, 35, 116, 41, 122, 47, 128, 53, 134, 59, 140, 65, 146, 71, 152, 77, 158, 79, 160, 75, 156, 68, 149, 61, 142, 57, 138, 50, 131, 43, 124, 39, 120, 32, 113, 25, 106, 21, 102, 10, 91, 3, 84, 7, 88, 15, 96, 13, 94, 18, 99, 24, 105, 30, 111, 36, 117, 42, 123, 48, 129, 54, 135, 60, 141, 66, 147, 72, 153, 78, 159, 80, 161, 73, 154, 69, 150, 62, 143, 55, 136, 51, 132, 44, 125, 37, 118, 33, 114, 26, 107, 19, 100, 11, 92, 4, 85)(163, 244, 165, 246, 171, 252, 181, 262, 187, 268, 193, 274, 199, 280, 205, 286, 211, 292, 217, 298, 223, 304, 229, 310, 235, 316, 241, 322, 238, 319, 234, 315, 227, 308, 220, 301, 216, 297, 209, 290, 202, 283, 198, 279, 191, 272, 184, 265, 180, 261, 170, 251, 164, 245, 169, 250, 179, 260, 173, 254, 183, 264, 189, 270, 195, 276, 201, 282, 207, 288, 213, 294, 219, 300, 225, 306, 231, 312, 237, 318, 243, 324, 240, 321, 233, 314, 226, 307, 222, 303, 215, 296, 208, 289, 204, 285, 197, 278, 190, 271, 186, 267, 178, 259, 168, 249, 177, 258, 174, 255, 166, 247, 172, 253, 182, 263, 188, 269, 194, 275, 200, 281, 206, 287, 212, 293, 218, 299, 224, 305, 230, 311, 236, 317, 242, 323, 239, 320, 232, 313, 228, 309, 221, 302, 214, 295, 210, 291, 203, 284, 196, 277, 192, 273, 185, 266, 176, 257, 175, 256, 167, 248)
	L = (1, 165)(2, 169)(3, 171)(4, 172)(5, 163)(6, 177)(7, 179)(8, 164)(9, 181)(10, 182)(11, 183)(12, 166)(13, 167)(14, 175)(15, 174)(16, 168)(17, 173)(18, 170)(19, 187)(20, 188)(21, 189)(22, 180)(23, 176)(24, 178)(25, 193)(26, 194)(27, 195)(28, 186)(29, 184)(30, 185)(31, 199)(32, 200)(33, 201)(34, 192)(35, 190)(36, 191)(37, 205)(38, 206)(39, 207)(40, 198)(41, 196)(42, 197)(43, 211)(44, 212)(45, 213)(46, 204)(47, 202)(48, 203)(49, 217)(50, 218)(51, 219)(52, 210)(53, 208)(54, 209)(55, 223)(56, 224)(57, 225)(58, 216)(59, 214)(60, 215)(61, 229)(62, 230)(63, 231)(64, 222)(65, 220)(66, 221)(67, 235)(68, 236)(69, 237)(70, 228)(71, 226)(72, 227)(73, 241)(74, 242)(75, 243)(76, 234)(77, 232)(78, 233)(79, 238)(80, 239)(81, 240)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1737
Graph:: bipartite
	v = 2 e = 162 f = 108
	degree seq :: [ 162^2 ]

E27.1737 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^27, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2, (Y3^-1 * Y1^-1)^81 ]
Map::
	R = (1, 82)(2, 83)(3, 84)(4, 85)(5, 86)(6, 87)(7, 88)(8, 89)(9, 90)(10, 91)(11, 92)(12, 93)(13, 94)(14, 95)(15, 96)(16, 97)(17, 98)(18, 99)(19, 100)(20, 101)(21, 102)(22, 103)(23, 104)(24, 105)(25, 106)(26, 107)(27, 108)(28, 109)(29, 110)(30, 111)(31, 112)(32, 113)(33, 114)(34, 115)(35, 116)(36, 117)(37, 118)(38, 119)(39, 120)(40, 121)(41, 122)(42, 123)(43, 124)(44, 125)(45, 126)(46, 127)(47, 128)(48, 129)(49, 130)(50, 131)(51, 132)(52, 133)(53, 134)(54, 135)(55, 136)(56, 137)(57, 138)(58, 139)(59, 140)(60, 141)(61, 142)(62, 143)(63, 144)(64, 145)(65, 146)(66, 147)(67, 148)(68, 149)(69, 150)(70, 151)(71, 152)(72, 153)(73, 154)(74, 155)(75, 156)(76, 157)(77, 158)(78, 159)(79, 160)(80, 161)(81, 162)(163, 244, 164, 245, 166, 247)(165, 246, 168, 249, 171, 252)(167, 248, 169, 250, 172, 253)(170, 251, 174, 255, 177, 258)(173, 254, 175, 256, 178, 259)(176, 257, 180, 261, 183, 264)(179, 260, 181, 262, 184, 265)(182, 263, 186, 267, 189, 270)(185, 266, 187, 268, 190, 271)(188, 269, 192, 273, 195, 276)(191, 272, 193, 274, 196, 277)(194, 275, 198, 279, 201, 282)(197, 278, 199, 280, 202, 283)(200, 281, 204, 285, 207, 288)(203, 284, 205, 286, 208, 289)(206, 287, 210, 291, 213, 294)(209, 290, 211, 292, 214, 295)(212, 293, 216, 297, 219, 300)(215, 296, 217, 298, 220, 301)(218, 299, 222, 303, 225, 306)(221, 302, 223, 304, 226, 307)(224, 305, 228, 309, 231, 312)(227, 308, 229, 310, 232, 313)(230, 311, 234, 315, 237, 318)(233, 314, 235, 316, 238, 319)(236, 317, 240, 321, 242, 323)(239, 320, 241, 322, 243, 324)
	L = (1, 165)(2, 168)(3, 170)(4, 171)(5, 163)(6, 174)(7, 164)(8, 176)(9, 177)(10, 166)(11, 167)(12, 180)(13, 169)(14, 182)(15, 183)(16, 172)(17, 173)(18, 186)(19, 175)(20, 188)(21, 189)(22, 178)(23, 179)(24, 192)(25, 181)(26, 194)(27, 195)(28, 184)(29, 185)(30, 198)(31, 187)(32, 200)(33, 201)(34, 190)(35, 191)(36, 204)(37, 193)(38, 206)(39, 207)(40, 196)(41, 197)(42, 210)(43, 199)(44, 212)(45, 213)(46, 202)(47, 203)(48, 216)(49, 205)(50, 218)(51, 219)(52, 208)(53, 209)(54, 222)(55, 211)(56, 224)(57, 225)(58, 214)(59, 215)(60, 228)(61, 217)(62, 230)(63, 231)(64, 220)(65, 221)(66, 234)(67, 223)(68, 236)(69, 237)(70, 226)(71, 227)(72, 240)(73, 229)(74, 241)(75, 242)(76, 232)(77, 233)(78, 243)(79, 235)(80, 239)(81, 238)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 162, 162 ), ( 162^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1736
Graph:: simple bipartite
	v = 108 e = 162 f = 2
	degree seq :: [ 2^81, 6^27 ]

E27.1738 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^-27, (Y1^-1 * Y3^-1)^81 ]
Map::
	R = (1, 82, 2, 83, 6, 87, 12, 93, 18, 99, 24, 105, 30, 111, 36, 117, 42, 123, 48, 129, 54, 135, 60, 141, 66, 147, 72, 153, 78, 159, 75, 156, 69, 150, 63, 144, 57, 138, 51, 132, 45, 126, 39, 120, 33, 114, 27, 108, 21, 102, 15, 96, 9, 90, 3, 84, 7, 88, 13, 94, 19, 100, 25, 106, 31, 112, 37, 118, 43, 124, 49, 130, 55, 136, 61, 142, 67, 148, 73, 154, 79, 160, 81, 162, 77, 158, 71, 152, 65, 146, 59, 140, 53, 134, 47, 128, 41, 122, 35, 116, 29, 110, 23, 104, 17, 98, 11, 92, 5, 86, 8, 89, 14, 95, 20, 101, 26, 107, 32, 113, 38, 119, 44, 125, 50, 131, 56, 137, 62, 143, 68, 149, 74, 155, 80, 161, 76, 157, 70, 151, 64, 145, 58, 139, 52, 133, 46, 127, 40, 121, 34, 115, 28, 109, 22, 103, 16, 97, 10, 91, 4, 85)(163, 244)(164, 245)(165, 246)(166, 247)(167, 248)(168, 249)(169, 250)(170, 251)(171, 252)(172, 253)(173, 254)(174, 255)(175, 256)(176, 257)(177, 258)(178, 259)(179, 260)(180, 261)(181, 262)(182, 263)(183, 264)(184, 265)(185, 266)(186, 267)(187, 268)(188, 269)(189, 270)(190, 271)(191, 272)(192, 273)(193, 274)(194, 275)(195, 276)(196, 277)(197, 278)(198, 279)(199, 280)(200, 281)(201, 282)(202, 283)(203, 284)(204, 285)(205, 286)(206, 287)(207, 288)(208, 289)(209, 290)(210, 291)(211, 292)(212, 293)(213, 294)(214, 295)(215, 296)(216, 297)(217, 298)(218, 299)(219, 300)(220, 301)(221, 302)(222, 303)(223, 304)(224, 305)(225, 306)(226, 307)(227, 308)(228, 309)(229, 310)(230, 311)(231, 312)(232, 313)(233, 314)(234, 315)(235, 316)(236, 317)(237, 318)(238, 319)(239, 320)(240, 321)(241, 322)(242, 323)(243, 324)
	L = (1, 165)(2, 169)(3, 167)(4, 171)(5, 163)(6, 175)(7, 170)(8, 164)(9, 173)(10, 177)(11, 166)(12, 181)(13, 176)(14, 168)(15, 179)(16, 183)(17, 172)(18, 187)(19, 182)(20, 174)(21, 185)(22, 189)(23, 178)(24, 193)(25, 188)(26, 180)(27, 191)(28, 195)(29, 184)(30, 199)(31, 194)(32, 186)(33, 197)(34, 201)(35, 190)(36, 205)(37, 200)(38, 192)(39, 203)(40, 207)(41, 196)(42, 211)(43, 206)(44, 198)(45, 209)(46, 213)(47, 202)(48, 217)(49, 212)(50, 204)(51, 215)(52, 219)(53, 208)(54, 223)(55, 218)(56, 210)(57, 221)(58, 225)(59, 214)(60, 229)(61, 224)(62, 216)(63, 227)(64, 231)(65, 220)(66, 235)(67, 230)(68, 222)(69, 233)(70, 237)(71, 226)(72, 241)(73, 236)(74, 228)(75, 239)(76, 240)(77, 232)(78, 243)(79, 242)(80, 234)(81, 238)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 6, 162 ), ( 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162 ) }
Outer automorphisms :: reflexible
Dual of E27.1734
Graph:: bipartite
	v = 82 e = 162 f = 28
	degree seq :: [ 2^81, 162 ]

E27.1739 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 81, 81})
Quotient :: dipole
Aut^+ = C81 (small group id <81, 1>)
Aut   = D162 (small group id <162, 1>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^-27, (Y1^-1 * Y3^-1)^81 ]
Map::
	R = (1, 82, 2, 83, 6, 87, 12, 93, 18, 99, 24, 105, 30, 111, 36, 117, 42, 123, 48, 129, 54, 135, 60, 141, 66, 147, 72, 153, 78, 159, 77, 158, 71, 152, 65, 146, 59, 140, 53, 134, 47, 128, 41, 122, 35, 116, 29, 110, 23, 104, 17, 98, 11, 92, 5, 86, 8, 89, 14, 95, 20, 101, 26, 107, 32, 113, 38, 119, 44, 125, 50, 131, 56, 137, 62, 143, 68, 149, 74, 155, 80, 161, 81, 162, 75, 156, 69, 150, 63, 144, 57, 138, 51, 132, 45, 126, 39, 120, 33, 114, 27, 108, 21, 102, 15, 96, 9, 90, 3, 84, 7, 88, 13, 94, 19, 100, 25, 106, 31, 112, 37, 118, 43, 124, 49, 130, 55, 136, 61, 142, 67, 148, 73, 154, 79, 160, 76, 157, 70, 151, 64, 145, 58, 139, 52, 133, 46, 127, 40, 121, 34, 115, 28, 109, 22, 103, 16, 97, 10, 91, 4, 85)(163, 244)(164, 245)(165, 246)(166, 247)(167, 248)(168, 249)(169, 250)(170, 251)(171, 252)(172, 253)(173, 254)(174, 255)(175, 256)(176, 257)(177, 258)(178, 259)(179, 260)(180, 261)(181, 262)(182, 263)(183, 264)(184, 265)(185, 266)(186, 267)(187, 268)(188, 269)(189, 270)(190, 271)(191, 272)(192, 273)(193, 274)(194, 275)(195, 276)(196, 277)(197, 278)(198, 279)(199, 280)(200, 281)(201, 282)(202, 283)(203, 284)(204, 285)(205, 286)(206, 287)(207, 288)(208, 289)(209, 290)(210, 291)(211, 292)(212, 293)(213, 294)(214, 295)(215, 296)(216, 297)(217, 298)(218, 299)(219, 300)(220, 301)(221, 302)(222, 303)(223, 304)(224, 305)(225, 306)(226, 307)(227, 308)(228, 309)(229, 310)(230, 311)(231, 312)(232, 313)(233, 314)(234, 315)(235, 316)(236, 317)(237, 318)(238, 319)(239, 320)(240, 321)(241, 322)(242, 323)(243, 324)
	L = (1, 165)(2, 169)(3, 167)(4, 171)(5, 163)(6, 175)(7, 170)(8, 164)(9, 173)(10, 177)(11, 166)(12, 181)(13, 176)(14, 168)(15, 179)(16, 183)(17, 172)(18, 187)(19, 182)(20, 174)(21, 185)(22, 189)(23, 178)(24, 193)(25, 188)(26, 180)(27, 191)(28, 195)(29, 184)(30, 199)(31, 194)(32, 186)(33, 197)(34, 201)(35, 190)(36, 205)(37, 200)(38, 192)(39, 203)(40, 207)(41, 196)(42, 211)(43, 206)(44, 198)(45, 209)(46, 213)(47, 202)(48, 217)(49, 212)(50, 204)(51, 215)(52, 219)(53, 208)(54, 223)(55, 218)(56, 210)(57, 221)(58, 225)(59, 214)(60, 229)(61, 224)(62, 216)(63, 227)(64, 231)(65, 220)(66, 235)(67, 230)(68, 222)(69, 233)(70, 237)(71, 226)(72, 241)(73, 236)(74, 228)(75, 239)(76, 243)(77, 232)(78, 238)(79, 242)(80, 234)(81, 240)(82, 244)(83, 245)(84, 246)(85, 247)(86, 248)(87, 249)(88, 250)(89, 251)(90, 252)(91, 253)(92, 254)(93, 255)(94, 256)(95, 257)(96, 258)(97, 259)(98, 260)(99, 261)(100, 262)(101, 263)(102, 264)(103, 265)(104, 266)(105, 267)(106, 268)(107, 269)(108, 270)(109, 271)(110, 272)(111, 273)(112, 274)(113, 275)(114, 276)(115, 277)(116, 278)(117, 279)(118, 280)(119, 281)(120, 282)(121, 283)(122, 284)(123, 285)(124, 286)(125, 287)(126, 288)(127, 289)(128, 290)(129, 291)(130, 292)(131, 293)(132, 294)(133, 295)(134, 296)(135, 297)(136, 298)(137, 299)(138, 300)(139, 301)(140, 302)(141, 303)(142, 304)(143, 305)(144, 306)(145, 307)(146, 308)(147, 309)(148, 310)(149, 311)(150, 312)(151, 313)(152, 314)(153, 315)(154, 316)(155, 317)(156, 318)(157, 319)(158, 320)(159, 321)(160, 322)(161, 323)(162, 324)
	local type(s) :: { ( 6, 162 ), ( 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162, 6, 162 ) }
Outer automorphisms :: reflexible
Dual of E27.1735
Graph:: bipartite
	v = 82 e = 162 f = 28
	degree seq :: [ 2^81, 162 ]

E27.1740 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 12, 21})
Quotient :: edge
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1^-1 * T2^-2 * T1, T1^2 * T2^6, T2^-3 * T1 * T2^-2 * T1 * T2^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 36, 18, 6, 17, 35, 34, 16, 5)(2, 7, 20, 39, 31, 13, 4, 12, 28, 44, 24, 8)(9, 25, 46, 33, 15, 30, 11, 29, 50, 32, 14, 26)(19, 37, 54, 43, 23, 41, 21, 40, 58, 42, 22, 38)(45, 61, 52, 66, 49, 64, 47, 63, 51, 65, 48, 62)(53, 67, 60, 72, 57, 70, 55, 69, 59, 71, 56, 68)(73, 81, 78, 79, 76, 84, 74, 82, 77, 80, 75, 83)(85, 86, 90, 88)(87, 93, 101, 95)(89, 98, 102, 99)(91, 103, 96, 105)(92, 106, 97, 107)(94, 104, 119, 112)(100, 108, 120, 115)(109, 129, 113, 131)(110, 132, 114, 133)(111, 130, 118, 134)(116, 135, 117, 136)(121, 137, 124, 139)(122, 140, 125, 141)(123, 138, 128, 142)(126, 143, 127, 144)(145, 157, 147, 158)(146, 159, 148, 160)(149, 161, 150, 162)(151, 163, 153, 164)(152, 165, 154, 166)(155, 167, 156, 168)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 42^4 ), ( 42^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1744
Transitivity :: ET+
Graph:: bipartite
	v = 28 e = 84 f = 4
	degree seq :: [ 4^21, 12^7 ]

E27.1741 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 12, 21})
Quotient :: edge
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1 * T2^2 * T1 * T2^2 * T1^2, (T2^-1 * T1^-1)^4, T2^4 * T1 * T2^-2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 65, 53, 76, 57, 25, 56, 83, 81, 54, 23, 44, 75, 59, 74, 43, 17, 5)(2, 7, 22, 52, 64, 29, 63, 34, 15, 38, 70, 62, 28, 9, 27, 61, 41, 72, 60, 26, 8)(4, 12, 33, 69, 67, 31, 46, 40, 16, 39, 71, 68, 32, 11, 18, 45, 42, 73, 66, 37, 14)(6, 19, 47, 77, 80, 51, 35, 13, 24, 55, 82, 79, 50, 21, 49, 36, 58, 84, 78, 48, 20)(85, 86, 90, 102, 128, 111, 133, 124, 141, 118, 97, 88)(87, 93, 103, 130, 159, 147, 120, 98, 109, 92, 108, 95)(89, 99, 104, 96, 107, 91, 105, 129, 160, 145, 119, 100)(94, 113, 131, 121, 143, 110, 142, 116, 140, 112, 139, 115)(101, 125, 132, 123, 138, 122, 134, 117, 137, 106, 135, 126)(114, 144, 161, 152, 158, 146, 168, 151, 167, 148, 166, 150)(127, 136, 162, 157, 165, 156, 163, 155, 149, 154, 164, 153)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 8^12 ), ( 8^21 ) }
Outer automorphisms :: reflexible
Dual of E27.1745
Transitivity :: ET+
Graph:: bipartite
	v = 11 e = 84 f = 21
	degree seq :: [ 12^7, 21^4 ]

E27.1742 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 12, 21})
Quotient :: edge
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^2 * T2 * T1^3 * T2^-1 * T1, T1^5 * T2 * T1^-2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 62, 36)(17, 42, 73, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 58, 39, 59)(30, 64, 40, 65)(32, 60, 37, 61)(33, 63, 38, 66)(35, 57, 81, 70)(41, 67, 82, 72)(44, 74, 47, 75)(46, 76, 48, 77)(49, 78, 55, 79)(53, 80, 56, 69)(68, 83, 71, 84)(85, 86, 90, 101, 125, 143, 163, 150, 115, 138, 161, 168, 145, 111, 135, 159, 149, 153, 119, 97, 88)(87, 93, 109, 141, 130, 102, 128, 117, 96, 116, 151, 137, 106, 91, 104, 133, 118, 152, 126, 114, 95)(89, 99, 123, 154, 132, 103, 131, 122, 98, 121, 156, 140, 108, 92, 107, 139, 120, 155, 127, 124, 100)(94, 105, 129, 157, 166, 142, 162, 147, 113, 136, 160, 167, 144, 110, 134, 158, 148, 164, 165, 146, 112)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 24^4 ), ( 24^21 ) }
Outer automorphisms :: reflexible
Dual of E27.1743
Transitivity :: ET+
Graph:: simple bipartite
	v = 25 e = 84 f = 7
	degree seq :: [ 4^21, 21^4 ]

E27.1743 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 12, 21})
Quotient :: loop
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1^-1 * T2^-2 * T1, T1^2 * T2^6, T2^-3 * T1 * T2^-2 * T1 * T2^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 10, 94, 27, 111, 36, 120, 18, 102, 6, 90, 17, 101, 35, 119, 34, 118, 16, 100, 5, 89)(2, 86, 7, 91, 20, 104, 39, 123, 31, 115, 13, 97, 4, 88, 12, 96, 28, 112, 44, 128, 24, 108, 8, 92)(9, 93, 25, 109, 46, 130, 33, 117, 15, 99, 30, 114, 11, 95, 29, 113, 50, 134, 32, 116, 14, 98, 26, 110)(19, 103, 37, 121, 54, 138, 43, 127, 23, 107, 41, 125, 21, 105, 40, 124, 58, 142, 42, 126, 22, 106, 38, 122)(45, 129, 61, 145, 52, 136, 66, 150, 49, 133, 64, 148, 47, 131, 63, 147, 51, 135, 65, 149, 48, 132, 62, 146)(53, 137, 67, 151, 60, 144, 72, 156, 57, 141, 70, 154, 55, 139, 69, 153, 59, 143, 71, 155, 56, 140, 68, 152)(73, 157, 81, 165, 78, 162, 79, 163, 76, 160, 84, 168, 74, 158, 82, 166, 77, 161, 80, 164, 75, 159, 83, 167)
	L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 98)(6, 88)(7, 103)(8, 106)(9, 101)(10, 104)(11, 87)(12, 105)(13, 107)(14, 102)(15, 89)(16, 108)(17, 95)(18, 99)(19, 96)(20, 119)(21, 91)(22, 97)(23, 92)(24, 120)(25, 129)(26, 132)(27, 130)(28, 94)(29, 131)(30, 133)(31, 100)(32, 135)(33, 136)(34, 134)(35, 112)(36, 115)(37, 137)(38, 140)(39, 138)(40, 139)(41, 141)(42, 143)(43, 144)(44, 142)(45, 113)(46, 118)(47, 109)(48, 114)(49, 110)(50, 111)(51, 117)(52, 116)(53, 124)(54, 128)(55, 121)(56, 125)(57, 122)(58, 123)(59, 127)(60, 126)(61, 157)(62, 159)(63, 158)(64, 160)(65, 161)(66, 162)(67, 163)(68, 165)(69, 164)(70, 166)(71, 167)(72, 168)(73, 147)(74, 145)(75, 148)(76, 146)(77, 150)(78, 149)(79, 153)(80, 151)(81, 154)(82, 152)(83, 156)(84, 155)
	local type(s) :: { ( 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21, 4, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.1742
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 84 f = 25
	degree seq :: [ 24^7 ]

E27.1744 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 12, 21})
Quotient :: loop
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T1 * T2 * T1^-2 * T2^-1 * T1, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1 * T2^2 * T1 * T2^2 * T1^2, (T2^-1 * T1^-1)^4, T2^4 * T1 * T2^-2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 10, 94, 30, 114, 65, 149, 53, 137, 76, 160, 57, 141, 25, 109, 56, 140, 83, 167, 81, 165, 54, 138, 23, 107, 44, 128, 75, 159, 59, 143, 74, 158, 43, 127, 17, 101, 5, 89)(2, 86, 7, 91, 22, 106, 52, 136, 64, 148, 29, 113, 63, 147, 34, 118, 15, 99, 38, 122, 70, 154, 62, 146, 28, 112, 9, 93, 27, 111, 61, 145, 41, 125, 72, 156, 60, 144, 26, 110, 8, 92)(4, 88, 12, 96, 33, 117, 69, 153, 67, 151, 31, 115, 46, 130, 40, 124, 16, 100, 39, 123, 71, 155, 68, 152, 32, 116, 11, 95, 18, 102, 45, 129, 42, 126, 73, 157, 66, 150, 37, 121, 14, 98)(6, 90, 19, 103, 47, 131, 77, 161, 80, 164, 51, 135, 35, 119, 13, 97, 24, 108, 55, 139, 82, 166, 79, 163, 50, 134, 21, 105, 49, 133, 36, 120, 58, 142, 84, 168, 78, 162, 48, 132, 20, 104)
	L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 99)(6, 102)(7, 105)(8, 108)(9, 103)(10, 113)(11, 87)(12, 107)(13, 88)(14, 109)(15, 104)(16, 89)(17, 125)(18, 128)(19, 130)(20, 96)(21, 129)(22, 135)(23, 91)(24, 95)(25, 92)(26, 142)(27, 133)(28, 139)(29, 131)(30, 144)(31, 94)(32, 140)(33, 137)(34, 97)(35, 100)(36, 98)(37, 143)(38, 134)(39, 138)(40, 141)(41, 132)(42, 101)(43, 136)(44, 111)(45, 160)(46, 159)(47, 121)(48, 123)(49, 124)(50, 117)(51, 126)(52, 162)(53, 106)(54, 122)(55, 115)(56, 112)(57, 118)(58, 116)(59, 110)(60, 161)(61, 119)(62, 168)(63, 120)(64, 166)(65, 154)(66, 114)(67, 167)(68, 158)(69, 127)(70, 164)(71, 149)(72, 163)(73, 165)(74, 146)(75, 147)(76, 145)(77, 152)(78, 157)(79, 155)(80, 153)(81, 156)(82, 150)(83, 148)(84, 151)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1740
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 84 f = 28
	degree seq :: [ 42^4 ]

E27.1745 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 12, 21})
Quotient :: loop
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^2 * T2 * T1^3 * T2^-1 * T1, T1^5 * T2 * T1^-2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 10, 94, 5, 89)(2, 86, 7, 91, 21, 105, 8, 92)(4, 88, 12, 96, 28, 112, 14, 98)(6, 90, 18, 102, 45, 129, 19, 103)(9, 93, 26, 110, 15, 99, 27, 111)(11, 95, 29, 113, 16, 100, 31, 115)(13, 97, 34, 118, 62, 146, 36, 120)(17, 101, 42, 126, 73, 157, 43, 127)(20, 104, 50, 134, 23, 107, 51, 135)(22, 106, 52, 136, 24, 108, 54, 138)(25, 109, 58, 142, 39, 123, 59, 143)(30, 114, 64, 148, 40, 124, 65, 149)(32, 116, 60, 144, 37, 121, 61, 145)(33, 117, 63, 147, 38, 122, 66, 150)(35, 119, 57, 141, 81, 165, 70, 154)(41, 125, 67, 151, 82, 166, 72, 156)(44, 128, 74, 158, 47, 131, 75, 159)(46, 130, 76, 160, 48, 132, 77, 161)(49, 133, 78, 162, 55, 139, 79, 163)(53, 137, 80, 164, 56, 140, 69, 153)(68, 152, 83, 167, 71, 155, 84, 168)
	L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 99)(6, 101)(7, 104)(8, 107)(9, 109)(10, 105)(11, 87)(12, 116)(13, 88)(14, 121)(15, 123)(16, 89)(17, 125)(18, 128)(19, 131)(20, 133)(21, 129)(22, 91)(23, 139)(24, 92)(25, 141)(26, 134)(27, 135)(28, 94)(29, 136)(30, 95)(31, 138)(32, 151)(33, 96)(34, 152)(35, 97)(36, 155)(37, 156)(38, 98)(39, 154)(40, 100)(41, 143)(42, 114)(43, 124)(44, 117)(45, 157)(46, 102)(47, 122)(48, 103)(49, 118)(50, 158)(51, 159)(52, 160)(53, 106)(54, 161)(55, 120)(56, 108)(57, 130)(58, 162)(59, 163)(60, 110)(61, 111)(62, 112)(63, 113)(64, 164)(65, 153)(66, 115)(67, 137)(68, 126)(69, 119)(70, 132)(71, 127)(72, 140)(73, 166)(74, 148)(75, 149)(76, 167)(77, 168)(78, 147)(79, 150)(80, 165)(81, 146)(82, 142)(83, 144)(84, 145)
	local type(s) :: { ( 12, 21, 12, 21, 12, 21, 12, 21 ) }
Outer automorphisms :: reflexible
Dual of E27.1741
Transitivity :: ET+ VT+ AT
Graph::
	v = 21 e = 84 f = 11
	degree seq :: [ 8^21 ]

E27.1746 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^2 * Y1^-2, (Y1 * Y3^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-3 * Y3^-1 * Y1 * Y2^-3, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^21 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 4, 88)(3, 87, 9, 93, 17, 101, 11, 95)(5, 89, 14, 98, 18, 102, 15, 99)(7, 91, 19, 103, 12, 96, 21, 105)(8, 92, 22, 106, 13, 97, 23, 107)(10, 94, 20, 104, 35, 119, 28, 112)(16, 100, 24, 108, 36, 120, 31, 115)(25, 109, 45, 129, 29, 113, 47, 131)(26, 110, 48, 132, 30, 114, 49, 133)(27, 111, 46, 130, 34, 118, 50, 134)(32, 116, 51, 135, 33, 117, 52, 136)(37, 121, 53, 137, 40, 124, 55, 139)(38, 122, 56, 140, 41, 125, 57, 141)(39, 123, 54, 138, 44, 128, 58, 142)(42, 126, 59, 143, 43, 127, 60, 144)(61, 145, 73, 157, 63, 147, 74, 158)(62, 146, 75, 159, 64, 148, 76, 160)(65, 149, 77, 161, 66, 150, 78, 162)(67, 151, 79, 163, 69, 153, 80, 164)(68, 152, 81, 165, 70, 154, 82, 166)(71, 155, 83, 167, 72, 156, 84, 168)(169, 253, 171, 255, 178, 262, 195, 279, 204, 288, 186, 270, 174, 258, 185, 269, 203, 287, 202, 286, 184, 268, 173, 257)(170, 254, 175, 259, 188, 272, 207, 291, 199, 283, 181, 265, 172, 256, 180, 264, 196, 280, 212, 296, 192, 276, 176, 260)(177, 261, 193, 277, 214, 298, 201, 285, 183, 267, 198, 282, 179, 263, 197, 281, 218, 302, 200, 284, 182, 266, 194, 278)(187, 271, 205, 289, 222, 306, 211, 295, 191, 275, 209, 293, 189, 273, 208, 292, 226, 310, 210, 294, 190, 274, 206, 290)(213, 297, 229, 313, 220, 304, 234, 318, 217, 301, 232, 316, 215, 299, 231, 315, 219, 303, 233, 317, 216, 300, 230, 314)(221, 305, 235, 319, 228, 312, 240, 324, 225, 309, 238, 322, 223, 307, 237, 321, 227, 311, 239, 323, 224, 308, 236, 320)(241, 325, 249, 333, 246, 330, 247, 331, 244, 328, 252, 336, 242, 326, 250, 334, 245, 329, 248, 332, 243, 327, 251, 335)
	L = (1, 172)(2, 169)(3, 179)(4, 174)(5, 183)(6, 170)(7, 189)(8, 191)(9, 171)(10, 196)(11, 185)(12, 187)(13, 190)(14, 173)(15, 186)(16, 199)(17, 177)(18, 182)(19, 175)(20, 178)(21, 180)(22, 176)(23, 181)(24, 184)(25, 215)(26, 217)(27, 218)(28, 203)(29, 213)(30, 216)(31, 204)(32, 220)(33, 219)(34, 214)(35, 188)(36, 192)(37, 223)(38, 225)(39, 226)(40, 221)(41, 224)(42, 228)(43, 227)(44, 222)(45, 193)(46, 195)(47, 197)(48, 194)(49, 198)(50, 202)(51, 200)(52, 201)(53, 205)(54, 207)(55, 208)(56, 206)(57, 209)(58, 212)(59, 210)(60, 211)(61, 242)(62, 244)(63, 241)(64, 243)(65, 246)(66, 245)(67, 248)(68, 250)(69, 247)(70, 249)(71, 252)(72, 251)(73, 229)(74, 231)(75, 230)(76, 232)(77, 233)(78, 234)(79, 235)(80, 237)(81, 236)(82, 238)(83, 239)(84, 240)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 42, 2, 42, 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1749
Graph:: bipartite
	v = 28 e = 168 f = 88
	degree seq :: [ 8^21, 24^7 ]

E27.1747 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-3 * Y2 * Y1^-1, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1 * Y2^2 * Y1 * Y2^2 * Y1^2, (Y2^-1 * Y1^-1)^4, (Y3^-1 * Y1^-1)^4, Y1 * Y2^-2 * Y1^-1 * Y2^5 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 18, 102, 44, 128, 27, 111, 49, 133, 40, 124, 57, 141, 34, 118, 13, 97, 4, 88)(3, 87, 9, 93, 19, 103, 46, 130, 75, 159, 63, 147, 36, 120, 14, 98, 25, 109, 8, 92, 24, 108, 11, 95)(5, 89, 15, 99, 20, 104, 12, 96, 23, 107, 7, 91, 21, 105, 45, 129, 76, 160, 61, 145, 35, 119, 16, 100)(10, 94, 29, 113, 47, 131, 37, 121, 59, 143, 26, 110, 58, 142, 32, 116, 56, 140, 28, 112, 55, 139, 31, 115)(17, 101, 41, 125, 48, 132, 39, 123, 54, 138, 38, 122, 50, 134, 33, 117, 53, 137, 22, 106, 51, 135, 42, 126)(30, 114, 60, 144, 77, 161, 68, 152, 74, 158, 62, 146, 84, 168, 67, 151, 83, 167, 64, 148, 82, 166, 66, 150)(43, 127, 52, 136, 78, 162, 73, 157, 81, 165, 72, 156, 79, 163, 71, 155, 65, 149, 70, 154, 80, 164, 69, 153)(169, 253, 171, 255, 178, 262, 198, 282, 233, 317, 221, 305, 244, 328, 225, 309, 193, 277, 224, 308, 251, 335, 249, 333, 222, 306, 191, 275, 212, 296, 243, 327, 227, 311, 242, 326, 211, 295, 185, 269, 173, 257)(170, 254, 175, 259, 190, 274, 220, 304, 232, 316, 197, 281, 231, 315, 202, 286, 183, 267, 206, 290, 238, 322, 230, 314, 196, 280, 177, 261, 195, 279, 229, 313, 209, 293, 240, 324, 228, 312, 194, 278, 176, 260)(172, 256, 180, 264, 201, 285, 237, 321, 235, 319, 199, 283, 214, 298, 208, 292, 184, 268, 207, 291, 239, 323, 236, 320, 200, 284, 179, 263, 186, 270, 213, 297, 210, 294, 241, 325, 234, 318, 205, 289, 182, 266)(174, 258, 187, 271, 215, 299, 245, 329, 248, 332, 219, 303, 203, 287, 181, 265, 192, 276, 223, 307, 250, 334, 247, 331, 218, 302, 189, 273, 217, 301, 204, 288, 226, 310, 252, 336, 246, 330, 216, 300, 188, 272)
	L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 187)(7, 190)(8, 170)(9, 195)(10, 198)(11, 186)(12, 201)(13, 192)(14, 172)(15, 206)(16, 207)(17, 173)(18, 213)(19, 215)(20, 174)(21, 217)(22, 220)(23, 212)(24, 223)(25, 224)(26, 176)(27, 229)(28, 177)(29, 231)(30, 233)(31, 214)(32, 179)(33, 237)(34, 183)(35, 181)(36, 226)(37, 182)(38, 238)(39, 239)(40, 184)(41, 240)(42, 241)(43, 185)(44, 243)(45, 210)(46, 208)(47, 245)(48, 188)(49, 204)(50, 189)(51, 203)(52, 232)(53, 244)(54, 191)(55, 250)(56, 251)(57, 193)(58, 252)(59, 242)(60, 194)(61, 209)(62, 196)(63, 202)(64, 197)(65, 221)(66, 205)(67, 199)(68, 200)(69, 235)(70, 230)(71, 236)(72, 228)(73, 234)(74, 211)(75, 227)(76, 225)(77, 248)(78, 216)(79, 218)(80, 219)(81, 222)(82, 247)(83, 249)(84, 246)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1748
Graph:: bipartite
	v = 11 e = 168 f = 105
	degree seq :: [ 24^7, 42^4 ]

E27.1748 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3^-3 * Y2^-1 * Y3^-3 * Y2, Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1, Y2 * Y3^-5 * Y2^-1 * Y3^2, Y3 * Y2^2 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^21 ]
Map::
	R = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)(169, 253, 170, 254, 174, 258, 172, 256)(171, 255, 177, 261, 185, 269, 179, 263)(173, 257, 182, 266, 186, 270, 183, 267)(175, 259, 187, 271, 180, 264, 189, 273)(176, 260, 190, 274, 181, 265, 191, 275)(178, 262, 195, 279, 209, 293, 197, 281)(184, 268, 206, 290, 210, 294, 207, 291)(188, 272, 213, 297, 200, 284, 215, 299)(192, 276, 222, 306, 201, 285, 223, 307)(193, 277, 211, 295, 198, 282, 216, 300)(194, 278, 218, 302, 199, 283, 220, 304)(196, 280, 224, 308, 241, 325, 230, 314)(202, 286, 212, 296, 204, 288, 217, 301)(203, 287, 219, 303, 205, 289, 221, 305)(208, 292, 214, 298, 242, 326, 235, 319)(225, 309, 245, 329, 233, 317, 247, 331)(226, 310, 252, 336, 234, 318, 240, 324)(227, 311, 243, 327, 231, 315, 248, 332)(228, 312, 250, 334, 232, 316, 251, 335)(229, 313, 236, 320, 246, 330, 237, 321)(238, 322, 244, 328, 239, 323, 249, 333)
	L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 185)(7, 188)(8, 170)(9, 193)(10, 196)(11, 198)(12, 200)(13, 172)(14, 202)(15, 204)(16, 173)(17, 209)(18, 174)(19, 211)(20, 214)(21, 216)(22, 218)(23, 220)(24, 176)(25, 225)(26, 177)(27, 227)(28, 229)(29, 231)(30, 233)(31, 179)(32, 235)(33, 181)(34, 236)(35, 182)(36, 237)(37, 183)(38, 238)(39, 239)(40, 184)(41, 241)(42, 186)(43, 243)(44, 187)(45, 245)(46, 228)(47, 247)(48, 248)(49, 189)(50, 250)(51, 190)(52, 251)(53, 191)(54, 252)(55, 240)(56, 192)(57, 206)(58, 194)(59, 203)(60, 195)(61, 215)(62, 201)(63, 205)(64, 197)(65, 207)(66, 199)(67, 232)(68, 226)(69, 234)(70, 224)(71, 230)(72, 208)(73, 246)(74, 210)(75, 222)(76, 212)(77, 219)(78, 213)(79, 221)(80, 223)(81, 217)(82, 244)(83, 249)(84, 242)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 24, 42 ), ( 24, 42, 24, 42, 24, 42, 24, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1747
Graph:: simple bipartite
	v = 105 e = 168 f = 11
	degree seq :: [ 2^84, 8^21 ]

E27.1749 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^2 * Y3^-1 * Y1^3 * Y3 * Y1, (Y3 * Y2^-1)^4, Y1^5 * Y3 * Y1^-2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 17, 101, 41, 125, 59, 143, 79, 163, 66, 150, 31, 115, 54, 138, 77, 161, 84, 168, 61, 145, 27, 111, 51, 135, 75, 159, 65, 149, 69, 153, 35, 119, 13, 97, 4, 88)(3, 87, 9, 93, 25, 109, 57, 141, 46, 130, 18, 102, 44, 128, 33, 117, 12, 96, 32, 116, 67, 151, 53, 137, 22, 106, 7, 91, 20, 104, 49, 133, 34, 118, 68, 152, 42, 126, 30, 114, 11, 95)(5, 89, 15, 99, 39, 123, 70, 154, 48, 132, 19, 103, 47, 131, 38, 122, 14, 98, 37, 121, 72, 156, 56, 140, 24, 108, 8, 92, 23, 107, 55, 139, 36, 120, 71, 155, 43, 127, 40, 124, 16, 100)(10, 94, 21, 105, 45, 129, 73, 157, 82, 166, 58, 142, 78, 162, 63, 147, 29, 113, 52, 136, 76, 160, 83, 167, 60, 144, 26, 110, 50, 134, 74, 158, 64, 148, 80, 164, 81, 165, 62, 146, 28, 112)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336)
	L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 186)(7, 189)(8, 170)(9, 194)(10, 173)(11, 197)(12, 196)(13, 202)(14, 172)(15, 195)(16, 199)(17, 210)(18, 213)(19, 174)(20, 218)(21, 176)(22, 220)(23, 219)(24, 222)(25, 226)(26, 183)(27, 177)(28, 182)(29, 184)(30, 232)(31, 179)(32, 228)(33, 231)(34, 230)(35, 225)(36, 181)(37, 229)(38, 234)(39, 227)(40, 233)(41, 235)(42, 241)(43, 185)(44, 242)(45, 187)(46, 244)(47, 243)(48, 245)(49, 246)(50, 191)(51, 188)(52, 192)(53, 248)(54, 190)(55, 247)(56, 237)(57, 249)(58, 207)(59, 193)(60, 205)(61, 200)(62, 204)(63, 206)(64, 208)(65, 198)(66, 201)(67, 250)(68, 251)(69, 221)(70, 203)(71, 252)(72, 209)(73, 211)(74, 215)(75, 212)(76, 216)(77, 214)(78, 223)(79, 217)(80, 224)(81, 238)(82, 240)(83, 239)(84, 236)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1746
Graph:: simple bipartite
	v = 88 e = 168 f = 28
	degree seq :: [ 2^84, 42^4 ]

E27.1750 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1, Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2^2 * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^2 * Y1 * Y2^3 * Y1^-1 * Y2, Y3 * Y2^-3 * Y3^-1 * Y2^-3, Y2^-1 * R * Y2^3 * R * Y2^-2, Y2^-3 * Y1 * Y2^2 * Y1^-1 * Y2^-2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 4, 88)(3, 87, 9, 93, 17, 101, 11, 95)(5, 89, 14, 98, 18, 102, 15, 99)(7, 91, 19, 103, 12, 96, 21, 105)(8, 92, 22, 106, 13, 97, 23, 107)(10, 94, 27, 111, 41, 125, 29, 113)(16, 100, 38, 122, 42, 126, 39, 123)(20, 104, 45, 129, 32, 116, 47, 131)(24, 108, 54, 138, 33, 117, 55, 139)(25, 109, 43, 127, 30, 114, 48, 132)(26, 110, 50, 134, 31, 115, 52, 136)(28, 112, 56, 140, 73, 157, 62, 146)(34, 118, 44, 128, 36, 120, 49, 133)(35, 119, 51, 135, 37, 121, 53, 137)(40, 124, 46, 130, 74, 158, 67, 151)(57, 141, 77, 161, 65, 149, 79, 163)(58, 142, 84, 168, 66, 150, 72, 156)(59, 143, 75, 159, 63, 147, 80, 164)(60, 144, 82, 166, 64, 148, 83, 167)(61, 145, 68, 152, 78, 162, 69, 153)(70, 154, 76, 160, 71, 155, 81, 165)(169, 253, 171, 255, 178, 262, 196, 280, 229, 313, 215, 299, 247, 331, 221, 305, 191, 275, 220, 304, 251, 335, 249, 333, 217, 301, 189, 273, 216, 300, 248, 332, 223, 307, 240, 324, 208, 292, 184, 268, 173, 257)(170, 254, 175, 259, 188, 272, 214, 298, 228, 312, 195, 279, 227, 311, 203, 287, 182, 266, 202, 286, 236, 320, 226, 310, 194, 278, 177, 261, 193, 277, 225, 309, 206, 290, 238, 322, 224, 308, 192, 276, 176, 260)(172, 256, 180, 264, 200, 284, 235, 319, 232, 316, 197, 281, 231, 315, 205, 289, 183, 267, 204, 288, 237, 321, 234, 318, 199, 283, 179, 263, 198, 282, 233, 317, 207, 291, 239, 323, 230, 314, 201, 285, 181, 265)(174, 258, 185, 269, 209, 293, 241, 325, 246, 330, 213, 297, 245, 329, 219, 303, 190, 274, 218, 302, 250, 334, 244, 328, 212, 296, 187, 271, 211, 295, 243, 327, 222, 306, 252, 336, 242, 326, 210, 294, 186, 270)
	L = (1, 172)(2, 169)(3, 179)(4, 174)(5, 183)(6, 170)(7, 189)(8, 191)(9, 171)(10, 197)(11, 185)(12, 187)(13, 190)(14, 173)(15, 186)(16, 207)(17, 177)(18, 182)(19, 175)(20, 215)(21, 180)(22, 176)(23, 181)(24, 223)(25, 216)(26, 220)(27, 178)(28, 230)(29, 209)(30, 211)(31, 218)(32, 213)(33, 222)(34, 217)(35, 221)(36, 212)(37, 219)(38, 184)(39, 210)(40, 235)(41, 195)(42, 206)(43, 193)(44, 202)(45, 188)(46, 208)(47, 200)(48, 198)(49, 204)(50, 194)(51, 203)(52, 199)(53, 205)(54, 192)(55, 201)(56, 196)(57, 247)(58, 240)(59, 248)(60, 251)(61, 237)(62, 241)(63, 243)(64, 250)(65, 245)(66, 252)(67, 242)(68, 229)(69, 246)(70, 249)(71, 244)(72, 234)(73, 224)(74, 214)(75, 227)(76, 238)(77, 225)(78, 236)(79, 233)(80, 231)(81, 239)(82, 228)(83, 232)(84, 226)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1751
Graph:: bipartite
	v = 25 e = 168 f = 91
	degree seq :: [ 8^21, 42^4 ]

E27.1751 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 12, 21})
Quotient :: dipole
Aut^+ = C3 x (C7 : C4) (small group id <84, 4>)
Aut   = (C14 x S3) : C2 (small group id <168, 17>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1 * Y3^2 * Y1 * Y3^2 * Y1^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1)^4, Y3^4 * Y1 * Y3^-2 * Y1^-1 * Y3, (Y3 * Y2^-1)^21 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 18, 102, 44, 128, 27, 111, 49, 133, 40, 124, 57, 141, 34, 118, 13, 97, 4, 88)(3, 87, 9, 93, 19, 103, 46, 130, 75, 159, 63, 147, 36, 120, 14, 98, 25, 109, 8, 92, 24, 108, 11, 95)(5, 89, 15, 99, 20, 104, 12, 96, 23, 107, 7, 91, 21, 105, 45, 129, 76, 160, 61, 145, 35, 119, 16, 100)(10, 94, 29, 113, 47, 131, 37, 121, 59, 143, 26, 110, 58, 142, 32, 116, 56, 140, 28, 112, 55, 139, 31, 115)(17, 101, 41, 125, 48, 132, 39, 123, 54, 138, 38, 122, 50, 134, 33, 117, 53, 137, 22, 106, 51, 135, 42, 126)(30, 114, 60, 144, 77, 161, 68, 152, 74, 158, 62, 146, 84, 168, 67, 151, 83, 167, 64, 148, 82, 166, 66, 150)(43, 127, 52, 136, 78, 162, 73, 157, 81, 165, 72, 156, 79, 163, 71, 155, 65, 149, 70, 154, 80, 164, 69, 153)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336)
	L = (1, 171)(2, 175)(3, 178)(4, 180)(5, 169)(6, 187)(7, 190)(8, 170)(9, 195)(10, 198)(11, 186)(12, 201)(13, 192)(14, 172)(15, 206)(16, 207)(17, 173)(18, 213)(19, 215)(20, 174)(21, 217)(22, 220)(23, 212)(24, 223)(25, 224)(26, 176)(27, 229)(28, 177)(29, 231)(30, 233)(31, 214)(32, 179)(33, 237)(34, 183)(35, 181)(36, 226)(37, 182)(38, 238)(39, 239)(40, 184)(41, 240)(42, 241)(43, 185)(44, 243)(45, 210)(46, 208)(47, 245)(48, 188)(49, 204)(50, 189)(51, 203)(52, 232)(53, 244)(54, 191)(55, 250)(56, 251)(57, 193)(58, 252)(59, 242)(60, 194)(61, 209)(62, 196)(63, 202)(64, 197)(65, 221)(66, 205)(67, 199)(68, 200)(69, 235)(70, 230)(71, 236)(72, 228)(73, 234)(74, 211)(75, 227)(76, 225)(77, 248)(78, 216)(79, 218)(80, 219)(81, 222)(82, 247)(83, 249)(84, 246)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 8, 42 ), ( 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42, 8, 42 ) }
Outer automorphisms :: reflexible
Dual of E27.1750
Graph:: simple bipartite
	v = 91 e = 168 f = 25
	degree seq :: [ 2^84, 24^7 ]

E27.1752 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 28, 84})
Quotient :: edge
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T2^28 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 77, 71, 65, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 83, 79, 73, 67, 61, 55, 49, 43, 37, 31, 25, 19, 13, 7)(4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 84, 82, 76, 70, 64, 58, 52, 46, 40, 34, 28, 22, 16, 10)(85, 86, 88)(87, 90, 93)(89, 91, 94)(92, 96, 99)(95, 97, 100)(98, 102, 105)(101, 103, 106)(104, 108, 111)(107, 109, 112)(110, 114, 117)(113, 115, 118)(116, 120, 123)(119, 121, 124)(122, 126, 129)(125, 127, 130)(128, 132, 135)(131, 133, 136)(134, 138, 141)(137, 139, 142)(140, 144, 147)(143, 145, 148)(146, 150, 153)(149, 151, 154)(152, 156, 159)(155, 157, 160)(158, 162, 165)(161, 163, 166)(164, 167, 168)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 168^3 ), ( 168^28 ) }
Outer automorphisms :: reflexible
Dual of E27.1756
Transitivity :: ET+
Graph:: simple bipartite
	v = 31 e = 84 f = 1
	degree seq :: [ 3^28, 28^3 ]

E27.1753 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 28, 84})
Quotient :: edge
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^3, (T1^-1 * T2^-1)^3, T2^5 * T1^6 * T2, T1^-7 * T2 * T1^-6 * T2^2 * T1^-12 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 83, 76, 72, 65, 58, 54, 47, 40, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 82, 78, 71, 64, 60, 53, 46, 42, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 84, 77, 70, 66, 59, 52, 48, 41, 34, 30, 23, 14, 13, 5)(85, 86, 90, 98, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 164, 157, 153, 146, 139, 135, 128, 121, 117, 110, 103, 95, 88)(87, 91, 99, 97, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 163, 159, 152, 145, 141, 134, 127, 123, 116, 109, 105, 94)(89, 92, 100, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 165, 158, 151, 147, 140, 133, 129, 122, 115, 111, 104, 93, 101, 96)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 6^28 ), ( 6^84 ) }
Outer automorphisms :: reflexible
Dual of E27.1757
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 84 f = 28
	degree seq :: [ 28^3, 84 ]

E27.1754 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 28, 84})
Quotient :: edge
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2, T1), T2 * T1^28, (T1^-1 * T2^-1)^28 ]
Map:: non-degenerate
	R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 15, 17)(12, 19, 20)(16, 21, 23)(18, 25, 26)(22, 27, 29)(24, 31, 32)(28, 33, 35)(30, 37, 38)(34, 39, 41)(36, 43, 44)(40, 45, 47)(42, 49, 50)(46, 51, 53)(48, 55, 56)(52, 57, 59)(54, 61, 62)(58, 63, 65)(60, 67, 68)(64, 69, 71)(66, 73, 74)(70, 75, 77)(72, 79, 80)(76, 81, 83)(78, 82, 84)(85, 86, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 167, 161, 155, 149, 143, 137, 131, 125, 119, 113, 107, 101, 95, 89, 92, 98, 104, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 168, 165, 159, 153, 147, 141, 135, 129, 123, 117, 111, 105, 99, 93, 87, 91, 97, 103, 109, 115, 121, 127, 133, 139, 145, 151, 157, 163, 166, 160, 154, 148, 142, 136, 130, 124, 118, 112, 106, 100, 94, 88)
	L = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)
	local type(s) :: { ( 56^3 ), ( 56^84 ) }
Outer automorphisms :: reflexible
Dual of E27.1755
Transitivity :: ET+
Graph:: bipartite
	v = 29 e = 84 f = 3
	degree seq :: [ 3^28, 84 ]

E27.1755 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 28, 84})
Quotient :: loop
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T2^28 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 8, 92, 14, 98, 20, 104, 26, 110, 32, 116, 38, 122, 44, 128, 50, 134, 56, 140, 62, 146, 68, 152, 74, 158, 80, 164, 77, 161, 71, 155, 65, 149, 59, 143, 53, 137, 47, 131, 41, 125, 35, 119, 29, 113, 23, 107, 17, 101, 11, 95, 5, 89)(2, 86, 6, 90, 12, 96, 18, 102, 24, 108, 30, 114, 36, 120, 42, 126, 48, 132, 54, 138, 60, 144, 66, 150, 72, 156, 78, 162, 83, 167, 79, 163, 73, 157, 67, 151, 61, 145, 55, 139, 49, 133, 43, 127, 37, 121, 31, 115, 25, 109, 19, 103, 13, 97, 7, 91)(4, 88, 9, 93, 15, 99, 21, 105, 27, 111, 33, 117, 39, 123, 45, 129, 51, 135, 57, 141, 63, 147, 69, 153, 75, 159, 81, 165, 84, 168, 82, 166, 76, 160, 70, 154, 64, 148, 58, 142, 52, 136, 46, 130, 40, 124, 34, 118, 28, 112, 22, 106, 16, 100, 10, 94)
	L = (1, 86)(2, 88)(3, 90)(4, 85)(5, 91)(6, 93)(7, 94)(8, 96)(9, 87)(10, 89)(11, 97)(12, 99)(13, 100)(14, 102)(15, 92)(16, 95)(17, 103)(18, 105)(19, 106)(20, 108)(21, 98)(22, 101)(23, 109)(24, 111)(25, 112)(26, 114)(27, 104)(28, 107)(29, 115)(30, 117)(31, 118)(32, 120)(33, 110)(34, 113)(35, 121)(36, 123)(37, 124)(38, 126)(39, 116)(40, 119)(41, 127)(42, 129)(43, 130)(44, 132)(45, 122)(46, 125)(47, 133)(48, 135)(49, 136)(50, 138)(51, 128)(52, 131)(53, 139)(54, 141)(55, 142)(56, 144)(57, 134)(58, 137)(59, 145)(60, 147)(61, 148)(62, 150)(63, 140)(64, 143)(65, 151)(66, 153)(67, 154)(68, 156)(69, 146)(70, 149)(71, 157)(72, 159)(73, 160)(74, 162)(75, 152)(76, 155)(77, 163)(78, 165)(79, 166)(80, 167)(81, 158)(82, 161)(83, 168)(84, 164)
	local type(s) :: { ( 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84, 3, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.1754
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 84 f = 29
	degree seq :: [ 56^3 ]

E27.1756 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 28, 84})
Quotient :: loop
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2^3, (T1^-1 * T2^-1)^3, T2^5 * T1^6 * T2, T1^-7 * T2 * T1^-6 * T2^2 * T1^-12 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 9, 93, 19, 103, 25, 109, 31, 115, 37, 121, 43, 127, 49, 133, 55, 139, 61, 145, 67, 151, 73, 157, 79, 163, 83, 167, 76, 160, 72, 156, 65, 149, 58, 142, 54, 138, 47, 131, 40, 124, 36, 120, 29, 113, 22, 106, 18, 102, 8, 92, 2, 86, 7, 91, 17, 101, 11, 95, 21, 105, 27, 111, 33, 117, 39, 123, 45, 129, 51, 135, 57, 141, 63, 147, 69, 153, 75, 159, 81, 165, 82, 166, 78, 162, 71, 155, 64, 148, 60, 144, 53, 137, 46, 130, 42, 126, 35, 119, 28, 112, 24, 108, 16, 100, 6, 90, 15, 99, 12, 96, 4, 88, 10, 94, 20, 104, 26, 110, 32, 116, 38, 122, 44, 128, 50, 134, 56, 140, 62, 146, 68, 152, 74, 158, 80, 164, 84, 168, 77, 161, 70, 154, 66, 150, 59, 143, 52, 136, 48, 132, 41, 125, 34, 118, 30, 114, 23, 107, 14, 98, 13, 97, 5, 89)
	L = (1, 86)(2, 90)(3, 91)(4, 85)(5, 92)(6, 98)(7, 99)(8, 100)(9, 101)(10, 87)(11, 88)(12, 89)(13, 102)(14, 106)(15, 97)(16, 107)(17, 96)(18, 108)(19, 95)(20, 93)(21, 94)(22, 112)(23, 113)(24, 114)(25, 105)(26, 103)(27, 104)(28, 118)(29, 119)(30, 120)(31, 111)(32, 109)(33, 110)(34, 124)(35, 125)(36, 126)(37, 117)(38, 115)(39, 116)(40, 130)(41, 131)(42, 132)(43, 123)(44, 121)(45, 122)(46, 136)(47, 137)(48, 138)(49, 129)(50, 127)(51, 128)(52, 142)(53, 143)(54, 144)(55, 135)(56, 133)(57, 134)(58, 148)(59, 149)(60, 150)(61, 141)(62, 139)(63, 140)(64, 154)(65, 155)(66, 156)(67, 147)(68, 145)(69, 146)(70, 160)(71, 161)(72, 162)(73, 153)(74, 151)(75, 152)(76, 166)(77, 167)(78, 168)(79, 159)(80, 157)(81, 158)(82, 164)(83, 165)(84, 163)
	local type(s) :: { ( 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28, 3, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.1752
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 84 f = 31
	degree seq :: [ 168 ]

E27.1757 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 28, 84})
Quotient :: loop
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2, T1), T2 * T1^28, (T1^-1 * T2^-1)^28 ]
Map:: non-degenerate
	R = (1, 85, 3, 87, 5, 89)(2, 86, 7, 91, 8, 92)(4, 88, 9, 93, 11, 95)(6, 90, 13, 97, 14, 98)(10, 94, 15, 99, 17, 101)(12, 96, 19, 103, 20, 104)(16, 100, 21, 105, 23, 107)(18, 102, 25, 109, 26, 110)(22, 106, 27, 111, 29, 113)(24, 108, 31, 115, 32, 116)(28, 112, 33, 117, 35, 119)(30, 114, 37, 121, 38, 122)(34, 118, 39, 123, 41, 125)(36, 120, 43, 127, 44, 128)(40, 124, 45, 129, 47, 131)(42, 126, 49, 133, 50, 134)(46, 130, 51, 135, 53, 137)(48, 132, 55, 139, 56, 140)(52, 136, 57, 141, 59, 143)(54, 138, 61, 145, 62, 146)(58, 142, 63, 147, 65, 149)(60, 144, 67, 151, 68, 152)(64, 148, 69, 153, 71, 155)(66, 150, 73, 157, 74, 158)(70, 154, 75, 159, 77, 161)(72, 156, 79, 163, 80, 164)(76, 160, 81, 165, 83, 167)(78, 162, 82, 166, 84, 168)
	L = (1, 86)(2, 90)(3, 91)(4, 85)(5, 92)(6, 96)(7, 97)(8, 98)(9, 87)(10, 88)(11, 89)(12, 102)(13, 103)(14, 104)(15, 93)(16, 94)(17, 95)(18, 108)(19, 109)(20, 110)(21, 99)(22, 100)(23, 101)(24, 114)(25, 115)(26, 116)(27, 105)(28, 106)(29, 107)(30, 120)(31, 121)(32, 122)(33, 111)(34, 112)(35, 113)(36, 126)(37, 127)(38, 128)(39, 117)(40, 118)(41, 119)(42, 132)(43, 133)(44, 134)(45, 123)(46, 124)(47, 125)(48, 138)(49, 139)(50, 140)(51, 129)(52, 130)(53, 131)(54, 144)(55, 145)(56, 146)(57, 135)(58, 136)(59, 137)(60, 150)(61, 151)(62, 152)(63, 141)(64, 142)(65, 143)(66, 156)(67, 157)(68, 158)(69, 147)(70, 148)(71, 149)(72, 162)(73, 163)(74, 164)(75, 153)(76, 154)(77, 155)(78, 167)(79, 166)(80, 168)(81, 159)(82, 160)(83, 161)(84, 165)
	local type(s) :: { ( 28, 84, 28, 84, 28, 84 ) }
Outer automorphisms :: reflexible
Dual of E27.1753
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 28 e = 84 f = 4
	degree seq :: [ 6^28 ]

E27.1758 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^28, Y3^84 ]
Map::
	R = (1, 85, 2, 86, 4, 88)(3, 87, 6, 90, 9, 93)(5, 89, 7, 91, 10, 94)(8, 92, 12, 96, 15, 99)(11, 95, 13, 97, 16, 100)(14, 98, 18, 102, 21, 105)(17, 101, 19, 103, 22, 106)(20, 104, 24, 108, 27, 111)(23, 107, 25, 109, 28, 112)(26, 110, 30, 114, 33, 117)(29, 113, 31, 115, 34, 118)(32, 116, 36, 120, 39, 123)(35, 119, 37, 121, 40, 124)(38, 122, 42, 126, 45, 129)(41, 125, 43, 127, 46, 130)(44, 128, 48, 132, 51, 135)(47, 131, 49, 133, 52, 136)(50, 134, 54, 138, 57, 141)(53, 137, 55, 139, 58, 142)(56, 140, 60, 144, 63, 147)(59, 143, 61, 145, 64, 148)(62, 146, 66, 150, 69, 153)(65, 149, 67, 151, 70, 154)(68, 152, 72, 156, 75, 159)(71, 155, 73, 157, 76, 160)(74, 158, 78, 162, 81, 165)(77, 161, 79, 163, 82, 166)(80, 164, 83, 167, 84, 168)(169, 253, 171, 255, 176, 260, 182, 266, 188, 272, 194, 278, 200, 284, 206, 290, 212, 296, 218, 302, 224, 308, 230, 314, 236, 320, 242, 326, 248, 332, 245, 329, 239, 323, 233, 317, 227, 311, 221, 305, 215, 299, 209, 293, 203, 287, 197, 281, 191, 275, 185, 269, 179, 263, 173, 257)(170, 254, 174, 258, 180, 264, 186, 270, 192, 276, 198, 282, 204, 288, 210, 294, 216, 300, 222, 306, 228, 312, 234, 318, 240, 324, 246, 330, 251, 335, 247, 331, 241, 325, 235, 319, 229, 313, 223, 307, 217, 301, 211, 295, 205, 289, 199, 283, 193, 277, 187, 271, 181, 265, 175, 259)(172, 256, 177, 261, 183, 267, 189, 273, 195, 279, 201, 285, 207, 291, 213, 297, 219, 303, 225, 309, 231, 315, 237, 321, 243, 327, 249, 333, 252, 336, 250, 334, 244, 328, 238, 322, 232, 316, 226, 310, 220, 304, 214, 298, 208, 292, 202, 286, 196, 280, 190, 274, 184, 268, 178, 262)
	L = (1, 172)(2, 169)(3, 177)(4, 170)(5, 178)(6, 171)(7, 173)(8, 183)(9, 174)(10, 175)(11, 184)(12, 176)(13, 179)(14, 189)(15, 180)(16, 181)(17, 190)(18, 182)(19, 185)(20, 195)(21, 186)(22, 187)(23, 196)(24, 188)(25, 191)(26, 201)(27, 192)(28, 193)(29, 202)(30, 194)(31, 197)(32, 207)(33, 198)(34, 199)(35, 208)(36, 200)(37, 203)(38, 213)(39, 204)(40, 205)(41, 214)(42, 206)(43, 209)(44, 219)(45, 210)(46, 211)(47, 220)(48, 212)(49, 215)(50, 225)(51, 216)(52, 217)(53, 226)(54, 218)(55, 221)(56, 231)(57, 222)(58, 223)(59, 232)(60, 224)(61, 227)(62, 237)(63, 228)(64, 229)(65, 238)(66, 230)(67, 233)(68, 243)(69, 234)(70, 235)(71, 244)(72, 236)(73, 239)(74, 249)(75, 240)(76, 241)(77, 250)(78, 242)(79, 245)(80, 252)(81, 246)(82, 247)(83, 248)(84, 251)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 168, 2, 168, 2, 168 ), ( 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168, 2, 168 ) }
Outer automorphisms :: reflexible
Dual of E27.1761
Graph:: bipartite
	v = 31 e = 168 f = 85
	degree seq :: [ 6^28, 56^3 ]

E27.1759 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^3, Y2^9 * Y1^9, Y1^-13 * Y2^15, Y1^28 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 14, 98, 22, 106, 28, 112, 34, 118, 40, 124, 46, 130, 52, 136, 58, 142, 64, 148, 70, 154, 76, 160, 82, 166, 80, 164, 73, 157, 69, 153, 62, 146, 55, 139, 51, 135, 44, 128, 37, 121, 33, 117, 26, 110, 19, 103, 11, 95, 4, 88)(3, 87, 7, 91, 15, 99, 13, 97, 18, 102, 24, 108, 30, 114, 36, 120, 42, 126, 48, 132, 54, 138, 60, 144, 66, 150, 72, 156, 78, 162, 84, 168, 79, 163, 75, 159, 68, 152, 61, 145, 57, 141, 50, 134, 43, 127, 39, 123, 32, 116, 25, 109, 21, 105, 10, 94)(5, 89, 8, 92, 16, 100, 23, 107, 29, 113, 35, 119, 41, 125, 47, 131, 53, 137, 59, 143, 65, 149, 71, 155, 77, 161, 83, 167, 81, 165, 74, 158, 67, 151, 63, 147, 56, 140, 49, 133, 45, 129, 38, 122, 31, 115, 27, 111, 20, 104, 9, 93, 17, 101, 12, 96)(169, 253, 171, 255, 177, 261, 187, 271, 193, 277, 199, 283, 205, 289, 211, 295, 217, 301, 223, 307, 229, 313, 235, 319, 241, 325, 247, 331, 251, 335, 244, 328, 240, 324, 233, 317, 226, 310, 222, 306, 215, 299, 208, 292, 204, 288, 197, 281, 190, 274, 186, 270, 176, 260, 170, 254, 175, 259, 185, 269, 179, 263, 189, 273, 195, 279, 201, 285, 207, 291, 213, 297, 219, 303, 225, 309, 231, 315, 237, 321, 243, 327, 249, 333, 250, 334, 246, 330, 239, 323, 232, 316, 228, 312, 221, 305, 214, 298, 210, 294, 203, 287, 196, 280, 192, 276, 184, 268, 174, 258, 183, 267, 180, 264, 172, 256, 178, 262, 188, 272, 194, 278, 200, 284, 206, 290, 212, 296, 218, 302, 224, 308, 230, 314, 236, 320, 242, 326, 248, 332, 252, 336, 245, 329, 238, 322, 234, 318, 227, 311, 220, 304, 216, 300, 209, 293, 202, 286, 198, 282, 191, 275, 182, 266, 181, 265, 173, 257)
	L = (1, 171)(2, 175)(3, 177)(4, 178)(5, 169)(6, 183)(7, 185)(8, 170)(9, 187)(10, 188)(11, 189)(12, 172)(13, 173)(14, 181)(15, 180)(16, 174)(17, 179)(18, 176)(19, 193)(20, 194)(21, 195)(22, 186)(23, 182)(24, 184)(25, 199)(26, 200)(27, 201)(28, 192)(29, 190)(30, 191)(31, 205)(32, 206)(33, 207)(34, 198)(35, 196)(36, 197)(37, 211)(38, 212)(39, 213)(40, 204)(41, 202)(42, 203)(43, 217)(44, 218)(45, 219)(46, 210)(47, 208)(48, 209)(49, 223)(50, 224)(51, 225)(52, 216)(53, 214)(54, 215)(55, 229)(56, 230)(57, 231)(58, 222)(59, 220)(60, 221)(61, 235)(62, 236)(63, 237)(64, 228)(65, 226)(66, 227)(67, 241)(68, 242)(69, 243)(70, 234)(71, 232)(72, 233)(73, 247)(74, 248)(75, 249)(76, 240)(77, 238)(78, 239)(79, 251)(80, 252)(81, 250)(82, 246)(83, 244)(84, 245)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1760
Graph:: bipartite
	v = 4 e = 168 f = 112
	degree seq :: [ 56^3, 168 ]

E27.1760 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-28 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2, (Y3^-1 * Y1^-1)^84 ]
Map::
	R = (1, 85)(2, 86)(3, 87)(4, 88)(5, 89)(6, 90)(7, 91)(8, 92)(9, 93)(10, 94)(11, 95)(12, 96)(13, 97)(14, 98)(15, 99)(16, 100)(17, 101)(18, 102)(19, 103)(20, 104)(21, 105)(22, 106)(23, 107)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 116)(33, 117)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 123)(40, 124)(41, 125)(42, 126)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168)(169, 253, 170, 254, 172, 256)(171, 255, 174, 258, 177, 261)(173, 257, 175, 259, 178, 262)(176, 260, 180, 264, 183, 267)(179, 263, 181, 265, 184, 268)(182, 266, 186, 270, 189, 273)(185, 269, 187, 271, 190, 274)(188, 272, 192, 276, 195, 279)(191, 275, 193, 277, 196, 280)(194, 278, 198, 282, 201, 285)(197, 281, 199, 283, 202, 286)(200, 284, 204, 288, 207, 291)(203, 287, 205, 289, 208, 292)(206, 290, 210, 294, 213, 297)(209, 293, 211, 295, 214, 298)(212, 296, 216, 300, 219, 303)(215, 299, 217, 301, 220, 304)(218, 302, 222, 306, 225, 309)(221, 305, 223, 307, 226, 310)(224, 308, 228, 312, 231, 315)(227, 311, 229, 313, 232, 316)(230, 314, 234, 318, 237, 321)(233, 317, 235, 319, 238, 322)(236, 320, 240, 324, 243, 327)(239, 323, 241, 325, 244, 328)(242, 326, 246, 330, 249, 333)(245, 329, 247, 331, 250, 334)(248, 332, 252, 336, 251, 335)
	L = (1, 171)(2, 174)(3, 176)(4, 177)(5, 169)(6, 180)(7, 170)(8, 182)(9, 183)(10, 172)(11, 173)(12, 186)(13, 175)(14, 188)(15, 189)(16, 178)(17, 179)(18, 192)(19, 181)(20, 194)(21, 195)(22, 184)(23, 185)(24, 198)(25, 187)(26, 200)(27, 201)(28, 190)(29, 191)(30, 204)(31, 193)(32, 206)(33, 207)(34, 196)(35, 197)(36, 210)(37, 199)(38, 212)(39, 213)(40, 202)(41, 203)(42, 216)(43, 205)(44, 218)(45, 219)(46, 208)(47, 209)(48, 222)(49, 211)(50, 224)(51, 225)(52, 214)(53, 215)(54, 228)(55, 217)(56, 230)(57, 231)(58, 220)(59, 221)(60, 234)(61, 223)(62, 236)(63, 237)(64, 226)(65, 227)(66, 240)(67, 229)(68, 242)(69, 243)(70, 232)(71, 233)(72, 246)(73, 235)(74, 248)(75, 249)(76, 238)(77, 239)(78, 252)(79, 241)(80, 247)(81, 251)(82, 244)(83, 245)(84, 250)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 56, 168 ), ( 56, 168, 56, 168, 56, 168 ) }
Outer automorphisms :: reflexible
Dual of E27.1759
Graph:: simple bipartite
	v = 112 e = 168 f = 4
	degree seq :: [ 2^84, 6^28 ]

E27.1761 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^28, (Y1^-1 * Y3^-1)^28 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 12, 96, 18, 102, 24, 108, 30, 114, 36, 120, 42, 126, 48, 132, 54, 138, 60, 144, 66, 150, 72, 156, 78, 162, 83, 167, 77, 161, 71, 155, 65, 149, 59, 143, 53, 137, 47, 131, 41, 125, 35, 119, 29, 113, 23, 107, 17, 101, 11, 95, 5, 89, 8, 92, 14, 98, 20, 104, 26, 110, 32, 116, 38, 122, 44, 128, 50, 134, 56, 140, 62, 146, 68, 152, 74, 158, 80, 164, 84, 168, 81, 165, 75, 159, 69, 153, 63, 147, 57, 141, 51, 135, 45, 129, 39, 123, 33, 117, 27, 111, 21, 105, 15, 99, 9, 93, 3, 87, 7, 91, 13, 97, 19, 103, 25, 109, 31, 115, 37, 121, 43, 127, 49, 133, 55, 139, 61, 145, 67, 151, 73, 157, 79, 163, 82, 166, 76, 160, 70, 154, 64, 148, 58, 142, 52, 136, 46, 130, 40, 124, 34, 118, 28, 112, 22, 106, 16, 100, 10, 94, 4, 88)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336)
	L = (1, 171)(2, 175)(3, 173)(4, 177)(5, 169)(6, 181)(7, 176)(8, 170)(9, 179)(10, 183)(11, 172)(12, 187)(13, 182)(14, 174)(15, 185)(16, 189)(17, 178)(18, 193)(19, 188)(20, 180)(21, 191)(22, 195)(23, 184)(24, 199)(25, 194)(26, 186)(27, 197)(28, 201)(29, 190)(30, 205)(31, 200)(32, 192)(33, 203)(34, 207)(35, 196)(36, 211)(37, 206)(38, 198)(39, 209)(40, 213)(41, 202)(42, 217)(43, 212)(44, 204)(45, 215)(46, 219)(47, 208)(48, 223)(49, 218)(50, 210)(51, 221)(52, 225)(53, 214)(54, 229)(55, 224)(56, 216)(57, 227)(58, 231)(59, 220)(60, 235)(61, 230)(62, 222)(63, 233)(64, 237)(65, 226)(66, 241)(67, 236)(68, 228)(69, 239)(70, 243)(71, 232)(72, 247)(73, 242)(74, 234)(75, 245)(76, 249)(77, 238)(78, 250)(79, 248)(80, 240)(81, 251)(82, 252)(83, 244)(84, 246)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 6, 56 ), ( 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56, 6, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1758
Graph:: bipartite
	v = 85 e = 168 f = 31
	degree seq :: [ 2^84, 168 ]

E27.1762 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3^-1 * Y2^28, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 85, 2, 86, 4, 88)(3, 87, 6, 90, 9, 93)(5, 89, 7, 91, 10, 94)(8, 92, 12, 96, 15, 99)(11, 95, 13, 97, 16, 100)(14, 98, 18, 102, 21, 105)(17, 101, 19, 103, 22, 106)(20, 104, 24, 108, 27, 111)(23, 107, 25, 109, 28, 112)(26, 110, 30, 114, 33, 117)(29, 113, 31, 115, 34, 118)(32, 116, 36, 120, 39, 123)(35, 119, 37, 121, 40, 124)(38, 122, 42, 126, 45, 129)(41, 125, 43, 127, 46, 130)(44, 128, 48, 132, 51, 135)(47, 131, 49, 133, 52, 136)(50, 134, 54, 138, 57, 141)(53, 137, 55, 139, 58, 142)(56, 140, 60, 144, 63, 147)(59, 143, 61, 145, 64, 148)(62, 146, 66, 150, 69, 153)(65, 149, 67, 151, 70, 154)(68, 152, 72, 156, 75, 159)(71, 155, 73, 157, 76, 160)(74, 158, 78, 162, 81, 165)(77, 161, 79, 163, 82, 166)(80, 164, 83, 167, 84, 168)(169, 253, 171, 255, 176, 260, 182, 266, 188, 272, 194, 278, 200, 284, 206, 290, 212, 296, 218, 302, 224, 308, 230, 314, 236, 320, 242, 326, 248, 332, 250, 334, 244, 328, 238, 322, 232, 316, 226, 310, 220, 304, 214, 298, 208, 292, 202, 286, 196, 280, 190, 274, 184, 268, 178, 262, 172, 256, 177, 261, 183, 267, 189, 273, 195, 279, 201, 285, 207, 291, 213, 297, 219, 303, 225, 309, 231, 315, 237, 321, 243, 327, 249, 333, 252, 336, 247, 331, 241, 325, 235, 319, 229, 313, 223, 307, 217, 301, 211, 295, 205, 289, 199, 283, 193, 277, 187, 271, 181, 265, 175, 259, 170, 254, 174, 258, 180, 264, 186, 270, 192, 276, 198, 282, 204, 288, 210, 294, 216, 300, 222, 306, 228, 312, 234, 318, 240, 324, 246, 330, 251, 335, 245, 329, 239, 323, 233, 317, 227, 311, 221, 305, 215, 299, 209, 293, 203, 287, 197, 281, 191, 275, 185, 269, 179, 263, 173, 257)
	L = (1, 172)(2, 169)(3, 177)(4, 170)(5, 178)(6, 171)(7, 173)(8, 183)(9, 174)(10, 175)(11, 184)(12, 176)(13, 179)(14, 189)(15, 180)(16, 181)(17, 190)(18, 182)(19, 185)(20, 195)(21, 186)(22, 187)(23, 196)(24, 188)(25, 191)(26, 201)(27, 192)(28, 193)(29, 202)(30, 194)(31, 197)(32, 207)(33, 198)(34, 199)(35, 208)(36, 200)(37, 203)(38, 213)(39, 204)(40, 205)(41, 214)(42, 206)(43, 209)(44, 219)(45, 210)(46, 211)(47, 220)(48, 212)(49, 215)(50, 225)(51, 216)(52, 217)(53, 226)(54, 218)(55, 221)(56, 231)(57, 222)(58, 223)(59, 232)(60, 224)(61, 227)(62, 237)(63, 228)(64, 229)(65, 238)(66, 230)(67, 233)(68, 243)(69, 234)(70, 235)(71, 244)(72, 236)(73, 239)(74, 249)(75, 240)(76, 241)(77, 250)(78, 242)(79, 245)(80, 252)(81, 246)(82, 247)(83, 248)(84, 251)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.1763
Graph:: bipartite
	v = 29 e = 168 f = 87
	degree seq :: [ 6^28, 168 ]

E27.1763 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 28, 84})
Quotient :: dipole
Aut^+ = C84 (small group id <84, 6>)
Aut   = D168 (small group id <168, 36>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y1^-3 * Y3^-3, (R * Y2 * Y3^-1)^2, Y1^-12 * Y3^-12, Y1^-1 * Y3^27, Y1^28, (Y3 * Y2^-1)^84 ]
Map::
	R = (1, 85, 2, 86, 6, 90, 14, 98, 22, 106, 28, 112, 34, 118, 40, 124, 46, 130, 52, 136, 58, 142, 64, 148, 70, 154, 76, 160, 82, 166, 80, 164, 73, 157, 69, 153, 62, 146, 55, 139, 51, 135, 44, 128, 37, 121, 33, 117, 26, 110, 19, 103, 11, 95, 4, 88)(3, 87, 7, 91, 15, 99, 13, 97, 18, 102, 24, 108, 30, 114, 36, 120, 42, 126, 48, 132, 54, 138, 60, 144, 66, 150, 72, 156, 78, 162, 84, 168, 79, 163, 75, 159, 68, 152, 61, 145, 57, 141, 50, 134, 43, 127, 39, 123, 32, 116, 25, 109, 21, 105, 10, 94)(5, 89, 8, 92, 16, 100, 23, 107, 29, 113, 35, 119, 41, 125, 47, 131, 53, 137, 59, 143, 65, 149, 71, 155, 77, 161, 83, 167, 81, 165, 74, 158, 67, 151, 63, 147, 56, 140, 49, 133, 45, 129, 38, 122, 31, 115, 27, 111, 20, 104, 9, 93, 17, 101, 12, 96)(169, 253)(170, 254)(171, 255)(172, 256)(173, 257)(174, 258)(175, 259)(176, 260)(177, 261)(178, 262)(179, 263)(180, 264)(181, 265)(182, 266)(183, 267)(184, 268)(185, 269)(186, 270)(187, 271)(188, 272)(189, 273)(190, 274)(191, 275)(192, 276)(193, 277)(194, 278)(195, 279)(196, 280)(197, 281)(198, 282)(199, 283)(200, 284)(201, 285)(202, 286)(203, 287)(204, 288)(205, 289)(206, 290)(207, 291)(208, 292)(209, 293)(210, 294)(211, 295)(212, 296)(213, 297)(214, 298)(215, 299)(216, 300)(217, 301)(218, 302)(219, 303)(220, 304)(221, 305)(222, 306)(223, 307)(224, 308)(225, 309)(226, 310)(227, 311)(228, 312)(229, 313)(230, 314)(231, 315)(232, 316)(233, 317)(234, 318)(235, 319)(236, 320)(237, 321)(238, 322)(239, 323)(240, 324)(241, 325)(242, 326)(243, 327)(244, 328)(245, 329)(246, 330)(247, 331)(248, 332)(249, 333)(250, 334)(251, 335)(252, 336)
	L = (1, 171)(2, 175)(3, 177)(4, 178)(5, 169)(6, 183)(7, 185)(8, 170)(9, 187)(10, 188)(11, 189)(12, 172)(13, 173)(14, 181)(15, 180)(16, 174)(17, 179)(18, 176)(19, 193)(20, 194)(21, 195)(22, 186)(23, 182)(24, 184)(25, 199)(26, 200)(27, 201)(28, 192)(29, 190)(30, 191)(31, 205)(32, 206)(33, 207)(34, 198)(35, 196)(36, 197)(37, 211)(38, 212)(39, 213)(40, 204)(41, 202)(42, 203)(43, 217)(44, 218)(45, 219)(46, 210)(47, 208)(48, 209)(49, 223)(50, 224)(51, 225)(52, 216)(53, 214)(54, 215)(55, 229)(56, 230)(57, 231)(58, 222)(59, 220)(60, 221)(61, 235)(62, 236)(63, 237)(64, 228)(65, 226)(66, 227)(67, 241)(68, 242)(69, 243)(70, 234)(71, 232)(72, 233)(73, 247)(74, 248)(75, 249)(76, 240)(77, 238)(78, 239)(79, 251)(80, 252)(81, 250)(82, 246)(83, 244)(84, 245)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)
	local type(s) :: { ( 6, 168 ), ( 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168, 6, 168 ) }
Outer automorphisms :: reflexible
Dual of E27.1762
Graph:: simple bipartite
	v = 87 e = 168 f = 29
	degree seq :: [ 2^84, 56^3 ]

E27.1764 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3^-1)^3, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2, (Y2 * Y3)^3, (R * Y1 * Y2)^2, Y2 * R * Y3^-1 * Y2 * Y3 * Y2 * R, Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3, Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3, (Y3 * Y1 * Y3^-1 * Y1)^3 ]
Map:: non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 16, 112)(7, 103, 19, 115)(8, 104, 21, 117)(10, 106, 25, 121)(11, 107, 27, 123)(13, 109, 32, 128)(15, 111, 35, 131)(17, 113, 37, 133)(18, 114, 39, 135)(20, 116, 43, 139)(22, 118, 46, 142)(23, 119, 36, 132)(24, 120, 47, 143)(26, 122, 29, 125)(28, 124, 52, 148)(30, 126, 55, 151)(31, 127, 57, 153)(33, 129, 59, 155)(34, 130, 61, 157)(38, 134, 40, 136)(41, 137, 51, 147)(42, 138, 69, 165)(44, 140, 71, 167)(45, 141, 56, 152)(48, 144, 74, 170)(49, 145, 76, 172)(50, 146, 77, 173)(53, 149, 73, 169)(54, 150, 79, 175)(58, 154, 82, 178)(60, 156, 81, 177)(62, 158, 67, 163)(63, 159, 64, 160)(65, 161, 85, 181)(66, 162, 86, 182)(68, 164, 87, 183)(70, 166, 90, 186)(72, 168, 89, 185)(75, 171, 91, 187)(78, 174, 83, 179)(80, 176, 88, 184)(84, 180, 92, 188)(93, 189, 96, 192)(94, 190, 95, 191)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 205, 301)(197, 293, 207, 303)(199, 295, 212, 308)(200, 296, 214, 310)(201, 297, 215, 311)(202, 298, 218, 314)(203, 299, 220, 316)(204, 300, 221, 317)(206, 302, 219, 315)(208, 304, 228, 324)(209, 305, 230, 326)(210, 306, 216, 312)(211, 307, 232, 328)(213, 309, 231, 327)(217, 313, 224, 320)(222, 318, 248, 344)(223, 319, 241, 337)(225, 321, 252, 348)(226, 322, 254, 350)(227, 323, 244, 340)(229, 325, 235, 331)(233, 329, 253, 349)(234, 330, 257, 353)(236, 332, 264, 360)(237, 333, 265, 361)(238, 334, 239, 335)(240, 336, 245, 341)(242, 338, 270, 366)(243, 339, 255, 351)(246, 342, 250, 346)(247, 343, 266, 362)(249, 345, 271, 367)(251, 347, 275, 371)(256, 352, 259, 355)(258, 354, 267, 363)(260, 356, 262, 358)(261, 357, 279, 375)(263, 359, 283, 379)(268, 364, 274, 370)(269, 365, 273, 369)(272, 368, 285, 381)(276, 372, 286, 382)(277, 373, 282, 378)(278, 374, 281, 377)(280, 376, 287, 383)(284, 380, 288, 384)
	L = (1, 196)(2, 199)(3, 202)(4, 197)(5, 193)(6, 209)(7, 200)(8, 194)(9, 212)(10, 203)(11, 195)(12, 222)(13, 220)(14, 225)(15, 228)(16, 205)(17, 210)(18, 198)(19, 233)(20, 216)(21, 236)(22, 215)(23, 230)(24, 201)(25, 240)(26, 207)(27, 242)(28, 208)(29, 245)(30, 223)(31, 204)(32, 248)(33, 226)(34, 206)(35, 252)(36, 218)(37, 256)(38, 214)(39, 258)(40, 259)(41, 234)(42, 211)(43, 253)(44, 237)(45, 213)(46, 264)(47, 267)(48, 241)(49, 217)(50, 243)(51, 219)(52, 270)(53, 246)(54, 221)(55, 231)(56, 250)(57, 272)(58, 224)(59, 271)(60, 255)(61, 262)(62, 244)(63, 227)(64, 257)(65, 229)(66, 247)(67, 260)(68, 232)(69, 280)(70, 235)(71, 279)(72, 266)(73, 239)(74, 238)(75, 265)(76, 285)(77, 274)(78, 254)(79, 276)(80, 273)(81, 249)(82, 286)(83, 268)(84, 251)(85, 287)(86, 282)(87, 284)(88, 281)(89, 261)(90, 288)(91, 277)(92, 263)(93, 275)(94, 269)(95, 283)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1773
Graph:: simple bipartite
	v = 96 e = 192 f = 44
	degree seq :: [ 4^96 ]

E27.1765 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y2^-1 * Y1)^3, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1, (R * Y2^-1 * Y1 * Y2)^2, R * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * R * Y2^-1 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y1 * Y2^-1, (Y3 * Y2 * Y3 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 7, 103)(5, 101, 13, 109)(6, 102, 15, 111)(8, 104, 19, 115)(10, 106, 21, 117)(11, 107, 25, 121)(12, 108, 27, 123)(14, 110, 30, 126)(16, 112, 33, 129)(17, 113, 36, 132)(18, 114, 38, 134)(20, 116, 40, 136)(22, 118, 29, 125)(23, 119, 34, 130)(24, 120, 47, 143)(26, 122, 49, 145)(28, 124, 53, 149)(31, 127, 58, 154)(32, 128, 42, 138)(35, 131, 44, 140)(37, 133, 64, 160)(39, 135, 67, 163)(41, 137, 56, 152)(43, 139, 61, 157)(45, 141, 50, 146)(46, 142, 62, 158)(48, 144, 75, 171)(51, 147, 65, 161)(52, 148, 78, 174)(54, 150, 74, 170)(55, 151, 69, 165)(57, 153, 70, 166)(59, 155, 83, 179)(60, 156, 72, 168)(63, 159, 73, 169)(66, 162, 77, 173)(68, 164, 80, 176)(71, 167, 82, 178)(76, 172, 84, 180)(79, 175, 92, 188)(81, 177, 88, 184)(85, 181, 91, 187)(86, 182, 93, 189)(87, 183, 89, 185)(90, 186, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 203, 299, 204, 300)(199, 295, 209, 305, 210, 306)(201, 297, 211, 307, 214, 310)(202, 298, 215, 311, 216, 312)(205, 301, 221, 317, 207, 303)(206, 302, 223, 319, 224, 320)(208, 304, 226, 322, 227, 323)(212, 308, 233, 329, 234, 330)(213, 309, 235, 331, 236, 332)(217, 313, 230, 326, 242, 338)(218, 314, 243, 339, 244, 340)(219, 315, 237, 333, 228, 324)(220, 316, 246, 342, 247, 343)(222, 318, 248, 344, 249, 345)(225, 321, 253, 349, 239, 335)(229, 325, 257, 353, 258, 354)(231, 327, 260, 356, 261, 357)(232, 328, 250, 346, 262, 358)(238, 334, 259, 355, 266, 362)(240, 336, 268, 364, 263, 359)(241, 337, 264, 360, 269, 365)(245, 341, 272, 368, 254, 350)(251, 347, 255, 351, 276, 372)(252, 348, 270, 366, 256, 352)(265, 361, 279, 375, 274, 370)(267, 363, 281, 377, 275, 371)(271, 367, 282, 378, 278, 374)(273, 369, 277, 373, 286, 382)(280, 376, 284, 380, 287, 383)(283, 379, 288, 384, 285, 381)
	L = (1, 196)(2, 199)(3, 202)(4, 193)(5, 206)(6, 208)(7, 194)(8, 212)(9, 213)(10, 195)(11, 218)(12, 220)(13, 222)(14, 197)(15, 225)(16, 198)(17, 229)(18, 231)(19, 232)(20, 200)(21, 201)(22, 237)(23, 238)(24, 240)(25, 241)(26, 203)(27, 245)(28, 204)(29, 242)(30, 205)(31, 251)(32, 252)(33, 207)(34, 254)(35, 255)(36, 256)(37, 209)(38, 259)(39, 210)(40, 211)(41, 263)(42, 264)(43, 261)(44, 265)(45, 214)(46, 215)(47, 267)(48, 216)(49, 217)(50, 221)(51, 262)(52, 271)(53, 219)(54, 273)(55, 253)(56, 274)(57, 257)(58, 275)(59, 223)(60, 224)(61, 247)(62, 226)(63, 227)(64, 228)(65, 249)(66, 277)(67, 230)(68, 278)(69, 235)(70, 243)(71, 233)(72, 234)(73, 236)(74, 280)(75, 239)(76, 282)(77, 283)(78, 284)(79, 244)(80, 285)(81, 246)(82, 248)(83, 250)(84, 286)(85, 258)(86, 260)(87, 287)(88, 266)(89, 288)(90, 268)(91, 269)(92, 270)(93, 272)(94, 276)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1770
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1766 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, (Y1 * Y2 * Y3)^3, Y2 * Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 7, 103)(5, 101, 13, 109)(6, 102, 15, 111)(8, 104, 19, 115)(10, 106, 22, 118)(11, 107, 26, 122)(12, 108, 28, 124)(14, 110, 31, 127)(16, 112, 36, 132)(17, 113, 40, 136)(18, 114, 42, 138)(20, 116, 45, 141)(21, 117, 49, 145)(23, 119, 52, 148)(24, 120, 54, 150)(25, 121, 55, 151)(27, 123, 58, 154)(29, 125, 63, 159)(30, 126, 65, 161)(32, 128, 60, 156)(33, 129, 69, 165)(34, 130, 57, 153)(35, 131, 71, 167)(37, 133, 73, 169)(38, 134, 75, 171)(39, 135, 76, 172)(41, 137, 68, 164)(43, 139, 50, 146)(44, 140, 84, 180)(46, 142, 80, 176)(47, 143, 87, 183)(48, 144, 78, 174)(51, 147, 86, 182)(53, 149, 81, 177)(56, 152, 79, 175)(59, 155, 77, 173)(61, 157, 74, 170)(62, 158, 88, 184)(64, 160, 85, 181)(66, 162, 83, 179)(67, 163, 72, 168)(70, 166, 82, 178)(89, 185, 93, 189)(90, 186, 95, 191)(91, 187, 94, 190)(92, 188, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 203, 299, 204, 300)(199, 295, 209, 305, 210, 306)(201, 297, 213, 309, 215, 311)(202, 298, 216, 312, 217, 313)(205, 301, 222, 318, 224, 320)(206, 302, 225, 321, 226, 322)(207, 303, 227, 323, 229, 325)(208, 304, 230, 326, 231, 327)(211, 307, 236, 332, 238, 334)(212, 308, 239, 335, 240, 336)(214, 310, 242, 338, 243, 339)(218, 314, 249, 345, 251, 347)(219, 315, 252, 348, 253, 349)(220, 316, 254, 350, 246, 342)(221, 317, 256, 352, 241, 337)(223, 319, 259, 355, 260, 356)(228, 324, 255, 351, 264, 360)(232, 328, 270, 366, 271, 367)(233, 329, 272, 368, 273, 369)(234, 330, 274, 370, 267, 363)(235, 331, 275, 371, 263, 359)(237, 333, 278, 374, 250, 346)(244, 340, 281, 377, 262, 358)(245, 341, 282, 378, 258, 354)(247, 343, 283, 379, 261, 357)(248, 344, 284, 380, 257, 353)(265, 361, 285, 381, 280, 376)(266, 362, 286, 382, 277, 373)(268, 364, 287, 383, 279, 375)(269, 365, 288, 384, 276, 372)
	L = (1, 196)(2, 199)(3, 202)(4, 193)(5, 206)(6, 208)(7, 194)(8, 212)(9, 214)(10, 195)(11, 219)(12, 221)(13, 223)(14, 197)(15, 228)(16, 198)(17, 233)(18, 235)(19, 237)(20, 200)(21, 240)(22, 201)(23, 245)(24, 238)(25, 248)(26, 250)(27, 203)(28, 255)(29, 204)(30, 258)(31, 205)(32, 230)(33, 262)(34, 227)(35, 226)(36, 207)(37, 266)(38, 224)(39, 269)(40, 260)(41, 209)(42, 242)(43, 210)(44, 277)(45, 211)(46, 216)(47, 280)(48, 213)(49, 270)(50, 234)(51, 264)(52, 273)(53, 215)(54, 272)(55, 271)(56, 217)(57, 263)(58, 218)(59, 268)(60, 267)(61, 265)(62, 279)(63, 220)(64, 276)(65, 275)(66, 222)(67, 278)(68, 232)(69, 274)(70, 225)(71, 249)(72, 243)(73, 253)(74, 229)(75, 252)(76, 251)(77, 231)(78, 241)(79, 247)(80, 246)(81, 244)(82, 261)(83, 257)(84, 256)(85, 236)(86, 259)(87, 254)(88, 239)(89, 288)(90, 286)(91, 287)(92, 285)(93, 284)(94, 282)(95, 283)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1769
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1767 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (Y3 * Y1)^2, (Y1 * R)^2, Y3^4, (R * Y3)^2, Y3^-1 * Y2 * Y1 * Y2^-1 * Y3^-1, R * Y3^2 * R * Y3^-2, (Y2 * Y1)^3, Y2 * R * Y3 * Y2 * Y3^-1 * R, Y3^-2 * Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2^-1 * R * Y2 * R * Y2^-1 * Y3^-1 * Y2^-1, (Y1 * R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3 * Y2^-1 * R * Y2^-1 * R * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 22, 118)(9, 105, 28, 124)(12, 108, 23, 119)(13, 109, 24, 120)(14, 110, 20, 116)(15, 111, 26, 122)(16, 112, 27, 123)(18, 114, 40, 136)(19, 115, 39, 135)(21, 117, 30, 126)(25, 121, 29, 125)(31, 127, 33, 129)(32, 128, 52, 148)(34, 130, 50, 146)(35, 131, 46, 142)(36, 132, 45, 141)(37, 133, 47, 143)(38, 134, 48, 144)(41, 137, 43, 139)(42, 138, 68, 164)(44, 140, 70, 166)(49, 145, 51, 147)(53, 149, 58, 154)(54, 150, 57, 153)(55, 151, 59, 155)(56, 152, 60, 156)(61, 157, 63, 159)(62, 158, 77, 173)(64, 160, 78, 174)(65, 161, 66, 162)(67, 163, 69, 165)(71, 167, 75, 171)(72, 168, 74, 170)(73, 169, 76, 172)(79, 175, 80, 176)(81, 177, 82, 178)(83, 179, 84, 180)(85, 181, 87, 183)(86, 182, 88, 184)(89, 185, 92, 188)(90, 186, 91, 187)(93, 189, 96, 192)(94, 190, 95, 191)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 217, 313, 219, 315)(202, 298, 221, 317, 222, 318)(203, 299, 220, 316, 207, 303)(204, 300, 223, 319, 224, 320)(205, 301, 225, 321, 226, 322)(209, 305, 218, 314, 214, 310)(210, 306, 233, 329, 234, 330)(211, 307, 235, 331, 236, 332)(215, 311, 241, 337, 242, 338)(216, 312, 243, 339, 244, 340)(227, 323, 253, 349, 254, 350)(228, 324, 255, 351, 256, 352)(229, 325, 257, 353, 245, 341)(230, 326, 258, 354, 249, 345)(231, 327, 259, 355, 260, 356)(232, 328, 261, 357, 262, 358)(237, 333, 265, 361, 269, 365)(238, 334, 268, 364, 270, 366)(239, 335, 271, 367, 246, 342)(240, 336, 272, 368, 250, 346)(247, 343, 273, 369, 263, 359)(248, 344, 274, 370, 266, 362)(251, 347, 275, 371, 264, 360)(252, 348, 276, 372, 267, 363)(277, 373, 285, 381, 281, 377)(278, 374, 288, 384, 283, 379)(279, 375, 287, 383, 282, 378)(280, 376, 286, 382, 284, 380)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 215)(8, 218)(9, 211)(10, 194)(11, 216)(12, 214)(13, 195)(14, 227)(15, 198)(16, 229)(17, 231)(18, 201)(19, 197)(20, 237)(21, 239)(22, 205)(23, 203)(24, 199)(25, 228)(26, 202)(27, 240)(28, 232)(29, 238)(30, 230)(31, 245)(32, 247)(33, 249)(34, 251)(35, 217)(36, 206)(37, 222)(38, 208)(39, 220)(40, 209)(41, 263)(42, 253)(43, 266)(44, 255)(45, 221)(46, 212)(47, 219)(48, 213)(49, 250)(50, 248)(51, 246)(52, 252)(53, 243)(54, 223)(55, 242)(56, 224)(57, 241)(58, 225)(59, 244)(60, 226)(61, 262)(62, 277)(63, 260)(64, 279)(65, 281)(66, 283)(67, 264)(68, 268)(69, 267)(70, 265)(71, 259)(72, 233)(73, 234)(74, 261)(75, 235)(76, 236)(77, 280)(78, 278)(79, 284)(80, 282)(81, 285)(82, 287)(83, 288)(84, 286)(85, 270)(86, 254)(87, 269)(88, 256)(89, 272)(90, 257)(91, 271)(92, 258)(93, 276)(94, 273)(95, 275)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1771
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1768 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (Y1 * R)^2, Y3^4, (R * Y3)^2, Y2 * Y3^2 * Y2^-1 * Y1, Y3^-1 * Y2^-1 * Y1 * Y2 * Y3^-1, (Y2^-1 * Y3^-1 * R)^2, Y3 * Y2^-1 * Y3^-1 * R * Y2^-1 * R, Y2^-1 * Y3^-2 * Y1 * Y2 * Y1, R * Y3^-1 * Y2 * Y3^-1 * Y1 * R * Y2, R * Y1 * Y3^2 * Y1 * R * Y3^-2, Y3 * Y2^-1 * R * Y2 * R * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1 * R * Y2^-1 * R * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 22, 118)(9, 105, 26, 122)(12, 108, 32, 128)(13, 109, 31, 127)(14, 110, 23, 119)(15, 111, 24, 120)(16, 112, 21, 117)(18, 114, 27, 123)(19, 115, 28, 124)(20, 116, 29, 125)(25, 121, 30, 126)(33, 129, 53, 149)(34, 130, 36, 132)(35, 131, 55, 151)(37, 133, 45, 141)(38, 134, 46, 142)(39, 135, 48, 144)(40, 136, 47, 143)(41, 137, 51, 147)(42, 138, 44, 140)(43, 139, 49, 145)(50, 146, 52, 148)(54, 150, 56, 152)(57, 153, 61, 157)(58, 154, 62, 158)(59, 155, 64, 160)(60, 156, 63, 159)(65, 161, 76, 172)(66, 162, 68, 164)(67, 163, 73, 169)(69, 165, 79, 175)(70, 166, 80, 176)(71, 167, 74, 170)(72, 168, 75, 171)(77, 173, 78, 174)(81, 177, 83, 179)(82, 178, 84, 180)(85, 181, 88, 184)(86, 182, 87, 183)(89, 185, 91, 187)(90, 186, 92, 188)(93, 189, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 215, 311, 217, 313)(202, 298, 221, 317, 222, 318)(203, 299, 218, 314, 216, 312)(204, 300, 225, 321, 226, 322)(205, 301, 227, 323, 228, 324)(207, 303, 214, 310, 209, 305)(210, 306, 233, 329, 234, 330)(211, 307, 235, 331, 236, 332)(219, 315, 241, 337, 242, 338)(220, 316, 243, 339, 244, 340)(223, 319, 245, 341, 246, 342)(224, 320, 247, 343, 248, 344)(229, 325, 257, 353, 258, 354)(230, 326, 259, 355, 260, 356)(231, 327, 261, 357, 249, 345)(232, 328, 262, 358, 253, 349)(237, 333, 265, 361, 269, 365)(238, 334, 268, 364, 270, 366)(239, 335, 271, 367, 250, 346)(240, 336, 272, 368, 254, 350)(251, 347, 273, 369, 263, 359)(252, 348, 274, 370, 266, 362)(255, 351, 275, 371, 264, 360)(256, 352, 276, 372, 267, 363)(277, 373, 285, 381, 281, 377)(278, 374, 288, 384, 283, 379)(279, 375, 287, 383, 282, 378)(280, 376, 286, 382, 284, 380)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 205)(8, 216)(9, 219)(10, 194)(11, 223)(12, 199)(13, 195)(14, 229)(15, 198)(16, 231)(17, 220)(18, 218)(19, 197)(20, 237)(21, 239)(22, 224)(23, 238)(24, 202)(25, 232)(26, 211)(27, 209)(28, 201)(29, 230)(30, 240)(31, 214)(32, 203)(33, 249)(34, 251)(35, 253)(36, 255)(37, 221)(38, 206)(39, 217)(40, 208)(41, 263)(42, 257)(43, 266)(44, 259)(45, 215)(46, 212)(47, 222)(48, 213)(49, 264)(50, 268)(51, 267)(52, 265)(53, 254)(54, 252)(55, 250)(56, 256)(57, 247)(58, 225)(59, 246)(60, 226)(61, 245)(62, 227)(63, 248)(64, 228)(65, 244)(66, 277)(67, 242)(68, 279)(69, 281)(70, 283)(71, 241)(72, 233)(73, 234)(74, 243)(75, 235)(76, 236)(77, 280)(78, 278)(79, 284)(80, 282)(81, 285)(82, 287)(83, 288)(84, 286)(85, 270)(86, 258)(87, 269)(88, 260)(89, 272)(90, 261)(91, 271)(92, 262)(93, 276)(94, 273)(95, 275)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1772
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1769 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1^-3 * Y2, (Y1 * Y3)^3, Y1^3 * Y3 * Y2 * Y3 * Y1 * Y2, (Y2 * Y1^-1 * Y2 * Y1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 17, 113, 38, 134, 25, 121, 16, 112, 5, 101)(3, 99, 9, 105, 18, 114, 14, 110, 22, 118, 7, 103, 20, 116, 11, 107)(4, 100, 12, 108, 30, 126, 57, 153, 46, 142, 55, 151, 34, 130, 13, 109)(8, 104, 23, 119, 47, 143, 53, 149, 26, 122, 52, 148, 50, 146, 24, 120)(10, 106, 27, 123, 54, 150, 33, 129, 62, 158, 31, 127, 58, 154, 28, 124)(15, 111, 36, 132, 67, 163, 56, 152, 29, 125, 59, 155, 63, 159, 32, 128)(19, 115, 41, 137, 73, 169, 76, 172, 43, 139, 75, 171, 74, 170, 42, 138)(21, 117, 44, 140, 77, 173, 49, 145, 51, 147, 48, 144, 78, 174, 45, 141)(35, 131, 65, 161, 85, 181, 61, 157, 39, 135, 68, 164, 86, 182, 66, 162)(37, 133, 70, 166, 90, 186, 72, 168, 40, 136, 71, 167, 89, 185, 69, 165)(60, 156, 83, 179, 91, 187, 80, 176, 82, 178, 95, 191, 96, 192, 84, 180)(64, 160, 87, 183, 92, 188, 93, 189, 81, 177, 88, 184, 94, 190, 79, 175)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 206, 302)(198, 294, 210, 306)(200, 296, 213, 309)(201, 297, 217, 313)(203, 299, 209, 305)(204, 300, 223, 319)(205, 301, 225, 321)(207, 303, 227, 323)(208, 304, 212, 308)(211, 307, 232, 328)(214, 310, 230, 326)(215, 311, 240, 336)(216, 312, 241, 337)(218, 314, 243, 339)(219, 315, 247, 343)(220, 316, 249, 345)(221, 317, 231, 327)(222, 318, 246, 342)(224, 320, 253, 349)(226, 322, 250, 346)(228, 324, 260, 356)(229, 325, 235, 331)(233, 329, 262, 358)(234, 330, 261, 357)(236, 332, 244, 340)(237, 333, 245, 341)(238, 334, 254, 350)(239, 335, 269, 365)(242, 338, 270, 366)(248, 344, 258, 354)(251, 347, 257, 353)(252, 348, 273, 369)(255, 351, 278, 374)(256, 352, 274, 370)(259, 355, 277, 373)(263, 359, 267, 363)(264, 360, 268, 364)(265, 361, 281, 377)(266, 362, 282, 378)(271, 367, 276, 372)(272, 368, 285, 381)(275, 371, 279, 375)(280, 376, 287, 383)(283, 379, 286, 382)(284, 380, 288, 384)
	L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 207)(6, 211)(7, 213)(8, 194)(9, 218)(10, 195)(11, 221)(12, 224)(13, 215)(14, 227)(15, 197)(16, 229)(17, 231)(18, 232)(19, 198)(20, 235)(21, 199)(22, 238)(23, 205)(24, 233)(25, 243)(26, 201)(27, 248)(28, 244)(29, 203)(30, 252)(31, 253)(32, 204)(33, 240)(34, 256)(35, 206)(36, 261)(37, 208)(38, 254)(39, 209)(40, 210)(41, 216)(42, 260)(43, 212)(44, 249)(45, 267)(46, 214)(47, 271)(48, 225)(49, 262)(50, 272)(51, 217)(52, 220)(53, 263)(54, 273)(55, 258)(56, 219)(57, 236)(58, 274)(59, 268)(60, 222)(61, 223)(62, 230)(63, 275)(64, 226)(65, 264)(66, 247)(67, 280)(68, 234)(69, 228)(70, 241)(71, 245)(72, 257)(73, 283)(74, 284)(75, 237)(76, 251)(77, 276)(78, 285)(79, 239)(80, 242)(81, 246)(82, 250)(83, 255)(84, 269)(85, 287)(86, 279)(87, 278)(88, 259)(89, 286)(90, 288)(91, 265)(92, 266)(93, 270)(94, 281)(95, 277)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1766
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1770 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^3, (Y3 * Y1^-1)^3, Y2 * Y1^3 * Y2 * Y3 * Y1 * Y3, Y1^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 17, 113, 43, 139, 42, 138, 16, 112, 5, 101)(3, 99, 9, 105, 25, 121, 58, 154, 76, 172, 70, 166, 31, 127, 11, 107)(4, 100, 12, 108, 32, 128, 52, 148, 75, 171, 63, 159, 36, 132, 13, 109)(7, 103, 20, 116, 51, 147, 83, 179, 66, 162, 35, 131, 56, 152, 22, 118)(8, 104, 23, 119, 57, 153, 80, 176, 67, 163, 30, 126, 60, 156, 24, 120)(10, 106, 28, 124, 47, 143, 38, 134, 54, 150, 21, 117, 53, 149, 29, 125)(14, 110, 37, 133, 71, 167, 33, 129, 45, 141, 78, 174, 64, 160, 26, 122)(15, 111, 39, 135, 65, 161, 27, 123, 44, 140, 77, 173, 72, 168, 34, 130)(18, 114, 46, 142, 79, 175, 74, 170, 41, 137, 59, 155, 81, 177, 48, 144)(19, 115, 49, 145, 82, 178, 73, 169, 40, 136, 55, 151, 84, 180, 50, 146)(61, 157, 89, 185, 93, 189, 87, 183, 69, 165, 92, 188, 96, 192, 86, 182)(62, 158, 90, 186, 94, 190, 85, 181, 68, 164, 91, 187, 95, 191, 88, 184)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 206, 302)(198, 294, 210, 306)(200, 296, 213, 309)(201, 297, 218, 314)(203, 299, 212, 308)(204, 300, 225, 321)(205, 301, 227, 323)(207, 303, 230, 326)(208, 304, 232, 328)(209, 305, 236, 332)(211, 307, 239, 335)(214, 310, 238, 334)(215, 311, 250, 346)(216, 312, 251, 347)(217, 313, 253, 349)(219, 315, 255, 351)(220, 316, 258, 354)(221, 317, 237, 333)(222, 318, 244, 340)(223, 319, 260, 356)(224, 320, 254, 350)(226, 322, 262, 358)(228, 324, 261, 357)(229, 325, 265, 361)(231, 327, 242, 338)(233, 329, 245, 341)(234, 330, 259, 355)(235, 331, 267, 363)(240, 336, 269, 365)(241, 337, 275, 371)(243, 339, 277, 373)(246, 342, 268, 364)(247, 343, 272, 368)(248, 344, 279, 375)(249, 345, 278, 374)(252, 348, 280, 376)(256, 352, 281, 377)(257, 353, 284, 380)(263, 359, 282, 378)(264, 360, 283, 379)(266, 362, 270, 366)(271, 367, 285, 381)(273, 369, 287, 383)(274, 370, 286, 382)(276, 372, 288, 384)
	L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 207)(6, 211)(7, 213)(8, 194)(9, 219)(10, 195)(11, 222)(12, 226)(13, 215)(14, 230)(15, 197)(16, 233)(17, 237)(18, 239)(19, 198)(20, 244)(21, 199)(22, 247)(23, 205)(24, 241)(25, 254)(26, 255)(27, 201)(28, 259)(29, 236)(30, 203)(31, 261)(32, 253)(33, 262)(34, 204)(35, 250)(36, 260)(37, 240)(38, 206)(39, 266)(40, 245)(41, 208)(42, 258)(43, 268)(44, 221)(45, 209)(46, 272)(47, 210)(48, 229)(49, 216)(50, 270)(51, 278)(52, 212)(53, 232)(54, 267)(55, 214)(56, 280)(57, 277)(58, 227)(59, 275)(60, 279)(61, 224)(62, 217)(63, 218)(64, 283)(65, 282)(66, 234)(67, 220)(68, 228)(69, 223)(70, 225)(71, 284)(72, 281)(73, 269)(74, 231)(75, 246)(76, 235)(77, 265)(78, 242)(79, 286)(80, 238)(81, 288)(82, 285)(83, 251)(84, 287)(85, 249)(86, 243)(87, 252)(88, 248)(89, 264)(90, 257)(91, 256)(92, 263)(93, 274)(94, 271)(95, 276)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1765
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1771 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3^2 * Y1 * Y3^-1, Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3, Y1^-2 * Y3 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1)^3, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, (Y2 * Y1^-1)^3, Y3 * Y1^2 * Y3^-1 * Y2 * Y1^-2 * Y2 ]
Map:: non-degenerate
	R = (1, 97, 2, 98, 7, 103, 24, 120, 14, 110, 31, 127, 20, 116, 5, 101)(3, 99, 11, 107, 37, 133, 23, 119, 6, 102, 22, 118, 44, 140, 13, 109)(4, 100, 15, 111, 45, 141, 63, 159, 41, 137, 72, 168, 48, 144, 17, 113)(8, 104, 28, 124, 62, 158, 36, 132, 10, 106, 35, 131, 66, 162, 30, 126)(9, 105, 32, 128, 67, 163, 81, 177, 64, 160, 43, 139, 68, 164, 34, 130)(12, 108, 33, 129, 55, 151, 47, 143, 16, 112, 29, 125, 58, 154, 42, 138)(18, 114, 49, 145, 75, 171, 40, 136, 21, 117, 52, 148, 73, 169, 38, 134)(19, 115, 50, 146, 74, 170, 39, 135, 53, 149, 79, 175, 77, 173, 46, 142)(25, 121, 54, 150, 80, 176, 61, 157, 27, 123, 60, 156, 82, 178, 56, 152)(26, 122, 57, 153, 83, 179, 78, 174, 51, 147, 65, 161, 84, 180, 59, 155)(69, 165, 89, 185, 93, 189, 86, 182, 71, 167, 91, 187, 95, 191, 88, 184)(70, 166, 90, 186, 94, 190, 87, 183, 76, 172, 92, 188, 96, 192, 85, 181)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 217, 313)(201, 297, 223, 319)(202, 298, 221, 317)(203, 299, 230, 326)(205, 301, 220, 316)(207, 303, 238, 334)(208, 304, 233, 329)(209, 305, 224, 320)(211, 307, 216, 312)(212, 308, 218, 314)(213, 309, 239, 335)(214, 310, 231, 327)(215, 311, 235, 331)(219, 315, 247, 343)(222, 318, 246, 342)(225, 321, 256, 352)(226, 322, 249, 345)(227, 323, 255, 351)(228, 324, 257, 353)(229, 325, 261, 357)(232, 328, 264, 360)(234, 330, 245, 341)(236, 332, 262, 358)(237, 333, 263, 359)(240, 336, 268, 364)(241, 337, 251, 347)(242, 338, 248, 344)(243, 339, 250, 346)(244, 340, 253, 349)(252, 348, 273, 369)(254, 350, 277, 373)(258, 354, 278, 374)(259, 355, 279, 375)(260, 356, 280, 376)(265, 361, 281, 377)(266, 362, 282, 378)(267, 363, 284, 380)(269, 365, 283, 379)(270, 366, 271, 367)(272, 368, 285, 381)(274, 370, 286, 382)(275, 371, 287, 383)(276, 372, 288, 384)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 218)(8, 221)(9, 225)(10, 194)(11, 231)(12, 233)(13, 235)(14, 195)(15, 232)(16, 198)(17, 227)(18, 239)(19, 234)(20, 217)(21, 197)(22, 230)(23, 220)(24, 210)(25, 247)(26, 250)(27, 199)(28, 255)(29, 256)(30, 257)(31, 200)(32, 215)(33, 202)(34, 252)(35, 205)(36, 246)(37, 262)(38, 264)(39, 207)(40, 203)(41, 206)(42, 213)(43, 209)(44, 261)(45, 268)(46, 214)(47, 245)(48, 263)(49, 253)(50, 270)(51, 212)(52, 251)(53, 216)(54, 273)(55, 243)(56, 244)(57, 228)(58, 219)(59, 271)(60, 222)(61, 242)(62, 278)(63, 224)(64, 223)(65, 226)(66, 277)(67, 280)(68, 279)(69, 237)(70, 240)(71, 229)(72, 238)(73, 284)(74, 283)(75, 281)(76, 236)(77, 282)(78, 241)(79, 248)(80, 286)(81, 249)(82, 285)(83, 288)(84, 287)(85, 259)(86, 260)(87, 254)(88, 258)(89, 269)(90, 267)(91, 265)(92, 266)(93, 275)(94, 276)(95, 272)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1767
Graph:: bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1772 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, (Y2 * Y3^-1)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y3 * Y2)^2, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2, Y3^2 * Y1 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y2 * Y1^-2, (Y2 * Y1)^3, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y2, (Y3 * Y1^-1)^3, (Y3^-1 * Y1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 24, 120, 12, 108, 29, 125, 20, 116, 5, 101)(3, 99, 11, 107, 37, 133, 17, 113, 4, 100, 15, 111, 42, 138, 13, 109)(6, 102, 22, 118, 51, 147, 63, 159, 41, 137, 73, 169, 52, 148, 23, 119)(8, 104, 28, 124, 62, 158, 34, 130, 9, 105, 32, 128, 65, 161, 30, 126)(10, 106, 35, 131, 67, 163, 81, 177, 64, 160, 43, 139, 68, 164, 36, 132)(14, 110, 33, 129, 56, 152, 46, 142, 16, 112, 31, 127, 58, 154, 44, 140)(18, 114, 47, 143, 74, 170, 39, 135, 19, 115, 48, 144, 72, 168, 38, 134)(21, 117, 50, 146, 75, 171, 40, 136, 53, 149, 79, 175, 77, 173, 45, 141)(25, 121, 54, 150, 80, 176, 59, 155, 26, 122, 57, 153, 82, 178, 55, 151)(27, 123, 60, 156, 83, 179, 78, 174, 49, 145, 66, 162, 84, 180, 61, 157)(69, 165, 89, 185, 93, 189, 87, 183, 70, 166, 90, 186, 94, 190, 88, 184)(71, 167, 91, 187, 95, 191, 86, 182, 76, 172, 92, 188, 96, 192, 85, 181)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 217, 313)(201, 297, 223, 319)(202, 298, 221, 317)(203, 299, 230, 326)(205, 301, 220, 316)(207, 303, 232, 328)(208, 304, 233, 329)(209, 305, 235, 331)(211, 307, 238, 334)(212, 308, 219, 315)(213, 309, 216, 312)(214, 310, 237, 333)(215, 311, 227, 323)(218, 314, 248, 344)(222, 318, 246, 342)(224, 320, 255, 351)(225, 321, 256, 352)(226, 322, 258, 354)(228, 324, 252, 348)(229, 325, 261, 357)(231, 327, 265, 361)(234, 330, 263, 359)(236, 332, 245, 341)(239, 335, 253, 349)(240, 336, 251, 347)(241, 337, 250, 346)(242, 338, 247, 343)(243, 339, 262, 358)(244, 340, 268, 364)(249, 345, 273, 369)(254, 350, 277, 373)(257, 353, 279, 375)(259, 355, 278, 374)(260, 356, 280, 376)(264, 360, 281, 377)(266, 362, 284, 380)(267, 363, 283, 379)(269, 365, 282, 378)(270, 366, 271, 367)(272, 368, 285, 381)(274, 370, 287, 383)(275, 371, 286, 382)(276, 372, 288, 384)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 218)(8, 221)(9, 225)(10, 194)(11, 231)(12, 233)(13, 224)(14, 195)(15, 237)(16, 198)(17, 227)(18, 216)(19, 236)(20, 241)(21, 197)(22, 232)(23, 235)(24, 245)(25, 212)(26, 250)(27, 199)(28, 209)(29, 256)(30, 249)(31, 200)(32, 215)(33, 202)(34, 252)(35, 255)(36, 258)(37, 262)(38, 207)(39, 214)(40, 203)(41, 206)(42, 268)(43, 205)(44, 213)(45, 265)(46, 210)(47, 270)(48, 247)(49, 248)(50, 251)(51, 261)(52, 263)(53, 238)(54, 226)(55, 271)(56, 217)(57, 228)(58, 219)(59, 239)(60, 273)(61, 240)(62, 278)(63, 220)(64, 223)(65, 280)(66, 222)(67, 277)(68, 279)(69, 234)(70, 244)(71, 229)(72, 282)(73, 230)(74, 283)(75, 284)(76, 243)(77, 281)(78, 242)(79, 253)(80, 286)(81, 246)(82, 288)(83, 285)(84, 287)(85, 257)(86, 260)(87, 254)(88, 259)(89, 266)(90, 267)(91, 269)(92, 264)(93, 274)(94, 276)(95, 272)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1768
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1773 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>)
Aut   = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^3, (Y3 * Y1)^2, (Y3 * Y1)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * R * Y2^-1 * R, Y2 * Y3 * Y1^-1 * Y2 * Y1, Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, (Y3 * Y2 * Y1^-1)^2, (Y1 * Y3^-1)^3, Y3 * Y2^-4 * Y1, Y1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 97, 2, 98, 5, 101)(3, 99, 12, 108, 15, 111)(4, 100, 17, 113, 19, 115)(6, 102, 23, 119, 25, 121)(7, 103, 28, 124, 9, 105)(8, 104, 30, 126, 32, 128)(10, 106, 35, 131, 37, 133)(11, 107, 40, 136, 21, 117)(13, 109, 43, 139, 45, 141)(14, 110, 47, 143, 22, 118)(16, 112, 52, 148, 34, 130)(18, 114, 55, 151, 39, 135)(20, 116, 29, 125, 59, 155)(24, 120, 62, 158, 64, 160)(26, 122, 46, 142, 67, 163)(27, 123, 60, 156, 33, 129)(31, 127, 70, 166, 72, 168)(36, 132, 58, 154, 57, 153)(38, 134, 61, 157, 77, 173)(41, 137, 78, 174, 80, 176)(42, 138, 54, 150, 50, 146)(44, 140, 83, 179, 51, 147)(48, 144, 75, 171, 81, 177)(49, 145, 53, 149, 89, 185)(56, 152, 74, 170, 79, 175)(63, 159, 73, 169, 71, 167)(65, 161, 68, 164, 76, 172)(66, 162, 69, 165, 86, 182)(82, 178, 92, 188, 91, 187)(84, 180, 96, 192, 94, 190)(85, 181, 87, 183, 93, 189)(88, 184, 95, 191, 90, 186)(193, 289, 195, 291, 205, 301, 225, 321, 201, 297, 226, 322, 218, 314, 198, 294)(194, 290, 200, 296, 223, 319, 247, 343, 213, 309, 252, 348, 230, 326, 202, 298)(196, 292, 210, 306, 248, 344, 214, 310, 197, 293, 212, 308, 245, 341, 208, 304)(199, 295, 216, 312, 255, 351, 250, 346, 211, 307, 217, 313, 257, 353, 221, 317)(203, 299, 228, 324, 267, 363, 242, 338, 220, 316, 229, 325, 233, 329, 204, 300)(206, 302, 240, 336, 280, 376, 243, 339, 207, 303, 241, 337, 279, 375, 238, 334)(209, 305, 246, 342, 275, 371, 254, 350, 232, 328, 239, 335, 261, 357, 222, 318)(215, 311, 236, 332, 276, 372, 265, 361, 224, 320, 237, 333, 277, 373, 253, 349)(219, 315, 258, 354, 282, 378, 262, 358, 256, 352, 259, 355, 283, 379, 260, 356)(227, 323, 263, 359, 284, 380, 273, 369, 251, 347, 264, 360, 285, 381, 266, 362)(231, 327, 268, 364, 286, 382, 281, 377, 249, 345, 269, 365, 287, 383, 270, 366)(234, 330, 271, 367, 288, 384, 278, 374, 244, 340, 272, 368, 274, 370, 235, 331)
	L = (1, 196)(2, 201)(3, 206)(4, 199)(5, 213)(6, 216)(7, 193)(8, 215)(9, 203)(10, 228)(11, 194)(12, 226)(13, 236)(14, 208)(15, 242)(16, 195)(17, 197)(18, 249)(19, 232)(20, 227)(21, 209)(22, 246)(23, 225)(24, 219)(25, 224)(26, 258)(27, 198)(28, 211)(29, 210)(30, 252)(31, 263)(32, 254)(33, 200)(34, 234)(35, 247)(36, 231)(37, 251)(38, 268)(39, 202)(40, 220)(41, 271)(42, 204)(43, 218)(44, 238)(45, 278)(46, 205)(47, 207)(48, 266)(49, 270)(50, 239)(51, 261)(52, 214)(53, 240)(54, 244)(55, 212)(56, 272)(57, 221)(58, 229)(59, 250)(60, 256)(61, 223)(62, 217)(63, 264)(64, 222)(65, 269)(66, 235)(67, 243)(68, 255)(69, 259)(70, 230)(71, 253)(72, 260)(73, 257)(74, 245)(75, 241)(76, 262)(77, 265)(78, 267)(79, 273)(80, 281)(81, 233)(82, 282)(83, 237)(84, 287)(85, 284)(86, 275)(87, 276)(88, 283)(89, 248)(90, 286)(91, 285)(92, 288)(93, 280)(94, 274)(95, 279)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4^6 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1764
Graph:: bipartite
	v = 44 e = 192 f = 96
	degree seq :: [ 6^32, 16^12 ]

E27.1774 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-3 * Y2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y2, (Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1)^2, (Y3^-1 * Y1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 6, 102)(4, 100, 11, 107)(5, 101, 12, 108)(7, 103, 15, 111)(8, 104, 16, 112)(9, 105, 17, 113)(10, 106, 18, 114)(13, 109, 23, 119)(14, 110, 24, 120)(19, 115, 33, 129)(20, 116, 34, 130)(21, 117, 35, 131)(22, 118, 36, 132)(25, 121, 41, 137)(26, 122, 42, 138)(27, 123, 43, 139)(28, 124, 44, 140)(29, 125, 45, 141)(30, 126, 46, 142)(31, 127, 47, 143)(32, 128, 48, 144)(37, 133, 57, 153)(38, 134, 58, 154)(39, 135, 59, 155)(40, 136, 60, 156)(49, 145, 77, 173)(50, 146, 64, 160)(51, 147, 66, 162)(52, 148, 62, 158)(53, 149, 67, 163)(54, 150, 63, 159)(55, 151, 65, 161)(56, 152, 78, 174)(61, 157, 87, 183)(68, 164, 88, 184)(69, 165, 89, 185)(70, 166, 82, 178)(71, 167, 84, 180)(72, 168, 80, 176)(73, 169, 85, 181)(74, 170, 81, 177)(75, 171, 83, 179)(76, 172, 90, 186)(79, 175, 92, 188)(86, 182, 93, 189)(91, 187, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 201, 297)(197, 293, 202, 298)(199, 295, 205, 301)(200, 296, 206, 302)(203, 299, 209, 305)(204, 300, 210, 306)(207, 303, 215, 311)(208, 304, 216, 312)(211, 307, 221, 317)(212, 308, 222, 318)(213, 309, 223, 319)(214, 310, 224, 320)(217, 313, 229, 325)(218, 314, 230, 326)(219, 315, 231, 327)(220, 316, 232, 328)(225, 321, 237, 333)(226, 322, 238, 334)(227, 323, 239, 335)(228, 324, 240, 336)(233, 329, 249, 345)(234, 330, 250, 346)(235, 331, 251, 347)(236, 332, 252, 348)(241, 337, 261, 357)(242, 338, 262, 358)(243, 339, 263, 359)(244, 340, 264, 360)(245, 341, 265, 361)(246, 342, 266, 362)(247, 343, 267, 363)(248, 344, 268, 364)(253, 349, 271, 367)(254, 350, 272, 368)(255, 351, 273, 369)(256, 352, 274, 370)(257, 353, 275, 371)(258, 354, 276, 372)(259, 355, 277, 373)(260, 356, 278, 374)(269, 365, 281, 377)(270, 366, 282, 378)(279, 375, 284, 380)(280, 376, 285, 381)(283, 379, 287, 383)(286, 382, 288, 384)
	L = (1, 196)(2, 199)(3, 201)(4, 202)(5, 193)(6, 205)(7, 206)(8, 194)(9, 197)(10, 195)(11, 211)(12, 213)(13, 200)(14, 198)(15, 217)(16, 219)(17, 221)(18, 223)(19, 222)(20, 203)(21, 224)(22, 204)(23, 229)(24, 231)(25, 230)(26, 207)(27, 232)(28, 208)(29, 212)(30, 209)(31, 214)(32, 210)(33, 241)(34, 243)(35, 245)(36, 247)(37, 218)(38, 215)(39, 220)(40, 216)(41, 253)(42, 255)(43, 257)(44, 259)(45, 261)(46, 263)(47, 265)(48, 267)(49, 262)(50, 225)(51, 264)(52, 226)(53, 266)(54, 227)(55, 268)(56, 228)(57, 271)(58, 273)(59, 275)(60, 277)(61, 272)(62, 233)(63, 274)(64, 234)(65, 276)(66, 235)(67, 278)(68, 236)(69, 242)(70, 237)(71, 244)(72, 238)(73, 246)(74, 239)(75, 248)(76, 240)(77, 283)(78, 281)(79, 254)(80, 249)(81, 256)(82, 250)(83, 258)(84, 251)(85, 260)(86, 252)(87, 286)(88, 284)(89, 287)(90, 269)(91, 270)(92, 288)(93, 279)(94, 280)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1793
Graph:: simple bipartite
	v = 96 e = 192 f = 44
	degree seq :: [ 4^96 ]

E27.1775 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^2 * Y1 * Y3^-1 * Y1 * Y2, (Y1 * Y2 * Y3^-2)^2, Y3^-3 * Y2 * Y3^3 * Y2, R * Y2 * Y1 * Y2 * Y1 * Y2 * R * Y2, Y3^2 * Y2 * R * Y2 * R * Y3^-1 * Y1 * Y3 * Y1, Y3^-2 * Y2 * R * Y2 * R * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 15, 111)(6, 102, 18, 114)(7, 103, 21, 117)(8, 104, 24, 120)(10, 106, 25, 121)(11, 107, 31, 127)(13, 109, 35, 131)(14, 110, 28, 124)(16, 112, 19, 115)(17, 113, 42, 138)(20, 116, 48, 144)(22, 118, 52, 148)(23, 119, 45, 141)(26, 122, 59, 155)(27, 123, 61, 157)(29, 125, 65, 161)(30, 126, 49, 145)(32, 128, 47, 143)(33, 129, 54, 150)(34, 130, 68, 164)(36, 132, 71, 167)(37, 133, 50, 146)(38, 134, 60, 156)(39, 135, 72, 168)(40, 136, 69, 165)(41, 137, 58, 154)(43, 139, 55, 151)(44, 140, 74, 170)(46, 142, 78, 174)(51, 147, 81, 177)(53, 149, 84, 180)(56, 152, 85, 181)(57, 153, 82, 178)(62, 158, 83, 179)(63, 159, 86, 182)(64, 160, 87, 183)(66, 162, 80, 176)(67, 163, 79, 175)(70, 166, 75, 171)(73, 169, 76, 172)(77, 173, 92, 188)(88, 184, 93, 189)(89, 185, 94, 190)(90, 186, 96, 192)(91, 187, 95, 191)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 205, 301)(197, 293, 208, 304)(199, 295, 214, 310)(200, 296, 217, 313)(201, 297, 219, 315)(202, 298, 222, 318)(203, 299, 224, 320)(204, 300, 221, 317)(206, 302, 229, 325)(207, 303, 218, 314)(209, 305, 216, 312)(210, 306, 236, 332)(211, 307, 239, 335)(212, 308, 241, 337)(213, 309, 238, 334)(215, 311, 246, 342)(220, 316, 255, 351)(223, 319, 258, 354)(225, 321, 257, 353)(226, 322, 247, 343)(227, 323, 254, 350)(228, 324, 253, 349)(230, 326, 243, 339)(231, 327, 265, 361)(232, 328, 250, 346)(233, 329, 249, 345)(234, 330, 256, 352)(235, 331, 261, 357)(237, 333, 268, 364)(240, 336, 271, 367)(242, 338, 270, 366)(244, 340, 267, 363)(245, 341, 266, 362)(248, 344, 278, 374)(251, 347, 269, 365)(252, 348, 274, 370)(259, 355, 282, 378)(260, 356, 281, 377)(262, 358, 277, 373)(263, 359, 280, 376)(264, 360, 275, 371)(272, 368, 287, 383)(273, 369, 286, 382)(276, 372, 285, 381)(279, 375, 288, 384)(283, 379, 284, 380)
	L = (1, 196)(2, 199)(3, 202)(4, 206)(5, 193)(6, 211)(7, 215)(8, 194)(9, 220)(10, 213)(11, 195)(12, 226)(13, 224)(14, 230)(15, 231)(16, 233)(17, 197)(18, 237)(19, 204)(20, 198)(21, 243)(22, 241)(23, 247)(24, 248)(25, 250)(26, 200)(27, 239)(28, 256)(29, 201)(30, 208)(31, 259)(32, 260)(33, 203)(34, 262)(35, 252)(36, 205)(37, 253)(38, 240)(39, 245)(40, 207)(41, 264)(42, 263)(43, 209)(44, 222)(45, 269)(46, 210)(47, 217)(48, 272)(49, 273)(50, 212)(51, 275)(52, 235)(53, 214)(54, 266)(55, 223)(56, 228)(57, 216)(58, 277)(59, 276)(60, 218)(61, 279)(62, 219)(63, 227)(64, 232)(65, 267)(66, 221)(67, 280)(68, 271)(69, 225)(70, 234)(71, 283)(72, 229)(73, 274)(74, 284)(75, 236)(76, 244)(77, 249)(78, 254)(79, 238)(80, 285)(81, 258)(82, 242)(83, 251)(84, 288)(85, 246)(86, 261)(87, 287)(88, 255)(89, 257)(90, 286)(91, 265)(92, 282)(93, 268)(94, 270)(95, 281)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1794
Graph:: simple bipartite
	v = 96 e = 192 f = 44
	degree seq :: [ 4^96 ]

E27.1776 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1485>$ (small group id <192, 1485>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-3 * Y2, Y2 * Y3^-1 * Y2 * Y3, (Y2 * R)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^4, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3^-1, (Y3 * Y1 * Y3^-1 * Y1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 13, 109)(6, 102, 14, 110)(7, 103, 17, 113)(8, 104, 18, 114)(10, 106, 22, 118)(11, 107, 23, 119)(15, 111, 33, 129)(16, 112, 34, 130)(19, 115, 30, 126)(20, 116, 35, 131)(21, 117, 38, 134)(24, 120, 31, 127)(25, 121, 51, 147)(26, 122, 52, 148)(27, 123, 32, 128)(28, 124, 55, 151)(29, 125, 56, 152)(36, 132, 67, 163)(37, 133, 68, 164)(39, 135, 71, 167)(40, 136, 72, 168)(41, 137, 59, 155)(42, 138, 62, 158)(43, 139, 57, 153)(44, 140, 64, 160)(45, 141, 74, 170)(46, 142, 58, 154)(47, 143, 76, 172)(48, 144, 60, 156)(49, 145, 70, 166)(50, 146, 77, 173)(53, 149, 79, 175)(54, 150, 65, 161)(61, 157, 82, 178)(63, 159, 84, 180)(66, 162, 85, 181)(69, 165, 87, 183)(73, 169, 89, 185)(75, 171, 91, 187)(78, 174, 86, 182)(80, 176, 88, 184)(81, 177, 93, 189)(83, 179, 95, 191)(90, 186, 96, 192)(92, 188, 94, 190)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 202, 298)(197, 293, 203, 299)(199, 295, 207, 303)(200, 296, 208, 304)(201, 297, 211, 307)(204, 300, 216, 312)(205, 301, 219, 315)(206, 302, 222, 318)(209, 305, 227, 323)(210, 306, 230, 326)(212, 308, 233, 329)(213, 309, 234, 330)(214, 310, 235, 331)(215, 311, 238, 334)(217, 313, 241, 337)(218, 314, 242, 338)(220, 316, 245, 341)(221, 317, 246, 342)(223, 319, 249, 345)(224, 320, 250, 346)(225, 321, 251, 347)(226, 322, 254, 350)(228, 324, 257, 353)(229, 325, 258, 354)(231, 327, 261, 357)(232, 328, 262, 358)(236, 332, 264, 360)(237, 333, 265, 361)(239, 335, 267, 363)(240, 336, 259, 355)(243, 339, 256, 352)(244, 340, 266, 362)(247, 343, 268, 364)(248, 344, 252, 348)(253, 349, 273, 369)(255, 351, 275, 371)(260, 356, 274, 370)(263, 359, 276, 372)(269, 365, 281, 377)(270, 366, 282, 378)(271, 367, 283, 379)(272, 368, 284, 380)(277, 373, 285, 381)(278, 374, 286, 382)(279, 375, 287, 383)(280, 376, 288, 384)
	L = (1, 196)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 208)(8, 194)(9, 212)(10, 197)(11, 195)(12, 217)(13, 220)(14, 223)(15, 200)(16, 198)(17, 228)(18, 231)(19, 233)(20, 234)(21, 201)(22, 236)(23, 239)(24, 241)(25, 242)(26, 204)(27, 245)(28, 246)(29, 205)(30, 249)(31, 250)(32, 206)(33, 252)(34, 255)(35, 257)(36, 258)(37, 209)(38, 261)(39, 262)(40, 210)(41, 213)(42, 211)(43, 264)(44, 265)(45, 214)(46, 267)(47, 259)(48, 215)(49, 218)(50, 216)(51, 254)(52, 270)(53, 221)(54, 219)(55, 269)(56, 253)(57, 224)(58, 222)(59, 248)(60, 273)(61, 225)(62, 275)(63, 243)(64, 226)(65, 229)(66, 227)(67, 238)(68, 278)(69, 232)(70, 230)(71, 277)(72, 237)(73, 235)(74, 282)(75, 240)(76, 281)(77, 284)(78, 283)(79, 244)(80, 247)(81, 251)(82, 286)(83, 256)(84, 285)(85, 288)(86, 287)(87, 260)(88, 263)(89, 272)(90, 271)(91, 266)(92, 268)(93, 280)(94, 279)(95, 274)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1795
Graph:: simple bipartite
	v = 96 e = 192 f = 44
	degree seq :: [ 4^96 ]

E27.1777 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1480>$ (small group id <192, 1480>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3)^2, Y3^4, (Y1 * Y3^-1 * Y2)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 22, 118)(9, 105, 28, 124)(12, 108, 32, 128)(13, 109, 27, 123)(14, 110, 30, 126)(15, 111, 26, 122)(16, 112, 24, 120)(18, 114, 31, 127)(19, 115, 25, 121)(20, 116, 29, 125)(21, 117, 23, 119)(33, 129, 65, 161)(34, 130, 68, 164)(35, 131, 51, 147)(36, 132, 58, 154)(37, 133, 67, 163)(38, 134, 54, 150)(39, 135, 66, 162)(40, 136, 57, 153)(41, 137, 56, 152)(42, 138, 52, 148)(43, 139, 70, 166)(44, 140, 73, 169)(45, 141, 75, 171)(46, 142, 62, 158)(47, 143, 74, 170)(48, 144, 64, 160)(49, 145, 77, 173)(50, 146, 80, 176)(53, 149, 79, 175)(55, 151, 78, 174)(59, 155, 82, 178)(60, 156, 85, 181)(61, 157, 87, 183)(63, 159, 86, 182)(69, 165, 84, 180)(71, 167, 88, 184)(72, 168, 81, 177)(76, 172, 83, 179)(89, 185, 93, 189)(90, 186, 95, 191)(91, 187, 94, 190)(92, 188, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 217, 313, 219, 315)(202, 298, 223, 319, 224, 320)(203, 299, 225, 321, 226, 322)(204, 300, 227, 323, 229, 325)(205, 301, 230, 326, 231, 327)(207, 303, 228, 324, 233, 329)(209, 305, 235, 331, 236, 332)(210, 306, 237, 333, 238, 334)(211, 307, 239, 335, 240, 336)(214, 310, 241, 337, 242, 338)(215, 311, 243, 339, 245, 341)(216, 312, 246, 342, 247, 343)(218, 314, 244, 340, 249, 345)(220, 316, 251, 347, 252, 348)(221, 317, 253, 349, 254, 350)(222, 318, 255, 351, 256, 352)(232, 328, 262, 358, 263, 359)(234, 330, 264, 360, 260, 356)(248, 344, 274, 370, 275, 371)(250, 346, 276, 372, 272, 368)(257, 353, 281, 377, 268, 364)(258, 354, 267, 363, 282, 378)(259, 355, 266, 362, 283, 379)(261, 357, 284, 380, 265, 361)(269, 365, 285, 381, 280, 376)(270, 366, 279, 375, 286, 382)(271, 367, 278, 374, 287, 383)(273, 369, 288, 384, 277, 373)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 215)(8, 218)(9, 221)(10, 194)(11, 219)(12, 228)(13, 195)(14, 232)(15, 198)(16, 234)(17, 217)(18, 233)(19, 197)(20, 220)(21, 214)(22, 208)(23, 244)(24, 199)(25, 248)(26, 202)(27, 250)(28, 206)(29, 249)(30, 201)(31, 209)(32, 203)(33, 258)(34, 246)(35, 242)(36, 205)(37, 261)(38, 260)(39, 257)(40, 212)(41, 211)(42, 213)(43, 256)(44, 266)(45, 268)(46, 251)(47, 265)(48, 262)(49, 270)(50, 230)(51, 226)(52, 216)(53, 273)(54, 272)(55, 269)(56, 223)(57, 222)(58, 224)(59, 240)(60, 278)(61, 280)(62, 235)(63, 277)(64, 274)(65, 229)(66, 276)(67, 225)(68, 227)(69, 231)(70, 238)(71, 279)(72, 271)(73, 237)(74, 275)(75, 236)(76, 239)(77, 245)(78, 264)(79, 241)(80, 243)(81, 247)(82, 254)(83, 267)(84, 259)(85, 253)(86, 263)(87, 252)(88, 255)(89, 286)(90, 288)(91, 285)(92, 287)(93, 282)(94, 284)(95, 281)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1785
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1778 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1480>$ (small group id <192, 1480>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (Y3^-1 * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y2^-1 * Y3^3 * Y2^-1, Y2 * Y3^2 * Y2 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y1 * Y3^-3 * Y1 * Y2^-1, Y2 * Y3^-1 * Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1, Y3^-2 * Y2 * Y1 * Y2 * Y3^2 * Y1 * Y2, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 23, 119)(9, 105, 29, 125)(12, 108, 36, 132)(13, 109, 28, 124)(14, 110, 31, 127)(15, 111, 34, 130)(16, 112, 25, 121)(18, 114, 30, 126)(19, 115, 26, 122)(20, 116, 32, 128)(21, 117, 55, 151)(22, 118, 27, 123)(24, 120, 58, 154)(33, 129, 77, 173)(35, 131, 79, 175)(37, 133, 74, 170)(38, 134, 48, 144)(39, 135, 61, 157)(40, 136, 81, 177)(41, 137, 63, 159)(42, 138, 68, 164)(43, 139, 75, 171)(44, 140, 78, 174)(45, 141, 76, 172)(46, 142, 64, 160)(47, 143, 87, 183)(49, 145, 73, 169)(50, 146, 88, 184)(51, 147, 71, 167)(52, 148, 59, 155)(53, 149, 65, 161)(54, 150, 67, 163)(56, 152, 66, 162)(57, 153, 90, 186)(60, 156, 70, 166)(62, 158, 91, 187)(69, 165, 95, 191)(72, 168, 96, 192)(80, 176, 86, 182)(82, 178, 89, 185)(83, 179, 92, 188)(84, 180, 93, 189)(85, 181, 94, 190)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 218, 314, 220, 316)(202, 298, 224, 320, 225, 321)(203, 299, 227, 323, 226, 322)(204, 300, 229, 325, 231, 327)(205, 301, 232, 328, 233, 329)(207, 303, 236, 332, 237, 333)(209, 305, 239, 335, 240, 336)(210, 306, 241, 337, 242, 338)(211, 307, 243, 339, 244, 340)(214, 310, 215, 311, 249, 345)(216, 312, 251, 347, 253, 349)(217, 313, 254, 350, 255, 351)(219, 315, 258, 354, 259, 355)(221, 317, 261, 357, 262, 358)(222, 318, 263, 359, 264, 360)(223, 319, 265, 361, 266, 362)(228, 324, 273, 369, 274, 370)(230, 326, 246, 342, 276, 372)(234, 330, 271, 367, 277, 373)(235, 331, 275, 371, 248, 344)(238, 334, 245, 341, 279, 375)(247, 343, 280, 376, 272, 368)(250, 346, 283, 379, 278, 374)(252, 348, 268, 364, 285, 381)(256, 352, 282, 378, 286, 382)(257, 353, 284, 380, 270, 366)(260, 356, 267, 363, 287, 383)(269, 365, 288, 384, 281, 377)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 216)(8, 219)(9, 222)(10, 194)(11, 220)(12, 230)(13, 195)(14, 235)(15, 229)(16, 238)(17, 218)(18, 221)(19, 197)(20, 237)(21, 234)(22, 198)(23, 208)(24, 252)(25, 199)(26, 257)(27, 251)(28, 260)(29, 206)(30, 209)(31, 201)(32, 259)(33, 256)(34, 202)(35, 272)(36, 203)(37, 275)(38, 241)(39, 249)(40, 276)(41, 245)(42, 205)(43, 233)(44, 243)(45, 278)(46, 269)(47, 254)(48, 228)(49, 248)(50, 277)(51, 262)(52, 214)(53, 211)(54, 212)(55, 258)(56, 213)(57, 281)(58, 215)(59, 284)(60, 263)(61, 227)(62, 285)(63, 267)(64, 217)(65, 255)(66, 265)(67, 274)(68, 247)(69, 232)(70, 250)(71, 270)(72, 286)(73, 240)(74, 226)(75, 223)(76, 224)(77, 236)(78, 225)(79, 231)(80, 268)(81, 287)(82, 282)(83, 244)(84, 283)(85, 288)(86, 271)(87, 242)(88, 239)(89, 246)(90, 253)(91, 279)(92, 266)(93, 273)(94, 280)(95, 264)(96, 261)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1786
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1779 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1)^2, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 6, 102)(4, 100, 7, 103)(5, 101, 8, 104)(9, 105, 13, 109)(10, 106, 14, 110)(11, 107, 15, 111)(12, 108, 16, 112)(17, 113, 23, 119)(18, 114, 24, 120)(19, 115, 25, 121)(20, 116, 26, 122)(21, 117, 27, 123)(22, 118, 28, 124)(29, 125, 37, 133)(30, 126, 38, 134)(31, 127, 39, 135)(32, 128, 40, 136)(33, 129, 41, 137)(34, 130, 42, 138)(35, 131, 43, 139)(36, 132, 44, 140)(45, 141, 57, 153)(46, 142, 58, 154)(47, 143, 59, 155)(48, 144, 60, 156)(49, 145, 61, 157)(50, 146, 62, 158)(51, 147, 63, 159)(52, 148, 64, 160)(53, 149, 65, 161)(54, 150, 66, 162)(55, 151, 67, 163)(56, 152, 68, 164)(69, 165, 79, 175)(70, 166, 80, 176)(71, 167, 81, 177)(72, 168, 82, 178)(73, 169, 83, 179)(74, 170, 84, 180)(75, 171, 85, 181)(76, 172, 86, 182)(77, 173, 87, 183)(78, 174, 88, 184)(89, 185, 92, 188)(90, 186, 93, 189)(91, 187, 94, 190)(95, 191, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 202, 298, 203, 299)(199, 295, 206, 302, 207, 303)(201, 297, 209, 305, 210, 306)(204, 300, 213, 309, 214, 310)(205, 301, 215, 311, 216, 312)(208, 304, 219, 315, 220, 316)(211, 307, 223, 319, 224, 320)(212, 308, 225, 321, 226, 322)(217, 313, 231, 327, 232, 328)(218, 314, 233, 329, 234, 330)(221, 317, 237, 333, 238, 334)(222, 318, 239, 335, 240, 336)(227, 323, 245, 341, 246, 342)(228, 324, 247, 343, 248, 344)(229, 325, 249, 345, 250, 346)(230, 326, 251, 347, 252, 348)(235, 331, 257, 353, 258, 354)(236, 332, 259, 355, 260, 356)(241, 337, 265, 361, 264, 360)(242, 338, 266, 362, 262, 358)(243, 339, 267, 363, 263, 359)(244, 340, 268, 364, 269, 365)(253, 349, 275, 371, 274, 370)(254, 350, 276, 372, 272, 368)(255, 351, 277, 373, 273, 369)(256, 352, 278, 374, 279, 375)(261, 357, 281, 377, 270, 366)(271, 367, 284, 380, 280, 376)(282, 378, 287, 383, 283, 379)(285, 381, 288, 384, 286, 382)
	L = (1, 196)(2, 199)(3, 201)(4, 193)(5, 204)(6, 205)(7, 194)(8, 208)(9, 195)(10, 211)(11, 212)(12, 197)(13, 198)(14, 217)(15, 218)(16, 200)(17, 221)(18, 222)(19, 202)(20, 203)(21, 227)(22, 228)(23, 229)(24, 230)(25, 206)(26, 207)(27, 235)(28, 236)(29, 209)(30, 210)(31, 241)(32, 242)(33, 243)(34, 244)(35, 213)(36, 214)(37, 215)(38, 216)(39, 253)(40, 254)(41, 255)(42, 256)(43, 219)(44, 220)(45, 261)(46, 262)(47, 263)(48, 264)(49, 223)(50, 224)(51, 225)(52, 226)(53, 268)(54, 266)(55, 267)(56, 270)(57, 271)(58, 272)(59, 273)(60, 274)(61, 231)(62, 232)(63, 233)(64, 234)(65, 278)(66, 276)(67, 277)(68, 280)(69, 237)(70, 238)(71, 239)(72, 240)(73, 282)(74, 246)(75, 247)(76, 245)(77, 283)(78, 248)(79, 249)(80, 250)(81, 251)(82, 252)(83, 285)(84, 258)(85, 259)(86, 257)(87, 286)(88, 260)(89, 287)(90, 265)(91, 269)(92, 288)(93, 275)(94, 279)(95, 281)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1789
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1780 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1, Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 7, 103)(5, 101, 13, 109)(6, 102, 15, 111)(8, 104, 19, 115)(10, 106, 18, 114)(11, 107, 20, 116)(12, 108, 16, 112)(14, 110, 17, 113)(21, 117, 37, 133)(22, 118, 39, 135)(23, 119, 40, 136)(24, 120, 38, 134)(25, 121, 41, 137)(26, 122, 43, 139)(27, 123, 44, 140)(28, 124, 42, 138)(29, 125, 45, 141)(30, 126, 47, 143)(31, 127, 48, 144)(32, 128, 46, 142)(33, 129, 49, 145)(34, 130, 51, 147)(35, 131, 52, 148)(36, 132, 50, 146)(53, 149, 69, 165)(54, 150, 77, 173)(55, 151, 80, 176)(56, 152, 72, 168)(57, 153, 85, 181)(58, 154, 81, 177)(59, 155, 84, 180)(60, 156, 86, 182)(61, 157, 70, 166)(62, 158, 87, 183)(63, 159, 88, 184)(64, 160, 71, 167)(65, 161, 74, 170)(66, 162, 82, 178)(67, 163, 83, 179)(68, 164, 75, 171)(73, 169, 89, 185)(76, 172, 90, 186)(78, 174, 91, 187)(79, 175, 92, 188)(93, 189, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 203, 299, 204, 300)(199, 295, 209, 305, 210, 306)(201, 297, 213, 309, 214, 310)(202, 298, 215, 311, 216, 312)(205, 301, 217, 313, 218, 314)(206, 302, 219, 315, 220, 316)(207, 303, 221, 317, 222, 318)(208, 304, 223, 319, 224, 320)(211, 307, 225, 321, 226, 322)(212, 308, 227, 323, 228, 324)(229, 325, 245, 341, 246, 342)(230, 326, 247, 343, 248, 344)(231, 327, 249, 345, 250, 346)(232, 328, 251, 347, 252, 348)(233, 329, 253, 349, 254, 350)(234, 330, 255, 351, 256, 352)(235, 331, 257, 353, 258, 354)(236, 332, 259, 355, 260, 356)(237, 333, 261, 357, 262, 358)(238, 334, 263, 359, 264, 360)(239, 335, 265, 361, 266, 362)(240, 336, 267, 363, 268, 364)(241, 337, 269, 365, 270, 366)(242, 338, 271, 367, 272, 368)(243, 339, 273, 369, 274, 370)(244, 340, 275, 371, 276, 372)(277, 373, 279, 375, 285, 381)(278, 374, 286, 382, 280, 376)(281, 377, 283, 379, 287, 383)(282, 378, 288, 384, 284, 380)
	L = (1, 196)(2, 199)(3, 202)(4, 193)(5, 206)(6, 208)(7, 194)(8, 212)(9, 210)(10, 195)(11, 211)(12, 207)(13, 209)(14, 197)(15, 204)(16, 198)(17, 205)(18, 201)(19, 203)(20, 200)(21, 230)(22, 232)(23, 231)(24, 229)(25, 234)(26, 236)(27, 235)(28, 233)(29, 238)(30, 240)(31, 239)(32, 237)(33, 242)(34, 244)(35, 243)(36, 241)(37, 216)(38, 213)(39, 215)(40, 214)(41, 220)(42, 217)(43, 219)(44, 218)(45, 224)(46, 221)(47, 223)(48, 222)(49, 228)(50, 225)(51, 227)(52, 226)(53, 264)(54, 272)(55, 269)(56, 261)(57, 278)(58, 276)(59, 273)(60, 277)(61, 263)(62, 280)(63, 279)(64, 262)(65, 267)(66, 275)(67, 274)(68, 266)(69, 248)(70, 256)(71, 253)(72, 245)(73, 282)(74, 260)(75, 257)(76, 281)(77, 247)(78, 284)(79, 283)(80, 246)(81, 251)(82, 259)(83, 258)(84, 250)(85, 252)(86, 249)(87, 255)(88, 254)(89, 268)(90, 265)(91, 271)(92, 270)(93, 288)(94, 287)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1790
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1781 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1, (R * Y2 * Y3)^2, (Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1)^2, (Y1 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 7, 103)(5, 101, 13, 109)(6, 102, 15, 111)(8, 104, 19, 115)(10, 106, 17, 113)(11, 107, 16, 112)(12, 108, 20, 116)(14, 110, 18, 114)(21, 117, 37, 133)(22, 118, 39, 135)(23, 119, 38, 134)(24, 120, 40, 136)(25, 121, 41, 137)(26, 122, 43, 139)(27, 123, 42, 138)(28, 124, 44, 140)(29, 125, 45, 141)(30, 126, 47, 143)(31, 127, 46, 142)(32, 128, 48, 144)(33, 129, 49, 145)(34, 130, 51, 147)(35, 131, 50, 146)(36, 132, 52, 148)(53, 149, 85, 181)(54, 150, 74, 170)(55, 151, 86, 182)(56, 152, 76, 172)(57, 153, 78, 174)(58, 154, 70, 166)(59, 155, 80, 176)(60, 156, 72, 168)(61, 157, 81, 177)(62, 158, 73, 169)(63, 159, 83, 179)(64, 160, 75, 171)(65, 161, 77, 173)(66, 162, 87, 183)(67, 163, 79, 175)(68, 164, 88, 184)(69, 165, 89, 185)(71, 167, 90, 186)(82, 178, 91, 187)(84, 180, 92, 188)(93, 189, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 203, 299, 204, 300)(199, 295, 209, 305, 210, 306)(201, 297, 213, 309, 214, 310)(202, 298, 215, 311, 216, 312)(205, 301, 217, 313, 218, 314)(206, 302, 219, 315, 220, 316)(207, 303, 221, 317, 222, 318)(208, 304, 223, 319, 224, 320)(211, 307, 225, 321, 226, 322)(212, 308, 227, 323, 228, 324)(229, 325, 245, 341, 246, 342)(230, 326, 247, 343, 248, 344)(231, 327, 249, 345, 250, 346)(232, 328, 251, 347, 252, 348)(233, 329, 253, 349, 254, 350)(234, 330, 255, 351, 256, 352)(235, 331, 257, 353, 258, 354)(236, 332, 259, 355, 260, 356)(237, 333, 261, 357, 262, 358)(238, 334, 263, 359, 264, 360)(239, 335, 265, 361, 266, 362)(240, 336, 267, 363, 268, 364)(241, 337, 269, 365, 270, 366)(242, 338, 271, 367, 272, 368)(243, 339, 273, 369, 274, 370)(244, 340, 275, 371, 276, 372)(277, 373, 285, 381, 279, 375)(278, 374, 286, 382, 280, 376)(281, 377, 287, 383, 283, 379)(282, 378, 288, 384, 284, 380)
	L = (1, 196)(2, 199)(3, 202)(4, 193)(5, 206)(6, 208)(7, 194)(8, 212)(9, 209)(10, 195)(11, 207)(12, 211)(13, 210)(14, 197)(15, 203)(16, 198)(17, 201)(18, 205)(19, 204)(20, 200)(21, 230)(22, 232)(23, 229)(24, 231)(25, 234)(26, 236)(27, 233)(28, 235)(29, 238)(30, 240)(31, 237)(32, 239)(33, 242)(34, 244)(35, 241)(36, 243)(37, 215)(38, 213)(39, 216)(40, 214)(41, 219)(42, 217)(43, 220)(44, 218)(45, 223)(46, 221)(47, 224)(48, 222)(49, 227)(50, 225)(51, 228)(52, 226)(53, 278)(54, 268)(55, 277)(56, 266)(57, 272)(58, 264)(59, 270)(60, 262)(61, 275)(62, 267)(63, 273)(64, 265)(65, 271)(66, 280)(67, 269)(68, 279)(69, 282)(70, 252)(71, 281)(72, 250)(73, 256)(74, 248)(75, 254)(76, 246)(77, 259)(78, 251)(79, 257)(80, 249)(81, 255)(82, 284)(83, 253)(84, 283)(85, 247)(86, 245)(87, 260)(88, 258)(89, 263)(90, 261)(91, 276)(92, 274)(93, 288)(94, 287)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1787
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1782 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 8, 104)(4, 100, 7, 103)(5, 101, 6, 102)(9, 105, 16, 112)(10, 106, 15, 111)(11, 107, 14, 110)(12, 108, 13, 109)(17, 113, 28, 124)(18, 114, 27, 123)(19, 115, 26, 122)(20, 116, 25, 121)(21, 117, 24, 120)(22, 118, 23, 119)(29, 125, 44, 140)(30, 126, 43, 139)(31, 127, 42, 138)(32, 128, 41, 137)(33, 129, 40, 136)(34, 130, 39, 135)(35, 131, 38, 134)(36, 132, 37, 133)(45, 141, 68, 164)(46, 142, 67, 163)(47, 143, 66, 162)(48, 144, 65, 161)(49, 145, 64, 160)(50, 146, 63, 159)(51, 147, 62, 158)(52, 148, 61, 157)(53, 149, 60, 156)(54, 150, 59, 155)(55, 151, 58, 154)(56, 152, 57, 153)(69, 165, 88, 184)(70, 166, 85, 181)(71, 167, 84, 180)(72, 168, 86, 182)(73, 169, 87, 183)(74, 170, 81, 177)(75, 171, 80, 176)(76, 172, 82, 178)(77, 173, 83, 179)(78, 174, 79, 175)(89, 185, 92, 188)(90, 186, 94, 190)(91, 187, 93, 189)(95, 191, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 198, 294, 200, 296)(196, 292, 202, 298, 203, 299)(199, 295, 206, 302, 207, 303)(201, 297, 209, 305, 210, 306)(204, 300, 213, 309, 214, 310)(205, 301, 215, 311, 216, 312)(208, 304, 219, 315, 220, 316)(211, 307, 223, 319, 224, 320)(212, 308, 225, 321, 226, 322)(217, 313, 231, 327, 232, 328)(218, 314, 233, 329, 234, 330)(221, 317, 237, 333, 238, 334)(222, 318, 239, 335, 240, 336)(227, 323, 245, 341, 246, 342)(228, 324, 247, 343, 248, 344)(229, 325, 249, 345, 250, 346)(230, 326, 251, 347, 252, 348)(235, 331, 257, 353, 258, 354)(236, 332, 259, 355, 260, 356)(241, 337, 265, 361, 264, 360)(242, 338, 266, 362, 262, 358)(243, 339, 267, 363, 263, 359)(244, 340, 268, 364, 269, 365)(253, 349, 275, 371, 274, 370)(254, 350, 276, 372, 272, 368)(255, 351, 277, 373, 273, 369)(256, 352, 278, 374, 279, 375)(261, 357, 281, 377, 270, 366)(271, 367, 284, 380, 280, 376)(282, 378, 287, 383, 283, 379)(285, 381, 288, 384, 286, 382)
	L = (1, 196)(2, 199)(3, 201)(4, 193)(5, 204)(6, 205)(7, 194)(8, 208)(9, 195)(10, 211)(11, 212)(12, 197)(13, 198)(14, 217)(15, 218)(16, 200)(17, 221)(18, 222)(19, 202)(20, 203)(21, 227)(22, 228)(23, 229)(24, 230)(25, 206)(26, 207)(27, 235)(28, 236)(29, 209)(30, 210)(31, 241)(32, 242)(33, 243)(34, 244)(35, 213)(36, 214)(37, 215)(38, 216)(39, 253)(40, 254)(41, 255)(42, 256)(43, 219)(44, 220)(45, 261)(46, 262)(47, 263)(48, 264)(49, 223)(50, 224)(51, 225)(52, 226)(53, 268)(54, 266)(55, 267)(56, 270)(57, 271)(58, 272)(59, 273)(60, 274)(61, 231)(62, 232)(63, 233)(64, 234)(65, 278)(66, 276)(67, 277)(68, 280)(69, 237)(70, 238)(71, 239)(72, 240)(73, 282)(74, 246)(75, 247)(76, 245)(77, 283)(78, 248)(79, 249)(80, 250)(81, 251)(82, 252)(83, 285)(84, 258)(85, 259)(86, 257)(87, 286)(88, 260)(89, 287)(90, 265)(91, 269)(92, 288)(93, 275)(94, 279)(95, 281)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1788
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1783 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y2^3, (R * Y3)^2, (Y3 * Y2)^2, (Y1 * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y2 * Y3 * Y2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^8, (Y3^-3 * Y2)^2, Y1 * Y2 * Y3^-2 * Y2 * Y3 * Y1 * Y2^-1 * Y3, Y2 * Y3 * Y1 * Y3^-3 * Y2^-1 * Y3^2 * Y1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-2 * Y2^-1 * Y1, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 21, 117)(9, 105, 27, 123)(12, 108, 32, 128)(13, 109, 26, 122)(14, 110, 24, 120)(15, 111, 30, 126)(16, 112, 23, 119)(18, 114, 41, 137)(19, 115, 43, 139)(20, 116, 25, 121)(22, 118, 48, 144)(28, 124, 54, 150)(29, 125, 56, 152)(31, 127, 45, 141)(33, 129, 63, 159)(34, 130, 66, 162)(35, 131, 40, 136)(36, 132, 60, 156)(37, 133, 58, 154)(38, 134, 51, 147)(39, 135, 68, 164)(42, 138, 77, 173)(44, 140, 81, 177)(46, 142, 83, 179)(47, 143, 52, 148)(49, 145, 79, 175)(50, 146, 87, 183)(53, 149, 89, 185)(55, 151, 92, 188)(57, 153, 69, 165)(59, 155, 95, 191)(61, 157, 72, 168)(62, 158, 91, 187)(64, 160, 96, 192)(65, 161, 86, 182)(67, 163, 88, 184)(70, 166, 75, 171)(71, 167, 90, 186)(73, 169, 80, 176)(74, 170, 85, 181)(76, 172, 84, 180)(78, 174, 93, 189)(82, 178, 94, 190)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 211, 307, 204, 300)(200, 296, 216, 312, 218, 314)(202, 298, 221, 317, 214, 310)(203, 299, 223, 319, 217, 313)(205, 301, 226, 322, 210, 306)(207, 303, 213, 309, 229, 325)(209, 305, 231, 327, 232, 328)(212, 308, 238, 334, 236, 332)(215, 311, 242, 338, 220, 316)(219, 315, 245, 341, 230, 326)(222, 318, 251, 347, 249, 345)(224, 320, 254, 350, 253, 349)(225, 321, 237, 333, 257, 353)(227, 323, 261, 357, 259, 355)(228, 324, 248, 344, 262, 358)(233, 329, 268, 364, 266, 362)(234, 330, 260, 356, 271, 367)(235, 331, 272, 368, 244, 340)(239, 335, 270, 366, 276, 372)(240, 336, 277, 373, 264, 360)(241, 337, 250, 346, 278, 374)(243, 339, 273, 369, 280, 376)(246, 342, 256, 352, 283, 379)(247, 343, 281, 377, 255, 351)(252, 348, 285, 381, 288, 384)(258, 354, 286, 382, 267, 363)(263, 359, 287, 383, 284, 380)(265, 361, 279, 375, 274, 370)(269, 365, 282, 378, 275, 371)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 218)(12, 225)(13, 195)(14, 197)(15, 228)(16, 230)(17, 216)(18, 234)(19, 236)(20, 198)(21, 208)(22, 241)(23, 199)(24, 201)(25, 244)(26, 232)(27, 206)(28, 247)(29, 249)(30, 202)(31, 253)(32, 203)(33, 256)(34, 259)(35, 205)(36, 263)(37, 264)(38, 265)(39, 266)(40, 267)(41, 209)(42, 270)(43, 223)(44, 274)(45, 211)(46, 276)(47, 212)(48, 213)(49, 268)(50, 280)(51, 215)(52, 282)(53, 283)(54, 219)(55, 285)(56, 229)(57, 286)(58, 221)(59, 288)(60, 222)(61, 250)(62, 281)(63, 224)(64, 287)(65, 277)(66, 231)(67, 279)(68, 226)(69, 248)(70, 227)(71, 239)(72, 237)(73, 238)(74, 278)(75, 251)(76, 275)(77, 233)(78, 284)(79, 240)(80, 243)(81, 235)(82, 261)(83, 272)(84, 271)(85, 260)(86, 254)(87, 245)(88, 258)(89, 242)(90, 252)(91, 257)(92, 246)(93, 269)(94, 273)(95, 262)(96, 255)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1791
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1784 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1485>$ (small group id <192, 1485>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y1 * Y3^-1)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^2 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 22, 118)(9, 105, 28, 124)(12, 108, 31, 127)(13, 109, 25, 121)(14, 110, 24, 120)(15, 111, 26, 122)(16, 112, 30, 126)(18, 114, 32, 128)(19, 115, 27, 123)(20, 116, 23, 119)(21, 117, 29, 125)(33, 129, 65, 161)(34, 130, 66, 162)(35, 131, 62, 158)(36, 132, 56, 152)(37, 133, 68, 164)(38, 134, 64, 160)(39, 135, 67, 163)(40, 136, 52, 148)(41, 137, 58, 154)(42, 138, 57, 153)(43, 139, 73, 169)(44, 140, 70, 166)(45, 141, 75, 171)(46, 142, 51, 147)(47, 143, 74, 170)(48, 144, 54, 150)(49, 145, 77, 173)(50, 146, 78, 174)(53, 149, 80, 176)(55, 151, 79, 175)(59, 155, 85, 181)(60, 156, 82, 178)(61, 157, 87, 183)(63, 159, 86, 182)(69, 165, 83, 179)(71, 167, 81, 177)(72, 168, 88, 184)(76, 172, 84, 180)(89, 185, 96, 192)(90, 186, 94, 190)(91, 187, 95, 191)(92, 188, 93, 189)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 217, 313, 219, 315)(202, 298, 223, 319, 224, 320)(203, 299, 225, 321, 226, 322)(204, 300, 227, 323, 229, 325)(205, 301, 230, 326, 231, 327)(207, 303, 228, 324, 233, 329)(209, 305, 235, 331, 236, 332)(210, 306, 237, 333, 238, 334)(211, 307, 239, 335, 240, 336)(214, 310, 241, 337, 242, 338)(215, 311, 243, 339, 245, 341)(216, 312, 246, 342, 247, 343)(218, 314, 244, 340, 249, 345)(220, 316, 251, 347, 252, 348)(221, 317, 253, 349, 254, 350)(222, 318, 255, 351, 256, 352)(232, 328, 262, 358, 263, 359)(234, 330, 264, 360, 257, 353)(248, 344, 274, 370, 275, 371)(250, 346, 276, 372, 269, 365)(258, 354, 281, 377, 268, 364)(259, 355, 282, 378, 267, 363)(260, 356, 283, 379, 266, 362)(261, 357, 284, 380, 265, 361)(270, 366, 285, 381, 280, 376)(271, 367, 286, 382, 279, 375)(272, 368, 287, 383, 278, 374)(273, 369, 288, 384, 277, 373)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 215)(8, 218)(9, 221)(10, 194)(11, 217)(12, 228)(13, 195)(14, 232)(15, 198)(16, 234)(17, 219)(18, 233)(19, 197)(20, 214)(21, 220)(22, 206)(23, 244)(24, 199)(25, 248)(26, 202)(27, 250)(28, 208)(29, 249)(30, 201)(31, 203)(32, 209)(33, 256)(34, 259)(35, 252)(36, 205)(37, 261)(38, 257)(39, 258)(40, 212)(41, 211)(42, 213)(43, 266)(44, 246)(45, 268)(46, 241)(47, 265)(48, 262)(49, 240)(50, 271)(51, 236)(52, 216)(53, 273)(54, 269)(55, 270)(56, 223)(57, 222)(58, 224)(59, 278)(60, 230)(61, 280)(62, 225)(63, 277)(64, 274)(65, 227)(66, 229)(67, 275)(68, 226)(69, 231)(70, 238)(71, 272)(72, 279)(73, 237)(74, 276)(75, 235)(76, 239)(77, 243)(78, 245)(79, 263)(80, 242)(81, 247)(82, 254)(83, 260)(84, 267)(85, 253)(86, 264)(87, 251)(88, 255)(89, 287)(90, 285)(91, 288)(92, 286)(93, 283)(94, 281)(95, 284)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1792
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1785 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1480>$ (small group id <192, 1480>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, Y3^4, (Y2 * Y3)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y2 * Y1^-1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y3, Y1^-2 * Y3^2 * Y1^-2, (Y3^-1 * Y2 * Y1^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 24, 120, 16, 112, 33, 129, 20, 116, 5, 101)(3, 99, 11, 107, 37, 133, 69, 165, 40, 136, 66, 162, 43, 139, 13, 109)(4, 100, 15, 111, 46, 142, 23, 119, 6, 102, 22, 118, 48, 144, 17, 113)(8, 104, 28, 124, 62, 158, 38, 134, 64, 160, 82, 178, 65, 161, 30, 126)(9, 105, 32, 128, 67, 163, 36, 132, 10, 106, 35, 131, 68, 164, 34, 130)(12, 108, 39, 135, 57, 153, 31, 127, 14, 110, 45, 141, 55, 151, 29, 125)(18, 114, 42, 138, 74, 170, 79, 175, 53, 149, 44, 140, 76, 172, 49, 145)(19, 115, 50, 146, 77, 173, 47, 143, 21, 117, 52, 148, 73, 169, 41, 137)(25, 121, 54, 150, 80, 176, 63, 159, 51, 147, 78, 174, 81, 177, 56, 152)(26, 122, 58, 154, 83, 179, 61, 157, 27, 123, 60, 156, 84, 180, 59, 155)(70, 166, 89, 185, 96, 192, 88, 184, 75, 171, 92, 188, 93, 189, 85, 181)(71, 167, 86, 182, 94, 190, 91, 187, 72, 168, 87, 183, 95, 191, 90, 186)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 217, 313)(201, 297, 223, 319)(202, 298, 221, 317)(203, 299, 227, 323)(205, 301, 233, 329)(207, 303, 236, 332)(208, 304, 232, 328)(209, 305, 222, 318)(211, 307, 237, 333)(212, 308, 243, 339)(213, 309, 231, 327)(214, 310, 234, 330)(215, 311, 230, 326)(216, 312, 245, 341)(218, 314, 249, 345)(219, 315, 247, 343)(220, 316, 252, 348)(224, 320, 258, 354)(225, 321, 256, 352)(226, 322, 248, 344)(228, 324, 255, 351)(229, 325, 262, 358)(235, 331, 267, 363)(238, 334, 263, 359)(239, 335, 261, 357)(240, 336, 264, 360)(241, 337, 253, 349)(242, 338, 246, 342)(244, 340, 270, 366)(250, 346, 274, 370)(251, 347, 271, 367)(254, 350, 277, 373)(257, 353, 280, 376)(259, 355, 278, 374)(260, 356, 279, 375)(265, 361, 283, 379)(266, 362, 281, 377)(268, 364, 284, 380)(269, 365, 282, 378)(272, 368, 285, 381)(273, 369, 288, 384)(275, 371, 286, 382)(276, 372, 287, 383)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 218)(8, 221)(9, 225)(10, 194)(11, 230)(12, 232)(13, 234)(14, 195)(15, 239)(16, 198)(17, 224)(18, 231)(19, 216)(20, 219)(21, 197)(22, 233)(23, 227)(24, 213)(25, 247)(26, 212)(27, 199)(28, 255)(29, 256)(30, 203)(31, 200)(32, 215)(33, 202)(34, 250)(35, 209)(36, 252)(37, 263)(38, 258)(39, 245)(40, 206)(41, 207)(42, 261)(43, 264)(44, 205)(45, 210)(46, 262)(47, 214)(48, 267)(49, 270)(50, 251)(51, 249)(52, 253)(53, 237)(54, 241)(55, 243)(56, 220)(57, 217)(58, 228)(59, 244)(60, 226)(61, 242)(62, 278)(63, 274)(64, 223)(65, 279)(66, 222)(67, 277)(68, 280)(69, 236)(70, 240)(71, 235)(72, 229)(73, 284)(74, 282)(75, 238)(76, 283)(77, 281)(78, 271)(79, 246)(80, 286)(81, 287)(82, 248)(83, 285)(84, 288)(85, 260)(86, 257)(87, 254)(88, 259)(89, 265)(90, 268)(91, 266)(92, 269)(93, 276)(94, 273)(95, 272)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1777
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1786 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1480>$ (small group id <192, 1480>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3^-1 * Y1^-1)^3, (Y3^-1 * Y1)^3, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * R * Y2 * R, Y1^-1 * Y3^2 * Y1^-1 * Y3^-2, Y1^8, Y2 * Y1^-2 * R * Y2 * R * Y1^-2, Y2 * Y1 * Y3^-1 * Y1^3 * Y2 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 25, 121, 63, 159, 60, 156, 20, 116, 5, 101)(3, 99, 11, 107, 39, 135, 83, 179, 92, 188, 77, 173, 47, 143, 13, 109)(4, 100, 15, 111, 28, 124, 73, 169, 62, 158, 76, 172, 54, 150, 17, 113)(6, 102, 22, 118, 27, 123, 71, 167, 53, 149, 80, 176, 59, 155, 23, 119)(8, 104, 29, 125, 75, 171, 46, 142, 88, 184, 42, 138, 82, 178, 31, 127)(9, 105, 33, 129, 66, 162, 45, 141, 86, 182, 51, 147, 21, 117, 35, 131)(10, 106, 36, 132, 65, 161, 40, 136, 85, 181, 57, 153, 19, 115, 37, 133)(12, 108, 30, 126, 68, 164, 93, 189, 91, 187, 96, 192, 90, 186, 44, 140)(14, 110, 49, 145, 87, 183, 95, 191, 89, 185, 94, 190, 70, 166, 32, 128)(16, 112, 52, 148, 74, 170, 38, 134, 24, 120, 61, 157, 72, 168, 34, 130)(18, 114, 55, 151, 79, 175, 48, 144, 64, 160, 41, 137, 84, 180, 56, 152)(26, 122, 67, 163, 50, 146, 81, 177, 58, 154, 78, 174, 43, 139, 69, 165)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 218, 314)(201, 297, 224, 320)(202, 298, 222, 318)(203, 299, 232, 328)(205, 301, 237, 333)(207, 303, 234, 330)(208, 304, 242, 338)(209, 305, 240, 336)(211, 307, 241, 337)(212, 308, 250, 346)(213, 309, 236, 332)(214, 310, 238, 334)(215, 311, 233, 329)(216, 312, 235, 331)(217, 313, 256, 352)(219, 315, 262, 358)(220, 316, 260, 356)(221, 317, 268, 364)(223, 319, 272, 368)(225, 321, 270, 366)(226, 322, 276, 372)(227, 323, 275, 371)(228, 324, 273, 369)(229, 325, 269, 365)(230, 326, 271, 367)(231, 327, 266, 362)(239, 335, 264, 360)(243, 339, 259, 355)(244, 340, 267, 363)(245, 341, 283, 379)(246, 342, 282, 378)(247, 343, 263, 359)(248, 344, 265, 361)(249, 345, 261, 357)(251, 347, 279, 375)(252, 348, 280, 376)(253, 349, 274, 370)(254, 350, 281, 377)(255, 351, 284, 380)(257, 353, 286, 382)(258, 354, 285, 381)(277, 373, 288, 384)(278, 374, 287, 383)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 219)(8, 222)(9, 226)(10, 194)(11, 233)(12, 235)(13, 238)(14, 195)(15, 243)(16, 245)(17, 228)(18, 236)(19, 244)(20, 251)(21, 197)(22, 237)(23, 232)(24, 198)(25, 257)(26, 260)(27, 264)(28, 199)(29, 269)(30, 271)(31, 273)(32, 200)(33, 215)(34, 277)(35, 265)(36, 272)(37, 268)(38, 202)(39, 279)(40, 207)(41, 270)(42, 203)(43, 281)(44, 274)(45, 209)(46, 261)(47, 262)(48, 205)(49, 210)(50, 206)(51, 263)(52, 258)(53, 255)(54, 212)(55, 259)(56, 275)(57, 214)(58, 282)(59, 266)(60, 278)(61, 213)(62, 216)(63, 254)(64, 285)(65, 253)(66, 217)(67, 234)(68, 231)(69, 248)(70, 218)(71, 229)(72, 246)(73, 249)(74, 220)(75, 241)(76, 225)(77, 247)(78, 221)(79, 287)(80, 227)(81, 240)(82, 286)(83, 223)(84, 224)(85, 252)(86, 230)(87, 250)(88, 288)(89, 284)(90, 239)(91, 242)(92, 283)(93, 267)(94, 256)(95, 280)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1778
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1787 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^3, Y1^8, Y3 * Y1^4 * Y3 * Y1^-4 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 15, 111, 31, 127, 30, 126, 14, 110, 5, 101)(3, 99, 7, 103, 16, 112, 32, 128, 56, 152, 46, 142, 24, 120, 10, 106)(4, 100, 11, 107, 25, 121, 47, 143, 57, 153, 51, 147, 27, 123, 12, 108)(8, 104, 19, 115, 39, 135, 67, 163, 55, 151, 70, 166, 40, 136, 20, 116)(9, 105, 21, 117, 41, 137, 71, 167, 82, 178, 75, 171, 43, 139, 22, 118)(13, 109, 28, 124, 52, 148, 60, 156, 33, 129, 59, 155, 49, 145, 26, 122)(17, 113, 35, 131, 63, 159, 53, 149, 29, 125, 54, 150, 64, 160, 36, 132)(18, 114, 37, 133, 65, 161, 89, 185, 79, 175, 92, 188, 66, 162, 38, 134)(23, 119, 44, 140, 76, 172, 84, 180, 58, 154, 83, 179, 73, 169, 42, 138)(34, 130, 61, 157, 85, 181, 77, 173, 45, 141, 78, 174, 86, 182, 62, 158)(48, 144, 80, 176, 88, 184, 68, 164, 50, 146, 81, 177, 87, 183, 69, 165)(72, 168, 93, 189, 96, 192, 90, 186, 74, 170, 94, 190, 95, 191, 91, 187)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 201, 297)(197, 293, 202, 298)(198, 294, 208, 304)(200, 296, 210, 306)(203, 299, 213, 309)(204, 300, 214, 310)(205, 301, 215, 311)(206, 302, 216, 312)(207, 303, 224, 320)(209, 305, 226, 322)(211, 307, 229, 325)(212, 308, 230, 326)(217, 313, 233, 329)(218, 314, 234, 330)(219, 315, 235, 331)(220, 316, 236, 332)(221, 317, 237, 333)(222, 318, 238, 334)(223, 319, 248, 344)(225, 321, 250, 346)(227, 323, 253, 349)(228, 324, 254, 350)(231, 327, 257, 353)(232, 328, 258, 354)(239, 335, 263, 359)(240, 336, 264, 360)(241, 337, 265, 361)(242, 338, 266, 362)(243, 339, 267, 363)(244, 340, 268, 364)(245, 341, 269, 365)(246, 342, 270, 366)(247, 343, 271, 367)(249, 345, 274, 370)(251, 347, 275, 371)(252, 348, 276, 372)(255, 351, 277, 373)(256, 352, 278, 374)(259, 355, 281, 377)(260, 356, 282, 378)(261, 357, 283, 379)(262, 358, 284, 380)(272, 368, 285, 381)(273, 369, 286, 382)(279, 375, 287, 383)(280, 376, 288, 384)
	L = (1, 196)(2, 200)(3, 201)(4, 193)(5, 205)(6, 209)(7, 210)(8, 194)(9, 195)(10, 215)(11, 218)(12, 211)(13, 197)(14, 221)(15, 225)(16, 226)(17, 198)(18, 199)(19, 204)(20, 227)(21, 234)(22, 229)(23, 202)(24, 237)(25, 240)(26, 203)(27, 242)(28, 245)(29, 206)(30, 247)(31, 249)(32, 250)(33, 207)(34, 208)(35, 212)(36, 251)(37, 214)(38, 253)(39, 260)(40, 261)(41, 264)(42, 213)(43, 266)(44, 269)(45, 216)(46, 271)(47, 262)(48, 217)(49, 272)(50, 219)(51, 252)(52, 273)(53, 220)(54, 259)(55, 222)(56, 274)(57, 223)(58, 224)(59, 228)(60, 243)(61, 230)(62, 275)(63, 279)(64, 280)(65, 282)(66, 283)(67, 246)(68, 231)(69, 232)(70, 239)(71, 284)(72, 233)(73, 285)(74, 235)(75, 276)(76, 286)(77, 236)(78, 281)(79, 238)(80, 241)(81, 244)(82, 248)(83, 254)(84, 267)(85, 287)(86, 288)(87, 255)(88, 256)(89, 270)(90, 257)(91, 258)(92, 263)(93, 265)(94, 268)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1781
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1788 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^3, Y1^8, (Y3 * Y1^-4)^2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 15, 111, 31, 127, 30, 126, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 41, 137, 56, 152, 32, 128, 16, 112, 7, 103)(4, 100, 11, 107, 25, 121, 47, 143, 57, 153, 51, 147, 27, 123, 12, 108)(8, 104, 19, 115, 39, 135, 67, 163, 55, 151, 70, 166, 40, 136, 20, 116)(10, 106, 23, 119, 45, 141, 76, 172, 82, 178, 79, 175, 46, 142, 24, 120)(13, 109, 28, 124, 52, 148, 60, 156, 33, 129, 59, 155, 49, 145, 26, 122)(17, 113, 35, 131, 63, 159, 53, 149, 29, 125, 54, 150, 64, 160, 36, 132)(18, 114, 37, 133, 65, 161, 89, 185, 71, 167, 92, 188, 66, 162, 38, 134)(22, 118, 43, 139, 74, 170, 84, 180, 58, 154, 83, 179, 75, 171, 44, 140)(34, 130, 61, 157, 85, 181, 73, 169, 42, 138, 72, 168, 86, 182, 62, 158)(48, 144, 80, 176, 88, 184, 68, 164, 50, 146, 81, 177, 87, 183, 69, 165)(77, 173, 91, 187, 95, 191, 93, 189, 78, 174, 90, 186, 96, 192, 94, 190)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 201, 297)(198, 294, 208, 304)(200, 296, 210, 306)(203, 299, 216, 312)(204, 300, 215, 311)(205, 301, 214, 310)(206, 302, 213, 309)(207, 303, 224, 320)(209, 305, 226, 322)(211, 307, 230, 326)(212, 308, 229, 325)(217, 313, 238, 334)(218, 314, 235, 331)(219, 315, 237, 333)(220, 316, 236, 332)(221, 317, 234, 330)(222, 318, 233, 329)(223, 319, 248, 344)(225, 321, 250, 346)(227, 323, 254, 350)(228, 324, 253, 349)(231, 327, 258, 354)(232, 328, 257, 353)(239, 335, 271, 367)(240, 336, 270, 366)(241, 337, 266, 362)(242, 338, 269, 365)(243, 339, 268, 364)(244, 340, 267, 363)(245, 341, 264, 360)(246, 342, 265, 361)(247, 343, 263, 359)(249, 345, 274, 370)(251, 347, 276, 372)(252, 348, 275, 371)(255, 351, 278, 374)(256, 352, 277, 373)(259, 355, 284, 380)(260, 356, 283, 379)(261, 357, 282, 378)(262, 358, 281, 377)(272, 368, 285, 381)(273, 369, 286, 382)(279, 375, 288, 384)(280, 376, 287, 383)
	L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 205)(6, 209)(7, 210)(8, 194)(9, 214)(10, 195)(11, 218)(12, 211)(13, 197)(14, 221)(15, 225)(16, 226)(17, 198)(18, 199)(19, 204)(20, 227)(21, 234)(22, 201)(23, 230)(24, 235)(25, 240)(26, 203)(27, 242)(28, 245)(29, 206)(30, 247)(31, 249)(32, 250)(33, 207)(34, 208)(35, 212)(36, 251)(37, 254)(38, 215)(39, 260)(40, 261)(41, 263)(42, 213)(43, 216)(44, 264)(45, 269)(46, 270)(47, 262)(48, 217)(49, 272)(50, 219)(51, 252)(52, 273)(53, 220)(54, 259)(55, 222)(56, 274)(57, 223)(58, 224)(59, 228)(60, 243)(61, 276)(62, 229)(63, 279)(64, 280)(65, 282)(66, 283)(67, 246)(68, 231)(69, 232)(70, 239)(71, 233)(72, 236)(73, 284)(74, 285)(75, 286)(76, 275)(77, 237)(78, 238)(79, 281)(80, 241)(81, 244)(82, 248)(83, 268)(84, 253)(85, 287)(86, 288)(87, 255)(88, 256)(89, 271)(90, 257)(91, 258)(92, 265)(93, 266)(94, 267)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1782
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1789 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y2 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1^-1)^3, Y1^8, (Y3 * Y1^-4)^2, (Y2 * Y1^2 * Y3 * Y1^-1)^2, (Y2 * Y1^-4)^2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 17, 113, 37, 133, 36, 132, 16, 112, 5, 101)(3, 99, 9, 105, 25, 121, 49, 145, 68, 164, 57, 153, 29, 125, 11, 107)(4, 100, 12, 108, 30, 126, 58, 154, 69, 165, 59, 155, 31, 127, 13, 109)(7, 103, 20, 116, 45, 141, 79, 175, 66, 162, 84, 180, 46, 142, 22, 118)(8, 104, 23, 119, 47, 143, 85, 181, 67, 163, 86, 182, 48, 144, 24, 120)(10, 106, 21, 117, 41, 137, 71, 167, 92, 188, 89, 185, 54, 150, 28, 124)(14, 110, 32, 128, 60, 156, 72, 168, 38, 134, 70, 166, 53, 149, 27, 123)(15, 111, 33, 129, 63, 159, 74, 170, 39, 135, 73, 169, 52, 148, 26, 122)(18, 114, 40, 136, 75, 171, 62, 158, 34, 130, 64, 160, 76, 172, 42, 138)(19, 115, 43, 139, 77, 173, 61, 157, 35, 131, 65, 161, 78, 174, 44, 140)(50, 146, 87, 183, 95, 191, 80, 176, 55, 151, 90, 186, 93, 189, 82, 178)(51, 147, 88, 184, 96, 192, 81, 177, 56, 152, 91, 187, 94, 190, 83, 179)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 206, 302)(198, 294, 210, 306)(200, 296, 213, 309)(201, 297, 218, 314)(203, 299, 215, 311)(204, 300, 219, 315)(205, 301, 212, 308)(207, 303, 220, 316)(208, 304, 226, 322)(209, 305, 230, 326)(211, 307, 233, 329)(214, 310, 235, 331)(216, 312, 232, 328)(217, 313, 242, 338)(221, 317, 247, 343)(222, 318, 243, 339)(223, 319, 248, 344)(224, 320, 253, 349)(225, 321, 254, 350)(227, 323, 246, 342)(228, 324, 258, 354)(229, 325, 260, 356)(231, 327, 263, 359)(234, 330, 265, 361)(236, 332, 262, 358)(237, 333, 272, 368)(238, 334, 274, 370)(239, 335, 273, 369)(240, 336, 275, 371)(241, 337, 278, 374)(244, 340, 280, 376)(245, 341, 279, 375)(249, 345, 266, 362)(250, 346, 276, 372)(251, 347, 264, 360)(252, 348, 282, 378)(255, 351, 283, 379)(256, 352, 277, 373)(257, 353, 271, 367)(259, 355, 281, 377)(261, 357, 284, 380)(267, 363, 285, 381)(268, 364, 287, 383)(269, 365, 286, 382)(270, 366, 288, 384)
	L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 207)(6, 211)(7, 213)(8, 194)(9, 219)(10, 195)(11, 212)(12, 218)(13, 215)(14, 220)(15, 197)(16, 227)(17, 231)(18, 233)(19, 198)(20, 203)(21, 199)(22, 232)(23, 205)(24, 235)(25, 243)(26, 204)(27, 201)(28, 206)(29, 248)(30, 242)(31, 247)(32, 254)(33, 253)(34, 246)(35, 208)(36, 259)(37, 261)(38, 263)(39, 209)(40, 214)(41, 210)(42, 262)(43, 216)(44, 265)(45, 273)(46, 275)(47, 272)(48, 274)(49, 276)(50, 222)(51, 217)(52, 279)(53, 280)(54, 226)(55, 223)(56, 221)(57, 264)(58, 278)(59, 266)(60, 283)(61, 225)(62, 224)(63, 282)(64, 271)(65, 277)(66, 281)(67, 228)(68, 284)(69, 229)(70, 234)(71, 230)(72, 249)(73, 236)(74, 251)(75, 286)(76, 288)(77, 285)(78, 287)(79, 256)(80, 239)(81, 237)(82, 240)(83, 238)(84, 241)(85, 257)(86, 250)(87, 244)(88, 245)(89, 258)(90, 255)(91, 252)(92, 260)(93, 269)(94, 267)(95, 270)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1779
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1790 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^3, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y3, Y1^8, (Y1^-1 * Y2 * Y1^-3)^2, Y1^-1 * Y3 * Y1^4 * Y3 * Y1^-3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 6, 102, 17, 113, 37, 133, 36, 132, 16, 112, 5, 101)(3, 99, 9, 105, 25, 121, 49, 145, 68, 164, 57, 153, 29, 125, 11, 107)(4, 100, 12, 108, 30, 126, 58, 154, 69, 165, 59, 155, 31, 127, 13, 109)(7, 103, 20, 116, 45, 141, 79, 175, 66, 162, 84, 180, 46, 142, 22, 118)(8, 104, 23, 119, 47, 143, 85, 181, 67, 163, 86, 182, 48, 144, 24, 120)(10, 106, 26, 122, 52, 148, 89, 185, 92, 188, 71, 167, 41, 137, 21, 117)(14, 110, 28, 124, 54, 150, 72, 168, 38, 134, 70, 166, 62, 158, 32, 128)(15, 111, 33, 129, 63, 159, 74, 170, 39, 135, 73, 169, 53, 149, 27, 123)(18, 114, 40, 136, 75, 171, 64, 160, 34, 130, 61, 157, 76, 172, 42, 138)(19, 115, 43, 139, 77, 173, 60, 156, 35, 131, 65, 161, 78, 174, 44, 140)(50, 146, 87, 183, 95, 191, 80, 176, 55, 151, 91, 187, 93, 189, 82, 178)(51, 147, 83, 179, 94, 190, 90, 186, 56, 152, 81, 177, 96, 192, 88, 184)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 206, 302)(198, 294, 210, 306)(200, 296, 213, 309)(201, 297, 215, 311)(203, 299, 219, 315)(204, 300, 220, 316)(205, 301, 214, 310)(207, 303, 218, 314)(208, 304, 226, 322)(209, 305, 230, 326)(211, 307, 233, 329)(212, 308, 235, 331)(216, 312, 234, 330)(217, 313, 242, 338)(221, 317, 247, 343)(222, 318, 248, 344)(223, 319, 243, 339)(224, 320, 252, 348)(225, 321, 253, 349)(227, 323, 244, 340)(228, 324, 258, 354)(229, 325, 260, 356)(231, 327, 263, 359)(232, 328, 265, 361)(236, 332, 264, 360)(237, 333, 272, 368)(238, 334, 274, 370)(239, 335, 275, 371)(240, 336, 273, 369)(241, 337, 266, 362)(245, 341, 282, 378)(246, 342, 283, 379)(249, 345, 278, 374)(250, 346, 271, 367)(251, 347, 262, 358)(254, 350, 279, 375)(255, 351, 280, 376)(256, 352, 277, 373)(257, 353, 276, 372)(259, 355, 281, 377)(261, 357, 284, 380)(267, 363, 285, 381)(268, 364, 287, 383)(269, 365, 288, 384)(270, 366, 286, 382)
	L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 207)(6, 211)(7, 213)(8, 194)(9, 214)(10, 195)(11, 220)(12, 219)(13, 215)(14, 218)(15, 197)(16, 227)(17, 231)(18, 233)(19, 198)(20, 234)(21, 199)(22, 201)(23, 205)(24, 235)(25, 243)(26, 206)(27, 204)(28, 203)(29, 248)(30, 247)(31, 242)(32, 253)(33, 252)(34, 244)(35, 208)(36, 259)(37, 261)(38, 263)(39, 209)(40, 264)(41, 210)(42, 212)(43, 216)(44, 265)(45, 273)(46, 275)(47, 274)(48, 272)(49, 262)(50, 223)(51, 217)(52, 226)(53, 283)(54, 282)(55, 222)(56, 221)(57, 271)(58, 278)(59, 266)(60, 225)(61, 224)(62, 280)(63, 279)(64, 276)(65, 277)(66, 281)(67, 228)(68, 284)(69, 229)(70, 241)(71, 230)(72, 232)(73, 236)(74, 251)(75, 286)(76, 288)(77, 287)(78, 285)(79, 249)(80, 240)(81, 237)(82, 239)(83, 238)(84, 256)(85, 257)(86, 250)(87, 255)(88, 254)(89, 258)(90, 246)(91, 245)(92, 260)(93, 270)(94, 267)(95, 269)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1780
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1791 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y3, (Y3^-2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1^-1 * Y3 * Y2 * Y1^-1, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, (Y1^-1 * Y3^2)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y3^-1 * Y2 * Y1^2 * Y3^-1 * Y2 * Y1^-2, Y1^8, Y3 * Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1 * Y2 * Y1^3 * Y2, Y1^3 * Y2 * Y3 * Y1 * Y2 * Y3, Y2 * Y3 * Y1^-3 * Y2 * Y3 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 25, 121, 63, 159, 61, 157, 20, 116, 5, 101)(3, 99, 11, 107, 39, 135, 81, 177, 92, 188, 90, 186, 45, 141, 13, 109)(4, 100, 15, 111, 49, 145, 85, 181, 62, 158, 73, 169, 28, 124, 17, 113)(6, 102, 22, 118, 60, 156, 91, 187, 53, 149, 72, 168, 27, 123, 23, 119)(8, 104, 29, 125, 75, 171, 44, 140, 87, 183, 50, 146, 80, 176, 31, 127)(9, 105, 33, 129, 21, 117, 56, 152, 86, 182, 95, 191, 66, 162, 35, 131)(10, 106, 36, 132, 19, 115, 51, 147, 84, 180, 55, 151, 65, 161, 37, 133)(12, 108, 41, 137, 68, 164, 57, 153, 78, 174, 30, 126, 76, 172, 43, 139)(14, 110, 47, 143, 89, 185, 96, 192, 88, 184, 94, 190, 70, 166, 32, 128)(16, 112, 52, 148, 74, 170, 34, 130, 24, 120, 58, 154, 71, 167, 38, 134)(18, 114, 40, 136, 82, 178, 46, 142, 64, 160, 93, 189, 77, 173, 54, 150)(26, 122, 67, 163, 42, 138, 79, 175, 59, 155, 83, 179, 48, 144, 69, 165)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 218, 314)(201, 297, 224, 320)(202, 298, 222, 318)(203, 299, 229, 325)(205, 301, 227, 323)(207, 303, 242, 338)(208, 304, 240, 336)(209, 305, 246, 342)(211, 307, 239, 335)(212, 308, 251, 347)(213, 309, 249, 345)(214, 310, 236, 332)(215, 311, 232, 328)(216, 312, 234, 330)(217, 313, 256, 352)(219, 315, 262, 358)(220, 316, 260, 356)(221, 317, 265, 361)(223, 319, 264, 360)(225, 321, 275, 371)(226, 322, 274, 370)(228, 324, 271, 367)(230, 326, 269, 365)(231, 327, 263, 359)(233, 329, 276, 372)(235, 331, 258, 354)(237, 333, 266, 362)(238, 334, 277, 373)(241, 337, 268, 364)(243, 339, 282, 378)(244, 340, 267, 363)(245, 341, 270, 366)(247, 343, 261, 357)(248, 344, 273, 369)(250, 346, 272, 368)(252, 348, 281, 377)(253, 349, 279, 375)(254, 350, 280, 376)(255, 351, 284, 380)(257, 353, 286, 382)(259, 355, 287, 383)(278, 374, 288, 384)(283, 379, 285, 381)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 219)(8, 222)(9, 226)(10, 194)(11, 232)(12, 234)(13, 236)(14, 195)(15, 225)(16, 245)(17, 247)(18, 249)(19, 250)(20, 252)(21, 197)(22, 227)(23, 229)(24, 198)(25, 257)(26, 260)(27, 263)(28, 199)(29, 203)(30, 269)(31, 271)(32, 200)(33, 215)(34, 276)(35, 277)(36, 264)(37, 265)(38, 202)(39, 262)(40, 275)(41, 274)(42, 280)(43, 272)(44, 261)(45, 281)(46, 205)(47, 210)(48, 206)(49, 212)(50, 282)(51, 207)(52, 213)(53, 255)(54, 273)(55, 214)(56, 209)(57, 267)(58, 258)(59, 268)(60, 266)(61, 278)(62, 216)(63, 254)(64, 235)(65, 244)(66, 217)(67, 221)(68, 237)(69, 246)(70, 218)(71, 241)(72, 248)(73, 287)(74, 220)(75, 286)(76, 231)(77, 288)(78, 240)(79, 238)(80, 239)(81, 223)(82, 224)(83, 242)(84, 253)(85, 228)(86, 230)(87, 233)(88, 284)(89, 251)(90, 285)(91, 243)(92, 270)(93, 259)(94, 256)(95, 283)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1783
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1792 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1485>$ (small group id <192, 1485>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y2 * Y3)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y3, (Y1^-1 * R * Y2)^2, Y1^-1 * Y3^-2 * Y1^-3, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y1 * Y3^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 24, 120, 16, 112, 33, 129, 20, 116, 5, 101)(3, 99, 11, 107, 25, 121, 18, 114, 30, 126, 8, 104, 28, 124, 13, 109)(4, 100, 15, 111, 43, 139, 23, 119, 6, 102, 22, 118, 46, 142, 17, 113)(9, 105, 32, 128, 59, 155, 36, 132, 10, 106, 35, 131, 60, 156, 34, 130)(12, 108, 37, 133, 61, 157, 42, 138, 14, 110, 41, 137, 64, 160, 38, 134)(19, 115, 47, 143, 69, 165, 44, 140, 21, 117, 48, 144, 70, 166, 45, 141)(26, 122, 51, 147, 75, 171, 54, 150, 27, 123, 53, 149, 76, 172, 52, 148)(29, 125, 55, 151, 77, 173, 58, 154, 31, 127, 57, 153, 78, 174, 56, 152)(39, 135, 65, 161, 83, 179, 62, 158, 40, 136, 66, 162, 84, 180, 63, 159)(49, 145, 71, 167, 87, 183, 74, 170, 50, 146, 73, 169, 88, 184, 72, 168)(67, 163, 85, 181, 90, 186, 80, 176, 68, 164, 86, 182, 89, 185, 79, 175)(81, 177, 93, 189, 96, 192, 91, 187, 82, 178, 94, 190, 95, 191, 92, 188)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 217, 313)(201, 297, 223, 319)(202, 298, 221, 317)(203, 299, 225, 321)(205, 301, 216, 312)(207, 303, 229, 325)(208, 304, 222, 318)(209, 305, 230, 326)(211, 307, 231, 327)(212, 308, 220, 316)(213, 309, 232, 328)(214, 310, 233, 329)(215, 311, 234, 330)(218, 314, 242, 338)(219, 315, 241, 337)(224, 320, 247, 343)(226, 322, 248, 344)(227, 323, 249, 345)(228, 324, 250, 346)(235, 331, 256, 352)(236, 332, 255, 351)(237, 333, 254, 350)(238, 334, 253, 349)(239, 335, 258, 354)(240, 336, 257, 353)(243, 339, 263, 359)(244, 340, 264, 360)(245, 341, 265, 361)(246, 342, 266, 362)(251, 347, 270, 366)(252, 348, 269, 365)(259, 355, 273, 369)(260, 356, 274, 370)(261, 357, 275, 371)(262, 358, 276, 372)(267, 363, 280, 376)(268, 364, 279, 375)(271, 367, 283, 379)(272, 368, 284, 380)(277, 373, 286, 382)(278, 374, 285, 381)(281, 377, 287, 383)(282, 378, 288, 384)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 218)(8, 221)(9, 225)(10, 194)(11, 223)(12, 222)(13, 231)(14, 195)(15, 236)(16, 198)(17, 224)(18, 232)(19, 216)(20, 219)(21, 197)(22, 237)(23, 227)(24, 213)(25, 241)(26, 212)(27, 199)(28, 242)(29, 203)(30, 206)(31, 200)(32, 215)(33, 202)(34, 243)(35, 209)(36, 245)(37, 254)(38, 249)(39, 210)(40, 205)(41, 255)(42, 247)(43, 259)(44, 214)(45, 207)(46, 260)(47, 244)(48, 246)(49, 220)(50, 217)(51, 228)(52, 240)(53, 226)(54, 239)(55, 230)(56, 265)(57, 234)(58, 263)(59, 271)(60, 272)(61, 273)(62, 233)(63, 229)(64, 274)(65, 264)(66, 266)(67, 238)(68, 235)(69, 277)(70, 278)(71, 248)(72, 258)(73, 250)(74, 257)(75, 281)(76, 282)(77, 283)(78, 284)(79, 252)(80, 251)(81, 256)(82, 253)(83, 285)(84, 286)(85, 262)(86, 261)(87, 287)(88, 288)(89, 268)(90, 267)(91, 270)(92, 269)(93, 276)(94, 275)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1784
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1793 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = C2 x GL(2,3) (small group id <96, 189>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1^-1 * Y3^2, (Y2 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2 * Y3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y3 * Y1, (Y1 * Y2^-3)^2, (Y2^-3 * Y3^-1)^2, Y2^8, Y2^-2 * Y1 * Y2 * Y1^-1 * Y2^-3 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1 * Y2^-2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 5, 101)(3, 99, 11, 107, 14, 110)(4, 100, 9, 105, 7, 103)(6, 102, 18, 114, 8, 104)(10, 106, 26, 122, 17, 113)(12, 108, 30, 126, 33, 129)(13, 109, 25, 121, 15, 111)(16, 112, 22, 118, 28, 124)(19, 115, 24, 120, 21, 117)(20, 116, 43, 139, 40, 136)(23, 119, 41, 137, 51, 147)(27, 123, 56, 152, 54, 150)(29, 125, 61, 157, 36, 132)(31, 127, 65, 161, 58, 154)(32, 128, 53, 149, 34, 130)(35, 131, 37, 133, 63, 159)(38, 134, 60, 156, 77, 173)(39, 135, 55, 151, 76, 172)(42, 138, 47, 143, 50, 146)(44, 140, 52, 148, 46, 142)(45, 141, 78, 174, 81, 177)(48, 144, 59, 155, 57, 153)(49, 145, 84, 180, 62, 158)(64, 160, 88, 184, 70, 166)(66, 162, 85, 181, 93, 189)(67, 163, 90, 186, 68, 164)(69, 165, 71, 167, 87, 183)(72, 168, 92, 188, 82, 178)(73, 169, 91, 187, 79, 175)(74, 170, 80, 176, 86, 182)(75, 171, 83, 179, 89, 185)(94, 190, 96, 192, 95, 191)(193, 289, 195, 291, 204, 300, 223, 319, 258, 354, 237, 333, 212, 308, 198, 294)(194, 290, 200, 296, 215, 311, 241, 337, 277, 373, 250, 346, 219, 315, 202, 298)(196, 292, 208, 304, 230, 326, 267, 363, 286, 382, 266, 362, 229, 325, 207, 303)(197, 293, 209, 305, 231, 327, 270, 366, 285, 381, 254, 350, 221, 317, 203, 299)(199, 295, 211, 307, 234, 330, 272, 368, 287, 383, 259, 355, 240, 336, 214, 310)(201, 297, 217, 313, 245, 341, 282, 378, 288, 384, 281, 377, 244, 340, 216, 312)(205, 301, 227, 323, 264, 360, 238, 334, 275, 371, 269, 365, 263, 359, 226, 322)(206, 302, 228, 324, 265, 361, 235, 331, 273, 369, 268, 364, 256, 352, 222, 318)(210, 306, 232, 328, 271, 367, 248, 344, 257, 353, 225, 321, 262, 358, 233, 329)(213, 309, 236, 332, 274, 370, 251, 347, 260, 356, 224, 320, 261, 357, 239, 335)(218, 314, 246, 342, 283, 379, 253, 349, 276, 372, 243, 339, 280, 376, 247, 343)(220, 316, 249, 345, 284, 380, 255, 351, 278, 374, 242, 338, 279, 375, 252, 348)
	L = (1, 196)(2, 201)(3, 205)(4, 194)(5, 199)(6, 211)(7, 193)(8, 213)(9, 197)(10, 208)(11, 217)(12, 224)(13, 203)(14, 207)(15, 195)(16, 218)(17, 220)(18, 216)(19, 210)(20, 236)(21, 198)(22, 209)(23, 242)(24, 200)(25, 206)(26, 214)(27, 249)(28, 202)(29, 227)(30, 245)(31, 259)(32, 222)(33, 226)(34, 204)(35, 253)(36, 255)(37, 228)(38, 268)(39, 269)(40, 238)(41, 234)(42, 243)(43, 244)(44, 235)(45, 275)(46, 212)(47, 215)(48, 246)(49, 266)(50, 233)(51, 239)(52, 232)(53, 225)(54, 251)(55, 230)(56, 240)(57, 248)(58, 260)(59, 219)(60, 231)(61, 229)(62, 278)(63, 221)(64, 261)(65, 282)(66, 286)(67, 257)(68, 223)(69, 280)(70, 279)(71, 262)(72, 271)(73, 274)(74, 276)(75, 237)(76, 252)(77, 247)(78, 281)(79, 284)(80, 254)(81, 267)(82, 283)(83, 270)(84, 272)(85, 288)(86, 241)(87, 256)(88, 263)(89, 273)(90, 250)(91, 264)(92, 265)(93, 287)(94, 277)(95, 258)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4^6 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1774
Graph:: simple bipartite
	v = 44 e = 192 f = 96
	degree seq :: [ 6^32, 16^12 ]

E27.1794 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1481>$ (small group id <192, 1481>)
|r| :: 2
Presentation :: [ R^2, Y1^3, (Y1^-1 * Y3^-1)^2, (Y1 * R)^2, Y3^-2 * Y2^-2, (R * Y3)^2, (Y1 * Y2^-1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2^3 * Y1 * Y3^-1 * Y2^-1, Y2 * Y3 * Y1^-1 * Y2^3 * Y3^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 5, 101)(3, 99, 12, 108, 10, 106)(4, 100, 16, 112, 19, 115)(6, 102, 20, 116, 24, 120)(7, 103, 25, 121, 9, 105)(8, 104, 26, 122, 22, 118)(11, 107, 33, 129, 21, 117)(13, 109, 38, 134, 36, 132)(14, 110, 28, 124, 42, 138)(15, 111, 43, 139, 35, 131)(17, 113, 30, 126, 45, 141)(18, 114, 48, 144, 49, 145)(23, 119, 54, 150, 55, 151)(27, 123, 62, 158, 60, 156)(29, 125, 57, 153, 59, 155)(31, 127, 34, 130, 67, 163)(32, 128, 37, 133, 68, 164)(39, 135, 79, 175, 77, 173)(40, 136, 81, 177, 76, 172)(41, 137, 72, 168, 64, 160)(44, 140, 61, 157, 51, 147)(46, 142, 85, 181, 50, 146)(47, 143, 86, 182, 63, 159)(52, 148, 69, 165, 56, 152)(53, 149, 58, 154, 88, 184)(65, 161, 91, 187, 82, 178)(66, 162, 95, 191, 84, 180)(70, 166, 87, 183, 89, 185)(71, 167, 83, 179, 90, 186)(73, 169, 75, 171, 92, 188)(74, 170, 78, 174, 93, 189)(80, 176, 94, 190, 96, 192)(193, 289, 195, 291, 205, 301, 231, 327, 272, 368, 239, 335, 210, 306, 198, 294)(194, 290, 200, 296, 219, 315, 255, 351, 286, 382, 258, 354, 223, 319, 202, 298)(196, 292, 209, 305, 199, 295, 215, 311, 232, 328, 206, 302, 233, 329, 207, 303)(197, 293, 212, 308, 238, 334, 276, 372, 288, 384, 271, 367, 245, 341, 214, 310)(201, 297, 222, 318, 203, 299, 224, 320, 256, 352, 220, 316, 257, 353, 221, 317)(204, 300, 226, 322, 262, 358, 241, 337, 278, 374, 254, 350, 265, 361, 228, 324)(208, 304, 236, 332, 274, 370, 234, 330, 273, 369, 244, 340, 213, 309, 237, 333)(211, 307, 235, 331, 275, 371, 248, 344, 268, 364, 246, 342, 270, 366, 243, 339)(216, 312, 240, 336, 279, 375, 280, 376, 269, 365, 230, 326, 267, 363, 242, 338)(217, 313, 249, 345, 263, 359, 227, 323, 264, 360, 229, 325, 266, 362, 247, 343)(218, 314, 250, 346, 281, 377, 259, 355, 287, 383, 277, 373, 284, 380, 252, 348)(225, 321, 261, 357, 282, 378, 251, 347, 283, 379, 253, 349, 285, 381, 260, 356)
	L = (1, 196)(2, 201)(3, 206)(4, 210)(5, 213)(6, 215)(7, 193)(8, 220)(9, 223)(10, 224)(11, 194)(12, 227)(13, 199)(14, 198)(15, 195)(16, 197)(17, 231)(18, 233)(19, 242)(20, 234)(21, 245)(22, 236)(23, 239)(24, 248)(25, 228)(26, 251)(27, 203)(28, 202)(29, 200)(30, 255)(31, 257)(32, 258)(33, 252)(34, 217)(35, 265)(36, 266)(37, 204)(38, 268)(39, 207)(40, 205)(41, 272)(42, 214)(43, 269)(44, 271)(45, 276)(46, 208)(47, 209)(48, 211)(49, 263)(50, 270)(51, 279)(52, 212)(53, 273)(54, 216)(55, 262)(56, 267)(57, 278)(58, 225)(59, 284)(60, 285)(61, 218)(62, 264)(63, 221)(64, 219)(65, 286)(66, 222)(67, 282)(68, 281)(69, 287)(70, 229)(71, 226)(72, 241)(73, 249)(74, 254)(75, 235)(76, 280)(77, 243)(78, 230)(79, 237)(80, 232)(81, 288)(82, 238)(83, 240)(84, 244)(85, 283)(86, 247)(87, 246)(88, 275)(89, 253)(90, 250)(91, 259)(92, 261)(93, 277)(94, 256)(95, 260)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4^6 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1775
Graph:: simple bipartite
	v = 44 e = 192 f = 96
	degree seq :: [ 6^32, 16^12 ]

E27.1795 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1485>$ (small group id <192, 1485>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y3)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y1 * Y2^-3 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 5, 101)(3, 99, 11, 107, 14, 110)(4, 100, 9, 105, 7, 103)(6, 102, 19, 115, 21, 117)(8, 104, 25, 121, 28, 124)(10, 106, 31, 127, 32, 128)(12, 108, 38, 134, 40, 136)(13, 109, 36, 132, 15, 111)(16, 112, 46, 142, 34, 130)(17, 113, 48, 144, 50, 146)(18, 114, 51, 147, 52, 148)(20, 116, 55, 151, 23, 119)(22, 118, 44, 140, 60, 156)(24, 120, 49, 145, 63, 159)(26, 122, 56, 152, 68, 164)(27, 123, 66, 162, 29, 125)(30, 126, 72, 168, 54, 150)(33, 129, 70, 166, 76, 172)(35, 131, 65, 161, 58, 154)(37, 133, 74, 170, 80, 176)(39, 135, 73, 169, 41, 137)(42, 138, 47, 143, 81, 177)(43, 139, 53, 149, 87, 183)(45, 141, 77, 173, 89, 185)(57, 153, 69, 165, 67, 163)(59, 155, 71, 167, 61, 157)(62, 158, 75, 171, 64, 160)(78, 174, 91, 187, 79, 175)(82, 178, 95, 191, 90, 186)(83, 179, 86, 182, 93, 189)(84, 180, 88, 184, 94, 190)(85, 181, 96, 192, 92, 188)(193, 289, 195, 291, 204, 300, 217, 313, 257, 353, 244, 340, 214, 310, 198, 294)(194, 290, 200, 296, 218, 314, 240, 336, 250, 346, 213, 309, 225, 321, 202, 298)(196, 292, 208, 304, 239, 335, 264, 360, 283, 379, 255, 351, 237, 333, 207, 303)(197, 293, 209, 305, 229, 325, 203, 299, 227, 323, 224, 320, 245, 341, 210, 306)(199, 295, 212, 308, 249, 345, 238, 334, 270, 366, 258, 354, 256, 352, 216, 312)(201, 297, 222, 318, 265, 361, 247, 343, 271, 367, 228, 324, 263, 359, 221, 317)(205, 301, 234, 330, 278, 374, 253, 349, 246, 342, 281, 377, 277, 373, 233, 329)(206, 302, 235, 331, 274, 370, 230, 326, 243, 339, 272, 368, 280, 376, 236, 332)(211, 307, 232, 328, 276, 372, 262, 358, 220, 316, 252, 348, 282, 378, 248, 344)(215, 311, 251, 347, 284, 380, 261, 357, 219, 315, 231, 327, 275, 371, 254, 350)(223, 319, 260, 356, 286, 382, 279, 375, 242, 338, 268, 364, 287, 383, 266, 362)(226, 322, 267, 363, 288, 384, 273, 369, 241, 337, 259, 355, 285, 381, 269, 365)
	L = (1, 196)(2, 201)(3, 205)(4, 194)(5, 199)(6, 212)(7, 193)(8, 219)(9, 197)(10, 208)(11, 228)(12, 231)(13, 203)(14, 207)(15, 195)(16, 223)(17, 241)(18, 222)(19, 247)(20, 211)(21, 215)(22, 251)(23, 198)(24, 209)(25, 258)(26, 259)(27, 217)(28, 221)(29, 200)(30, 243)(31, 238)(32, 226)(33, 267)(34, 202)(35, 270)(36, 206)(37, 234)(38, 265)(39, 230)(40, 233)(41, 204)(42, 266)(43, 269)(44, 263)(45, 235)(46, 224)(47, 272)(48, 255)(49, 240)(50, 216)(51, 264)(52, 246)(53, 281)(54, 210)(55, 213)(56, 249)(57, 260)(58, 271)(59, 236)(60, 253)(61, 214)(62, 225)(63, 242)(64, 268)(65, 283)(66, 220)(67, 248)(68, 261)(69, 218)(70, 256)(71, 252)(72, 244)(73, 232)(74, 239)(75, 262)(76, 254)(77, 245)(78, 257)(79, 227)(80, 273)(81, 229)(82, 275)(83, 287)(84, 288)(85, 276)(86, 282)(87, 237)(88, 284)(89, 279)(90, 285)(91, 250)(92, 286)(93, 274)(94, 277)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4^6 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1776
Graph:: simple bipartite
	v = 44 e = 192 f = 96
	degree seq :: [ 6^32, 16^12 ]

E27.1796 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3^4, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^2 * Y2 * Y3, Y3 * Y2 * Y1 * R * Y3^-1 * Y2 * Y1 * R, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y2 * Y3^-1 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 10, 106)(5, 101, 9, 105)(6, 102, 8, 104)(11, 107, 21, 117)(12, 108, 20, 116)(13, 109, 27, 123)(14, 110, 23, 119)(15, 111, 28, 124)(16, 112, 26, 122)(17, 113, 25, 121)(18, 114, 22, 118)(19, 115, 24, 120)(29, 125, 46, 142)(30, 126, 44, 140)(31, 127, 47, 143)(32, 128, 43, 139)(33, 129, 45, 141)(34, 130, 48, 144)(35, 131, 49, 145)(36, 132, 50, 146)(37, 133, 51, 147)(38, 134, 52, 148)(39, 135, 55, 151)(40, 136, 56, 152)(41, 137, 53, 149)(42, 138, 54, 150)(57, 153, 69, 165)(58, 154, 70, 166)(59, 155, 71, 167)(60, 156, 72, 168)(61, 157, 73, 169)(62, 158, 74, 170)(63, 159, 75, 171)(64, 160, 76, 172)(65, 161, 77, 173)(66, 162, 78, 174)(67, 163, 79, 175)(68, 164, 80, 176)(81, 177, 87, 183)(82, 178, 88, 184)(83, 179, 90, 186)(84, 180, 89, 185)(85, 181, 92, 188)(86, 182, 91, 187)(93, 189, 96, 192)(94, 190, 95, 191)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 205, 301, 207, 303)(198, 294, 210, 306, 211, 307)(200, 296, 214, 310, 216, 312)(202, 298, 219, 315, 220, 316)(203, 299, 221, 317, 223, 319)(204, 300, 224, 320, 225, 321)(206, 302, 222, 318, 228, 324)(208, 304, 231, 327, 232, 328)(209, 305, 233, 329, 234, 330)(212, 308, 235, 331, 237, 333)(213, 309, 238, 334, 239, 335)(215, 311, 236, 332, 242, 338)(217, 313, 245, 341, 246, 342)(218, 314, 247, 343, 248, 344)(226, 322, 253, 349, 254, 350)(227, 323, 255, 351, 256, 352)(229, 325, 257, 353, 250, 346)(230, 326, 258, 354, 249, 345)(240, 336, 265, 361, 266, 362)(241, 337, 267, 363, 268, 364)(243, 339, 269, 365, 262, 358)(244, 340, 270, 366, 261, 357)(251, 347, 273, 369, 260, 356)(252, 348, 274, 370, 259, 355)(263, 359, 279, 375, 272, 368)(264, 360, 280, 376, 271, 367)(275, 371, 286, 382, 278, 374)(276, 372, 285, 381, 277, 373)(281, 377, 288, 384, 284, 380)(282, 378, 287, 383, 283, 379)
	L = (1, 196)(2, 200)(3, 203)(4, 206)(5, 208)(6, 193)(7, 212)(8, 215)(9, 217)(10, 194)(11, 222)(12, 195)(13, 226)(14, 198)(15, 229)(16, 228)(17, 197)(18, 227)(19, 230)(20, 236)(21, 199)(22, 240)(23, 202)(24, 243)(25, 242)(26, 201)(27, 241)(28, 244)(29, 249)(30, 204)(31, 251)(32, 250)(33, 252)(34, 210)(35, 205)(36, 209)(37, 211)(38, 207)(39, 259)(40, 255)(41, 260)(42, 253)(43, 261)(44, 213)(45, 263)(46, 262)(47, 264)(48, 219)(49, 214)(50, 218)(51, 220)(52, 216)(53, 271)(54, 267)(55, 272)(56, 265)(57, 224)(58, 221)(59, 225)(60, 223)(61, 232)(62, 275)(63, 234)(64, 276)(65, 277)(66, 278)(67, 233)(68, 231)(69, 238)(70, 235)(71, 239)(72, 237)(73, 246)(74, 281)(75, 248)(76, 282)(77, 283)(78, 284)(79, 247)(80, 245)(81, 285)(82, 286)(83, 256)(84, 254)(85, 258)(86, 257)(87, 287)(88, 288)(89, 268)(90, 266)(91, 270)(92, 269)(93, 274)(94, 273)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1797
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1797 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^4, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y1^-1 * Y3^-2 * Y1^-3, (Y3^-1 * Y1^-1)^3, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1^-3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 24, 120, 16, 112, 33, 129, 20, 116, 5, 101)(3, 99, 11, 107, 37, 133, 63, 159, 41, 137, 73, 169, 44, 140, 13, 109)(4, 100, 15, 111, 46, 142, 23, 119, 6, 102, 22, 118, 48, 144, 17, 113)(8, 104, 28, 124, 62, 158, 81, 177, 64, 160, 43, 139, 66, 162, 30, 126)(9, 105, 32, 128, 67, 163, 36, 132, 10, 106, 35, 131, 68, 164, 34, 130)(12, 108, 31, 127, 55, 151, 45, 141, 14, 110, 29, 125, 57, 153, 42, 138)(18, 114, 49, 145, 75, 171, 40, 136, 53, 149, 79, 175, 74, 170, 39, 135)(19, 115, 50, 146, 72, 168, 38, 134, 21, 117, 52, 148, 77, 173, 47, 143)(25, 121, 54, 150, 80, 176, 78, 174, 51, 147, 65, 161, 82, 178, 56, 152)(26, 122, 58, 154, 83, 179, 61, 157, 27, 123, 60, 156, 84, 180, 59, 155)(69, 165, 89, 185, 96, 192, 88, 184, 76, 172, 92, 188, 93, 189, 85, 181)(70, 166, 90, 186, 95, 191, 86, 182, 71, 167, 91, 187, 94, 190, 87, 183)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 217, 313)(201, 297, 223, 319)(202, 298, 221, 317)(203, 299, 230, 326)(205, 301, 224, 320)(207, 303, 231, 327)(208, 304, 233, 329)(209, 305, 235, 331)(211, 307, 234, 330)(212, 308, 243, 339)(213, 309, 237, 333)(214, 310, 232, 328)(215, 311, 220, 316)(216, 312, 245, 341)(218, 314, 249, 345)(219, 315, 247, 343)(222, 318, 250, 346)(225, 321, 256, 352)(226, 322, 257, 353)(227, 323, 255, 351)(228, 324, 246, 342)(229, 325, 261, 357)(236, 332, 268, 364)(238, 334, 263, 359)(239, 335, 265, 361)(240, 336, 262, 358)(241, 337, 251, 347)(242, 338, 270, 366)(244, 340, 248, 344)(252, 348, 273, 369)(253, 349, 271, 367)(254, 350, 277, 373)(258, 354, 280, 376)(259, 355, 279, 375)(260, 356, 278, 374)(264, 360, 282, 378)(266, 362, 284, 380)(267, 363, 281, 377)(269, 365, 283, 379)(272, 368, 285, 381)(274, 370, 288, 384)(275, 371, 287, 383)(276, 372, 286, 382)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 218)(8, 221)(9, 225)(10, 194)(11, 231)(12, 233)(13, 235)(14, 195)(15, 230)(16, 198)(17, 224)(18, 237)(19, 216)(20, 219)(21, 197)(22, 239)(23, 227)(24, 213)(25, 247)(26, 212)(27, 199)(28, 205)(29, 256)(30, 257)(31, 200)(32, 215)(33, 202)(34, 250)(35, 209)(36, 252)(37, 262)(38, 214)(39, 265)(40, 203)(41, 206)(42, 210)(43, 255)(44, 263)(45, 245)(46, 268)(47, 207)(48, 261)(49, 270)(50, 251)(51, 249)(52, 253)(53, 234)(54, 222)(55, 243)(56, 241)(57, 217)(58, 228)(59, 244)(60, 226)(61, 242)(62, 278)(63, 220)(64, 223)(65, 273)(66, 279)(67, 280)(68, 277)(69, 238)(70, 236)(71, 229)(72, 284)(73, 232)(74, 282)(75, 283)(76, 240)(77, 281)(78, 271)(79, 248)(80, 286)(81, 246)(82, 287)(83, 288)(84, 285)(85, 259)(86, 258)(87, 254)(88, 260)(89, 264)(90, 267)(91, 266)(92, 269)(93, 275)(94, 274)(95, 272)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1796
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1798 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y2, (R * Y1 * Y2)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y3)^3, (Y2 * Y3 * Y1)^2, Y3^3 * Y1 * Y3^-3 * Y1, Y1 * Y3 * Y2 * Y3^3 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 15, 111)(6, 102, 18, 114)(7, 103, 21, 117)(8, 104, 24, 120)(10, 106, 25, 121)(11, 107, 31, 127)(13, 109, 36, 132)(14, 110, 37, 133)(16, 112, 19, 115)(17, 113, 43, 139)(20, 116, 50, 146)(22, 118, 55, 151)(23, 119, 56, 152)(26, 122, 62, 158)(27, 123, 65, 161)(28, 124, 67, 163)(29, 125, 68, 164)(30, 126, 69, 165)(32, 128, 66, 162)(33, 129, 72, 168)(34, 130, 74, 170)(35, 131, 75, 171)(38, 134, 78, 174)(39, 135, 58, 154)(40, 136, 73, 169)(41, 137, 70, 166)(42, 138, 79, 175)(44, 140, 71, 167)(45, 141, 64, 160)(46, 142, 80, 176)(47, 143, 82, 178)(48, 144, 83, 179)(49, 145, 84, 180)(51, 147, 81, 177)(52, 148, 87, 183)(53, 149, 89, 185)(54, 150, 90, 186)(57, 153, 93, 189)(59, 155, 88, 184)(60, 156, 85, 181)(61, 157, 94, 190)(63, 159, 86, 182)(76, 172, 92, 188)(77, 173, 91, 187)(95, 191, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 205, 301)(197, 293, 208, 304)(199, 295, 214, 310)(200, 296, 217, 313)(201, 297, 219, 315)(202, 298, 221, 317)(203, 299, 224, 320)(204, 300, 220, 316)(206, 302, 230, 326)(207, 303, 223, 319)(209, 305, 236, 332)(210, 306, 238, 334)(211, 307, 240, 336)(212, 308, 243, 339)(213, 309, 239, 335)(215, 311, 249, 345)(216, 312, 242, 338)(218, 314, 255, 351)(222, 318, 251, 347)(225, 321, 265, 361)(226, 322, 256, 352)(227, 323, 258, 354)(228, 324, 264, 360)(229, 325, 261, 357)(231, 327, 262, 358)(232, 328, 241, 337)(233, 329, 271, 367)(234, 330, 266, 362)(235, 331, 260, 356)(237, 333, 245, 341)(244, 340, 280, 376)(246, 342, 273, 369)(247, 343, 279, 375)(248, 344, 276, 372)(250, 346, 277, 373)(252, 348, 286, 382)(253, 349, 281, 377)(254, 350, 275, 371)(257, 353, 284, 380)(259, 355, 285, 381)(263, 359, 282, 378)(267, 363, 278, 374)(268, 364, 287, 383)(269, 365, 272, 368)(270, 366, 274, 370)(283, 379, 288, 384)
	L = (1, 196)(2, 199)(3, 202)(4, 206)(5, 193)(6, 211)(7, 215)(8, 194)(9, 214)(10, 222)(11, 195)(12, 226)(13, 224)(14, 231)(15, 232)(16, 234)(17, 197)(18, 205)(19, 241)(20, 198)(21, 245)(22, 243)(23, 250)(24, 251)(25, 253)(26, 200)(27, 258)(28, 201)(29, 208)(30, 262)(31, 263)(32, 252)(33, 203)(34, 244)(35, 204)(36, 256)(37, 260)(38, 238)(39, 242)(40, 269)(41, 207)(42, 259)(43, 268)(44, 239)(45, 209)(46, 273)(47, 210)(48, 217)(49, 277)(50, 278)(51, 233)(52, 212)(53, 225)(54, 213)(55, 237)(56, 275)(57, 219)(58, 223)(59, 284)(60, 216)(61, 274)(62, 283)(63, 220)(64, 218)(65, 221)(66, 282)(67, 230)(68, 281)(69, 228)(70, 285)(71, 287)(72, 272)(73, 279)(74, 236)(75, 286)(76, 227)(77, 229)(78, 235)(79, 280)(80, 240)(81, 267)(82, 249)(83, 266)(84, 247)(85, 270)(86, 288)(87, 257)(88, 264)(89, 255)(90, 271)(91, 246)(92, 248)(93, 254)(94, 265)(95, 261)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1805
Graph:: simple bipartite
	v = 96 e = 192 f = 44
	degree seq :: [ 4^96 ]

E27.1799 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^4, (Y2 * Y1)^2, Y1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2 * Y3^2, R * Y1 * Y2 * R * Y3 * Y1 * Y2^-1 * Y3, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y3 * Y2 * Y1 * R * Y3^-1 * Y2^-1 * Y1 * R, Y2 * Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y1, (Y3^-1 * Y2 * Y3^-1 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 10, 106)(5, 101, 7, 103)(6, 102, 8, 104)(11, 107, 26, 122)(12, 108, 25, 121)(13, 109, 28, 124)(14, 110, 23, 119)(15, 111, 27, 123)(16, 112, 21, 117)(17, 113, 20, 116)(18, 114, 24, 120)(19, 115, 22, 118)(29, 125, 56, 152)(30, 126, 50, 146)(31, 127, 55, 151)(32, 128, 54, 150)(33, 129, 53, 149)(34, 130, 51, 147)(35, 131, 52, 148)(36, 132, 44, 140)(37, 133, 48, 144)(38, 134, 49, 145)(39, 135, 47, 143)(40, 136, 46, 142)(41, 137, 45, 141)(42, 138, 43, 139)(57, 153, 75, 171)(58, 154, 73, 169)(59, 155, 79, 175)(60, 156, 80, 176)(61, 157, 70, 166)(62, 158, 77, 173)(63, 159, 69, 165)(64, 160, 78, 174)(65, 161, 74, 170)(66, 162, 76, 172)(67, 163, 71, 167)(68, 164, 72, 168)(81, 177, 88, 184)(82, 178, 87, 183)(83, 179, 92, 188)(84, 180, 91, 187)(85, 181, 90, 186)(86, 182, 89, 185)(93, 189, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 205, 301, 207, 303)(198, 294, 210, 306, 211, 307)(200, 296, 214, 310, 216, 312)(202, 298, 219, 315, 220, 316)(203, 299, 221, 317, 223, 319)(204, 300, 224, 320, 225, 321)(206, 302, 222, 318, 228, 324)(208, 304, 231, 327, 232, 328)(209, 305, 233, 329, 234, 330)(212, 308, 235, 331, 237, 333)(213, 309, 238, 334, 239, 335)(215, 311, 236, 332, 242, 338)(217, 313, 245, 341, 246, 342)(218, 314, 247, 343, 248, 344)(226, 322, 253, 349, 254, 350)(227, 323, 255, 351, 256, 352)(229, 325, 257, 353, 250, 346)(230, 326, 258, 354, 249, 345)(240, 336, 265, 361, 266, 362)(241, 337, 267, 363, 268, 364)(243, 339, 269, 365, 262, 358)(244, 340, 270, 366, 261, 357)(251, 347, 273, 369, 260, 356)(252, 348, 274, 370, 259, 355)(263, 359, 279, 375, 272, 368)(264, 360, 280, 376, 271, 367)(275, 371, 286, 382, 278, 374)(276, 372, 285, 381, 277, 373)(281, 377, 288, 384, 284, 380)(282, 378, 287, 383, 283, 379)
	L = (1, 196)(2, 200)(3, 203)(4, 206)(5, 208)(6, 193)(7, 212)(8, 215)(9, 217)(10, 194)(11, 222)(12, 195)(13, 226)(14, 198)(15, 229)(16, 228)(17, 197)(18, 227)(19, 230)(20, 236)(21, 199)(22, 240)(23, 202)(24, 243)(25, 242)(26, 201)(27, 241)(28, 244)(29, 249)(30, 204)(31, 251)(32, 250)(33, 252)(34, 210)(35, 205)(36, 209)(37, 211)(38, 207)(39, 259)(40, 255)(41, 260)(42, 253)(43, 261)(44, 213)(45, 263)(46, 262)(47, 264)(48, 219)(49, 214)(50, 218)(51, 220)(52, 216)(53, 271)(54, 267)(55, 272)(56, 265)(57, 224)(58, 221)(59, 225)(60, 223)(61, 232)(62, 275)(63, 234)(64, 276)(65, 277)(66, 278)(67, 233)(68, 231)(69, 238)(70, 235)(71, 239)(72, 237)(73, 246)(74, 281)(75, 248)(76, 282)(77, 283)(78, 284)(79, 247)(80, 245)(81, 285)(82, 286)(83, 256)(84, 254)(85, 258)(86, 257)(87, 287)(88, 288)(89, 268)(90, 266)(91, 270)(92, 269)(93, 274)(94, 273)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1802
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1800 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, Y2 * Y3^-2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y3^2 * Y2 * Y3 * Y2^-1 * Y3, (R * Y2 * Y1 * Y2^-1)^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1 * Y2^-1, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 23, 119)(9, 105, 29, 125)(12, 108, 33, 129)(13, 109, 25, 121)(14, 110, 42, 138)(15, 111, 34, 130)(16, 112, 28, 124)(18, 114, 32, 128)(19, 115, 48, 144)(20, 116, 30, 126)(21, 117, 24, 120)(22, 118, 27, 123)(26, 122, 65, 161)(31, 127, 70, 166)(35, 131, 54, 150)(36, 132, 79, 175)(37, 133, 74, 170)(38, 134, 77, 173)(39, 135, 64, 160)(40, 136, 80, 176)(41, 137, 62, 158)(43, 139, 78, 174)(44, 140, 76, 172)(45, 141, 85, 181)(46, 142, 69, 165)(47, 143, 68, 164)(49, 145, 84, 180)(50, 146, 71, 167)(51, 147, 90, 186)(52, 148, 73, 169)(53, 149, 60, 156)(55, 151, 67, 163)(56, 152, 61, 157)(57, 153, 66, 162)(58, 154, 75, 171)(59, 155, 91, 187)(63, 159, 92, 188)(72, 168, 96, 192)(81, 177, 93, 189)(82, 178, 94, 190)(83, 179, 88, 184)(86, 182, 89, 185)(87, 183, 95, 191)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 212, 308, 213, 309)(200, 296, 218, 314, 220, 316)(202, 298, 224, 320, 225, 321)(203, 299, 227, 323, 228, 324)(204, 300, 229, 325, 231, 327)(205, 301, 232, 328, 233, 329)(207, 303, 237, 333, 221, 317)(209, 305, 219, 315, 241, 337)(210, 306, 242, 338, 243, 339)(211, 307, 244, 340, 245, 341)(214, 310, 239, 335, 249, 345)(215, 311, 250, 346, 251, 347)(216, 312, 252, 348, 254, 350)(217, 313, 255, 351, 256, 352)(222, 318, 263, 359, 264, 360)(223, 319, 265, 361, 266, 362)(226, 322, 261, 357, 270, 366)(230, 326, 247, 343, 271, 367)(234, 330, 275, 371, 272, 368)(235, 331, 273, 369, 248, 344)(236, 332, 274, 370, 276, 372)(238, 334, 246, 342, 279, 375)(240, 336, 281, 377, 282, 378)(253, 349, 268, 364, 283, 379)(257, 353, 278, 374, 284, 380)(258, 354, 285, 381, 269, 365)(259, 355, 286, 382, 277, 373)(260, 356, 267, 363, 287, 383)(262, 358, 280, 376, 288, 384)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 216)(8, 219)(9, 222)(10, 194)(11, 217)(12, 230)(13, 195)(14, 235)(15, 229)(16, 238)(17, 240)(18, 236)(19, 197)(20, 221)(21, 215)(22, 198)(23, 205)(24, 253)(25, 199)(26, 258)(27, 252)(28, 260)(29, 262)(30, 259)(31, 201)(32, 209)(33, 203)(34, 202)(35, 254)(36, 272)(37, 273)(38, 242)(39, 249)(40, 271)(41, 246)(42, 268)(43, 233)(44, 206)(45, 244)(46, 278)(47, 208)(48, 227)(49, 265)(50, 248)(51, 251)(52, 276)(53, 214)(54, 211)(55, 212)(56, 213)(57, 257)(58, 231)(59, 284)(60, 285)(61, 263)(62, 270)(63, 283)(64, 267)(65, 247)(66, 256)(67, 218)(68, 275)(69, 220)(70, 250)(71, 269)(72, 228)(73, 277)(74, 226)(75, 223)(76, 224)(77, 225)(78, 234)(79, 288)(80, 286)(81, 245)(82, 232)(83, 241)(84, 280)(85, 281)(86, 237)(87, 243)(88, 239)(89, 261)(90, 287)(91, 282)(92, 274)(93, 266)(94, 255)(95, 264)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1803
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1801 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1 * Y3^-2 * Y2^-1 * Y1 * Y2, (Y3 * Y1 * Y2)^2, Y2^-1 * Y3^-2 * R * Y2 * R, Y3 * Y2^-1 * R * Y2^-1 * Y3^-1 * Y2 * R, (R * Y2 * Y1 * Y2^-1)^2, R * Y2^-1 * Y3 * Y1 * Y2^-1 * R * Y3^-1 * Y1, (Y3^3 * Y2^-1)^2, Y3^8, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y3^2 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y3^-1, (Y3 * Y2^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98)(3, 99, 11, 107)(4, 100, 10, 106)(5, 101, 17, 113)(6, 102, 8, 104)(7, 103, 21, 117)(9, 105, 27, 123)(12, 108, 22, 118)(13, 109, 32, 128)(14, 110, 36, 132)(15, 111, 30, 126)(16, 112, 41, 137)(18, 114, 29, 125)(19, 115, 28, 124)(20, 116, 25, 121)(23, 119, 48, 144)(24, 120, 52, 148)(26, 122, 57, 153)(31, 127, 44, 140)(33, 129, 65, 161)(34, 130, 66, 162)(35, 131, 63, 159)(37, 133, 71, 167)(38, 134, 75, 171)(39, 135, 60, 156)(40, 136, 79, 175)(42, 138, 43, 139)(45, 141, 59, 155)(46, 142, 58, 154)(47, 143, 55, 151)(49, 145, 87, 183)(50, 146, 88, 184)(51, 147, 86, 182)(53, 149, 68, 164)(54, 150, 84, 180)(56, 152, 96, 192)(61, 157, 83, 179)(62, 158, 91, 187)(64, 160, 77, 173)(67, 163, 89, 185)(69, 165, 90, 186)(70, 166, 82, 178)(72, 168, 85, 181)(73, 169, 92, 188)(74, 170, 94, 190)(76, 172, 93, 189)(78, 174, 95, 191)(80, 176, 81, 177)(193, 289, 195, 291, 197, 293)(194, 290, 199, 295, 201, 297)(196, 292, 206, 302, 208, 304)(198, 294, 211, 307, 204, 300)(200, 296, 216, 312, 218, 314)(202, 298, 221, 317, 214, 310)(203, 299, 223, 319, 225, 321)(205, 301, 226, 322, 210, 306)(207, 303, 230, 326, 232, 328)(209, 305, 222, 318, 235, 331)(212, 308, 238, 334, 219, 315)(213, 309, 237, 333, 241, 337)(215, 311, 242, 338, 220, 316)(217, 313, 246, 342, 248, 344)(224, 320, 254, 350, 256, 352)(227, 323, 260, 356, 257, 353)(228, 324, 262, 358, 264, 360)(229, 325, 265, 361, 234, 330)(231, 327, 269, 365, 261, 357)(233, 329, 252, 348, 273, 369)(236, 332, 259, 355, 276, 372)(239, 335, 275, 371, 249, 345)(240, 336, 277, 373, 266, 362)(243, 339, 263, 359, 279, 375)(244, 340, 274, 370, 283, 379)(245, 341, 284, 380, 250, 346)(247, 343, 286, 382, 282, 378)(251, 347, 281, 377, 267, 363)(253, 349, 285, 381, 258, 354)(255, 351, 271, 367, 287, 383)(268, 364, 280, 376, 272, 368)(270, 366, 278, 374, 288, 384)
	L = (1, 196)(2, 200)(3, 204)(4, 207)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 224)(12, 213)(13, 195)(14, 197)(15, 231)(16, 234)(17, 228)(18, 236)(19, 219)(20, 198)(21, 240)(22, 203)(23, 199)(24, 201)(25, 247)(26, 250)(27, 244)(28, 251)(29, 209)(30, 202)(31, 221)(32, 255)(33, 258)(34, 257)(35, 205)(36, 263)(37, 206)(38, 208)(39, 270)(40, 272)(41, 267)(42, 274)(43, 233)(44, 275)(45, 211)(46, 249)(47, 212)(48, 278)(49, 280)(50, 279)(51, 215)(52, 260)(53, 216)(54, 218)(55, 287)(56, 253)(57, 276)(58, 262)(59, 273)(60, 222)(61, 223)(62, 225)(63, 282)(64, 245)(65, 283)(66, 281)(67, 226)(68, 269)(69, 227)(70, 235)(71, 286)(72, 284)(73, 277)(74, 229)(75, 285)(76, 230)(77, 232)(78, 239)(79, 256)(80, 237)(81, 271)(82, 238)(83, 288)(84, 268)(85, 241)(86, 261)(87, 264)(88, 259)(89, 242)(90, 243)(91, 265)(92, 254)(93, 246)(94, 248)(95, 252)(96, 266)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1804
Graph:: simple bipartite
	v = 80 e = 192 f = 60
	degree seq :: [ 4^48, 6^32 ]

E27.1802 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^4 * Y3, (Y3^-1 * Y1^-1)^3, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 22, 118, 15, 111, 29, 125, 18, 114, 5, 101)(3, 99, 11, 107, 33, 129, 55, 151, 37, 133, 47, 143, 23, 119, 8, 104)(4, 100, 14, 110, 41, 137, 21, 117, 6, 102, 20, 116, 44, 140, 16, 112)(9, 105, 28, 124, 59, 155, 32, 128, 10, 106, 31, 127, 60, 156, 30, 126)(12, 108, 36, 132, 65, 161, 40, 136, 13, 109, 39, 135, 66, 162, 38, 134)(17, 113, 45, 141, 69, 165, 42, 138, 19, 115, 46, 142, 70, 166, 43, 139)(24, 120, 50, 146, 75, 171, 53, 149, 25, 121, 52, 148, 76, 172, 51, 147)(26, 122, 54, 150, 77, 173, 58, 154, 27, 123, 57, 153, 78, 174, 56, 152)(34, 130, 61, 157, 81, 177, 64, 160, 35, 131, 63, 159, 82, 178, 62, 158)(48, 144, 71, 167, 87, 183, 74, 170, 49, 145, 73, 169, 88, 184, 72, 168)(67, 163, 85, 181, 90, 186, 80, 176, 68, 164, 86, 182, 89, 185, 79, 175)(83, 179, 91, 187, 95, 191, 94, 190, 84, 180, 92, 188, 96, 192, 93, 189)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 205, 301)(197, 293, 203, 299)(198, 294, 204, 300)(199, 295, 215, 311)(201, 297, 219, 315)(202, 298, 218, 314)(206, 302, 232, 328)(207, 303, 229, 325)(208, 304, 231, 327)(209, 305, 227, 323)(210, 306, 225, 321)(211, 307, 226, 322)(212, 308, 230, 326)(213, 309, 228, 324)(214, 310, 239, 335)(216, 312, 241, 337)(217, 313, 240, 336)(220, 316, 250, 346)(221, 317, 247, 343)(222, 318, 249, 345)(223, 319, 248, 344)(224, 320, 246, 342)(233, 329, 257, 353)(234, 330, 253, 349)(235, 331, 255, 351)(236, 332, 258, 354)(237, 333, 256, 352)(238, 334, 254, 350)(242, 338, 266, 362)(243, 339, 265, 361)(244, 340, 264, 360)(245, 341, 263, 359)(251, 347, 269, 365)(252, 348, 270, 366)(259, 355, 276, 372)(260, 356, 275, 371)(261, 357, 273, 369)(262, 358, 274, 370)(267, 363, 279, 375)(268, 364, 280, 376)(271, 367, 284, 380)(272, 368, 283, 379)(277, 373, 286, 382)(278, 374, 285, 381)(281, 377, 288, 384)(282, 378, 287, 383)
	L = (1, 196)(2, 201)(3, 204)(4, 207)(5, 209)(6, 193)(7, 216)(8, 218)(9, 221)(10, 194)(11, 226)(12, 229)(13, 195)(14, 234)(15, 198)(16, 220)(17, 214)(18, 217)(19, 197)(20, 235)(21, 223)(22, 211)(23, 240)(24, 210)(25, 199)(26, 247)(27, 200)(28, 213)(29, 202)(30, 242)(31, 208)(32, 244)(33, 241)(34, 239)(35, 203)(36, 250)(37, 205)(38, 253)(39, 248)(40, 255)(41, 259)(42, 212)(43, 206)(44, 260)(45, 243)(46, 245)(47, 227)(48, 225)(49, 215)(50, 224)(51, 238)(52, 222)(53, 237)(54, 266)(55, 219)(56, 228)(57, 264)(58, 231)(59, 271)(60, 272)(61, 232)(62, 265)(63, 230)(64, 263)(65, 275)(66, 276)(67, 236)(68, 233)(69, 277)(70, 278)(71, 254)(72, 246)(73, 256)(74, 249)(75, 281)(76, 282)(77, 283)(78, 284)(79, 252)(80, 251)(81, 285)(82, 286)(83, 258)(84, 257)(85, 262)(86, 261)(87, 287)(88, 288)(89, 268)(90, 267)(91, 270)(92, 269)(93, 274)(94, 273)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1799
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1803 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3 * Y1^-1)^2, (Y3 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y3^2 * Y1^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y3 * Y1^3 * Y2 * Y1^-1, Y2 * Y1^-1 * R * Y2 * Y1 * Y3 * R * Y1^-1, Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-3, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y3^2, Y1^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 25, 121, 63, 159, 60, 156, 20, 116, 5, 101)(3, 99, 11, 107, 39, 135, 81, 177, 92, 188, 78, 174, 47, 143, 13, 109)(4, 100, 15, 111, 28, 124, 73, 169, 62, 158, 80, 176, 54, 150, 17, 113)(6, 102, 22, 118, 27, 123, 71, 167, 53, 149, 76, 172, 59, 155, 23, 119)(8, 104, 29, 125, 75, 171, 48, 144, 88, 184, 41, 137, 82, 178, 31, 127)(9, 105, 33, 129, 66, 162, 40, 136, 86, 182, 51, 147, 21, 117, 35, 131)(10, 106, 36, 132, 65, 161, 45, 141, 85, 181, 57, 153, 19, 115, 37, 133)(12, 108, 43, 139, 87, 183, 96, 192, 91, 187, 93, 189, 68, 164, 30, 126)(14, 110, 32, 128, 70, 166, 94, 190, 89, 185, 95, 191, 90, 186, 49, 145)(16, 112, 52, 148, 74, 170, 38, 134, 24, 120, 61, 157, 72, 168, 34, 130)(18, 114, 55, 151, 84, 180, 46, 142, 64, 160, 42, 138, 79, 175, 56, 152)(26, 122, 67, 163, 44, 140, 83, 179, 58, 154, 77, 173, 50, 146, 69, 165)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 218, 314)(201, 297, 224, 320)(202, 298, 222, 318)(203, 299, 232, 328)(205, 301, 237, 333)(207, 303, 240, 336)(208, 304, 242, 338)(209, 305, 234, 330)(211, 307, 241, 337)(212, 308, 250, 346)(213, 309, 235, 331)(214, 310, 233, 329)(215, 311, 238, 334)(216, 312, 236, 332)(217, 313, 256, 352)(219, 315, 262, 358)(220, 316, 260, 356)(221, 317, 268, 364)(223, 319, 272, 368)(225, 321, 275, 371)(226, 322, 276, 372)(227, 323, 270, 366)(228, 324, 269, 365)(229, 325, 273, 369)(230, 326, 271, 367)(231, 327, 264, 360)(239, 335, 266, 362)(243, 339, 261, 357)(244, 340, 274, 370)(245, 341, 283, 379)(246, 342, 279, 375)(247, 343, 265, 361)(248, 344, 263, 359)(249, 345, 259, 355)(251, 347, 282, 378)(252, 348, 280, 376)(253, 349, 267, 363)(254, 350, 281, 377)(255, 351, 284, 380)(257, 353, 286, 382)(258, 354, 285, 381)(277, 373, 288, 384)(278, 374, 287, 383)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 219)(8, 222)(9, 226)(10, 194)(11, 233)(12, 236)(13, 238)(14, 195)(15, 243)(16, 245)(17, 228)(18, 235)(19, 244)(20, 251)(21, 197)(22, 232)(23, 237)(24, 198)(25, 257)(26, 260)(27, 264)(28, 199)(29, 269)(30, 271)(31, 273)(32, 200)(33, 215)(34, 277)(35, 265)(36, 268)(37, 272)(38, 202)(39, 262)(40, 209)(41, 259)(42, 203)(43, 267)(44, 281)(45, 207)(46, 275)(47, 282)(48, 205)(49, 210)(50, 206)(51, 263)(52, 258)(53, 255)(54, 212)(55, 270)(56, 261)(57, 214)(58, 279)(59, 266)(60, 278)(61, 213)(62, 216)(63, 254)(64, 285)(65, 253)(66, 217)(67, 247)(68, 239)(69, 240)(70, 218)(71, 229)(72, 246)(73, 249)(74, 220)(75, 286)(76, 227)(77, 234)(78, 221)(79, 287)(80, 225)(81, 248)(82, 241)(83, 223)(84, 224)(85, 252)(86, 230)(87, 231)(88, 288)(89, 284)(90, 250)(91, 242)(92, 283)(93, 274)(94, 256)(95, 280)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1800
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1804 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (SL(2,3) : C2) : C2 (small group id <96, 193>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * R)^2, (Y2 * Y3)^2, (R * Y1)^2, (Y3^2 * Y1)^2, (Y3 * Y1)^3, Y2 * Y1 * Y2 * Y1^-1 * Y3 * Y1, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y3, (Y3 * Y1^2)^2, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-2)^2, (Y3^-2 * Y1)^2, Y2 * Y1^-1 * R * Y3^-1 * Y1 * Y2 * R * Y1^-1, Y2 * Y1^3 * Y2 * Y3^-1 * Y1 * Y3, Y3^2 * Y1 * Y3^-2 * Y1^-3, Y1^8, Y2 * Y1^-2 * R * Y2 * R * Y1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 7, 103, 25, 121, 63, 159, 60, 156, 20, 116, 5, 101)(3, 99, 11, 107, 39, 135, 85, 181, 92, 188, 77, 173, 47, 143, 13, 109)(4, 100, 15, 111, 51, 147, 84, 180, 62, 158, 73, 169, 28, 124, 17, 113)(6, 102, 22, 118, 59, 155, 89, 185, 53, 149, 72, 168, 27, 123, 23, 119)(8, 104, 29, 125, 75, 171, 95, 191, 87, 183, 41, 137, 79, 175, 31, 127)(9, 105, 33, 129, 21, 117, 40, 136, 86, 182, 94, 190, 66, 162, 35, 131)(10, 106, 36, 132, 19, 115, 45, 141, 83, 179, 54, 150, 65, 161, 37, 133)(12, 108, 43, 139, 88, 184, 96, 192, 91, 187, 93, 189, 68, 164, 30, 126)(14, 110, 48, 144, 70, 166, 56, 152, 81, 177, 32, 128, 80, 176, 49, 145)(16, 112, 52, 148, 74, 170, 34, 130, 24, 120, 57, 153, 71, 167, 38, 134)(18, 114, 55, 151, 78, 174, 61, 157, 64, 160, 42, 138, 82, 178, 46, 142)(26, 122, 67, 163, 50, 146, 90, 186, 58, 154, 76, 172, 44, 140, 69, 165)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 218, 314)(201, 297, 224, 320)(202, 298, 222, 318)(203, 299, 232, 328)(205, 301, 237, 333)(207, 303, 223, 319)(208, 304, 242, 338)(209, 305, 234, 330)(211, 307, 248, 344)(212, 308, 250, 346)(213, 309, 235, 331)(214, 310, 221, 317)(215, 311, 253, 349)(216, 312, 236, 332)(217, 313, 256, 352)(219, 315, 262, 358)(220, 316, 260, 356)(225, 321, 261, 357)(226, 322, 274, 370)(227, 323, 269, 365)(228, 324, 259, 355)(229, 325, 277, 373)(230, 326, 270, 366)(231, 327, 266, 362)(233, 329, 264, 360)(238, 334, 281, 377)(239, 335, 263, 359)(240, 336, 278, 374)(241, 337, 257, 353)(243, 339, 280, 376)(244, 340, 271, 367)(245, 341, 283, 379)(246, 342, 268, 364)(247, 343, 276, 372)(249, 345, 267, 363)(251, 347, 272, 368)(252, 348, 279, 375)(254, 350, 273, 369)(255, 351, 284, 380)(258, 354, 285, 381)(265, 361, 287, 383)(275, 371, 288, 384)(282, 378, 286, 382)
	L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 219)(8, 222)(9, 226)(10, 194)(11, 233)(12, 236)(13, 238)(14, 195)(15, 225)(16, 245)(17, 246)(18, 235)(19, 249)(20, 251)(21, 197)(22, 227)(23, 229)(24, 198)(25, 257)(26, 260)(27, 263)(28, 199)(29, 268)(30, 270)(31, 205)(32, 200)(33, 215)(34, 275)(35, 276)(36, 264)(37, 265)(38, 202)(39, 272)(40, 209)(41, 259)(42, 203)(43, 271)(44, 273)(45, 207)(46, 282)(47, 262)(48, 279)(49, 256)(50, 206)(51, 212)(52, 213)(53, 255)(54, 214)(55, 269)(56, 210)(57, 258)(58, 280)(59, 266)(60, 278)(61, 261)(62, 216)(63, 254)(64, 285)(65, 244)(66, 217)(67, 247)(68, 231)(69, 223)(70, 218)(71, 243)(72, 232)(73, 286)(74, 220)(75, 248)(76, 234)(77, 221)(78, 240)(79, 241)(80, 250)(81, 284)(82, 224)(83, 252)(84, 228)(85, 253)(86, 230)(87, 288)(88, 239)(89, 237)(90, 287)(91, 242)(92, 283)(93, 267)(94, 281)(95, 277)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1801
Graph:: simple bipartite
	v = 60 e = 192 f = 80
	degree seq :: [ 4^48, 16^12 ]

E27.1805 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 8})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^-2 * Y3^2, (Y2^-1 * Y3)^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y1)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1, Y3 * Y2 * Y3 * Y2^5 ]
Map:: polytopal non-degenerate
	R = (1, 97, 2, 98, 5, 101)(3, 99, 12, 108, 15, 111)(4, 100, 17, 113, 18, 114)(6, 102, 22, 118, 23, 119)(7, 103, 26, 122, 9, 105)(8, 104, 27, 123, 30, 126)(10, 106, 32, 128, 33, 129)(11, 107, 36, 132, 20, 116)(13, 109, 41, 137, 44, 140)(14, 110, 29, 125, 45, 141)(16, 112, 48, 144, 38, 134)(19, 115, 55, 151, 42, 138)(21, 117, 57, 153, 58, 154)(24, 120, 62, 158, 39, 135)(25, 121, 35, 131, 50, 146)(28, 124, 65, 161, 71, 167)(31, 127, 72, 168, 67, 163)(34, 130, 37, 133, 68, 164)(40, 136, 76, 172, 47, 143)(43, 139, 79, 175, 75, 171)(46, 142, 59, 155, 73, 169)(49, 145, 88, 184, 89, 185)(51, 147, 66, 162, 53, 149)(52, 148, 64, 160, 74, 170)(54, 150, 60, 156, 69, 165)(56, 152, 77, 173, 61, 157)(63, 159, 85, 181, 86, 182)(70, 166, 93, 189, 90, 186)(78, 174, 87, 183, 92, 188)(80, 176, 91, 187, 94, 190)(81, 177, 82, 178, 95, 191)(83, 179, 96, 192, 84, 180)(193, 289, 195, 291, 205, 301, 234, 330, 265, 361, 224, 320, 216, 312, 198, 294)(194, 290, 200, 296, 220, 316, 207, 303, 238, 334, 249, 345, 226, 322, 202, 298)(196, 292, 206, 302, 235, 331, 266, 362, 255, 351, 217, 313, 199, 295, 208, 304)(197, 293, 211, 307, 248, 344, 222, 318, 251, 347, 214, 310, 243, 339, 213, 309)(201, 297, 221, 317, 262, 358, 239, 335, 267, 363, 227, 323, 203, 299, 223, 319)(204, 300, 229, 325, 270, 366, 236, 332, 225, 321, 257, 353, 273, 369, 231, 327)(209, 305, 241, 337, 212, 308, 237, 333, 277, 373, 252, 348, 282, 378, 242, 338)(210, 306, 244, 340, 283, 379, 281, 377, 278, 374, 240, 336, 275, 371, 246, 342)(215, 311, 233, 329, 274, 370, 245, 341, 247, 343, 254, 350, 279, 375, 253, 349)(218, 314, 232, 328, 272, 368, 230, 326, 271, 367, 264, 360, 276, 372, 256, 352)(219, 315, 258, 354, 284, 380, 263, 359, 250, 346, 269, 365, 287, 383, 260, 356)(228, 324, 261, 357, 286, 382, 259, 355, 285, 381, 280, 376, 288, 384, 268, 364)
	L = (1, 196)(2, 201)(3, 206)(4, 205)(5, 212)(6, 208)(7, 193)(8, 221)(9, 220)(10, 223)(11, 194)(12, 230)(13, 235)(14, 234)(15, 239)(16, 195)(17, 197)(18, 245)(19, 237)(20, 248)(21, 241)(22, 242)(23, 246)(24, 199)(25, 198)(26, 231)(27, 259)(28, 262)(29, 207)(30, 252)(31, 200)(32, 217)(33, 256)(34, 203)(35, 202)(36, 260)(37, 271)(38, 270)(39, 272)(40, 204)(41, 210)(42, 266)(43, 265)(44, 276)(45, 222)(46, 267)(47, 249)(48, 215)(49, 211)(50, 213)(51, 209)(52, 247)(53, 283)(54, 274)(55, 281)(56, 277)(57, 227)(58, 268)(59, 282)(60, 214)(61, 275)(62, 278)(63, 216)(64, 273)(65, 218)(66, 285)(67, 284)(68, 286)(69, 219)(70, 238)(71, 288)(72, 225)(73, 255)(74, 224)(75, 226)(76, 287)(77, 228)(78, 264)(79, 236)(80, 229)(81, 232)(82, 244)(83, 233)(84, 257)(85, 251)(86, 253)(87, 240)(88, 250)(89, 279)(90, 243)(91, 254)(92, 280)(93, 263)(94, 258)(95, 261)(96, 269)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 4^6 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E27.1798
Graph:: simple bipartite
	v = 44 e = 192 f = 96
	degree seq :: [ 6^32, 16^12 ]

E27.1806 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^2 * T2^-3, T2^-1 * T1^2 * T2 * T1^2, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 15, 28, 11, 27, 14, 26)(19, 29, 23, 32, 21, 31, 22, 30)(33, 41, 36, 44, 34, 43, 35, 42)(37, 45, 40, 48, 38, 47, 39, 46)(49, 57, 52, 60, 50, 59, 51, 58)(53, 61, 56, 64, 54, 63, 55, 62)(65, 73, 68, 76, 66, 75, 67, 74)(69, 77, 72, 80, 70, 79, 71, 78)(81, 89, 84, 92, 82, 91, 83, 90)(85, 93, 88, 96, 86, 95, 87, 94)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 116, 112, 120)(121, 129, 123, 130)(122, 131, 124, 132)(125, 133, 127, 134)(126, 135, 128, 136)(137, 145, 139, 146)(138, 147, 140, 148)(141, 149, 143, 150)(142, 151, 144, 152)(153, 161, 155, 162)(154, 163, 156, 164)(157, 165, 159, 166)(158, 167, 160, 168)(169, 177, 171, 178)(170, 179, 172, 180)(173, 181, 175, 182)(174, 183, 176, 184)(185, 191, 187, 189)(186, 192, 188, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1810
Transitivity :: ET+
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1807 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1^-1)^2, (T1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2 * T1^-2, (T2^-3 * T1^-1)^2, (T2^-1 * T1^-1)^4, T1^8, T2^12, T2^5 * T1 * T2^-1 * T1^-1 * T2^4 * T1^-1 * T2^-2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 25, 48, 64, 80, 68, 52, 33, 15, 5)(2, 7, 20, 41, 57, 73, 88, 76, 60, 44, 22, 8)(4, 11, 26, 49, 65, 81, 93, 79, 63, 47, 30, 13)(6, 17, 37, 53, 69, 84, 94, 85, 70, 54, 38, 18)(9, 16, 35, 32, 51, 67, 83, 91, 77, 61, 45, 23)(12, 21, 42, 58, 74, 89, 96, 87, 72, 56, 40, 28)(14, 31, 50, 66, 82, 92, 78, 62, 46, 24, 36, 27)(19, 34, 29, 43, 59, 75, 90, 95, 86, 71, 55, 39)(97, 98, 102, 112, 130, 123, 108, 100)(99, 105, 113, 132, 125, 109, 117, 104)(101, 107, 114, 103, 115, 131, 124, 110)(106, 120, 133, 126, 139, 118, 138, 119)(111, 127, 134, 122, 135, 116, 136, 128)(121, 143, 149, 140, 155, 141, 154, 142)(129, 147, 150, 146, 151, 145, 152, 137)(144, 156, 165, 157, 171, 158, 170, 159)(148, 153, 166, 163, 167, 162, 168, 161)(160, 173, 180, 174, 186, 175, 185, 172)(164, 177, 181, 169, 182, 179, 183, 178)(176, 188, 190, 189, 191, 184, 192, 187)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1811
Transitivity :: ET+
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1808 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, (T2 * T1^-2)^2, (T2^-1 * T1^-2)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1, T1^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 32, 46, 25)(17, 36, 56, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 47, 34, 48)(33, 51, 64, 49)(35, 54, 72, 55)(39, 59, 40, 60)(45, 62, 50, 63)(52, 61, 78, 66)(53, 70, 86, 71)(57, 75, 58, 76)(65, 79, 67, 80)(68, 81, 93, 83)(69, 84, 94, 85)(73, 89, 74, 90)(77, 91, 82, 92)(87, 95, 88, 96)(97, 98, 102, 113, 131, 149, 165, 164, 148, 129, 109, 100)(99, 105, 121, 141, 157, 173, 181, 169, 150, 136, 115, 107)(101, 111, 128, 146, 162, 178, 180, 170, 151, 135, 114, 112)(103, 116, 110, 130, 147, 163, 179, 183, 166, 154, 133, 118)(104, 119, 108, 127, 145, 161, 177, 184, 167, 153, 132, 120)(106, 117, 134, 152, 168, 182, 190, 189, 174, 160, 142, 124)(122, 137, 126, 140, 156, 172, 186, 192, 187, 176, 159, 143)(123, 138, 125, 139, 155, 171, 185, 191, 188, 175, 158, 144)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1809
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1809 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^2 * T2^-3, T2^-1 * T1^2 * T2 * T1^2, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 18, 114, 6, 102, 17, 113, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 13, 109, 4, 100, 12, 108, 24, 120, 8, 104)(9, 105, 25, 121, 15, 111, 28, 124, 11, 107, 27, 123, 14, 110, 26, 122)(19, 115, 29, 125, 23, 119, 32, 128, 21, 117, 31, 127, 22, 118, 30, 126)(33, 129, 41, 137, 36, 132, 44, 140, 34, 130, 43, 139, 35, 131, 42, 138)(37, 133, 45, 141, 40, 136, 48, 144, 38, 134, 47, 143, 39, 135, 46, 142)(49, 145, 57, 153, 52, 148, 60, 156, 50, 146, 59, 155, 51, 147, 58, 154)(53, 149, 61, 157, 56, 152, 64, 160, 54, 150, 63, 159, 55, 151, 62, 158)(65, 161, 73, 169, 68, 164, 76, 172, 66, 162, 75, 171, 67, 163, 74, 170)(69, 165, 77, 173, 72, 168, 80, 176, 70, 166, 79, 175, 71, 167, 78, 174)(81, 177, 89, 185, 84, 180, 92, 188, 82, 178, 91, 187, 83, 179, 90, 186)(85, 181, 93, 189, 88, 184, 96, 192, 86, 182, 95, 191, 87, 183, 94, 190)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 129)(26, 131)(27, 130)(28, 132)(29, 133)(30, 135)(31, 134)(32, 136)(33, 123)(34, 121)(35, 124)(36, 122)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 191)(90, 192)(91, 189)(92, 190)(93, 185)(94, 186)(95, 187)(96, 188)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1808
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1810 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1^-1)^2, (T1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2 * T1^-2, (T2^-3 * T1^-1)^2, (T2^-1 * T1^-1)^4, T1^8, T2^12, T2^5 * T1 * T2^-1 * T1^-1 * T2^4 * T1^-1 * T2^-2 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 25, 121, 48, 144, 64, 160, 80, 176, 68, 164, 52, 148, 33, 129, 15, 111, 5, 101)(2, 98, 7, 103, 20, 116, 41, 137, 57, 153, 73, 169, 88, 184, 76, 172, 60, 156, 44, 140, 22, 118, 8, 104)(4, 100, 11, 107, 26, 122, 49, 145, 65, 161, 81, 177, 93, 189, 79, 175, 63, 159, 47, 143, 30, 126, 13, 109)(6, 102, 17, 113, 37, 133, 53, 149, 69, 165, 84, 180, 94, 190, 85, 181, 70, 166, 54, 150, 38, 134, 18, 114)(9, 105, 16, 112, 35, 131, 32, 128, 51, 147, 67, 163, 83, 179, 91, 187, 77, 173, 61, 157, 45, 141, 23, 119)(12, 108, 21, 117, 42, 138, 58, 154, 74, 170, 89, 185, 96, 192, 87, 183, 72, 168, 56, 152, 40, 136, 28, 124)(14, 110, 31, 127, 50, 146, 66, 162, 82, 178, 92, 188, 78, 174, 62, 158, 46, 142, 24, 120, 36, 132, 27, 123)(19, 115, 34, 130, 29, 125, 43, 139, 59, 155, 75, 171, 90, 186, 95, 191, 86, 182, 71, 167, 55, 151, 39, 135)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 112)(7, 115)(8, 99)(9, 113)(10, 120)(11, 114)(12, 100)(13, 117)(14, 101)(15, 127)(16, 130)(17, 132)(18, 103)(19, 131)(20, 136)(21, 104)(22, 138)(23, 106)(24, 133)(25, 143)(26, 135)(27, 108)(28, 110)(29, 109)(30, 139)(31, 134)(32, 111)(33, 147)(34, 123)(35, 124)(36, 125)(37, 126)(38, 122)(39, 116)(40, 128)(41, 129)(42, 119)(43, 118)(44, 155)(45, 154)(46, 121)(47, 149)(48, 156)(49, 152)(50, 151)(51, 150)(52, 153)(53, 140)(54, 146)(55, 145)(56, 137)(57, 166)(58, 142)(59, 141)(60, 165)(61, 171)(62, 170)(63, 144)(64, 173)(65, 148)(66, 168)(67, 167)(68, 177)(69, 157)(70, 163)(71, 162)(72, 161)(73, 182)(74, 159)(75, 158)(76, 160)(77, 180)(78, 186)(79, 185)(80, 188)(81, 181)(82, 164)(83, 183)(84, 174)(85, 169)(86, 179)(87, 178)(88, 192)(89, 172)(90, 175)(91, 176)(92, 190)(93, 191)(94, 189)(95, 184)(96, 187)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1806
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1811 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1 * T2^-2 * T1^-1, (T2 * T1^-2)^2, (T2^-1 * T1^-2)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1, T1^12 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 32, 128, 46, 142, 25, 121)(17, 113, 36, 132, 56, 152, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 47, 143, 34, 130, 48, 144)(33, 129, 51, 147, 64, 160, 49, 145)(35, 131, 54, 150, 72, 168, 55, 151)(39, 135, 59, 155, 40, 136, 60, 156)(45, 141, 62, 158, 50, 146, 63, 159)(52, 148, 61, 157, 78, 174, 66, 162)(53, 149, 70, 166, 86, 182, 71, 167)(57, 153, 75, 171, 58, 154, 76, 172)(65, 161, 79, 175, 67, 163, 80, 176)(68, 164, 81, 177, 93, 189, 83, 179)(69, 165, 84, 180, 94, 190, 85, 181)(73, 169, 89, 185, 74, 170, 90, 186)(77, 173, 91, 187, 82, 178, 92, 188)(87, 183, 95, 191, 88, 184, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 128)(16, 101)(17, 131)(18, 112)(19, 107)(20, 110)(21, 134)(22, 103)(23, 108)(24, 104)(25, 141)(26, 137)(27, 138)(28, 106)(29, 139)(30, 140)(31, 145)(32, 146)(33, 109)(34, 147)(35, 149)(36, 120)(37, 118)(38, 152)(39, 114)(40, 115)(41, 126)(42, 125)(43, 155)(44, 156)(45, 157)(46, 124)(47, 122)(48, 123)(49, 161)(50, 162)(51, 163)(52, 129)(53, 165)(54, 136)(55, 135)(56, 168)(57, 132)(58, 133)(59, 171)(60, 172)(61, 173)(62, 144)(63, 143)(64, 142)(65, 177)(66, 178)(67, 179)(68, 148)(69, 164)(70, 154)(71, 153)(72, 182)(73, 150)(74, 151)(75, 185)(76, 186)(77, 181)(78, 160)(79, 158)(80, 159)(81, 184)(82, 180)(83, 183)(84, 170)(85, 169)(86, 190)(87, 166)(88, 167)(89, 191)(90, 192)(91, 176)(92, 175)(93, 174)(94, 189)(95, 188)(96, 187)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1807
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1812 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y3 * Y1^-3, Y1^4, Y1 * Y3^-1 * Y1^2, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1^-1)^2, Y2^4 * Y1^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 20, 116, 16, 112, 24, 120)(25, 121, 33, 129, 27, 123, 34, 130)(26, 122, 35, 131, 28, 124, 36, 132)(29, 125, 37, 133, 31, 127, 38, 134)(30, 126, 39, 135, 32, 128, 40, 136)(41, 137, 49, 145, 43, 139, 50, 146)(42, 138, 51, 147, 44, 140, 52, 148)(45, 141, 53, 149, 47, 143, 54, 150)(46, 142, 55, 151, 48, 144, 56, 152)(57, 153, 65, 161, 59, 155, 66, 162)(58, 154, 67, 163, 60, 156, 68, 164)(61, 157, 69, 165, 63, 159, 70, 166)(62, 158, 71, 167, 64, 160, 72, 168)(73, 169, 81, 177, 75, 171, 82, 178)(74, 170, 83, 179, 76, 172, 84, 180)(77, 173, 85, 181, 79, 175, 86, 182)(78, 174, 87, 183, 80, 176, 88, 184)(89, 185, 95, 191, 91, 187, 93, 189)(90, 186, 96, 192, 92, 188, 94, 190)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 207, 303, 220, 316, 203, 299, 219, 315, 206, 302, 218, 314)(211, 307, 221, 317, 215, 311, 224, 320, 213, 309, 223, 319, 214, 310, 222, 318)(225, 321, 233, 329, 228, 324, 236, 332, 226, 322, 235, 331, 227, 323, 234, 330)(229, 325, 237, 333, 232, 328, 240, 336, 230, 326, 239, 335, 231, 327, 238, 334)(241, 337, 249, 345, 244, 340, 252, 348, 242, 338, 251, 347, 243, 339, 250, 346)(245, 341, 253, 349, 248, 344, 256, 352, 246, 342, 255, 351, 247, 343, 254, 350)(257, 353, 265, 361, 260, 356, 268, 364, 258, 354, 267, 363, 259, 355, 266, 362)(261, 357, 269, 365, 264, 360, 272, 368, 262, 358, 271, 367, 263, 359, 270, 366)(273, 369, 281, 377, 276, 372, 284, 380, 274, 370, 283, 379, 275, 371, 282, 378)(277, 373, 285, 381, 280, 376, 288, 384, 278, 374, 287, 383, 279, 375, 286, 382)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 216)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 212)(17, 201)(18, 206)(19, 199)(20, 202)(21, 204)(22, 200)(23, 205)(24, 208)(25, 226)(26, 228)(27, 225)(28, 227)(29, 230)(30, 232)(31, 229)(32, 231)(33, 217)(34, 219)(35, 218)(36, 220)(37, 221)(38, 223)(39, 222)(40, 224)(41, 242)(42, 244)(43, 241)(44, 243)(45, 246)(46, 248)(47, 245)(48, 247)(49, 233)(50, 235)(51, 234)(52, 236)(53, 237)(54, 239)(55, 238)(56, 240)(57, 258)(58, 260)(59, 257)(60, 259)(61, 262)(62, 264)(63, 261)(64, 263)(65, 249)(66, 251)(67, 250)(68, 252)(69, 253)(70, 255)(71, 254)(72, 256)(73, 274)(74, 276)(75, 273)(76, 275)(77, 278)(78, 280)(79, 277)(80, 279)(81, 265)(82, 267)(83, 266)(84, 268)(85, 269)(86, 271)(87, 270)(88, 272)(89, 285)(90, 286)(91, 287)(92, 288)(93, 283)(94, 284)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1815
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1813 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1^-1)^2, (Y1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, (Y2^-1 * Y1^-1)^4, (Y3^-1 * Y1^-1)^4, (Y2^-3 * Y1^-1)^2, Y1^8, Y2^12, Y2^5 * Y1 * Y2^-1 * Y1^-1 * Y2^4 * Y1^-1 * Y2^-2 * Y1^-1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 27, 123, 12, 108, 4, 100)(3, 99, 9, 105, 17, 113, 36, 132, 29, 125, 13, 109, 21, 117, 8, 104)(5, 101, 11, 107, 18, 114, 7, 103, 19, 115, 35, 131, 28, 124, 14, 110)(10, 106, 24, 120, 37, 133, 30, 126, 43, 139, 22, 118, 42, 138, 23, 119)(15, 111, 31, 127, 38, 134, 26, 122, 39, 135, 20, 116, 40, 136, 32, 128)(25, 121, 47, 143, 53, 149, 44, 140, 59, 155, 45, 141, 58, 154, 46, 142)(33, 129, 51, 147, 54, 150, 50, 146, 55, 151, 49, 145, 56, 152, 41, 137)(48, 144, 60, 156, 69, 165, 61, 157, 75, 171, 62, 158, 74, 170, 63, 159)(52, 148, 57, 153, 70, 166, 67, 163, 71, 167, 66, 162, 72, 168, 65, 161)(64, 160, 77, 173, 84, 180, 78, 174, 90, 186, 79, 175, 89, 185, 76, 172)(68, 164, 81, 177, 85, 181, 73, 169, 86, 182, 83, 179, 87, 183, 82, 178)(80, 176, 92, 188, 94, 190, 93, 189, 95, 191, 88, 184, 96, 192, 91, 187)(193, 289, 195, 291, 202, 298, 217, 313, 240, 336, 256, 352, 272, 368, 260, 356, 244, 340, 225, 321, 207, 303, 197, 293)(194, 290, 199, 295, 212, 308, 233, 329, 249, 345, 265, 361, 280, 376, 268, 364, 252, 348, 236, 332, 214, 310, 200, 296)(196, 292, 203, 299, 218, 314, 241, 337, 257, 353, 273, 369, 285, 381, 271, 367, 255, 351, 239, 335, 222, 318, 205, 301)(198, 294, 209, 305, 229, 325, 245, 341, 261, 357, 276, 372, 286, 382, 277, 373, 262, 358, 246, 342, 230, 326, 210, 306)(201, 297, 208, 304, 227, 323, 224, 320, 243, 339, 259, 355, 275, 371, 283, 379, 269, 365, 253, 349, 237, 333, 215, 311)(204, 300, 213, 309, 234, 330, 250, 346, 266, 362, 281, 377, 288, 384, 279, 375, 264, 360, 248, 344, 232, 328, 220, 316)(206, 302, 223, 319, 242, 338, 258, 354, 274, 370, 284, 380, 270, 366, 254, 350, 238, 334, 216, 312, 228, 324, 219, 315)(211, 307, 226, 322, 221, 317, 235, 331, 251, 347, 267, 363, 282, 378, 287, 383, 278, 374, 263, 359, 247, 343, 231, 327)
	L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 209)(7, 212)(8, 194)(9, 208)(10, 217)(11, 218)(12, 213)(13, 196)(14, 223)(15, 197)(16, 227)(17, 229)(18, 198)(19, 226)(20, 233)(21, 234)(22, 200)(23, 201)(24, 228)(25, 240)(26, 241)(27, 206)(28, 204)(29, 235)(30, 205)(31, 242)(32, 243)(33, 207)(34, 221)(35, 224)(36, 219)(37, 245)(38, 210)(39, 211)(40, 220)(41, 249)(42, 250)(43, 251)(44, 214)(45, 215)(46, 216)(47, 222)(48, 256)(49, 257)(50, 258)(51, 259)(52, 225)(53, 261)(54, 230)(55, 231)(56, 232)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 248)(73, 280)(74, 281)(75, 282)(76, 252)(77, 253)(78, 254)(79, 255)(80, 260)(81, 285)(82, 284)(83, 283)(84, 286)(85, 262)(86, 263)(87, 264)(88, 268)(89, 288)(90, 287)(91, 269)(92, 270)(93, 271)(94, 277)(95, 278)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1814
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1814 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3 * Y2^-2 * Y3^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4 * Y2 * Y3^-8 * Y2^-1, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 227, 323, 216, 312)(208, 304, 223, 319, 228, 324, 212, 308)(217, 313, 229, 325, 221, 317, 232, 328)(218, 314, 234, 330, 222, 318, 235, 331)(220, 316, 239, 335, 245, 341, 237, 333)(224, 320, 230, 326, 225, 321, 233, 329)(226, 322, 243, 339, 246, 342, 242, 338)(231, 327, 248, 344, 241, 337, 247, 343)(236, 332, 251, 347, 238, 334, 250, 346)(240, 336, 252, 348, 261, 357, 254, 350)(244, 340, 249, 345, 262, 358, 257, 353)(253, 349, 267, 363, 255, 351, 266, 362)(256, 352, 269, 365, 276, 372, 271, 367)(258, 354, 264, 360, 259, 355, 263, 359)(260, 356, 274, 370, 277, 373, 275, 371)(265, 361, 278, 374, 273, 369, 279, 375)(268, 364, 281, 377, 270, 366, 282, 378)(272, 368, 284, 380, 286, 382, 280, 376)(283, 379, 288, 384, 285, 381, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 207)(26, 201)(27, 205)(28, 240)(29, 206)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 215)(38, 211)(39, 249)(40, 214)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 219)(47, 222)(48, 256)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 233)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 248)(73, 280)(74, 281)(75, 282)(76, 252)(77, 253)(78, 254)(79, 255)(80, 260)(81, 284)(82, 285)(83, 283)(84, 286)(85, 262)(86, 263)(87, 264)(88, 268)(89, 288)(90, 287)(91, 269)(92, 270)(93, 271)(94, 277)(95, 278)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1813
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1815 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y1^12, (Y1 * Y3 * Y1 * Y3^-1)^4 ]
Map:: polytopal
	R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 68, 164, 52, 148, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 61, 157, 77, 173, 85, 181, 73, 169, 54, 150, 40, 136, 19, 115, 11, 107)(5, 101, 15, 111, 32, 128, 50, 146, 66, 162, 82, 178, 84, 180, 74, 170, 55, 151, 39, 135, 18, 114, 16, 112)(7, 103, 20, 116, 14, 110, 34, 130, 51, 147, 67, 163, 83, 179, 87, 183, 70, 166, 58, 154, 37, 133, 22, 118)(8, 104, 23, 119, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 88, 184, 71, 167, 57, 153, 36, 132, 24, 120)(10, 106, 21, 117, 38, 134, 56, 152, 72, 168, 86, 182, 94, 190, 93, 189, 78, 174, 64, 160, 46, 142, 28, 124)(26, 122, 41, 137, 30, 126, 44, 140, 60, 156, 76, 172, 90, 186, 96, 192, 91, 187, 80, 176, 63, 159, 47, 143)(27, 123, 42, 138, 29, 125, 43, 139, 59, 155, 75, 171, 89, 185, 95, 191, 92, 188, 79, 175, 62, 158, 48, 144)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 224)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 205)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 239)(32, 238)(33, 243)(34, 240)(35, 246)(36, 248)(37, 209)(38, 211)(39, 251)(40, 252)(41, 215)(42, 212)(43, 216)(44, 214)(45, 254)(46, 217)(47, 226)(48, 223)(49, 225)(50, 255)(51, 256)(52, 253)(53, 262)(54, 264)(55, 227)(56, 229)(57, 267)(58, 268)(59, 232)(60, 231)(61, 270)(62, 242)(63, 237)(64, 241)(65, 271)(66, 244)(67, 272)(68, 273)(69, 276)(70, 278)(71, 245)(72, 247)(73, 281)(74, 282)(75, 250)(76, 249)(77, 283)(78, 258)(79, 259)(80, 257)(81, 285)(82, 284)(83, 260)(84, 286)(85, 261)(86, 263)(87, 287)(88, 288)(89, 266)(90, 265)(91, 274)(92, 269)(93, 275)(94, 277)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1812
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1816 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2 * Y1 * Y2, Y2^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 35, 131, 24, 120)(16, 112, 31, 127, 36, 132, 20, 116)(25, 121, 37, 133, 29, 125, 40, 136)(26, 122, 42, 138, 30, 126, 43, 139)(28, 124, 47, 143, 53, 149, 45, 141)(32, 128, 38, 134, 33, 129, 41, 137)(34, 130, 51, 147, 54, 150, 50, 146)(39, 135, 56, 152, 49, 145, 55, 151)(44, 140, 59, 155, 46, 142, 58, 154)(48, 144, 60, 156, 69, 165, 62, 158)(52, 148, 57, 153, 70, 166, 65, 161)(61, 157, 75, 171, 63, 159, 74, 170)(64, 160, 77, 173, 84, 180, 79, 175)(66, 162, 72, 168, 67, 163, 71, 167)(68, 164, 82, 178, 85, 181, 83, 179)(73, 169, 86, 182, 81, 177, 87, 183)(76, 172, 89, 185, 78, 174, 90, 186)(80, 176, 92, 188, 94, 190, 88, 184)(91, 187, 96, 192, 93, 189, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 240, 336, 256, 352, 272, 368, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 249, 345, 265, 361, 280, 376, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 284, 380, 270, 366, 254, 350, 238, 334, 219, 315, 205, 301)(198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 276, 372, 286, 382, 277, 373, 262, 358, 246, 342, 228, 324, 210, 306)(201, 297, 217, 313, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 283, 379, 269, 365, 253, 349, 237, 333, 218, 314)(203, 299, 221, 317, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 285, 381, 271, 367, 255, 351, 239, 335, 222, 318)(211, 307, 229, 325, 215, 311, 235, 331, 251, 347, 267, 363, 282, 378, 287, 383, 278, 374, 263, 359, 247, 343, 230, 326)(213, 309, 232, 328, 214, 310, 234, 330, 250, 346, 266, 362, 281, 377, 288, 384, 279, 375, 264, 360, 248, 344, 233, 329)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 216)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 212)(17, 201)(18, 206)(19, 199)(20, 228)(21, 204)(22, 200)(23, 205)(24, 227)(25, 232)(26, 235)(27, 202)(28, 237)(29, 229)(30, 234)(31, 208)(32, 233)(33, 230)(34, 242)(35, 219)(36, 223)(37, 217)(38, 224)(39, 247)(40, 221)(41, 225)(42, 218)(43, 222)(44, 250)(45, 245)(46, 251)(47, 220)(48, 254)(49, 248)(50, 246)(51, 226)(52, 257)(53, 239)(54, 243)(55, 241)(56, 231)(57, 244)(58, 238)(59, 236)(60, 240)(61, 266)(62, 261)(63, 267)(64, 271)(65, 262)(66, 263)(67, 264)(68, 275)(69, 252)(70, 249)(71, 259)(72, 258)(73, 279)(74, 255)(75, 253)(76, 282)(77, 256)(78, 281)(79, 276)(80, 280)(81, 278)(82, 260)(83, 277)(84, 269)(85, 274)(86, 265)(87, 273)(88, 286)(89, 268)(90, 270)(91, 287)(92, 272)(93, 288)(94, 284)(95, 285)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1817
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1817 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C12 x C4) : C2 (small group id <96, 12>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (Y1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (Y3^-3 * Y1^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^4, Y3^6 * Y1^-2 * Y3^4 * Y1^-1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 16, 112, 34, 130, 27, 123, 12, 108, 4, 100)(3, 99, 9, 105, 17, 113, 36, 132, 29, 125, 13, 109, 21, 117, 8, 104)(5, 101, 11, 107, 18, 114, 7, 103, 19, 115, 35, 131, 28, 124, 14, 110)(10, 106, 24, 120, 37, 133, 30, 126, 43, 139, 22, 118, 42, 138, 23, 119)(15, 111, 31, 127, 38, 134, 26, 122, 39, 135, 20, 116, 40, 136, 32, 128)(25, 121, 47, 143, 53, 149, 44, 140, 59, 155, 45, 141, 58, 154, 46, 142)(33, 129, 51, 147, 54, 150, 50, 146, 55, 151, 49, 145, 56, 152, 41, 137)(48, 144, 60, 156, 69, 165, 61, 157, 75, 171, 62, 158, 74, 170, 63, 159)(52, 148, 57, 153, 70, 166, 67, 163, 71, 167, 66, 162, 72, 168, 65, 161)(64, 160, 77, 173, 84, 180, 78, 174, 90, 186, 79, 175, 89, 185, 76, 172)(68, 164, 81, 177, 85, 181, 73, 169, 86, 182, 83, 179, 87, 183, 82, 178)(80, 176, 92, 188, 94, 190, 93, 189, 95, 191, 88, 184, 96, 192, 91, 187)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 209)(7, 212)(8, 194)(9, 208)(10, 217)(11, 218)(12, 213)(13, 196)(14, 223)(15, 197)(16, 227)(17, 229)(18, 198)(19, 226)(20, 233)(21, 234)(22, 200)(23, 201)(24, 228)(25, 240)(26, 241)(27, 206)(28, 204)(29, 235)(30, 205)(31, 242)(32, 243)(33, 207)(34, 221)(35, 224)(36, 219)(37, 245)(38, 210)(39, 211)(40, 220)(41, 249)(42, 250)(43, 251)(44, 214)(45, 215)(46, 216)(47, 222)(48, 256)(49, 257)(50, 258)(51, 259)(52, 225)(53, 261)(54, 230)(55, 231)(56, 232)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 248)(73, 280)(74, 281)(75, 282)(76, 252)(77, 253)(78, 254)(79, 255)(80, 260)(81, 285)(82, 284)(83, 283)(84, 286)(85, 262)(86, 263)(87, 264)(88, 268)(89, 288)(90, 287)(91, 269)(92, 270)(93, 271)(94, 277)(95, 278)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1816
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1818 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 50, 34, 16, 5)(2, 7, 20, 39, 65, 44, 24, 8)(4, 12, 31, 53, 78, 52, 28, 13)(6, 17, 35, 58, 82, 59, 36, 18)(9, 25, 14, 32, 55, 77, 49, 26)(11, 29, 15, 33, 57, 79, 51, 30)(19, 37, 22, 42, 68, 89, 64, 38)(21, 40, 23, 43, 70, 90, 66, 41)(45, 71, 47, 75, 93, 80, 54, 72)(46, 73, 48, 76, 94, 81, 56, 74)(60, 83, 62, 87, 95, 91, 67, 84)(61, 85, 63, 88, 96, 92, 69, 86)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 141, 125, 142)(122, 143, 126, 144)(123, 145, 154, 147)(128, 150, 129, 152)(130, 151, 155, 153)(133, 156, 136, 157)(134, 158, 137, 159)(135, 160, 149, 162)(138, 163, 139, 165)(140, 164, 148, 166)(146, 161, 178, 174)(167, 180, 169, 182)(168, 179, 170, 181)(171, 187, 172, 188)(173, 189, 175, 190)(176, 183, 177, 184)(185, 191, 186, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1822
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1819 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1, T2^2 * T1^-1 * T2^-3 * T1^-1 * T2, T1^8 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 50, 21, 49, 24, 54, 41, 17, 5)(2, 7, 22, 51, 33, 11, 32, 16, 40, 56, 26, 8)(4, 12, 35, 61, 29, 9, 28, 15, 39, 62, 31, 14)(6, 19, 45, 74, 53, 23, 52, 25, 55, 78, 48, 20)(13, 27, 58, 81, 64, 34, 59, 38, 60, 83, 65, 37)(18, 43, 70, 88, 76, 46, 75, 47, 77, 92, 73, 44)(36, 63, 84, 93, 80, 57, 79, 67, 85, 94, 82, 66)(42, 68, 86, 95, 90, 71, 89, 72, 91, 96, 87, 69)(97, 98, 102, 114, 138, 132, 109, 100)(99, 105, 123, 153, 164, 142, 115, 107)(101, 111, 133, 163, 165, 143, 116, 112)(103, 117, 108, 130, 159, 167, 139, 119)(104, 120, 110, 134, 162, 168, 140, 121)(106, 122, 141, 169, 182, 178, 154, 127)(113, 118, 144, 166, 183, 180, 161, 131)(124, 145, 128, 148, 171, 185, 175, 155)(125, 150, 129, 151, 172, 187, 176, 156)(126, 157, 177, 189, 191, 184, 170, 147)(135, 146, 136, 149, 173, 186, 181, 160)(137, 158, 179, 190, 192, 188, 174, 152)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1823
Transitivity :: ET+
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1820 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T1 * T2 * T1^2 * T2^-1 * T1, T1^3 * T2^-2 * T1^3, (T2 * T1^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 35, 33)(17, 36, 32, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 51, 34, 52)(39, 53, 40, 54)(45, 61, 47, 62)(46, 63, 48, 64)(49, 65, 50, 66)(55, 67, 57, 68)(56, 69, 58, 70)(59, 71, 60, 72)(73, 85, 75, 86)(74, 87, 76, 88)(77, 89, 78, 90)(79, 91, 81, 92)(80, 93, 82, 94)(83, 95, 84, 96)(97, 98, 102, 113, 131, 124, 106, 117, 134, 128, 109, 100)(99, 105, 121, 136, 115, 112, 101, 111, 129, 135, 114, 107)(103, 116, 108, 127, 133, 120, 104, 119, 110, 130, 132, 118)(122, 141, 125, 145, 149, 144, 123, 143, 126, 146, 150, 142)(137, 151, 139, 155, 148, 154, 138, 153, 140, 156, 147, 152)(157, 169, 159, 173, 162, 172, 158, 171, 160, 174, 161, 170)(163, 175, 165, 179, 168, 178, 164, 177, 166, 180, 167, 176)(181, 187, 183, 189, 186, 192, 182, 188, 184, 190, 185, 191)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1821
Transitivity :: ET+
Graph:: bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1821 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^12 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 27, 123, 50, 146, 34, 130, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 39, 135, 65, 161, 44, 140, 24, 120, 8, 104)(4, 100, 12, 108, 31, 127, 53, 149, 78, 174, 52, 148, 28, 124, 13, 109)(6, 102, 17, 113, 35, 131, 58, 154, 82, 178, 59, 155, 36, 132, 18, 114)(9, 105, 25, 121, 14, 110, 32, 128, 55, 151, 77, 173, 49, 145, 26, 122)(11, 107, 29, 125, 15, 111, 33, 129, 57, 153, 79, 175, 51, 147, 30, 126)(19, 115, 37, 133, 22, 118, 42, 138, 68, 164, 89, 185, 64, 160, 38, 134)(21, 117, 40, 136, 23, 119, 43, 139, 70, 166, 90, 186, 66, 162, 41, 137)(45, 141, 71, 167, 47, 143, 75, 171, 93, 189, 80, 176, 54, 150, 72, 168)(46, 142, 73, 169, 48, 144, 76, 172, 94, 190, 81, 177, 56, 152, 74, 170)(60, 156, 83, 179, 62, 158, 87, 183, 95, 191, 91, 187, 67, 163, 84, 180)(61, 157, 85, 181, 63, 159, 88, 184, 96, 192, 92, 188, 69, 165, 86, 182)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 132)(21, 103)(22, 109)(23, 104)(24, 131)(25, 141)(26, 143)(27, 145)(28, 106)(29, 142)(30, 144)(31, 112)(32, 150)(33, 152)(34, 151)(35, 124)(36, 127)(37, 156)(38, 158)(39, 160)(40, 157)(41, 159)(42, 163)(43, 165)(44, 164)(45, 125)(46, 121)(47, 126)(48, 122)(49, 154)(50, 161)(51, 123)(52, 166)(53, 162)(54, 129)(55, 155)(56, 128)(57, 130)(58, 147)(59, 153)(60, 136)(61, 133)(62, 137)(63, 134)(64, 149)(65, 178)(66, 135)(67, 139)(68, 148)(69, 138)(70, 140)(71, 180)(72, 179)(73, 182)(74, 181)(75, 187)(76, 188)(77, 189)(78, 146)(79, 190)(80, 183)(81, 184)(82, 174)(83, 170)(84, 169)(85, 168)(86, 167)(87, 177)(88, 176)(89, 191)(90, 192)(91, 172)(92, 171)(93, 175)(94, 173)(95, 186)(96, 185)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1820
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1822 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2^-2 * T1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1, T2^2 * T1^-1 * T2^-3 * T1^-1 * T2, T1^8 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 50, 146, 21, 117, 49, 145, 24, 120, 54, 150, 41, 137, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 51, 147, 33, 129, 11, 107, 32, 128, 16, 112, 40, 136, 56, 152, 26, 122, 8, 104)(4, 100, 12, 108, 35, 131, 61, 157, 29, 125, 9, 105, 28, 124, 15, 111, 39, 135, 62, 158, 31, 127, 14, 110)(6, 102, 19, 115, 45, 141, 74, 170, 53, 149, 23, 119, 52, 148, 25, 121, 55, 151, 78, 174, 48, 144, 20, 116)(13, 109, 27, 123, 58, 154, 81, 177, 64, 160, 34, 130, 59, 155, 38, 134, 60, 156, 83, 179, 65, 161, 37, 133)(18, 114, 43, 139, 70, 166, 88, 184, 76, 172, 46, 142, 75, 171, 47, 143, 77, 173, 92, 188, 73, 169, 44, 140)(36, 132, 63, 159, 84, 180, 93, 189, 80, 176, 57, 153, 79, 175, 67, 163, 85, 181, 94, 190, 82, 178, 66, 162)(42, 138, 68, 164, 86, 182, 95, 191, 90, 186, 71, 167, 89, 185, 72, 168, 91, 187, 96, 192, 87, 183, 69, 165)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 122)(11, 99)(12, 130)(13, 100)(14, 134)(15, 133)(16, 101)(17, 118)(18, 138)(19, 107)(20, 112)(21, 108)(22, 144)(23, 103)(24, 110)(25, 104)(26, 141)(27, 153)(28, 145)(29, 150)(30, 157)(31, 106)(32, 148)(33, 151)(34, 159)(35, 113)(36, 109)(37, 163)(38, 162)(39, 146)(40, 149)(41, 158)(42, 132)(43, 119)(44, 121)(45, 169)(46, 115)(47, 116)(48, 166)(49, 128)(50, 136)(51, 126)(52, 171)(53, 173)(54, 129)(55, 172)(56, 137)(57, 164)(58, 127)(59, 124)(60, 125)(61, 177)(62, 179)(63, 167)(64, 135)(65, 131)(66, 168)(67, 165)(68, 142)(69, 143)(70, 183)(71, 139)(72, 140)(73, 182)(74, 147)(75, 185)(76, 187)(77, 186)(78, 152)(79, 155)(80, 156)(81, 189)(82, 154)(83, 190)(84, 161)(85, 160)(86, 178)(87, 180)(88, 170)(89, 175)(90, 181)(91, 176)(92, 174)(93, 191)(94, 192)(95, 184)(96, 188)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1818
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1823 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T1 * T2 * T1^2 * T2^-1 * T1, T1^3 * T2^-2 * T1^3, (T2 * T1^-1)^8 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 25, 121, 35, 131, 33, 129)(17, 113, 36, 132, 32, 128, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 51, 147, 34, 130, 52, 148)(39, 135, 53, 149, 40, 136, 54, 150)(45, 141, 61, 157, 47, 143, 62, 158)(46, 142, 63, 159, 48, 144, 64, 160)(49, 145, 65, 161, 50, 146, 66, 162)(55, 151, 67, 163, 57, 153, 68, 164)(56, 152, 69, 165, 58, 154, 70, 166)(59, 155, 71, 167, 60, 156, 72, 168)(73, 169, 85, 181, 75, 171, 86, 182)(74, 170, 87, 183, 76, 172, 88, 184)(77, 173, 89, 185, 78, 174, 90, 186)(79, 175, 91, 187, 81, 177, 92, 188)(80, 176, 93, 189, 82, 178, 94, 190)(83, 179, 95, 191, 84, 180, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 129)(16, 101)(17, 131)(18, 107)(19, 112)(20, 108)(21, 134)(22, 103)(23, 110)(24, 104)(25, 136)(26, 141)(27, 143)(28, 106)(29, 145)(30, 146)(31, 133)(32, 109)(33, 135)(34, 132)(35, 124)(36, 118)(37, 120)(38, 128)(39, 114)(40, 115)(41, 151)(42, 153)(43, 155)(44, 156)(45, 125)(46, 122)(47, 126)(48, 123)(49, 149)(50, 150)(51, 152)(52, 154)(53, 144)(54, 142)(55, 139)(56, 137)(57, 140)(58, 138)(59, 148)(60, 147)(61, 169)(62, 171)(63, 173)(64, 174)(65, 170)(66, 172)(67, 175)(68, 177)(69, 179)(70, 180)(71, 176)(72, 178)(73, 159)(74, 157)(75, 160)(76, 158)(77, 162)(78, 161)(79, 165)(80, 163)(81, 166)(82, 164)(83, 168)(84, 167)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 183)(92, 184)(93, 186)(94, 185)(95, 181)(96, 182)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1819
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1824 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * R * Y2^-2 * R * Y2, Y2^8, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 58, 154, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 59, 155, 57, 153)(37, 133, 60, 156, 40, 136, 61, 157)(38, 134, 62, 158, 41, 137, 63, 159)(39, 135, 64, 160, 53, 149, 66, 162)(42, 138, 67, 163, 43, 139, 69, 165)(44, 140, 68, 164, 52, 148, 70, 166)(50, 146, 65, 161, 82, 178, 78, 174)(71, 167, 84, 180, 73, 169, 86, 182)(72, 168, 83, 179, 74, 170, 85, 181)(75, 171, 91, 187, 76, 172, 92, 188)(77, 173, 93, 189, 79, 175, 94, 190)(80, 176, 87, 183, 81, 177, 88, 184)(89, 185, 95, 191, 90, 186, 96, 192)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 257, 353, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 250, 346, 274, 370, 251, 347, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 269, 365, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 271, 367, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 260, 356, 281, 377, 256, 352, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 262, 358, 282, 378, 258, 354, 233, 329)(237, 333, 263, 359, 239, 335, 267, 363, 285, 381, 272, 368, 246, 342, 264, 360)(238, 334, 265, 361, 240, 336, 268, 364, 286, 382, 273, 369, 248, 344, 266, 362)(252, 348, 275, 371, 254, 350, 279, 375, 287, 383, 283, 379, 259, 355, 276, 372)(253, 349, 277, 373, 255, 351, 280, 376, 288, 384, 284, 380, 261, 357, 278, 374)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 253)(38, 255)(39, 258)(40, 252)(41, 254)(42, 261)(43, 259)(44, 262)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 250)(52, 260)(53, 256)(54, 224)(55, 226)(56, 225)(57, 251)(58, 241)(59, 247)(60, 229)(61, 232)(62, 230)(63, 233)(64, 231)(65, 242)(66, 245)(67, 234)(68, 236)(69, 235)(70, 244)(71, 278)(72, 277)(73, 276)(74, 275)(75, 284)(76, 283)(77, 286)(78, 274)(79, 285)(80, 280)(81, 279)(82, 257)(83, 264)(84, 263)(85, 266)(86, 265)(87, 272)(88, 273)(89, 288)(90, 287)(91, 267)(92, 268)(93, 269)(94, 271)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1827
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1825 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2^3 * Y1 * Y2^-3 * Y1, Y1^8, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 68, 164, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 67, 163, 69, 165, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 63, 159, 71, 167, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 66, 162, 72, 168, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 73, 169, 86, 182, 82, 178, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 70, 166, 87, 183, 84, 180, 65, 161, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 75, 171, 89, 185, 79, 175, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 76, 172, 91, 187, 80, 176, 60, 156)(30, 126, 61, 157, 81, 177, 93, 189, 95, 191, 88, 184, 74, 170, 51, 147)(39, 135, 50, 146, 40, 136, 53, 149, 77, 173, 90, 186, 85, 181, 64, 160)(41, 137, 62, 158, 83, 179, 94, 190, 96, 192, 92, 188, 78, 174, 56, 152)(193, 289, 195, 291, 202, 298, 222, 318, 242, 338, 213, 309, 241, 337, 216, 312, 246, 342, 233, 329, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 243, 339, 225, 321, 203, 299, 224, 320, 208, 304, 232, 328, 248, 344, 218, 314, 200, 296)(196, 292, 204, 300, 227, 323, 253, 349, 221, 317, 201, 297, 220, 316, 207, 303, 231, 327, 254, 350, 223, 319, 206, 302)(198, 294, 211, 307, 237, 333, 266, 362, 245, 341, 215, 311, 244, 340, 217, 313, 247, 343, 270, 366, 240, 336, 212, 308)(205, 301, 219, 315, 250, 346, 273, 369, 256, 352, 226, 322, 251, 347, 230, 326, 252, 348, 275, 371, 257, 353, 229, 325)(210, 306, 235, 331, 262, 358, 280, 376, 268, 364, 238, 334, 267, 363, 239, 335, 269, 365, 284, 380, 265, 361, 236, 332)(228, 324, 255, 351, 276, 372, 285, 381, 272, 368, 249, 345, 271, 367, 259, 355, 277, 373, 286, 382, 274, 370, 258, 354)(234, 330, 260, 356, 278, 374, 287, 383, 282, 378, 263, 359, 281, 377, 264, 360, 283, 379, 288, 384, 279, 375, 261, 357)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 242)(31, 206)(32, 208)(33, 203)(34, 251)(35, 253)(36, 255)(37, 205)(38, 252)(39, 254)(40, 248)(41, 209)(42, 260)(43, 262)(44, 210)(45, 266)(46, 267)(47, 269)(48, 212)(49, 216)(50, 213)(51, 225)(52, 217)(53, 215)(54, 233)(55, 270)(56, 218)(57, 271)(58, 273)(59, 230)(60, 275)(61, 221)(62, 223)(63, 276)(64, 226)(65, 229)(66, 228)(67, 277)(68, 278)(69, 234)(70, 280)(71, 281)(72, 283)(73, 236)(74, 245)(75, 239)(76, 238)(77, 284)(78, 240)(79, 259)(80, 249)(81, 256)(82, 258)(83, 257)(84, 285)(85, 286)(86, 287)(87, 261)(88, 268)(89, 264)(90, 263)(91, 288)(92, 265)(93, 272)(94, 274)(95, 282)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1826
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1826 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y3^-1 * Y2 * Y3^-2 * Y2^-1 * Y3^-1, Y3^3 * Y2^2 * Y3^3, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 237, 333, 221, 317, 238, 334)(218, 314, 239, 335, 222, 318, 240, 336)(219, 315, 241, 337, 226, 322, 242, 338)(224, 320, 243, 339, 225, 321, 244, 340)(229, 325, 245, 341, 232, 328, 246, 342)(230, 326, 247, 343, 233, 329, 248, 344)(231, 327, 249, 345, 236, 332, 250, 346)(234, 330, 251, 347, 235, 331, 252, 348)(253, 349, 265, 361, 255, 351, 266, 362)(254, 350, 267, 363, 256, 352, 268, 364)(257, 353, 269, 365, 258, 354, 270, 366)(259, 355, 271, 367, 261, 357, 272, 368)(260, 356, 273, 369, 262, 358, 274, 370)(263, 359, 275, 371, 264, 360, 276, 372)(277, 373, 283, 379, 279, 375, 285, 381)(278, 374, 287, 383, 280, 376, 288, 384)(281, 377, 284, 380, 282, 378, 286, 382)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 228)(28, 205)(29, 207)(30, 203)(31, 236)(32, 242)(33, 241)(34, 208)(35, 226)(36, 210)(37, 214)(38, 211)(39, 220)(40, 215)(41, 213)(42, 250)(43, 249)(44, 216)(45, 253)(46, 255)(47, 257)(48, 258)(49, 218)(50, 222)(51, 254)(52, 256)(53, 259)(54, 261)(55, 263)(56, 264)(57, 230)(58, 233)(59, 260)(60, 262)(61, 239)(62, 237)(63, 240)(64, 238)(65, 244)(66, 243)(67, 247)(68, 245)(69, 248)(70, 246)(71, 252)(72, 251)(73, 277)(74, 279)(75, 281)(76, 282)(77, 278)(78, 280)(79, 283)(80, 285)(81, 287)(82, 288)(83, 284)(84, 286)(85, 267)(86, 265)(87, 268)(88, 266)(89, 270)(90, 269)(91, 273)(92, 271)(93, 274)(94, 272)(95, 276)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1825
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1827 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y1^2 * Y3^-1 * Y1^2, Y1^-1 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-3, (Y3 * Y2^-1)^4, (Y3 * Y1^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 28, 124, 10, 106, 21, 117, 38, 134, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 40, 136, 19, 115, 16, 112, 5, 101, 15, 111, 33, 129, 39, 135, 18, 114, 11, 107)(7, 103, 20, 116, 12, 108, 31, 127, 37, 133, 24, 120, 8, 104, 23, 119, 14, 110, 34, 130, 36, 132, 22, 118)(26, 122, 45, 141, 29, 125, 49, 145, 53, 149, 48, 144, 27, 123, 47, 143, 30, 126, 50, 146, 54, 150, 46, 142)(41, 137, 55, 151, 43, 139, 59, 155, 52, 148, 58, 154, 42, 138, 57, 153, 44, 140, 60, 156, 51, 147, 56, 152)(61, 157, 73, 169, 63, 159, 77, 173, 66, 162, 76, 172, 62, 158, 75, 171, 64, 160, 78, 174, 65, 161, 74, 170)(67, 163, 79, 175, 69, 165, 83, 179, 72, 168, 82, 178, 68, 164, 81, 177, 70, 166, 84, 180, 71, 167, 80, 176)(85, 181, 91, 187, 87, 183, 93, 189, 90, 186, 96, 192, 86, 182, 92, 188, 88, 184, 94, 190, 89, 185, 95, 191)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 227)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 243)(32, 229)(33, 205)(34, 244)(35, 225)(36, 224)(37, 209)(38, 211)(39, 245)(40, 246)(41, 215)(42, 212)(43, 216)(44, 214)(45, 253)(46, 255)(47, 254)(48, 256)(49, 257)(50, 258)(51, 226)(52, 223)(53, 232)(54, 231)(55, 259)(56, 261)(57, 260)(58, 262)(59, 263)(60, 264)(61, 239)(62, 237)(63, 240)(64, 238)(65, 242)(66, 241)(67, 249)(68, 247)(69, 250)(70, 248)(71, 252)(72, 251)(73, 277)(74, 279)(75, 278)(76, 280)(77, 281)(78, 282)(79, 283)(80, 285)(81, 284)(82, 286)(83, 287)(84, 288)(85, 267)(86, 265)(87, 268)(88, 266)(89, 270)(90, 269)(91, 273)(92, 271)(93, 274)(94, 272)(95, 276)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1824
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1828 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, Y3^-1 * Y1^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y2^2 * Y1^-1 * Y2^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^4 * Y1 * Y2^-2 * Y1, (Y3 * Y2)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 34, 130, 50, 146)(32, 128, 51, 147, 33, 129, 52, 148)(37, 133, 53, 149, 40, 136, 54, 150)(38, 134, 55, 151, 41, 137, 56, 152)(39, 135, 57, 153, 44, 140, 58, 154)(42, 138, 59, 155, 43, 139, 60, 156)(61, 157, 73, 169, 63, 159, 74, 170)(62, 158, 75, 171, 64, 160, 76, 172)(65, 161, 77, 173, 66, 162, 78, 174)(67, 163, 79, 175, 69, 165, 80, 176)(68, 164, 81, 177, 70, 166, 82, 178)(71, 167, 83, 179, 72, 168, 84, 180)(85, 181, 91, 187, 87, 183, 93, 189)(86, 182, 95, 191, 88, 184, 96, 192)(89, 185, 92, 188, 90, 186, 94, 190)(193, 289, 195, 291, 202, 298, 219, 315, 228, 324, 210, 306, 198, 294, 209, 305, 227, 323, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 220, 316, 205, 301, 196, 292, 204, 300, 223, 319, 236, 332, 216, 312, 200, 296)(201, 297, 217, 313, 206, 302, 224, 320, 242, 338, 222, 318, 203, 299, 221, 317, 207, 303, 225, 321, 241, 337, 218, 314)(211, 307, 229, 325, 214, 310, 234, 330, 250, 346, 233, 329, 213, 309, 232, 328, 215, 311, 235, 331, 249, 345, 230, 326)(237, 333, 253, 349, 239, 335, 257, 353, 244, 340, 256, 352, 238, 334, 255, 351, 240, 336, 258, 354, 243, 339, 254, 350)(245, 341, 259, 355, 247, 343, 263, 359, 252, 348, 262, 358, 246, 342, 261, 357, 248, 344, 264, 360, 251, 347, 260, 356)(265, 361, 277, 373, 267, 363, 281, 377, 270, 366, 280, 376, 266, 362, 279, 375, 268, 364, 282, 378, 269, 365, 278, 374)(271, 367, 283, 379, 273, 369, 287, 383, 276, 372, 286, 382, 272, 368, 285, 381, 274, 370, 288, 384, 275, 371, 284, 380)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 242)(28, 227)(29, 237)(30, 239)(31, 228)(32, 244)(33, 243)(34, 241)(35, 216)(36, 212)(37, 246)(38, 248)(39, 250)(40, 245)(41, 247)(42, 252)(43, 251)(44, 249)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 226)(51, 224)(52, 225)(53, 229)(54, 232)(55, 230)(56, 233)(57, 231)(58, 236)(59, 234)(60, 235)(61, 266)(62, 268)(63, 265)(64, 267)(65, 270)(66, 269)(67, 272)(68, 274)(69, 271)(70, 273)(71, 276)(72, 275)(73, 253)(74, 255)(75, 254)(76, 256)(77, 257)(78, 258)(79, 259)(80, 261)(81, 260)(82, 262)(83, 263)(84, 264)(85, 285)(86, 288)(87, 283)(88, 287)(89, 286)(90, 284)(91, 277)(92, 281)(93, 279)(94, 282)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1829
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1829 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 14>)
Aut   = $<192, 334>$ (small group id <192, 334>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, Y3^2 * Y1^-1 * Y3^-3 * Y1^-1 * Y3, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y1^8, (Y3 * Y2^-1)^12 ]
Map:: polytopal
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 68, 164, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 67, 163, 69, 165, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 63, 159, 71, 167, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 66, 162, 72, 168, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 73, 169, 86, 182, 82, 178, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 70, 166, 87, 183, 84, 180, 65, 161, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 75, 171, 89, 185, 79, 175, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 76, 172, 91, 187, 80, 176, 60, 156)(30, 126, 61, 157, 81, 177, 93, 189, 95, 191, 88, 184, 74, 170, 51, 147)(39, 135, 50, 146, 40, 136, 53, 149, 77, 173, 90, 186, 85, 181, 64, 160)(41, 137, 62, 158, 83, 179, 94, 190, 96, 192, 92, 188, 78, 174, 56, 152)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 242)(31, 206)(32, 208)(33, 203)(34, 251)(35, 253)(36, 255)(37, 205)(38, 252)(39, 254)(40, 248)(41, 209)(42, 260)(43, 262)(44, 210)(45, 266)(46, 267)(47, 269)(48, 212)(49, 216)(50, 213)(51, 225)(52, 217)(53, 215)(54, 233)(55, 270)(56, 218)(57, 271)(58, 273)(59, 230)(60, 275)(61, 221)(62, 223)(63, 276)(64, 226)(65, 229)(66, 228)(67, 277)(68, 278)(69, 234)(70, 280)(71, 281)(72, 283)(73, 236)(74, 245)(75, 239)(76, 238)(77, 284)(78, 240)(79, 259)(80, 249)(81, 256)(82, 258)(83, 257)(84, 285)(85, 286)(86, 287)(87, 261)(88, 268)(89, 264)(90, 263)(91, 288)(92, 265)(93, 272)(94, 274)(95, 282)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1828
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1830 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^12 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 27, 50, 34, 16, 5)(2, 7, 20, 39, 65, 44, 24, 8)(4, 12, 31, 53, 78, 52, 28, 13)(6, 17, 35, 58, 82, 59, 36, 18)(9, 25, 14, 32, 55, 77, 49, 26)(11, 29, 15, 33, 57, 79, 51, 30)(19, 37, 22, 42, 68, 89, 64, 38)(21, 40, 23, 43, 70, 90, 66, 41)(45, 71, 47, 75, 93, 80, 54, 72)(46, 73, 48, 76, 94, 81, 56, 74)(60, 83, 62, 87, 95, 91, 67, 84)(61, 85, 63, 88, 96, 92, 69, 86)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 141, 125, 142)(122, 143, 126, 144)(123, 145, 154, 147)(128, 150, 129, 152)(130, 151, 155, 153)(133, 156, 136, 157)(134, 158, 137, 159)(135, 160, 149, 162)(138, 163, 139, 165)(140, 164, 148, 166)(146, 161, 178, 174)(167, 183, 169, 184)(168, 187, 170, 188)(171, 179, 172, 181)(173, 189, 175, 190)(176, 180, 177, 182)(185, 191, 186, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1834
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1831 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^2 * T1^-1, T2^-1 * T1^-2 * T2 * T1^-2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^8, T1^-3 * T2^-1 * T1 * T2^5, T1^-2 * T2 * T1 * T2^-5 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 30, 62, 77, 96, 78, 73, 41, 17, 5)(2, 7, 22, 51, 86, 57, 91, 70, 90, 56, 26, 8)(4, 12, 35, 67, 82, 46, 81, 47, 83, 64, 31, 14)(6, 19, 45, 80, 66, 34, 59, 38, 60, 84, 48, 20)(9, 28, 15, 39, 71, 79, 44, 18, 43, 76, 61, 29)(11, 32, 16, 40, 72, 92, 69, 36, 65, 93, 63, 33)(13, 27, 58, 87, 53, 23, 52, 25, 55, 89, 68, 37)(21, 49, 24, 54, 88, 95, 75, 42, 74, 94, 85, 50)(97, 98, 102, 114, 138, 132, 109, 100)(99, 105, 123, 153, 170, 142, 115, 107)(101, 111, 133, 166, 171, 143, 116, 112)(103, 117, 108, 130, 161, 173, 139, 119)(104, 120, 110, 134, 165, 174, 140, 121)(106, 122, 141, 175, 190, 188, 154, 127)(113, 118, 144, 172, 191, 189, 164, 131)(124, 145, 128, 148, 177, 192, 187, 155)(125, 150, 129, 151, 178, 169, 182, 156)(126, 157, 183, 147, 181, 163, 176, 159)(135, 146, 136, 149, 179, 158, 186, 162)(137, 167, 185, 152, 184, 160, 180, 168)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1835
Transitivity :: ET+
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1832 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T1^-2 * T2 * T1^-2 * T2^-1, T2 * T1^3 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^12, (T2 * T1^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 46, 33)(17, 36, 62, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 54, 34, 55)(32, 53, 74, 57)(35, 60, 84, 61)(39, 65, 40, 66)(45, 72, 58, 71)(47, 75, 49, 76)(48, 63, 50, 64)(51, 77, 52, 78)(56, 73, 89, 80)(59, 82, 94, 83)(67, 87, 69, 88)(68, 85, 70, 86)(79, 90, 95, 91)(81, 92, 96, 93)(97, 98, 102, 113, 131, 155, 177, 175, 152, 128, 109, 100)(99, 105, 121, 141, 169, 183, 188, 181, 156, 135, 114, 107)(101, 111, 129, 154, 176, 184, 189, 182, 157, 136, 115, 112)(103, 116, 108, 127, 149, 173, 186, 171, 178, 159, 132, 118)(104, 119, 110, 130, 153, 174, 187, 172, 179, 160, 133, 120)(106, 117, 134, 158, 180, 190, 192, 191, 185, 170, 142, 124)(122, 143, 125, 147, 161, 151, 166, 138, 165, 140, 168, 144)(123, 145, 126, 148, 162, 150, 164, 137, 163, 139, 167, 146)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1833
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1833 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^12 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 27, 123, 50, 146, 34, 130, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 39, 135, 65, 161, 44, 140, 24, 120, 8, 104)(4, 100, 12, 108, 31, 127, 53, 149, 78, 174, 52, 148, 28, 124, 13, 109)(6, 102, 17, 113, 35, 131, 58, 154, 82, 178, 59, 155, 36, 132, 18, 114)(9, 105, 25, 121, 14, 110, 32, 128, 55, 151, 77, 173, 49, 145, 26, 122)(11, 107, 29, 125, 15, 111, 33, 129, 57, 153, 79, 175, 51, 147, 30, 126)(19, 115, 37, 133, 22, 118, 42, 138, 68, 164, 89, 185, 64, 160, 38, 134)(21, 117, 40, 136, 23, 119, 43, 139, 70, 166, 90, 186, 66, 162, 41, 137)(45, 141, 71, 167, 47, 143, 75, 171, 93, 189, 80, 176, 54, 150, 72, 168)(46, 142, 73, 169, 48, 144, 76, 172, 94, 190, 81, 177, 56, 152, 74, 170)(60, 156, 83, 179, 62, 158, 87, 183, 95, 191, 91, 187, 67, 163, 84, 180)(61, 157, 85, 181, 63, 159, 88, 184, 96, 192, 92, 188, 69, 165, 86, 182)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 132)(21, 103)(22, 109)(23, 104)(24, 131)(25, 141)(26, 143)(27, 145)(28, 106)(29, 142)(30, 144)(31, 112)(32, 150)(33, 152)(34, 151)(35, 124)(36, 127)(37, 156)(38, 158)(39, 160)(40, 157)(41, 159)(42, 163)(43, 165)(44, 164)(45, 125)(46, 121)(47, 126)(48, 122)(49, 154)(50, 161)(51, 123)(52, 166)(53, 162)(54, 129)(55, 155)(56, 128)(57, 130)(58, 147)(59, 153)(60, 136)(61, 133)(62, 137)(63, 134)(64, 149)(65, 178)(66, 135)(67, 139)(68, 148)(69, 138)(70, 140)(71, 183)(72, 187)(73, 184)(74, 188)(75, 179)(76, 181)(77, 189)(78, 146)(79, 190)(80, 180)(81, 182)(82, 174)(83, 172)(84, 177)(85, 171)(86, 176)(87, 169)(88, 167)(89, 191)(90, 192)(91, 170)(92, 168)(93, 175)(94, 173)(95, 186)(96, 185)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1832
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1834 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^2 * T1^-1, T2^-1 * T1^-2 * T2 * T1^-2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^8, T1^-3 * T2^-1 * T1 * T2^5, T1^-2 * T2 * T1 * T2^-5 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 62, 158, 77, 173, 96, 192, 78, 174, 73, 169, 41, 137, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 51, 147, 86, 182, 57, 153, 91, 187, 70, 166, 90, 186, 56, 152, 26, 122, 8, 104)(4, 100, 12, 108, 35, 131, 67, 163, 82, 178, 46, 142, 81, 177, 47, 143, 83, 179, 64, 160, 31, 127, 14, 110)(6, 102, 19, 115, 45, 141, 80, 176, 66, 162, 34, 130, 59, 155, 38, 134, 60, 156, 84, 180, 48, 144, 20, 116)(9, 105, 28, 124, 15, 111, 39, 135, 71, 167, 79, 175, 44, 140, 18, 114, 43, 139, 76, 172, 61, 157, 29, 125)(11, 107, 32, 128, 16, 112, 40, 136, 72, 168, 92, 188, 69, 165, 36, 132, 65, 161, 93, 189, 63, 159, 33, 129)(13, 109, 27, 123, 58, 154, 87, 183, 53, 149, 23, 119, 52, 148, 25, 121, 55, 151, 89, 185, 68, 164, 37, 133)(21, 117, 49, 145, 24, 120, 54, 150, 88, 184, 95, 191, 75, 171, 42, 138, 74, 170, 94, 190, 85, 181, 50, 146)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 122)(11, 99)(12, 130)(13, 100)(14, 134)(15, 133)(16, 101)(17, 118)(18, 138)(19, 107)(20, 112)(21, 108)(22, 144)(23, 103)(24, 110)(25, 104)(26, 141)(27, 153)(28, 145)(29, 150)(30, 157)(31, 106)(32, 148)(33, 151)(34, 161)(35, 113)(36, 109)(37, 166)(38, 165)(39, 146)(40, 149)(41, 167)(42, 132)(43, 119)(44, 121)(45, 175)(46, 115)(47, 116)(48, 172)(49, 128)(50, 136)(51, 181)(52, 177)(53, 179)(54, 129)(55, 178)(56, 184)(57, 170)(58, 127)(59, 124)(60, 125)(61, 183)(62, 186)(63, 126)(64, 180)(65, 173)(66, 135)(67, 176)(68, 131)(69, 174)(70, 171)(71, 185)(72, 137)(73, 182)(74, 142)(75, 143)(76, 191)(77, 139)(78, 140)(79, 190)(80, 159)(81, 192)(82, 169)(83, 158)(84, 168)(85, 163)(86, 156)(87, 147)(88, 160)(89, 152)(90, 162)(91, 155)(92, 154)(93, 164)(94, 188)(95, 189)(96, 187)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1830
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1835 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T1^-2 * T2 * T1^-2 * T2^-1, T2 * T1^3 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^12, (T2 * T1^-1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 25, 121, 46, 142, 33, 129)(17, 113, 36, 132, 62, 158, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 54, 150, 34, 130, 55, 151)(32, 128, 53, 149, 74, 170, 57, 153)(35, 131, 60, 156, 84, 180, 61, 157)(39, 135, 65, 161, 40, 136, 66, 162)(45, 141, 72, 168, 58, 154, 71, 167)(47, 143, 75, 171, 49, 145, 76, 172)(48, 144, 63, 159, 50, 146, 64, 160)(51, 147, 77, 173, 52, 148, 78, 174)(56, 152, 73, 169, 89, 185, 80, 176)(59, 155, 82, 178, 94, 190, 83, 179)(67, 163, 87, 183, 69, 165, 88, 184)(68, 164, 85, 181, 70, 166, 86, 182)(79, 175, 90, 186, 95, 191, 91, 187)(81, 177, 92, 188, 96, 192, 93, 189)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 129)(16, 101)(17, 131)(18, 107)(19, 112)(20, 108)(21, 134)(22, 103)(23, 110)(24, 104)(25, 141)(26, 143)(27, 145)(28, 106)(29, 147)(30, 148)(31, 149)(32, 109)(33, 154)(34, 153)(35, 155)(36, 118)(37, 120)(38, 158)(39, 114)(40, 115)(41, 163)(42, 165)(43, 167)(44, 168)(45, 169)(46, 124)(47, 125)(48, 122)(49, 126)(50, 123)(51, 161)(52, 162)(53, 173)(54, 164)(55, 166)(56, 128)(57, 174)(58, 176)(59, 177)(60, 135)(61, 136)(62, 180)(63, 132)(64, 133)(65, 151)(66, 150)(67, 139)(68, 137)(69, 140)(70, 138)(71, 146)(72, 144)(73, 183)(74, 142)(75, 178)(76, 179)(77, 186)(78, 187)(79, 152)(80, 184)(81, 175)(82, 159)(83, 160)(84, 190)(85, 156)(86, 157)(87, 188)(88, 189)(89, 170)(90, 171)(91, 172)(92, 181)(93, 182)(94, 192)(95, 185)(96, 191)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1831
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1836 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * R * Y2^-2 * R * Y2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2^8, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 58, 154, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 59, 155, 57, 153)(37, 133, 60, 156, 40, 136, 61, 157)(38, 134, 62, 158, 41, 137, 63, 159)(39, 135, 64, 160, 53, 149, 66, 162)(42, 138, 67, 163, 43, 139, 69, 165)(44, 140, 68, 164, 52, 148, 70, 166)(50, 146, 65, 161, 82, 178, 78, 174)(71, 167, 87, 183, 73, 169, 88, 184)(72, 168, 91, 187, 74, 170, 92, 188)(75, 171, 83, 179, 76, 172, 85, 181)(77, 173, 93, 189, 79, 175, 94, 190)(80, 176, 84, 180, 81, 177, 86, 182)(89, 185, 95, 191, 90, 186, 96, 192)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 257, 353, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 250, 346, 274, 370, 251, 347, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 269, 365, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 271, 367, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 260, 356, 281, 377, 256, 352, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 262, 358, 282, 378, 258, 354, 233, 329)(237, 333, 263, 359, 239, 335, 267, 363, 285, 381, 272, 368, 246, 342, 264, 360)(238, 334, 265, 361, 240, 336, 268, 364, 286, 382, 273, 369, 248, 344, 266, 362)(252, 348, 275, 371, 254, 350, 279, 375, 287, 383, 283, 379, 259, 355, 276, 372)(253, 349, 277, 373, 255, 351, 280, 376, 288, 384, 284, 380, 261, 357, 278, 374)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 253)(38, 255)(39, 258)(40, 252)(41, 254)(42, 261)(43, 259)(44, 262)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 250)(52, 260)(53, 256)(54, 224)(55, 226)(56, 225)(57, 251)(58, 241)(59, 247)(60, 229)(61, 232)(62, 230)(63, 233)(64, 231)(65, 242)(66, 245)(67, 234)(68, 236)(69, 235)(70, 244)(71, 280)(72, 284)(73, 279)(74, 283)(75, 277)(76, 275)(77, 286)(78, 274)(79, 285)(80, 278)(81, 276)(82, 257)(83, 267)(84, 272)(85, 268)(86, 273)(87, 263)(88, 265)(89, 288)(90, 287)(91, 264)(92, 266)(93, 269)(94, 271)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1839
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1837 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-2 * Y1^-1 * Y2^-2, Y1^-1 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y1^8, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^5 * Y1 * Y2^-1 * Y1^-3, Y2 * Y1 * Y2^-3 * Y1^-1 * Y2^2 * Y1^-2, (Y1^3 * Y2 * Y1^-1 * Y2)^2 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 74, 170, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 70, 166, 75, 171, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 65, 161, 77, 173, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 69, 165, 78, 174, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 79, 175, 94, 190, 92, 188, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 76, 172, 95, 191, 93, 189, 68, 164, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 81, 177, 96, 192, 91, 187, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 82, 178, 73, 169, 86, 182, 60, 156)(30, 126, 61, 157, 87, 183, 51, 147, 85, 181, 67, 163, 80, 176, 63, 159)(39, 135, 50, 146, 40, 136, 53, 149, 83, 179, 62, 158, 90, 186, 66, 162)(41, 137, 71, 167, 89, 185, 56, 152, 88, 184, 64, 160, 84, 180, 72, 168)(193, 289, 195, 291, 202, 298, 222, 318, 254, 350, 269, 365, 288, 384, 270, 366, 265, 361, 233, 329, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 243, 339, 278, 374, 249, 345, 283, 379, 262, 358, 282, 378, 248, 344, 218, 314, 200, 296)(196, 292, 204, 300, 227, 323, 259, 355, 274, 370, 238, 334, 273, 369, 239, 335, 275, 371, 256, 352, 223, 319, 206, 302)(198, 294, 211, 307, 237, 333, 272, 368, 258, 354, 226, 322, 251, 347, 230, 326, 252, 348, 276, 372, 240, 336, 212, 308)(201, 297, 220, 316, 207, 303, 231, 327, 263, 359, 271, 367, 236, 332, 210, 306, 235, 331, 268, 364, 253, 349, 221, 317)(203, 299, 224, 320, 208, 304, 232, 328, 264, 360, 284, 380, 261, 357, 228, 324, 257, 353, 285, 381, 255, 351, 225, 321)(205, 301, 219, 315, 250, 346, 279, 375, 245, 341, 215, 311, 244, 340, 217, 313, 247, 343, 281, 377, 260, 356, 229, 325)(213, 309, 241, 337, 216, 312, 246, 342, 280, 376, 287, 383, 267, 363, 234, 330, 266, 362, 286, 382, 277, 373, 242, 338)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 254)(31, 206)(32, 208)(33, 203)(34, 251)(35, 259)(36, 257)(37, 205)(38, 252)(39, 263)(40, 264)(41, 209)(42, 266)(43, 268)(44, 210)(45, 272)(46, 273)(47, 275)(48, 212)(49, 216)(50, 213)(51, 278)(52, 217)(53, 215)(54, 280)(55, 281)(56, 218)(57, 283)(58, 279)(59, 230)(60, 276)(61, 221)(62, 269)(63, 225)(64, 223)(65, 285)(66, 226)(67, 274)(68, 229)(69, 228)(70, 282)(71, 271)(72, 284)(73, 233)(74, 286)(75, 234)(76, 253)(77, 288)(78, 265)(79, 236)(80, 258)(81, 239)(82, 238)(83, 256)(84, 240)(85, 242)(86, 249)(87, 245)(88, 287)(89, 260)(90, 248)(91, 262)(92, 261)(93, 255)(94, 277)(95, 267)(96, 270)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1838
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1838 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2 * Y3^2, Y3^-1 * Y2^-1 * Y3^3 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y2^-1)^8, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 237, 333, 221, 317, 238, 334)(218, 314, 239, 335, 222, 318, 240, 336)(219, 315, 241, 337, 251, 347, 243, 339)(224, 320, 246, 342, 225, 321, 248, 344)(226, 322, 247, 343, 252, 348, 249, 345)(229, 325, 253, 349, 232, 328, 254, 350)(230, 326, 255, 351, 233, 329, 256, 352)(231, 327, 257, 353, 245, 341, 259, 355)(234, 330, 260, 356, 235, 331, 262, 358)(236, 332, 261, 357, 244, 340, 263, 359)(242, 338, 264, 360, 273, 369, 270, 366)(250, 346, 258, 354, 274, 370, 271, 367)(265, 361, 279, 375, 267, 363, 281, 377)(266, 362, 280, 376, 268, 364, 282, 378)(269, 365, 275, 371, 284, 380, 277, 373)(272, 368, 276, 372, 285, 381, 278, 374)(283, 379, 286, 382, 288, 384, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 242)(28, 205)(29, 207)(30, 203)(31, 245)(32, 247)(33, 249)(34, 208)(35, 251)(36, 210)(37, 214)(38, 211)(39, 258)(40, 215)(41, 213)(42, 261)(43, 263)(44, 216)(45, 265)(46, 267)(47, 259)(48, 257)(49, 218)(50, 269)(51, 222)(52, 220)(53, 271)(54, 266)(55, 260)(56, 268)(57, 262)(58, 226)(59, 273)(60, 228)(61, 275)(62, 277)(63, 241)(64, 243)(65, 230)(66, 279)(67, 233)(68, 276)(69, 248)(70, 278)(71, 246)(72, 236)(73, 239)(74, 237)(75, 240)(76, 238)(77, 283)(78, 244)(79, 281)(80, 250)(81, 284)(82, 252)(83, 255)(84, 253)(85, 256)(86, 254)(87, 286)(88, 264)(89, 287)(90, 270)(91, 272)(92, 288)(93, 274)(94, 280)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1837
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1839 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^4, Y1^-3 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^3 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-5, Y1^12 ]
Map:: polytopal
	R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 59, 155, 81, 177, 79, 175, 56, 152, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 73, 169, 87, 183, 92, 188, 85, 181, 60, 156, 39, 135, 18, 114, 11, 107)(5, 101, 15, 111, 33, 129, 58, 154, 80, 176, 88, 184, 93, 189, 86, 182, 61, 157, 40, 136, 19, 115, 16, 112)(7, 103, 20, 116, 12, 108, 31, 127, 53, 149, 77, 173, 90, 186, 75, 171, 82, 178, 63, 159, 36, 132, 22, 118)(8, 104, 23, 119, 14, 110, 34, 130, 57, 153, 78, 174, 91, 187, 76, 172, 83, 179, 64, 160, 37, 133, 24, 120)(10, 106, 21, 117, 38, 134, 62, 158, 84, 180, 94, 190, 96, 192, 95, 191, 89, 185, 74, 170, 46, 142, 28, 124)(26, 122, 47, 143, 29, 125, 51, 147, 65, 161, 55, 151, 70, 166, 42, 138, 69, 165, 44, 140, 72, 168, 48, 144)(27, 123, 49, 145, 30, 126, 52, 148, 66, 162, 54, 150, 68, 164, 41, 137, 67, 163, 43, 139, 71, 167, 50, 146)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 238)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 246)(32, 245)(33, 205)(34, 247)(35, 252)(36, 254)(37, 209)(38, 211)(39, 257)(40, 258)(41, 215)(42, 212)(43, 216)(44, 214)(45, 264)(46, 225)(47, 267)(48, 255)(49, 268)(50, 256)(51, 269)(52, 270)(53, 266)(54, 226)(55, 223)(56, 265)(57, 224)(58, 263)(59, 274)(60, 276)(61, 227)(62, 229)(63, 242)(64, 240)(65, 232)(66, 231)(67, 279)(68, 277)(69, 280)(70, 278)(71, 237)(72, 250)(73, 281)(74, 249)(75, 241)(76, 239)(77, 244)(78, 243)(79, 282)(80, 248)(81, 284)(82, 286)(83, 251)(84, 253)(85, 262)(86, 260)(87, 261)(88, 259)(89, 272)(90, 287)(91, 271)(92, 288)(93, 273)(94, 275)(95, 283)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1836
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1840 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^3, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^2, Y1 * Y2^-1 * Y3^2 * Y2 * Y3^-1, Y3 * Y2^2 * Y1 * Y2^2, Y1 * Y2^-2 * Y1 * Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-3 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-3 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2^12, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 59, 155, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 60, 156, 57, 153)(37, 133, 61, 157, 40, 136, 62, 158)(38, 134, 63, 159, 41, 137, 64, 160)(39, 135, 65, 161, 53, 149, 67, 163)(42, 138, 68, 164, 43, 139, 70, 166)(44, 140, 69, 165, 52, 148, 71, 167)(50, 146, 72, 168, 81, 177, 78, 174)(58, 154, 66, 162, 82, 178, 79, 175)(73, 169, 87, 183, 75, 171, 89, 185)(74, 170, 88, 184, 76, 172, 90, 186)(77, 173, 83, 179, 92, 188, 85, 181)(80, 176, 84, 180, 93, 189, 86, 182)(91, 187, 94, 190, 96, 192, 95, 191)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 269, 365, 283, 379, 272, 368, 250, 346, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 258, 354, 279, 375, 286, 382, 280, 376, 264, 360, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 271, 367, 281, 377, 287, 383, 282, 378, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 251, 347, 273, 369, 284, 380, 288, 384, 285, 381, 274, 370, 252, 348, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 260, 356, 276, 372, 253, 349, 275, 371, 255, 351, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 262, 358, 278, 374, 254, 350, 277, 373, 256, 352, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 261, 357, 248, 344, 268, 364, 238, 334, 267, 363, 240, 336, 257, 353, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 263, 359, 246, 342, 266, 362, 237, 333, 265, 361, 239, 335, 259, 355, 233, 329)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 254)(38, 256)(39, 259)(40, 253)(41, 255)(42, 262)(43, 260)(44, 263)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 251)(52, 261)(53, 257)(54, 224)(55, 226)(56, 225)(57, 252)(58, 271)(59, 241)(60, 247)(61, 229)(62, 232)(63, 230)(64, 233)(65, 231)(66, 250)(67, 245)(68, 234)(69, 236)(70, 235)(71, 244)(72, 242)(73, 281)(74, 282)(75, 279)(76, 280)(77, 277)(78, 273)(79, 274)(80, 278)(81, 264)(82, 258)(83, 269)(84, 272)(85, 284)(86, 285)(87, 265)(88, 266)(89, 267)(90, 268)(91, 287)(92, 275)(93, 276)(94, 283)(95, 288)(96, 286)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1841
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1841 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : C8) : C4 (small group id <96, 15>)
Aut   = $<192, 341>$ (small group id <192, 341>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, Y1^8, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y1^-2 * Y3 * Y1 * Y3^-5 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map:: polytopal
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 74, 170, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 70, 166, 75, 171, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 65, 161, 77, 173, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 69, 165, 78, 174, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 79, 175, 94, 190, 92, 188, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 76, 172, 95, 191, 93, 189, 68, 164, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 81, 177, 96, 192, 91, 187, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 82, 178, 73, 169, 86, 182, 60, 156)(30, 126, 61, 157, 87, 183, 51, 147, 85, 181, 67, 163, 80, 176, 63, 159)(39, 135, 50, 146, 40, 136, 53, 149, 83, 179, 62, 158, 90, 186, 66, 162)(41, 137, 71, 167, 89, 185, 56, 152, 88, 184, 64, 160, 84, 180, 72, 168)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 254)(31, 206)(32, 208)(33, 203)(34, 251)(35, 259)(36, 257)(37, 205)(38, 252)(39, 263)(40, 264)(41, 209)(42, 266)(43, 268)(44, 210)(45, 272)(46, 273)(47, 275)(48, 212)(49, 216)(50, 213)(51, 278)(52, 217)(53, 215)(54, 280)(55, 281)(56, 218)(57, 283)(58, 279)(59, 230)(60, 276)(61, 221)(62, 269)(63, 225)(64, 223)(65, 285)(66, 226)(67, 274)(68, 229)(69, 228)(70, 282)(71, 271)(72, 284)(73, 233)(74, 286)(75, 234)(76, 253)(77, 288)(78, 265)(79, 236)(80, 258)(81, 239)(82, 238)(83, 256)(84, 240)(85, 242)(86, 249)(87, 245)(88, 287)(89, 260)(90, 248)(91, 262)(92, 261)(93, 255)(94, 277)(95, 267)(96, 270)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1840
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1842 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^-3 * T1^2 * T2^-1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, (T2 * T1^-1)^12 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 14, 28, 11, 27, 15, 26)(19, 29, 22, 32, 21, 31, 23, 30)(33, 41, 35, 44, 34, 43, 36, 42)(37, 45, 39, 48, 38, 47, 40, 46)(49, 57, 51, 60, 50, 59, 52, 58)(53, 61, 55, 64, 54, 63, 56, 62)(65, 73, 67, 76, 66, 75, 68, 74)(69, 77, 71, 80, 70, 79, 72, 78)(81, 89, 83, 92, 82, 91, 84, 90)(85, 93, 87, 96, 86, 95, 88, 94)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 112, 116)(121, 129, 123, 130)(122, 131, 124, 132)(125, 133, 127, 134)(126, 135, 128, 136)(137, 145, 139, 146)(138, 147, 140, 148)(141, 149, 143, 150)(142, 151, 144, 152)(153, 161, 155, 162)(154, 163, 156, 164)(157, 165, 159, 166)(158, 167, 160, 168)(169, 177, 171, 178)(170, 179, 172, 180)(173, 181, 175, 182)(174, 183, 176, 184)(185, 189, 187, 191)(186, 192, 188, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1846
Transitivity :: ET+
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1843 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2^-1 * T1^2, T1^-2 * T2 * T1 * T2 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T1^-1 * T2^-2 * T1 * T2^-2, (T2 * T1^-1)^4, T2^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 28, 46, 62, 78, 68, 52, 35, 17, 5)(2, 7, 22, 40, 56, 72, 87, 76, 60, 44, 26, 8)(4, 12, 32, 49, 65, 81, 92, 80, 63, 48, 29, 14)(6, 19, 37, 53, 69, 84, 94, 85, 70, 54, 38, 20)(9, 18, 15, 33, 50, 66, 82, 91, 77, 61, 45, 27)(11, 30, 16, 34, 51, 67, 83, 93, 79, 64, 47, 31)(13, 25, 43, 59, 75, 90, 96, 88, 73, 57, 41, 23)(21, 36, 24, 42, 58, 74, 89, 95, 86, 71, 55, 39)(97, 98, 102, 114, 132, 126, 109, 100)(99, 105, 121, 104, 120, 110, 115, 107)(101, 111, 119, 103, 117, 108, 116, 112)(106, 122, 133, 123, 138, 127, 139, 125)(113, 118, 134, 129, 135, 130, 137, 128)(124, 141, 155, 140, 154, 144, 149, 143)(131, 146, 153, 136, 151, 145, 150, 147)(142, 156, 165, 157, 170, 160, 171, 159)(148, 152, 166, 162, 167, 163, 169, 161)(158, 173, 186, 172, 185, 176, 180, 175)(164, 178, 184, 168, 182, 177, 181, 179)(174, 183, 190, 187, 191, 189, 192, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1847
Transitivity :: ET+
Graph:: simple bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1844 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-2 * T1 * T2^-2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 46, 33)(17, 36, 56, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 48, 34, 47)(32, 49, 64, 51)(35, 54, 72, 55)(39, 59, 40, 60)(45, 62, 52, 63)(50, 61, 78, 67)(53, 70, 86, 71)(57, 75, 58, 76)(65, 80, 68, 79)(66, 81, 93, 82)(69, 84, 94, 85)(73, 89, 74, 90)(77, 91, 83, 92)(87, 95, 88, 96)(97, 98, 102, 113, 131, 149, 165, 162, 146, 128, 109, 100)(99, 105, 121, 141, 157, 173, 180, 169, 150, 135, 114, 107)(101, 111, 129, 148, 163, 179, 181, 170, 151, 136, 115, 112)(103, 116, 108, 127, 145, 161, 177, 183, 166, 153, 132, 118)(104, 119, 110, 130, 147, 164, 178, 184, 167, 154, 133, 120)(106, 117, 134, 152, 168, 182, 190, 189, 174, 160, 142, 124)(122, 138, 125, 140, 155, 172, 185, 192, 187, 175, 158, 143)(123, 137, 126, 139, 156, 171, 186, 191, 188, 176, 159, 144)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1845
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1845 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^-3 * T1^2 * T2^-1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, (T2 * T1^-1)^12 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 18, 114, 6, 102, 17, 113, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 13, 109, 4, 100, 12, 108, 24, 120, 8, 104)(9, 105, 25, 121, 14, 110, 28, 124, 11, 107, 27, 123, 15, 111, 26, 122)(19, 115, 29, 125, 22, 118, 32, 128, 21, 117, 31, 127, 23, 119, 30, 126)(33, 129, 41, 137, 35, 131, 44, 140, 34, 130, 43, 139, 36, 132, 42, 138)(37, 133, 45, 141, 39, 135, 48, 144, 38, 134, 47, 143, 40, 136, 46, 142)(49, 145, 57, 153, 51, 147, 60, 156, 50, 146, 59, 155, 52, 148, 58, 154)(53, 149, 61, 157, 55, 151, 64, 160, 54, 150, 63, 159, 56, 152, 62, 158)(65, 161, 73, 169, 67, 163, 76, 172, 66, 162, 75, 171, 68, 164, 74, 170)(69, 165, 77, 173, 71, 167, 80, 176, 70, 166, 79, 175, 72, 168, 78, 174)(81, 177, 89, 185, 83, 179, 92, 188, 82, 178, 91, 187, 84, 180, 90, 186)(85, 181, 93, 189, 87, 183, 96, 192, 86, 182, 95, 191, 88, 184, 94, 190)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 106)(21, 103)(22, 109)(23, 104)(24, 112)(25, 129)(26, 131)(27, 130)(28, 132)(29, 133)(30, 135)(31, 134)(32, 136)(33, 123)(34, 121)(35, 124)(36, 122)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 189)(90, 192)(91, 191)(92, 190)(93, 187)(94, 186)(95, 185)(96, 188)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1844
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1846 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2^-1 * T1^2, T1^-2 * T2 * T1 * T2 * T1^-1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T1^-1 * T2^-2 * T1 * T2^-2, (T2 * T1^-1)^4, T2^12 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 28, 124, 46, 142, 62, 158, 78, 174, 68, 164, 52, 148, 35, 131, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 40, 136, 56, 152, 72, 168, 87, 183, 76, 172, 60, 156, 44, 140, 26, 122, 8, 104)(4, 100, 12, 108, 32, 128, 49, 145, 65, 161, 81, 177, 92, 188, 80, 176, 63, 159, 48, 144, 29, 125, 14, 110)(6, 102, 19, 115, 37, 133, 53, 149, 69, 165, 84, 180, 94, 190, 85, 181, 70, 166, 54, 150, 38, 134, 20, 116)(9, 105, 18, 114, 15, 111, 33, 129, 50, 146, 66, 162, 82, 178, 91, 187, 77, 173, 61, 157, 45, 141, 27, 123)(11, 107, 30, 126, 16, 112, 34, 130, 51, 147, 67, 163, 83, 179, 93, 189, 79, 175, 64, 160, 47, 143, 31, 127)(13, 109, 25, 121, 43, 139, 59, 155, 75, 171, 90, 186, 96, 192, 88, 184, 73, 169, 57, 153, 41, 137, 23, 119)(21, 117, 36, 132, 24, 120, 42, 138, 58, 154, 74, 170, 89, 185, 95, 191, 86, 182, 71, 167, 55, 151, 39, 135)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 121)(10, 122)(11, 99)(12, 116)(13, 100)(14, 115)(15, 119)(16, 101)(17, 118)(18, 132)(19, 107)(20, 112)(21, 108)(22, 134)(23, 103)(24, 110)(25, 104)(26, 133)(27, 138)(28, 141)(29, 106)(30, 109)(31, 139)(32, 113)(33, 135)(34, 137)(35, 146)(36, 126)(37, 123)(38, 129)(39, 130)(40, 151)(41, 128)(42, 127)(43, 125)(44, 154)(45, 155)(46, 156)(47, 124)(48, 149)(49, 150)(50, 153)(51, 131)(52, 152)(53, 143)(54, 147)(55, 145)(56, 166)(57, 136)(58, 144)(59, 140)(60, 165)(61, 170)(62, 173)(63, 142)(64, 171)(65, 148)(66, 167)(67, 169)(68, 178)(69, 157)(70, 162)(71, 163)(72, 182)(73, 161)(74, 160)(75, 159)(76, 185)(77, 186)(78, 183)(79, 158)(80, 180)(81, 181)(82, 184)(83, 164)(84, 175)(85, 179)(86, 177)(87, 190)(88, 168)(89, 176)(90, 172)(91, 191)(92, 174)(93, 192)(94, 187)(95, 189)(96, 188)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1842
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1847 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-2 * T1 * T2^-2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1, T1^12 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 25, 121, 46, 142, 33, 129)(17, 113, 36, 132, 56, 152, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 48, 144, 34, 130, 47, 143)(32, 128, 49, 145, 64, 160, 51, 147)(35, 131, 54, 150, 72, 168, 55, 151)(39, 135, 59, 155, 40, 136, 60, 156)(45, 141, 62, 158, 52, 148, 63, 159)(50, 146, 61, 157, 78, 174, 67, 163)(53, 149, 70, 166, 86, 182, 71, 167)(57, 153, 75, 171, 58, 154, 76, 172)(65, 161, 80, 176, 68, 164, 79, 175)(66, 162, 81, 177, 93, 189, 82, 178)(69, 165, 84, 180, 94, 190, 85, 181)(73, 169, 89, 185, 74, 170, 90, 186)(77, 173, 91, 187, 83, 179, 92, 188)(87, 183, 95, 191, 88, 184, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 129)(16, 101)(17, 131)(18, 107)(19, 112)(20, 108)(21, 134)(22, 103)(23, 110)(24, 104)(25, 141)(26, 138)(27, 137)(28, 106)(29, 140)(30, 139)(31, 145)(32, 109)(33, 148)(34, 147)(35, 149)(36, 118)(37, 120)(38, 152)(39, 114)(40, 115)(41, 126)(42, 125)(43, 156)(44, 155)(45, 157)(46, 124)(47, 122)(48, 123)(49, 161)(50, 128)(51, 164)(52, 163)(53, 165)(54, 135)(55, 136)(56, 168)(57, 132)(58, 133)(59, 172)(60, 171)(61, 173)(62, 143)(63, 144)(64, 142)(65, 177)(66, 146)(67, 179)(68, 178)(69, 162)(70, 153)(71, 154)(72, 182)(73, 150)(74, 151)(75, 186)(76, 185)(77, 180)(78, 160)(79, 158)(80, 159)(81, 183)(82, 184)(83, 181)(84, 169)(85, 170)(86, 190)(87, 166)(88, 167)(89, 192)(90, 191)(91, 175)(92, 176)(93, 174)(94, 189)(95, 188)(96, 187)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1843
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1848 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y3 * Y2^2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1^-1 * Y2^2 * Y1^-1, Y2^4 * Y1^2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 16, 112, 20, 116)(25, 121, 33, 129, 27, 123, 34, 130)(26, 122, 35, 131, 28, 124, 36, 132)(29, 125, 37, 133, 31, 127, 38, 134)(30, 126, 39, 135, 32, 128, 40, 136)(41, 137, 49, 145, 43, 139, 50, 146)(42, 138, 51, 147, 44, 140, 52, 148)(45, 141, 53, 149, 47, 143, 54, 150)(46, 142, 55, 151, 48, 144, 56, 152)(57, 153, 65, 161, 59, 155, 66, 162)(58, 154, 67, 163, 60, 156, 68, 164)(61, 157, 69, 165, 63, 159, 70, 166)(62, 158, 71, 167, 64, 160, 72, 168)(73, 169, 81, 177, 75, 171, 82, 178)(74, 170, 83, 179, 76, 172, 84, 180)(77, 173, 85, 181, 79, 175, 86, 182)(78, 174, 87, 183, 80, 176, 88, 184)(89, 185, 93, 189, 91, 187, 95, 191)(90, 186, 96, 192, 92, 188, 94, 190)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 206, 302, 220, 316, 203, 299, 219, 315, 207, 303, 218, 314)(211, 307, 221, 317, 214, 310, 224, 320, 213, 309, 223, 319, 215, 311, 222, 318)(225, 321, 233, 329, 227, 323, 236, 332, 226, 322, 235, 331, 228, 324, 234, 330)(229, 325, 237, 333, 231, 327, 240, 336, 230, 326, 239, 335, 232, 328, 238, 334)(241, 337, 249, 345, 243, 339, 252, 348, 242, 338, 251, 347, 244, 340, 250, 346)(245, 341, 253, 349, 247, 343, 256, 352, 246, 342, 255, 351, 248, 344, 254, 350)(257, 353, 265, 361, 259, 355, 268, 364, 258, 354, 267, 363, 260, 356, 266, 362)(261, 357, 269, 365, 263, 359, 272, 368, 262, 358, 271, 367, 264, 360, 270, 366)(273, 369, 281, 377, 275, 371, 284, 380, 274, 370, 283, 379, 276, 372, 282, 378)(277, 373, 285, 381, 279, 375, 288, 384, 278, 374, 287, 383, 280, 376, 286, 382)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 212)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 216)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 226)(26, 228)(27, 225)(28, 227)(29, 230)(30, 232)(31, 229)(32, 231)(33, 217)(34, 219)(35, 218)(36, 220)(37, 221)(38, 223)(39, 222)(40, 224)(41, 242)(42, 244)(43, 241)(44, 243)(45, 246)(46, 248)(47, 245)(48, 247)(49, 233)(50, 235)(51, 234)(52, 236)(53, 237)(54, 239)(55, 238)(56, 240)(57, 258)(58, 260)(59, 257)(60, 259)(61, 262)(62, 264)(63, 261)(64, 263)(65, 249)(66, 251)(67, 250)(68, 252)(69, 253)(70, 255)(71, 254)(72, 256)(73, 274)(74, 276)(75, 273)(76, 275)(77, 278)(78, 280)(79, 277)(80, 279)(81, 265)(82, 267)(83, 266)(84, 268)(85, 269)(86, 271)(87, 270)(88, 272)(89, 287)(90, 286)(91, 285)(92, 288)(93, 281)(94, 284)(95, 283)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1851
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1849 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y2 * Y1^3 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1 * Y2 * Y1^-2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^12, Y2^-6 * Y1 * Y2^-6 * Y1^-1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 36, 132, 30, 126, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 8, 104, 24, 120, 14, 110, 19, 115, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 12, 108, 20, 116, 16, 112)(10, 106, 26, 122, 37, 133, 27, 123, 42, 138, 31, 127, 43, 139, 29, 125)(17, 113, 22, 118, 38, 134, 33, 129, 39, 135, 34, 130, 41, 137, 32, 128)(28, 124, 45, 141, 59, 155, 44, 140, 58, 154, 48, 144, 53, 149, 47, 143)(35, 131, 50, 146, 57, 153, 40, 136, 55, 151, 49, 145, 54, 150, 51, 147)(46, 142, 60, 156, 69, 165, 61, 157, 74, 170, 64, 160, 75, 171, 63, 159)(52, 148, 56, 152, 70, 166, 66, 162, 71, 167, 67, 163, 73, 169, 65, 161)(62, 158, 77, 173, 90, 186, 76, 172, 89, 185, 80, 176, 84, 180, 79, 175)(68, 164, 82, 178, 88, 184, 72, 168, 86, 182, 81, 177, 85, 181, 83, 179)(78, 174, 87, 183, 94, 190, 91, 187, 95, 191, 93, 189, 96, 192, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 238, 334, 254, 350, 270, 366, 260, 356, 244, 340, 227, 323, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 232, 328, 248, 344, 264, 360, 279, 375, 268, 364, 252, 348, 236, 332, 218, 314, 200, 296)(196, 292, 204, 300, 224, 320, 241, 337, 257, 353, 273, 369, 284, 380, 272, 368, 255, 351, 240, 336, 221, 317, 206, 302)(198, 294, 211, 307, 229, 325, 245, 341, 261, 357, 276, 372, 286, 382, 277, 373, 262, 358, 246, 342, 230, 326, 212, 308)(201, 297, 210, 306, 207, 303, 225, 321, 242, 338, 258, 354, 274, 370, 283, 379, 269, 365, 253, 349, 237, 333, 219, 315)(203, 299, 222, 318, 208, 304, 226, 322, 243, 339, 259, 355, 275, 371, 285, 381, 271, 367, 256, 352, 239, 335, 223, 319)(205, 301, 217, 313, 235, 331, 251, 347, 267, 363, 282, 378, 288, 384, 280, 376, 265, 361, 249, 345, 233, 329, 215, 311)(213, 309, 228, 324, 216, 312, 234, 330, 250, 346, 266, 362, 281, 377, 287, 383, 278, 374, 263, 359, 247, 343, 231, 327)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 220)(11, 222)(12, 224)(13, 217)(14, 196)(15, 225)(16, 226)(17, 197)(18, 207)(19, 229)(20, 198)(21, 228)(22, 232)(23, 205)(24, 234)(25, 235)(26, 200)(27, 201)(28, 238)(29, 206)(30, 208)(31, 203)(32, 241)(33, 242)(34, 243)(35, 209)(36, 216)(37, 245)(38, 212)(39, 213)(40, 248)(41, 215)(42, 250)(43, 251)(44, 218)(45, 219)(46, 254)(47, 223)(48, 221)(49, 257)(50, 258)(51, 259)(52, 227)(53, 261)(54, 230)(55, 231)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 279)(73, 249)(74, 281)(75, 282)(76, 252)(77, 253)(78, 260)(79, 256)(80, 255)(81, 284)(82, 283)(83, 285)(84, 286)(85, 262)(86, 263)(87, 268)(88, 265)(89, 287)(90, 288)(91, 269)(92, 272)(93, 271)(94, 277)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1850
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1850 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y2 * Y3^2 * Y2^-1, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4 * Y2 * Y3^-8 * Y2^-1, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 232, 328, 221, 317, 229, 325)(218, 314, 235, 331, 222, 318, 234, 330)(219, 315, 237, 333, 245, 341, 239, 335)(224, 320, 233, 329, 225, 321, 230, 326)(226, 322, 242, 338, 246, 342, 243, 339)(231, 327, 247, 343, 241, 337, 249, 345)(236, 332, 250, 346, 240, 336, 251, 347)(238, 334, 252, 348, 261, 357, 255, 351)(244, 340, 248, 344, 262, 358, 257, 353)(253, 349, 267, 363, 256, 352, 266, 362)(254, 350, 269, 365, 276, 372, 271, 367)(258, 354, 265, 361, 259, 355, 263, 359)(260, 356, 274, 370, 277, 373, 275, 371)(264, 360, 278, 374, 273, 369, 280, 376)(268, 364, 281, 377, 272, 368, 282, 378)(270, 366, 279, 375, 286, 382, 284, 380)(283, 379, 288, 384, 285, 381, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 279)(73, 249)(74, 281)(75, 282)(76, 252)(77, 253)(78, 260)(79, 256)(80, 255)(81, 284)(82, 283)(83, 285)(84, 286)(85, 262)(86, 263)(87, 268)(88, 265)(89, 287)(90, 288)(91, 269)(92, 272)(93, 271)(94, 277)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1849
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1851 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^2 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y1^12 ]
Map:: polytopal
	R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 66, 162, 50, 146, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 61, 157, 77, 173, 84, 180, 73, 169, 54, 150, 39, 135, 18, 114, 11, 107)(5, 101, 15, 111, 33, 129, 52, 148, 67, 163, 83, 179, 85, 181, 74, 170, 55, 151, 40, 136, 19, 115, 16, 112)(7, 103, 20, 116, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 87, 183, 70, 166, 57, 153, 36, 132, 22, 118)(8, 104, 23, 119, 14, 110, 34, 130, 51, 147, 68, 164, 82, 178, 88, 184, 71, 167, 58, 154, 37, 133, 24, 120)(10, 106, 21, 117, 38, 134, 56, 152, 72, 168, 86, 182, 94, 190, 93, 189, 78, 174, 64, 160, 46, 142, 28, 124)(26, 122, 42, 138, 29, 125, 44, 140, 59, 155, 76, 172, 89, 185, 96, 192, 91, 187, 79, 175, 62, 158, 47, 143)(27, 123, 41, 137, 30, 126, 43, 139, 60, 156, 75, 171, 90, 186, 95, 191, 92, 188, 80, 176, 63, 159, 48, 144)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 238)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 240)(32, 241)(33, 205)(34, 239)(35, 246)(36, 248)(37, 209)(38, 211)(39, 251)(40, 252)(41, 215)(42, 212)(43, 216)(44, 214)(45, 254)(46, 225)(47, 223)(48, 226)(49, 256)(50, 253)(51, 224)(52, 255)(53, 262)(54, 264)(55, 227)(56, 229)(57, 267)(58, 268)(59, 232)(60, 231)(61, 270)(62, 244)(63, 237)(64, 243)(65, 272)(66, 273)(67, 242)(68, 271)(69, 276)(70, 278)(71, 245)(72, 247)(73, 281)(74, 282)(75, 250)(76, 249)(77, 283)(78, 259)(79, 257)(80, 260)(81, 285)(82, 258)(83, 284)(84, 286)(85, 261)(86, 263)(87, 287)(88, 288)(89, 266)(90, 265)(91, 275)(92, 269)(93, 274)(94, 277)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1848
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1852 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^2 * Y3^-2, Y1 * Y3^-2 * Y1, (R * Y1)^2, (R * Y3)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^12, Y2 * Y1 * Y2^-5 * Y1 * Y2^5 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 40, 136, 29, 125, 37, 133)(26, 122, 43, 139, 30, 126, 42, 138)(27, 123, 45, 141, 53, 149, 47, 143)(32, 128, 41, 137, 33, 129, 38, 134)(34, 130, 50, 146, 54, 150, 51, 147)(39, 135, 55, 151, 49, 145, 57, 153)(44, 140, 58, 154, 48, 144, 59, 155)(46, 142, 60, 156, 69, 165, 63, 159)(52, 148, 56, 152, 70, 166, 65, 161)(61, 157, 75, 171, 64, 160, 74, 170)(62, 158, 77, 173, 84, 180, 79, 175)(66, 162, 73, 169, 67, 163, 71, 167)(68, 164, 82, 178, 85, 181, 83, 179)(72, 168, 86, 182, 81, 177, 88, 184)(76, 172, 89, 185, 80, 176, 90, 186)(78, 174, 87, 183, 94, 190, 92, 188)(91, 187, 96, 192, 93, 189, 95, 191)(193, 289, 195, 291, 202, 298, 219, 315, 238, 334, 254, 350, 270, 366, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 248, 344, 264, 360, 279, 375, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 284, 380, 272, 368, 255, 351, 240, 336, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 276, 372, 286, 382, 277, 373, 262, 358, 246, 342, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 283, 379, 269, 365, 253, 349, 237, 333, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 285, 381, 271, 367, 256, 352, 239, 335, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 250, 346, 266, 362, 281, 377, 287, 383, 278, 374, 263, 359, 247, 343, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 251, 347, 267, 363, 282, 378, 288, 384, 280, 376, 265, 361, 249, 345, 233, 329)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 229)(26, 234)(27, 239)(28, 227)(29, 232)(30, 235)(31, 228)(32, 230)(33, 233)(34, 243)(35, 216)(36, 212)(37, 221)(38, 225)(39, 249)(40, 217)(41, 224)(42, 222)(43, 218)(44, 251)(45, 219)(46, 255)(47, 245)(48, 250)(49, 247)(50, 226)(51, 246)(52, 257)(53, 237)(54, 242)(55, 231)(56, 244)(57, 241)(58, 236)(59, 240)(60, 238)(61, 266)(62, 271)(63, 261)(64, 267)(65, 262)(66, 263)(67, 265)(68, 275)(69, 252)(70, 248)(71, 259)(72, 280)(73, 258)(74, 256)(75, 253)(76, 282)(77, 254)(78, 284)(79, 276)(80, 281)(81, 278)(82, 260)(83, 277)(84, 269)(85, 274)(86, 264)(87, 270)(88, 273)(89, 268)(90, 272)(91, 287)(92, 286)(93, 288)(94, 279)(95, 285)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1853
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1853 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 : Q8) : C4 (small group id <96, 17>)
Aut   = $<192, 340>$ (small group id <192, 340>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2, Y3 * Y1^3 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3^6 * Y1 * Y3^-6 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 36, 132, 30, 126, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 8, 104, 24, 120, 14, 110, 19, 115, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 12, 108, 20, 116, 16, 112)(10, 106, 26, 122, 37, 133, 27, 123, 42, 138, 31, 127, 43, 139, 29, 125)(17, 113, 22, 118, 38, 134, 33, 129, 39, 135, 34, 130, 41, 137, 32, 128)(28, 124, 45, 141, 59, 155, 44, 140, 58, 154, 48, 144, 53, 149, 47, 143)(35, 131, 50, 146, 57, 153, 40, 136, 55, 151, 49, 145, 54, 150, 51, 147)(46, 142, 60, 156, 69, 165, 61, 157, 74, 170, 64, 160, 75, 171, 63, 159)(52, 148, 56, 152, 70, 166, 66, 162, 71, 167, 67, 163, 73, 169, 65, 161)(62, 158, 77, 173, 90, 186, 76, 172, 89, 185, 80, 176, 84, 180, 79, 175)(68, 164, 82, 178, 88, 184, 72, 168, 86, 182, 81, 177, 85, 181, 83, 179)(78, 174, 87, 183, 94, 190, 91, 187, 95, 191, 93, 189, 96, 192, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 220)(11, 222)(12, 224)(13, 217)(14, 196)(15, 225)(16, 226)(17, 197)(18, 207)(19, 229)(20, 198)(21, 228)(22, 232)(23, 205)(24, 234)(25, 235)(26, 200)(27, 201)(28, 238)(29, 206)(30, 208)(31, 203)(32, 241)(33, 242)(34, 243)(35, 209)(36, 216)(37, 245)(38, 212)(39, 213)(40, 248)(41, 215)(42, 250)(43, 251)(44, 218)(45, 219)(46, 254)(47, 223)(48, 221)(49, 257)(50, 258)(51, 259)(52, 227)(53, 261)(54, 230)(55, 231)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 276)(70, 246)(71, 247)(72, 279)(73, 249)(74, 281)(75, 282)(76, 252)(77, 253)(78, 260)(79, 256)(80, 255)(81, 284)(82, 283)(83, 285)(84, 286)(85, 262)(86, 263)(87, 268)(88, 265)(89, 287)(90, 288)(91, 269)(92, 272)(93, 271)(94, 277)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1852
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1854 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1)^3 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 50, 34, 16, 5)(2, 7, 20, 39, 65, 44, 24, 8)(4, 12, 31, 53, 78, 52, 28, 13)(6, 17, 35, 58, 82, 59, 36, 18)(9, 25, 14, 32, 55, 77, 49, 26)(11, 29, 15, 33, 57, 79, 51, 30)(19, 37, 22, 42, 68, 89, 64, 38)(21, 40, 23, 43, 70, 90, 66, 41)(45, 71, 47, 75, 93, 80, 54, 72)(46, 73, 48, 76, 94, 81, 56, 74)(60, 83, 62, 87, 95, 91, 67, 84)(61, 85, 63, 88, 96, 92, 69, 86)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 141, 125, 142)(122, 143, 126, 144)(123, 145, 154, 147)(128, 150, 129, 152)(130, 151, 155, 153)(133, 156, 136, 157)(134, 158, 137, 159)(135, 160, 149, 162)(138, 163, 139, 165)(140, 164, 148, 166)(146, 161, 178, 174)(167, 184, 169, 183)(168, 188, 170, 187)(171, 181, 172, 179)(173, 189, 175, 190)(176, 182, 177, 180)(185, 191, 186, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1858
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1855 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^2 * T2^-1 * T1^2, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1, T1^8, T2^5 * T1^2 * T2 * T1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 30, 62, 75, 42, 74, 73, 41, 17, 5)(2, 7, 22, 51, 86, 69, 36, 65, 90, 56, 26, 8)(4, 12, 35, 67, 79, 44, 18, 43, 76, 64, 31, 14)(6, 19, 45, 80, 68, 37, 13, 27, 58, 84, 48, 20)(9, 28, 15, 39, 71, 82, 46, 81, 47, 83, 61, 29)(11, 32, 16, 40, 72, 92, 57, 91, 70, 93, 63, 33)(21, 49, 24, 54, 88, 95, 77, 94, 78, 96, 85, 50)(23, 52, 25, 55, 89, 66, 34, 59, 38, 60, 87, 53)(97, 98, 102, 114, 138, 132, 109, 100)(99, 105, 123, 153, 170, 142, 115, 107)(101, 111, 133, 166, 171, 143, 116, 112)(103, 117, 108, 130, 161, 173, 139, 119)(104, 120, 110, 134, 165, 174, 140, 121)(106, 122, 141, 175, 169, 182, 154, 127)(113, 118, 144, 172, 158, 186, 164, 131)(124, 145, 128, 148, 177, 190, 187, 155)(125, 150, 129, 151, 178, 192, 188, 156)(126, 157, 180, 168, 137, 167, 176, 159)(135, 146, 136, 149, 179, 191, 189, 162)(147, 181, 163, 185, 152, 184, 160, 183)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1859
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1856 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, T1^-2 * T2 * T1^-2 * T2^-1, T1^-1 * T2 * T1^3 * T2 * T1^-1 * T2^-1 * T1 * T2^-1, T1^12, (T2^-1 * T1)^8 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 46, 33)(17, 36, 62, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 54, 34, 55)(32, 53, 74, 57)(35, 60, 84, 61)(39, 65, 40, 66)(45, 71, 58, 72)(47, 75, 49, 76)(48, 64, 50, 63)(51, 77, 52, 78)(56, 73, 89, 80)(59, 82, 94, 83)(67, 87, 69, 88)(68, 86, 70, 85)(79, 91, 95, 90)(81, 92, 96, 93)(97, 98, 102, 113, 131, 155, 177, 175, 152, 128, 109, 100)(99, 105, 121, 141, 169, 184, 188, 181, 156, 135, 114, 107)(101, 111, 129, 154, 176, 183, 189, 182, 157, 136, 115, 112)(103, 116, 108, 127, 149, 174, 187, 172, 178, 159, 132, 118)(104, 119, 110, 130, 153, 173, 186, 171, 179, 160, 133, 120)(106, 117, 134, 158, 180, 190, 192, 191, 185, 170, 142, 124)(122, 143, 125, 147, 161, 150, 164, 137, 163, 139, 167, 144)(123, 145, 126, 148, 162, 151, 166, 138, 165, 140, 168, 146)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1857
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1857 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T2^8, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1)^3 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 27, 123, 50, 146, 34, 130, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 39, 135, 65, 161, 44, 140, 24, 120, 8, 104)(4, 100, 12, 108, 31, 127, 53, 149, 78, 174, 52, 148, 28, 124, 13, 109)(6, 102, 17, 113, 35, 131, 58, 154, 82, 178, 59, 155, 36, 132, 18, 114)(9, 105, 25, 121, 14, 110, 32, 128, 55, 151, 77, 173, 49, 145, 26, 122)(11, 107, 29, 125, 15, 111, 33, 129, 57, 153, 79, 175, 51, 147, 30, 126)(19, 115, 37, 133, 22, 118, 42, 138, 68, 164, 89, 185, 64, 160, 38, 134)(21, 117, 40, 136, 23, 119, 43, 139, 70, 166, 90, 186, 66, 162, 41, 137)(45, 141, 71, 167, 47, 143, 75, 171, 93, 189, 80, 176, 54, 150, 72, 168)(46, 142, 73, 169, 48, 144, 76, 172, 94, 190, 81, 177, 56, 152, 74, 170)(60, 156, 83, 179, 62, 158, 87, 183, 95, 191, 91, 187, 67, 163, 84, 180)(61, 157, 85, 181, 63, 159, 88, 184, 96, 192, 92, 188, 69, 165, 86, 182)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 132)(21, 103)(22, 109)(23, 104)(24, 131)(25, 141)(26, 143)(27, 145)(28, 106)(29, 142)(30, 144)(31, 112)(32, 150)(33, 152)(34, 151)(35, 124)(36, 127)(37, 156)(38, 158)(39, 160)(40, 157)(41, 159)(42, 163)(43, 165)(44, 164)(45, 125)(46, 121)(47, 126)(48, 122)(49, 154)(50, 161)(51, 123)(52, 166)(53, 162)(54, 129)(55, 155)(56, 128)(57, 130)(58, 147)(59, 153)(60, 136)(61, 133)(62, 137)(63, 134)(64, 149)(65, 178)(66, 135)(67, 139)(68, 148)(69, 138)(70, 140)(71, 184)(72, 188)(73, 183)(74, 187)(75, 181)(76, 179)(77, 189)(78, 146)(79, 190)(80, 182)(81, 180)(82, 174)(83, 171)(84, 176)(85, 172)(86, 177)(87, 167)(88, 169)(89, 191)(90, 192)(91, 168)(92, 170)(93, 175)(94, 173)(95, 186)(96, 185)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1856
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1858 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^2 * T2^-1 * T1^2, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1, T1^8, T2^5 * T1^2 * T2 * T1^-2 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 62, 158, 75, 171, 42, 138, 74, 170, 73, 169, 41, 137, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 51, 147, 86, 182, 69, 165, 36, 132, 65, 161, 90, 186, 56, 152, 26, 122, 8, 104)(4, 100, 12, 108, 35, 131, 67, 163, 79, 175, 44, 140, 18, 114, 43, 139, 76, 172, 64, 160, 31, 127, 14, 110)(6, 102, 19, 115, 45, 141, 80, 176, 68, 164, 37, 133, 13, 109, 27, 123, 58, 154, 84, 180, 48, 144, 20, 116)(9, 105, 28, 124, 15, 111, 39, 135, 71, 167, 82, 178, 46, 142, 81, 177, 47, 143, 83, 179, 61, 157, 29, 125)(11, 107, 32, 128, 16, 112, 40, 136, 72, 168, 92, 188, 57, 153, 91, 187, 70, 166, 93, 189, 63, 159, 33, 129)(21, 117, 49, 145, 24, 120, 54, 150, 88, 184, 95, 191, 77, 173, 94, 190, 78, 174, 96, 192, 85, 181, 50, 146)(23, 119, 52, 148, 25, 121, 55, 151, 89, 185, 66, 162, 34, 130, 59, 155, 38, 134, 60, 156, 87, 183, 53, 149)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 122)(11, 99)(12, 130)(13, 100)(14, 134)(15, 133)(16, 101)(17, 118)(18, 138)(19, 107)(20, 112)(21, 108)(22, 144)(23, 103)(24, 110)(25, 104)(26, 141)(27, 153)(28, 145)(29, 150)(30, 157)(31, 106)(32, 148)(33, 151)(34, 161)(35, 113)(36, 109)(37, 166)(38, 165)(39, 146)(40, 149)(41, 167)(42, 132)(43, 119)(44, 121)(45, 175)(46, 115)(47, 116)(48, 172)(49, 128)(50, 136)(51, 181)(52, 177)(53, 179)(54, 129)(55, 178)(56, 184)(57, 170)(58, 127)(59, 124)(60, 125)(61, 180)(62, 186)(63, 126)(64, 183)(65, 173)(66, 135)(67, 185)(68, 131)(69, 174)(70, 171)(71, 176)(72, 137)(73, 182)(74, 142)(75, 143)(76, 158)(77, 139)(78, 140)(79, 169)(80, 159)(81, 190)(82, 192)(83, 191)(84, 168)(85, 163)(86, 154)(87, 147)(88, 160)(89, 152)(90, 164)(91, 155)(92, 156)(93, 162)(94, 187)(95, 189)(96, 188)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1854
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1859 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, T1^-2 * T2 * T1^-2 * T2^-1, T1^-1 * T2 * T1^3 * T2 * T1^-1 * T2^-1 * T1 * T2^-1, T1^12, (T2^-1 * T1)^8 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 25, 121, 46, 142, 33, 129)(17, 113, 36, 132, 62, 158, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 54, 150, 34, 130, 55, 151)(32, 128, 53, 149, 74, 170, 57, 153)(35, 131, 60, 156, 84, 180, 61, 157)(39, 135, 65, 161, 40, 136, 66, 162)(45, 141, 71, 167, 58, 154, 72, 168)(47, 143, 75, 171, 49, 145, 76, 172)(48, 144, 64, 160, 50, 146, 63, 159)(51, 147, 77, 173, 52, 148, 78, 174)(56, 152, 73, 169, 89, 185, 80, 176)(59, 155, 82, 178, 94, 190, 83, 179)(67, 163, 87, 183, 69, 165, 88, 184)(68, 164, 86, 182, 70, 166, 85, 181)(79, 175, 91, 187, 95, 191, 90, 186)(81, 177, 92, 188, 96, 192, 93, 189)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 129)(16, 101)(17, 131)(18, 107)(19, 112)(20, 108)(21, 134)(22, 103)(23, 110)(24, 104)(25, 141)(26, 143)(27, 145)(28, 106)(29, 147)(30, 148)(31, 149)(32, 109)(33, 154)(34, 153)(35, 155)(36, 118)(37, 120)(38, 158)(39, 114)(40, 115)(41, 163)(42, 165)(43, 167)(44, 168)(45, 169)(46, 124)(47, 125)(48, 122)(49, 126)(50, 123)(51, 161)(52, 162)(53, 174)(54, 164)(55, 166)(56, 128)(57, 173)(58, 176)(59, 177)(60, 135)(61, 136)(62, 180)(63, 132)(64, 133)(65, 150)(66, 151)(67, 139)(68, 137)(69, 140)(70, 138)(71, 144)(72, 146)(73, 184)(74, 142)(75, 179)(76, 178)(77, 186)(78, 187)(79, 152)(80, 183)(81, 175)(82, 159)(83, 160)(84, 190)(85, 156)(86, 157)(87, 189)(88, 188)(89, 170)(90, 171)(91, 172)(92, 181)(93, 182)(94, 192)(95, 185)(96, 191)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1855
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1860 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y1^-2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2 * R * Y2^-2 * R * Y2, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 58, 154, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 59, 155, 57, 153)(37, 133, 60, 156, 40, 136, 61, 157)(38, 134, 62, 158, 41, 137, 63, 159)(39, 135, 64, 160, 53, 149, 66, 162)(42, 138, 67, 163, 43, 139, 69, 165)(44, 140, 68, 164, 52, 148, 70, 166)(50, 146, 65, 161, 82, 178, 78, 174)(71, 167, 88, 184, 73, 169, 87, 183)(72, 168, 92, 188, 74, 170, 91, 187)(75, 171, 85, 181, 76, 172, 83, 179)(77, 173, 93, 189, 79, 175, 94, 190)(80, 176, 86, 182, 81, 177, 84, 180)(89, 185, 95, 191, 90, 186, 96, 192)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 257, 353, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 250, 346, 274, 370, 251, 347, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 269, 365, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 271, 367, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 260, 356, 281, 377, 256, 352, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 262, 358, 282, 378, 258, 354, 233, 329)(237, 333, 263, 359, 239, 335, 267, 363, 285, 381, 272, 368, 246, 342, 264, 360)(238, 334, 265, 361, 240, 336, 268, 364, 286, 382, 273, 369, 248, 344, 266, 362)(252, 348, 275, 371, 254, 350, 279, 375, 287, 383, 283, 379, 259, 355, 276, 372)(253, 349, 277, 373, 255, 351, 280, 376, 288, 384, 284, 380, 261, 357, 278, 374)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 253)(38, 255)(39, 258)(40, 252)(41, 254)(42, 261)(43, 259)(44, 262)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 250)(52, 260)(53, 256)(54, 224)(55, 226)(56, 225)(57, 251)(58, 241)(59, 247)(60, 229)(61, 232)(62, 230)(63, 233)(64, 231)(65, 242)(66, 245)(67, 234)(68, 236)(69, 235)(70, 244)(71, 279)(72, 283)(73, 280)(74, 284)(75, 275)(76, 277)(77, 286)(78, 274)(79, 285)(80, 276)(81, 278)(82, 257)(83, 268)(84, 273)(85, 267)(86, 272)(87, 265)(88, 263)(89, 288)(90, 287)(91, 266)(92, 264)(93, 269)(94, 271)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1863
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1861 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^8, (Y3^-1 * Y1^-1)^4, Y1^-2 * Y2^2 * Y1^-1 * Y2^-4 * Y1^-1, Y2^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 74, 170, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 70, 166, 75, 171, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 65, 161, 77, 173, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 69, 165, 78, 174, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 79, 175, 73, 169, 86, 182, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 76, 172, 62, 158, 90, 186, 68, 164, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 81, 177, 94, 190, 91, 187, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 82, 178, 96, 192, 92, 188, 60, 156)(30, 126, 61, 157, 84, 180, 72, 168, 41, 137, 71, 167, 80, 176, 63, 159)(39, 135, 50, 146, 40, 136, 53, 149, 83, 179, 95, 191, 93, 189, 66, 162)(51, 147, 85, 181, 67, 163, 89, 185, 56, 152, 88, 184, 64, 160, 87, 183)(193, 289, 195, 291, 202, 298, 222, 318, 254, 350, 267, 363, 234, 330, 266, 362, 265, 361, 233, 329, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 243, 339, 278, 374, 261, 357, 228, 324, 257, 353, 282, 378, 248, 344, 218, 314, 200, 296)(196, 292, 204, 300, 227, 323, 259, 355, 271, 367, 236, 332, 210, 306, 235, 331, 268, 364, 256, 352, 223, 319, 206, 302)(198, 294, 211, 307, 237, 333, 272, 368, 260, 356, 229, 325, 205, 301, 219, 315, 250, 346, 276, 372, 240, 336, 212, 308)(201, 297, 220, 316, 207, 303, 231, 327, 263, 359, 274, 370, 238, 334, 273, 369, 239, 335, 275, 371, 253, 349, 221, 317)(203, 299, 224, 320, 208, 304, 232, 328, 264, 360, 284, 380, 249, 345, 283, 379, 262, 358, 285, 381, 255, 351, 225, 321)(213, 309, 241, 337, 216, 312, 246, 342, 280, 376, 287, 383, 269, 365, 286, 382, 270, 366, 288, 384, 277, 373, 242, 338)(215, 311, 244, 340, 217, 313, 247, 343, 281, 377, 258, 354, 226, 322, 251, 347, 230, 326, 252, 348, 279, 375, 245, 341)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 254)(31, 206)(32, 208)(33, 203)(34, 251)(35, 259)(36, 257)(37, 205)(38, 252)(39, 263)(40, 264)(41, 209)(42, 266)(43, 268)(44, 210)(45, 272)(46, 273)(47, 275)(48, 212)(49, 216)(50, 213)(51, 278)(52, 217)(53, 215)(54, 280)(55, 281)(56, 218)(57, 283)(58, 276)(59, 230)(60, 279)(61, 221)(62, 267)(63, 225)(64, 223)(65, 282)(66, 226)(67, 271)(68, 229)(69, 228)(70, 285)(71, 274)(72, 284)(73, 233)(74, 265)(75, 234)(76, 256)(77, 286)(78, 288)(79, 236)(80, 260)(81, 239)(82, 238)(83, 253)(84, 240)(85, 242)(86, 261)(87, 245)(88, 287)(89, 258)(90, 248)(91, 262)(92, 249)(93, 255)(94, 270)(95, 269)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1862
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1862 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^3 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 237, 333, 221, 317, 238, 334)(218, 314, 239, 335, 222, 318, 240, 336)(219, 315, 241, 337, 251, 347, 243, 339)(224, 320, 246, 342, 225, 321, 248, 344)(226, 322, 247, 343, 252, 348, 249, 345)(229, 325, 253, 349, 232, 328, 254, 350)(230, 326, 255, 351, 233, 329, 256, 352)(231, 327, 257, 353, 245, 341, 259, 355)(234, 330, 260, 356, 235, 331, 262, 358)(236, 332, 261, 357, 244, 340, 263, 359)(242, 338, 264, 360, 273, 369, 270, 366)(250, 346, 258, 354, 274, 370, 271, 367)(265, 361, 281, 377, 267, 363, 279, 375)(266, 362, 282, 378, 268, 364, 280, 376)(269, 365, 277, 373, 284, 380, 275, 371)(272, 368, 278, 374, 285, 381, 276, 372)(283, 379, 286, 382, 288, 384, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 242)(28, 205)(29, 207)(30, 203)(31, 245)(32, 247)(33, 249)(34, 208)(35, 251)(36, 210)(37, 214)(38, 211)(39, 258)(40, 215)(41, 213)(42, 261)(43, 263)(44, 216)(45, 265)(46, 267)(47, 257)(48, 259)(49, 218)(50, 269)(51, 222)(52, 220)(53, 271)(54, 266)(55, 262)(56, 268)(57, 260)(58, 226)(59, 273)(60, 228)(61, 275)(62, 277)(63, 243)(64, 241)(65, 230)(66, 279)(67, 233)(68, 276)(69, 246)(70, 278)(71, 248)(72, 236)(73, 239)(74, 237)(75, 240)(76, 238)(77, 283)(78, 244)(79, 281)(80, 250)(81, 284)(82, 252)(83, 255)(84, 253)(85, 256)(86, 254)(87, 286)(88, 264)(89, 287)(90, 270)(91, 272)(92, 288)(93, 274)(94, 280)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1861
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1863 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1^12, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 59, 155, 81, 177, 79, 175, 56, 152, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 73, 169, 88, 184, 92, 188, 85, 181, 60, 156, 39, 135, 18, 114, 11, 107)(5, 101, 15, 111, 33, 129, 58, 154, 80, 176, 87, 183, 93, 189, 86, 182, 61, 157, 40, 136, 19, 115, 16, 112)(7, 103, 20, 116, 12, 108, 31, 127, 53, 149, 78, 174, 91, 187, 76, 172, 82, 178, 63, 159, 36, 132, 22, 118)(8, 104, 23, 119, 14, 110, 34, 130, 57, 153, 77, 173, 90, 186, 75, 171, 83, 179, 64, 160, 37, 133, 24, 120)(10, 106, 21, 117, 38, 134, 62, 158, 84, 180, 94, 190, 96, 192, 95, 191, 89, 185, 74, 170, 46, 142, 28, 124)(26, 122, 47, 143, 29, 125, 51, 147, 65, 161, 54, 150, 68, 164, 41, 137, 67, 163, 43, 139, 71, 167, 48, 144)(27, 123, 49, 145, 30, 126, 52, 148, 66, 162, 55, 151, 70, 166, 42, 138, 69, 165, 44, 140, 72, 168, 50, 146)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 238)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 246)(32, 245)(33, 205)(34, 247)(35, 252)(36, 254)(37, 209)(38, 211)(39, 257)(40, 258)(41, 215)(42, 212)(43, 216)(44, 214)(45, 263)(46, 225)(47, 267)(48, 256)(49, 268)(50, 255)(51, 269)(52, 270)(53, 266)(54, 226)(55, 223)(56, 265)(57, 224)(58, 264)(59, 274)(60, 276)(61, 227)(62, 229)(63, 240)(64, 242)(65, 232)(66, 231)(67, 279)(68, 278)(69, 280)(70, 277)(71, 250)(72, 237)(73, 281)(74, 249)(75, 241)(76, 239)(77, 244)(78, 243)(79, 283)(80, 248)(81, 284)(82, 286)(83, 251)(84, 253)(85, 260)(86, 262)(87, 261)(88, 259)(89, 272)(90, 271)(91, 287)(92, 288)(93, 273)(94, 275)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1860
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1864 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y1^-2 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y1 * Y2^-2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y3^-1, Y1 * Y2^2 * Y3 * Y2^2, Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1, Y2^-2 * Y1^-2 * Y2 * Y3 * Y2^-2 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y2^3 * Y1^-1 * Y2^-1, Y2^-1 * Y3^-1 * Y2^3 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^12, (Y3 * Y2 * Y1^-1 * Y2)^4 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 59, 155, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 60, 156, 57, 153)(37, 133, 61, 157, 40, 136, 62, 158)(38, 134, 63, 159, 41, 137, 64, 160)(39, 135, 65, 161, 53, 149, 67, 163)(42, 138, 68, 164, 43, 139, 70, 166)(44, 140, 69, 165, 52, 148, 71, 167)(50, 146, 72, 168, 81, 177, 78, 174)(58, 154, 66, 162, 82, 178, 79, 175)(73, 169, 89, 185, 75, 171, 87, 183)(74, 170, 90, 186, 76, 172, 88, 184)(77, 173, 85, 181, 92, 188, 83, 179)(80, 176, 86, 182, 93, 189, 84, 180)(91, 187, 94, 190, 96, 192, 95, 191)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 269, 365, 283, 379, 272, 368, 250, 346, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 258, 354, 279, 375, 286, 382, 280, 376, 264, 360, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 271, 367, 281, 377, 287, 383, 282, 378, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 251, 347, 273, 369, 284, 380, 288, 384, 285, 381, 274, 370, 252, 348, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 262, 358, 278, 374, 254, 350, 277, 373, 256, 352, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 260, 356, 276, 372, 253, 349, 275, 371, 255, 351, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 261, 357, 246, 342, 266, 362, 237, 333, 265, 361, 239, 335, 257, 353, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 263, 359, 248, 344, 268, 364, 238, 334, 267, 363, 240, 336, 259, 355, 233, 329)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 254)(38, 256)(39, 259)(40, 253)(41, 255)(42, 262)(43, 260)(44, 263)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 251)(52, 261)(53, 257)(54, 224)(55, 226)(56, 225)(57, 252)(58, 271)(59, 241)(60, 247)(61, 229)(62, 232)(63, 230)(64, 233)(65, 231)(66, 250)(67, 245)(68, 234)(69, 236)(70, 235)(71, 244)(72, 242)(73, 279)(74, 280)(75, 281)(76, 282)(77, 275)(78, 273)(79, 274)(80, 276)(81, 264)(82, 258)(83, 284)(84, 285)(85, 269)(86, 272)(87, 267)(88, 268)(89, 265)(90, 266)(91, 287)(92, 277)(93, 278)(94, 283)(95, 288)(96, 286)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1865
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1865 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C3 x Q8) : C4 (small group id <96, 42>)
Aut   = $<192, 731>$ (small group id <192, 731>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y1^8, Y1^2 * Y3^6 * Y1^2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 57, 153, 74, 170, 46, 142, 19, 115, 11, 107)(5, 101, 15, 111, 37, 133, 70, 166, 75, 171, 47, 143, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 65, 161, 77, 173, 43, 139, 23, 119)(8, 104, 24, 120, 14, 110, 38, 134, 69, 165, 78, 174, 44, 140, 25, 121)(10, 106, 26, 122, 45, 141, 79, 175, 73, 169, 86, 182, 58, 154, 31, 127)(17, 113, 22, 118, 48, 144, 76, 172, 62, 158, 90, 186, 68, 164, 35, 131)(28, 124, 49, 145, 32, 128, 52, 148, 81, 177, 94, 190, 91, 187, 59, 155)(29, 125, 54, 150, 33, 129, 55, 151, 82, 178, 96, 192, 92, 188, 60, 156)(30, 126, 61, 157, 84, 180, 72, 168, 41, 137, 71, 167, 80, 176, 63, 159)(39, 135, 50, 146, 40, 136, 53, 149, 83, 179, 95, 191, 93, 189, 66, 162)(51, 147, 85, 181, 67, 163, 89, 185, 56, 152, 88, 184, 64, 160, 87, 183)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 237)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 250)(28, 207)(29, 201)(30, 254)(31, 206)(32, 208)(33, 203)(34, 251)(35, 259)(36, 257)(37, 205)(38, 252)(39, 263)(40, 264)(41, 209)(42, 266)(43, 268)(44, 210)(45, 272)(46, 273)(47, 275)(48, 212)(49, 216)(50, 213)(51, 278)(52, 217)(53, 215)(54, 280)(55, 281)(56, 218)(57, 283)(58, 276)(59, 230)(60, 279)(61, 221)(62, 267)(63, 225)(64, 223)(65, 282)(66, 226)(67, 271)(68, 229)(69, 228)(70, 285)(71, 274)(72, 284)(73, 233)(74, 265)(75, 234)(76, 256)(77, 286)(78, 288)(79, 236)(80, 260)(81, 239)(82, 238)(83, 253)(84, 240)(85, 242)(86, 261)(87, 245)(88, 287)(89, 258)(90, 248)(91, 262)(92, 249)(93, 255)(94, 270)(95, 269)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1864
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1866 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^-1 * T2^-2 * T1 * T2^2, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^-2 * T2^-1 * T1^2 * T2^-3, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2^-1 * T1)^6 ]
Map:: non-degenerate
	R = (1, 3, 10, 28, 62, 40, 16, 5)(2, 7, 20, 50, 76, 56, 24, 8)(4, 12, 29, 53, 71, 47, 36, 13)(6, 17, 42, 37, 57, 25, 46, 18)(9, 26, 45, 70, 43, 38, 14, 27)(11, 30, 44, 69, 41, 39, 15, 31)(19, 48, 35, 68, 33, 54, 22, 49)(21, 51, 34, 67, 32, 55, 23, 52)(58, 81, 66, 88, 64, 85, 60, 82)(59, 83, 65, 87, 63, 86, 61, 84)(72, 89, 80, 96, 78, 93, 74, 90)(73, 91, 79, 95, 77, 94, 75, 92)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 133, 111)(103, 115, 143, 117)(104, 118, 149, 119)(106, 116, 138, 125)(108, 128, 152, 129)(109, 130, 146, 131)(112, 120, 142, 132)(113, 137, 136, 139)(114, 140, 124, 141)(122, 154, 135, 155)(123, 156, 165, 157)(126, 159, 134, 160)(127, 161, 166, 162)(144, 168, 151, 169)(145, 170, 163, 171)(147, 173, 150, 174)(148, 175, 164, 176)(153, 167, 158, 172)(177, 191, 182, 186)(178, 187, 183, 189)(179, 192, 181, 188)(180, 185, 184, 190)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1870
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1867 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-1 * T2^-2 * T1, T1 * T2^-1 * T1^-2 * T2 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2, (T2 * T1^-1)^4, T1^8, T2 * T1 * T2^-3 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T1 * T2^-6 * T1^3 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 29, 62, 78, 42, 77, 76, 41, 17, 5)(2, 7, 22, 51, 91, 71, 36, 69, 96, 56, 26, 8)(4, 12, 34, 67, 82, 44, 18, 43, 80, 65, 30, 14)(6, 19, 46, 85, 68, 37, 13, 32, 64, 87, 48, 20)(9, 27, 15, 39, 73, 94, 66, 88, 72, 89, 61, 28)(11, 31, 16, 40, 75, 84, 45, 83, 47, 86, 63, 33)(21, 49, 24, 54, 93, 70, 35, 57, 38, 59, 90, 50)(23, 52, 25, 55, 95, 74, 79, 58, 81, 60, 92, 53)(97, 98, 102, 114, 138, 132, 109, 100)(99, 105, 115, 141, 173, 162, 128, 107)(101, 111, 116, 143, 174, 168, 133, 112)(103, 117, 139, 175, 165, 131, 108, 119)(104, 120, 140, 177, 167, 134, 110, 121)(106, 122, 142, 178, 172, 187, 160, 126)(113, 118, 144, 176, 158, 192, 164, 130)(123, 153, 179, 148, 184, 145, 127, 154)(124, 155, 180, 151, 190, 150, 129, 156)(125, 157, 181, 171, 137, 169, 183, 159)(135, 166, 182, 149, 185, 146, 136, 170)(147, 186, 161, 191, 152, 189, 163, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1871
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1868 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1^-2 * T2 * T1^-2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2^2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-2 * T1 * T2 * T1^-1 * T2^-1, T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^3 * T2 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 * T1 * T2 * T1^-1 * T2^-1, T1^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 33, 14)(6, 18, 44, 19)(9, 26, 59, 27)(11, 30, 66, 31)(13, 25, 58, 35)(15, 37, 74, 38)(16, 39, 75, 40)(17, 42, 79, 43)(20, 47, 87, 48)(22, 51, 92, 52)(23, 53, 93, 54)(24, 55, 94, 56)(28, 62, 95, 63)(29, 64, 76, 65)(32, 60, 81, 68)(34, 67, 82, 71)(36, 61, 80, 73)(41, 77, 69, 78)(45, 83, 72, 84)(46, 85, 57, 86)(49, 88, 70, 89)(50, 90, 96, 91)(97, 98, 102, 113, 137, 172, 192, 191, 166, 130, 109, 100)(99, 105, 121, 153, 185, 171, 187, 170, 173, 141, 114, 107)(101, 111, 131, 168, 184, 162, 186, 155, 174, 142, 115, 112)(103, 116, 108, 128, 163, 190, 159, 189, 161, 176, 138, 118)(104, 119, 110, 132, 167, 188, 158, 183, 160, 177, 139, 120)(106, 124, 140, 178, 165, 129, 146, 117, 145, 175, 154, 125)(122, 143, 126, 147, 179, 169, 134, 150, 136, 152, 182, 156)(123, 149, 127, 151, 180, 164, 133, 144, 135, 148, 181, 157)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1869
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1869 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^-1 * T2^-2 * T1 * T2^2, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^-2 * T2^-1 * T1^2 * T2^-3, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1, (T2^-1 * T1)^6 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 28, 124, 62, 158, 40, 136, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 50, 146, 76, 172, 56, 152, 24, 120, 8, 104)(4, 100, 12, 108, 29, 125, 53, 149, 71, 167, 47, 143, 36, 132, 13, 109)(6, 102, 17, 113, 42, 138, 37, 133, 57, 153, 25, 121, 46, 142, 18, 114)(9, 105, 26, 122, 45, 141, 70, 166, 43, 139, 38, 134, 14, 110, 27, 123)(11, 107, 30, 126, 44, 140, 69, 165, 41, 137, 39, 135, 15, 111, 31, 127)(19, 115, 48, 144, 35, 131, 68, 164, 33, 129, 54, 150, 22, 118, 49, 145)(21, 117, 51, 147, 34, 130, 67, 163, 32, 128, 55, 151, 23, 119, 52, 148)(58, 154, 81, 177, 66, 162, 88, 184, 64, 160, 85, 181, 60, 156, 82, 178)(59, 155, 83, 179, 65, 161, 87, 183, 63, 159, 86, 182, 61, 157, 84, 180)(72, 168, 89, 185, 80, 176, 96, 192, 78, 174, 93, 189, 74, 170, 90, 186)(73, 169, 91, 187, 79, 175, 95, 191, 77, 173, 94, 190, 75, 171, 92, 188)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 116)(11, 99)(12, 128)(13, 130)(14, 133)(15, 101)(16, 120)(17, 137)(18, 140)(19, 143)(20, 138)(21, 103)(22, 149)(23, 104)(24, 142)(25, 107)(26, 154)(27, 156)(28, 141)(29, 106)(30, 159)(31, 161)(32, 152)(33, 108)(34, 146)(35, 109)(36, 112)(37, 111)(38, 160)(39, 155)(40, 139)(41, 136)(42, 125)(43, 113)(44, 124)(45, 114)(46, 132)(47, 117)(48, 168)(49, 170)(50, 131)(51, 173)(52, 175)(53, 119)(54, 174)(55, 169)(56, 129)(57, 167)(58, 135)(59, 122)(60, 165)(61, 123)(62, 172)(63, 134)(64, 126)(65, 166)(66, 127)(67, 171)(68, 176)(69, 157)(70, 162)(71, 158)(72, 151)(73, 144)(74, 163)(75, 145)(76, 153)(77, 150)(78, 147)(79, 164)(80, 148)(81, 191)(82, 187)(83, 192)(84, 185)(85, 188)(86, 186)(87, 189)(88, 190)(89, 184)(90, 177)(91, 183)(92, 179)(93, 178)(94, 180)(95, 182)(96, 181)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1868
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1870 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-1 * T2^-2 * T1, T1 * T2^-1 * T1^-2 * T2 * T1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2, (T2 * T1^-1)^4, T1^8, T2 * T1 * T2^-3 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T1 * T2^-6 * T1^3 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 29, 125, 62, 158, 78, 174, 42, 138, 77, 173, 76, 172, 41, 137, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 51, 147, 91, 187, 71, 167, 36, 132, 69, 165, 96, 192, 56, 152, 26, 122, 8, 104)(4, 100, 12, 108, 34, 130, 67, 163, 82, 178, 44, 140, 18, 114, 43, 139, 80, 176, 65, 161, 30, 126, 14, 110)(6, 102, 19, 115, 46, 142, 85, 181, 68, 164, 37, 133, 13, 109, 32, 128, 64, 160, 87, 183, 48, 144, 20, 116)(9, 105, 27, 123, 15, 111, 39, 135, 73, 169, 94, 190, 66, 162, 88, 184, 72, 168, 89, 185, 61, 157, 28, 124)(11, 107, 31, 127, 16, 112, 40, 136, 75, 171, 84, 180, 45, 141, 83, 179, 47, 143, 86, 182, 63, 159, 33, 129)(21, 117, 49, 145, 24, 120, 54, 150, 93, 189, 70, 166, 35, 131, 57, 153, 38, 134, 59, 155, 90, 186, 50, 146)(23, 119, 52, 148, 25, 121, 55, 151, 95, 191, 74, 170, 79, 175, 58, 154, 81, 177, 60, 156, 92, 188, 53, 149)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 115)(10, 122)(11, 99)(12, 119)(13, 100)(14, 121)(15, 116)(16, 101)(17, 118)(18, 138)(19, 141)(20, 143)(21, 139)(22, 144)(23, 103)(24, 140)(25, 104)(26, 142)(27, 153)(28, 155)(29, 157)(30, 106)(31, 154)(32, 107)(33, 156)(34, 113)(35, 108)(36, 109)(37, 112)(38, 110)(39, 166)(40, 170)(41, 169)(42, 132)(43, 175)(44, 177)(45, 173)(46, 178)(47, 174)(48, 176)(49, 127)(50, 136)(51, 186)(52, 184)(53, 185)(54, 129)(55, 190)(56, 189)(57, 179)(58, 123)(59, 180)(60, 124)(61, 181)(62, 192)(63, 125)(64, 126)(65, 191)(66, 128)(67, 188)(68, 130)(69, 131)(70, 182)(71, 134)(72, 133)(73, 183)(74, 135)(75, 137)(76, 187)(77, 162)(78, 168)(79, 165)(80, 158)(81, 167)(82, 172)(83, 148)(84, 151)(85, 171)(86, 149)(87, 159)(88, 145)(89, 146)(90, 161)(91, 160)(92, 147)(93, 163)(94, 150)(95, 152)(96, 164)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1866
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1871 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1^-2 * T2 * T1^-2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T1^-2 * T2 * T1^2 * T2 * T1^-1 * T2^2 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-2 * T1 * T2 * T1^-1 * T2^-1, T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^3 * T2 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 * T2^2 * T1 * T2 * T1^-1 * T2^-1, T1^12 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 33, 129, 14, 110)(6, 102, 18, 114, 44, 140, 19, 115)(9, 105, 26, 122, 59, 155, 27, 123)(11, 107, 30, 126, 66, 162, 31, 127)(13, 109, 25, 121, 58, 154, 35, 131)(15, 111, 37, 133, 74, 170, 38, 134)(16, 112, 39, 135, 75, 171, 40, 136)(17, 113, 42, 138, 79, 175, 43, 139)(20, 116, 47, 143, 87, 183, 48, 144)(22, 118, 51, 147, 92, 188, 52, 148)(23, 119, 53, 149, 93, 189, 54, 150)(24, 120, 55, 151, 94, 190, 56, 152)(28, 124, 62, 158, 95, 191, 63, 159)(29, 125, 64, 160, 76, 172, 65, 161)(32, 128, 60, 156, 81, 177, 68, 164)(34, 130, 67, 163, 82, 178, 71, 167)(36, 132, 61, 157, 80, 176, 73, 169)(41, 137, 77, 173, 69, 165, 78, 174)(45, 141, 83, 179, 72, 168, 84, 180)(46, 142, 85, 181, 57, 153, 86, 182)(49, 145, 88, 184, 70, 166, 89, 185)(50, 146, 90, 186, 96, 192, 91, 187)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 124)(11, 99)(12, 128)(13, 100)(14, 132)(15, 131)(16, 101)(17, 137)(18, 107)(19, 112)(20, 108)(21, 145)(22, 103)(23, 110)(24, 104)(25, 153)(26, 143)(27, 149)(28, 140)(29, 106)(30, 147)(31, 151)(32, 163)(33, 146)(34, 109)(35, 168)(36, 167)(37, 144)(38, 150)(39, 148)(40, 152)(41, 172)(42, 118)(43, 120)(44, 178)(45, 114)(46, 115)(47, 126)(48, 135)(49, 175)(50, 117)(51, 179)(52, 181)(53, 127)(54, 136)(55, 180)(56, 182)(57, 185)(58, 125)(59, 174)(60, 122)(61, 123)(62, 183)(63, 189)(64, 177)(65, 176)(66, 186)(67, 190)(68, 133)(69, 129)(70, 130)(71, 188)(72, 184)(73, 134)(74, 173)(75, 187)(76, 192)(77, 141)(78, 142)(79, 154)(80, 138)(81, 139)(82, 165)(83, 169)(84, 164)(85, 157)(86, 156)(87, 160)(88, 162)(89, 171)(90, 155)(91, 170)(92, 158)(93, 161)(94, 159)(95, 166)(96, 191)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1867
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1872 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y3 * Y1^-3, Y3^2 * Y1^-2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^2 * Y3 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2, Y3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-2 * Y2^-1 * Y1^-2 * Y2^-2, Y1^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y2^2, Y1^-2 * Y2^-3 * Y3 * Y1^-1 * Y2^-1, Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^-2 * Y3, Y2^8, Y1 * Y2^3 * Y3 * R * Y2^-1 * R, Y2^-2 * Y3 * Y2^-1 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 47, 143, 21, 117)(8, 104, 22, 118, 53, 149, 23, 119)(10, 106, 20, 116, 42, 138, 29, 125)(12, 108, 32, 128, 56, 152, 33, 129)(13, 109, 34, 130, 50, 146, 35, 131)(16, 112, 24, 120, 46, 142, 36, 132)(17, 113, 41, 137, 40, 136, 43, 139)(18, 114, 44, 140, 28, 124, 45, 141)(26, 122, 58, 154, 39, 135, 59, 155)(27, 123, 60, 156, 69, 165, 61, 157)(30, 126, 63, 159, 38, 134, 64, 160)(31, 127, 65, 161, 70, 166, 66, 162)(48, 144, 72, 168, 55, 151, 73, 169)(49, 145, 74, 170, 67, 163, 75, 171)(51, 147, 77, 173, 54, 150, 78, 174)(52, 148, 79, 175, 68, 164, 80, 176)(57, 153, 71, 167, 62, 158, 76, 172)(81, 177, 95, 191, 86, 182, 90, 186)(82, 178, 91, 187, 87, 183, 93, 189)(83, 179, 96, 192, 85, 181, 92, 188)(84, 180, 89, 185, 88, 184, 94, 190)(193, 289, 195, 291, 202, 298, 220, 316, 254, 350, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 242, 338, 268, 364, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 245, 341, 263, 359, 239, 335, 228, 324, 205, 301)(198, 294, 209, 305, 234, 330, 229, 325, 249, 345, 217, 313, 238, 334, 210, 306)(201, 297, 218, 314, 237, 333, 262, 358, 235, 331, 230, 326, 206, 302, 219, 315)(203, 299, 222, 318, 236, 332, 261, 357, 233, 329, 231, 327, 207, 303, 223, 319)(211, 307, 240, 336, 227, 323, 260, 356, 225, 321, 246, 342, 214, 310, 241, 337)(213, 309, 243, 339, 226, 322, 259, 355, 224, 320, 247, 343, 215, 311, 244, 340)(250, 346, 273, 369, 258, 354, 280, 376, 256, 352, 277, 373, 252, 348, 274, 370)(251, 347, 275, 371, 257, 353, 279, 375, 255, 351, 278, 374, 253, 349, 276, 372)(264, 360, 281, 377, 272, 368, 288, 384, 270, 366, 285, 381, 266, 362, 282, 378)(265, 361, 283, 379, 271, 367, 287, 383, 269, 365, 286, 382, 267, 363, 284, 380)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 225)(13, 227)(14, 197)(15, 229)(16, 228)(17, 235)(18, 237)(19, 199)(20, 202)(21, 239)(22, 200)(23, 245)(24, 208)(25, 201)(26, 251)(27, 253)(28, 236)(29, 234)(30, 256)(31, 258)(32, 204)(33, 248)(34, 205)(35, 242)(36, 238)(37, 206)(38, 255)(39, 250)(40, 233)(41, 209)(42, 212)(43, 232)(44, 210)(45, 220)(46, 216)(47, 211)(48, 265)(49, 267)(50, 226)(51, 270)(52, 272)(53, 214)(54, 269)(55, 264)(56, 224)(57, 268)(58, 218)(59, 231)(60, 219)(61, 261)(62, 263)(63, 222)(64, 230)(65, 223)(66, 262)(67, 266)(68, 271)(69, 252)(70, 257)(71, 249)(72, 240)(73, 247)(74, 241)(75, 259)(76, 254)(77, 243)(78, 246)(79, 244)(80, 260)(81, 282)(82, 285)(83, 284)(84, 286)(85, 288)(86, 287)(87, 283)(88, 281)(89, 276)(90, 278)(91, 274)(92, 277)(93, 279)(94, 280)(95, 273)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1875
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1873 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-2 * Y2^-1 * Y1^2, Y2^2 * Y1^-1 * Y2^2 * Y1, (Y1^-1 * Y2^-1)^4, Y1^8, (Y3^-1 * Y1^-1)^4, Y2 * Y1 * Y2^-3 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-6 * Y1^3, (Y2 * Y1^-1 * Y2^-2 * Y1^-1)^2 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 45, 141, 77, 173, 66, 162, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 47, 143, 78, 174, 72, 168, 37, 133, 16, 112)(7, 103, 21, 117, 43, 139, 79, 175, 69, 165, 35, 131, 12, 108, 23, 119)(8, 104, 24, 120, 44, 140, 81, 177, 71, 167, 38, 134, 14, 110, 25, 121)(10, 106, 26, 122, 46, 142, 82, 178, 76, 172, 91, 187, 64, 160, 30, 126)(17, 113, 22, 118, 48, 144, 80, 176, 62, 158, 96, 192, 68, 164, 34, 130)(27, 123, 57, 153, 83, 179, 52, 148, 88, 184, 49, 145, 31, 127, 58, 154)(28, 124, 59, 155, 84, 180, 55, 151, 94, 190, 54, 150, 33, 129, 60, 156)(29, 125, 61, 157, 85, 181, 75, 171, 41, 137, 73, 169, 87, 183, 63, 159)(39, 135, 70, 166, 86, 182, 53, 149, 89, 185, 50, 146, 40, 136, 74, 170)(51, 147, 90, 186, 65, 161, 95, 191, 56, 152, 93, 189, 67, 163, 92, 188)(193, 289, 195, 291, 202, 298, 221, 317, 254, 350, 270, 366, 234, 330, 269, 365, 268, 364, 233, 329, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 243, 339, 283, 379, 263, 359, 228, 324, 261, 357, 288, 384, 248, 344, 218, 314, 200, 296)(196, 292, 204, 300, 226, 322, 259, 355, 274, 370, 236, 332, 210, 306, 235, 331, 272, 368, 257, 353, 222, 318, 206, 302)(198, 294, 211, 307, 238, 334, 277, 373, 260, 356, 229, 325, 205, 301, 224, 320, 256, 352, 279, 375, 240, 336, 212, 308)(201, 297, 219, 315, 207, 303, 231, 327, 265, 361, 286, 382, 258, 354, 280, 376, 264, 360, 281, 377, 253, 349, 220, 316)(203, 299, 223, 319, 208, 304, 232, 328, 267, 363, 276, 372, 237, 333, 275, 371, 239, 335, 278, 374, 255, 351, 225, 321)(213, 309, 241, 337, 216, 312, 246, 342, 285, 381, 262, 358, 227, 323, 249, 345, 230, 326, 251, 347, 282, 378, 242, 338)(215, 311, 244, 340, 217, 313, 247, 343, 287, 383, 266, 362, 271, 367, 250, 346, 273, 369, 252, 348, 284, 380, 245, 341)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 221)(11, 223)(12, 226)(13, 224)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 238)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 207)(28, 201)(29, 254)(30, 206)(31, 208)(32, 256)(33, 203)(34, 259)(35, 249)(36, 261)(37, 205)(38, 251)(39, 265)(40, 267)(41, 209)(42, 269)(43, 272)(44, 210)(45, 275)(46, 277)(47, 278)(48, 212)(49, 216)(50, 213)(51, 283)(52, 217)(53, 215)(54, 285)(55, 287)(56, 218)(57, 230)(58, 273)(59, 282)(60, 284)(61, 220)(62, 270)(63, 225)(64, 279)(65, 222)(66, 280)(67, 274)(68, 229)(69, 288)(70, 227)(71, 228)(72, 281)(73, 286)(74, 271)(75, 276)(76, 233)(77, 268)(78, 234)(79, 250)(80, 257)(81, 252)(82, 236)(83, 239)(84, 237)(85, 260)(86, 255)(87, 240)(88, 264)(89, 253)(90, 242)(91, 263)(92, 245)(93, 262)(94, 258)(95, 266)(96, 248)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1874
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1874 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3^2 * Y2 * Y3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-2 * Y2 * Y3^-2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3^-5 * Y2^-2 * Y3^-1 * Y2, Y3 * Y2^-2 * Y3^3 * Y2^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 217, 313, 203, 299)(197, 293, 206, 302, 229, 325, 207, 303)(199, 295, 211, 307, 239, 335, 213, 309)(200, 296, 214, 310, 245, 341, 215, 311)(202, 298, 216, 312, 234, 330, 221, 317)(204, 300, 224, 320, 259, 355, 226, 322)(205, 301, 227, 323, 263, 359, 228, 324)(208, 304, 212, 308, 238, 334, 225, 321)(209, 305, 233, 329, 268, 364, 235, 331)(210, 306, 236, 332, 274, 370, 237, 333)(218, 314, 240, 336, 269, 365, 251, 347)(219, 315, 246, 342, 270, 366, 252, 348)(220, 316, 253, 349, 277, 373, 255, 351)(222, 318, 243, 339, 272, 368, 257, 353)(223, 319, 247, 343, 273, 369, 258, 354)(230, 326, 241, 337, 275, 371, 260, 356)(231, 327, 244, 340, 276, 372, 262, 358)(232, 328, 265, 361, 271, 367, 266, 362)(242, 338, 280, 376, 256, 352, 282, 378)(248, 344, 284, 380, 261, 357, 285, 381)(249, 345, 283, 379, 267, 363, 281, 377)(250, 346, 279, 375, 288, 384, 287, 383)(254, 350, 286, 382, 264, 360, 278, 374)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 220)(11, 222)(12, 225)(13, 196)(14, 230)(15, 231)(16, 197)(17, 234)(18, 198)(19, 240)(20, 242)(21, 243)(22, 246)(23, 247)(24, 200)(25, 249)(26, 206)(27, 201)(28, 254)(29, 205)(30, 207)(31, 203)(32, 251)(33, 261)(34, 257)(35, 252)(36, 258)(37, 250)(38, 265)(39, 266)(40, 208)(41, 269)(42, 271)(43, 272)(44, 275)(45, 276)(46, 210)(47, 278)(48, 214)(49, 211)(50, 281)(51, 215)(52, 213)(53, 279)(54, 284)(55, 285)(56, 216)(57, 277)(58, 217)(59, 227)(60, 282)(61, 219)(62, 274)(63, 223)(64, 221)(65, 228)(66, 280)(67, 286)(68, 224)(69, 283)(70, 226)(71, 287)(72, 229)(73, 273)(74, 270)(75, 232)(76, 267)(77, 236)(78, 233)(79, 264)(80, 237)(81, 235)(82, 288)(83, 255)(84, 253)(85, 238)(86, 256)(87, 239)(88, 241)(89, 263)(90, 244)(91, 245)(92, 262)(93, 260)(94, 248)(95, 259)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1873
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1875 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3 * Y2^-1)^4, Y3 * Y1^3 * Y3^-2 * Y1 * Y3 * Y1^-2, Y3^-2 * Y1^-1 * Y3^-1 * Y1^4 * Y3^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3 * Y1 * Y3^2 * Y1^-1, Y1 * Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3 * Y1^-1 * Y3^-2, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-2 * Y1 * Y3 * Y1^-1 * Y3^-1, Y1^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 76, 172, 96, 192, 95, 191, 70, 166, 34, 130, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 57, 153, 89, 185, 75, 171, 91, 187, 74, 170, 77, 173, 45, 141, 18, 114, 11, 107)(5, 101, 15, 111, 35, 131, 72, 168, 88, 184, 66, 162, 90, 186, 59, 155, 78, 174, 46, 142, 19, 115, 16, 112)(7, 103, 20, 116, 12, 108, 32, 128, 67, 163, 94, 190, 63, 159, 93, 189, 65, 161, 80, 176, 42, 138, 22, 118)(8, 104, 23, 119, 14, 110, 36, 132, 71, 167, 92, 188, 62, 158, 87, 183, 64, 160, 81, 177, 43, 139, 24, 120)(10, 106, 28, 124, 44, 140, 82, 178, 69, 165, 33, 129, 50, 146, 21, 117, 49, 145, 79, 175, 58, 154, 29, 125)(26, 122, 47, 143, 30, 126, 51, 147, 83, 179, 73, 169, 38, 134, 54, 150, 40, 136, 56, 152, 86, 182, 60, 156)(27, 123, 53, 149, 31, 127, 55, 151, 84, 180, 68, 164, 37, 133, 48, 144, 39, 135, 52, 148, 85, 181, 61, 157)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 222)(12, 225)(13, 217)(14, 196)(15, 229)(16, 231)(17, 234)(18, 236)(19, 198)(20, 239)(21, 200)(22, 243)(23, 245)(24, 247)(25, 250)(26, 251)(27, 201)(28, 254)(29, 256)(30, 258)(31, 203)(32, 252)(33, 206)(34, 259)(35, 205)(36, 253)(37, 266)(38, 207)(39, 267)(40, 208)(41, 269)(42, 271)(43, 209)(44, 211)(45, 275)(46, 277)(47, 279)(48, 212)(49, 280)(50, 282)(51, 284)(52, 214)(53, 285)(54, 215)(55, 286)(56, 216)(57, 278)(58, 227)(59, 219)(60, 273)(61, 272)(62, 287)(63, 220)(64, 268)(65, 221)(66, 223)(67, 274)(68, 224)(69, 270)(70, 281)(71, 226)(72, 276)(73, 228)(74, 230)(75, 232)(76, 257)(77, 261)(78, 233)(79, 235)(80, 265)(81, 260)(82, 263)(83, 264)(84, 237)(85, 249)(86, 238)(87, 240)(88, 262)(89, 241)(90, 288)(91, 242)(92, 244)(93, 246)(94, 248)(95, 255)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1872
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1876 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^2 * Y3 * Y2^2 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-4 * Y1^-1 * Y2 * Y1^2, Y1^-1 * Y2^-3 * Y1 * Y3^-1 * Y2^-3 * Y1^-1, Y3 * Y2 * Y1^-2 * Y2^-1 * Y3^-1 * Y2 * Y1^-2 * Y2^-1, Y2^3 * Y3^-1 * Y2^-1 * Y1^-2 * Y2^-1 * Y3^-1 * Y2, Y2 * Y1^-2 * Y2^3 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^-2 * Y3 * Y2^3 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y1^2 * Y2^-1 * Y3^2, Y2^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 47, 143, 21, 117)(8, 104, 22, 118, 53, 149, 23, 119)(10, 106, 24, 120, 42, 138, 29, 125)(12, 108, 32, 128, 67, 163, 34, 130)(13, 109, 35, 131, 71, 167, 36, 132)(16, 112, 20, 116, 46, 142, 33, 129)(17, 113, 41, 137, 76, 172, 43, 139)(18, 114, 44, 140, 82, 178, 45, 141)(26, 122, 48, 144, 77, 173, 59, 155)(27, 123, 54, 150, 78, 174, 60, 156)(28, 124, 61, 157, 85, 181, 63, 159)(30, 126, 51, 147, 80, 176, 65, 161)(31, 127, 55, 151, 81, 177, 66, 162)(38, 134, 49, 145, 83, 179, 68, 164)(39, 135, 52, 148, 84, 180, 70, 166)(40, 136, 73, 169, 79, 175, 74, 170)(50, 146, 88, 184, 64, 160, 90, 186)(56, 152, 92, 188, 69, 165, 93, 189)(57, 153, 91, 187, 75, 171, 89, 185)(58, 154, 87, 183, 96, 192, 95, 191)(62, 158, 94, 190, 72, 168, 86, 182)(193, 289, 195, 291, 202, 298, 220, 316, 254, 350, 274, 370, 288, 384, 268, 364, 267, 363, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 242, 338, 281, 377, 263, 359, 287, 383, 259, 355, 286, 382, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 225, 321, 261, 357, 283, 379, 245, 341, 279, 375, 239, 335, 278, 374, 256, 352, 221, 317, 205, 301)(198, 294, 209, 305, 234, 330, 271, 367, 264, 360, 229, 325, 250, 346, 217, 313, 249, 345, 277, 373, 238, 334, 210, 306)(201, 297, 218, 314, 206, 302, 230, 326, 265, 361, 273, 369, 235, 331, 272, 368, 237, 333, 276, 372, 253, 349, 219, 315)(203, 299, 222, 318, 207, 303, 231, 327, 266, 362, 270, 366, 233, 329, 269, 365, 236, 332, 275, 371, 255, 351, 223, 319)(211, 307, 240, 336, 214, 310, 246, 342, 284, 380, 262, 358, 226, 322, 257, 353, 228, 324, 258, 354, 280, 376, 241, 337)(213, 309, 243, 339, 215, 311, 247, 343, 285, 381, 260, 356, 224, 320, 251, 347, 227, 323, 252, 348, 282, 378, 244, 340)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 226)(13, 228)(14, 197)(15, 229)(16, 225)(17, 235)(18, 237)(19, 199)(20, 208)(21, 239)(22, 200)(23, 245)(24, 202)(25, 201)(26, 251)(27, 252)(28, 255)(29, 234)(30, 257)(31, 258)(32, 204)(33, 238)(34, 259)(35, 205)(36, 263)(37, 206)(38, 260)(39, 262)(40, 266)(41, 209)(42, 216)(43, 268)(44, 210)(45, 274)(46, 212)(47, 211)(48, 218)(49, 230)(50, 282)(51, 222)(52, 231)(53, 214)(54, 219)(55, 223)(56, 285)(57, 281)(58, 287)(59, 269)(60, 270)(61, 220)(62, 278)(63, 277)(64, 280)(65, 272)(66, 273)(67, 224)(68, 275)(69, 284)(70, 276)(71, 227)(72, 286)(73, 232)(74, 271)(75, 283)(76, 233)(77, 240)(78, 246)(79, 265)(80, 243)(81, 247)(82, 236)(83, 241)(84, 244)(85, 253)(86, 264)(87, 250)(88, 242)(89, 267)(90, 256)(91, 249)(92, 248)(93, 261)(94, 254)(95, 288)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1877
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1877 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>)
Aut   = $<192, 757>$ (small group id <192, 757>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1 * Y3^2 * Y1^-1, Y1 * Y3^2 * Y1^-1 * Y3^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y1^-1 * Y3^-1)^4, Y1^8, Y3^3 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3^-6 * Y1^3, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 42, 138, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 45, 141, 77, 173, 66, 162, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 47, 143, 78, 174, 72, 168, 37, 133, 16, 112)(7, 103, 21, 117, 43, 139, 79, 175, 69, 165, 35, 131, 12, 108, 23, 119)(8, 104, 24, 120, 44, 140, 81, 177, 71, 167, 38, 134, 14, 110, 25, 121)(10, 106, 26, 122, 46, 142, 82, 178, 76, 172, 91, 187, 64, 160, 30, 126)(17, 113, 22, 118, 48, 144, 80, 176, 62, 158, 96, 192, 68, 164, 34, 130)(27, 123, 57, 153, 83, 179, 52, 148, 88, 184, 49, 145, 31, 127, 58, 154)(28, 124, 59, 155, 84, 180, 55, 151, 94, 190, 54, 150, 33, 129, 60, 156)(29, 125, 61, 157, 85, 181, 75, 171, 41, 137, 73, 169, 87, 183, 63, 159)(39, 135, 70, 166, 86, 182, 53, 149, 89, 185, 50, 146, 40, 136, 74, 170)(51, 147, 90, 186, 65, 161, 95, 191, 56, 152, 93, 189, 67, 163, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 221)(11, 223)(12, 226)(13, 224)(14, 196)(15, 231)(16, 232)(17, 197)(18, 235)(19, 238)(20, 198)(21, 241)(22, 243)(23, 244)(24, 246)(25, 247)(26, 200)(27, 207)(28, 201)(29, 254)(30, 206)(31, 208)(32, 256)(33, 203)(34, 259)(35, 249)(36, 261)(37, 205)(38, 251)(39, 265)(40, 267)(41, 209)(42, 269)(43, 272)(44, 210)(45, 275)(46, 277)(47, 278)(48, 212)(49, 216)(50, 213)(51, 283)(52, 217)(53, 215)(54, 285)(55, 287)(56, 218)(57, 230)(58, 273)(59, 282)(60, 284)(61, 220)(62, 270)(63, 225)(64, 279)(65, 222)(66, 280)(67, 274)(68, 229)(69, 288)(70, 227)(71, 228)(72, 281)(73, 286)(74, 271)(75, 276)(76, 233)(77, 268)(78, 234)(79, 250)(80, 257)(81, 252)(82, 236)(83, 239)(84, 237)(85, 260)(86, 255)(87, 240)(88, 264)(89, 253)(90, 242)(91, 263)(92, 245)(93, 262)(94, 258)(95, 266)(96, 248)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1876
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1878 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-2 * T1 * T2^2 * T1^-1, (T2^-1 * T1)^3, T2^3 * T1 * T2 * T1 * T2 * T1, T2^8, T2 * T1 * T2 * T1^-2 * T2^-1 * T1 * T2 * T1^-2 ]
Map:: non-degenerate
	R = (1, 3, 10, 28, 60, 38, 16, 5)(2, 7, 20, 48, 81, 52, 24, 8)(4, 12, 29, 58, 88, 55, 35, 13)(6, 17, 40, 72, 93, 76, 44, 18)(9, 26, 56, 34, 65, 32, 14, 27)(11, 22, 47, 19, 46, 37, 15, 30)(21, 42, 71, 39, 70, 51, 23, 49)(25, 53, 80, 96, 79, 67, 36, 54)(31, 63, 75, 43, 73, 41, 33, 64)(45, 77, 68, 86, 61, 83, 50, 78)(57, 87, 66, 85, 62, 90, 59, 89)(69, 91, 84, 95, 82, 94, 74, 92)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 132, 111)(103, 115, 141, 117)(104, 118, 146, 119)(106, 116, 136, 125)(108, 127, 158, 128)(109, 129, 162, 130)(112, 120, 140, 131)(113, 135, 165, 137)(114, 138, 170, 139)(122, 151, 169, 153)(123, 154, 171, 155)(124, 152, 176, 143)(126, 157, 166, 148)(133, 164, 167, 144)(134, 161, 175, 142)(145, 178, 159, 172)(147, 180, 160, 168)(149, 181, 190, 182)(150, 183, 191, 173)(156, 177, 189, 184)(163, 185, 187, 174)(179, 192, 186, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1887
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1879 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2 * T1 * T2 * T1, T2^-2 * T1^-1 * T2^2 * T1, T2^8, T2 * T1^-2 * T2 * T1 * T2 * T1^2 * T2^-1 * T1, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 28, 54, 36, 16, 5)(2, 7, 20, 44, 71, 48, 24, 8)(4, 12, 29, 56, 83, 59, 33, 13)(6, 17, 38, 64, 89, 68, 42, 18)(9, 26, 51, 81, 62, 35, 14, 27)(11, 30, 55, 76, 47, 22, 15, 19)(21, 45, 72, 94, 67, 40, 23, 37)(25, 49, 78, 96, 75, 60, 34, 50)(31, 39, 65, 90, 85, 58, 32, 41)(43, 69, 57, 79, 93, 74, 46, 70)(52, 82, 91, 86, 61, 80, 53, 77)(63, 87, 73, 95, 84, 92, 66, 88)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 130, 111)(103, 115, 139, 117)(104, 118, 142, 119)(106, 116, 134, 125)(108, 127, 148, 122)(109, 128, 149, 123)(112, 120, 138, 129)(113, 133, 159, 135)(114, 136, 162, 137)(124, 147, 174, 151)(126, 153, 168, 140)(131, 155, 181, 157)(132, 158, 171, 143)(141, 169, 186, 160)(144, 172, 189, 163)(145, 173, 188, 175)(146, 176, 191, 165)(150, 167, 185, 179)(152, 161, 187, 177)(154, 164, 190, 180)(156, 182, 183, 166)(170, 192, 178, 184)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1886
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1880 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^3, (T1 * T2)^4, (T1 * T2^-1)^4, T1^8 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 13, 29, 59, 40, 43, 19, 6, 17, 5)(2, 7, 14, 4, 12, 31, 33, 66, 41, 18, 24, 8)(9, 25, 30, 11, 28, 61, 62, 81, 74, 39, 57, 26)(15, 35, 38, 16, 37, 60, 27, 58, 75, 42, 72, 36)(20, 44, 47, 21, 46, 67, 32, 65, 84, 52, 71, 45)(22, 48, 51, 23, 50, 53, 34, 68, 54, 64, 82, 49)(55, 85, 69, 56, 87, 70, 63, 89, 73, 88, 96, 86)(76, 92, 79, 77, 93, 80, 78, 94, 83, 90, 95, 91)(97, 98, 102, 114, 136, 129, 109, 100)(99, 105, 113, 135, 139, 158, 125, 107)(101, 111, 115, 138, 155, 123, 106, 112)(103, 116, 120, 148, 162, 128, 108, 117)(104, 118, 137, 160, 127, 130, 110, 119)(121, 149, 153, 147, 177, 145, 124, 150)(122, 151, 170, 184, 157, 159, 126, 152)(131, 165, 168, 182, 154, 169, 133, 166)(132, 161, 171, 142, 156, 140, 134, 167)(141, 172, 180, 186, 163, 174, 143, 173)(144, 175, 178, 187, 164, 179, 146, 176)(181, 190, 192, 189, 185, 188, 183, 191)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1888
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1881 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, (T2 * T1^-1)^4, T1^8, (T2^-1 * T1^-1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 6, 19, 43, 40, 66, 32, 13, 17, 5)(2, 7, 21, 18, 41, 64, 31, 34, 14, 4, 12, 8)(9, 25, 54, 42, 75, 74, 39, 61, 29, 11, 28, 26)(15, 35, 59, 27, 58, 77, 65, 73, 38, 16, 37, 36)(20, 44, 76, 68, 71, 63, 30, 62, 48, 22, 47, 45)(23, 49, 55, 46, 80, 53, 33, 67, 52, 24, 51, 50)(56, 86, 69, 85, 95, 88, 60, 89, 72, 57, 87, 70)(78, 92, 82, 90, 96, 91, 81, 94, 84, 79, 93, 83)(97, 98, 102, 114, 136, 127, 109, 100)(99, 105, 115, 138, 162, 135, 113, 107)(101, 111, 106, 123, 139, 161, 128, 112)(103, 116, 137, 164, 130, 126, 108, 118)(104, 119, 117, 142, 160, 129, 110, 120)(121, 149, 171, 148, 157, 146, 124, 151)(122, 152, 150, 181, 170, 156, 125, 153)(131, 165, 154, 184, 169, 168, 133, 166)(132, 158, 155, 143, 173, 140, 134, 167)(141, 174, 172, 186, 159, 177, 144, 175)(145, 178, 176, 187, 163, 180, 147, 179)(182, 190, 191, 189, 185, 188, 183, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1889
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1882 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2^-1 * T1^-1 * T2^-1 * T1, (T2 * T1^-1)^4, T1^12 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 20, 8)(4, 12, 28, 14)(6, 18, 23, 9)(11, 26, 50, 27)(13, 16, 35, 31)(15, 33, 58, 34)(17, 38, 41, 19)(21, 44, 70, 45)(22, 46, 48, 24)(25, 49, 60, 36)(29, 43, 69, 53)(30, 32, 51, 55)(37, 62, 65, 39)(40, 66, 68, 42)(47, 64, 89, 72)(52, 76, 82, 57)(54, 56, 77, 79)(59, 73, 92, 81)(61, 86, 71, 63)(67, 88, 94, 83)(74, 90, 93, 75)(78, 80, 84, 95)(85, 96, 91, 87)(97, 98, 102, 113, 133, 157, 181, 174, 150, 126, 109, 100)(99, 105, 118, 134, 159, 184, 192, 175, 153, 128, 110, 107)(101, 111, 103, 115, 136, 158, 183, 189, 176, 151, 132, 112)(104, 117, 114, 135, 160, 182, 191, 177, 152, 127, 125, 108)(106, 120, 129, 137, 163, 162, 187, 178, 171, 147, 123, 121)(116, 138, 140, 161, 186, 185, 180, 156, 155, 131, 130, 139)(119, 143, 142, 167, 188, 190, 173, 149, 148, 124, 141, 122)(144, 169, 154, 179, 165, 164, 172, 166, 170, 146, 168, 145)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1885
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1883 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^4 * T2 * T1 * T2, T1^2 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^2, T2^-1 * T1^-2 * T2 * T1^-1 * T2 * T1 * T2^-1, (T1^-1 * T2)^4, T2^-2 * T1 * T2^2 * T1 * T2^2 * T1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 34, 14)(6, 18, 48, 19)(9, 26, 58, 27)(11, 30, 73, 32)(13, 36, 81, 38)(15, 42, 82, 43)(16, 44, 79, 46)(17, 40, 76, 47)(20, 37, 74, 52)(22, 55, 89, 57)(23, 59, 91, 60)(24, 61, 31, 63)(25, 64, 92, 65)(28, 50, 78, 69)(29, 70, 53, 72)(33, 66, 41, 77)(35, 54, 88, 80)(39, 68, 94, 71)(45, 75, 96, 84)(49, 83, 95, 85)(51, 86, 56, 87)(62, 90, 93, 67)(97, 98, 102, 113, 142, 159, 183, 162, 122, 133, 109, 100)(99, 105, 121, 136, 110, 135, 147, 115, 146, 170, 127, 107)(101, 111, 137, 143, 168, 132, 152, 118, 103, 116, 141, 112)(104, 119, 154, 175, 131, 108, 129, 145, 114, 134, 158, 120)(106, 124, 151, 172, 128, 171, 182, 161, 138, 148, 167, 125)(117, 149, 179, 140, 153, 186, 173, 180, 155, 177, 139, 150)(123, 163, 174, 130, 156, 126, 144, 176, 160, 157, 181, 164)(165, 191, 178, 169, 189, 166, 188, 187, 185, 190, 184, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1884
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1884 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-2 * T1 * T2^2 * T1^-1, (T2^-1 * T1)^3, T2^3 * T1 * T2 * T1 * T2 * T1, T2^8, T2 * T1 * T2 * T1^-2 * T2^-1 * T1 * T2 * T1^-2 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 28, 124, 60, 156, 38, 134, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 48, 144, 81, 177, 52, 148, 24, 120, 8, 104)(4, 100, 12, 108, 29, 125, 58, 154, 88, 184, 55, 151, 35, 131, 13, 109)(6, 102, 17, 113, 40, 136, 72, 168, 93, 189, 76, 172, 44, 140, 18, 114)(9, 105, 26, 122, 56, 152, 34, 130, 65, 161, 32, 128, 14, 110, 27, 123)(11, 107, 22, 118, 47, 143, 19, 115, 46, 142, 37, 133, 15, 111, 30, 126)(21, 117, 42, 138, 71, 167, 39, 135, 70, 166, 51, 147, 23, 119, 49, 145)(25, 121, 53, 149, 80, 176, 96, 192, 79, 175, 67, 163, 36, 132, 54, 150)(31, 127, 63, 159, 75, 171, 43, 139, 73, 169, 41, 137, 33, 129, 64, 160)(45, 141, 77, 173, 68, 164, 86, 182, 61, 157, 83, 179, 50, 146, 78, 174)(57, 153, 87, 183, 66, 162, 85, 181, 62, 158, 90, 186, 59, 155, 89, 185)(69, 165, 91, 187, 84, 180, 95, 191, 82, 178, 94, 190, 74, 170, 92, 188)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 116)(11, 99)(12, 127)(13, 129)(14, 132)(15, 101)(16, 120)(17, 135)(18, 138)(19, 141)(20, 136)(21, 103)(22, 146)(23, 104)(24, 140)(25, 107)(26, 151)(27, 154)(28, 152)(29, 106)(30, 157)(31, 158)(32, 108)(33, 162)(34, 109)(35, 112)(36, 111)(37, 164)(38, 161)(39, 165)(40, 125)(41, 113)(42, 170)(43, 114)(44, 131)(45, 117)(46, 134)(47, 124)(48, 133)(49, 178)(50, 119)(51, 180)(52, 126)(53, 181)(54, 183)(55, 169)(56, 176)(57, 122)(58, 171)(59, 123)(60, 177)(61, 166)(62, 128)(63, 172)(64, 168)(65, 175)(66, 130)(67, 185)(68, 167)(69, 137)(70, 148)(71, 144)(72, 147)(73, 153)(74, 139)(75, 155)(76, 145)(77, 150)(78, 163)(79, 142)(80, 143)(81, 189)(82, 159)(83, 192)(84, 160)(85, 190)(86, 149)(87, 191)(88, 156)(89, 187)(90, 188)(91, 174)(92, 179)(93, 184)(94, 182)(95, 173)(96, 186)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1883
Transitivity :: ET+ VT+ AT
Graph::
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1885 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2 * T1 * T2 * T1, T2^-2 * T1^-1 * T2^2 * T1, T2^8, T2 * T1^-2 * T2 * T1 * T2 * T1^2 * T2^-1 * T1, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2^-1 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 28, 124, 54, 150, 36, 132, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 44, 140, 71, 167, 48, 144, 24, 120, 8, 104)(4, 100, 12, 108, 29, 125, 56, 152, 83, 179, 59, 155, 33, 129, 13, 109)(6, 102, 17, 113, 38, 134, 64, 160, 89, 185, 68, 164, 42, 138, 18, 114)(9, 105, 26, 122, 51, 147, 81, 177, 62, 158, 35, 131, 14, 110, 27, 123)(11, 107, 30, 126, 55, 151, 76, 172, 47, 143, 22, 118, 15, 111, 19, 115)(21, 117, 45, 141, 72, 168, 94, 190, 67, 163, 40, 136, 23, 119, 37, 133)(25, 121, 49, 145, 78, 174, 96, 192, 75, 171, 60, 156, 34, 130, 50, 146)(31, 127, 39, 135, 65, 161, 90, 186, 85, 181, 58, 154, 32, 128, 41, 137)(43, 139, 69, 165, 57, 153, 79, 175, 93, 189, 74, 170, 46, 142, 70, 166)(52, 148, 82, 178, 91, 187, 86, 182, 61, 157, 80, 176, 53, 149, 77, 173)(63, 159, 87, 183, 73, 169, 95, 191, 84, 180, 92, 188, 66, 162, 88, 184)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 116)(11, 99)(12, 127)(13, 128)(14, 130)(15, 101)(16, 120)(17, 133)(18, 136)(19, 139)(20, 134)(21, 103)(22, 142)(23, 104)(24, 138)(25, 107)(26, 108)(27, 109)(28, 147)(29, 106)(30, 153)(31, 148)(32, 149)(33, 112)(34, 111)(35, 155)(36, 158)(37, 159)(38, 125)(39, 113)(40, 162)(41, 114)(42, 129)(43, 117)(44, 126)(45, 169)(46, 119)(47, 132)(48, 172)(49, 173)(50, 176)(51, 174)(52, 122)(53, 123)(54, 167)(55, 124)(56, 161)(57, 168)(58, 164)(59, 181)(60, 182)(61, 131)(62, 171)(63, 135)(64, 141)(65, 187)(66, 137)(67, 144)(68, 190)(69, 146)(70, 156)(71, 185)(72, 140)(73, 186)(74, 192)(75, 143)(76, 189)(77, 188)(78, 151)(79, 145)(80, 191)(81, 152)(82, 184)(83, 150)(84, 154)(85, 157)(86, 183)(87, 166)(88, 170)(89, 179)(90, 160)(91, 177)(92, 175)(93, 163)(94, 180)(95, 165)(96, 178)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1882
Transitivity :: ET+ VT+ AT
Graph::
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1886 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^3, (T1 * T2)^4, (T1 * T2^-1)^4, T1^8 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 13, 109, 29, 125, 59, 155, 40, 136, 43, 139, 19, 115, 6, 102, 17, 113, 5, 101)(2, 98, 7, 103, 14, 110, 4, 100, 12, 108, 31, 127, 33, 129, 66, 162, 41, 137, 18, 114, 24, 120, 8, 104)(9, 105, 25, 121, 30, 126, 11, 107, 28, 124, 61, 157, 62, 158, 81, 177, 74, 170, 39, 135, 57, 153, 26, 122)(15, 111, 35, 131, 38, 134, 16, 112, 37, 133, 60, 156, 27, 123, 58, 154, 75, 171, 42, 138, 72, 168, 36, 132)(20, 116, 44, 140, 47, 143, 21, 117, 46, 142, 67, 163, 32, 128, 65, 161, 84, 180, 52, 148, 71, 167, 45, 141)(22, 118, 48, 144, 51, 147, 23, 119, 50, 146, 53, 149, 34, 130, 68, 164, 54, 150, 64, 160, 82, 178, 49, 145)(55, 151, 85, 181, 69, 165, 56, 152, 87, 183, 70, 166, 63, 159, 89, 185, 73, 169, 88, 184, 96, 192, 86, 182)(76, 172, 92, 188, 79, 175, 77, 173, 93, 189, 80, 176, 78, 174, 94, 190, 83, 179, 90, 186, 95, 191, 91, 187)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 116)(8, 118)(9, 113)(10, 112)(11, 99)(12, 117)(13, 100)(14, 119)(15, 115)(16, 101)(17, 135)(18, 136)(19, 138)(20, 120)(21, 103)(22, 137)(23, 104)(24, 148)(25, 149)(26, 151)(27, 106)(28, 150)(29, 107)(30, 152)(31, 130)(32, 108)(33, 109)(34, 110)(35, 165)(36, 161)(37, 166)(38, 167)(39, 139)(40, 129)(41, 160)(42, 155)(43, 158)(44, 134)(45, 172)(46, 156)(47, 173)(48, 175)(49, 124)(50, 176)(51, 177)(52, 162)(53, 153)(54, 121)(55, 170)(56, 122)(57, 147)(58, 169)(59, 123)(60, 140)(61, 159)(62, 125)(63, 126)(64, 127)(65, 171)(66, 128)(67, 174)(68, 179)(69, 168)(70, 131)(71, 132)(72, 182)(73, 133)(74, 184)(75, 142)(76, 180)(77, 141)(78, 143)(79, 178)(80, 144)(81, 145)(82, 187)(83, 146)(84, 186)(85, 190)(86, 154)(87, 191)(88, 157)(89, 188)(90, 163)(91, 164)(92, 183)(93, 185)(94, 192)(95, 181)(96, 189)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1879
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1887 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, (T2 * T1^-1)^4, T1^8, (T2^-1 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 6, 102, 19, 115, 43, 139, 40, 136, 66, 162, 32, 128, 13, 109, 17, 113, 5, 101)(2, 98, 7, 103, 21, 117, 18, 114, 41, 137, 64, 160, 31, 127, 34, 130, 14, 110, 4, 100, 12, 108, 8, 104)(9, 105, 25, 121, 54, 150, 42, 138, 75, 171, 74, 170, 39, 135, 61, 157, 29, 125, 11, 107, 28, 124, 26, 122)(15, 111, 35, 131, 59, 155, 27, 123, 58, 154, 77, 173, 65, 161, 73, 169, 38, 134, 16, 112, 37, 133, 36, 132)(20, 116, 44, 140, 76, 172, 68, 164, 71, 167, 63, 159, 30, 126, 62, 158, 48, 144, 22, 118, 47, 143, 45, 141)(23, 119, 49, 145, 55, 151, 46, 142, 80, 176, 53, 149, 33, 129, 67, 163, 52, 148, 24, 120, 51, 147, 50, 146)(56, 152, 86, 182, 69, 165, 85, 181, 95, 191, 88, 184, 60, 156, 89, 185, 72, 168, 57, 153, 87, 183, 70, 166)(78, 174, 92, 188, 82, 178, 90, 186, 96, 192, 91, 187, 81, 177, 94, 190, 84, 180, 79, 175, 93, 189, 83, 179)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 116)(8, 119)(9, 115)(10, 123)(11, 99)(12, 118)(13, 100)(14, 120)(15, 106)(16, 101)(17, 107)(18, 136)(19, 138)(20, 137)(21, 142)(22, 103)(23, 117)(24, 104)(25, 149)(26, 152)(27, 139)(28, 151)(29, 153)(30, 108)(31, 109)(32, 112)(33, 110)(34, 126)(35, 165)(36, 158)(37, 166)(38, 167)(39, 113)(40, 127)(41, 164)(42, 162)(43, 161)(44, 134)(45, 174)(46, 160)(47, 173)(48, 175)(49, 178)(50, 124)(51, 179)(52, 157)(53, 171)(54, 181)(55, 121)(56, 150)(57, 122)(58, 184)(59, 143)(60, 125)(61, 146)(62, 155)(63, 177)(64, 129)(65, 128)(66, 135)(67, 180)(68, 130)(69, 154)(70, 131)(71, 132)(72, 133)(73, 168)(74, 156)(75, 148)(76, 186)(77, 140)(78, 172)(79, 141)(80, 187)(81, 144)(82, 176)(83, 145)(84, 147)(85, 170)(86, 190)(87, 192)(88, 169)(89, 188)(90, 159)(91, 163)(92, 183)(93, 185)(94, 191)(95, 189)(96, 182)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1878
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1888 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2^-1 * T1^-1 * T2^-1 * T1, (T2 * T1^-1)^4, T1^12 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 20, 116, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 23, 119, 9, 105)(11, 107, 26, 122, 50, 146, 27, 123)(13, 109, 16, 112, 35, 131, 31, 127)(15, 111, 33, 129, 58, 154, 34, 130)(17, 113, 38, 134, 41, 137, 19, 115)(21, 117, 44, 140, 70, 166, 45, 141)(22, 118, 46, 142, 48, 144, 24, 120)(25, 121, 49, 145, 60, 156, 36, 132)(29, 125, 43, 139, 69, 165, 53, 149)(30, 126, 32, 128, 51, 147, 55, 151)(37, 133, 62, 158, 65, 161, 39, 135)(40, 136, 66, 162, 68, 164, 42, 138)(47, 143, 64, 160, 89, 185, 72, 168)(52, 148, 76, 172, 82, 178, 57, 153)(54, 150, 56, 152, 77, 173, 79, 175)(59, 155, 73, 169, 92, 188, 81, 177)(61, 157, 86, 182, 71, 167, 63, 159)(67, 163, 88, 184, 94, 190, 83, 179)(74, 170, 90, 186, 93, 189, 75, 171)(78, 174, 80, 176, 84, 180, 95, 191)(85, 181, 96, 192, 91, 187, 87, 183)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 115)(8, 117)(9, 118)(10, 120)(11, 99)(12, 104)(13, 100)(14, 107)(15, 103)(16, 101)(17, 133)(18, 135)(19, 136)(20, 138)(21, 114)(22, 134)(23, 143)(24, 129)(25, 106)(26, 119)(27, 121)(28, 141)(29, 108)(30, 109)(31, 125)(32, 110)(33, 137)(34, 139)(35, 130)(36, 112)(37, 157)(38, 159)(39, 160)(40, 158)(41, 163)(42, 140)(43, 116)(44, 161)(45, 122)(46, 167)(47, 142)(48, 169)(49, 144)(50, 168)(51, 123)(52, 124)(53, 148)(54, 126)(55, 132)(56, 127)(57, 128)(58, 179)(59, 131)(60, 155)(61, 181)(62, 183)(63, 184)(64, 182)(65, 186)(66, 187)(67, 162)(68, 172)(69, 164)(70, 170)(71, 188)(72, 145)(73, 154)(74, 146)(75, 147)(76, 166)(77, 149)(78, 150)(79, 153)(80, 151)(81, 152)(82, 171)(83, 165)(84, 156)(85, 174)(86, 191)(87, 189)(88, 192)(89, 180)(90, 185)(91, 178)(92, 190)(93, 176)(94, 173)(95, 177)(96, 175)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1880
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1889 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^4 * T2 * T1 * T2, T1^2 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^2, T2^-1 * T1^-2 * T2 * T1^-1 * T2 * T1 * T2^-1, (T1^-1 * T2)^4, T2^-2 * T1 * T2^2 * T1 * T2^2 * T1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 34, 130, 14, 110)(6, 102, 18, 114, 48, 144, 19, 115)(9, 105, 26, 122, 58, 154, 27, 123)(11, 107, 30, 126, 73, 169, 32, 128)(13, 109, 36, 132, 81, 177, 38, 134)(15, 111, 42, 138, 82, 178, 43, 139)(16, 112, 44, 140, 79, 175, 46, 142)(17, 113, 40, 136, 76, 172, 47, 143)(20, 116, 37, 133, 74, 170, 52, 148)(22, 118, 55, 151, 89, 185, 57, 153)(23, 119, 59, 155, 91, 187, 60, 156)(24, 120, 61, 157, 31, 127, 63, 159)(25, 121, 64, 160, 92, 188, 65, 161)(28, 124, 50, 146, 78, 174, 69, 165)(29, 125, 70, 166, 53, 149, 72, 168)(33, 129, 66, 162, 41, 137, 77, 173)(35, 131, 54, 150, 88, 184, 80, 176)(39, 135, 68, 164, 94, 190, 71, 167)(45, 141, 75, 171, 96, 192, 84, 180)(49, 145, 83, 179, 95, 191, 85, 181)(51, 147, 86, 182, 56, 152, 87, 183)(62, 158, 90, 186, 93, 189, 67, 163)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 124)(11, 99)(12, 129)(13, 100)(14, 135)(15, 137)(16, 101)(17, 142)(18, 134)(19, 146)(20, 141)(21, 149)(22, 103)(23, 154)(24, 104)(25, 136)(26, 133)(27, 163)(28, 151)(29, 106)(30, 144)(31, 107)(32, 171)(33, 145)(34, 156)(35, 108)(36, 152)(37, 109)(38, 158)(39, 147)(40, 110)(41, 143)(42, 148)(43, 150)(44, 153)(45, 112)(46, 159)(47, 168)(48, 176)(49, 114)(50, 170)(51, 115)(52, 167)(53, 179)(54, 117)(55, 172)(56, 118)(57, 186)(58, 175)(59, 177)(60, 126)(61, 181)(62, 120)(63, 183)(64, 157)(65, 138)(66, 122)(67, 174)(68, 123)(69, 191)(70, 188)(71, 125)(72, 132)(73, 189)(74, 127)(75, 182)(76, 128)(77, 180)(78, 130)(79, 131)(80, 160)(81, 139)(82, 169)(83, 140)(84, 155)(85, 164)(86, 161)(87, 162)(88, 192)(89, 190)(90, 173)(91, 185)(92, 187)(93, 166)(94, 184)(95, 178)(96, 165)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1881
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1890 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y1^-2 * Y3, Y3 * Y1^-3, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-2 * Y1 * Y2^2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2^-2)^2, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-1 * Y1)^6, Y2 * Y3 * Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 34, 130, 15, 111)(7, 103, 19, 115, 43, 139, 21, 117)(8, 104, 22, 118, 46, 142, 23, 119)(10, 106, 20, 116, 38, 134, 29, 125)(12, 108, 31, 127, 52, 148, 26, 122)(13, 109, 32, 128, 53, 149, 27, 123)(16, 112, 24, 120, 42, 138, 33, 129)(17, 113, 37, 133, 63, 159, 39, 135)(18, 114, 40, 136, 66, 162, 41, 137)(28, 124, 51, 147, 78, 174, 55, 151)(30, 126, 57, 153, 72, 168, 44, 140)(35, 131, 59, 155, 85, 181, 61, 157)(36, 132, 62, 158, 75, 171, 47, 143)(45, 141, 73, 169, 90, 186, 64, 160)(48, 144, 76, 172, 93, 189, 67, 163)(49, 145, 77, 173, 92, 188, 79, 175)(50, 146, 80, 176, 95, 191, 69, 165)(54, 150, 71, 167, 89, 185, 83, 179)(56, 152, 65, 161, 91, 187, 81, 177)(58, 154, 68, 164, 94, 190, 84, 180)(60, 156, 86, 182, 87, 183, 70, 166)(74, 170, 96, 192, 82, 178, 88, 184)(193, 289, 195, 291, 202, 298, 220, 316, 246, 342, 228, 324, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 236, 332, 263, 359, 240, 336, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 248, 344, 275, 371, 251, 347, 225, 321, 205, 301)(198, 294, 209, 305, 230, 326, 256, 352, 281, 377, 260, 356, 234, 330, 210, 306)(201, 297, 218, 314, 243, 339, 273, 369, 254, 350, 227, 323, 206, 302, 219, 315)(203, 299, 222, 318, 247, 343, 268, 364, 239, 335, 214, 310, 207, 303, 211, 307)(213, 309, 237, 333, 264, 360, 286, 382, 259, 355, 232, 328, 215, 311, 229, 325)(217, 313, 241, 337, 270, 366, 288, 384, 267, 363, 252, 348, 226, 322, 242, 338)(223, 319, 231, 327, 257, 353, 282, 378, 277, 373, 250, 346, 224, 320, 233, 329)(235, 331, 261, 357, 249, 345, 271, 367, 285, 381, 266, 362, 238, 334, 262, 358)(244, 340, 274, 370, 283, 379, 278, 374, 253, 349, 272, 368, 245, 341, 269, 365)(255, 351, 279, 375, 265, 361, 287, 383, 276, 372, 284, 380, 258, 354, 280, 376)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 218)(13, 219)(14, 197)(15, 226)(16, 225)(17, 231)(18, 233)(19, 199)(20, 202)(21, 235)(22, 200)(23, 238)(24, 208)(25, 201)(26, 244)(27, 245)(28, 247)(29, 230)(30, 236)(31, 204)(32, 205)(33, 234)(34, 206)(35, 253)(36, 239)(37, 209)(38, 212)(39, 255)(40, 210)(41, 258)(42, 216)(43, 211)(44, 264)(45, 256)(46, 214)(47, 267)(48, 259)(49, 271)(50, 261)(51, 220)(52, 223)(53, 224)(54, 275)(55, 270)(56, 273)(57, 222)(58, 276)(59, 227)(60, 262)(61, 277)(62, 228)(63, 229)(64, 282)(65, 248)(66, 232)(67, 285)(68, 250)(69, 287)(70, 279)(71, 246)(72, 249)(73, 237)(74, 280)(75, 254)(76, 240)(77, 241)(78, 243)(79, 284)(80, 242)(81, 283)(82, 288)(83, 281)(84, 286)(85, 251)(86, 252)(87, 278)(88, 274)(89, 263)(90, 265)(91, 257)(92, 269)(93, 268)(94, 260)(95, 272)(96, 266)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1896
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1891 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, Y3^2 * Y1^-2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^-2 * Y3^-1 * Y2^2 * Y3, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-3 * Y3, Y1 * R * Y2^-1 * R * Y3^-3 * Y2^-1, Y2^8, Y2^-1 * Y1 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y1^-2, Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^2 * Y1^-2 * Y2, Y2 * Y1 * Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y2 * Y1^-2, Y2^3 * Y1 * Y2^3 * Y1 * Y2^3 * Y1 * Y2^2 * Y3 * Y2^2 * Y1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 36, 132, 15, 111)(7, 103, 19, 115, 45, 141, 21, 117)(8, 104, 22, 118, 50, 146, 23, 119)(10, 106, 20, 116, 40, 136, 29, 125)(12, 108, 31, 127, 62, 158, 32, 128)(13, 109, 33, 129, 66, 162, 34, 130)(16, 112, 24, 120, 44, 140, 35, 131)(17, 113, 39, 135, 69, 165, 41, 137)(18, 114, 42, 138, 74, 170, 43, 139)(26, 122, 55, 151, 73, 169, 57, 153)(27, 123, 58, 154, 75, 171, 59, 155)(28, 124, 56, 152, 80, 176, 47, 143)(30, 126, 61, 157, 70, 166, 52, 148)(37, 133, 68, 164, 71, 167, 48, 144)(38, 134, 65, 161, 79, 175, 46, 142)(49, 145, 82, 178, 63, 159, 76, 172)(51, 147, 84, 180, 64, 160, 72, 168)(53, 149, 85, 181, 94, 190, 86, 182)(54, 150, 87, 183, 95, 191, 77, 173)(60, 156, 81, 177, 93, 189, 88, 184)(67, 163, 89, 185, 91, 187, 78, 174)(83, 179, 96, 192, 90, 186, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 252, 348, 230, 326, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 240, 336, 273, 369, 244, 340, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 250, 346, 280, 376, 247, 343, 227, 323, 205, 301)(198, 294, 209, 305, 232, 328, 264, 360, 285, 381, 268, 364, 236, 332, 210, 306)(201, 297, 218, 314, 248, 344, 226, 322, 257, 353, 224, 320, 206, 302, 219, 315)(203, 299, 214, 310, 239, 335, 211, 307, 238, 334, 229, 325, 207, 303, 222, 318)(213, 309, 234, 330, 263, 359, 231, 327, 262, 358, 243, 339, 215, 311, 241, 337)(217, 313, 245, 341, 272, 368, 288, 384, 271, 367, 259, 355, 228, 324, 246, 342)(223, 319, 255, 351, 267, 363, 235, 331, 265, 361, 233, 329, 225, 321, 256, 352)(237, 333, 269, 365, 260, 356, 278, 374, 253, 349, 275, 371, 242, 338, 270, 366)(249, 345, 279, 375, 258, 354, 277, 373, 254, 350, 282, 378, 251, 347, 281, 377)(261, 357, 283, 379, 276, 372, 287, 383, 274, 370, 286, 382, 266, 362, 284, 380)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 224)(13, 226)(14, 197)(15, 228)(16, 227)(17, 233)(18, 235)(19, 199)(20, 202)(21, 237)(22, 200)(23, 242)(24, 208)(25, 201)(26, 249)(27, 251)(28, 239)(29, 232)(30, 244)(31, 204)(32, 254)(33, 205)(34, 258)(35, 236)(36, 206)(37, 240)(38, 238)(39, 209)(40, 212)(41, 261)(42, 210)(43, 266)(44, 216)(45, 211)(46, 271)(47, 272)(48, 263)(49, 268)(50, 214)(51, 264)(52, 262)(53, 278)(54, 269)(55, 218)(56, 220)(57, 265)(58, 219)(59, 267)(60, 280)(61, 222)(62, 223)(63, 274)(64, 276)(65, 230)(66, 225)(67, 270)(68, 229)(69, 231)(70, 253)(71, 260)(72, 256)(73, 247)(74, 234)(75, 250)(76, 255)(77, 287)(78, 283)(79, 257)(80, 248)(81, 252)(82, 241)(83, 284)(84, 243)(85, 245)(86, 286)(87, 246)(88, 285)(89, 259)(90, 288)(91, 281)(92, 282)(93, 273)(94, 277)(95, 279)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1897
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1892 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^3 * Y1^2, (Y1 * Y2)^4, (Y1 * Y2^-1)^4, (Y3^-1 * Y1^-1)^4, Y1^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 40, 136, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 39, 135, 43, 139, 62, 158, 29, 125, 11, 107)(5, 101, 15, 111, 19, 115, 42, 138, 59, 155, 27, 123, 10, 106, 16, 112)(7, 103, 20, 116, 24, 120, 52, 148, 66, 162, 32, 128, 12, 108, 21, 117)(8, 104, 22, 118, 41, 137, 64, 160, 31, 127, 34, 130, 14, 110, 23, 119)(25, 121, 53, 149, 57, 153, 51, 147, 81, 177, 49, 145, 28, 124, 54, 150)(26, 122, 55, 151, 74, 170, 88, 184, 61, 157, 63, 159, 30, 126, 56, 152)(35, 131, 69, 165, 72, 168, 86, 182, 58, 154, 73, 169, 37, 133, 70, 166)(36, 132, 65, 161, 75, 171, 46, 142, 60, 156, 44, 140, 38, 134, 71, 167)(45, 141, 76, 172, 84, 180, 90, 186, 67, 163, 78, 174, 47, 143, 77, 173)(48, 144, 79, 175, 82, 178, 91, 187, 68, 164, 83, 179, 50, 146, 80, 176)(85, 181, 94, 190, 96, 192, 93, 189, 89, 185, 92, 188, 87, 183, 95, 191)(193, 289, 195, 291, 202, 298, 205, 301, 221, 317, 251, 347, 232, 328, 235, 331, 211, 307, 198, 294, 209, 305, 197, 293)(194, 290, 199, 295, 206, 302, 196, 292, 204, 300, 223, 319, 225, 321, 258, 354, 233, 329, 210, 306, 216, 312, 200, 296)(201, 297, 217, 313, 222, 318, 203, 299, 220, 316, 253, 349, 254, 350, 273, 369, 266, 362, 231, 327, 249, 345, 218, 314)(207, 303, 227, 323, 230, 326, 208, 304, 229, 325, 252, 348, 219, 315, 250, 346, 267, 363, 234, 330, 264, 360, 228, 324)(212, 308, 236, 332, 239, 335, 213, 309, 238, 334, 259, 355, 224, 320, 257, 353, 276, 372, 244, 340, 263, 359, 237, 333)(214, 310, 240, 336, 243, 339, 215, 311, 242, 338, 245, 341, 226, 322, 260, 356, 246, 342, 256, 352, 274, 370, 241, 337)(247, 343, 277, 373, 261, 357, 248, 344, 279, 375, 262, 358, 255, 351, 281, 377, 265, 361, 280, 376, 288, 384, 278, 374)(268, 364, 284, 380, 271, 367, 269, 365, 285, 381, 272, 368, 270, 366, 286, 382, 275, 371, 282, 378, 287, 383, 283, 379)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 206)(8, 194)(9, 217)(10, 205)(11, 220)(12, 223)(13, 221)(14, 196)(15, 227)(16, 229)(17, 197)(18, 216)(19, 198)(20, 236)(21, 238)(22, 240)(23, 242)(24, 200)(25, 222)(26, 201)(27, 250)(28, 253)(29, 251)(30, 203)(31, 225)(32, 257)(33, 258)(34, 260)(35, 230)(36, 207)(37, 252)(38, 208)(39, 249)(40, 235)(41, 210)(42, 264)(43, 211)(44, 239)(45, 212)(46, 259)(47, 213)(48, 243)(49, 214)(50, 245)(51, 215)(52, 263)(53, 226)(54, 256)(55, 277)(56, 279)(57, 218)(58, 267)(59, 232)(60, 219)(61, 254)(62, 273)(63, 281)(64, 274)(65, 276)(66, 233)(67, 224)(68, 246)(69, 248)(70, 255)(71, 237)(72, 228)(73, 280)(74, 231)(75, 234)(76, 284)(77, 285)(78, 286)(79, 269)(80, 270)(81, 266)(82, 241)(83, 282)(84, 244)(85, 261)(86, 247)(87, 262)(88, 288)(89, 265)(90, 287)(91, 268)(92, 271)(93, 272)(94, 275)(95, 283)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1894
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1893 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y2^3, Y1^8, (Y3^-1 * Y1^-1)^4, (Y1^-1 * Y2)^4 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 40, 136, 31, 127, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 42, 138, 66, 162, 39, 135, 17, 113, 11, 107)(5, 101, 15, 111, 10, 106, 27, 123, 43, 139, 65, 161, 32, 128, 16, 112)(7, 103, 20, 116, 41, 137, 68, 164, 34, 130, 30, 126, 12, 108, 22, 118)(8, 104, 23, 119, 21, 117, 46, 142, 64, 160, 33, 129, 14, 110, 24, 120)(25, 121, 53, 149, 75, 171, 52, 148, 61, 157, 50, 146, 28, 124, 55, 151)(26, 122, 56, 152, 54, 150, 85, 181, 74, 170, 60, 156, 29, 125, 57, 153)(35, 131, 69, 165, 58, 154, 88, 184, 73, 169, 72, 168, 37, 133, 70, 166)(36, 132, 62, 158, 59, 155, 47, 143, 77, 173, 44, 140, 38, 134, 71, 167)(45, 141, 78, 174, 76, 172, 90, 186, 63, 159, 81, 177, 48, 144, 79, 175)(49, 145, 82, 178, 80, 176, 91, 187, 67, 163, 84, 180, 51, 147, 83, 179)(86, 182, 94, 190, 95, 191, 93, 189, 89, 185, 92, 188, 87, 183, 96, 192)(193, 289, 195, 291, 202, 298, 198, 294, 211, 307, 235, 331, 232, 328, 258, 354, 224, 320, 205, 301, 209, 305, 197, 293)(194, 290, 199, 295, 213, 309, 210, 306, 233, 329, 256, 352, 223, 319, 226, 322, 206, 302, 196, 292, 204, 300, 200, 296)(201, 297, 217, 313, 246, 342, 234, 330, 267, 363, 266, 362, 231, 327, 253, 349, 221, 317, 203, 299, 220, 316, 218, 314)(207, 303, 227, 323, 251, 347, 219, 315, 250, 346, 269, 365, 257, 353, 265, 361, 230, 326, 208, 304, 229, 325, 228, 324)(212, 308, 236, 332, 268, 364, 260, 356, 263, 359, 255, 351, 222, 318, 254, 350, 240, 336, 214, 310, 239, 335, 237, 333)(215, 311, 241, 337, 247, 343, 238, 334, 272, 368, 245, 341, 225, 321, 259, 355, 244, 340, 216, 312, 243, 339, 242, 338)(248, 344, 278, 374, 261, 357, 277, 373, 287, 383, 280, 376, 252, 348, 281, 377, 264, 360, 249, 345, 279, 375, 262, 358)(270, 366, 284, 380, 274, 370, 282, 378, 288, 384, 283, 379, 273, 369, 286, 382, 276, 372, 271, 367, 285, 381, 275, 371)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 213)(8, 194)(9, 217)(10, 198)(11, 220)(12, 200)(13, 209)(14, 196)(15, 227)(16, 229)(17, 197)(18, 233)(19, 235)(20, 236)(21, 210)(22, 239)(23, 241)(24, 243)(25, 246)(26, 201)(27, 250)(28, 218)(29, 203)(30, 254)(31, 226)(32, 205)(33, 259)(34, 206)(35, 251)(36, 207)(37, 228)(38, 208)(39, 253)(40, 258)(41, 256)(42, 267)(43, 232)(44, 268)(45, 212)(46, 272)(47, 237)(48, 214)(49, 247)(50, 215)(51, 242)(52, 216)(53, 225)(54, 234)(55, 238)(56, 278)(57, 279)(58, 269)(59, 219)(60, 281)(61, 221)(62, 240)(63, 222)(64, 223)(65, 265)(66, 224)(67, 244)(68, 263)(69, 277)(70, 248)(71, 255)(72, 249)(73, 230)(74, 231)(75, 266)(76, 260)(77, 257)(78, 284)(79, 285)(80, 245)(81, 286)(82, 282)(83, 270)(84, 271)(85, 287)(86, 261)(87, 262)(88, 252)(89, 264)(90, 288)(91, 273)(92, 274)(93, 275)(94, 276)(95, 280)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1895
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1894 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, R * Y2 * Y3 * R * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^2, (Y2 * Y3)^4, Y3^12, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 215, 311, 203, 299)(197, 293, 206, 302, 224, 320, 207, 303)(199, 295, 211, 307, 231, 327, 212, 308)(200, 296, 208, 304, 227, 323, 213, 309)(202, 298, 204, 300, 220, 316, 218, 314)(205, 301, 222, 318, 246, 342, 223, 319)(209, 305, 229, 325, 245, 341, 221, 317)(210, 306, 214, 310, 235, 331, 230, 326)(216, 312, 238, 334, 262, 358, 239, 335)(217, 313, 219, 315, 233, 329, 241, 337)(225, 321, 228, 324, 236, 332, 247, 343)(226, 322, 250, 346, 256, 352, 232, 328)(234, 330, 258, 354, 277, 373, 253, 349)(237, 333, 261, 357, 268, 364, 243, 339)(240, 336, 242, 338, 263, 359, 265, 361)(244, 340, 254, 350, 278, 374, 267, 363)(248, 344, 249, 345, 273, 369, 272, 368)(251, 347, 252, 348, 274, 370, 275, 371)(255, 351, 279, 375, 280, 376, 257, 353)(259, 355, 260, 356, 276, 372, 281, 377)(264, 360, 266, 362, 269, 365, 285, 381)(270, 366, 271, 367, 282, 378, 283, 379)(284, 380, 286, 382, 287, 383, 288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 203)(8, 194)(9, 216)(10, 217)(11, 219)(12, 221)(13, 196)(14, 205)(15, 201)(16, 197)(17, 212)(18, 198)(19, 232)(20, 233)(21, 211)(22, 200)(23, 237)(24, 218)(25, 240)(26, 242)(27, 243)(28, 244)(29, 241)(30, 210)(31, 220)(32, 238)(33, 206)(34, 207)(35, 226)(36, 208)(37, 253)(38, 229)(39, 255)(40, 215)(41, 257)(42, 213)(43, 234)(44, 214)(45, 239)(46, 223)(47, 263)(48, 264)(49, 266)(50, 267)(51, 265)(52, 245)(53, 269)(54, 254)(55, 222)(56, 224)(57, 225)(58, 248)(59, 227)(60, 228)(61, 231)(62, 230)(63, 256)(64, 261)(65, 268)(66, 251)(67, 235)(68, 236)(69, 272)(70, 270)(71, 283)(72, 284)(73, 286)(74, 280)(75, 285)(76, 287)(77, 277)(78, 246)(79, 247)(80, 262)(81, 271)(82, 249)(83, 250)(84, 252)(85, 279)(86, 259)(87, 275)(88, 288)(89, 258)(90, 260)(91, 278)(92, 276)(93, 281)(94, 282)(95, 273)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1892
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1895 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3^-2 * Y2^-2 * Y3 * Y2^-1 * Y3^-1, (Y2^-2 * Y3^-1)^3, Y2^-1 * Y3 * Y2^2 * Y3^3 * Y2 * Y3, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 217, 313, 203, 299)(197, 293, 206, 302, 231, 327, 207, 303)(199, 295, 211, 307, 245, 341, 213, 309)(200, 296, 214, 310, 253, 349, 215, 311)(202, 298, 220, 316, 265, 361, 222, 318)(204, 300, 225, 321, 261, 357, 227, 323)(205, 301, 228, 324, 272, 368, 229, 325)(208, 304, 236, 332, 247, 343, 237, 333)(209, 305, 239, 335, 275, 371, 241, 337)(210, 306, 242, 338, 259, 355, 243, 339)(212, 308, 248, 344, 234, 330, 250, 346)(216, 312, 257, 353, 278, 374, 258, 354)(218, 314, 260, 356, 287, 383, 262, 358)(219, 315, 254, 350, 230, 326, 263, 359)(221, 317, 249, 345, 273, 369, 233, 329)(223, 319, 251, 347, 274, 370, 238, 334)(224, 320, 255, 351, 279, 375, 240, 336)(226, 322, 252, 348, 280, 376, 271, 367)(232, 328, 244, 340, 282, 378, 270, 366)(235, 331, 276, 372, 283, 379, 246, 342)(256, 352, 267, 363, 288, 384, 277, 373)(264, 360, 269, 365, 281, 377, 285, 381)(266, 362, 284, 380, 268, 364, 286, 382)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 221)(11, 223)(12, 226)(13, 196)(14, 232)(15, 234)(16, 197)(17, 240)(18, 198)(19, 246)(20, 249)(21, 251)(22, 254)(23, 255)(24, 200)(25, 259)(26, 261)(27, 201)(28, 241)(29, 214)(30, 236)(31, 216)(32, 203)(33, 269)(34, 233)(35, 238)(36, 258)(37, 265)(38, 205)(39, 260)(40, 266)(41, 206)(42, 267)(43, 207)(44, 264)(45, 268)(46, 208)(47, 277)(48, 273)(49, 274)(50, 237)(51, 280)(52, 210)(53, 272)(54, 217)(55, 211)(56, 227)(57, 242)(58, 257)(59, 244)(60, 213)(61, 235)(62, 284)(63, 285)(64, 215)(65, 262)(66, 286)(67, 256)(68, 229)(69, 253)(70, 247)(71, 288)(72, 219)(73, 276)(74, 220)(75, 222)(76, 224)(77, 275)(78, 225)(79, 263)(80, 281)(81, 228)(82, 230)(83, 231)(84, 271)(85, 245)(86, 239)(87, 282)(88, 287)(89, 243)(90, 283)(91, 278)(92, 248)(93, 250)(94, 252)(95, 279)(96, 270)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1893
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1896 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3 * Y1^-2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1)^4, (Y3 * Y2^-1)^4, Y1^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 37, 133, 61, 157, 85, 181, 78, 174, 54, 150, 30, 126, 13, 109, 4, 100)(3, 99, 9, 105, 22, 118, 38, 134, 63, 159, 88, 184, 96, 192, 79, 175, 57, 153, 32, 128, 14, 110, 11, 107)(5, 101, 15, 111, 7, 103, 19, 115, 40, 136, 62, 158, 87, 183, 93, 189, 80, 176, 55, 151, 36, 132, 16, 112)(8, 104, 21, 117, 18, 114, 39, 135, 64, 160, 86, 182, 95, 191, 81, 177, 56, 152, 31, 127, 29, 125, 12, 108)(10, 106, 24, 120, 33, 129, 41, 137, 67, 163, 66, 162, 91, 187, 82, 178, 75, 171, 51, 147, 27, 123, 25, 121)(20, 116, 42, 138, 44, 140, 65, 161, 90, 186, 89, 185, 84, 180, 60, 156, 59, 155, 35, 131, 34, 130, 43, 139)(23, 119, 47, 143, 46, 142, 71, 167, 92, 188, 94, 190, 77, 173, 53, 149, 52, 148, 28, 124, 45, 141, 26, 122)(48, 144, 73, 169, 58, 154, 83, 179, 69, 165, 68, 164, 76, 172, 70, 166, 74, 170, 50, 146, 72, 168, 49, 145)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 212)(8, 194)(9, 198)(10, 197)(11, 218)(12, 220)(13, 208)(14, 196)(15, 225)(16, 227)(17, 230)(18, 215)(19, 209)(20, 200)(21, 236)(22, 238)(23, 201)(24, 214)(25, 241)(26, 242)(27, 203)(28, 206)(29, 235)(30, 224)(31, 205)(32, 243)(33, 250)(34, 207)(35, 223)(36, 217)(37, 254)(38, 233)(39, 229)(40, 258)(41, 211)(42, 232)(43, 261)(44, 262)(45, 213)(46, 240)(47, 256)(48, 216)(49, 252)(50, 219)(51, 247)(52, 268)(53, 221)(54, 248)(55, 222)(56, 269)(57, 244)(58, 226)(59, 265)(60, 228)(61, 278)(62, 257)(63, 253)(64, 281)(65, 231)(66, 260)(67, 280)(68, 234)(69, 245)(70, 237)(71, 255)(72, 239)(73, 284)(74, 282)(75, 266)(76, 274)(77, 271)(78, 272)(79, 246)(80, 276)(81, 251)(82, 249)(83, 259)(84, 287)(85, 288)(86, 263)(87, 277)(88, 286)(89, 264)(90, 285)(91, 279)(92, 273)(93, 267)(94, 275)(95, 270)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1890
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1897 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^2 * Y3 * Y1 * Y3 * Y1^2, Y1 * Y3^-2 * Y1^-2 * Y3 * Y1^-1 * Y3, Y1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3 * Y1^-3 * Y3^2 * Y1^-1 * Y3^-1, (Y3^2 * Y1)^3, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 46, 142, 63, 159, 87, 183, 66, 162, 26, 122, 37, 133, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 40, 136, 14, 110, 39, 135, 51, 147, 19, 115, 50, 146, 74, 170, 31, 127, 11, 107)(5, 101, 15, 111, 41, 137, 47, 143, 72, 168, 36, 132, 56, 152, 22, 118, 7, 103, 20, 116, 45, 141, 16, 112)(8, 104, 23, 119, 58, 154, 79, 175, 35, 131, 12, 108, 33, 129, 49, 145, 18, 114, 38, 134, 62, 158, 24, 120)(10, 106, 28, 124, 55, 151, 76, 172, 32, 128, 75, 171, 86, 182, 65, 161, 42, 138, 52, 148, 71, 167, 29, 125)(21, 117, 53, 149, 83, 179, 44, 140, 57, 153, 90, 186, 77, 173, 84, 180, 59, 155, 81, 177, 43, 139, 54, 150)(27, 123, 67, 163, 78, 174, 34, 130, 60, 156, 30, 126, 48, 144, 80, 176, 64, 160, 61, 157, 85, 181, 68, 164)(69, 165, 95, 191, 82, 178, 73, 169, 93, 189, 70, 166, 92, 188, 91, 187, 89, 185, 94, 190, 88, 184, 96, 192)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 222)(12, 226)(13, 228)(14, 196)(15, 234)(16, 236)(17, 232)(18, 240)(19, 198)(20, 229)(21, 200)(22, 247)(23, 251)(24, 253)(25, 256)(26, 250)(27, 201)(28, 242)(29, 262)(30, 265)(31, 255)(32, 203)(33, 258)(34, 206)(35, 246)(36, 273)(37, 266)(38, 205)(39, 260)(40, 268)(41, 269)(42, 274)(43, 207)(44, 271)(45, 267)(46, 208)(47, 209)(48, 211)(49, 275)(50, 270)(51, 278)(52, 212)(53, 264)(54, 280)(55, 281)(56, 279)(57, 214)(58, 219)(59, 283)(60, 215)(61, 223)(62, 282)(63, 216)(64, 284)(65, 217)(66, 233)(67, 254)(68, 286)(69, 220)(70, 245)(71, 231)(72, 221)(73, 224)(74, 244)(75, 288)(76, 239)(77, 225)(78, 261)(79, 238)(80, 227)(81, 230)(82, 235)(83, 287)(84, 237)(85, 241)(86, 248)(87, 243)(88, 272)(89, 249)(90, 285)(91, 252)(92, 257)(93, 259)(94, 263)(95, 277)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1891
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1898 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2, Y1 * Y2^-2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3, Y2^12, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 23, 119, 11, 107)(5, 101, 14, 110, 32, 128, 15, 111)(7, 103, 10, 106, 25, 121, 20, 116)(8, 104, 21, 117, 42, 138, 22, 118)(12, 108, 28, 124, 52, 148, 29, 125)(13, 109, 30, 126, 35, 131, 16, 112)(17, 113, 19, 115, 39, 135, 37, 133)(18, 114, 38, 134, 54, 150, 31, 127)(24, 120, 26, 122, 40, 136, 48, 144)(27, 123, 51, 147, 67, 163, 43, 139)(33, 129, 46, 142, 70, 166, 57, 153)(34, 130, 44, 140, 55, 151, 36, 132)(41, 137, 65, 161, 86, 182, 62, 158)(45, 141, 47, 143, 71, 167, 69, 165)(49, 145, 50, 146, 72, 168, 74, 170)(53, 149, 61, 157, 85, 181, 77, 173)(56, 152, 80, 176, 82, 178, 58, 154)(59, 155, 81, 177, 83, 179, 60, 156)(63, 159, 64, 160, 75, 171, 87, 183)(66, 162, 89, 185, 90, 186, 68, 164)(73, 169, 88, 184, 94, 190, 76, 172)(78, 174, 95, 191, 84, 180, 79, 175)(91, 187, 92, 188, 93, 189, 96, 192)(193, 289, 195, 291, 202, 298, 218, 314, 242, 338, 267, 363, 285, 381, 276, 372, 252, 348, 228, 324, 208, 304, 197, 293)(194, 290, 199, 295, 211, 307, 232, 328, 256, 352, 280, 376, 288, 384, 275, 371, 250, 346, 226, 322, 207, 303, 200, 296)(196, 292, 204, 300, 201, 297, 216, 312, 239, 335, 264, 360, 284, 380, 282, 378, 271, 367, 247, 343, 223, 319, 205, 301)(198, 294, 209, 305, 220, 316, 240, 336, 265, 361, 263, 359, 283, 379, 274, 370, 260, 356, 236, 332, 214, 310, 210, 306)(203, 299, 219, 315, 217, 313, 241, 337, 257, 353, 279, 375, 287, 383, 269, 365, 251, 347, 227, 323, 225, 321, 206, 302)(212, 308, 233, 329, 231, 327, 255, 351, 277, 373, 286, 382, 273, 369, 249, 345, 248, 344, 224, 320, 235, 331, 213, 309)(215, 311, 237, 333, 243, 339, 266, 362, 281, 377, 278, 374, 270, 366, 246, 342, 245, 341, 222, 318, 221, 317, 238, 334)(229, 325, 253, 349, 244, 340, 268, 364, 262, 358, 261, 357, 272, 368, 259, 355, 258, 354, 234, 330, 254, 350, 230, 326)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 212)(8, 214)(9, 195)(10, 199)(11, 215)(12, 221)(13, 208)(14, 197)(15, 224)(16, 227)(17, 229)(18, 223)(19, 209)(20, 217)(21, 200)(22, 234)(23, 201)(24, 240)(25, 202)(26, 216)(27, 235)(28, 204)(29, 244)(30, 205)(31, 246)(32, 206)(33, 249)(34, 228)(35, 222)(36, 247)(37, 231)(38, 210)(39, 211)(40, 218)(41, 254)(42, 213)(43, 259)(44, 226)(45, 261)(46, 225)(47, 237)(48, 232)(49, 266)(50, 241)(51, 219)(52, 220)(53, 269)(54, 230)(55, 236)(56, 250)(57, 262)(58, 274)(59, 252)(60, 275)(61, 245)(62, 278)(63, 279)(64, 255)(65, 233)(66, 260)(67, 243)(68, 282)(69, 263)(70, 238)(71, 239)(72, 242)(73, 268)(74, 264)(75, 256)(76, 286)(77, 277)(78, 271)(79, 276)(80, 248)(81, 251)(82, 272)(83, 273)(84, 287)(85, 253)(86, 257)(87, 267)(88, 265)(89, 258)(90, 281)(91, 288)(92, 283)(93, 284)(94, 280)(95, 270)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1900
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1899 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, Y1^-3 * Y3, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^4 * Y3^-1 * Y2, Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y1 * Y2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y1, Y1 * Y2 * Y3^2 * Y2^-2 * Y3^-1 * Y2^-1, (Y2^-2 * R * Y2^-1)^2, Y1 * Y2^-2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * R * Y3^-1 * Y2^2 * R * Y2^-1 * Y1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^2 * Y2^-3 * Y1, Y3 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 39, 135, 15, 111)(7, 103, 19, 115, 53, 149, 21, 117)(8, 104, 22, 118, 59, 155, 23, 119)(10, 106, 28, 124, 60, 156, 30, 126)(12, 108, 33, 129, 77, 173, 35, 131)(13, 109, 36, 132, 80, 176, 37, 133)(16, 112, 44, 140, 79, 175, 45, 141)(17, 113, 47, 143, 83, 179, 49, 145)(18, 114, 50, 146, 67, 163, 51, 147)(20, 116, 55, 151, 88, 184, 56, 152)(24, 120, 64, 160, 32, 128, 65, 161)(26, 122, 46, 142, 66, 162, 69, 165)(27, 123, 48, 144, 85, 181, 70, 166)(29, 125, 43, 139, 63, 159, 73, 169)(31, 127, 75, 171, 94, 190, 61, 157)(34, 130, 78, 174, 40, 136, 54, 150)(38, 134, 62, 158, 87, 183, 82, 178)(41, 137, 68, 164, 95, 191, 84, 180)(42, 138, 58, 154, 90, 186, 52, 148)(57, 153, 76, 172, 96, 192, 89, 185)(71, 167, 91, 187, 74, 170, 92, 188)(72, 168, 81, 177, 86, 182, 93, 189)(193, 289, 195, 291, 202, 298, 221, 317, 229, 325, 256, 352, 283, 379, 246, 342, 211, 307, 238, 334, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 235, 331, 207, 303, 234, 330, 266, 362, 222, 318, 239, 335, 258, 354, 216, 312, 200, 296)(196, 292, 204, 300, 226, 322, 265, 361, 243, 339, 236, 332, 263, 359, 219, 315, 201, 297, 218, 314, 230, 326, 205, 301)(198, 294, 209, 305, 240, 336, 255, 351, 215, 311, 254, 350, 284, 380, 248, 344, 225, 321, 261, 357, 244, 340, 210, 306)(203, 299, 223, 319, 245, 341, 272, 368, 233, 329, 206, 302, 232, 328, 264, 360, 220, 316, 237, 333, 268, 364, 224, 320)(213, 309, 249, 345, 275, 371, 231, 327, 253, 349, 214, 310, 252, 348, 276, 372, 247, 343, 257, 353, 285, 381, 250, 346)(217, 313, 259, 355, 273, 369, 228, 324, 262, 358, 288, 384, 270, 366, 274, 370, 267, 363, 271, 367, 227, 323, 260, 356)(241, 337, 278, 374, 269, 365, 251, 347, 281, 377, 242, 338, 280, 376, 286, 382, 277, 373, 282, 378, 287, 383, 279, 375)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 222)(11, 217)(12, 227)(13, 229)(14, 197)(15, 231)(16, 237)(17, 241)(18, 243)(19, 199)(20, 248)(21, 245)(22, 200)(23, 251)(24, 257)(25, 201)(26, 261)(27, 262)(28, 202)(29, 265)(30, 252)(31, 253)(32, 256)(33, 204)(34, 246)(35, 269)(36, 205)(37, 272)(38, 274)(39, 206)(40, 270)(41, 276)(42, 244)(43, 221)(44, 208)(45, 271)(46, 218)(47, 209)(48, 219)(49, 275)(50, 210)(51, 259)(52, 282)(53, 211)(54, 232)(55, 212)(56, 280)(57, 281)(58, 234)(59, 214)(60, 220)(61, 286)(62, 230)(63, 235)(64, 216)(65, 224)(66, 238)(67, 242)(68, 233)(69, 258)(70, 277)(71, 284)(72, 285)(73, 255)(74, 283)(75, 223)(76, 249)(77, 225)(78, 226)(79, 236)(80, 228)(81, 264)(82, 279)(83, 239)(84, 287)(85, 240)(86, 273)(87, 254)(88, 247)(89, 288)(90, 250)(91, 263)(92, 266)(93, 278)(94, 267)(95, 260)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1901
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1900 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^3 * Y1, (R * Y2 * Y3^-1)^2, (Y1 * Y3)^4, Y1^8, (Y1 * Y3^-1)^4, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 40, 136, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 17, 113, 39, 135, 43, 139, 62, 158, 29, 125, 11, 107)(5, 101, 15, 111, 19, 115, 42, 138, 59, 155, 27, 123, 10, 106, 16, 112)(7, 103, 20, 116, 24, 120, 52, 148, 66, 162, 32, 128, 12, 108, 21, 117)(8, 104, 22, 118, 41, 137, 64, 160, 31, 127, 34, 130, 14, 110, 23, 119)(25, 121, 53, 149, 57, 153, 51, 147, 81, 177, 49, 145, 28, 124, 54, 150)(26, 122, 55, 151, 74, 170, 88, 184, 61, 157, 63, 159, 30, 126, 56, 152)(35, 131, 69, 165, 72, 168, 86, 182, 58, 154, 73, 169, 37, 133, 70, 166)(36, 132, 65, 161, 75, 171, 46, 142, 60, 156, 44, 140, 38, 134, 71, 167)(45, 141, 76, 172, 84, 180, 90, 186, 67, 163, 78, 174, 47, 143, 77, 173)(48, 144, 79, 175, 82, 178, 91, 187, 68, 164, 83, 179, 50, 146, 80, 176)(85, 181, 94, 190, 96, 192, 93, 189, 89, 185, 92, 188, 87, 183, 95, 191)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 206)(8, 194)(9, 217)(10, 205)(11, 220)(12, 223)(13, 221)(14, 196)(15, 227)(16, 229)(17, 197)(18, 216)(19, 198)(20, 236)(21, 238)(22, 240)(23, 242)(24, 200)(25, 222)(26, 201)(27, 250)(28, 253)(29, 251)(30, 203)(31, 225)(32, 257)(33, 258)(34, 260)(35, 230)(36, 207)(37, 252)(38, 208)(39, 249)(40, 235)(41, 210)(42, 264)(43, 211)(44, 239)(45, 212)(46, 259)(47, 213)(48, 243)(49, 214)(50, 245)(51, 215)(52, 263)(53, 226)(54, 256)(55, 277)(56, 279)(57, 218)(58, 267)(59, 232)(60, 219)(61, 254)(62, 273)(63, 281)(64, 274)(65, 276)(66, 233)(67, 224)(68, 246)(69, 248)(70, 255)(71, 237)(72, 228)(73, 280)(74, 231)(75, 234)(76, 284)(77, 285)(78, 286)(79, 269)(80, 270)(81, 266)(82, 241)(83, 282)(84, 244)(85, 261)(86, 247)(87, 262)(88, 288)(89, 265)(90, 287)(91, 268)(92, 271)(93, 272)(94, 275)(95, 283)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1898
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1901 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = SL(2,3) : C4 (small group id <96, 67>)
Aut   = (SL(2,3) : C4) : C2 (small group id <192, 988>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1^-2 * Y3, (R * Y2 * Y3^-1)^2, Y1^8, (Y3 * Y1^-1)^4, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 40, 136, 31, 127, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 42, 138, 66, 162, 39, 135, 17, 113, 11, 107)(5, 101, 15, 111, 10, 106, 27, 123, 43, 139, 65, 161, 32, 128, 16, 112)(7, 103, 20, 116, 41, 137, 68, 164, 34, 130, 30, 126, 12, 108, 22, 118)(8, 104, 23, 119, 21, 117, 46, 142, 64, 160, 33, 129, 14, 110, 24, 120)(25, 121, 53, 149, 75, 171, 52, 148, 61, 157, 50, 146, 28, 124, 55, 151)(26, 122, 56, 152, 54, 150, 85, 181, 74, 170, 60, 156, 29, 125, 57, 153)(35, 131, 69, 165, 58, 154, 88, 184, 73, 169, 72, 168, 37, 133, 70, 166)(36, 132, 62, 158, 59, 155, 47, 143, 77, 173, 44, 140, 38, 134, 71, 167)(45, 141, 78, 174, 76, 172, 90, 186, 63, 159, 81, 177, 48, 144, 79, 175)(49, 145, 82, 178, 80, 176, 91, 187, 67, 163, 84, 180, 51, 147, 83, 179)(86, 182, 94, 190, 95, 191, 93, 189, 89, 185, 92, 188, 87, 183, 96, 192)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 213)(8, 194)(9, 217)(10, 198)(11, 220)(12, 200)(13, 209)(14, 196)(15, 227)(16, 229)(17, 197)(18, 233)(19, 235)(20, 236)(21, 210)(22, 239)(23, 241)(24, 243)(25, 246)(26, 201)(27, 250)(28, 218)(29, 203)(30, 254)(31, 226)(32, 205)(33, 259)(34, 206)(35, 251)(36, 207)(37, 228)(38, 208)(39, 253)(40, 258)(41, 256)(42, 267)(43, 232)(44, 268)(45, 212)(46, 272)(47, 237)(48, 214)(49, 247)(50, 215)(51, 242)(52, 216)(53, 225)(54, 234)(55, 238)(56, 278)(57, 279)(58, 269)(59, 219)(60, 281)(61, 221)(62, 240)(63, 222)(64, 223)(65, 265)(66, 224)(67, 244)(68, 263)(69, 277)(70, 248)(71, 255)(72, 249)(73, 230)(74, 231)(75, 266)(76, 260)(77, 257)(78, 284)(79, 285)(80, 245)(81, 286)(82, 282)(83, 270)(84, 271)(85, 287)(86, 261)(87, 262)(88, 252)(89, 264)(90, 288)(91, 273)(92, 274)(93, 275)(94, 276)(95, 280)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1899
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1902 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-2 * T1^2 * T2^-2, T1 * T2 * T1^2 * T2^-1 * T1, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1 * T2^-2 * T1^-1 * T2 * T1 * T2^-1, T2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 46, 30, 11, 29, 50, 26)(14, 31, 56, 34, 15, 33, 60, 32)(19, 35, 62, 40, 21, 39, 66, 36)(22, 41, 72, 44, 23, 43, 76, 42)(27, 51, 85, 54, 28, 53, 86, 52)(37, 67, 95, 70, 38, 69, 96, 68)(45, 77, 59, 80, 47, 79, 58, 78)(48, 81, 57, 84, 49, 83, 55, 82)(61, 87, 75, 90, 63, 89, 74, 88)(64, 91, 73, 94, 65, 93, 71, 92)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 112, 124)(116, 133, 120, 134)(121, 141, 125, 143)(122, 144, 126, 145)(127, 151, 129, 153)(128, 154, 130, 155)(131, 157, 135, 159)(132, 160, 136, 161)(137, 167, 139, 169)(138, 170, 140, 171)(142, 164, 146, 166)(147, 168, 149, 172)(148, 158, 150, 162)(152, 163, 156, 165)(173, 185, 175, 183)(174, 190, 176, 188)(177, 187, 179, 189)(178, 186, 180, 184)(181, 192, 182, 191)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1906
Transitivity :: ET+
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1903 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-3, T2^3 * T1 * T2^-2 * T1 * T2, T1 * T2^-2 * T1^2 * T2 * T1 * T2^-1, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-2 * T1^-3 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 56, 21, 48, 39, 66, 47, 17, 5)(2, 7, 22, 58, 31, 50, 37, 16, 43, 68, 26, 8)(4, 12, 35, 73, 28, 9, 18, 49, 45, 75, 40, 14)(6, 19, 51, 84, 59, 38, 13, 25, 64, 90, 54, 20)(11, 32, 55, 46, 74, 29, 69, 42, 15, 41, 77, 34)(23, 60, 82, 67, 91, 57, 44, 63, 24, 62, 92, 61)(27, 70, 93, 78, 81, 76, 33, 72, 94, 80, 36, 71)(52, 85, 79, 89, 95, 83, 65, 88, 53, 87, 96, 86)(97, 98, 102, 114, 144, 133, 109, 100)(99, 105, 123, 165, 135, 110, 129, 107)(101, 111, 119, 103, 117, 151, 140, 112)(104, 120, 148, 115, 146, 178, 161, 121)(106, 125, 163, 122, 162, 130, 158, 127)(108, 116, 149, 177, 145, 134, 175, 132)(113, 141, 176, 137, 152, 131, 174, 142)(118, 153, 185, 150, 139, 157, 183, 155)(124, 160, 182, 166, 136, 147, 179, 168)(126, 164, 180, 169, 143, 154, 186, 171)(128, 167, 184, 159, 138, 172, 181, 156)(170, 190, 192, 187, 173, 189, 191, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1907
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1904 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2 * T1^-3 * T2^-1 * T1^-3, T1 * T2^-1 * T1^3 * T2 * T1^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-4 * T2^2 * T1^-2, T1^-1 * T2^-1 * T1^3 * T2^-1 * T1^-2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^8 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 41, 36)(17, 42, 35, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 57, 39, 58)(30, 64, 40, 65)(32, 67, 37, 68)(33, 61, 38, 59)(44, 69, 47, 70)(46, 71, 48, 72)(49, 73, 55, 74)(53, 78, 56, 79)(60, 82, 62, 83)(63, 85, 66, 86)(75, 89, 76, 90)(77, 91, 80, 92)(81, 93, 84, 94)(87, 95, 88, 96)(97, 98, 102, 113, 137, 124, 106, 117, 141, 131, 109, 100)(99, 105, 121, 139, 136, 112, 101, 111, 135, 138, 126, 107)(103, 116, 145, 130, 152, 120, 104, 119, 151, 132, 149, 118)(108, 128, 144, 115, 143, 134, 110, 133, 142, 114, 140, 129)(122, 155, 177, 160, 168, 158, 123, 157, 180, 161, 167, 156)(125, 159, 175, 154, 171, 146, 127, 162, 174, 153, 172, 147)(148, 173, 163, 170, 183, 165, 150, 176, 164, 169, 184, 166)(178, 187, 181, 190, 192, 186, 179, 188, 182, 189, 191, 185)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1905
Transitivity :: ET+
Graph:: bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1905 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-2 * T1^2 * T2^-2, T1 * T2 * T1^2 * T2^-1 * T1, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1, T2^-1 * T1 * T2 * T1 * T2^-2 * T1^-1 * T2 * T1 * T2^-1, T2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 18, 114, 6, 102, 17, 113, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 13, 109, 4, 100, 12, 108, 24, 120, 8, 104)(9, 105, 25, 121, 46, 142, 30, 126, 11, 107, 29, 125, 50, 146, 26, 122)(14, 110, 31, 127, 56, 152, 34, 130, 15, 111, 33, 129, 60, 156, 32, 128)(19, 115, 35, 131, 62, 158, 40, 136, 21, 117, 39, 135, 66, 162, 36, 132)(22, 118, 41, 137, 72, 168, 44, 140, 23, 119, 43, 139, 76, 172, 42, 138)(27, 123, 51, 147, 85, 181, 54, 150, 28, 124, 53, 149, 86, 182, 52, 148)(37, 133, 67, 163, 95, 191, 70, 166, 38, 134, 69, 165, 96, 192, 68, 164)(45, 141, 77, 173, 59, 155, 80, 176, 47, 143, 79, 175, 58, 154, 78, 174)(48, 144, 81, 177, 57, 153, 84, 180, 49, 145, 83, 179, 55, 151, 82, 178)(61, 157, 87, 183, 75, 171, 90, 186, 63, 159, 89, 185, 74, 170, 88, 184)(64, 160, 91, 187, 73, 169, 94, 190, 65, 161, 93, 189, 71, 167, 92, 188)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 124)(17, 107)(18, 111)(19, 108)(20, 133)(21, 103)(22, 109)(23, 104)(24, 134)(25, 141)(26, 144)(27, 112)(28, 106)(29, 143)(30, 145)(31, 151)(32, 154)(33, 153)(34, 155)(35, 157)(36, 160)(37, 120)(38, 116)(39, 159)(40, 161)(41, 167)(42, 170)(43, 169)(44, 171)(45, 125)(46, 164)(47, 121)(48, 126)(49, 122)(50, 166)(51, 168)(52, 158)(53, 172)(54, 162)(55, 129)(56, 163)(57, 127)(58, 130)(59, 128)(60, 165)(61, 135)(62, 150)(63, 131)(64, 136)(65, 132)(66, 148)(67, 156)(68, 146)(69, 152)(70, 142)(71, 139)(72, 149)(73, 137)(74, 140)(75, 138)(76, 147)(77, 185)(78, 190)(79, 183)(80, 188)(81, 187)(82, 186)(83, 189)(84, 184)(85, 192)(86, 191)(87, 173)(88, 178)(89, 175)(90, 180)(91, 179)(92, 174)(93, 177)(94, 176)(95, 181)(96, 182)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1904
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1906 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-3, T2^3 * T1 * T2^-2 * T1 * T2, T1 * T2^-2 * T1^2 * T2 * T1 * T2^-1, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-2 * T1^-3 * T2^-1 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 56, 152, 21, 117, 48, 144, 39, 135, 66, 162, 47, 143, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 58, 154, 31, 127, 50, 146, 37, 133, 16, 112, 43, 139, 68, 164, 26, 122, 8, 104)(4, 100, 12, 108, 35, 131, 73, 169, 28, 124, 9, 105, 18, 114, 49, 145, 45, 141, 75, 171, 40, 136, 14, 110)(6, 102, 19, 115, 51, 147, 84, 180, 59, 155, 38, 134, 13, 109, 25, 121, 64, 160, 90, 186, 54, 150, 20, 116)(11, 107, 32, 128, 55, 151, 46, 142, 74, 170, 29, 125, 69, 165, 42, 138, 15, 111, 41, 137, 77, 173, 34, 130)(23, 119, 60, 156, 82, 178, 67, 163, 91, 187, 57, 153, 44, 140, 63, 159, 24, 120, 62, 158, 92, 188, 61, 157)(27, 123, 70, 166, 93, 189, 78, 174, 81, 177, 76, 172, 33, 129, 72, 168, 94, 190, 80, 176, 36, 132, 71, 167)(52, 148, 85, 181, 79, 175, 89, 185, 95, 191, 83, 179, 65, 161, 88, 184, 53, 149, 87, 183, 96, 192, 86, 182)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 125)(11, 99)(12, 116)(13, 100)(14, 129)(15, 119)(16, 101)(17, 141)(18, 144)(19, 146)(20, 149)(21, 151)(22, 153)(23, 103)(24, 148)(25, 104)(26, 162)(27, 165)(28, 160)(29, 163)(30, 164)(31, 106)(32, 167)(33, 107)(34, 158)(35, 174)(36, 108)(37, 109)(38, 175)(39, 110)(40, 147)(41, 152)(42, 172)(43, 157)(44, 112)(45, 176)(46, 113)(47, 154)(48, 133)(49, 134)(50, 178)(51, 179)(52, 115)(53, 177)(54, 139)(55, 140)(56, 131)(57, 185)(58, 186)(59, 118)(60, 128)(61, 183)(62, 127)(63, 138)(64, 182)(65, 121)(66, 130)(67, 122)(68, 180)(69, 135)(70, 136)(71, 184)(72, 124)(73, 143)(74, 190)(75, 126)(76, 181)(77, 189)(78, 142)(79, 132)(80, 137)(81, 145)(82, 161)(83, 168)(84, 169)(85, 156)(86, 166)(87, 155)(88, 159)(89, 150)(90, 171)(91, 173)(92, 170)(93, 191)(94, 192)(95, 188)(96, 187)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1902
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1907 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2 * T1^-3 * T2^-1 * T1^-3, T1 * T2^-1 * T1^3 * T2 * T1^2, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T1^-4 * T2^2 * T1^-2, T1^-1 * T2^-1 * T1^3 * T2^-1 * T1^-2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^8 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 31, 127)(13, 109, 34, 130, 41, 137, 36, 132)(17, 113, 42, 138, 35, 131, 43, 139)(20, 116, 50, 146, 23, 119, 51, 147)(22, 118, 52, 148, 24, 120, 54, 150)(25, 121, 57, 153, 39, 135, 58, 154)(30, 126, 64, 160, 40, 136, 65, 161)(32, 128, 67, 163, 37, 133, 68, 164)(33, 129, 61, 157, 38, 134, 59, 155)(44, 140, 69, 165, 47, 143, 70, 166)(46, 142, 71, 167, 48, 144, 72, 168)(49, 145, 73, 169, 55, 151, 74, 170)(53, 149, 78, 174, 56, 152, 79, 175)(60, 156, 82, 178, 62, 158, 83, 179)(63, 159, 85, 181, 66, 162, 86, 182)(75, 171, 89, 185, 76, 172, 90, 186)(77, 173, 91, 187, 80, 176, 92, 188)(81, 177, 93, 189, 84, 180, 94, 190)(87, 183, 95, 191, 88, 184, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 128)(13, 100)(14, 133)(15, 135)(16, 101)(17, 137)(18, 140)(19, 143)(20, 145)(21, 141)(22, 103)(23, 151)(24, 104)(25, 139)(26, 155)(27, 157)(28, 106)(29, 159)(30, 107)(31, 162)(32, 144)(33, 108)(34, 152)(35, 109)(36, 149)(37, 142)(38, 110)(39, 138)(40, 112)(41, 124)(42, 126)(43, 136)(44, 129)(45, 131)(46, 114)(47, 134)(48, 115)(49, 130)(50, 127)(51, 125)(52, 173)(53, 118)(54, 176)(55, 132)(56, 120)(57, 172)(58, 171)(59, 177)(60, 122)(61, 180)(62, 123)(63, 175)(64, 168)(65, 167)(66, 174)(67, 170)(68, 169)(69, 150)(70, 148)(71, 156)(72, 158)(73, 184)(74, 183)(75, 146)(76, 147)(77, 163)(78, 153)(79, 154)(80, 164)(81, 160)(82, 187)(83, 188)(84, 161)(85, 190)(86, 189)(87, 165)(88, 166)(89, 178)(90, 179)(91, 181)(92, 182)(93, 191)(94, 192)(95, 185)(96, 186)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1903
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1908 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1^2 * Y3^-1, (Y1^-1 * Y3)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y2^-2 * Y3 * Y1^-1 * Y2^-2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (R * Y2^-2 * Y1^-1)^2, Y2^-2 * Y3 * Y2 * Y1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1 * Y2^-1 * Y3^-1 * Y2, Y2 * Y1 * Y2^2 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * R * Y2^2 * R * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y3 * Y2^3 * Y1^-1 * Y2^-2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 16, 112, 28, 124)(20, 116, 37, 133, 24, 120, 38, 134)(25, 121, 45, 141, 29, 125, 47, 143)(26, 122, 48, 144, 30, 126, 49, 145)(31, 127, 55, 151, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 59, 155)(35, 131, 61, 157, 39, 135, 63, 159)(36, 132, 64, 160, 40, 136, 65, 161)(41, 137, 71, 167, 43, 139, 73, 169)(42, 138, 74, 170, 44, 140, 75, 171)(46, 142, 68, 164, 50, 146, 70, 166)(51, 147, 72, 168, 53, 149, 76, 172)(52, 148, 62, 158, 54, 150, 66, 162)(56, 152, 67, 163, 60, 156, 69, 165)(77, 173, 89, 185, 79, 175, 87, 183)(78, 174, 94, 190, 80, 176, 92, 188)(81, 177, 91, 187, 83, 179, 93, 189)(82, 178, 90, 186, 84, 180, 88, 184)(85, 181, 96, 192, 86, 182, 95, 191)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 238, 334, 222, 318, 203, 299, 221, 317, 242, 338, 218, 314)(206, 302, 223, 319, 248, 344, 226, 322, 207, 303, 225, 321, 252, 348, 224, 320)(211, 307, 227, 323, 254, 350, 232, 328, 213, 309, 231, 327, 258, 354, 228, 324)(214, 310, 233, 329, 264, 360, 236, 332, 215, 311, 235, 331, 268, 364, 234, 330)(219, 315, 243, 339, 277, 373, 246, 342, 220, 316, 245, 341, 278, 374, 244, 340)(229, 325, 259, 355, 287, 383, 262, 358, 230, 326, 261, 357, 288, 384, 260, 356)(237, 333, 269, 365, 251, 347, 272, 368, 239, 335, 271, 367, 250, 346, 270, 366)(240, 336, 273, 369, 249, 345, 276, 372, 241, 337, 275, 371, 247, 343, 274, 370)(253, 349, 279, 375, 267, 363, 282, 378, 255, 351, 281, 377, 266, 362, 280, 376)(256, 352, 283, 379, 265, 361, 286, 382, 257, 353, 285, 381, 263, 359, 284, 380)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 219)(17, 201)(18, 206)(19, 199)(20, 230)(21, 204)(22, 200)(23, 205)(24, 229)(25, 239)(26, 241)(27, 202)(28, 208)(29, 237)(30, 240)(31, 249)(32, 251)(33, 247)(34, 250)(35, 255)(36, 257)(37, 212)(38, 216)(39, 253)(40, 256)(41, 265)(42, 267)(43, 263)(44, 266)(45, 217)(46, 262)(47, 221)(48, 218)(49, 222)(50, 260)(51, 268)(52, 258)(53, 264)(54, 254)(55, 223)(56, 261)(57, 225)(58, 224)(59, 226)(60, 259)(61, 227)(62, 244)(63, 231)(64, 228)(65, 232)(66, 246)(67, 248)(68, 238)(69, 252)(70, 242)(71, 233)(72, 243)(73, 235)(74, 234)(75, 236)(76, 245)(77, 279)(78, 284)(79, 281)(80, 286)(81, 285)(82, 280)(83, 283)(84, 282)(85, 287)(86, 288)(87, 271)(88, 276)(89, 269)(90, 274)(91, 273)(92, 272)(93, 275)(94, 270)(95, 278)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1911
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1909 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1^3 * Y2^-1 * Y1^-1, Y1^-2 * Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1^5, Y1 * Y2 * Y1^2 * Y2^-2 * Y1 * Y2^-1, Y2^-1 * Y1^-3 * Y2^-2 * Y1 * Y2^-1, Y1 * Y2^-5 * Y1 * Y2, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 48, 144, 37, 133, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 69, 165, 39, 135, 14, 110, 33, 129, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 55, 151, 44, 140, 16, 112)(8, 104, 24, 120, 52, 148, 19, 115, 50, 146, 82, 178, 65, 161, 25, 121)(10, 106, 29, 125, 67, 163, 26, 122, 66, 162, 34, 130, 62, 158, 31, 127)(12, 108, 20, 116, 53, 149, 81, 177, 49, 145, 38, 134, 79, 175, 36, 132)(17, 113, 45, 141, 80, 176, 41, 137, 56, 152, 35, 131, 78, 174, 46, 142)(22, 118, 57, 153, 89, 185, 54, 150, 43, 139, 61, 157, 87, 183, 59, 155)(28, 124, 64, 160, 86, 182, 70, 166, 40, 136, 51, 147, 83, 179, 72, 168)(30, 126, 68, 164, 84, 180, 73, 169, 47, 143, 58, 154, 90, 186, 75, 171)(32, 128, 71, 167, 88, 184, 63, 159, 42, 138, 76, 172, 85, 181, 60, 156)(74, 170, 94, 190, 96, 192, 91, 187, 77, 173, 93, 189, 95, 191, 92, 188)(193, 289, 195, 291, 202, 298, 222, 318, 248, 344, 213, 309, 240, 336, 231, 327, 258, 354, 239, 335, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 250, 346, 223, 319, 242, 338, 229, 325, 208, 304, 235, 331, 260, 356, 218, 314, 200, 296)(196, 292, 204, 300, 227, 323, 265, 361, 220, 316, 201, 297, 210, 306, 241, 337, 237, 333, 267, 363, 232, 328, 206, 302)(198, 294, 211, 307, 243, 339, 276, 372, 251, 347, 230, 326, 205, 301, 217, 313, 256, 352, 282, 378, 246, 342, 212, 308)(203, 299, 224, 320, 247, 343, 238, 334, 266, 362, 221, 317, 261, 357, 234, 330, 207, 303, 233, 329, 269, 365, 226, 322)(215, 311, 252, 348, 274, 370, 259, 355, 283, 379, 249, 345, 236, 332, 255, 351, 216, 312, 254, 350, 284, 380, 253, 349)(219, 315, 262, 358, 285, 381, 270, 366, 273, 369, 268, 364, 225, 321, 264, 360, 286, 382, 272, 368, 228, 324, 263, 359)(244, 340, 277, 373, 271, 367, 281, 377, 287, 383, 275, 371, 257, 353, 280, 376, 245, 341, 279, 375, 288, 384, 278, 374)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 222)(11, 224)(12, 227)(13, 217)(14, 196)(15, 233)(16, 235)(17, 197)(18, 241)(19, 243)(20, 198)(21, 240)(22, 250)(23, 252)(24, 254)(25, 256)(26, 200)(27, 262)(28, 201)(29, 261)(30, 248)(31, 242)(32, 247)(33, 264)(34, 203)(35, 265)(36, 263)(37, 208)(38, 205)(39, 258)(40, 206)(41, 269)(42, 207)(43, 260)(44, 255)(45, 267)(46, 266)(47, 209)(48, 231)(49, 237)(50, 229)(51, 276)(52, 277)(53, 279)(54, 212)(55, 238)(56, 213)(57, 236)(58, 223)(59, 230)(60, 274)(61, 215)(62, 284)(63, 216)(64, 282)(65, 280)(66, 239)(67, 283)(68, 218)(69, 234)(70, 285)(71, 219)(72, 286)(73, 220)(74, 221)(75, 232)(76, 225)(77, 226)(78, 273)(79, 281)(80, 228)(81, 268)(82, 259)(83, 257)(84, 251)(85, 271)(86, 244)(87, 288)(88, 245)(89, 287)(90, 246)(91, 249)(92, 253)(93, 270)(94, 272)(95, 275)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1910
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1910 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y3^3 * Y2 * Y3^3 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-6 * Y2^-1, (Y3^2 * Y2^-1 * Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 233, 329, 221, 317)(208, 304, 230, 326, 234, 330, 231, 327)(212, 308, 237, 333, 224, 320, 239, 335)(216, 312, 246, 342, 225, 321, 247, 343)(217, 313, 245, 341, 222, 318, 243, 339)(218, 314, 250, 346, 223, 319, 251, 347)(220, 316, 248, 344, 232, 328, 238, 334)(226, 322, 259, 355, 228, 324, 260, 356)(227, 323, 240, 336, 229, 325, 235, 331)(236, 332, 262, 358, 241, 337, 263, 359)(242, 338, 271, 367, 244, 340, 272, 368)(249, 345, 273, 369, 257, 353, 274, 370)(252, 348, 266, 362, 258, 354, 268, 364)(253, 349, 278, 374, 255, 351, 276, 372)(254, 350, 264, 360, 256, 352, 270, 366)(261, 357, 279, 375, 269, 365, 280, 376)(265, 361, 284, 380, 267, 363, 282, 378)(275, 371, 281, 377, 277, 373, 283, 379)(285, 381, 288, 384, 286, 382, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 222)(12, 224)(13, 196)(14, 226)(15, 228)(16, 197)(17, 233)(18, 198)(19, 235)(20, 238)(21, 240)(22, 242)(23, 244)(24, 200)(25, 249)(26, 201)(27, 253)(28, 234)(29, 255)(30, 257)(31, 203)(32, 248)(33, 205)(34, 256)(35, 206)(36, 254)(37, 207)(38, 258)(39, 252)(40, 208)(41, 232)(42, 210)(43, 261)(44, 211)(45, 265)(46, 225)(47, 267)(48, 269)(49, 213)(50, 268)(51, 214)(52, 266)(53, 215)(54, 270)(55, 264)(56, 216)(57, 230)(58, 275)(59, 277)(60, 218)(61, 227)(62, 219)(63, 229)(64, 221)(65, 231)(66, 223)(67, 274)(68, 273)(69, 246)(70, 281)(71, 283)(72, 236)(73, 243)(74, 237)(75, 245)(76, 239)(77, 247)(78, 241)(79, 280)(80, 279)(81, 285)(82, 286)(83, 259)(84, 250)(85, 260)(86, 251)(87, 287)(88, 288)(89, 271)(90, 262)(91, 272)(92, 263)(93, 276)(94, 278)(95, 282)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1909
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1911 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^2 * Y1 * Y3^-1, Y1^-3 * Y3^-2 * Y1^-3, Y1^-1 * Y3^-1 * Y1^-3 * Y3 * Y1^-2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^4, Y3 * Y1^3 * Y3 * Y1^-3, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 28, 124, 10, 106, 21, 117, 45, 141, 35, 131, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 43, 139, 40, 136, 16, 112, 5, 101, 15, 111, 39, 135, 42, 138, 30, 126, 11, 107)(7, 103, 20, 116, 49, 145, 34, 130, 56, 152, 24, 120, 8, 104, 23, 119, 55, 151, 36, 132, 53, 149, 22, 118)(12, 108, 32, 128, 48, 144, 19, 115, 47, 143, 38, 134, 14, 110, 37, 133, 46, 142, 18, 114, 44, 140, 33, 129)(26, 122, 59, 155, 81, 177, 64, 160, 72, 168, 62, 158, 27, 123, 61, 157, 84, 180, 65, 161, 71, 167, 60, 156)(29, 125, 63, 159, 79, 175, 58, 154, 75, 171, 50, 146, 31, 127, 66, 162, 78, 174, 57, 153, 76, 172, 51, 147)(52, 148, 77, 173, 67, 163, 74, 170, 87, 183, 69, 165, 54, 150, 80, 176, 68, 164, 73, 169, 88, 184, 70, 166)(82, 178, 91, 187, 85, 181, 94, 190, 96, 192, 90, 186, 83, 179, 92, 188, 86, 182, 93, 189, 95, 191, 89, 185)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 226)(14, 196)(15, 219)(16, 223)(17, 234)(18, 237)(19, 198)(20, 242)(21, 200)(22, 244)(23, 243)(24, 246)(25, 249)(26, 207)(27, 201)(28, 206)(29, 208)(30, 256)(31, 203)(32, 259)(33, 253)(34, 233)(35, 235)(36, 205)(37, 260)(38, 251)(39, 250)(40, 257)(41, 228)(42, 227)(43, 209)(44, 261)(45, 211)(46, 263)(47, 262)(48, 264)(49, 265)(50, 215)(51, 212)(52, 216)(53, 270)(54, 214)(55, 266)(56, 271)(57, 231)(58, 217)(59, 225)(60, 274)(61, 230)(62, 275)(63, 277)(64, 232)(65, 222)(66, 278)(67, 229)(68, 224)(69, 239)(70, 236)(71, 240)(72, 238)(73, 247)(74, 241)(75, 281)(76, 282)(77, 283)(78, 248)(79, 245)(80, 284)(81, 285)(82, 254)(83, 252)(84, 286)(85, 258)(86, 255)(87, 287)(88, 288)(89, 268)(90, 267)(91, 272)(92, 269)(93, 276)(94, 273)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1908
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1912 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y3 * Y1^-1)^2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1^-1 * Y2^2 * Y1^-2 * Y2^-2 * Y1^-1, (R * Y2^2 * Y1^-1)^2, Y2^-1 * Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-1 * Y2^-1, Y2^2 * Y1^-1 * Y2^-3 * Y1^-1 * Y2, Y2^3 * Y3 * Y1^-1 * Y2^3, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^3 * Y1 * Y2^3 * Y1^-1, Y2^-1 * R * Y2^3 * R * Y2^-2, Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-2 * Y3 * Y2^-1, Y2^-1 * Y3 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, (Y2^-1 * Y1 * Y2^2 * Y1^-1)^2, Y2^-2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 41, 137, 29, 125)(16, 112, 38, 134, 42, 138, 39, 135)(20, 116, 45, 141, 32, 128, 47, 143)(24, 120, 54, 150, 33, 129, 55, 151)(25, 121, 53, 149, 30, 126, 51, 147)(26, 122, 58, 154, 31, 127, 59, 155)(28, 124, 56, 152, 40, 136, 46, 142)(34, 130, 67, 163, 36, 132, 68, 164)(35, 131, 48, 144, 37, 133, 43, 139)(44, 140, 70, 166, 49, 145, 71, 167)(50, 146, 79, 175, 52, 148, 80, 176)(57, 153, 81, 177, 65, 161, 82, 178)(60, 156, 74, 170, 66, 162, 76, 172)(61, 157, 86, 182, 63, 159, 84, 180)(62, 158, 72, 168, 64, 160, 78, 174)(69, 165, 87, 183, 77, 173, 88, 184)(73, 169, 92, 188, 75, 171, 90, 186)(83, 179, 89, 185, 85, 181, 91, 187)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 234, 330, 210, 306, 198, 294, 209, 305, 233, 329, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 238, 334, 225, 321, 205, 301, 196, 292, 204, 300, 224, 320, 248, 344, 216, 312, 200, 296)(201, 297, 217, 313, 249, 345, 230, 326, 258, 354, 223, 319, 203, 299, 222, 318, 257, 353, 231, 327, 252, 348, 218, 314)(206, 302, 226, 322, 256, 352, 221, 317, 255, 351, 229, 325, 207, 303, 228, 324, 254, 350, 219, 315, 253, 349, 227, 323)(211, 307, 235, 331, 261, 357, 246, 342, 270, 366, 241, 337, 213, 309, 240, 336, 269, 365, 247, 343, 264, 360, 236, 332)(214, 310, 242, 338, 268, 364, 239, 335, 267, 363, 245, 341, 215, 311, 244, 340, 266, 362, 237, 333, 265, 361, 243, 339)(250, 346, 275, 371, 259, 355, 274, 370, 286, 382, 278, 374, 251, 347, 277, 373, 260, 356, 273, 369, 285, 381, 276, 372)(262, 358, 281, 377, 271, 367, 280, 376, 288, 384, 284, 380, 263, 359, 283, 379, 272, 368, 279, 375, 287, 383, 282, 378)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 239)(21, 204)(22, 200)(23, 205)(24, 247)(25, 243)(26, 251)(27, 202)(28, 238)(29, 233)(30, 245)(31, 250)(32, 237)(33, 246)(34, 260)(35, 235)(36, 259)(37, 240)(38, 208)(39, 234)(40, 248)(41, 219)(42, 230)(43, 229)(44, 263)(45, 212)(46, 232)(47, 224)(48, 227)(49, 262)(50, 272)(51, 222)(52, 271)(53, 217)(54, 216)(55, 225)(56, 220)(57, 274)(58, 218)(59, 223)(60, 268)(61, 276)(62, 270)(63, 278)(64, 264)(65, 273)(66, 266)(67, 226)(68, 228)(69, 280)(70, 236)(71, 241)(72, 254)(73, 282)(74, 252)(75, 284)(76, 258)(77, 279)(78, 256)(79, 242)(80, 244)(81, 249)(82, 257)(83, 283)(84, 255)(85, 281)(86, 253)(87, 261)(88, 269)(89, 275)(90, 267)(91, 277)(92, 265)(93, 287)(94, 288)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1913
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1913 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 191>)
Aut   = $<192, 1482>$ (small group id <192, 1482>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1 * Y3^-3 * Y1^-1, Y1^-1 * Y3^5 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-5 * Y3^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 48, 144, 37, 133, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 69, 165, 39, 135, 14, 110, 33, 129, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 55, 151, 44, 140, 16, 112)(8, 104, 24, 120, 52, 148, 19, 115, 50, 146, 82, 178, 65, 161, 25, 121)(10, 106, 29, 125, 67, 163, 26, 122, 66, 162, 34, 130, 62, 158, 31, 127)(12, 108, 20, 116, 53, 149, 81, 177, 49, 145, 38, 134, 79, 175, 36, 132)(17, 113, 45, 141, 80, 176, 41, 137, 56, 152, 35, 131, 78, 174, 46, 142)(22, 118, 57, 153, 89, 185, 54, 150, 43, 139, 61, 157, 87, 183, 59, 155)(28, 124, 64, 160, 86, 182, 70, 166, 40, 136, 51, 147, 83, 179, 72, 168)(30, 126, 68, 164, 84, 180, 73, 169, 47, 143, 58, 154, 90, 186, 75, 171)(32, 128, 71, 167, 88, 184, 63, 159, 42, 138, 76, 172, 85, 181, 60, 156)(74, 170, 94, 190, 96, 192, 91, 187, 77, 173, 93, 189, 95, 191, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 222)(11, 224)(12, 227)(13, 217)(14, 196)(15, 233)(16, 235)(17, 197)(18, 241)(19, 243)(20, 198)(21, 240)(22, 250)(23, 252)(24, 254)(25, 256)(26, 200)(27, 262)(28, 201)(29, 261)(30, 248)(31, 242)(32, 247)(33, 264)(34, 203)(35, 265)(36, 263)(37, 208)(38, 205)(39, 258)(40, 206)(41, 269)(42, 207)(43, 260)(44, 255)(45, 267)(46, 266)(47, 209)(48, 231)(49, 237)(50, 229)(51, 276)(52, 277)(53, 279)(54, 212)(55, 238)(56, 213)(57, 236)(58, 223)(59, 230)(60, 274)(61, 215)(62, 284)(63, 216)(64, 282)(65, 280)(66, 239)(67, 283)(68, 218)(69, 234)(70, 285)(71, 219)(72, 286)(73, 220)(74, 221)(75, 232)(76, 225)(77, 226)(78, 273)(79, 281)(80, 228)(81, 268)(82, 259)(83, 257)(84, 251)(85, 271)(86, 244)(87, 288)(88, 245)(89, 287)(90, 246)(91, 249)(92, 253)(93, 270)(94, 272)(95, 275)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1912
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1914 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-1 * T1^2 * T2^-3, T2^-1 * T1^-1 * T2 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-1, T2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 18, 6, 17, 16, 5)(2, 7, 20, 13, 4, 12, 24, 8)(9, 25, 46, 30, 11, 29, 50, 26)(14, 31, 56, 34, 15, 33, 60, 32)(19, 35, 62, 40, 21, 39, 66, 36)(22, 41, 72, 44, 23, 43, 76, 42)(27, 51, 85, 54, 28, 53, 86, 52)(37, 67, 95, 70, 38, 69, 96, 68)(45, 77, 58, 80, 47, 79, 59, 78)(48, 81, 55, 84, 49, 83, 57, 82)(61, 87, 74, 90, 63, 89, 75, 88)(64, 91, 71, 94, 65, 93, 73, 92)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 112, 124)(116, 133, 120, 134)(121, 141, 125, 143)(122, 144, 126, 145)(127, 151, 129, 153)(128, 154, 130, 155)(131, 157, 135, 159)(132, 160, 136, 161)(137, 167, 139, 169)(138, 170, 140, 171)(142, 166, 146, 164)(147, 172, 149, 168)(148, 162, 150, 158)(152, 165, 156, 163)(173, 183, 175, 185)(174, 190, 176, 188)(177, 189, 179, 187)(178, 186, 180, 184)(181, 192, 182, 191)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 24^4 ), ( 24^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1918
Transitivity :: ET+
Graph:: bipartite
	v = 36 e = 96 f = 8
	degree seq :: [ 4^24, 8^12 ]

E27.1915 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1^-1 * T2^-1, (T2^-1 * T1 * T2^-1)^2, T2 * T1 * T2^2 * T1 * T2 * T1^2, T2^-2 * T1 * T2^3 * T1^-1 * T2^-1, T1^8 ]
Map:: non-degenerate
	R = (1, 3, 10, 30, 53, 21, 45, 38, 71, 44, 17, 5)(2, 7, 22, 55, 81, 47, 36, 16, 41, 62, 26, 8)(4, 12, 34, 67, 28, 9, 18, 46, 78, 77, 39, 14)(6, 19, 48, 83, 76, 37, 13, 25, 59, 88, 51, 20)(11, 31, 15, 40, 68, 29, 63, 89, 52, 43, 72, 33)(23, 56, 24, 58, 90, 54, 42, 69, 80, 61, 92, 57)(27, 64, 93, 75, 35, 70, 32, 66, 94, 73, 79, 65)(49, 84, 50, 86, 95, 82, 60, 91, 74, 87, 96, 85)(97, 98, 102, 114, 141, 132, 109, 100)(99, 105, 123, 159, 134, 110, 128, 107)(101, 111, 119, 103, 117, 148, 138, 112)(104, 120, 145, 115, 143, 176, 156, 121)(106, 125, 154, 177, 167, 129, 157, 122)(108, 116, 146, 175, 142, 133, 170, 131)(113, 130, 169, 136, 149, 174, 171, 139)(118, 150, 182, 172, 137, 153, 183, 147)(124, 144, 178, 160, 135, 155, 181, 162)(126, 151, 179, 173, 140, 158, 184, 163)(127, 161, 187, 152, 185, 166, 180, 165)(164, 189, 192, 186, 168, 190, 191, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1919
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 8^12, 12^8 ]

E27.1916 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 8, 12})
Quotient :: edge
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^-1 * T2^-2 * T1^-5, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T1 * T2 * T1^2)^2, (T1^2 * T2^-1 * T1)^2, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 41, 36)(17, 42, 35, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 57, 39, 58)(30, 64, 40, 65)(32, 67, 37, 68)(33, 61, 38, 59)(44, 69, 47, 70)(46, 71, 48, 72)(49, 73, 55, 74)(53, 78, 56, 79)(60, 82, 62, 83)(63, 85, 66, 86)(75, 89, 76, 90)(77, 91, 80, 92)(81, 93, 84, 94)(87, 95, 88, 96)(97, 98, 102, 113, 137, 124, 106, 117, 141, 131, 109, 100)(99, 105, 121, 138, 136, 112, 101, 111, 135, 139, 126, 107)(103, 116, 145, 132, 152, 120, 104, 119, 151, 130, 149, 118)(108, 128, 142, 114, 140, 134, 110, 133, 144, 115, 143, 129)(122, 155, 177, 161, 168, 158, 123, 157, 180, 160, 167, 156)(125, 159, 174, 153, 171, 146, 127, 162, 175, 154, 172, 147)(148, 173, 163, 169, 183, 165, 150, 176, 164, 170, 184, 166)(178, 188, 181, 189, 192, 185, 179, 187, 182, 190, 191, 186)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 16^4 ), ( 16^12 ) }
Outer automorphisms :: reflexible
Dual of E27.1917
Transitivity :: ET+
Graph:: bipartite
	v = 32 e = 96 f = 12
	degree seq :: [ 4^24, 12^8 ]

E27.1917 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T2^-1 * T1^2 * T2^-3, T2^-1 * T1^-1 * T2 * T1 * T2^2 * T1^-1 * T2 * T1^-1 * T2^-1, T2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 18, 114, 6, 102, 17, 113, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 13, 109, 4, 100, 12, 108, 24, 120, 8, 104)(9, 105, 25, 121, 46, 142, 30, 126, 11, 107, 29, 125, 50, 146, 26, 122)(14, 110, 31, 127, 56, 152, 34, 130, 15, 111, 33, 129, 60, 156, 32, 128)(19, 115, 35, 131, 62, 158, 40, 136, 21, 117, 39, 135, 66, 162, 36, 132)(22, 118, 41, 137, 72, 168, 44, 140, 23, 119, 43, 139, 76, 172, 42, 138)(27, 123, 51, 147, 85, 181, 54, 150, 28, 124, 53, 149, 86, 182, 52, 148)(37, 133, 67, 163, 95, 191, 70, 166, 38, 134, 69, 165, 96, 192, 68, 164)(45, 141, 77, 173, 58, 154, 80, 176, 47, 143, 79, 175, 59, 155, 78, 174)(48, 144, 81, 177, 55, 151, 84, 180, 49, 145, 83, 179, 57, 153, 82, 178)(61, 157, 87, 183, 74, 170, 90, 186, 63, 159, 89, 185, 75, 171, 88, 184)(64, 160, 91, 187, 71, 167, 94, 190, 65, 161, 93, 189, 73, 169, 92, 188)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 124)(17, 107)(18, 111)(19, 108)(20, 133)(21, 103)(22, 109)(23, 104)(24, 134)(25, 141)(26, 144)(27, 112)(28, 106)(29, 143)(30, 145)(31, 151)(32, 154)(33, 153)(34, 155)(35, 157)(36, 160)(37, 120)(38, 116)(39, 159)(40, 161)(41, 167)(42, 170)(43, 169)(44, 171)(45, 125)(46, 166)(47, 121)(48, 126)(49, 122)(50, 164)(51, 172)(52, 162)(53, 168)(54, 158)(55, 129)(56, 165)(57, 127)(58, 130)(59, 128)(60, 163)(61, 135)(62, 148)(63, 131)(64, 136)(65, 132)(66, 150)(67, 152)(68, 142)(69, 156)(70, 146)(71, 139)(72, 147)(73, 137)(74, 140)(75, 138)(76, 149)(77, 183)(78, 190)(79, 185)(80, 188)(81, 189)(82, 186)(83, 187)(84, 184)(85, 192)(86, 191)(87, 175)(88, 178)(89, 173)(90, 180)(91, 177)(92, 174)(93, 179)(94, 176)(95, 181)(96, 182)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1916
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 96 f = 32
	degree seq :: [ 16^12 ]

E27.1918 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2^-1 * T1^-1 * T2^-1, (T2^-1 * T1 * T2^-1)^2, T2 * T1 * T2^2 * T1 * T2 * T1^2, T2^-2 * T1 * T2^3 * T1^-1 * T2^-1, T1^8 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 53, 149, 21, 117, 45, 141, 38, 134, 71, 167, 44, 140, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 55, 151, 81, 177, 47, 143, 36, 132, 16, 112, 41, 137, 62, 158, 26, 122, 8, 104)(4, 100, 12, 108, 34, 130, 67, 163, 28, 124, 9, 105, 18, 114, 46, 142, 78, 174, 77, 173, 39, 135, 14, 110)(6, 102, 19, 115, 48, 144, 83, 179, 76, 172, 37, 133, 13, 109, 25, 121, 59, 155, 88, 184, 51, 147, 20, 116)(11, 107, 31, 127, 15, 111, 40, 136, 68, 164, 29, 125, 63, 159, 89, 185, 52, 148, 43, 139, 72, 168, 33, 129)(23, 119, 56, 152, 24, 120, 58, 154, 90, 186, 54, 150, 42, 138, 69, 165, 80, 176, 61, 157, 92, 188, 57, 153)(27, 123, 64, 160, 93, 189, 75, 171, 35, 131, 70, 166, 32, 128, 66, 162, 94, 190, 73, 169, 79, 175, 65, 161)(49, 145, 84, 180, 50, 146, 86, 182, 95, 191, 82, 178, 60, 156, 91, 187, 74, 170, 87, 183, 96, 192, 85, 181)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 125)(11, 99)(12, 116)(13, 100)(14, 128)(15, 119)(16, 101)(17, 130)(18, 141)(19, 143)(20, 146)(21, 148)(22, 150)(23, 103)(24, 145)(25, 104)(26, 106)(27, 159)(28, 144)(29, 154)(30, 151)(31, 161)(32, 107)(33, 157)(34, 169)(35, 108)(36, 109)(37, 170)(38, 110)(39, 155)(40, 149)(41, 153)(42, 112)(43, 113)(44, 158)(45, 132)(46, 133)(47, 176)(48, 178)(49, 115)(50, 175)(51, 118)(52, 138)(53, 174)(54, 182)(55, 179)(56, 185)(57, 183)(58, 177)(59, 181)(60, 121)(61, 122)(62, 184)(63, 134)(64, 135)(65, 187)(66, 124)(67, 126)(68, 189)(69, 127)(70, 180)(71, 129)(72, 190)(73, 136)(74, 131)(75, 139)(76, 137)(77, 140)(78, 171)(79, 142)(80, 156)(81, 167)(82, 160)(83, 173)(84, 165)(85, 162)(86, 172)(87, 147)(88, 163)(89, 166)(90, 168)(91, 152)(92, 164)(93, 192)(94, 191)(95, 188)(96, 186)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1914
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 96 f = 36
	degree seq :: [ 24^8 ]

E27.1919 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 8, 12})
Quotient :: loop
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^-1 * T2^-2 * T1^-5, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, (T1 * T2 * T1^2)^2, (T1^2 * T2^-1 * T1)^2, T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 31, 127)(13, 109, 34, 130, 41, 137, 36, 132)(17, 113, 42, 138, 35, 131, 43, 139)(20, 116, 50, 146, 23, 119, 51, 147)(22, 118, 52, 148, 24, 120, 54, 150)(25, 121, 57, 153, 39, 135, 58, 154)(30, 126, 64, 160, 40, 136, 65, 161)(32, 128, 67, 163, 37, 133, 68, 164)(33, 129, 61, 157, 38, 134, 59, 155)(44, 140, 69, 165, 47, 143, 70, 166)(46, 142, 71, 167, 48, 144, 72, 168)(49, 145, 73, 169, 55, 151, 74, 170)(53, 149, 78, 174, 56, 152, 79, 175)(60, 156, 82, 178, 62, 158, 83, 179)(63, 159, 85, 181, 66, 162, 86, 182)(75, 171, 89, 185, 76, 172, 90, 186)(77, 173, 91, 187, 80, 176, 92, 188)(81, 177, 93, 189, 84, 180, 94, 190)(87, 183, 95, 191, 88, 184, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 128)(13, 100)(14, 133)(15, 135)(16, 101)(17, 137)(18, 140)(19, 143)(20, 145)(21, 141)(22, 103)(23, 151)(24, 104)(25, 138)(26, 155)(27, 157)(28, 106)(29, 159)(30, 107)(31, 162)(32, 142)(33, 108)(34, 149)(35, 109)(36, 152)(37, 144)(38, 110)(39, 139)(40, 112)(41, 124)(42, 136)(43, 126)(44, 134)(45, 131)(46, 114)(47, 129)(48, 115)(49, 132)(50, 127)(51, 125)(52, 173)(53, 118)(54, 176)(55, 130)(56, 120)(57, 171)(58, 172)(59, 177)(60, 122)(61, 180)(62, 123)(63, 174)(64, 167)(65, 168)(66, 175)(67, 169)(68, 170)(69, 150)(70, 148)(71, 156)(72, 158)(73, 183)(74, 184)(75, 146)(76, 147)(77, 163)(78, 153)(79, 154)(80, 164)(81, 161)(82, 188)(83, 187)(84, 160)(85, 189)(86, 190)(87, 165)(88, 166)(89, 179)(90, 178)(91, 182)(92, 181)(93, 192)(94, 191)(95, 186)(96, 185)
	local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1915
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1920 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, Y3 * Y1, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-4 * Y1, (R * Y2^-2 * Y1)^2, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2^2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2, (Y2 * Y1 * Y2^-1 * Y3^-1 * Y2)^2, Y2 * Y1 * Y2 * Y3 * Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * R * Y2 * Y3^-1 * Y2^2 * R * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1, Y2^-1 * Y3 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 16, 112, 28, 124)(20, 116, 37, 133, 24, 120, 38, 134)(25, 121, 45, 141, 29, 125, 47, 143)(26, 122, 48, 144, 30, 126, 49, 145)(31, 127, 55, 151, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 59, 155)(35, 131, 61, 157, 39, 135, 63, 159)(36, 132, 64, 160, 40, 136, 65, 161)(41, 137, 71, 167, 43, 139, 73, 169)(42, 138, 74, 170, 44, 140, 75, 171)(46, 142, 70, 166, 50, 146, 68, 164)(51, 147, 76, 172, 53, 149, 72, 168)(52, 148, 66, 162, 54, 150, 62, 158)(56, 152, 69, 165, 60, 156, 67, 163)(77, 173, 87, 183, 79, 175, 89, 185)(78, 174, 94, 190, 80, 176, 92, 188)(81, 177, 93, 189, 83, 179, 91, 187)(82, 178, 90, 186, 84, 180, 88, 184)(85, 181, 96, 192, 86, 182, 95, 191)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 238, 334, 222, 318, 203, 299, 221, 317, 242, 338, 218, 314)(206, 302, 223, 319, 248, 344, 226, 322, 207, 303, 225, 321, 252, 348, 224, 320)(211, 307, 227, 323, 254, 350, 232, 328, 213, 309, 231, 327, 258, 354, 228, 324)(214, 310, 233, 329, 264, 360, 236, 332, 215, 311, 235, 331, 268, 364, 234, 330)(219, 315, 243, 339, 277, 373, 246, 342, 220, 316, 245, 341, 278, 374, 244, 340)(229, 325, 259, 355, 287, 383, 262, 358, 230, 326, 261, 357, 288, 384, 260, 356)(237, 333, 269, 365, 250, 346, 272, 368, 239, 335, 271, 367, 251, 347, 270, 366)(240, 336, 273, 369, 247, 343, 276, 372, 241, 337, 275, 371, 249, 345, 274, 370)(253, 349, 279, 375, 266, 362, 282, 378, 255, 351, 281, 377, 267, 363, 280, 376)(256, 352, 283, 379, 263, 359, 286, 382, 257, 353, 285, 381, 265, 361, 284, 380)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 219)(17, 201)(18, 206)(19, 199)(20, 230)(21, 204)(22, 200)(23, 205)(24, 229)(25, 239)(26, 241)(27, 202)(28, 208)(29, 237)(30, 240)(31, 249)(32, 251)(33, 247)(34, 250)(35, 255)(36, 257)(37, 212)(38, 216)(39, 253)(40, 256)(41, 265)(42, 267)(43, 263)(44, 266)(45, 217)(46, 260)(47, 221)(48, 218)(49, 222)(50, 262)(51, 264)(52, 254)(53, 268)(54, 258)(55, 223)(56, 259)(57, 225)(58, 224)(59, 226)(60, 261)(61, 227)(62, 246)(63, 231)(64, 228)(65, 232)(66, 244)(67, 252)(68, 242)(69, 248)(70, 238)(71, 233)(72, 245)(73, 235)(74, 234)(75, 236)(76, 243)(77, 281)(78, 284)(79, 279)(80, 286)(81, 283)(82, 280)(83, 285)(84, 282)(85, 287)(86, 288)(87, 269)(88, 276)(89, 271)(90, 274)(91, 275)(92, 272)(93, 273)(94, 270)(95, 278)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1923
Graph:: bipartite
	v = 36 e = 192 f = 104
	degree seq :: [ 8^24, 16^12 ]

E27.1921 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^2)^2, Y2^-1 * Y1^3 * Y2^-1 * Y1^-1, Y2^-4 * Y1 * Y2 * Y1 * Y2^-1, Y2 * Y1 * Y2^2 * Y1 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2 * Y1^2 * Y2^-2 * Y1^-3 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 45, 141, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 63, 159, 38, 134, 14, 110, 32, 128, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 52, 148, 42, 138, 16, 112)(8, 104, 24, 120, 49, 145, 19, 115, 47, 143, 80, 176, 60, 156, 25, 121)(10, 106, 29, 125, 58, 154, 81, 177, 71, 167, 33, 129, 61, 157, 26, 122)(12, 108, 20, 116, 50, 146, 79, 175, 46, 142, 37, 133, 74, 170, 35, 131)(17, 113, 34, 130, 73, 169, 40, 136, 53, 149, 78, 174, 75, 171, 43, 139)(22, 118, 54, 150, 86, 182, 76, 172, 41, 137, 57, 153, 87, 183, 51, 147)(28, 124, 48, 144, 82, 178, 64, 160, 39, 135, 59, 155, 85, 181, 66, 162)(30, 126, 55, 151, 83, 179, 77, 173, 44, 140, 62, 158, 88, 184, 67, 163)(31, 127, 65, 161, 91, 187, 56, 152, 89, 185, 70, 166, 84, 180, 69, 165)(68, 164, 93, 189, 96, 192, 90, 186, 72, 168, 94, 190, 95, 191, 92, 188)(193, 289, 195, 291, 202, 298, 222, 318, 245, 341, 213, 309, 237, 333, 230, 326, 263, 359, 236, 332, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 247, 343, 273, 369, 239, 335, 228, 324, 208, 304, 233, 329, 254, 350, 218, 314, 200, 296)(196, 292, 204, 300, 226, 322, 259, 355, 220, 316, 201, 297, 210, 306, 238, 334, 270, 366, 269, 365, 231, 327, 206, 302)(198, 294, 211, 307, 240, 336, 275, 371, 268, 364, 229, 325, 205, 301, 217, 313, 251, 347, 280, 376, 243, 339, 212, 308)(203, 299, 223, 319, 207, 303, 232, 328, 260, 356, 221, 317, 255, 351, 281, 377, 244, 340, 235, 331, 264, 360, 225, 321)(215, 311, 248, 344, 216, 312, 250, 346, 282, 378, 246, 342, 234, 330, 261, 357, 272, 368, 253, 349, 284, 380, 249, 345)(219, 315, 256, 352, 285, 381, 267, 363, 227, 323, 262, 358, 224, 320, 258, 354, 286, 382, 265, 361, 271, 367, 257, 353)(241, 337, 276, 372, 242, 338, 278, 374, 287, 383, 274, 370, 252, 348, 283, 379, 266, 362, 279, 375, 288, 384, 277, 373)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 222)(11, 223)(12, 226)(13, 217)(14, 196)(15, 232)(16, 233)(17, 197)(18, 238)(19, 240)(20, 198)(21, 237)(22, 247)(23, 248)(24, 250)(25, 251)(26, 200)(27, 256)(28, 201)(29, 255)(30, 245)(31, 207)(32, 258)(33, 203)(34, 259)(35, 262)(36, 208)(37, 205)(38, 263)(39, 206)(40, 260)(41, 254)(42, 261)(43, 264)(44, 209)(45, 230)(46, 270)(47, 228)(48, 275)(49, 276)(50, 278)(51, 212)(52, 235)(53, 213)(54, 234)(55, 273)(56, 216)(57, 215)(58, 282)(59, 280)(60, 283)(61, 284)(62, 218)(63, 281)(64, 285)(65, 219)(66, 286)(67, 220)(68, 221)(69, 272)(70, 224)(71, 236)(72, 225)(73, 271)(74, 279)(75, 227)(76, 229)(77, 231)(78, 269)(79, 257)(80, 253)(81, 239)(82, 252)(83, 268)(84, 242)(85, 241)(86, 287)(87, 288)(88, 243)(89, 244)(90, 246)(91, 266)(92, 249)(93, 267)(94, 265)(95, 274)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1922
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 16^12, 24^8 ]

E27.1922 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^2 * Y3^-1 * Y2^2 * Y3, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y3^-6 * Y2^-1, (Y3^3 * Y2^-1)^2, (Y3^-2 * Y2^-1 * Y3^-1)^2, Y3^2 * Y2 * Y3^-3 * Y2^-1 * Y3, Y3^-1 * Y2^-1 * Y3^-2 * Y2^-2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1 * Y3^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 233, 329, 221, 317)(208, 304, 230, 326, 234, 330, 231, 327)(212, 308, 237, 333, 224, 320, 239, 335)(216, 312, 246, 342, 225, 321, 247, 343)(217, 313, 245, 341, 222, 318, 243, 339)(218, 314, 250, 346, 223, 319, 251, 347)(220, 316, 238, 334, 232, 328, 248, 344)(226, 322, 259, 355, 228, 324, 260, 356)(227, 323, 240, 336, 229, 325, 235, 331)(236, 332, 262, 358, 241, 337, 263, 359)(242, 338, 271, 367, 244, 340, 272, 368)(249, 345, 273, 369, 257, 353, 274, 370)(252, 348, 266, 362, 258, 354, 268, 364)(253, 349, 278, 374, 255, 351, 276, 372)(254, 350, 264, 360, 256, 352, 270, 366)(261, 357, 279, 375, 269, 365, 280, 376)(265, 361, 284, 380, 267, 363, 282, 378)(275, 371, 283, 379, 277, 373, 281, 377)(285, 381, 288, 384, 286, 382, 287, 383)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 222)(12, 224)(13, 196)(14, 226)(15, 228)(16, 197)(17, 233)(18, 198)(19, 235)(20, 238)(21, 240)(22, 242)(23, 244)(24, 200)(25, 249)(26, 201)(27, 253)(28, 234)(29, 255)(30, 257)(31, 203)(32, 248)(33, 205)(34, 254)(35, 206)(36, 256)(37, 207)(38, 252)(39, 258)(40, 208)(41, 232)(42, 210)(43, 261)(44, 211)(45, 265)(46, 225)(47, 267)(48, 269)(49, 213)(50, 266)(51, 214)(52, 268)(53, 215)(54, 264)(55, 270)(56, 216)(57, 231)(58, 275)(59, 277)(60, 218)(61, 229)(62, 219)(63, 227)(64, 221)(65, 230)(66, 223)(67, 273)(68, 274)(69, 247)(70, 281)(71, 283)(72, 236)(73, 245)(74, 237)(75, 243)(76, 239)(77, 246)(78, 241)(79, 279)(80, 280)(81, 285)(82, 286)(83, 259)(84, 250)(85, 260)(86, 251)(87, 287)(88, 288)(89, 271)(90, 262)(91, 272)(92, 263)(93, 278)(94, 276)(95, 284)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 16, 24 ), ( 16, 24, 16, 24, 16, 24, 16, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1921
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1923 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-2 * Y1^-1 * Y3, Y3^-1 * Y1^2 * Y3^2 * Y1^-2 * Y3^-1, Y1 * Y3^-2 * Y1^5, (Y3 * Y2^-1)^4, (Y3 * Y1^-3)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 28, 124, 10, 106, 21, 117, 45, 141, 35, 131, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 42, 138, 40, 136, 16, 112, 5, 101, 15, 111, 39, 135, 43, 139, 30, 126, 11, 107)(7, 103, 20, 116, 49, 145, 36, 132, 56, 152, 24, 120, 8, 104, 23, 119, 55, 151, 34, 130, 53, 149, 22, 118)(12, 108, 32, 128, 46, 142, 18, 114, 44, 140, 38, 134, 14, 110, 37, 133, 48, 144, 19, 115, 47, 143, 33, 129)(26, 122, 59, 155, 81, 177, 65, 161, 72, 168, 62, 158, 27, 123, 61, 157, 84, 180, 64, 160, 71, 167, 60, 156)(29, 125, 63, 159, 78, 174, 57, 153, 75, 171, 50, 146, 31, 127, 66, 162, 79, 175, 58, 154, 76, 172, 51, 147)(52, 148, 77, 173, 67, 163, 73, 169, 87, 183, 69, 165, 54, 150, 80, 176, 68, 164, 74, 170, 88, 184, 70, 166)(82, 178, 92, 188, 85, 181, 93, 189, 96, 192, 89, 185, 83, 179, 91, 187, 86, 182, 94, 190, 95, 191, 90, 186)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 226)(14, 196)(15, 219)(16, 223)(17, 234)(18, 237)(19, 198)(20, 242)(21, 200)(22, 244)(23, 243)(24, 246)(25, 249)(26, 207)(27, 201)(28, 206)(29, 208)(30, 256)(31, 203)(32, 259)(33, 253)(34, 233)(35, 235)(36, 205)(37, 260)(38, 251)(39, 250)(40, 257)(41, 228)(42, 227)(43, 209)(44, 261)(45, 211)(46, 263)(47, 262)(48, 264)(49, 265)(50, 215)(51, 212)(52, 216)(53, 270)(54, 214)(55, 266)(56, 271)(57, 231)(58, 217)(59, 225)(60, 274)(61, 230)(62, 275)(63, 277)(64, 232)(65, 222)(66, 278)(67, 229)(68, 224)(69, 239)(70, 236)(71, 240)(72, 238)(73, 247)(74, 241)(75, 281)(76, 282)(77, 283)(78, 248)(79, 245)(80, 284)(81, 285)(82, 254)(83, 252)(84, 286)(85, 258)(86, 255)(87, 287)(88, 288)(89, 268)(90, 267)(91, 272)(92, 269)(93, 276)(94, 273)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1920
Graph:: simple bipartite
	v = 104 e = 192 f = 36
	degree seq :: [ 2^96, 24^8 ]

E27.1924 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y3^-1 * Y1^2 * Y3^-1, Y1 * Y3^-3, Y1 * Y3^-2 * Y1, (R * Y1)^2, Y3^4, (R * Y3)^2, R * Y2^-1 * R * Y1^-1 * Y2^-1 * Y1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y2^-1 * Y1^2 * Y2^2 * Y1^-2 * Y2^-1, (Y1 * Y2^2 * R)^2, Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, (Y2^-1 * R * Y2^-2)^2, Y2^3 * Y3 * Y2^3 * Y1^-1, Y2^6 * Y3 * Y1^-1, Y2 * Y1 * Y2^-2 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y3, Y2 * Y1^3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 41, 137, 29, 125)(16, 112, 38, 134, 42, 138, 39, 135)(20, 116, 45, 141, 32, 128, 47, 143)(24, 120, 54, 150, 33, 129, 55, 151)(25, 121, 53, 149, 30, 126, 51, 147)(26, 122, 58, 154, 31, 127, 59, 155)(28, 124, 46, 142, 40, 136, 56, 152)(34, 130, 67, 163, 36, 132, 68, 164)(35, 131, 48, 144, 37, 133, 43, 139)(44, 140, 70, 166, 49, 145, 71, 167)(50, 146, 79, 175, 52, 148, 80, 176)(57, 153, 81, 177, 65, 161, 82, 178)(60, 156, 74, 170, 66, 162, 76, 172)(61, 157, 86, 182, 63, 159, 84, 180)(62, 158, 72, 168, 64, 160, 78, 174)(69, 165, 87, 183, 77, 173, 88, 184)(73, 169, 92, 188, 75, 171, 90, 186)(83, 179, 91, 187, 85, 181, 89, 185)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 234, 330, 210, 306, 198, 294, 209, 305, 233, 329, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 238, 334, 225, 321, 205, 301, 196, 292, 204, 300, 224, 320, 248, 344, 216, 312, 200, 296)(201, 297, 217, 313, 249, 345, 231, 327, 258, 354, 223, 319, 203, 299, 222, 318, 257, 353, 230, 326, 252, 348, 218, 314)(206, 302, 226, 322, 254, 350, 219, 315, 253, 349, 229, 325, 207, 303, 228, 324, 256, 352, 221, 317, 255, 351, 227, 323)(211, 307, 235, 331, 261, 357, 247, 343, 270, 366, 241, 337, 213, 309, 240, 336, 269, 365, 246, 342, 264, 360, 236, 332)(214, 310, 242, 338, 266, 362, 237, 333, 265, 361, 245, 341, 215, 311, 244, 340, 268, 364, 239, 335, 267, 363, 243, 339)(250, 346, 275, 371, 259, 355, 273, 369, 285, 381, 278, 374, 251, 347, 277, 373, 260, 356, 274, 370, 286, 382, 276, 372)(262, 358, 281, 377, 271, 367, 279, 375, 287, 383, 284, 380, 263, 359, 283, 379, 272, 368, 280, 376, 288, 384, 282, 378)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 239)(21, 204)(22, 200)(23, 205)(24, 247)(25, 243)(26, 251)(27, 202)(28, 248)(29, 233)(30, 245)(31, 250)(32, 237)(33, 246)(34, 260)(35, 235)(36, 259)(37, 240)(38, 208)(39, 234)(40, 238)(41, 219)(42, 230)(43, 229)(44, 263)(45, 212)(46, 220)(47, 224)(48, 227)(49, 262)(50, 272)(51, 222)(52, 271)(53, 217)(54, 216)(55, 225)(56, 232)(57, 274)(58, 218)(59, 223)(60, 268)(61, 276)(62, 270)(63, 278)(64, 264)(65, 273)(66, 266)(67, 226)(68, 228)(69, 280)(70, 236)(71, 241)(72, 254)(73, 282)(74, 252)(75, 284)(76, 258)(77, 279)(78, 256)(79, 242)(80, 244)(81, 249)(82, 257)(83, 281)(84, 255)(85, 283)(86, 253)(87, 261)(88, 269)(89, 277)(90, 267)(91, 275)(92, 265)(93, 287)(94, 288)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.1925
Graph:: bipartite
	v = 32 e = 192 f = 108
	degree seq :: [ 8^24, 24^8 ]

E27.1925 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 8, 12})
Quotient :: dipole
Aut^+ = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>)
Aut   = $<192, 1484>$ (small group id <192, 1484>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^2)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1^3, Y3^-4 * Y1 * Y3 * Y1 * Y3^-1, Y1^8, Y3 * Y1 * Y3^2 * Y1 * Y3 * Y1^2, Y1^-3 * Y3^-1 * Y1 * Y3 * Y1^2 * Y3^-2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 45, 141, 36, 132, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 63, 159, 38, 134, 14, 110, 32, 128, 11, 107)(5, 101, 15, 111, 23, 119, 7, 103, 21, 117, 52, 148, 42, 138, 16, 112)(8, 104, 24, 120, 49, 145, 19, 115, 47, 143, 80, 176, 60, 156, 25, 121)(10, 106, 29, 125, 58, 154, 81, 177, 71, 167, 33, 129, 61, 157, 26, 122)(12, 108, 20, 116, 50, 146, 79, 175, 46, 142, 37, 133, 74, 170, 35, 131)(17, 113, 34, 130, 73, 169, 40, 136, 53, 149, 78, 174, 75, 171, 43, 139)(22, 118, 54, 150, 86, 182, 76, 172, 41, 137, 57, 153, 87, 183, 51, 147)(28, 124, 48, 144, 82, 178, 64, 160, 39, 135, 59, 155, 85, 181, 66, 162)(30, 126, 55, 151, 83, 179, 77, 173, 44, 140, 62, 158, 88, 184, 67, 163)(31, 127, 65, 161, 91, 187, 56, 152, 89, 185, 70, 166, 84, 180, 69, 165)(68, 164, 93, 189, 96, 192, 90, 186, 72, 168, 94, 190, 95, 191, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 210)(10, 222)(11, 223)(12, 226)(13, 217)(14, 196)(15, 232)(16, 233)(17, 197)(18, 238)(19, 240)(20, 198)(21, 237)(22, 247)(23, 248)(24, 250)(25, 251)(26, 200)(27, 256)(28, 201)(29, 255)(30, 245)(31, 207)(32, 258)(33, 203)(34, 259)(35, 262)(36, 208)(37, 205)(38, 263)(39, 206)(40, 260)(41, 254)(42, 261)(43, 264)(44, 209)(45, 230)(46, 270)(47, 228)(48, 275)(49, 276)(50, 278)(51, 212)(52, 235)(53, 213)(54, 234)(55, 273)(56, 216)(57, 215)(58, 282)(59, 280)(60, 283)(61, 284)(62, 218)(63, 281)(64, 285)(65, 219)(66, 286)(67, 220)(68, 221)(69, 272)(70, 224)(71, 236)(72, 225)(73, 271)(74, 279)(75, 227)(76, 229)(77, 231)(78, 269)(79, 257)(80, 253)(81, 239)(82, 252)(83, 268)(84, 242)(85, 241)(86, 287)(87, 288)(88, 243)(89, 244)(90, 246)(91, 266)(92, 249)(93, 267)(94, 265)(95, 274)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1924
Graph:: simple bipartite
	v = 108 e = 192 f = 32
	degree seq :: [ 2^96, 16^12 ]

E27.1926 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^2 * T1, T2^6, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1)^24 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 28, 49, 31, 13)(6, 17, 34, 52, 35, 18)(9, 25, 44, 32, 14, 26)(11, 29, 48, 33, 15, 30)(19, 36, 54, 41, 22, 37)(21, 39, 58, 42, 23, 40)(43, 61, 50, 65, 46, 62)(45, 63, 51, 66, 47, 64)(53, 67, 59, 71, 56, 68)(55, 69, 60, 72, 57, 70)(73, 85, 77, 89, 75, 86)(74, 87, 78, 90, 76, 88)(79, 91, 83, 95, 81, 92)(80, 93, 84, 96, 82, 94)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 116, 130, 124)(112, 120, 131, 127)(121, 139, 125, 141)(122, 142, 126, 143)(123, 140, 148, 144)(128, 146, 129, 147)(132, 149, 135, 151)(133, 152, 136, 153)(134, 150, 145, 154)(137, 155, 138, 156)(157, 169, 159, 170)(158, 171, 160, 172)(161, 173, 162, 174)(163, 175, 165, 176)(164, 177, 166, 178)(167, 179, 168, 180)(181, 187, 183, 189)(182, 188, 184, 190)(185, 191, 186, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 48^4 ), ( 48^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1930
Transitivity :: ET+
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.1927 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1 * T2 * T1^-2 * T2^-1 * T1, (T2^-2 * T1)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, (T2 * T1)^4, T1 * T2^-6 * T1 * T2^2 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 30, 64, 80, 52, 36, 13, 32, 59, 86, 93, 78, 49, 20, 6, 19, 47, 76, 74, 43, 17, 5)(2, 7, 22, 53, 82, 69, 38, 14, 4, 12, 34, 67, 90, 62, 29, 45, 18, 44, 42, 72, 88, 60, 26, 8)(9, 27, 48, 77, 73, 92, 66, 33, 11, 31, 15, 39, 70, 91, 63, 75, 46, 41, 16, 40, 71, 89, 61, 28)(21, 50, 37, 65, 87, 96, 83, 55, 23, 54, 24, 56, 84, 95, 81, 68, 35, 58, 25, 57, 85, 94, 79, 51)(97, 98, 102, 114, 109, 100)(99, 105, 115, 142, 128, 107)(101, 111, 116, 144, 132, 112)(103, 117, 140, 131, 108, 119)(104, 120, 141, 133, 110, 121)(106, 125, 143, 134, 155, 122)(113, 130, 145, 118, 148, 138)(123, 146, 137, 154, 127, 150)(124, 152, 171, 161, 129, 153)(126, 159, 172, 162, 182, 157)(135, 147, 173, 164, 136, 151)(139, 167, 174, 166, 176, 169)(149, 177, 168, 179, 163, 175)(156, 181, 158, 180, 165, 183)(160, 178, 170, 184, 189, 186)(185, 190, 187, 191, 188, 192)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.1931
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.1928 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T1^-2 * T2^-1 * T1^-1)^2, (T1^-1 * T2 * T1^-2)^2, T2 * T1^4 * T2^-1 * T1^-4 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 62, 36)(17, 42, 76, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 58, 39, 59)(30, 64, 40, 65)(32, 60, 37, 61)(33, 63, 38, 66)(35, 69, 89, 57)(41, 74, 93, 75)(44, 79, 47, 80)(46, 81, 48, 83)(49, 85, 55, 86)(53, 87, 56, 88)(67, 90, 72, 91)(68, 73, 71, 92)(70, 78, 94, 77)(82, 95, 84, 96)(97, 98, 102, 113, 137, 169, 156, 122, 146, 175, 161, 184, 192, 187, 155, 182, 159, 125, 148, 177, 166, 131, 109, 100)(99, 105, 121, 153, 170, 152, 120, 104, 119, 151, 130, 164, 178, 142, 114, 140, 134, 110, 133, 168, 174, 139, 126, 107)(101, 111, 135, 165, 171, 149, 118, 103, 116, 145, 132, 167, 180, 144, 115, 143, 129, 108, 128, 163, 173, 138, 136, 112)(106, 117, 141, 172, 189, 188, 157, 123, 147, 176, 160, 183, 191, 186, 154, 181, 162, 127, 150, 179, 190, 185, 158, 124)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.1929
Transitivity :: ET+
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.1929 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^2 * T1, T2^6, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1)^24 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 27, 123, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 38, 134, 24, 120, 8, 104)(4, 100, 12, 108, 28, 124, 49, 145, 31, 127, 13, 109)(6, 102, 17, 113, 34, 130, 52, 148, 35, 131, 18, 114)(9, 105, 25, 121, 44, 140, 32, 128, 14, 110, 26, 122)(11, 107, 29, 125, 48, 144, 33, 129, 15, 111, 30, 126)(19, 115, 36, 132, 54, 150, 41, 137, 22, 118, 37, 133)(21, 117, 39, 135, 58, 154, 42, 138, 23, 119, 40, 136)(43, 139, 61, 157, 50, 146, 65, 161, 46, 142, 62, 158)(45, 141, 63, 159, 51, 147, 66, 162, 47, 143, 64, 160)(53, 149, 67, 163, 59, 155, 71, 167, 56, 152, 68, 164)(55, 151, 69, 165, 60, 156, 72, 168, 57, 153, 70, 166)(73, 169, 85, 181, 77, 173, 89, 185, 75, 171, 86, 182)(74, 170, 87, 183, 78, 174, 90, 186, 76, 172, 88, 184)(79, 175, 91, 187, 83, 179, 95, 191, 81, 177, 92, 188)(80, 176, 93, 189, 84, 180, 96, 192, 82, 178, 94, 190)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 116)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 120)(17, 107)(18, 111)(19, 108)(20, 130)(21, 103)(22, 109)(23, 104)(24, 131)(25, 139)(26, 142)(27, 140)(28, 106)(29, 141)(30, 143)(31, 112)(32, 146)(33, 147)(34, 124)(35, 127)(36, 149)(37, 152)(38, 150)(39, 151)(40, 153)(41, 155)(42, 156)(43, 125)(44, 148)(45, 121)(46, 126)(47, 122)(48, 123)(49, 154)(50, 129)(51, 128)(52, 144)(53, 135)(54, 145)(55, 132)(56, 136)(57, 133)(58, 134)(59, 138)(60, 137)(61, 169)(62, 171)(63, 170)(64, 172)(65, 173)(66, 174)(67, 175)(68, 177)(69, 176)(70, 178)(71, 179)(72, 180)(73, 159)(74, 157)(75, 160)(76, 158)(77, 162)(78, 161)(79, 165)(80, 163)(81, 166)(82, 164)(83, 168)(84, 167)(85, 187)(86, 188)(87, 189)(88, 190)(89, 191)(90, 192)(91, 183)(92, 184)(93, 181)(94, 182)(95, 186)(96, 185)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1928
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.1930 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1 * T2 * T1^-2 * T2^-1 * T1, (T2^-2 * T1)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, (T2 * T1)^4, T1 * T2^-6 * T1 * T2^2 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 30, 126, 64, 160, 80, 176, 52, 148, 36, 132, 13, 109, 32, 128, 59, 155, 86, 182, 93, 189, 78, 174, 49, 145, 20, 116, 6, 102, 19, 115, 47, 143, 76, 172, 74, 170, 43, 139, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 53, 149, 82, 178, 69, 165, 38, 134, 14, 110, 4, 100, 12, 108, 34, 130, 67, 163, 90, 186, 62, 158, 29, 125, 45, 141, 18, 114, 44, 140, 42, 138, 72, 168, 88, 184, 60, 156, 26, 122, 8, 104)(9, 105, 27, 123, 48, 144, 77, 173, 73, 169, 92, 188, 66, 162, 33, 129, 11, 107, 31, 127, 15, 111, 39, 135, 70, 166, 91, 187, 63, 159, 75, 171, 46, 142, 41, 137, 16, 112, 40, 136, 71, 167, 89, 185, 61, 157, 28, 124)(21, 117, 50, 146, 37, 133, 65, 161, 87, 183, 96, 192, 83, 179, 55, 151, 23, 119, 54, 150, 24, 120, 56, 152, 84, 180, 95, 191, 81, 177, 68, 164, 35, 131, 58, 154, 25, 121, 57, 153, 85, 181, 94, 190, 79, 175, 51, 147)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 115)(10, 125)(11, 99)(12, 119)(13, 100)(14, 121)(15, 116)(16, 101)(17, 130)(18, 109)(19, 142)(20, 144)(21, 140)(22, 148)(23, 103)(24, 141)(25, 104)(26, 106)(27, 146)(28, 152)(29, 143)(30, 159)(31, 150)(32, 107)(33, 153)(34, 145)(35, 108)(36, 112)(37, 110)(38, 155)(39, 147)(40, 151)(41, 154)(42, 113)(43, 167)(44, 131)(45, 133)(46, 128)(47, 134)(48, 132)(49, 118)(50, 137)(51, 173)(52, 138)(53, 177)(54, 123)(55, 135)(56, 171)(57, 124)(58, 127)(59, 122)(60, 181)(61, 126)(62, 180)(63, 172)(64, 178)(65, 129)(66, 182)(67, 175)(68, 136)(69, 183)(70, 176)(71, 174)(72, 179)(73, 139)(74, 184)(75, 161)(76, 162)(77, 164)(78, 166)(79, 149)(80, 169)(81, 168)(82, 170)(83, 163)(84, 165)(85, 158)(86, 157)(87, 156)(88, 189)(89, 190)(90, 160)(91, 191)(92, 192)(93, 186)(94, 187)(95, 188)(96, 185)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1926
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 96 f = 40
	degree seq :: [ 48^4 ]

E27.1931 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^2 * T1 * T2, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T1^-2 * T2^-1 * T1^-1)^2, (T1^-1 * T2 * T1^-2)^2, T2 * T1^4 * T2^-1 * T1^-4 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 31, 127)(13, 109, 34, 130, 62, 158, 36, 132)(17, 113, 42, 138, 76, 172, 43, 139)(20, 116, 50, 146, 23, 119, 51, 147)(22, 118, 52, 148, 24, 120, 54, 150)(25, 121, 58, 154, 39, 135, 59, 155)(30, 126, 64, 160, 40, 136, 65, 161)(32, 128, 60, 156, 37, 133, 61, 157)(33, 129, 63, 159, 38, 134, 66, 162)(35, 131, 69, 165, 89, 185, 57, 153)(41, 137, 74, 170, 93, 189, 75, 171)(44, 140, 79, 175, 47, 143, 80, 176)(46, 142, 81, 177, 48, 144, 83, 179)(49, 145, 85, 181, 55, 151, 86, 182)(53, 149, 87, 183, 56, 152, 88, 184)(67, 163, 90, 186, 72, 168, 91, 187)(68, 164, 73, 169, 71, 167, 92, 188)(70, 166, 78, 174, 94, 190, 77, 173)(82, 178, 95, 191, 84, 180, 96, 192)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 128)(13, 100)(14, 133)(15, 135)(16, 101)(17, 137)(18, 140)(19, 143)(20, 145)(21, 141)(22, 103)(23, 151)(24, 104)(25, 153)(26, 146)(27, 147)(28, 106)(29, 148)(30, 107)(31, 150)(32, 163)(33, 108)(34, 164)(35, 109)(36, 167)(37, 168)(38, 110)(39, 165)(40, 112)(41, 169)(42, 136)(43, 126)(44, 134)(45, 172)(46, 114)(47, 129)(48, 115)(49, 132)(50, 175)(51, 176)(52, 177)(53, 118)(54, 179)(55, 130)(56, 120)(57, 170)(58, 181)(59, 182)(60, 122)(61, 123)(62, 124)(63, 125)(64, 183)(65, 184)(66, 127)(67, 173)(68, 178)(69, 171)(70, 131)(71, 180)(72, 174)(73, 156)(74, 152)(75, 149)(76, 189)(77, 138)(78, 139)(79, 161)(80, 160)(81, 166)(82, 142)(83, 190)(84, 144)(85, 162)(86, 159)(87, 191)(88, 192)(89, 158)(90, 154)(91, 155)(92, 157)(93, 188)(94, 185)(95, 186)(96, 187)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1927
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1932 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (R * Y2^2)^2, Y2^6, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 20, 116, 34, 130, 28, 124)(16, 112, 24, 120, 35, 131, 31, 127)(25, 121, 43, 139, 29, 125, 45, 141)(26, 122, 46, 142, 30, 126, 47, 143)(27, 123, 44, 140, 52, 148, 48, 144)(32, 128, 50, 146, 33, 129, 51, 147)(36, 132, 53, 149, 39, 135, 55, 151)(37, 133, 56, 152, 40, 136, 57, 153)(38, 134, 54, 150, 49, 145, 58, 154)(41, 137, 59, 155, 42, 138, 60, 156)(61, 157, 73, 169, 63, 159, 74, 170)(62, 158, 75, 171, 64, 160, 76, 172)(65, 161, 77, 173, 66, 162, 78, 174)(67, 163, 79, 175, 69, 165, 80, 176)(68, 164, 81, 177, 70, 166, 82, 178)(71, 167, 83, 179, 72, 168, 84, 180)(85, 181, 91, 187, 87, 183, 93, 189)(86, 182, 92, 188, 88, 184, 94, 190)(89, 185, 95, 191, 90, 186, 96, 192)(193, 289, 195, 291, 202, 298, 219, 315, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 230, 326, 216, 312, 200, 296)(196, 292, 204, 300, 220, 316, 241, 337, 223, 319, 205, 301)(198, 294, 209, 305, 226, 322, 244, 340, 227, 323, 210, 306)(201, 297, 217, 313, 236, 332, 224, 320, 206, 302, 218, 314)(203, 299, 221, 317, 240, 336, 225, 321, 207, 303, 222, 318)(211, 307, 228, 324, 246, 342, 233, 329, 214, 310, 229, 325)(213, 309, 231, 327, 250, 346, 234, 330, 215, 311, 232, 328)(235, 331, 253, 349, 242, 338, 257, 353, 238, 334, 254, 350)(237, 333, 255, 351, 243, 339, 258, 354, 239, 335, 256, 352)(245, 341, 259, 355, 251, 347, 263, 359, 248, 344, 260, 356)(247, 343, 261, 357, 252, 348, 264, 360, 249, 345, 262, 358)(265, 361, 277, 373, 269, 365, 281, 377, 267, 363, 278, 374)(266, 362, 279, 375, 270, 366, 282, 378, 268, 364, 280, 376)(271, 367, 283, 379, 275, 371, 287, 383, 273, 369, 284, 380)(272, 368, 285, 381, 276, 372, 288, 384, 274, 370, 286, 382)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 202)(21, 204)(22, 200)(23, 205)(24, 208)(25, 237)(26, 239)(27, 240)(28, 226)(29, 235)(30, 238)(31, 227)(32, 243)(33, 242)(34, 212)(35, 216)(36, 247)(37, 249)(38, 250)(39, 245)(40, 248)(41, 252)(42, 251)(43, 217)(44, 219)(45, 221)(46, 218)(47, 222)(48, 244)(49, 246)(50, 224)(51, 225)(52, 236)(53, 228)(54, 230)(55, 231)(56, 229)(57, 232)(58, 241)(59, 233)(60, 234)(61, 266)(62, 268)(63, 265)(64, 267)(65, 270)(66, 269)(67, 272)(68, 274)(69, 271)(70, 273)(71, 276)(72, 275)(73, 253)(74, 255)(75, 254)(76, 256)(77, 257)(78, 258)(79, 259)(80, 261)(81, 260)(82, 262)(83, 263)(84, 264)(85, 285)(86, 286)(87, 283)(88, 284)(89, 288)(90, 287)(91, 277)(92, 278)(93, 279)(94, 280)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1935
Graph:: bipartite
	v = 40 e = 192 f = 100
	degree seq :: [ 8^24, 12^16 ]

E27.1933 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y2^-1 * Y1^-2 * Y2, Y1^6, (Y2^2 * Y1^-1)^2, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-2 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^-2 * Y1^-2 * Y2^-6 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 46, 142, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 48, 144, 36, 132, 16, 112)(7, 103, 21, 117, 44, 140, 35, 131, 12, 108, 23, 119)(8, 104, 24, 120, 45, 141, 37, 133, 14, 110, 25, 121)(10, 106, 29, 125, 47, 143, 38, 134, 59, 155, 26, 122)(17, 113, 34, 130, 49, 145, 22, 118, 52, 148, 42, 138)(27, 123, 50, 146, 41, 137, 58, 154, 31, 127, 54, 150)(28, 124, 56, 152, 75, 171, 65, 161, 33, 129, 57, 153)(30, 126, 63, 159, 76, 172, 66, 162, 86, 182, 61, 157)(39, 135, 51, 147, 77, 173, 68, 164, 40, 136, 55, 151)(43, 139, 71, 167, 78, 174, 70, 166, 80, 176, 73, 169)(53, 149, 81, 177, 72, 168, 83, 179, 67, 163, 79, 175)(60, 156, 85, 181, 62, 158, 84, 180, 69, 165, 87, 183)(64, 160, 82, 178, 74, 170, 88, 184, 93, 189, 90, 186)(89, 185, 94, 190, 91, 187, 95, 191, 92, 188, 96, 192)(193, 289, 195, 291, 202, 298, 222, 318, 256, 352, 272, 368, 244, 340, 228, 324, 205, 301, 224, 320, 251, 347, 278, 374, 285, 381, 270, 366, 241, 337, 212, 308, 198, 294, 211, 307, 239, 335, 268, 364, 266, 362, 235, 331, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 245, 341, 274, 370, 261, 357, 230, 326, 206, 302, 196, 292, 204, 300, 226, 322, 259, 355, 282, 378, 254, 350, 221, 317, 237, 333, 210, 306, 236, 332, 234, 330, 264, 360, 280, 376, 252, 348, 218, 314, 200, 296)(201, 297, 219, 315, 240, 336, 269, 365, 265, 361, 284, 380, 258, 354, 225, 321, 203, 299, 223, 319, 207, 303, 231, 327, 262, 358, 283, 379, 255, 351, 267, 363, 238, 334, 233, 329, 208, 304, 232, 328, 263, 359, 281, 377, 253, 349, 220, 316)(213, 309, 242, 338, 229, 325, 257, 353, 279, 375, 288, 384, 275, 371, 247, 343, 215, 311, 246, 342, 216, 312, 248, 344, 276, 372, 287, 383, 273, 369, 260, 356, 227, 323, 250, 346, 217, 313, 249, 345, 277, 373, 286, 382, 271, 367, 243, 339)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 222)(11, 223)(12, 226)(13, 224)(14, 196)(15, 231)(16, 232)(17, 197)(18, 236)(19, 239)(20, 198)(21, 242)(22, 245)(23, 246)(24, 248)(25, 249)(26, 200)(27, 240)(28, 201)(29, 237)(30, 256)(31, 207)(32, 251)(33, 203)(34, 259)(35, 250)(36, 205)(37, 257)(38, 206)(39, 262)(40, 263)(41, 208)(42, 264)(43, 209)(44, 234)(45, 210)(46, 233)(47, 268)(48, 269)(49, 212)(50, 229)(51, 213)(52, 228)(53, 274)(54, 216)(55, 215)(56, 276)(57, 277)(58, 217)(59, 278)(60, 218)(61, 220)(62, 221)(63, 267)(64, 272)(65, 279)(66, 225)(67, 282)(68, 227)(69, 230)(70, 283)(71, 281)(72, 280)(73, 284)(74, 235)(75, 238)(76, 266)(77, 265)(78, 241)(79, 243)(80, 244)(81, 260)(82, 261)(83, 247)(84, 287)(85, 286)(86, 285)(87, 288)(88, 252)(89, 253)(90, 254)(91, 255)(92, 258)(93, 270)(94, 271)(95, 273)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1934
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 12^16, 48^4 ]

E27.1934 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^2 * Y3^-1 * Y2^2 * Y3, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1, (Y2^-1 * Y3^3)^2, Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y2^-1 * Y3^-3)^2, Y3 * Y2^-1 * Y3^-7 * Y2^-1, (Y3^-1 * Y1^-1)^24 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 233, 329, 221, 317)(208, 304, 230, 326, 234, 330, 231, 327)(212, 308, 237, 333, 224, 320, 239, 335)(216, 312, 246, 342, 225, 321, 247, 343)(217, 313, 235, 331, 222, 318, 240, 336)(218, 314, 242, 338, 223, 319, 244, 340)(220, 316, 253, 349, 265, 361, 248, 344)(226, 322, 236, 332, 228, 324, 241, 337)(227, 323, 243, 339, 229, 325, 245, 341)(232, 328, 259, 355, 266, 362, 238, 334)(249, 345, 269, 365, 257, 353, 272, 368)(250, 346, 278, 374, 258, 354, 279, 375)(251, 347, 267, 363, 255, 351, 274, 370)(252, 348, 276, 372, 256, 352, 277, 373)(254, 350, 271, 367, 285, 381, 281, 377)(260, 356, 270, 366, 261, 357, 273, 369)(262, 358, 268, 364, 263, 359, 275, 371)(264, 360, 280, 376, 286, 382, 283, 379)(282, 378, 287, 383, 284, 380, 288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 222)(12, 224)(13, 196)(14, 226)(15, 228)(16, 197)(17, 233)(18, 198)(19, 235)(20, 238)(21, 240)(22, 242)(23, 244)(24, 200)(25, 249)(26, 201)(27, 251)(28, 254)(29, 255)(30, 257)(31, 203)(32, 259)(33, 205)(34, 260)(35, 206)(36, 261)(37, 207)(38, 262)(39, 263)(40, 208)(41, 265)(42, 210)(43, 267)(44, 211)(45, 269)(46, 271)(47, 272)(48, 274)(49, 213)(50, 276)(51, 214)(52, 277)(53, 215)(54, 278)(55, 279)(56, 216)(57, 231)(58, 218)(59, 229)(60, 219)(61, 225)(62, 268)(63, 227)(64, 221)(65, 230)(66, 223)(67, 281)(68, 283)(69, 280)(70, 282)(71, 284)(72, 232)(73, 285)(74, 234)(75, 247)(76, 236)(77, 245)(78, 237)(79, 258)(80, 243)(81, 239)(82, 246)(83, 241)(84, 264)(85, 286)(86, 287)(87, 288)(88, 248)(89, 250)(90, 252)(91, 253)(92, 256)(93, 275)(94, 266)(95, 270)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1933
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1935 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1 * Y3^2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y1^-3 * Y3^-1)^2, (Y3 * Y1^-3)^2, (Y3 * Y2^-1)^4, Y1^-3 * Y3^-1 * Y1 * Y3^-1 * Y1^-4, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-2 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 73, 169, 60, 156, 26, 122, 50, 146, 79, 175, 65, 161, 88, 184, 96, 192, 91, 187, 59, 155, 86, 182, 63, 159, 29, 125, 52, 148, 81, 177, 70, 166, 35, 131, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 57, 153, 74, 170, 56, 152, 24, 120, 8, 104, 23, 119, 55, 151, 34, 130, 68, 164, 82, 178, 46, 142, 18, 114, 44, 140, 38, 134, 14, 110, 37, 133, 72, 168, 78, 174, 43, 139, 30, 126, 11, 107)(5, 101, 15, 111, 39, 135, 69, 165, 75, 171, 53, 149, 22, 118, 7, 103, 20, 116, 49, 145, 36, 132, 71, 167, 84, 180, 48, 144, 19, 115, 47, 143, 33, 129, 12, 108, 32, 128, 67, 163, 77, 173, 42, 138, 40, 136, 16, 112)(10, 106, 21, 117, 45, 141, 76, 172, 93, 189, 92, 188, 61, 157, 27, 123, 51, 147, 80, 176, 64, 160, 87, 183, 95, 191, 90, 186, 58, 154, 85, 181, 66, 162, 31, 127, 54, 150, 83, 179, 94, 190, 89, 185, 62, 158, 28, 124)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 226)(14, 196)(15, 219)(16, 223)(17, 234)(18, 237)(19, 198)(20, 242)(21, 200)(22, 244)(23, 243)(24, 246)(25, 250)(26, 207)(27, 201)(28, 206)(29, 208)(30, 256)(31, 203)(32, 252)(33, 255)(34, 254)(35, 261)(36, 205)(37, 253)(38, 258)(39, 251)(40, 257)(41, 266)(42, 268)(43, 209)(44, 271)(45, 211)(46, 273)(47, 272)(48, 275)(49, 277)(50, 215)(51, 212)(52, 216)(53, 279)(54, 214)(55, 278)(56, 280)(57, 227)(58, 231)(59, 217)(60, 229)(61, 224)(62, 228)(63, 230)(64, 232)(65, 222)(66, 225)(67, 282)(68, 265)(69, 281)(70, 270)(71, 284)(72, 283)(73, 263)(74, 285)(75, 233)(76, 235)(77, 262)(78, 286)(79, 239)(80, 236)(81, 240)(82, 287)(83, 238)(84, 288)(85, 247)(86, 241)(87, 248)(88, 245)(89, 249)(90, 264)(91, 259)(92, 260)(93, 267)(94, 269)(95, 276)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1932
Graph:: simple bipartite
	v = 100 e = 192 f = 40
	degree seq :: [ 2^96, 48^4 ]

E27.1936 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y1^-3 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y2^3 * Y1^-1 * Y2^3 * Y3, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2^-3 * Y1^-1 * Y2^-3, Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * R * Y2^-3)^2, Y2^-4 * Y1 * Y2^4 * Y1^-1, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 41, 137, 29, 125)(16, 112, 38, 134, 42, 138, 39, 135)(20, 116, 45, 141, 32, 128, 47, 143)(24, 120, 54, 150, 33, 129, 55, 151)(25, 121, 43, 139, 30, 126, 48, 144)(26, 122, 50, 146, 31, 127, 52, 148)(28, 124, 61, 157, 73, 169, 56, 152)(34, 130, 44, 140, 36, 132, 49, 145)(35, 131, 51, 147, 37, 133, 53, 149)(40, 136, 67, 163, 74, 170, 46, 142)(57, 153, 77, 173, 65, 161, 80, 176)(58, 154, 86, 182, 66, 162, 87, 183)(59, 155, 75, 171, 63, 159, 82, 178)(60, 156, 84, 180, 64, 160, 85, 181)(62, 158, 79, 175, 93, 189, 89, 185)(68, 164, 78, 174, 69, 165, 81, 177)(70, 166, 76, 172, 71, 167, 83, 179)(72, 168, 88, 184, 94, 190, 91, 187)(90, 186, 95, 191, 92, 188, 96, 192)(193, 289, 195, 291, 202, 298, 220, 316, 254, 350, 268, 364, 236, 332, 211, 307, 235, 331, 267, 363, 247, 343, 279, 375, 288, 384, 273, 369, 239, 335, 272, 368, 243, 339, 214, 310, 242, 338, 276, 372, 264, 360, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 238, 334, 271, 367, 258, 354, 223, 319, 203, 299, 222, 318, 257, 353, 230, 326, 262, 358, 282, 378, 252, 348, 219, 315, 251, 347, 229, 325, 207, 303, 228, 324, 261, 357, 280, 376, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 259, 355, 281, 377, 250, 346, 218, 314, 201, 297, 217, 313, 249, 345, 231, 327, 263, 359, 284, 380, 256, 352, 221, 317, 255, 351, 227, 323, 206, 302, 226, 322, 260, 356, 283, 379, 253, 349, 225, 321, 205, 301)(198, 294, 209, 305, 233, 329, 265, 361, 285, 381, 275, 371, 241, 337, 213, 309, 240, 336, 274, 370, 246, 342, 278, 374, 287, 383, 270, 366, 237, 333, 269, 365, 245, 341, 215, 311, 244, 340, 277, 373, 286, 382, 266, 362, 234, 330, 210, 306)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 239)(21, 204)(22, 200)(23, 205)(24, 247)(25, 240)(26, 244)(27, 202)(28, 248)(29, 233)(30, 235)(31, 242)(32, 237)(33, 246)(34, 241)(35, 245)(36, 236)(37, 243)(38, 208)(39, 234)(40, 238)(41, 219)(42, 230)(43, 217)(44, 226)(45, 212)(46, 266)(47, 224)(48, 222)(49, 228)(50, 218)(51, 227)(52, 223)(53, 229)(54, 216)(55, 225)(56, 265)(57, 272)(58, 279)(59, 274)(60, 277)(61, 220)(62, 281)(63, 267)(64, 276)(65, 269)(66, 278)(67, 232)(68, 273)(69, 270)(70, 275)(71, 268)(72, 283)(73, 253)(74, 259)(75, 251)(76, 262)(77, 249)(78, 260)(79, 254)(80, 257)(81, 261)(82, 255)(83, 263)(84, 252)(85, 256)(86, 250)(87, 258)(88, 264)(89, 285)(90, 288)(91, 286)(92, 287)(93, 271)(94, 280)(95, 282)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1937
Graph:: bipartite
	v = 28 e = 192 f = 112
	degree seq :: [ 8^24, 48^4 ]

E27.1937 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C8 x C2) : C2) (small group id <96, 52>)
Aut   = $<192, 332>$ (small group id <192, 332>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y1 * Y3 * Y1^-2 * Y3^-1 * Y1, (Y3^2 * Y1^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, Y3^-2 * Y1^-3 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y3^6 * Y1^-1 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 46, 142, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 48, 144, 36, 132, 16, 112)(7, 103, 21, 117, 44, 140, 35, 131, 12, 108, 23, 119)(8, 104, 24, 120, 45, 141, 37, 133, 14, 110, 25, 121)(10, 106, 29, 125, 47, 143, 38, 134, 59, 155, 26, 122)(17, 113, 34, 130, 49, 145, 22, 118, 52, 148, 42, 138)(27, 123, 50, 146, 41, 137, 58, 154, 31, 127, 54, 150)(28, 124, 56, 152, 75, 171, 65, 161, 33, 129, 57, 153)(30, 126, 63, 159, 76, 172, 66, 162, 86, 182, 61, 157)(39, 135, 51, 147, 77, 173, 68, 164, 40, 136, 55, 151)(43, 139, 71, 167, 78, 174, 70, 166, 80, 176, 73, 169)(53, 149, 81, 177, 72, 168, 83, 179, 67, 163, 79, 175)(60, 156, 85, 181, 62, 158, 84, 180, 69, 165, 87, 183)(64, 160, 82, 178, 74, 170, 88, 184, 93, 189, 90, 186)(89, 185, 94, 190, 91, 187, 95, 191, 92, 188, 96, 192)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 222)(11, 223)(12, 226)(13, 224)(14, 196)(15, 231)(16, 232)(17, 197)(18, 236)(19, 239)(20, 198)(21, 242)(22, 245)(23, 246)(24, 248)(25, 249)(26, 200)(27, 240)(28, 201)(29, 237)(30, 256)(31, 207)(32, 251)(33, 203)(34, 259)(35, 250)(36, 205)(37, 257)(38, 206)(39, 262)(40, 263)(41, 208)(42, 264)(43, 209)(44, 234)(45, 210)(46, 233)(47, 268)(48, 269)(49, 212)(50, 229)(51, 213)(52, 228)(53, 274)(54, 216)(55, 215)(56, 276)(57, 277)(58, 217)(59, 278)(60, 218)(61, 220)(62, 221)(63, 267)(64, 272)(65, 279)(66, 225)(67, 282)(68, 227)(69, 230)(70, 283)(71, 281)(72, 280)(73, 284)(74, 235)(75, 238)(76, 266)(77, 265)(78, 241)(79, 243)(80, 244)(81, 260)(82, 261)(83, 247)(84, 287)(85, 286)(86, 285)(87, 288)(88, 252)(89, 253)(90, 254)(91, 255)(92, 258)(93, 270)(94, 271)(95, 273)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1936
Graph:: simple bipartite
	v = 112 e = 192 f = 28
	degree seq :: [ 2^96, 12^16 ]

E27.1938 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-2 * T1 * T2^2 * T1^-1, T2^6, (T1, T2^-1, T1^-1), (T2^-1 * T1^-1)^24 ]
Map:: non-degenerate
	R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 49, 24, 8)(4, 12, 29, 61, 36, 13)(6, 17, 41, 72, 45, 18)(9, 26, 57, 38, 14, 27)(11, 30, 60, 39, 15, 31)(19, 47, 80, 53, 22, 48)(21, 50, 81, 54, 23, 51)(25, 55, 83, 68, 37, 56)(32, 58, 86, 66, 34, 59)(33, 62, 87, 67, 35, 63)(40, 70, 91, 76, 43, 71)(42, 73, 92, 77, 44, 74)(46, 78, 94, 82, 52, 79)(64, 84, 95, 88, 65, 85)(69, 89, 96, 93, 75, 90)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 133, 111)(103, 115, 142, 117)(104, 118, 148, 119)(106, 116, 137, 125)(108, 128, 160, 129)(109, 130, 161, 131)(112, 120, 141, 132)(113, 136, 165, 138)(114, 139, 171, 140)(122, 143, 166, 154)(123, 144, 167, 155)(124, 153, 179, 156)(126, 146, 169, 158)(127, 147, 170, 159)(134, 149, 172, 162)(135, 150, 173, 163)(145, 176, 190, 177)(151, 174, 185, 180)(152, 175, 186, 181)(157, 182, 191, 183)(164, 178, 189, 184)(168, 187, 192, 188)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 48^4 ), ( 48^6 ) }
Outer automorphisms :: reflexible
Dual of E27.1942
Transitivity :: ET+
Graph:: simple bipartite
	v = 40 e = 96 f = 4
	degree seq :: [ 4^24, 6^16 ]

E27.1939 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^6, T2^-1 * T1^-2 * T2 * T1^2, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^4, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-5 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 29, 59, 89, 66, 35, 13, 32, 62, 91, 96, 77, 46, 20, 6, 19, 44, 75, 70, 40, 17, 5)(2, 7, 22, 49, 81, 67, 37, 14, 4, 12, 30, 61, 90, 93, 72, 42, 18, 41, 71, 92, 86, 54, 26, 8)(9, 27, 56, 79, 69, 39, 16, 33, 11, 31, 60, 80, 95, 76, 45, 74, 43, 73, 94, 83, 68, 38, 15, 28)(21, 47, 78, 63, 85, 53, 25, 51, 23, 50, 82, 57, 87, 55, 36, 65, 34, 64, 88, 58, 84, 52, 24, 48)(97, 98, 102, 114, 109, 100)(99, 105, 115, 139, 128, 107)(101, 111, 116, 141, 131, 112)(103, 117, 137, 130, 108, 119)(104, 120, 138, 132, 110, 121)(106, 118, 140, 167, 158, 126)(113, 122, 142, 168, 162, 133)(123, 151, 169, 149, 127, 148)(124, 153, 170, 159, 129, 154)(125, 152, 171, 190, 187, 156)(134, 146, 172, 143, 135, 160)(136, 164, 173, 191, 185, 165)(144, 175, 161, 179, 147, 176)(145, 174, 188, 184, 157, 178)(150, 180, 189, 183, 163, 181)(155, 177, 166, 182, 192, 186)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8^6 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E27.1943
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 96 f = 24
	degree seq :: [ 6^16, 24^4 ]

E27.1940 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 24})
Quotient :: edge
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T2 * T1^-1 * T2^-2 * T1 * T2^-2 * T1^-1 * T2^-2 * T1 * T2, (T2^-1 * T1^-1)^6 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 32, 14)(6, 18, 45, 19)(9, 25, 57, 26)(11, 29, 63, 31)(13, 30, 61, 35)(15, 37, 70, 38)(16, 39, 71, 40)(17, 42, 74, 43)(20, 47, 79, 48)(22, 51, 84, 52)(23, 53, 85, 54)(24, 55, 86, 56)(27, 58, 87, 59)(28, 60, 88, 62)(33, 41, 72, 66)(34, 46, 78, 67)(36, 64, 89, 69)(44, 75, 93, 76)(49, 80, 95, 81)(50, 82, 96, 83)(65, 73, 92, 90)(68, 77, 94, 91)(97, 98, 102, 113, 137, 125, 147, 121, 143, 171, 188, 184, 192, 183, 191, 187, 165, 136, 152, 134, 150, 130, 109, 100)(99, 105, 114, 140, 168, 156, 180, 154, 175, 190, 186, 167, 179, 166, 177, 163, 132, 110, 120, 104, 119, 139, 126, 107)(101, 111, 115, 142, 129, 108, 118, 103, 116, 138, 169, 159, 178, 153, 176, 189, 185, 158, 182, 155, 181, 164, 131, 112)(106, 123, 141, 173, 162, 135, 148, 133, 144, 174, 161, 128, 146, 117, 145, 170, 160, 127, 151, 122, 149, 172, 157, 124)
	L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12^4 ), ( 12^24 ) }
Outer automorphisms :: reflexible
Dual of E27.1941
Transitivity :: ET+
Graph:: simple bipartite
	v = 28 e = 96 f = 16
	degree seq :: [ 4^24, 24^4 ]

E27.1941 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-2 * T1 * T2^2 * T1^-1, T2^6, (T1, T2^-1, T1^-1), (T2^-1 * T1^-1)^24 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 49, 145, 24, 120, 8, 104)(4, 100, 12, 108, 29, 125, 61, 157, 36, 132, 13, 109)(6, 102, 17, 113, 41, 137, 72, 168, 45, 141, 18, 114)(9, 105, 26, 122, 57, 153, 38, 134, 14, 110, 27, 123)(11, 107, 30, 126, 60, 156, 39, 135, 15, 111, 31, 127)(19, 115, 47, 143, 80, 176, 53, 149, 22, 118, 48, 144)(21, 117, 50, 146, 81, 177, 54, 150, 23, 119, 51, 147)(25, 121, 55, 151, 83, 179, 68, 164, 37, 133, 56, 152)(32, 128, 58, 154, 86, 182, 66, 162, 34, 130, 59, 155)(33, 129, 62, 158, 87, 183, 67, 163, 35, 131, 63, 159)(40, 136, 70, 166, 91, 187, 76, 172, 43, 139, 71, 167)(42, 138, 73, 169, 92, 188, 77, 173, 44, 140, 74, 170)(46, 142, 78, 174, 94, 190, 82, 178, 52, 148, 79, 175)(64, 160, 84, 180, 95, 191, 88, 184, 65, 161, 85, 181)(69, 165, 89, 185, 96, 192, 93, 189, 75, 171, 90, 186)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 116)(11, 99)(12, 128)(13, 130)(14, 133)(15, 101)(16, 120)(17, 136)(18, 139)(19, 142)(20, 137)(21, 103)(22, 148)(23, 104)(24, 141)(25, 107)(26, 143)(27, 144)(28, 153)(29, 106)(30, 146)(31, 147)(32, 160)(33, 108)(34, 161)(35, 109)(36, 112)(37, 111)(38, 149)(39, 150)(40, 165)(41, 125)(42, 113)(43, 171)(44, 114)(45, 132)(46, 117)(47, 166)(48, 167)(49, 176)(50, 169)(51, 170)(52, 119)(53, 172)(54, 173)(55, 174)(56, 175)(57, 179)(58, 122)(59, 123)(60, 124)(61, 182)(62, 126)(63, 127)(64, 129)(65, 131)(66, 134)(67, 135)(68, 178)(69, 138)(70, 154)(71, 155)(72, 187)(73, 158)(74, 159)(75, 140)(76, 162)(77, 163)(78, 185)(79, 186)(80, 190)(81, 145)(82, 189)(83, 156)(84, 151)(85, 152)(86, 191)(87, 157)(88, 164)(89, 180)(90, 181)(91, 192)(92, 168)(93, 184)(94, 177)(95, 183)(96, 188)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1940
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 16 e = 96 f = 28
	degree seq :: [ 12^16 ]

E27.1942 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-2 * T1^-1, T1^6, T2^-1 * T1^-2 * T2 * T1^2, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, (T2^-1 * T1^-1)^4, T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-5 ]
Map:: non-degenerate
	R = (1, 97, 3, 99, 10, 106, 29, 125, 59, 155, 89, 185, 66, 162, 35, 131, 13, 109, 32, 128, 62, 158, 91, 187, 96, 192, 77, 173, 46, 142, 20, 116, 6, 102, 19, 115, 44, 140, 75, 171, 70, 166, 40, 136, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 49, 145, 81, 177, 67, 163, 37, 133, 14, 110, 4, 100, 12, 108, 30, 126, 61, 157, 90, 186, 93, 189, 72, 168, 42, 138, 18, 114, 41, 137, 71, 167, 92, 188, 86, 182, 54, 150, 26, 122, 8, 104)(9, 105, 27, 123, 56, 152, 79, 175, 69, 165, 39, 135, 16, 112, 33, 129, 11, 107, 31, 127, 60, 156, 80, 176, 95, 191, 76, 172, 45, 141, 74, 170, 43, 139, 73, 169, 94, 190, 83, 179, 68, 164, 38, 134, 15, 111, 28, 124)(21, 117, 47, 143, 78, 174, 63, 159, 85, 181, 53, 149, 25, 121, 51, 147, 23, 119, 50, 146, 82, 178, 57, 153, 87, 183, 55, 151, 36, 132, 65, 161, 34, 130, 64, 160, 88, 184, 58, 154, 84, 180, 52, 148, 24, 120, 48, 144)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 115)(10, 118)(11, 99)(12, 119)(13, 100)(14, 121)(15, 116)(16, 101)(17, 122)(18, 109)(19, 139)(20, 141)(21, 137)(22, 140)(23, 103)(24, 138)(25, 104)(26, 142)(27, 151)(28, 153)(29, 152)(30, 106)(31, 148)(32, 107)(33, 154)(34, 108)(35, 112)(36, 110)(37, 113)(38, 146)(39, 160)(40, 164)(41, 130)(42, 132)(43, 128)(44, 167)(45, 131)(46, 168)(47, 135)(48, 175)(49, 174)(50, 172)(51, 176)(52, 123)(53, 127)(54, 180)(55, 169)(56, 171)(57, 170)(58, 124)(59, 177)(60, 125)(61, 178)(62, 126)(63, 129)(64, 134)(65, 179)(66, 133)(67, 181)(68, 173)(69, 136)(70, 182)(71, 158)(72, 162)(73, 149)(74, 159)(75, 190)(76, 143)(77, 191)(78, 188)(79, 161)(80, 144)(81, 166)(82, 145)(83, 147)(84, 189)(85, 150)(86, 192)(87, 163)(88, 157)(89, 165)(90, 155)(91, 156)(92, 184)(93, 183)(94, 187)(95, 185)(96, 186)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.1938
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 96 f = 40
	degree seq :: [ 48^4 ]

E27.1943 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 24})
Quotient :: loop
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2 * T1^-3)^2, T2 * T1^-1 * T2^-2 * T1 * T2^-2 * T1^-1 * T2^-2 * T1 * T2, (T2^-1 * T1^-1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 32, 128, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 25, 121, 57, 153, 26, 122)(11, 107, 29, 125, 63, 159, 31, 127)(13, 109, 30, 126, 61, 157, 35, 131)(15, 111, 37, 133, 70, 166, 38, 134)(16, 112, 39, 135, 71, 167, 40, 136)(17, 113, 42, 138, 74, 170, 43, 139)(20, 116, 47, 143, 79, 175, 48, 144)(22, 118, 51, 147, 84, 180, 52, 148)(23, 119, 53, 149, 85, 181, 54, 150)(24, 120, 55, 151, 86, 182, 56, 152)(27, 123, 58, 154, 87, 183, 59, 155)(28, 124, 60, 156, 88, 184, 62, 158)(33, 129, 41, 137, 72, 168, 66, 162)(34, 130, 46, 142, 78, 174, 67, 163)(36, 132, 64, 160, 89, 185, 69, 165)(44, 140, 75, 171, 93, 189, 76, 172)(49, 145, 80, 176, 95, 191, 81, 177)(50, 146, 82, 178, 96, 192, 83, 179)(65, 161, 73, 169, 92, 188, 90, 186)(68, 164, 77, 173, 94, 190, 91, 187)
	L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 114)(10, 123)(11, 99)(12, 118)(13, 100)(14, 120)(15, 115)(16, 101)(17, 137)(18, 140)(19, 142)(20, 138)(21, 145)(22, 103)(23, 139)(24, 104)(25, 143)(26, 149)(27, 141)(28, 106)(29, 147)(30, 107)(31, 151)(32, 146)(33, 108)(34, 109)(35, 112)(36, 110)(37, 144)(38, 150)(39, 148)(40, 152)(41, 125)(42, 169)(43, 126)(44, 168)(45, 173)(46, 129)(47, 171)(48, 174)(49, 170)(50, 117)(51, 121)(52, 133)(53, 172)(54, 130)(55, 122)(56, 134)(57, 176)(58, 175)(59, 181)(60, 180)(61, 124)(62, 182)(63, 178)(64, 127)(65, 128)(66, 135)(67, 132)(68, 131)(69, 136)(70, 177)(71, 179)(72, 156)(73, 159)(74, 160)(75, 188)(76, 157)(77, 162)(78, 161)(79, 190)(80, 189)(81, 163)(82, 153)(83, 166)(84, 154)(85, 164)(86, 155)(87, 191)(88, 192)(89, 158)(90, 167)(91, 165)(92, 184)(93, 185)(94, 186)(95, 187)(96, 183)
	local type(s) :: { ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.1939
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 24 e = 96 f = 20
	degree seq :: [ 8^24 ]

E27.1944 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^-2 * Y3 * Y2, (Y2^-1 * R * Y2^-1)^2, Y2^6, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y3^-1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y2^-1 * Y3)^24 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 46, 142, 21, 117)(8, 104, 22, 118, 52, 148, 23, 119)(10, 106, 20, 116, 41, 137, 29, 125)(12, 108, 32, 128, 64, 160, 33, 129)(13, 109, 34, 130, 65, 161, 35, 131)(16, 112, 24, 120, 45, 141, 36, 132)(17, 113, 40, 136, 69, 165, 42, 138)(18, 114, 43, 139, 75, 171, 44, 140)(26, 122, 47, 143, 70, 166, 58, 154)(27, 123, 48, 144, 71, 167, 59, 155)(28, 124, 57, 153, 83, 179, 60, 156)(30, 126, 50, 146, 73, 169, 62, 158)(31, 127, 51, 147, 74, 170, 63, 159)(38, 134, 53, 149, 76, 172, 66, 162)(39, 135, 54, 150, 77, 173, 67, 163)(49, 145, 80, 176, 94, 190, 81, 177)(55, 151, 78, 174, 89, 185, 84, 180)(56, 152, 79, 175, 90, 186, 85, 181)(61, 157, 86, 182, 95, 191, 87, 183)(68, 164, 82, 178, 93, 189, 88, 184)(72, 168, 91, 187, 96, 192, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 241, 337, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 253, 349, 228, 324, 205, 301)(198, 294, 209, 305, 233, 329, 264, 360, 237, 333, 210, 306)(201, 297, 218, 314, 249, 345, 230, 326, 206, 302, 219, 315)(203, 299, 222, 318, 252, 348, 231, 327, 207, 303, 223, 319)(211, 307, 239, 335, 272, 368, 245, 341, 214, 310, 240, 336)(213, 309, 242, 338, 273, 369, 246, 342, 215, 311, 243, 339)(217, 313, 247, 343, 275, 371, 260, 356, 229, 325, 248, 344)(224, 320, 250, 346, 278, 374, 258, 354, 226, 322, 251, 347)(225, 321, 254, 350, 279, 375, 259, 355, 227, 323, 255, 351)(232, 328, 262, 358, 283, 379, 268, 364, 235, 331, 263, 359)(234, 330, 265, 361, 284, 380, 269, 365, 236, 332, 266, 362)(238, 334, 270, 366, 286, 382, 274, 370, 244, 340, 271, 367)(256, 352, 276, 372, 287, 383, 280, 376, 257, 353, 277, 373)(261, 357, 281, 377, 288, 384, 285, 381, 267, 363, 282, 378)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 225)(13, 227)(14, 197)(15, 229)(16, 228)(17, 234)(18, 236)(19, 199)(20, 202)(21, 238)(22, 200)(23, 244)(24, 208)(25, 201)(26, 250)(27, 251)(28, 252)(29, 233)(30, 254)(31, 255)(32, 204)(33, 256)(34, 205)(35, 257)(36, 237)(37, 206)(38, 258)(39, 259)(40, 209)(41, 212)(42, 261)(43, 210)(44, 267)(45, 216)(46, 211)(47, 218)(48, 219)(49, 273)(50, 222)(51, 223)(52, 214)(53, 230)(54, 231)(55, 276)(56, 277)(57, 220)(58, 262)(59, 263)(60, 275)(61, 279)(62, 265)(63, 266)(64, 224)(65, 226)(66, 268)(67, 269)(68, 280)(69, 232)(70, 239)(71, 240)(72, 284)(73, 242)(74, 243)(75, 235)(76, 245)(77, 246)(78, 247)(79, 248)(80, 241)(81, 286)(82, 260)(83, 249)(84, 281)(85, 282)(86, 253)(87, 287)(88, 285)(89, 270)(90, 271)(91, 264)(92, 288)(93, 274)(94, 272)(95, 278)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1947
Graph:: bipartite
	v = 40 e = 192 f = 100
	degree seq :: [ 8^24, 12^16 ]

E27.1945 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y1^6, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1, (Y3^-1 * Y1^-1)^4, Y2^-8 * Y1^-2 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 43, 139, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 45, 141, 35, 131, 16, 112)(7, 103, 21, 117, 41, 137, 34, 130, 12, 108, 23, 119)(8, 104, 24, 120, 42, 138, 36, 132, 14, 110, 25, 121)(10, 106, 22, 118, 44, 140, 71, 167, 62, 158, 30, 126)(17, 113, 26, 122, 46, 142, 72, 168, 66, 162, 37, 133)(27, 123, 55, 151, 73, 169, 53, 149, 31, 127, 52, 148)(28, 124, 57, 153, 74, 170, 63, 159, 33, 129, 58, 154)(29, 125, 56, 152, 75, 171, 94, 190, 91, 187, 60, 156)(38, 134, 50, 146, 76, 172, 47, 143, 39, 135, 64, 160)(40, 136, 68, 164, 77, 173, 95, 191, 89, 185, 69, 165)(48, 144, 79, 175, 65, 161, 83, 179, 51, 147, 80, 176)(49, 145, 78, 174, 92, 188, 88, 184, 61, 157, 82, 178)(54, 150, 84, 180, 93, 189, 87, 183, 67, 163, 85, 181)(59, 155, 81, 177, 70, 166, 86, 182, 96, 192, 90, 186)(193, 289, 195, 291, 202, 298, 221, 317, 251, 347, 281, 377, 258, 354, 227, 323, 205, 301, 224, 320, 254, 350, 283, 379, 288, 384, 269, 365, 238, 334, 212, 308, 198, 294, 211, 307, 236, 332, 267, 363, 262, 358, 232, 328, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 241, 337, 273, 369, 259, 355, 229, 325, 206, 302, 196, 292, 204, 300, 222, 318, 253, 349, 282, 378, 285, 381, 264, 360, 234, 330, 210, 306, 233, 329, 263, 359, 284, 380, 278, 374, 246, 342, 218, 314, 200, 296)(201, 297, 219, 315, 248, 344, 271, 367, 261, 357, 231, 327, 208, 304, 225, 321, 203, 299, 223, 319, 252, 348, 272, 368, 287, 383, 268, 364, 237, 333, 266, 362, 235, 331, 265, 361, 286, 382, 275, 371, 260, 356, 230, 326, 207, 303, 220, 316)(213, 309, 239, 335, 270, 366, 255, 351, 277, 373, 245, 341, 217, 313, 243, 339, 215, 311, 242, 338, 274, 370, 249, 345, 279, 375, 247, 343, 228, 324, 257, 353, 226, 322, 256, 352, 280, 376, 250, 346, 276, 372, 244, 340, 216, 312, 240, 336)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 221)(11, 223)(12, 222)(13, 224)(14, 196)(15, 220)(16, 225)(17, 197)(18, 233)(19, 236)(20, 198)(21, 239)(22, 241)(23, 242)(24, 240)(25, 243)(26, 200)(27, 248)(28, 201)(29, 251)(30, 253)(31, 252)(32, 254)(33, 203)(34, 256)(35, 205)(36, 257)(37, 206)(38, 207)(39, 208)(40, 209)(41, 263)(42, 210)(43, 265)(44, 267)(45, 266)(46, 212)(47, 270)(48, 213)(49, 273)(50, 274)(51, 215)(52, 216)(53, 217)(54, 218)(55, 228)(56, 271)(57, 279)(58, 276)(59, 281)(60, 272)(61, 282)(62, 283)(63, 277)(64, 280)(65, 226)(66, 227)(67, 229)(68, 230)(69, 231)(70, 232)(71, 284)(72, 234)(73, 286)(74, 235)(75, 262)(76, 237)(77, 238)(78, 255)(79, 261)(80, 287)(81, 259)(82, 249)(83, 260)(84, 244)(85, 245)(86, 246)(87, 247)(88, 250)(89, 258)(90, 285)(91, 288)(92, 278)(93, 264)(94, 275)(95, 268)(96, 269)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1946
Graph:: bipartite
	v = 20 e = 192 f = 120
	degree seq :: [ 12^16, 48^4 ]

E27.1946 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^2 * Y2 * Y3^-2, Y3^-5 * Y2^-1 * Y3^-1 * Y2^-1, Y3^2 * Y2^-2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^2, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^24 ]
Map:: polytopal
	R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 217, 313, 203, 299)(197, 293, 206, 302, 229, 325, 207, 303)(199, 295, 211, 307, 239, 335, 213, 309)(200, 296, 214, 310, 245, 341, 215, 311)(202, 298, 212, 308, 234, 330, 221, 317)(204, 300, 224, 320, 259, 355, 225, 321)(205, 301, 226, 322, 260, 356, 227, 323)(208, 304, 216, 312, 238, 334, 228, 324)(209, 305, 233, 329, 264, 360, 235, 331)(210, 306, 236, 332, 270, 366, 237, 333)(218, 314, 240, 336, 265, 361, 252, 348)(219, 315, 241, 337, 266, 362, 253, 349)(220, 316, 251, 347, 279, 375, 255, 351)(222, 318, 243, 339, 268, 364, 257, 353)(223, 319, 244, 340, 269, 365, 258, 354)(230, 326, 246, 342, 271, 367, 261, 357)(231, 327, 247, 343, 272, 368, 254, 350)(232, 328, 263, 359, 276, 372, 242, 338)(248, 344, 278, 374, 286, 382, 267, 363)(249, 345, 274, 370, 284, 380, 280, 376)(250, 346, 275, 371, 285, 381, 281, 377)(256, 352, 273, 369, 288, 384, 283, 379)(262, 358, 277, 373, 287, 383, 282, 378)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 220)(11, 222)(12, 221)(13, 196)(14, 219)(15, 223)(16, 197)(17, 234)(18, 198)(19, 240)(20, 242)(21, 243)(22, 241)(23, 244)(24, 200)(25, 249)(26, 251)(27, 201)(28, 254)(29, 256)(30, 255)(31, 203)(32, 252)(33, 257)(34, 253)(35, 258)(36, 205)(37, 250)(38, 206)(39, 207)(40, 208)(41, 265)(42, 267)(43, 268)(44, 266)(45, 269)(46, 210)(47, 274)(48, 232)(49, 211)(50, 231)(51, 276)(52, 213)(53, 275)(54, 214)(55, 215)(56, 216)(57, 279)(58, 217)(59, 228)(60, 273)(61, 224)(62, 227)(63, 282)(64, 272)(65, 283)(66, 225)(67, 280)(68, 281)(69, 226)(70, 229)(71, 230)(72, 284)(73, 248)(74, 233)(75, 247)(76, 286)(77, 235)(78, 285)(79, 236)(80, 237)(81, 238)(82, 263)(83, 239)(84, 262)(85, 245)(86, 246)(87, 261)(88, 288)(89, 259)(90, 260)(91, 287)(92, 278)(93, 264)(94, 277)(95, 270)(96, 271)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 12, 48 ), ( 12, 48, 12, 48, 12, 48, 12, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1945
Graph:: simple bipartite
	v = 120 e = 192 f = 20
	degree seq :: [ 2^96, 8^24 ]

E27.1947 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^2, Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y1^-2 * Y3 * Y1^-1)^2, Y1^-1 * Y3^-2 * Y1^2 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^4, Y3 * Y1^-1 * Y3^-2 * Y1 * Y3^2 * Y1^-1 * Y3^2 * Y1 * Y3, (Y3^-1 * Y1^-1)^6 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 29, 125, 51, 147, 25, 121, 47, 143, 75, 171, 92, 188, 88, 184, 96, 192, 87, 183, 95, 191, 91, 187, 69, 165, 40, 136, 56, 152, 38, 134, 54, 150, 34, 130, 13, 109, 4, 100)(3, 99, 9, 105, 18, 114, 44, 140, 72, 168, 60, 156, 84, 180, 58, 154, 79, 175, 94, 190, 90, 186, 71, 167, 83, 179, 70, 166, 81, 177, 67, 163, 36, 132, 14, 110, 24, 120, 8, 104, 23, 119, 43, 139, 30, 126, 11, 107)(5, 101, 15, 111, 19, 115, 46, 142, 33, 129, 12, 108, 22, 118, 7, 103, 20, 116, 42, 138, 73, 169, 63, 159, 82, 178, 57, 153, 80, 176, 93, 189, 89, 185, 62, 158, 86, 182, 59, 155, 85, 181, 68, 164, 35, 131, 16, 112)(10, 106, 27, 123, 45, 141, 77, 173, 66, 162, 39, 135, 52, 148, 37, 133, 48, 144, 78, 174, 65, 161, 32, 128, 50, 146, 21, 117, 49, 145, 74, 170, 64, 160, 31, 127, 55, 151, 26, 122, 53, 149, 76, 172, 61, 157, 28, 124)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 217)(10, 197)(11, 221)(12, 224)(13, 222)(14, 196)(15, 229)(16, 231)(17, 234)(18, 237)(19, 198)(20, 239)(21, 200)(22, 243)(23, 245)(24, 247)(25, 249)(26, 201)(27, 250)(28, 252)(29, 255)(30, 253)(31, 203)(32, 206)(33, 233)(34, 238)(35, 205)(36, 256)(37, 262)(38, 207)(39, 263)(40, 208)(41, 264)(42, 266)(43, 209)(44, 267)(45, 211)(46, 270)(47, 271)(48, 212)(49, 272)(50, 274)(51, 276)(52, 214)(53, 277)(54, 215)(55, 278)(56, 216)(57, 218)(58, 279)(59, 219)(60, 280)(61, 227)(62, 220)(63, 223)(64, 281)(65, 265)(66, 225)(67, 226)(68, 269)(69, 228)(70, 230)(71, 232)(72, 258)(73, 284)(74, 235)(75, 285)(76, 236)(77, 286)(78, 259)(79, 240)(80, 287)(81, 241)(82, 288)(83, 242)(84, 244)(85, 246)(86, 248)(87, 251)(88, 254)(89, 261)(90, 257)(91, 260)(92, 282)(93, 268)(94, 283)(95, 273)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1944
Graph:: simple bipartite
	v = 100 e = 192 f = 40
	degree seq :: [ 2^96, 48^4 ]

E27.1948 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-2 * Y1^-2 * Y2^2 * Y1^-2, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y2^-2 * Y3^-1 * Y2^-1)^2, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y2^3 * Y1 * Y2^2 * Y1^2 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 47, 143, 21, 117)(8, 104, 22, 118, 53, 149, 23, 119)(10, 106, 20, 116, 42, 138, 29, 125)(12, 108, 32, 128, 65, 161, 33, 129)(13, 109, 34, 130, 66, 162, 35, 131)(16, 112, 24, 120, 46, 142, 36, 132)(17, 113, 41, 137, 72, 168, 43, 139)(18, 114, 44, 140, 78, 174, 45, 141)(26, 122, 48, 144, 73, 169, 60, 156)(27, 123, 49, 145, 74, 170, 61, 157)(28, 124, 59, 155, 86, 182, 56, 152)(30, 126, 51, 147, 76, 172, 63, 159)(31, 127, 52, 148, 77, 173, 64, 160)(38, 134, 54, 150, 79, 175, 67, 163)(39, 135, 55, 151, 80, 176, 68, 164)(40, 136, 62, 158, 89, 185, 71, 167)(50, 146, 84, 180, 96, 192, 81, 177)(57, 153, 82, 178, 92, 188, 87, 183)(58, 154, 83, 179, 93, 189, 88, 184)(69, 165, 75, 171, 94, 190, 91, 187)(70, 166, 85, 181, 95, 191, 90, 186)(193, 289, 195, 291, 202, 298, 220, 316, 246, 342, 214, 310, 241, 337, 211, 307, 240, 336, 276, 372, 287, 383, 270, 366, 285, 381, 264, 360, 284, 380, 283, 379, 260, 356, 227, 323, 256, 352, 225, 321, 255, 351, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 242, 338, 271, 367, 236, 332, 266, 362, 233, 329, 265, 361, 286, 382, 282, 378, 258, 354, 280, 376, 257, 353, 279, 375, 263, 359, 231, 327, 207, 303, 223, 319, 203, 299, 222, 318, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 254, 350, 230, 326, 206, 302, 219, 315, 201, 297, 218, 314, 251, 347, 277, 373, 245, 341, 275, 371, 239, 335, 274, 370, 288, 384, 272, 368, 237, 333, 269, 365, 235, 331, 268, 364, 261, 357, 228, 324, 205, 301)(198, 294, 209, 305, 234, 330, 267, 363, 259, 355, 226, 322, 253, 349, 224, 320, 252, 348, 281, 377, 262, 358, 229, 325, 250, 346, 217, 313, 249, 345, 278, 374, 247, 343, 215, 311, 244, 340, 213, 309, 243, 339, 273, 369, 238, 334, 210, 306)
	L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 225)(13, 227)(14, 197)(15, 229)(16, 228)(17, 235)(18, 237)(19, 199)(20, 202)(21, 239)(22, 200)(23, 245)(24, 208)(25, 201)(26, 252)(27, 253)(28, 248)(29, 234)(30, 255)(31, 256)(32, 204)(33, 257)(34, 205)(35, 258)(36, 238)(37, 206)(38, 259)(39, 260)(40, 263)(41, 209)(42, 212)(43, 264)(44, 210)(45, 270)(46, 216)(47, 211)(48, 218)(49, 219)(50, 273)(51, 222)(52, 223)(53, 214)(54, 230)(55, 231)(56, 278)(57, 279)(58, 280)(59, 220)(60, 265)(61, 266)(62, 232)(63, 268)(64, 269)(65, 224)(66, 226)(67, 271)(68, 272)(69, 283)(70, 282)(71, 281)(72, 233)(73, 240)(74, 241)(75, 261)(76, 243)(77, 244)(78, 236)(79, 246)(80, 247)(81, 288)(82, 249)(83, 250)(84, 242)(85, 262)(86, 251)(87, 284)(88, 285)(89, 254)(90, 287)(91, 286)(92, 274)(93, 275)(94, 267)(95, 277)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.1949
Graph:: bipartite
	v = 28 e = 192 f = 112
	degree seq :: [ 8^24, 48^4 ]

E27.1949 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 24})
Quotient :: dipole
Aut^+ = C3 x ((C4 x C4) : C2) (small group id <96, 54>)
Aut   = $<192, 381>$ (small group id <192, 381>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y1^6, Y3 * Y1^2 * Y3^-1 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-5, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 19, 115, 43, 139, 32, 128, 11, 107)(5, 101, 15, 111, 20, 116, 45, 141, 35, 131, 16, 112)(7, 103, 21, 117, 41, 137, 34, 130, 12, 108, 23, 119)(8, 104, 24, 120, 42, 138, 36, 132, 14, 110, 25, 121)(10, 106, 22, 118, 44, 140, 71, 167, 62, 158, 30, 126)(17, 113, 26, 122, 46, 142, 72, 168, 66, 162, 37, 133)(27, 123, 55, 151, 73, 169, 53, 149, 31, 127, 52, 148)(28, 124, 57, 153, 74, 170, 63, 159, 33, 129, 58, 154)(29, 125, 56, 152, 75, 171, 94, 190, 91, 187, 60, 156)(38, 134, 50, 146, 76, 172, 47, 143, 39, 135, 64, 160)(40, 136, 68, 164, 77, 173, 95, 191, 89, 185, 69, 165)(48, 144, 79, 175, 65, 161, 83, 179, 51, 147, 80, 176)(49, 145, 78, 174, 92, 188, 88, 184, 61, 157, 82, 178)(54, 150, 84, 180, 93, 189, 87, 183, 67, 163, 85, 181)(59, 155, 81, 177, 70, 166, 86, 182, 96, 192, 90, 186)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384)
	L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 219)(10, 221)(11, 223)(12, 222)(13, 224)(14, 196)(15, 220)(16, 225)(17, 197)(18, 233)(19, 236)(20, 198)(21, 239)(22, 241)(23, 242)(24, 240)(25, 243)(26, 200)(27, 248)(28, 201)(29, 251)(30, 253)(31, 252)(32, 254)(33, 203)(34, 256)(35, 205)(36, 257)(37, 206)(38, 207)(39, 208)(40, 209)(41, 263)(42, 210)(43, 265)(44, 267)(45, 266)(46, 212)(47, 270)(48, 213)(49, 273)(50, 274)(51, 215)(52, 216)(53, 217)(54, 218)(55, 228)(56, 271)(57, 279)(58, 276)(59, 281)(60, 272)(61, 282)(62, 283)(63, 277)(64, 280)(65, 226)(66, 227)(67, 229)(68, 230)(69, 231)(70, 232)(71, 284)(72, 234)(73, 286)(74, 235)(75, 262)(76, 237)(77, 238)(78, 255)(79, 261)(80, 287)(81, 259)(82, 249)(83, 260)(84, 244)(85, 245)(86, 246)(87, 247)(88, 250)(89, 258)(90, 285)(91, 288)(92, 278)(93, 264)(94, 275)(95, 268)(96, 269)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384)
	local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48, 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E27.1948
Graph:: simple bipartite
	v = 112 e = 192 f = 28
	degree seq :: [ 2^96, 12^16 ]

E27.1950 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: halfedge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = (C52 x C2) : C2 (small group id <208, 38>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 106, 2, 110, 6, 109, 5, 105)(3, 113, 9, 108, 4, 114, 10, 107)(7, 115, 11, 112, 8, 116, 12, 111)(13, 121, 17, 118, 14, 122, 18, 117)(15, 123, 19, 120, 16, 124, 20, 119)(21, 129, 25, 126, 22, 130, 26, 125)(23, 131, 27, 128, 24, 132, 28, 127)(29, 137, 33, 134, 30, 138, 34, 133)(31, 148, 44, 136, 32, 147, 43, 135)(35, 163, 59, 144, 40, 166, 62, 139)(36, 161, 57, 143, 39, 162, 58, 140)(37, 167, 63, 142, 38, 168, 64, 141)(41, 165, 61, 146, 42, 164, 60, 145)(45, 170, 66, 150, 46, 169, 65, 149)(47, 172, 68, 152, 48, 171, 67, 151)(49, 174, 70, 154, 50, 173, 69, 153)(51, 176, 72, 156, 52, 175, 71, 155)(53, 178, 74, 158, 54, 177, 73, 157)(55, 180, 76, 160, 56, 179, 75, 159)(77, 185, 81, 182, 78, 186, 82, 181)(79, 190, 86, 184, 80, 187, 83, 183)(84, 206, 102, 189, 85, 205, 101, 188)(87, 208, 104, 192, 88, 207, 103, 191)(89, 204, 100, 194, 90, 203, 99, 193)(91, 201, 97, 196, 92, 202, 98, 195)(93, 199, 95, 198, 94, 200, 96, 197)
	L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 57)(34, 58)(35, 60)(36, 63)(37, 65)(38, 66)(39, 64)(40, 61)(41, 67)(42, 68)(43, 59)(44, 62)(45, 69)(46, 70)(47, 71)(48, 72)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(81, 104)(82, 103)(83, 102)(84, 98)(85, 97)(86, 101)(87, 100)(88, 99)(89, 96)(90, 95)(91, 93)(92, 94)(105, 108)(106, 112)(107, 110)(109, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 126)(122, 125)(123, 128)(124, 127)(129, 134)(130, 133)(131, 136)(132, 135)(137, 162)(138, 161)(139, 165)(140, 168)(141, 170)(142, 169)(143, 167)(144, 164)(145, 172)(146, 171)(147, 166)(148, 163)(149, 174)(150, 173)(151, 176)(152, 175)(153, 178)(154, 177)(155, 180)(156, 179)(157, 182)(158, 181)(159, 184)(160, 183)(185, 207)(186, 208)(187, 205)(188, 201)(189, 202)(190, 206)(191, 203)(192, 204)(193, 199)(194, 200)(195, 198)(196, 197)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.1951 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: halfedge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, Y1^4, R * Y3 * R * Y2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map::
	R = (1, 106, 2, 109, 5, 108, 4, 105)(3, 111, 7, 114, 10, 112, 8, 107)(6, 115, 11, 113, 9, 116, 12, 110)(13, 121, 17, 118, 14, 122, 18, 117)(15, 123, 19, 120, 16, 124, 20, 119)(21, 129, 25, 126, 22, 130, 26, 125)(23, 131, 27, 128, 24, 132, 28, 127)(29, 137, 33, 134, 30, 138, 34, 133)(31, 155, 51, 136, 32, 156, 52, 135)(35, 159, 55, 142, 38, 160, 56, 139)(36, 161, 57, 141, 37, 162, 58, 140)(39, 163, 59, 144, 40, 164, 60, 143)(41, 165, 61, 146, 42, 166, 62, 145)(43, 167, 63, 148, 44, 168, 64, 147)(45, 169, 65, 150, 46, 170, 66, 149)(47, 171, 67, 152, 48, 172, 68, 151)(49, 173, 69, 154, 50, 174, 70, 153)(53, 177, 73, 158, 54, 178, 74, 157)(71, 195, 91, 176, 72, 196, 92, 175)(75, 199, 95, 180, 76, 200, 96, 179)(77, 201, 97, 182, 78, 202, 98, 181)(79, 203, 99, 184, 80, 204, 100, 183)(81, 205, 101, 186, 82, 206, 102, 185)(83, 207, 103, 188, 84, 208, 104, 187)(85, 197, 93, 190, 86, 198, 94, 189)(87, 193, 89, 192, 88, 194, 90, 191)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 35)(34, 38)(36, 51)(37, 52)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64)(49, 65)(50, 66)(53, 67)(54, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 91)(78, 92)(79, 95)(80, 96)(81, 97)(82, 98)(83, 99)(84, 100)(85, 101)(86, 102)(87, 103)(88, 104)(89, 93)(90, 94)(105, 107)(106, 110)(108, 113)(109, 114)(111, 117)(112, 118)(115, 119)(116, 120)(121, 125)(122, 126)(123, 127)(124, 128)(129, 133)(130, 134)(131, 135)(132, 136)(137, 139)(138, 142)(140, 155)(141, 156)(143, 159)(144, 160)(145, 161)(146, 162)(147, 163)(148, 164)(149, 165)(150, 166)(151, 167)(152, 168)(153, 169)(154, 170)(157, 171)(158, 172)(173, 175)(174, 176)(177, 179)(178, 180)(181, 195)(182, 196)(183, 199)(184, 200)(185, 201)(186, 202)(187, 203)(188, 204)(189, 205)(190, 206)(191, 207)(192, 208)(193, 197)(194, 198)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.1952 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: halfedge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, Y1^4, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map::
	R = (1, 106, 2, 109, 5, 108, 4, 105)(3, 111, 7, 114, 10, 112, 8, 107)(6, 115, 11, 113, 9, 116, 12, 110)(13, 121, 17, 118, 14, 122, 18, 117)(15, 123, 19, 120, 16, 124, 20, 119)(21, 129, 25, 126, 22, 130, 26, 125)(23, 131, 27, 128, 24, 132, 28, 127)(29, 137, 33, 134, 30, 138, 34, 133)(31, 141, 37, 136, 32, 139, 35, 135)(36, 157, 53, 144, 40, 158, 54, 140)(38, 161, 57, 143, 39, 159, 55, 142)(41, 164, 60, 146, 42, 160, 56, 145)(43, 163, 59, 148, 44, 162, 58, 147)(45, 166, 62, 150, 46, 165, 61, 149)(47, 168, 64, 152, 48, 167, 63, 151)(49, 170, 66, 154, 50, 169, 65, 153)(51, 172, 68, 156, 52, 171, 67, 155)(69, 177, 73, 174, 70, 178, 74, 173)(71, 180, 76, 176, 72, 179, 75, 175)(77, 197, 93, 182, 78, 198, 94, 181)(79, 200, 96, 184, 80, 199, 95, 183)(81, 202, 98, 186, 82, 201, 97, 185)(83, 204, 100, 188, 84, 203, 99, 187)(85, 206, 102, 190, 86, 205, 101, 189)(87, 208, 104, 192, 88, 207, 103, 191)(89, 196, 92, 194, 90, 195, 91, 193)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 53)(34, 54)(35, 55)(36, 56)(37, 57)(38, 58)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(73, 93)(74, 94)(75, 95)(76, 96)(77, 97)(78, 98)(79, 99)(80, 100)(81, 101)(82, 102)(83, 103)(84, 104)(85, 91)(86, 92)(87, 90)(88, 89)(105, 107)(106, 110)(108, 113)(109, 114)(111, 117)(112, 118)(115, 119)(116, 120)(121, 125)(122, 126)(123, 127)(124, 128)(129, 133)(130, 134)(131, 135)(132, 136)(137, 157)(138, 158)(139, 159)(140, 160)(141, 161)(142, 162)(143, 163)(144, 164)(145, 165)(146, 166)(147, 167)(148, 168)(149, 169)(150, 170)(151, 171)(152, 172)(153, 173)(154, 174)(155, 175)(156, 176)(177, 197)(178, 198)(179, 199)(180, 200)(181, 201)(182, 202)(183, 203)(184, 204)(185, 205)(186, 206)(187, 207)(188, 208)(189, 195)(190, 196)(191, 194)(192, 193)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.1953 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = (C52 x C2) : C2 (small group id <208, 38>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 4, 108, 6, 110, 5, 109)(2, 106, 7, 111, 3, 107, 8, 112)(9, 113, 13, 117, 10, 114, 14, 118)(11, 115, 15, 119, 12, 116, 16, 120)(17, 121, 21, 125, 18, 122, 22, 126)(19, 123, 23, 127, 20, 124, 24, 128)(25, 129, 29, 133, 26, 130, 30, 134)(27, 131, 31, 135, 28, 132, 32, 136)(33, 137, 35, 139, 34, 138, 38, 142)(36, 140, 52, 156, 37, 141, 51, 155)(39, 143, 56, 160, 40, 144, 55, 159)(41, 145, 58, 162, 42, 146, 57, 161)(43, 147, 60, 164, 44, 148, 59, 163)(45, 149, 62, 166, 46, 150, 61, 165)(47, 151, 64, 168, 48, 152, 63, 167)(49, 153, 66, 170, 50, 154, 65, 169)(53, 157, 68, 172, 54, 158, 67, 171)(69, 173, 71, 175, 70, 174, 72, 176)(73, 177, 75, 179, 74, 178, 76, 180)(77, 181, 92, 196, 78, 182, 91, 195)(79, 183, 96, 200, 80, 184, 95, 199)(81, 185, 98, 202, 82, 186, 97, 201)(83, 187, 100, 204, 84, 188, 99, 203)(85, 189, 102, 206, 86, 190, 101, 205)(87, 191, 104, 208, 88, 192, 103, 207)(89, 193, 93, 197, 90, 194, 94, 198)(209, 210)(211, 214)(212, 217)(213, 218)(215, 219)(216, 220)(221, 225)(222, 226)(223, 227)(224, 228)(229, 233)(230, 234)(231, 235)(232, 236)(237, 241)(238, 242)(239, 259)(240, 260)(243, 263)(244, 265)(245, 266)(246, 264)(247, 267)(248, 268)(249, 269)(250, 270)(251, 271)(252, 272)(253, 273)(254, 274)(255, 275)(256, 276)(257, 277)(258, 278)(261, 281)(262, 282)(279, 299)(280, 300)(283, 303)(284, 304)(285, 305)(286, 306)(287, 307)(288, 308)(289, 309)(290, 310)(291, 311)(292, 312)(293, 302)(294, 301)(295, 297)(296, 298)(313, 315)(314, 318)(316, 322)(317, 321)(319, 324)(320, 323)(325, 330)(326, 329)(327, 332)(328, 331)(333, 338)(334, 337)(335, 340)(336, 339)(341, 346)(342, 345)(343, 364)(344, 363)(347, 368)(348, 370)(349, 369)(350, 367)(351, 372)(352, 371)(353, 374)(354, 373)(355, 376)(356, 375)(357, 378)(358, 377)(359, 380)(360, 379)(361, 382)(362, 381)(365, 386)(366, 385)(383, 404)(384, 403)(387, 408)(388, 407)(389, 410)(390, 409)(391, 412)(392, 411)(393, 414)(394, 413)(395, 416)(396, 415)(397, 405)(398, 406)(399, 402)(400, 401)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1959
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.1954 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 3, 107, 8, 112, 4, 108)(2, 106, 5, 109, 11, 115, 6, 110)(7, 111, 13, 117, 9, 113, 14, 118)(10, 114, 15, 119, 12, 116, 16, 120)(17, 121, 21, 125, 18, 122, 22, 126)(19, 123, 23, 127, 20, 124, 24, 128)(25, 129, 29, 133, 26, 130, 30, 134)(27, 131, 31, 135, 28, 132, 32, 136)(33, 137, 38, 142, 34, 138, 35, 139)(36, 140, 51, 155, 41, 145, 52, 156)(37, 141, 58, 162, 39, 143, 55, 159)(40, 144, 61, 165, 42, 146, 56, 160)(43, 147, 59, 163, 44, 148, 57, 161)(45, 149, 62, 166, 46, 150, 60, 164)(47, 151, 64, 168, 48, 152, 63, 167)(49, 153, 66, 170, 50, 154, 65, 169)(53, 157, 68, 172, 54, 158, 67, 171)(69, 173, 71, 175, 70, 174, 72, 176)(73, 177, 76, 180, 74, 178, 75, 179)(77, 181, 91, 195, 78, 182, 92, 196)(79, 183, 96, 200, 80, 184, 95, 199)(81, 185, 98, 202, 82, 186, 97, 201)(83, 187, 100, 204, 84, 188, 99, 203)(85, 189, 102, 206, 86, 190, 101, 205)(87, 191, 104, 208, 88, 192, 103, 207)(89, 193, 93, 197, 90, 194, 94, 198)(209, 210)(211, 215)(212, 217)(213, 218)(214, 220)(216, 219)(221, 225)(222, 226)(223, 227)(224, 228)(229, 233)(230, 234)(231, 235)(232, 236)(237, 241)(238, 242)(239, 259)(240, 260)(243, 263)(244, 264)(245, 265)(246, 266)(247, 267)(248, 268)(249, 269)(250, 270)(251, 271)(252, 272)(253, 273)(254, 274)(255, 275)(256, 276)(257, 277)(258, 278)(261, 281)(262, 282)(279, 299)(280, 300)(283, 303)(284, 304)(285, 305)(286, 306)(287, 307)(288, 308)(289, 309)(290, 310)(291, 311)(292, 312)(293, 302)(294, 301)(295, 297)(296, 298)(313, 314)(315, 319)(316, 321)(317, 322)(318, 324)(320, 323)(325, 329)(326, 330)(327, 331)(328, 332)(333, 337)(334, 338)(335, 339)(336, 340)(341, 345)(342, 346)(343, 363)(344, 364)(347, 367)(348, 368)(349, 369)(350, 370)(351, 371)(352, 372)(353, 373)(354, 374)(355, 375)(356, 376)(357, 377)(358, 378)(359, 379)(360, 380)(361, 381)(362, 382)(365, 385)(366, 386)(383, 403)(384, 404)(387, 407)(388, 408)(389, 409)(390, 410)(391, 411)(392, 412)(393, 413)(394, 414)(395, 415)(396, 416)(397, 406)(398, 405)(399, 401)(400, 402)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1960
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.1955 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 3, 107, 8, 112, 4, 108)(2, 106, 5, 109, 11, 115, 6, 110)(7, 111, 13, 117, 9, 113, 14, 118)(10, 114, 15, 119, 12, 116, 16, 120)(17, 121, 21, 125, 18, 122, 22, 126)(19, 123, 23, 127, 20, 124, 24, 128)(25, 129, 29, 133, 26, 130, 30, 134)(27, 131, 31, 135, 28, 132, 32, 136)(33, 137, 39, 143, 34, 138, 40, 144)(35, 139, 60, 164, 42, 146, 61, 165)(36, 140, 63, 167, 45, 149, 64, 168)(37, 141, 56, 160, 38, 142, 55, 159)(41, 145, 66, 170, 43, 147, 59, 163)(44, 148, 69, 173, 46, 150, 62, 166)(47, 151, 67, 171, 48, 152, 65, 169)(49, 153, 70, 174, 50, 154, 68, 172)(51, 155, 72, 176, 52, 156, 71, 175)(53, 157, 74, 178, 54, 158, 73, 177)(57, 161, 76, 180, 58, 162, 75, 179)(77, 181, 79, 183, 78, 182, 80, 184)(81, 185, 84, 188, 82, 186, 85, 189)(83, 187, 101, 205, 90, 194, 102, 206)(86, 190, 99, 203, 93, 197, 100, 204)(87, 191, 104, 208, 88, 192, 103, 207)(89, 193, 98, 202, 91, 195, 97, 201)(92, 196, 96, 200, 94, 198, 95, 199)(209, 210)(211, 215)(212, 217)(213, 218)(214, 220)(216, 219)(221, 225)(222, 226)(223, 227)(224, 228)(229, 233)(230, 234)(231, 235)(232, 236)(237, 241)(238, 242)(239, 263)(240, 264)(243, 267)(244, 270)(245, 271)(246, 272)(247, 268)(248, 269)(249, 273)(250, 274)(251, 275)(252, 276)(253, 277)(254, 278)(255, 279)(256, 280)(257, 281)(258, 282)(259, 283)(260, 284)(261, 285)(262, 286)(265, 289)(266, 290)(287, 311)(288, 312)(291, 305)(292, 309)(293, 310)(294, 303)(295, 307)(296, 308)(297, 302)(298, 306)(299, 300)(301, 304)(313, 314)(315, 319)(316, 321)(317, 322)(318, 324)(320, 323)(325, 329)(326, 330)(327, 331)(328, 332)(333, 337)(334, 338)(335, 339)(336, 340)(341, 345)(342, 346)(343, 367)(344, 368)(347, 371)(348, 374)(349, 375)(350, 376)(351, 372)(352, 373)(353, 377)(354, 378)(355, 379)(356, 380)(357, 381)(358, 382)(359, 383)(360, 384)(361, 385)(362, 386)(363, 387)(364, 388)(365, 389)(366, 390)(369, 393)(370, 394)(391, 415)(392, 416)(395, 409)(396, 413)(397, 414)(398, 407)(399, 411)(400, 412)(401, 406)(402, 410)(403, 404)(405, 408)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1961
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.1956 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = C2 x C4 x D26 (small group id <208, 36>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y1^4, Y2^4, R * Y2 * R * Y1, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 4, 108)(2, 106, 6, 110)(3, 107, 7, 111)(5, 109, 10, 114)(8, 112, 13, 117)(9, 113, 14, 118)(11, 115, 15, 119)(12, 116, 16, 120)(17, 121, 21, 125)(18, 122, 22, 126)(19, 123, 23, 127)(20, 124, 24, 128)(25, 129, 29, 133)(26, 130, 30, 134)(27, 131, 31, 135)(28, 132, 32, 136)(33, 137, 36, 140)(34, 138, 37, 141)(35, 139, 54, 158)(38, 142, 61, 165)(39, 143, 53, 157)(40, 144, 57, 161)(41, 145, 58, 162)(42, 146, 60, 164)(43, 147, 64, 168)(44, 148, 65, 169)(45, 149, 68, 172)(46, 150, 69, 173)(47, 151, 73, 177)(48, 152, 74, 178)(49, 153, 77, 181)(50, 154, 78, 182)(51, 155, 81, 185)(52, 156, 82, 186)(55, 159, 85, 189)(56, 160, 86, 190)(59, 163, 93, 197)(62, 166, 89, 193)(63, 167, 90, 194)(66, 170, 100, 204)(67, 171, 94, 198)(70, 174, 98, 202)(71, 175, 97, 201)(72, 176, 101, 205)(75, 179, 104, 208)(76, 180, 99, 203)(79, 183, 103, 207)(80, 184, 102, 206)(83, 187, 96, 200)(84, 188, 95, 199)(87, 191, 91, 195)(88, 192, 92, 196)(209, 210, 213, 211)(212, 216, 218, 217)(214, 219, 215, 220)(221, 225, 222, 226)(223, 227, 224, 228)(229, 233, 230, 234)(231, 235, 232, 236)(237, 241, 238, 242)(239, 261, 240, 262)(243, 265, 247, 266)(244, 268, 245, 269)(246, 272, 250, 273)(248, 276, 249, 277)(251, 281, 252, 282)(253, 285, 254, 286)(255, 289, 256, 290)(257, 293, 258, 294)(259, 297, 260, 298)(263, 302, 264, 301)(267, 306, 275, 305)(270, 309, 271, 308)(274, 312, 280, 307)(278, 311, 279, 310)(283, 304, 284, 303)(287, 299, 288, 300)(291, 295, 292, 296)(313, 315, 317, 314)(316, 321, 322, 320)(318, 324, 319, 323)(325, 330, 326, 329)(327, 332, 328, 331)(333, 338, 334, 337)(335, 340, 336, 339)(341, 346, 342, 345)(343, 366, 344, 365)(347, 370, 351, 369)(348, 373, 349, 372)(350, 377, 354, 376)(352, 381, 353, 380)(355, 386, 356, 385)(357, 390, 358, 389)(359, 394, 360, 393)(361, 398, 362, 397)(363, 402, 364, 401)(367, 405, 368, 406)(371, 409, 379, 410)(374, 412, 375, 413)(378, 411, 384, 416)(382, 414, 383, 415)(387, 407, 388, 408)(391, 404, 392, 403)(395, 400, 396, 399)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1962
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1957 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, (Y1^-1 * Y3 * Y2^-1)^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 105, 3, 107)(2, 106, 6, 110)(4, 108, 9, 113)(5, 109, 10, 114)(7, 111, 13, 117)(8, 112, 14, 118)(11, 115, 15, 119)(12, 116, 16, 120)(17, 121, 21, 125)(18, 122, 22, 126)(19, 123, 23, 127)(20, 124, 24, 128)(25, 129, 29, 133)(26, 130, 30, 134)(27, 131, 31, 135)(28, 132, 32, 136)(33, 137, 38, 142)(34, 138, 36, 140)(35, 139, 53, 157)(37, 141, 62, 166)(39, 143, 55, 159)(40, 144, 57, 161)(41, 145, 59, 163)(42, 146, 60, 164)(43, 147, 63, 167)(44, 148, 65, 169)(45, 149, 68, 172)(46, 150, 70, 174)(47, 151, 73, 177)(48, 152, 75, 179)(49, 153, 77, 181)(50, 154, 79, 183)(51, 155, 81, 185)(52, 156, 83, 187)(54, 158, 85, 189)(56, 160, 87, 191)(58, 162, 94, 198)(61, 165, 91, 195)(64, 168, 100, 204)(66, 170, 89, 193)(67, 171, 93, 197)(69, 173, 98, 202)(71, 175, 97, 201)(72, 176, 101, 205)(74, 178, 99, 203)(76, 180, 103, 207)(78, 182, 102, 206)(80, 184, 104, 208)(82, 186, 96, 200)(84, 188, 95, 199)(86, 190, 90, 194)(88, 192, 92, 196)(209, 210, 213, 212)(211, 215, 218, 216)(214, 219, 217, 220)(221, 225, 222, 226)(223, 227, 224, 228)(229, 233, 230, 234)(231, 235, 232, 236)(237, 241, 238, 242)(239, 261, 240, 263)(243, 265, 247, 267)(244, 268, 246, 270)(245, 271, 250, 273)(248, 276, 249, 278)(251, 281, 252, 283)(253, 285, 254, 287)(255, 289, 256, 291)(257, 293, 258, 295)(259, 297, 260, 299)(262, 302, 264, 301)(266, 306, 275, 305)(269, 309, 274, 308)(272, 307, 280, 311)(277, 310, 279, 312)(282, 304, 284, 303)(286, 298, 288, 300)(290, 294, 292, 296)(313, 314, 317, 316)(315, 319, 322, 320)(318, 323, 321, 324)(325, 329, 326, 330)(327, 331, 328, 332)(333, 337, 334, 338)(335, 339, 336, 340)(341, 345, 342, 346)(343, 365, 344, 367)(347, 369, 351, 371)(348, 372, 350, 374)(349, 375, 354, 377)(352, 380, 353, 382)(355, 385, 356, 387)(357, 389, 358, 391)(359, 393, 360, 395)(361, 397, 362, 399)(363, 401, 364, 403)(366, 406, 368, 405)(370, 410, 379, 409)(373, 413, 378, 412)(376, 411, 384, 415)(381, 414, 383, 416)(386, 408, 388, 407)(390, 402, 392, 404)(394, 398, 396, 400)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1963
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1958 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 105, 3, 107)(2, 106, 6, 110)(4, 108, 9, 113)(5, 109, 10, 114)(7, 111, 13, 117)(8, 112, 14, 118)(11, 115, 15, 119)(12, 116, 16, 120)(17, 121, 21, 125)(18, 122, 22, 126)(19, 123, 23, 127)(20, 124, 24, 128)(25, 129, 29, 133)(26, 130, 30, 134)(27, 131, 31, 135)(28, 132, 32, 136)(33, 137, 57, 161)(34, 138, 58, 162)(35, 139, 60, 164)(36, 140, 62, 166)(37, 141, 63, 167)(38, 142, 64, 168)(39, 143, 65, 169)(40, 144, 66, 170)(41, 145, 59, 163)(42, 146, 61, 165)(43, 147, 67, 171)(44, 148, 68, 172)(45, 149, 69, 173)(46, 150, 70, 174)(47, 151, 71, 175)(48, 152, 72, 176)(49, 153, 73, 177)(50, 154, 74, 178)(51, 155, 75, 179)(52, 156, 76, 180)(53, 157, 77, 181)(54, 158, 78, 182)(55, 159, 79, 183)(56, 160, 80, 184)(81, 185, 103, 207)(82, 186, 104, 208)(83, 187, 101, 205)(84, 188, 97, 201)(85, 189, 102, 206)(86, 190, 99, 203)(87, 191, 95, 199)(88, 192, 100, 204)(89, 193, 98, 202)(90, 194, 94, 198)(91, 195, 93, 197)(92, 196, 96, 200)(209, 210, 213, 212)(211, 215, 218, 216)(214, 219, 217, 220)(221, 225, 222, 226)(223, 227, 224, 228)(229, 233, 230, 234)(231, 235, 232, 236)(237, 241, 238, 242)(239, 250, 240, 249)(243, 267, 247, 269)(244, 265, 246, 266)(245, 270, 252, 272)(248, 273, 251, 268)(253, 276, 254, 271)(255, 275, 256, 274)(257, 278, 258, 277)(259, 280, 260, 279)(261, 282, 262, 281)(263, 284, 264, 283)(285, 289, 286, 290)(287, 293, 288, 291)(292, 309, 297, 310)(294, 311, 296, 312)(295, 307, 300, 308)(298, 306, 299, 305)(301, 304, 302, 303)(313, 314, 317, 316)(315, 319, 322, 320)(318, 323, 321, 324)(325, 329, 326, 330)(327, 331, 328, 332)(333, 337, 334, 338)(335, 339, 336, 340)(341, 345, 342, 346)(343, 354, 344, 353)(347, 371, 351, 373)(348, 369, 350, 370)(349, 374, 356, 376)(352, 377, 355, 372)(357, 380, 358, 375)(359, 379, 360, 378)(361, 382, 362, 381)(363, 384, 364, 383)(365, 386, 366, 385)(367, 388, 368, 387)(389, 393, 390, 394)(391, 397, 392, 395)(396, 413, 401, 414)(398, 415, 400, 416)(399, 411, 404, 412)(402, 410, 403, 409)(405, 408, 406, 407)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1964
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1959 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = (C52 x C2) : C2 (small group id <208, 38>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 209, 313, 4, 108, 212, 316, 6, 110, 214, 318, 5, 109, 213, 317)(2, 106, 210, 314, 7, 111, 215, 319, 3, 107, 211, 315, 8, 112, 216, 320)(9, 113, 217, 321, 13, 117, 221, 325, 10, 114, 218, 322, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327, 12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333, 18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335, 20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341, 26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343, 28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 53, 157, 261, 365, 34, 138, 242, 346, 55, 159, 263, 367)(35, 139, 243, 347, 57, 161, 265, 369, 40, 144, 248, 352, 59, 163, 267, 371)(36, 140, 244, 348, 62, 166, 270, 374, 37, 141, 245, 349, 64, 168, 272, 376)(38, 142, 246, 350, 61, 165, 269, 373, 39, 143, 247, 351, 60, 164, 268, 372)(41, 145, 249, 353, 69, 173, 277, 381, 42, 146, 250, 354, 71, 175, 279, 383)(43, 147, 251, 355, 73, 177, 281, 385, 44, 148, 252, 356, 75, 179, 283, 387)(45, 149, 253, 357, 77, 181, 285, 389, 46, 150, 254, 358, 79, 183, 287, 391)(47, 151, 255, 359, 81, 185, 289, 393, 48, 152, 256, 360, 83, 187, 291, 395)(49, 153, 257, 361, 85, 189, 293, 397, 50, 154, 258, 362, 87, 191, 295, 399)(51, 155, 259, 363, 89, 193, 297, 401, 52, 156, 260, 364, 91, 195, 299, 403)(54, 158, 262, 366, 94, 198, 302, 406, 56, 160, 264, 368, 93, 197, 301, 405)(58, 162, 266, 370, 98, 202, 306, 410, 68, 172, 276, 380, 97, 201, 305, 409)(63, 167, 271, 375, 102, 206, 310, 414, 65, 169, 273, 377, 99, 203, 307, 411)(66, 170, 274, 378, 100, 204, 308, 412, 67, 171, 275, 379, 101, 205, 309, 413)(70, 174, 278, 382, 104, 208, 312, 416, 72, 176, 280, 384, 103, 207, 311, 415)(74, 178, 282, 386, 96, 200, 304, 408, 76, 180, 284, 388, 95, 199, 303, 407)(78, 182, 286, 390, 90, 194, 298, 402, 80, 184, 288, 392, 92, 196, 300, 404)(82, 186, 290, 394, 86, 190, 294, 398, 84, 188, 292, 396, 88, 192, 296, 400)
	L = (1, 106)(2, 105)(3, 110)(4, 113)(5, 114)(6, 107)(7, 115)(8, 116)(9, 108)(10, 109)(11, 111)(12, 112)(13, 121)(14, 122)(15, 123)(16, 124)(17, 117)(18, 118)(19, 119)(20, 120)(21, 129)(22, 130)(23, 131)(24, 132)(25, 125)(26, 126)(27, 127)(28, 128)(29, 137)(30, 138)(31, 142)(32, 143)(33, 133)(34, 134)(35, 159)(36, 164)(37, 165)(38, 135)(39, 136)(40, 157)(41, 161)(42, 163)(43, 166)(44, 168)(45, 173)(46, 175)(47, 177)(48, 179)(49, 181)(50, 183)(51, 185)(52, 187)(53, 144)(54, 189)(55, 139)(56, 191)(57, 145)(58, 197)(59, 146)(60, 140)(61, 141)(62, 147)(63, 205)(64, 148)(65, 204)(66, 193)(67, 195)(68, 198)(69, 149)(70, 202)(71, 150)(72, 201)(73, 151)(74, 206)(75, 152)(76, 203)(77, 153)(78, 208)(79, 154)(80, 207)(81, 155)(82, 200)(83, 156)(84, 199)(85, 158)(86, 194)(87, 160)(88, 196)(89, 170)(90, 190)(91, 171)(92, 192)(93, 162)(94, 172)(95, 188)(96, 186)(97, 176)(98, 174)(99, 180)(100, 169)(101, 167)(102, 178)(103, 184)(104, 182)(209, 315)(210, 318)(211, 313)(212, 322)(213, 321)(214, 314)(215, 324)(216, 323)(217, 317)(218, 316)(219, 320)(220, 319)(221, 330)(222, 329)(223, 332)(224, 331)(225, 326)(226, 325)(227, 328)(228, 327)(229, 338)(230, 337)(231, 340)(232, 339)(233, 334)(234, 333)(235, 336)(236, 335)(237, 346)(238, 345)(239, 351)(240, 350)(241, 342)(242, 341)(243, 365)(244, 373)(245, 372)(246, 344)(247, 343)(248, 367)(249, 371)(250, 369)(251, 376)(252, 374)(253, 383)(254, 381)(255, 387)(256, 385)(257, 391)(258, 389)(259, 395)(260, 393)(261, 347)(262, 399)(263, 352)(264, 397)(265, 354)(266, 406)(267, 353)(268, 349)(269, 348)(270, 356)(271, 412)(272, 355)(273, 413)(274, 403)(275, 401)(276, 405)(277, 358)(278, 409)(279, 357)(280, 410)(281, 360)(282, 411)(283, 359)(284, 414)(285, 362)(286, 415)(287, 361)(288, 416)(289, 364)(290, 407)(291, 363)(292, 408)(293, 368)(294, 404)(295, 366)(296, 402)(297, 379)(298, 400)(299, 378)(300, 398)(301, 380)(302, 370)(303, 394)(304, 396)(305, 382)(306, 384)(307, 386)(308, 375)(309, 377)(310, 388)(311, 390)(312, 392)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1953
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.1960 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y1 * R * Y2, (R * Y3)^2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 209, 313, 3, 107, 211, 315, 8, 112, 216, 320, 4, 108, 212, 316)(2, 106, 210, 314, 5, 109, 213, 317, 11, 115, 219, 323, 6, 110, 214, 318)(7, 111, 215, 319, 13, 117, 221, 325, 9, 113, 217, 321, 14, 118, 222, 326)(10, 114, 218, 322, 15, 119, 223, 327, 12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333, 18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335, 20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341, 26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343, 28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 53, 157, 261, 365, 34, 138, 242, 346, 55, 159, 263, 367)(35, 139, 243, 347, 57, 161, 265, 369, 40, 144, 248, 352, 59, 163, 267, 371)(36, 140, 244, 348, 61, 165, 269, 373, 43, 147, 251, 355, 63, 167, 271, 375)(37, 141, 245, 349, 64, 168, 272, 376, 38, 142, 246, 350, 60, 164, 268, 372)(39, 143, 247, 351, 67, 171, 275, 379, 41, 145, 249, 353, 69, 173, 277, 381)(42, 146, 250, 354, 72, 176, 280, 384, 44, 148, 252, 356, 74, 178, 282, 386)(45, 149, 253, 357, 77, 181, 285, 389, 46, 150, 254, 358, 79, 183, 287, 391)(47, 151, 255, 359, 81, 185, 289, 393, 48, 152, 256, 360, 83, 187, 291, 395)(49, 153, 257, 361, 85, 189, 293, 397, 50, 154, 258, 362, 87, 191, 295, 399)(51, 155, 259, 363, 89, 193, 297, 401, 52, 156, 260, 364, 91, 195, 299, 403)(54, 158, 262, 366, 94, 198, 302, 406, 56, 160, 264, 368, 93, 197, 301, 405)(58, 162, 266, 370, 98, 202, 306, 410, 70, 174, 278, 382, 97, 201, 305, 409)(62, 166, 270, 374, 99, 203, 307, 411, 75, 179, 283, 387, 101, 205, 309, 413)(65, 169, 273, 377, 100, 204, 308, 412, 66, 170, 274, 378, 102, 206, 310, 414)(68, 172, 276, 380, 103, 207, 311, 415, 71, 175, 279, 383, 104, 208, 312, 416)(73, 177, 281, 385, 96, 200, 304, 408, 76, 180, 284, 388, 95, 199, 303, 407)(78, 182, 286, 390, 90, 194, 298, 402, 80, 184, 288, 392, 92, 196, 300, 404)(82, 186, 290, 394, 86, 190, 294, 398, 84, 188, 292, 396, 88, 192, 296, 400)
	L = (1, 106)(2, 105)(3, 111)(4, 113)(5, 114)(6, 116)(7, 107)(8, 115)(9, 108)(10, 109)(11, 112)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 117)(18, 118)(19, 119)(20, 120)(21, 129)(22, 130)(23, 131)(24, 132)(25, 125)(26, 126)(27, 127)(28, 128)(29, 137)(30, 138)(31, 142)(32, 141)(33, 133)(34, 134)(35, 157)(36, 164)(37, 136)(38, 135)(39, 161)(40, 159)(41, 163)(42, 165)(43, 168)(44, 167)(45, 171)(46, 173)(47, 176)(48, 178)(49, 181)(50, 183)(51, 185)(52, 187)(53, 139)(54, 189)(55, 144)(56, 191)(57, 143)(58, 198)(59, 145)(60, 140)(61, 146)(62, 206)(63, 148)(64, 147)(65, 195)(66, 193)(67, 149)(68, 202)(69, 150)(70, 197)(71, 201)(72, 151)(73, 203)(74, 152)(75, 204)(76, 205)(77, 153)(78, 207)(79, 154)(80, 208)(81, 155)(82, 200)(83, 156)(84, 199)(85, 158)(86, 194)(87, 160)(88, 196)(89, 170)(90, 190)(91, 169)(92, 192)(93, 174)(94, 162)(95, 188)(96, 186)(97, 175)(98, 172)(99, 177)(100, 179)(101, 180)(102, 166)(103, 182)(104, 184)(209, 314)(210, 313)(211, 319)(212, 321)(213, 322)(214, 324)(215, 315)(216, 323)(217, 316)(218, 317)(219, 320)(220, 318)(221, 329)(222, 330)(223, 331)(224, 332)(225, 325)(226, 326)(227, 327)(228, 328)(229, 337)(230, 338)(231, 339)(232, 340)(233, 333)(234, 334)(235, 335)(236, 336)(237, 345)(238, 346)(239, 350)(240, 349)(241, 341)(242, 342)(243, 365)(244, 372)(245, 344)(246, 343)(247, 369)(248, 367)(249, 371)(250, 373)(251, 376)(252, 375)(253, 379)(254, 381)(255, 384)(256, 386)(257, 389)(258, 391)(259, 393)(260, 395)(261, 347)(262, 397)(263, 352)(264, 399)(265, 351)(266, 406)(267, 353)(268, 348)(269, 354)(270, 414)(271, 356)(272, 355)(273, 403)(274, 401)(275, 357)(276, 410)(277, 358)(278, 405)(279, 409)(280, 359)(281, 411)(282, 360)(283, 412)(284, 413)(285, 361)(286, 415)(287, 362)(288, 416)(289, 363)(290, 408)(291, 364)(292, 407)(293, 366)(294, 402)(295, 368)(296, 404)(297, 378)(298, 398)(299, 377)(300, 400)(301, 382)(302, 370)(303, 396)(304, 394)(305, 383)(306, 380)(307, 385)(308, 387)(309, 388)(310, 374)(311, 390)(312, 392)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1954
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.1961 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 209, 313, 3, 107, 211, 315, 8, 112, 216, 320, 4, 108, 212, 316)(2, 106, 210, 314, 5, 109, 213, 317, 11, 115, 219, 323, 6, 110, 214, 318)(7, 111, 215, 319, 13, 117, 221, 325, 9, 113, 217, 321, 14, 118, 222, 326)(10, 114, 218, 322, 15, 119, 223, 327, 12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333, 18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335, 20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341, 26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343, 28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 38, 142, 246, 350, 34, 138, 242, 346, 35, 139, 243, 347)(36, 140, 244, 348, 51, 155, 259, 363, 41, 145, 249, 353, 52, 156, 260, 364)(37, 141, 245, 349, 58, 162, 266, 370, 39, 143, 247, 351, 55, 159, 263, 367)(40, 144, 248, 352, 61, 165, 269, 373, 42, 146, 250, 354, 56, 160, 264, 368)(43, 147, 251, 355, 59, 163, 267, 371, 44, 148, 252, 356, 57, 161, 265, 369)(45, 149, 253, 357, 62, 166, 270, 374, 46, 150, 254, 358, 60, 164, 268, 372)(47, 151, 255, 359, 64, 168, 272, 376, 48, 152, 256, 360, 63, 167, 271, 375)(49, 153, 257, 361, 66, 170, 274, 378, 50, 154, 258, 362, 65, 169, 273, 377)(53, 157, 261, 365, 68, 172, 276, 380, 54, 158, 262, 366, 67, 171, 275, 379)(69, 173, 277, 381, 71, 175, 279, 383, 70, 174, 278, 382, 72, 176, 280, 384)(73, 177, 281, 385, 76, 180, 284, 388, 74, 178, 282, 386, 75, 179, 283, 387)(77, 181, 285, 389, 91, 195, 299, 403, 78, 182, 286, 390, 92, 196, 300, 404)(79, 183, 287, 391, 96, 200, 304, 408, 80, 184, 288, 392, 95, 199, 303, 407)(81, 185, 289, 393, 98, 202, 306, 410, 82, 186, 290, 394, 97, 201, 305, 409)(83, 187, 291, 395, 100, 204, 308, 412, 84, 188, 292, 396, 99, 203, 307, 411)(85, 189, 293, 397, 102, 206, 310, 414, 86, 190, 294, 398, 101, 205, 309, 413)(87, 191, 295, 399, 104, 208, 312, 416, 88, 192, 296, 400, 103, 207, 311, 415)(89, 193, 297, 401, 94, 198, 302, 406, 90, 194, 298, 402, 93, 197, 301, 405)
	L = (1, 106)(2, 105)(3, 111)(4, 113)(5, 114)(6, 116)(7, 107)(8, 115)(9, 108)(10, 109)(11, 112)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 117)(18, 118)(19, 119)(20, 120)(21, 129)(22, 130)(23, 131)(24, 132)(25, 125)(26, 126)(27, 127)(28, 128)(29, 137)(30, 138)(31, 155)(32, 156)(33, 133)(34, 134)(35, 159)(36, 160)(37, 161)(38, 162)(39, 163)(40, 164)(41, 165)(42, 166)(43, 167)(44, 168)(45, 169)(46, 170)(47, 171)(48, 172)(49, 173)(50, 174)(51, 135)(52, 136)(53, 177)(54, 178)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 195)(72, 196)(73, 157)(74, 158)(75, 199)(76, 200)(77, 201)(78, 202)(79, 203)(80, 204)(81, 205)(82, 206)(83, 207)(84, 208)(85, 197)(86, 198)(87, 194)(88, 193)(89, 192)(90, 191)(91, 175)(92, 176)(93, 189)(94, 190)(95, 179)(96, 180)(97, 181)(98, 182)(99, 183)(100, 184)(101, 185)(102, 186)(103, 187)(104, 188)(209, 314)(210, 313)(211, 319)(212, 321)(213, 322)(214, 324)(215, 315)(216, 323)(217, 316)(218, 317)(219, 320)(220, 318)(221, 329)(222, 330)(223, 331)(224, 332)(225, 325)(226, 326)(227, 327)(228, 328)(229, 337)(230, 338)(231, 339)(232, 340)(233, 333)(234, 334)(235, 335)(236, 336)(237, 345)(238, 346)(239, 363)(240, 364)(241, 341)(242, 342)(243, 367)(244, 368)(245, 369)(246, 370)(247, 371)(248, 372)(249, 373)(250, 374)(251, 375)(252, 376)(253, 377)(254, 378)(255, 379)(256, 380)(257, 381)(258, 382)(259, 343)(260, 344)(261, 385)(262, 386)(263, 347)(264, 348)(265, 349)(266, 350)(267, 351)(268, 352)(269, 353)(270, 354)(271, 355)(272, 356)(273, 357)(274, 358)(275, 359)(276, 360)(277, 361)(278, 362)(279, 403)(280, 404)(281, 365)(282, 366)(283, 407)(284, 408)(285, 409)(286, 410)(287, 411)(288, 412)(289, 413)(290, 414)(291, 415)(292, 416)(293, 405)(294, 406)(295, 402)(296, 401)(297, 400)(298, 399)(299, 383)(300, 384)(301, 397)(302, 398)(303, 387)(304, 388)(305, 389)(306, 390)(307, 391)(308, 392)(309, 393)(310, 394)(311, 395)(312, 396)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1955
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.1962 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = C2 x C4 x D26 (small group id <208, 36>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y1^4, Y2^4, R * Y2 * R * Y1, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 6, 110, 214, 318)(3, 107, 211, 315, 7, 111, 215, 319)(5, 109, 213, 317, 10, 114, 218, 322)(8, 112, 216, 320, 13, 117, 221, 325)(9, 113, 217, 321, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327)(12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333)(18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335)(20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341)(26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343)(28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 49, 153, 257, 361)(34, 138, 242, 346, 50, 154, 258, 362)(35, 139, 243, 347, 65, 169, 273, 377)(36, 140, 244, 348, 68, 172, 276, 380)(37, 141, 245, 349, 69, 173, 277, 381)(38, 142, 246, 350, 70, 174, 278, 382)(39, 143, 247, 351, 71, 175, 279, 383)(40, 144, 248, 352, 72, 176, 280, 384)(41, 145, 249, 353, 73, 177, 281, 385)(42, 146, 250, 354, 63, 167, 271, 375)(43, 147, 251, 355, 64, 168, 272, 376)(44, 148, 252, 356, 76, 180, 284, 388)(45, 149, 253, 357, 66, 170, 274, 378)(46, 150, 254, 358, 67, 171, 275, 379)(47, 151, 255, 359, 60, 164, 268, 372)(48, 152, 256, 360, 59, 163, 267, 371)(51, 155, 259, 363, 74, 178, 282, 386)(52, 156, 260, 364, 75, 179, 283, 387)(53, 157, 261, 365, 77, 181, 285, 389)(54, 158, 262, 366, 78, 182, 286, 390)(55, 159, 263, 367, 79, 183, 287, 391)(56, 160, 264, 368, 80, 184, 288, 392)(57, 161, 265, 369, 81, 185, 289, 393)(58, 162, 266, 370, 82, 186, 290, 394)(61, 165, 269, 373, 83, 187, 291, 395)(62, 166, 270, 374, 84, 188, 292, 396)(85, 189, 293, 397, 87, 191, 295, 399)(86, 190, 294, 398, 88, 192, 296, 400)(89, 193, 297, 401, 101, 205, 309, 413)(90, 194, 298, 402, 100, 204, 308, 412)(91, 195, 299, 403, 96, 200, 304, 408)(92, 196, 300, 404, 97, 201, 305, 409)(93, 197, 301, 405, 95, 199, 303, 407)(94, 198, 302, 406, 99, 203, 307, 411)(98, 202, 306, 410, 103, 207, 311, 415)(102, 206, 310, 414, 104, 208, 312, 416)
	L = (1, 106)(2, 109)(3, 105)(4, 112)(5, 107)(6, 115)(7, 116)(8, 114)(9, 108)(10, 113)(11, 111)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 118)(18, 117)(19, 120)(20, 119)(21, 129)(22, 130)(23, 131)(24, 132)(25, 126)(26, 125)(27, 128)(28, 127)(29, 137)(30, 138)(31, 163)(32, 164)(33, 134)(34, 133)(35, 167)(36, 170)(37, 171)(38, 172)(39, 168)(40, 175)(41, 169)(42, 178)(43, 179)(44, 173)(45, 181)(46, 182)(47, 180)(48, 174)(49, 177)(50, 176)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 136)(60, 135)(61, 193)(62, 194)(63, 143)(64, 139)(65, 144)(66, 141)(67, 140)(68, 148)(69, 142)(70, 151)(71, 145)(72, 153)(73, 154)(74, 147)(75, 146)(76, 152)(77, 150)(78, 149)(79, 156)(80, 155)(81, 158)(82, 157)(83, 160)(84, 159)(85, 162)(86, 161)(87, 207)(88, 206)(89, 166)(90, 165)(91, 208)(92, 202)(93, 200)(94, 205)(95, 204)(96, 203)(97, 197)(98, 195)(99, 201)(100, 198)(101, 199)(102, 191)(103, 192)(104, 196)(209, 315)(210, 313)(211, 317)(212, 321)(213, 314)(214, 324)(215, 323)(216, 316)(217, 322)(218, 320)(219, 318)(220, 319)(221, 330)(222, 329)(223, 332)(224, 331)(225, 325)(226, 326)(227, 327)(228, 328)(229, 338)(230, 337)(231, 340)(232, 339)(233, 333)(234, 334)(235, 335)(236, 336)(237, 346)(238, 345)(239, 372)(240, 371)(241, 341)(242, 342)(243, 376)(244, 379)(245, 378)(246, 381)(247, 375)(248, 377)(249, 383)(250, 387)(251, 386)(252, 380)(253, 390)(254, 389)(255, 382)(256, 388)(257, 384)(258, 385)(259, 392)(260, 391)(261, 394)(262, 393)(263, 396)(264, 395)(265, 398)(266, 397)(267, 343)(268, 344)(269, 402)(270, 401)(271, 347)(272, 351)(273, 353)(274, 348)(275, 349)(276, 350)(277, 356)(278, 360)(279, 352)(280, 362)(281, 361)(282, 354)(283, 355)(284, 359)(285, 357)(286, 358)(287, 363)(288, 364)(289, 365)(290, 366)(291, 367)(292, 368)(293, 369)(294, 370)(295, 414)(296, 415)(297, 373)(298, 374)(299, 410)(300, 416)(301, 409)(302, 412)(303, 413)(304, 405)(305, 411)(306, 404)(307, 408)(308, 407)(309, 406)(310, 400)(311, 399)(312, 403)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1956
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1963 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, (Y1^-1 * Y3 * Y2^-1)^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 3, 107, 211, 315)(2, 106, 210, 314, 6, 110, 214, 318)(4, 108, 212, 316, 9, 113, 217, 321)(5, 109, 213, 317, 10, 114, 218, 322)(7, 111, 215, 319, 13, 117, 221, 325)(8, 112, 216, 320, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327)(12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333)(18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335)(20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341)(26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343)(28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 53, 157, 261, 365)(34, 138, 242, 346, 54, 158, 262, 366)(35, 139, 243, 347, 66, 170, 274, 378)(36, 140, 244, 348, 70, 174, 278, 382)(37, 141, 245, 349, 72, 176, 280, 384)(38, 142, 246, 350, 76, 180, 284, 388)(39, 143, 247, 351, 78, 182, 286, 390)(40, 144, 248, 352, 65, 169, 273, 377)(41, 145, 249, 353, 83, 187, 291, 395)(42, 146, 250, 354, 85, 189, 293, 397)(43, 147, 251, 355, 68, 172, 276, 380)(44, 148, 252, 356, 69, 173, 277, 381)(45, 149, 253, 357, 89, 193, 297, 401)(46, 150, 254, 358, 91, 195, 299, 403)(47, 151, 255, 359, 73, 177, 281, 385)(48, 152, 256, 360, 75, 179, 283, 387)(49, 153, 257, 361, 80, 184, 288, 392)(50, 154, 258, 362, 82, 186, 290, 394)(51, 155, 259, 363, 63, 167, 271, 375)(52, 156, 260, 364, 61, 165, 269, 373)(55, 159, 263, 367, 93, 197, 301, 405)(56, 160, 264, 368, 95, 199, 303, 407)(57, 161, 265, 369, 97, 201, 305, 409)(58, 162, 266, 370, 99, 203, 307, 411)(59, 163, 267, 371, 98, 202, 306, 410)(60, 164, 268, 372, 100, 204, 308, 412)(62, 166, 270, 374, 96, 200, 304, 408)(64, 168, 272, 376, 94, 198, 302, 406)(67, 171, 275, 379, 92, 196, 300, 404)(71, 175, 279, 383, 84, 188, 292, 396)(74, 178, 282, 386, 102, 206, 310, 414)(77, 181, 285, 389, 86, 190, 294, 398)(79, 183, 287, 391, 90, 194, 298, 402)(81, 185, 289, 393, 104, 208, 312, 416)(87, 191, 295, 399, 103, 207, 311, 415)(88, 192, 296, 400, 101, 205, 309, 413)
	L = (1, 106)(2, 109)(3, 111)(4, 105)(5, 108)(6, 115)(7, 114)(8, 107)(9, 116)(10, 112)(11, 113)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 118)(18, 117)(19, 120)(20, 119)(21, 129)(22, 130)(23, 131)(24, 132)(25, 126)(26, 125)(27, 128)(28, 127)(29, 137)(30, 138)(31, 165)(32, 167)(33, 134)(34, 133)(35, 169)(36, 173)(37, 177)(38, 176)(39, 172)(40, 184)(41, 182)(42, 170)(43, 186)(44, 179)(45, 180)(46, 174)(47, 197)(48, 199)(49, 201)(50, 203)(51, 189)(52, 187)(53, 195)(54, 193)(55, 202)(56, 204)(57, 200)(58, 198)(59, 191)(60, 185)(61, 136)(62, 178)(63, 135)(64, 192)(65, 143)(66, 145)(67, 208)(68, 139)(69, 142)(70, 149)(71, 205)(72, 140)(73, 148)(74, 168)(75, 141)(76, 150)(77, 206)(78, 146)(79, 207)(80, 147)(81, 163)(82, 144)(83, 155)(84, 194)(85, 156)(86, 196)(87, 164)(88, 166)(89, 157)(90, 190)(91, 158)(92, 188)(93, 152)(94, 161)(95, 151)(96, 162)(97, 154)(98, 160)(99, 153)(100, 159)(101, 181)(102, 175)(103, 171)(104, 183)(209, 314)(210, 317)(211, 319)(212, 313)(213, 316)(214, 323)(215, 322)(216, 315)(217, 324)(218, 320)(219, 321)(220, 318)(221, 329)(222, 330)(223, 331)(224, 332)(225, 326)(226, 325)(227, 328)(228, 327)(229, 337)(230, 338)(231, 339)(232, 340)(233, 334)(234, 333)(235, 336)(236, 335)(237, 345)(238, 346)(239, 373)(240, 375)(241, 342)(242, 341)(243, 377)(244, 381)(245, 385)(246, 384)(247, 380)(248, 392)(249, 390)(250, 378)(251, 394)(252, 387)(253, 388)(254, 382)(255, 405)(256, 407)(257, 409)(258, 411)(259, 397)(260, 395)(261, 403)(262, 401)(263, 410)(264, 412)(265, 408)(266, 406)(267, 399)(268, 393)(269, 344)(270, 386)(271, 343)(272, 400)(273, 351)(274, 353)(275, 416)(276, 347)(277, 350)(278, 357)(279, 413)(280, 348)(281, 356)(282, 376)(283, 349)(284, 358)(285, 414)(286, 354)(287, 415)(288, 355)(289, 371)(290, 352)(291, 363)(292, 402)(293, 364)(294, 404)(295, 372)(296, 374)(297, 365)(298, 398)(299, 366)(300, 396)(301, 360)(302, 369)(303, 359)(304, 370)(305, 362)(306, 368)(307, 361)(308, 367)(309, 389)(310, 383)(311, 379)(312, 391)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1957
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1964 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, (R * Y3)^2, R * Y2 * R * Y1, Y2^4, Y1^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 3, 107, 211, 315)(2, 106, 210, 314, 6, 110, 214, 318)(4, 108, 212, 316, 9, 113, 217, 321)(5, 109, 213, 317, 10, 114, 218, 322)(7, 111, 215, 319, 13, 117, 221, 325)(8, 112, 216, 320, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327)(12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333)(18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335)(20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341)(26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343)(28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 61, 165, 269, 373)(34, 138, 242, 346, 62, 166, 270, 374)(35, 139, 243, 347, 64, 168, 272, 376)(36, 140, 244, 348, 67, 171, 275, 379)(37, 141, 245, 349, 69, 173, 277, 381)(38, 142, 246, 350, 70, 174, 278, 382)(39, 143, 247, 351, 71, 175, 279, 383)(40, 144, 248, 352, 72, 176, 280, 384)(41, 145, 249, 353, 63, 167, 271, 375)(42, 146, 250, 354, 65, 169, 273, 377)(43, 147, 251, 355, 75, 179, 283, 387)(44, 148, 252, 356, 76, 180, 284, 388)(45, 149, 253, 357, 66, 170, 274, 378)(46, 150, 254, 358, 68, 172, 276, 380)(47, 151, 255, 359, 77, 181, 285, 389)(48, 152, 256, 360, 78, 182, 286, 390)(49, 153, 257, 361, 79, 183, 287, 391)(50, 154, 258, 362, 80, 184, 288, 392)(51, 155, 259, 363, 73, 177, 281, 385)(52, 156, 260, 364, 74, 178, 282, 386)(53, 157, 261, 365, 81, 185, 289, 393)(54, 158, 262, 366, 82, 186, 290, 394)(55, 159, 263, 367, 83, 187, 291, 395)(56, 160, 264, 368, 84, 188, 292, 396)(57, 161, 265, 369, 85, 189, 293, 397)(58, 162, 266, 370, 86, 190, 294, 398)(59, 163, 267, 371, 87, 191, 295, 399)(60, 164, 268, 372, 88, 192, 296, 400)(89, 193, 297, 401, 101, 205, 309, 413)(90, 194, 298, 402, 102, 206, 310, 414)(91, 195, 299, 403, 98, 202, 306, 410)(92, 196, 300, 404, 97, 201, 305, 409)(93, 197, 301, 405, 95, 199, 303, 407)(94, 198, 302, 406, 96, 200, 304, 408)(99, 203, 307, 411, 103, 207, 311, 415)(100, 204, 308, 412, 104, 208, 312, 416)
	L = (1, 106)(2, 109)(3, 111)(4, 105)(5, 108)(6, 115)(7, 114)(8, 107)(9, 116)(10, 112)(11, 113)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 118)(18, 117)(19, 120)(20, 119)(21, 129)(22, 130)(23, 131)(24, 132)(25, 126)(26, 125)(27, 128)(28, 127)(29, 137)(30, 138)(31, 156)(32, 155)(33, 134)(34, 133)(35, 167)(36, 170)(37, 171)(38, 172)(39, 169)(40, 175)(41, 177)(42, 178)(43, 168)(44, 174)(45, 165)(46, 166)(47, 180)(48, 173)(49, 179)(50, 176)(51, 135)(52, 136)(53, 182)(54, 181)(55, 184)(56, 183)(57, 186)(58, 185)(59, 188)(60, 187)(61, 150)(62, 149)(63, 143)(64, 144)(65, 139)(66, 142)(67, 148)(68, 140)(69, 151)(70, 141)(71, 147)(72, 153)(73, 146)(74, 145)(75, 154)(76, 152)(77, 157)(78, 158)(79, 159)(80, 160)(81, 161)(82, 162)(83, 163)(84, 164)(85, 193)(86, 194)(87, 208)(88, 207)(89, 190)(90, 189)(91, 203)(92, 204)(93, 202)(94, 201)(95, 205)(96, 206)(97, 197)(98, 198)(99, 196)(100, 195)(101, 200)(102, 199)(103, 191)(104, 192)(209, 314)(210, 317)(211, 319)(212, 313)(213, 316)(214, 323)(215, 322)(216, 315)(217, 324)(218, 320)(219, 321)(220, 318)(221, 329)(222, 330)(223, 331)(224, 332)(225, 326)(226, 325)(227, 328)(228, 327)(229, 337)(230, 338)(231, 339)(232, 340)(233, 334)(234, 333)(235, 336)(236, 335)(237, 345)(238, 346)(239, 364)(240, 363)(241, 342)(242, 341)(243, 375)(244, 378)(245, 379)(246, 380)(247, 377)(248, 383)(249, 385)(250, 386)(251, 376)(252, 382)(253, 373)(254, 374)(255, 388)(256, 381)(257, 387)(258, 384)(259, 343)(260, 344)(261, 390)(262, 389)(263, 392)(264, 391)(265, 394)(266, 393)(267, 396)(268, 395)(269, 358)(270, 357)(271, 351)(272, 352)(273, 347)(274, 350)(275, 356)(276, 348)(277, 359)(278, 349)(279, 355)(280, 361)(281, 354)(282, 353)(283, 362)(284, 360)(285, 365)(286, 366)(287, 367)(288, 368)(289, 369)(290, 370)(291, 371)(292, 372)(293, 401)(294, 402)(295, 416)(296, 415)(297, 398)(298, 397)(299, 411)(300, 412)(301, 410)(302, 409)(303, 413)(304, 414)(305, 405)(306, 406)(307, 404)(308, 403)(309, 408)(310, 407)(311, 399)(312, 400)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1958
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1965 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-1 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map::
	R = (1, 105, 2, 106)(3, 107, 7, 111)(4, 108, 9, 113)(5, 109, 10, 114)(6, 110, 12, 116)(8, 112, 11, 115)(13, 117, 17, 121)(14, 118, 18, 122)(15, 119, 19, 123)(16, 120, 20, 124)(21, 125, 25, 129)(22, 126, 26, 130)(23, 127, 27, 131)(24, 128, 28, 132)(29, 133, 33, 137)(30, 134, 34, 138)(31, 135, 55, 159)(32, 136, 56, 160)(35, 139, 65, 169)(36, 140, 69, 173)(37, 141, 73, 177)(38, 142, 76, 180)(39, 143, 78, 182)(40, 144, 81, 185)(41, 145, 66, 170)(42, 146, 79, 183)(43, 147, 68, 172)(44, 148, 70, 174)(45, 149, 74, 178)(46, 150, 72, 176)(47, 151, 93, 197)(48, 152, 95, 199)(49, 153, 63, 167)(50, 154, 61, 165)(51, 155, 83, 187)(52, 156, 85, 189)(53, 157, 88, 192)(54, 158, 90, 194)(57, 161, 99, 203)(58, 162, 101, 205)(59, 163, 100, 204)(60, 164, 102, 206)(62, 166, 92, 196)(64, 168, 89, 193)(67, 171, 96, 200)(71, 175, 98, 202)(75, 179, 80, 184)(77, 181, 82, 186)(84, 188, 104, 208)(86, 190, 94, 198)(87, 191, 103, 207)(91, 195, 97, 201)(209, 313, 211, 315, 216, 320, 212, 316)(210, 314, 213, 317, 219, 323, 214, 318)(215, 319, 221, 325, 217, 321, 222, 326)(218, 322, 223, 327, 220, 324, 224, 328)(225, 329, 229, 333, 226, 330, 230, 334)(227, 331, 231, 335, 228, 332, 232, 336)(233, 337, 237, 341, 234, 338, 238, 342)(235, 339, 239, 343, 236, 340, 240, 344)(241, 345, 269, 373, 242, 346, 271, 375)(243, 347, 274, 378, 250, 354, 276, 380)(244, 348, 278, 382, 253, 357, 280, 384)(245, 349, 282, 386, 246, 350, 277, 381)(247, 351, 287, 391, 248, 352, 273, 377)(249, 353, 291, 395, 251, 355, 293, 397)(252, 356, 296, 400, 254, 358, 298, 402)(255, 359, 284, 388, 256, 360, 281, 385)(257, 361, 289, 393, 258, 362, 286, 390)(259, 363, 307, 411, 260, 364, 309, 413)(261, 365, 308, 412, 262, 366, 310, 414)(263, 367, 303, 407, 264, 368, 301, 405)(265, 369, 300, 404, 266, 370, 297, 401)(267, 371, 295, 399, 268, 372, 292, 396)(270, 374, 279, 383, 272, 376, 299, 403)(275, 379, 312, 416, 294, 398, 311, 415)(283, 387, 305, 409, 285, 389, 306, 410)(288, 392, 302, 406, 290, 394, 304, 408)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1966 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, Y2^4, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map::
	R = (1, 105, 2, 106)(3, 107, 7, 111)(4, 108, 9, 113)(5, 109, 10, 114)(6, 110, 12, 116)(8, 112, 11, 115)(13, 117, 17, 121)(14, 118, 18, 122)(15, 119, 19, 123)(16, 120, 20, 124)(21, 125, 25, 129)(22, 126, 26, 130)(23, 127, 27, 131)(24, 128, 28, 132)(29, 133, 33, 137)(30, 134, 34, 138)(31, 135, 37, 141)(32, 136, 38, 142)(35, 139, 55, 159)(36, 140, 60, 164)(39, 143, 57, 161)(40, 144, 53, 157)(41, 145, 59, 163)(42, 146, 61, 165)(43, 147, 64, 168)(44, 148, 63, 167)(45, 149, 67, 171)(46, 150, 69, 173)(47, 151, 72, 176)(48, 152, 74, 178)(49, 153, 77, 181)(50, 154, 79, 183)(51, 155, 81, 185)(52, 156, 83, 187)(54, 158, 85, 189)(56, 160, 87, 191)(58, 162, 93, 197)(62, 166, 102, 206)(65, 169, 89, 193)(66, 170, 91, 195)(68, 172, 98, 202)(70, 174, 94, 198)(71, 175, 97, 201)(73, 177, 99, 203)(75, 179, 100, 204)(76, 180, 101, 205)(78, 182, 103, 207)(80, 184, 104, 208)(82, 186, 95, 199)(84, 188, 96, 200)(86, 190, 92, 196)(88, 192, 90, 194)(209, 313, 211, 315, 216, 320, 212, 316)(210, 314, 213, 317, 219, 323, 214, 318)(215, 319, 221, 325, 217, 321, 222, 326)(218, 322, 223, 327, 220, 324, 224, 328)(225, 329, 229, 333, 226, 330, 230, 334)(227, 331, 231, 335, 228, 332, 232, 336)(233, 337, 237, 341, 234, 338, 238, 342)(235, 339, 239, 343, 236, 340, 240, 344)(241, 345, 261, 365, 242, 346, 263, 367)(243, 347, 265, 369, 248, 352, 267, 371)(244, 348, 269, 373, 251, 355, 271, 375)(245, 349, 272, 376, 246, 350, 268, 372)(247, 351, 275, 379, 249, 353, 277, 381)(250, 354, 280, 384, 252, 356, 282, 386)(253, 357, 285, 389, 254, 358, 287, 391)(255, 359, 289, 393, 256, 360, 291, 395)(257, 361, 293, 397, 258, 362, 295, 399)(259, 363, 297, 401, 260, 364, 299, 403)(262, 366, 302, 406, 264, 368, 301, 405)(266, 370, 306, 410, 278, 382, 305, 409)(270, 374, 307, 411, 283, 387, 309, 413)(273, 377, 308, 412, 274, 378, 310, 414)(276, 380, 311, 415, 279, 383, 312, 416)(281, 385, 303, 407, 284, 388, 304, 408)(286, 390, 300, 404, 288, 392, 298, 402)(290, 394, 296, 400, 292, 396, 294, 398)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1967 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 9, 113)(4, 108, 7, 111)(5, 109, 10, 114)(6, 110, 11, 115)(8, 112, 12, 116)(13, 117, 17, 121)(14, 118, 18, 122)(15, 119, 19, 123)(16, 120, 20, 124)(21, 125, 25, 129)(22, 126, 26, 130)(23, 127, 27, 131)(24, 128, 28, 132)(29, 133, 33, 137)(30, 134, 34, 138)(31, 135, 37, 141)(32, 136, 39, 143)(35, 139, 55, 159)(36, 140, 60, 164)(38, 142, 53, 157)(40, 144, 64, 168)(41, 145, 57, 161)(42, 146, 59, 163)(43, 147, 61, 165)(44, 148, 63, 167)(45, 149, 69, 173)(46, 150, 71, 175)(47, 151, 73, 177)(48, 152, 75, 179)(49, 153, 77, 181)(50, 154, 79, 183)(51, 155, 81, 185)(52, 156, 83, 187)(54, 158, 85, 189)(56, 160, 87, 191)(58, 162, 93, 197)(62, 166, 101, 205)(65, 169, 89, 193)(66, 170, 94, 198)(67, 171, 91, 195)(68, 172, 100, 204)(70, 174, 98, 202)(72, 176, 97, 201)(74, 178, 102, 206)(76, 180, 99, 203)(78, 182, 104, 208)(80, 184, 103, 207)(82, 186, 96, 200)(84, 188, 95, 199)(86, 190, 90, 194)(88, 192, 92, 196)(209, 313, 211, 315, 212, 316, 213, 317)(210, 314, 214, 318, 215, 319, 216, 320)(217, 321, 221, 325, 218, 322, 222, 326)(219, 323, 223, 327, 220, 324, 224, 328)(225, 329, 229, 333, 226, 330, 230, 334)(227, 331, 231, 335, 228, 332, 232, 336)(233, 337, 237, 341, 234, 338, 238, 342)(235, 339, 239, 343, 236, 340, 240, 344)(241, 345, 261, 365, 242, 346, 263, 367)(243, 347, 265, 369, 246, 350, 267, 371)(244, 348, 269, 373, 248, 352, 271, 375)(245, 349, 272, 376, 247, 351, 268, 372)(249, 353, 277, 381, 250, 354, 279, 383)(251, 355, 281, 385, 252, 356, 283, 387)(253, 357, 285, 389, 254, 358, 287, 391)(255, 359, 289, 393, 256, 360, 291, 395)(257, 361, 293, 397, 258, 362, 295, 399)(259, 363, 297, 401, 260, 364, 299, 403)(262, 366, 302, 406, 264, 368, 301, 405)(266, 370, 306, 410, 274, 378, 305, 409)(270, 374, 310, 414, 276, 380, 307, 411)(273, 377, 308, 412, 275, 379, 309, 413)(278, 382, 312, 416, 280, 384, 311, 415)(282, 386, 304, 408, 284, 388, 303, 407)(286, 390, 298, 402, 288, 392, 300, 404)(290, 394, 294, 398, 292, 396, 296, 400)
	L = (1, 212)(2, 215)(3, 213)(4, 209)(5, 211)(6, 216)(7, 210)(8, 214)(9, 218)(10, 217)(11, 220)(12, 219)(13, 222)(14, 221)(15, 224)(16, 223)(17, 226)(18, 225)(19, 228)(20, 227)(21, 230)(22, 229)(23, 232)(24, 231)(25, 234)(26, 233)(27, 236)(28, 235)(29, 238)(30, 237)(31, 240)(32, 239)(33, 242)(34, 241)(35, 246)(36, 248)(37, 247)(38, 243)(39, 245)(40, 244)(41, 250)(42, 249)(43, 252)(44, 251)(45, 254)(46, 253)(47, 256)(48, 255)(49, 258)(50, 257)(51, 260)(52, 259)(53, 263)(54, 264)(55, 261)(56, 262)(57, 267)(58, 274)(59, 265)(60, 272)(61, 271)(62, 276)(63, 269)(64, 268)(65, 275)(66, 266)(67, 273)(68, 270)(69, 279)(70, 280)(71, 277)(72, 278)(73, 283)(74, 284)(75, 281)(76, 282)(77, 287)(78, 288)(79, 285)(80, 286)(81, 291)(82, 292)(83, 289)(84, 290)(85, 295)(86, 296)(87, 293)(88, 294)(89, 299)(90, 300)(91, 297)(92, 298)(93, 302)(94, 301)(95, 304)(96, 303)(97, 306)(98, 305)(99, 310)(100, 309)(101, 308)(102, 307)(103, 312)(104, 311)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1968 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 9, 113)(4, 108, 7, 111)(5, 109, 10, 114)(6, 110, 11, 115)(8, 112, 12, 116)(13, 117, 17, 121)(14, 118, 18, 122)(15, 119, 19, 123)(16, 120, 20, 124)(21, 125, 25, 129)(22, 126, 26, 130)(23, 127, 27, 131)(24, 128, 28, 132)(29, 133, 33, 137)(30, 134, 34, 138)(31, 135, 37, 141)(32, 136, 39, 143)(35, 139, 55, 159)(36, 140, 60, 164)(38, 142, 53, 157)(40, 144, 64, 168)(41, 145, 57, 161)(42, 146, 59, 163)(43, 147, 61, 165)(44, 148, 63, 167)(45, 149, 69, 173)(46, 150, 71, 175)(47, 151, 73, 177)(48, 152, 75, 179)(49, 153, 77, 181)(50, 154, 79, 183)(51, 155, 81, 185)(52, 156, 83, 187)(54, 158, 85, 189)(56, 160, 87, 191)(58, 162, 93, 197)(62, 166, 102, 206)(65, 169, 89, 193)(66, 170, 94, 198)(67, 171, 91, 195)(68, 172, 100, 204)(70, 174, 98, 202)(72, 176, 97, 201)(74, 178, 99, 203)(76, 180, 101, 205)(78, 182, 103, 207)(80, 184, 104, 208)(82, 186, 95, 199)(84, 188, 96, 200)(86, 190, 92, 196)(88, 192, 90, 194)(209, 313, 211, 315, 212, 316, 213, 317)(210, 314, 214, 318, 215, 319, 216, 320)(217, 321, 221, 325, 218, 322, 222, 326)(219, 323, 223, 327, 220, 324, 224, 328)(225, 329, 229, 333, 226, 330, 230, 334)(227, 331, 231, 335, 228, 332, 232, 336)(233, 337, 237, 341, 234, 338, 238, 342)(235, 339, 239, 343, 236, 340, 240, 344)(241, 345, 261, 365, 242, 346, 263, 367)(243, 347, 265, 369, 246, 350, 267, 371)(244, 348, 269, 373, 248, 352, 271, 375)(245, 349, 272, 376, 247, 351, 268, 372)(249, 353, 277, 381, 250, 354, 279, 383)(251, 355, 281, 385, 252, 356, 283, 387)(253, 357, 285, 389, 254, 358, 287, 391)(255, 359, 289, 393, 256, 360, 291, 395)(257, 361, 293, 397, 258, 362, 295, 399)(259, 363, 297, 401, 260, 364, 299, 403)(262, 366, 302, 406, 264, 368, 301, 405)(266, 370, 306, 410, 274, 378, 305, 409)(270, 374, 307, 411, 276, 380, 309, 413)(273, 377, 308, 412, 275, 379, 310, 414)(278, 382, 311, 415, 280, 384, 312, 416)(282, 386, 303, 407, 284, 388, 304, 408)(286, 390, 300, 404, 288, 392, 298, 402)(290, 394, 296, 400, 292, 396, 294, 398)
	L = (1, 212)(2, 215)(3, 213)(4, 209)(5, 211)(6, 216)(7, 210)(8, 214)(9, 218)(10, 217)(11, 220)(12, 219)(13, 222)(14, 221)(15, 224)(16, 223)(17, 226)(18, 225)(19, 228)(20, 227)(21, 230)(22, 229)(23, 232)(24, 231)(25, 234)(26, 233)(27, 236)(28, 235)(29, 238)(30, 237)(31, 240)(32, 239)(33, 242)(34, 241)(35, 246)(36, 248)(37, 247)(38, 243)(39, 245)(40, 244)(41, 250)(42, 249)(43, 252)(44, 251)(45, 254)(46, 253)(47, 256)(48, 255)(49, 258)(50, 257)(51, 260)(52, 259)(53, 263)(54, 264)(55, 261)(56, 262)(57, 267)(58, 274)(59, 265)(60, 272)(61, 271)(62, 276)(63, 269)(64, 268)(65, 275)(66, 266)(67, 273)(68, 270)(69, 279)(70, 280)(71, 277)(72, 278)(73, 283)(74, 284)(75, 281)(76, 282)(77, 287)(78, 288)(79, 285)(80, 286)(81, 291)(82, 292)(83, 289)(84, 290)(85, 295)(86, 296)(87, 293)(88, 294)(89, 299)(90, 300)(91, 297)(92, 298)(93, 302)(94, 301)(95, 304)(96, 303)(97, 306)(98, 305)(99, 309)(100, 310)(101, 307)(102, 308)(103, 312)(104, 311)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1969 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, (Y2^-2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^13, Y3^6 * Y1 * Y2 * Y3^5 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 11, 115)(4, 108, 10, 114)(5, 109, 17, 121)(6, 110, 8, 112)(7, 111, 20, 124)(9, 113, 26, 130)(12, 116, 21, 125)(13, 117, 30, 134)(14, 118, 23, 127)(15, 119, 28, 132)(16, 120, 25, 129)(18, 122, 35, 139)(19, 123, 24, 128)(22, 126, 39, 143)(27, 131, 44, 148)(29, 133, 47, 151)(31, 135, 41, 145)(32, 136, 40, 144)(33, 137, 49, 153)(34, 138, 46, 150)(36, 140, 52, 156)(37, 141, 43, 147)(38, 142, 55, 159)(42, 146, 57, 161)(45, 149, 60, 164)(48, 152, 63, 167)(50, 154, 65, 169)(51, 155, 62, 166)(53, 157, 68, 172)(54, 158, 59, 163)(56, 160, 71, 175)(58, 162, 73, 177)(61, 165, 76, 180)(64, 168, 79, 183)(66, 170, 81, 185)(67, 171, 78, 182)(69, 173, 84, 188)(70, 174, 75, 179)(72, 176, 87, 191)(74, 178, 89, 193)(77, 181, 92, 196)(80, 184, 95, 199)(82, 186, 97, 201)(83, 187, 94, 198)(85, 189, 99, 203)(86, 190, 91, 195)(88, 192, 101, 205)(90, 194, 98, 202)(93, 197, 100, 204)(96, 200, 103, 207)(102, 206, 104, 208)(209, 313, 211, 315, 220, 324, 213, 317)(210, 314, 215, 319, 229, 333, 217, 321)(212, 316, 222, 326, 239, 343, 224, 328)(214, 318, 221, 325, 240, 344, 226, 330)(216, 320, 231, 335, 248, 352, 233, 337)(218, 322, 230, 334, 249, 353, 235, 339)(219, 323, 237, 341, 225, 329, 232, 336)(223, 327, 228, 332, 246, 350, 234, 338)(227, 331, 241, 345, 255, 359, 244, 348)(236, 340, 250, 354, 263, 367, 253, 357)(238, 342, 256, 360, 243, 347, 251, 355)(242, 346, 247, 351, 264, 368, 252, 356)(245, 349, 258, 362, 271, 375, 261, 365)(254, 358, 266, 370, 279, 383, 269, 373)(257, 361, 272, 376, 260, 364, 267, 371)(259, 363, 265, 369, 280, 384, 268, 372)(262, 366, 274, 378, 287, 391, 277, 381)(270, 374, 282, 386, 295, 399, 285, 389)(273, 377, 288, 392, 276, 380, 283, 387)(275, 379, 281, 385, 296, 400, 284, 388)(278, 382, 290, 394, 303, 407, 293, 397)(286, 390, 298, 402, 309, 413, 301, 405)(289, 393, 304, 408, 292, 396, 299, 403)(291, 395, 297, 401, 310, 414, 300, 404)(294, 398, 306, 410, 311, 415, 308, 412)(302, 406, 305, 409, 312, 416, 307, 411)
	L = (1, 212)(2, 216)(3, 221)(4, 223)(5, 226)(6, 209)(7, 230)(8, 232)(9, 235)(10, 210)(11, 231)(12, 239)(13, 241)(14, 211)(15, 242)(16, 213)(17, 233)(18, 244)(19, 214)(20, 222)(21, 248)(22, 250)(23, 215)(24, 251)(25, 217)(26, 224)(27, 253)(28, 218)(29, 256)(30, 219)(31, 246)(32, 220)(33, 258)(34, 259)(35, 225)(36, 261)(37, 227)(38, 264)(39, 228)(40, 237)(41, 229)(42, 266)(43, 267)(44, 234)(45, 269)(46, 236)(47, 240)(48, 272)(49, 238)(50, 274)(51, 275)(52, 243)(53, 277)(54, 245)(55, 249)(56, 280)(57, 247)(58, 282)(59, 283)(60, 252)(61, 285)(62, 254)(63, 255)(64, 288)(65, 257)(66, 290)(67, 291)(68, 260)(69, 293)(70, 262)(71, 263)(72, 296)(73, 265)(74, 298)(75, 299)(76, 268)(77, 301)(78, 270)(79, 271)(80, 304)(81, 273)(82, 306)(83, 294)(84, 276)(85, 308)(86, 278)(87, 279)(88, 310)(89, 281)(90, 305)(91, 302)(92, 284)(93, 307)(94, 286)(95, 287)(96, 312)(97, 289)(98, 297)(99, 292)(100, 300)(101, 295)(102, 311)(103, 303)(104, 309)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1970 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = C4 x D26 (small group id <104, 5>)
Aut   = D8 x D26 (small group id <208, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y1 * Y2^-2)^2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^6 * Y1 * Y2^-1 * Y3^5 * Y1 * Y2^-1, Y3 * Y2 * Y3^-2 * Y2 * Y3^10 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 11, 115)(4, 108, 10, 114)(5, 109, 17, 121)(6, 110, 8, 112)(7, 111, 20, 124)(9, 113, 26, 130)(12, 116, 21, 125)(13, 117, 30, 134)(14, 118, 23, 127)(15, 119, 28, 132)(16, 120, 25, 129)(18, 122, 35, 139)(19, 123, 24, 128)(22, 126, 39, 143)(27, 131, 44, 148)(29, 133, 47, 151)(31, 135, 41, 145)(32, 136, 40, 144)(33, 137, 49, 153)(34, 138, 46, 150)(36, 140, 52, 156)(37, 141, 43, 147)(38, 142, 55, 159)(42, 146, 57, 161)(45, 149, 60, 164)(48, 152, 63, 167)(50, 154, 65, 169)(51, 155, 62, 166)(53, 157, 68, 172)(54, 158, 59, 163)(56, 160, 71, 175)(58, 162, 73, 177)(61, 165, 76, 180)(64, 168, 79, 183)(66, 170, 81, 185)(67, 171, 78, 182)(69, 173, 84, 188)(70, 174, 75, 179)(72, 176, 87, 191)(74, 178, 89, 193)(77, 181, 92, 196)(80, 184, 95, 199)(82, 186, 97, 201)(83, 187, 94, 198)(85, 189, 100, 204)(86, 190, 91, 195)(88, 192, 103, 207)(90, 194, 101, 205)(93, 197, 98, 202)(96, 200, 99, 203)(102, 206, 104, 208)(209, 313, 211, 315, 220, 324, 213, 317)(210, 314, 215, 319, 229, 333, 217, 321)(212, 316, 222, 326, 239, 343, 224, 328)(214, 318, 221, 325, 240, 344, 226, 330)(216, 320, 231, 335, 248, 352, 233, 337)(218, 322, 230, 334, 249, 353, 235, 339)(219, 323, 237, 341, 225, 329, 232, 336)(223, 327, 228, 332, 246, 350, 234, 338)(227, 331, 241, 345, 255, 359, 244, 348)(236, 340, 250, 354, 263, 367, 253, 357)(238, 342, 256, 360, 243, 347, 251, 355)(242, 346, 247, 351, 264, 368, 252, 356)(245, 349, 258, 362, 271, 375, 261, 365)(254, 358, 266, 370, 279, 383, 269, 373)(257, 361, 272, 376, 260, 364, 267, 371)(259, 363, 265, 369, 280, 384, 268, 372)(262, 366, 274, 378, 287, 391, 277, 381)(270, 374, 282, 386, 295, 399, 285, 389)(273, 377, 288, 392, 276, 380, 283, 387)(275, 379, 281, 385, 296, 400, 284, 388)(278, 382, 290, 394, 303, 407, 293, 397)(286, 390, 298, 402, 311, 415, 301, 405)(289, 393, 304, 408, 292, 396, 299, 403)(291, 395, 297, 401, 310, 414, 300, 404)(294, 398, 306, 410, 307, 411, 309, 413)(302, 406, 308, 412, 312, 416, 305, 409)
	L = (1, 212)(2, 216)(3, 221)(4, 223)(5, 226)(6, 209)(7, 230)(8, 232)(9, 235)(10, 210)(11, 231)(12, 239)(13, 241)(14, 211)(15, 242)(16, 213)(17, 233)(18, 244)(19, 214)(20, 222)(21, 248)(22, 250)(23, 215)(24, 251)(25, 217)(26, 224)(27, 253)(28, 218)(29, 256)(30, 219)(31, 246)(32, 220)(33, 258)(34, 259)(35, 225)(36, 261)(37, 227)(38, 264)(39, 228)(40, 237)(41, 229)(42, 266)(43, 267)(44, 234)(45, 269)(46, 236)(47, 240)(48, 272)(49, 238)(50, 274)(51, 275)(52, 243)(53, 277)(54, 245)(55, 249)(56, 280)(57, 247)(58, 282)(59, 283)(60, 252)(61, 285)(62, 254)(63, 255)(64, 288)(65, 257)(66, 290)(67, 291)(68, 260)(69, 293)(70, 262)(71, 263)(72, 296)(73, 265)(74, 298)(75, 299)(76, 268)(77, 301)(78, 270)(79, 271)(80, 304)(81, 273)(82, 306)(83, 307)(84, 276)(85, 309)(86, 278)(87, 279)(88, 310)(89, 281)(90, 308)(91, 312)(92, 284)(93, 305)(94, 286)(95, 287)(96, 302)(97, 289)(98, 300)(99, 303)(100, 292)(101, 297)(102, 294)(103, 295)(104, 311)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1971 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: halfedge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 106, 2, 110, 6, 109, 5, 105)(3, 113, 9, 108, 4, 114, 10, 107)(7, 115, 11, 112, 8, 116, 12, 111)(13, 121, 17, 118, 14, 122, 18, 117)(15, 123, 19, 120, 16, 124, 20, 119)(21, 129, 25, 126, 22, 130, 26, 125)(23, 131, 27, 128, 24, 132, 28, 127)(29, 137, 33, 134, 30, 138, 34, 133)(31, 160, 56, 136, 32, 159, 55, 135)(35, 169, 65, 144, 40, 173, 69, 139)(36, 174, 70, 143, 39, 178, 74, 140)(37, 179, 75, 142, 38, 181, 77, 141)(41, 185, 81, 146, 42, 187, 83, 145)(43, 171, 67, 148, 44, 170, 66, 147)(45, 176, 72, 150, 46, 175, 71, 149)(47, 197, 93, 152, 48, 199, 95, 151)(49, 165, 61, 154, 50, 166, 62, 153)(51, 190, 86, 156, 52, 189, 85, 155)(53, 194, 90, 158, 54, 193, 89, 157)(57, 204, 100, 162, 58, 203, 99, 161)(59, 205, 101, 164, 60, 206, 102, 163)(63, 195, 91, 168, 64, 196, 92, 167)(68, 200, 96, 184, 80, 198, 94, 172)(73, 202, 98, 183, 79, 201, 97, 177)(76, 188, 84, 182, 78, 186, 82, 180)(87, 208, 104, 192, 88, 207, 103, 191)
	L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 61)(34, 62)(35, 66)(36, 71)(37, 74)(38, 70)(39, 72)(40, 67)(41, 65)(42, 69)(43, 85)(44, 86)(45, 89)(46, 90)(47, 75)(48, 77)(49, 81)(50, 83)(51, 99)(52, 100)(53, 102)(54, 101)(55, 93)(56, 95)(57, 92)(58, 91)(59, 87)(60, 88)(63, 73)(64, 79)(68, 103)(76, 97)(78, 98)(80, 104)(82, 96)(84, 94)(105, 108)(106, 112)(107, 110)(109, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 126)(122, 125)(123, 128)(124, 127)(129, 134)(130, 133)(131, 136)(132, 135)(137, 166)(138, 165)(139, 171)(140, 176)(141, 174)(142, 178)(143, 175)(144, 170)(145, 173)(146, 169)(147, 190)(148, 189)(149, 194)(150, 193)(151, 181)(152, 179)(153, 187)(154, 185)(155, 204)(156, 203)(157, 205)(158, 206)(159, 199)(160, 197)(161, 195)(162, 196)(163, 192)(164, 191)(167, 183)(168, 177)(172, 208)(180, 202)(182, 201)(184, 207)(186, 198)(188, 200)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.1972 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 4, 108, 6, 110, 5, 109)(2, 106, 7, 111, 3, 107, 8, 112)(9, 113, 13, 117, 10, 114, 14, 118)(11, 115, 15, 119, 12, 116, 16, 120)(17, 121, 21, 125, 18, 122, 22, 126)(19, 123, 23, 127, 20, 124, 24, 128)(25, 129, 29, 133, 26, 130, 30, 134)(27, 131, 31, 135, 28, 132, 32, 136)(33, 137, 53, 157, 34, 138, 54, 158)(35, 139, 55, 159, 38, 142, 56, 160)(36, 140, 57, 161, 37, 141, 58, 162)(39, 143, 59, 163, 40, 144, 60, 164)(41, 145, 61, 165, 42, 146, 62, 166)(43, 147, 63, 167, 44, 148, 64, 168)(45, 149, 65, 169, 46, 150, 66, 170)(47, 151, 67, 171, 48, 152, 68, 172)(49, 153, 69, 173, 50, 154, 70, 174)(51, 155, 71, 175, 52, 156, 72, 176)(73, 177, 93, 197, 74, 178, 94, 198)(75, 179, 95, 199, 76, 180, 96, 200)(77, 181, 97, 201, 78, 182, 98, 202)(79, 183, 99, 203, 80, 184, 100, 204)(81, 185, 101, 205, 82, 186, 102, 206)(83, 187, 103, 207, 84, 188, 104, 208)(85, 189, 92, 196, 86, 190, 91, 195)(87, 191, 90, 194, 88, 192, 89, 193)(209, 210)(211, 214)(212, 217)(213, 218)(215, 219)(216, 220)(221, 225)(222, 226)(223, 227)(224, 228)(229, 233)(230, 234)(231, 235)(232, 236)(237, 241)(238, 242)(239, 246)(240, 243)(244, 262)(245, 261)(247, 263)(248, 264)(249, 265)(250, 266)(251, 267)(252, 268)(253, 269)(254, 270)(255, 271)(256, 272)(257, 273)(258, 274)(259, 275)(260, 276)(277, 281)(278, 282)(279, 284)(280, 283)(285, 302)(286, 301)(287, 303)(288, 304)(289, 305)(290, 306)(291, 307)(292, 308)(293, 309)(294, 310)(295, 311)(296, 312)(297, 300)(298, 299)(313, 315)(314, 318)(316, 322)(317, 321)(319, 324)(320, 323)(325, 330)(326, 329)(327, 332)(328, 331)(333, 338)(334, 337)(335, 340)(336, 339)(341, 346)(342, 345)(343, 347)(344, 350)(348, 365)(349, 366)(351, 368)(352, 367)(353, 370)(354, 369)(355, 372)(356, 371)(357, 374)(358, 373)(359, 376)(360, 375)(361, 378)(362, 377)(363, 380)(364, 379)(381, 386)(382, 385)(383, 387)(384, 388)(389, 405)(390, 406)(391, 408)(392, 407)(393, 410)(394, 409)(395, 412)(396, 411)(397, 414)(398, 413)(399, 416)(400, 415)(401, 403)(402, 404)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1974
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.1973 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2^2 * Y3 * Y1^-2, (Y2^-1 * Y3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 4, 108)(2, 106, 6, 110)(3, 107, 7, 111)(5, 109, 10, 114)(8, 112, 13, 117)(9, 113, 14, 118)(11, 115, 15, 119)(12, 116, 16, 120)(17, 121, 21, 125)(18, 122, 22, 126)(19, 123, 23, 127)(20, 124, 24, 128)(25, 129, 29, 133)(26, 130, 30, 134)(27, 131, 31, 135)(28, 132, 32, 136)(33, 137, 57, 161)(34, 138, 58, 162)(35, 139, 61, 165)(36, 140, 62, 166)(37, 141, 63, 167)(38, 142, 64, 168)(39, 143, 65, 169)(40, 144, 66, 170)(41, 145, 67, 171)(42, 146, 59, 163)(43, 147, 60, 164)(44, 148, 68, 172)(45, 149, 69, 173)(46, 150, 70, 174)(47, 151, 71, 175)(48, 152, 72, 176)(49, 153, 73, 177)(50, 154, 74, 178)(51, 155, 75, 179)(52, 156, 76, 180)(53, 157, 77, 181)(54, 158, 78, 182)(55, 159, 79, 183)(56, 160, 80, 184)(81, 185, 104, 208)(82, 186, 103, 207)(83, 187, 101, 205)(84, 188, 102, 206)(85, 189, 97, 201)(86, 190, 99, 203)(87, 191, 100, 204)(88, 192, 95, 199)(89, 193, 98, 202)(90, 194, 94, 198)(91, 195, 93, 197)(92, 196, 96, 200)(209, 210, 213, 211)(212, 216, 218, 217)(214, 219, 215, 220)(221, 225, 222, 226)(223, 227, 224, 228)(229, 233, 230, 234)(231, 235, 232, 236)(237, 241, 238, 242)(239, 250, 240, 251)(243, 267, 247, 268)(244, 266, 245, 265)(246, 270, 252, 271)(248, 273, 249, 269)(253, 276, 254, 272)(255, 275, 256, 274)(257, 278, 258, 277)(259, 280, 260, 279)(261, 282, 262, 281)(263, 284, 264, 283)(285, 289, 286, 290)(287, 291, 288, 292)(293, 309, 297, 310)(294, 311, 295, 312)(296, 307, 300, 308)(298, 306, 299, 305)(301, 304, 302, 303)(313, 315, 317, 314)(316, 321, 322, 320)(318, 324, 319, 323)(325, 330, 326, 329)(327, 332, 328, 331)(333, 338, 334, 337)(335, 340, 336, 339)(341, 346, 342, 345)(343, 355, 344, 354)(347, 372, 351, 371)(348, 369, 349, 370)(350, 375, 356, 374)(352, 373, 353, 377)(357, 376, 358, 380)(359, 378, 360, 379)(361, 381, 362, 382)(363, 383, 364, 384)(365, 385, 366, 386)(367, 387, 368, 388)(389, 394, 390, 393)(391, 396, 392, 395)(397, 414, 401, 413)(398, 416, 399, 415)(400, 412, 404, 411)(402, 409, 403, 410)(405, 407, 406, 408)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1975
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1974 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^-2 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 105, 209, 313, 4, 108, 212, 316, 6, 110, 214, 318, 5, 109, 213, 317)(2, 106, 210, 314, 7, 111, 215, 319, 3, 107, 211, 315, 8, 112, 216, 320)(9, 113, 217, 321, 13, 117, 221, 325, 10, 114, 218, 322, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327, 12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333, 18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335, 20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341, 26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343, 28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 57, 161, 265, 369, 34, 138, 242, 346, 58, 162, 266, 370)(35, 139, 243, 347, 61, 165, 269, 373, 40, 144, 248, 352, 62, 166, 270, 374)(36, 140, 244, 348, 63, 167, 271, 375, 37, 141, 245, 349, 64, 168, 272, 376)(38, 142, 246, 350, 65, 169, 273, 377, 39, 143, 247, 351, 66, 170, 274, 378)(41, 145, 249, 353, 67, 171, 275, 379, 42, 146, 250, 354, 68, 172, 276, 380)(43, 147, 251, 355, 60, 164, 268, 372, 44, 148, 252, 356, 59, 163, 267, 371)(45, 149, 253, 357, 69, 173, 277, 381, 46, 150, 254, 358, 70, 174, 278, 382)(47, 151, 255, 359, 71, 175, 279, 383, 48, 152, 256, 360, 72, 176, 280, 384)(49, 153, 257, 361, 73, 177, 281, 385, 50, 154, 258, 362, 74, 178, 282, 386)(51, 155, 259, 363, 75, 179, 283, 387, 52, 156, 260, 364, 76, 180, 284, 388)(53, 157, 261, 365, 77, 181, 285, 389, 54, 158, 262, 366, 78, 182, 286, 390)(55, 159, 263, 367, 79, 183, 287, 391, 56, 160, 264, 368, 80, 184, 288, 392)(81, 185, 289, 393, 103, 207, 311, 415, 82, 186, 290, 394, 104, 208, 312, 416)(83, 187, 291, 395, 102, 206, 310, 414, 84, 188, 292, 396, 101, 205, 309, 413)(85, 189, 293, 397, 97, 201, 305, 409, 86, 190, 294, 398, 98, 202, 306, 410)(87, 191, 295, 399, 99, 203, 307, 411, 88, 192, 296, 400, 100, 204, 308, 412)(89, 193, 297, 401, 96, 200, 304, 408, 90, 194, 298, 402, 95, 199, 303, 407)(91, 195, 299, 403, 94, 198, 302, 406, 92, 196, 300, 404, 93, 197, 301, 405)
	L = (1, 106)(2, 105)(3, 110)(4, 113)(5, 114)(6, 107)(7, 115)(8, 116)(9, 108)(10, 109)(11, 111)(12, 112)(13, 121)(14, 122)(15, 123)(16, 124)(17, 117)(18, 118)(19, 119)(20, 120)(21, 129)(22, 130)(23, 131)(24, 132)(25, 125)(26, 126)(27, 127)(28, 128)(29, 137)(30, 138)(31, 147)(32, 148)(33, 133)(34, 134)(35, 163)(36, 162)(37, 161)(38, 167)(39, 168)(40, 164)(41, 165)(42, 166)(43, 135)(44, 136)(45, 169)(46, 170)(47, 171)(48, 172)(49, 173)(50, 174)(51, 175)(52, 176)(53, 177)(54, 178)(55, 179)(56, 180)(57, 141)(58, 140)(59, 139)(60, 144)(61, 145)(62, 146)(63, 142)(64, 143)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 185)(78, 186)(79, 188)(80, 187)(81, 181)(82, 182)(83, 184)(84, 183)(85, 206)(86, 205)(87, 208)(88, 207)(89, 203)(90, 204)(91, 201)(92, 202)(93, 200)(94, 199)(95, 198)(96, 197)(97, 195)(98, 196)(99, 193)(100, 194)(101, 190)(102, 189)(103, 192)(104, 191)(209, 315)(210, 318)(211, 313)(212, 322)(213, 321)(214, 314)(215, 324)(216, 323)(217, 317)(218, 316)(219, 320)(220, 319)(221, 330)(222, 329)(223, 332)(224, 331)(225, 326)(226, 325)(227, 328)(228, 327)(229, 338)(230, 337)(231, 340)(232, 339)(233, 334)(234, 333)(235, 336)(236, 335)(237, 346)(238, 345)(239, 356)(240, 355)(241, 342)(242, 341)(243, 372)(244, 369)(245, 370)(246, 376)(247, 375)(248, 371)(249, 374)(250, 373)(251, 344)(252, 343)(253, 378)(254, 377)(255, 380)(256, 379)(257, 382)(258, 381)(259, 384)(260, 383)(261, 386)(262, 385)(263, 388)(264, 387)(265, 348)(266, 349)(267, 352)(268, 347)(269, 354)(270, 353)(271, 351)(272, 350)(273, 358)(274, 357)(275, 360)(276, 359)(277, 362)(278, 361)(279, 364)(280, 363)(281, 366)(282, 365)(283, 368)(284, 367)(285, 394)(286, 393)(287, 395)(288, 396)(289, 390)(290, 389)(291, 391)(292, 392)(293, 413)(294, 414)(295, 415)(296, 416)(297, 412)(298, 411)(299, 410)(300, 409)(301, 407)(302, 408)(303, 405)(304, 406)(305, 404)(306, 403)(307, 402)(308, 401)(309, 397)(310, 398)(311, 399)(312, 400)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1972
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.1975 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2^2 * Y3 * Y1^-2, (Y2^-1 * Y3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 6, 110, 214, 318)(3, 107, 211, 315, 7, 111, 215, 319)(5, 109, 213, 317, 10, 114, 218, 322)(8, 112, 216, 320, 13, 117, 221, 325)(9, 113, 217, 321, 14, 118, 222, 326)(11, 115, 219, 323, 15, 119, 223, 327)(12, 116, 220, 324, 16, 120, 224, 328)(17, 121, 225, 329, 21, 125, 229, 333)(18, 122, 226, 330, 22, 126, 230, 334)(19, 123, 227, 331, 23, 127, 231, 335)(20, 124, 228, 332, 24, 128, 232, 336)(25, 129, 233, 337, 29, 133, 237, 341)(26, 130, 234, 338, 30, 134, 238, 342)(27, 131, 235, 339, 31, 135, 239, 343)(28, 132, 236, 340, 32, 136, 240, 344)(33, 137, 241, 345, 57, 161, 265, 369)(34, 138, 242, 346, 59, 163, 267, 371)(35, 139, 243, 347, 63, 167, 271, 375)(36, 140, 244, 348, 67, 171, 275, 379)(37, 141, 245, 349, 69, 173, 277, 381)(38, 142, 246, 350, 66, 170, 274, 378)(39, 143, 247, 351, 74, 178, 282, 386)(40, 144, 248, 352, 61, 165, 269, 373)(41, 145, 249, 353, 62, 166, 270, 374)(42, 146, 250, 354, 78, 182, 286, 390)(43, 147, 251, 355, 80, 184, 288, 392)(44, 148, 252, 356, 65, 169, 273, 377)(45, 149, 253, 357, 83, 187, 291, 395)(46, 150, 254, 358, 85, 189, 293, 397)(47, 151, 255, 359, 71, 175, 279, 383)(48, 152, 256, 360, 72, 176, 280, 384)(49, 153, 257, 361, 89, 193, 297, 401)(50, 154, 258, 362, 91, 195, 299, 403)(51, 155, 259, 363, 93, 197, 301, 405)(52, 156, 260, 364, 95, 199, 303, 407)(53, 157, 261, 365, 97, 201, 305, 409)(54, 158, 262, 366, 99, 203, 307, 411)(55, 159, 263, 367, 101, 205, 309, 413)(56, 160, 264, 368, 103, 207, 311, 415)(58, 162, 266, 370, 102, 206, 310, 414)(60, 164, 268, 372, 104, 208, 312, 416)(64, 168, 272, 376, 84, 188, 292, 396)(68, 172, 276, 380, 81, 185, 289, 393)(70, 174, 278, 382, 79, 183, 287, 391)(73, 177, 281, 385, 90, 194, 298, 402)(75, 179, 283, 387, 86, 190, 294, 398)(76, 180, 284, 388, 94, 198, 302, 406)(77, 181, 285, 389, 96, 200, 304, 408)(82, 186, 290, 394, 92, 196, 300, 404)(87, 191, 295, 399, 98, 202, 306, 410)(88, 192, 296, 400, 100, 204, 308, 412)
	L = (1, 106)(2, 109)(3, 105)(4, 112)(5, 107)(6, 115)(7, 116)(8, 114)(9, 108)(10, 113)(11, 111)(12, 110)(13, 121)(14, 122)(15, 123)(16, 124)(17, 118)(18, 117)(19, 120)(20, 119)(21, 129)(22, 130)(23, 131)(24, 132)(25, 126)(26, 125)(27, 128)(28, 127)(29, 137)(30, 138)(31, 152)(32, 151)(33, 134)(34, 133)(35, 165)(36, 169)(37, 170)(38, 175)(39, 166)(40, 161)(41, 163)(42, 178)(43, 167)(44, 176)(45, 173)(46, 171)(47, 135)(48, 136)(49, 184)(50, 182)(51, 189)(52, 187)(53, 195)(54, 193)(55, 199)(56, 197)(57, 145)(58, 203)(59, 144)(60, 201)(61, 143)(62, 139)(63, 146)(64, 198)(65, 141)(66, 140)(67, 149)(68, 196)(69, 150)(70, 194)(71, 148)(72, 142)(73, 202)(74, 147)(75, 200)(76, 206)(77, 208)(78, 153)(79, 190)(80, 154)(81, 188)(82, 204)(83, 155)(84, 183)(85, 156)(86, 185)(87, 205)(88, 207)(89, 157)(90, 172)(91, 158)(92, 174)(93, 159)(94, 179)(95, 160)(96, 168)(97, 162)(98, 186)(99, 164)(100, 177)(101, 192)(102, 181)(103, 191)(104, 180)(209, 315)(210, 313)(211, 317)(212, 321)(213, 314)(214, 324)(215, 323)(216, 316)(217, 322)(218, 320)(219, 318)(220, 319)(221, 330)(222, 329)(223, 332)(224, 331)(225, 325)(226, 326)(227, 327)(228, 328)(229, 338)(230, 337)(231, 340)(232, 339)(233, 333)(234, 334)(235, 335)(236, 336)(237, 346)(238, 345)(239, 359)(240, 360)(241, 341)(242, 342)(243, 374)(244, 378)(245, 377)(246, 384)(247, 373)(248, 371)(249, 369)(250, 375)(251, 386)(252, 383)(253, 379)(254, 381)(255, 344)(256, 343)(257, 390)(258, 392)(259, 395)(260, 397)(261, 401)(262, 403)(263, 405)(264, 407)(265, 352)(266, 409)(267, 353)(268, 411)(269, 347)(270, 351)(271, 355)(272, 408)(273, 348)(274, 349)(275, 358)(276, 402)(277, 357)(278, 404)(279, 350)(280, 356)(281, 412)(282, 354)(283, 406)(284, 416)(285, 414)(286, 362)(287, 396)(288, 361)(289, 398)(290, 410)(291, 364)(292, 393)(293, 363)(294, 391)(295, 415)(296, 413)(297, 366)(298, 382)(299, 365)(300, 380)(301, 368)(302, 376)(303, 367)(304, 387)(305, 372)(306, 385)(307, 370)(308, 394)(309, 399)(310, 388)(311, 400)(312, 389)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1973
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1976 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1, (Y2^-2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^13, Y3^5 * Y1 * Y2 * Y3^6 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 11, 115)(4, 108, 10, 114)(5, 109, 17, 121)(6, 110, 8, 112)(7, 111, 20, 124)(9, 113, 26, 130)(12, 116, 21, 125)(13, 117, 30, 134)(14, 118, 25, 129)(15, 119, 28, 132)(16, 120, 23, 127)(18, 122, 35, 139)(19, 123, 24, 128)(22, 126, 39, 143)(27, 131, 44, 148)(29, 133, 47, 151)(31, 135, 41, 145)(32, 136, 40, 144)(33, 137, 49, 153)(34, 138, 46, 150)(36, 140, 52, 156)(37, 141, 43, 147)(38, 142, 55, 159)(42, 146, 57, 161)(45, 149, 60, 164)(48, 152, 63, 167)(50, 154, 65, 169)(51, 155, 62, 166)(53, 157, 68, 172)(54, 158, 59, 163)(56, 160, 71, 175)(58, 162, 73, 177)(61, 165, 76, 180)(64, 168, 79, 183)(66, 170, 81, 185)(67, 171, 78, 182)(69, 173, 84, 188)(70, 174, 75, 179)(72, 176, 87, 191)(74, 178, 89, 193)(77, 181, 92, 196)(80, 184, 95, 199)(82, 186, 97, 201)(83, 187, 94, 198)(85, 189, 99, 203)(86, 190, 91, 195)(88, 192, 101, 205)(90, 194, 100, 204)(93, 197, 98, 202)(96, 200, 103, 207)(102, 206, 104, 208)(209, 313, 211, 315, 220, 324, 213, 317)(210, 314, 215, 319, 229, 333, 217, 321)(212, 316, 222, 326, 239, 343, 224, 328)(214, 318, 221, 325, 240, 344, 226, 330)(216, 320, 231, 335, 248, 352, 233, 337)(218, 322, 230, 334, 249, 353, 235, 339)(219, 323, 232, 336, 225, 329, 237, 341)(223, 327, 234, 338, 246, 350, 228, 332)(227, 331, 241, 345, 255, 359, 244, 348)(236, 340, 250, 354, 263, 367, 253, 357)(238, 342, 251, 355, 243, 347, 256, 360)(242, 346, 252, 356, 264, 368, 247, 351)(245, 349, 258, 362, 271, 375, 261, 365)(254, 358, 266, 370, 279, 383, 269, 373)(257, 361, 267, 371, 260, 364, 272, 376)(259, 363, 268, 372, 280, 384, 265, 369)(262, 366, 274, 378, 287, 391, 277, 381)(270, 374, 282, 386, 295, 399, 285, 389)(273, 377, 283, 387, 276, 380, 288, 392)(275, 379, 284, 388, 296, 400, 281, 385)(278, 382, 290, 394, 303, 407, 293, 397)(286, 390, 298, 402, 309, 413, 301, 405)(289, 393, 299, 403, 292, 396, 304, 408)(291, 395, 300, 404, 310, 414, 297, 401)(294, 398, 306, 410, 311, 415, 308, 412)(302, 406, 307, 411, 312, 416, 305, 409)
	L = (1, 212)(2, 216)(3, 221)(4, 223)(5, 226)(6, 209)(7, 230)(8, 232)(9, 235)(10, 210)(11, 233)(12, 239)(13, 241)(14, 211)(15, 242)(16, 213)(17, 231)(18, 244)(19, 214)(20, 224)(21, 248)(22, 250)(23, 215)(24, 251)(25, 217)(26, 222)(27, 253)(28, 218)(29, 256)(30, 219)(31, 246)(32, 220)(33, 258)(34, 259)(35, 225)(36, 261)(37, 227)(38, 264)(39, 228)(40, 237)(41, 229)(42, 266)(43, 267)(44, 234)(45, 269)(46, 236)(47, 240)(48, 272)(49, 238)(50, 274)(51, 275)(52, 243)(53, 277)(54, 245)(55, 249)(56, 280)(57, 247)(58, 282)(59, 283)(60, 252)(61, 285)(62, 254)(63, 255)(64, 288)(65, 257)(66, 290)(67, 291)(68, 260)(69, 293)(70, 262)(71, 263)(72, 296)(73, 265)(74, 298)(75, 299)(76, 268)(77, 301)(78, 270)(79, 271)(80, 304)(81, 273)(82, 306)(83, 294)(84, 276)(85, 308)(86, 278)(87, 279)(88, 310)(89, 281)(90, 307)(91, 302)(92, 284)(93, 305)(94, 286)(95, 287)(96, 312)(97, 289)(98, 300)(99, 292)(100, 297)(101, 295)(102, 311)(103, 303)(104, 309)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1977 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 4})
Quotient :: dipole
Aut^+ = (C26 x C2) : C2 (small group id <104, 8>)
Aut   = C2 x ((C26 x C2) : C2) (small group id <208, 44>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^10, Y3^5 * Y1 * Y2 * Y3^6 * Y1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 105, 2, 106)(3, 107, 11, 115)(4, 108, 10, 114)(5, 109, 17, 121)(6, 110, 8, 112)(7, 111, 20, 124)(9, 113, 26, 130)(12, 116, 21, 125)(13, 117, 30, 134)(14, 118, 25, 129)(15, 119, 28, 132)(16, 120, 23, 127)(18, 122, 35, 139)(19, 123, 24, 128)(22, 126, 39, 143)(27, 131, 44, 148)(29, 133, 47, 151)(31, 135, 41, 145)(32, 136, 40, 144)(33, 137, 49, 153)(34, 138, 46, 150)(36, 140, 52, 156)(37, 141, 43, 147)(38, 142, 55, 159)(42, 146, 57, 161)(45, 149, 60, 164)(48, 152, 63, 167)(50, 154, 65, 169)(51, 155, 62, 166)(53, 157, 68, 172)(54, 158, 59, 163)(56, 160, 71, 175)(58, 162, 73, 177)(61, 165, 76, 180)(64, 168, 79, 183)(66, 170, 81, 185)(67, 171, 78, 182)(69, 173, 84, 188)(70, 174, 75, 179)(72, 176, 87, 191)(74, 178, 89, 193)(77, 181, 92, 196)(80, 184, 95, 199)(82, 186, 97, 201)(83, 187, 94, 198)(85, 189, 100, 204)(86, 190, 91, 195)(88, 192, 103, 207)(90, 194, 98, 202)(93, 197, 101, 205)(96, 200, 99, 203)(102, 206, 104, 208)(209, 313, 211, 315, 220, 324, 213, 317)(210, 314, 215, 319, 229, 333, 217, 321)(212, 316, 222, 326, 239, 343, 224, 328)(214, 318, 221, 325, 240, 344, 226, 330)(216, 320, 231, 335, 248, 352, 233, 337)(218, 322, 230, 334, 249, 353, 235, 339)(219, 323, 232, 336, 225, 329, 237, 341)(223, 327, 234, 338, 246, 350, 228, 332)(227, 331, 241, 345, 255, 359, 244, 348)(236, 340, 250, 354, 263, 367, 253, 357)(238, 342, 251, 355, 243, 347, 256, 360)(242, 346, 252, 356, 264, 368, 247, 351)(245, 349, 258, 362, 271, 375, 261, 365)(254, 358, 266, 370, 279, 383, 269, 373)(257, 361, 267, 371, 260, 364, 272, 376)(259, 363, 268, 372, 280, 384, 265, 369)(262, 366, 274, 378, 287, 391, 277, 381)(270, 374, 282, 386, 295, 399, 285, 389)(273, 377, 283, 387, 276, 380, 288, 392)(275, 379, 284, 388, 296, 400, 281, 385)(278, 382, 290, 394, 303, 407, 293, 397)(286, 390, 298, 402, 311, 415, 301, 405)(289, 393, 299, 403, 292, 396, 304, 408)(291, 395, 300, 404, 310, 414, 297, 401)(294, 398, 306, 410, 307, 411, 309, 413)(302, 406, 305, 409, 312, 416, 308, 412)
	L = (1, 212)(2, 216)(3, 221)(4, 223)(5, 226)(6, 209)(7, 230)(8, 232)(9, 235)(10, 210)(11, 233)(12, 239)(13, 241)(14, 211)(15, 242)(16, 213)(17, 231)(18, 244)(19, 214)(20, 224)(21, 248)(22, 250)(23, 215)(24, 251)(25, 217)(26, 222)(27, 253)(28, 218)(29, 256)(30, 219)(31, 246)(32, 220)(33, 258)(34, 259)(35, 225)(36, 261)(37, 227)(38, 264)(39, 228)(40, 237)(41, 229)(42, 266)(43, 267)(44, 234)(45, 269)(46, 236)(47, 240)(48, 272)(49, 238)(50, 274)(51, 275)(52, 243)(53, 277)(54, 245)(55, 249)(56, 280)(57, 247)(58, 282)(59, 283)(60, 252)(61, 285)(62, 254)(63, 255)(64, 288)(65, 257)(66, 290)(67, 291)(68, 260)(69, 293)(70, 262)(71, 263)(72, 296)(73, 265)(74, 298)(75, 299)(76, 268)(77, 301)(78, 270)(79, 271)(80, 304)(81, 273)(82, 306)(83, 307)(84, 276)(85, 309)(86, 278)(87, 279)(88, 310)(89, 281)(90, 305)(91, 312)(92, 284)(93, 308)(94, 286)(95, 287)(96, 302)(97, 289)(98, 297)(99, 303)(100, 292)(101, 300)(102, 294)(103, 295)(104, 311)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 78 e = 208 f = 78
	degree seq :: [ 4^52, 8^26 ]

E27.1978 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, Y1^4, R * Y1 * R * Y2, (Y2, Y1^-1), (R * Y3)^2, Y2^4, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2^2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 4, 108)(2, 106, 9, 113)(3, 107, 11, 115)(5, 109, 16, 120)(6, 110, 17, 121)(7, 111, 18, 122)(8, 112, 19, 123)(10, 114, 24, 128)(12, 116, 30, 134)(13, 117, 32, 136)(14, 118, 33, 137)(15, 119, 34, 138)(20, 124, 40, 144)(21, 125, 42, 146)(22, 126, 43, 147)(23, 127, 44, 148)(25, 129, 46, 150)(26, 130, 48, 152)(27, 131, 49, 153)(28, 132, 50, 154)(29, 133, 51, 155)(31, 135, 54, 158)(35, 139, 58, 162)(36, 140, 60, 164)(37, 141, 61, 165)(38, 142, 62, 166)(39, 143, 63, 167)(41, 145, 66, 170)(45, 149, 69, 173)(47, 151, 72, 176)(52, 156, 79, 183)(53, 157, 80, 184)(55, 159, 81, 185)(56, 160, 82, 186)(57, 161, 83, 187)(59, 163, 86, 190)(64, 168, 89, 193)(65, 169, 90, 194)(67, 171, 74, 178)(68, 172, 73, 177)(70, 174, 77, 181)(71, 175, 76, 180)(75, 179, 96, 200)(78, 182, 98, 202)(84, 188, 93, 197)(85, 189, 92, 196)(87, 191, 101, 205)(88, 192, 102, 206)(91, 195, 97, 201)(94, 198, 95, 199)(99, 203, 104, 208)(100, 204, 103, 207)(209, 210, 215, 213)(211, 216, 214, 218)(212, 220, 237, 222)(217, 228, 247, 230)(219, 233, 253, 235)(221, 227, 223, 239)(224, 236, 255, 234)(225, 231, 249, 229)(226, 243, 265, 245)(232, 246, 267, 244)(238, 256, 281, 261)(240, 263, 272, 252)(241, 264, 273, 248)(242, 257, 282, 260)(250, 275, 292, 270)(251, 276, 293, 266)(254, 268, 289, 279)(258, 269, 290, 278)(259, 283, 303, 285)(262, 286, 305, 284)(271, 295, 304, 288)(274, 296, 306, 287)(277, 299, 311, 301)(280, 302, 312, 300)(291, 307, 309, 298)(294, 308, 310, 297)(313, 315, 319, 318)(314, 320, 317, 322)(316, 325, 341, 327)(321, 333, 351, 335)(323, 338, 357, 340)(324, 331, 326, 343)(328, 339, 359, 337)(329, 334, 353, 332)(330, 348, 369, 350)(336, 349, 371, 347)(342, 364, 385, 361)(344, 352, 376, 368)(345, 356, 377, 367)(346, 365, 386, 360)(354, 370, 396, 380)(355, 374, 397, 379)(358, 382, 393, 373)(362, 383, 394, 372)(363, 388, 407, 390)(366, 389, 409, 387)(375, 391, 408, 400)(378, 392, 410, 399)(381, 404, 415, 406)(384, 405, 416, 403)(395, 401, 413, 412)(398, 402, 414, 411)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1987
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1979 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (Y2^-1, Y1^-1), R * Y1 * R * Y2, Y2^2 * Y1^-2, (R * Y3)^2, Y1^2 * Y2^2, (Y1 * Y3 * Y2)^2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2, Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 4, 108)(2, 106, 9, 113)(3, 107, 11, 115)(5, 109, 16, 120)(6, 110, 17, 121)(7, 111, 18, 122)(8, 112, 19, 123)(10, 114, 24, 128)(12, 116, 30, 134)(13, 117, 32, 136)(14, 118, 33, 137)(15, 119, 34, 138)(20, 124, 40, 144)(21, 125, 42, 146)(22, 126, 43, 147)(23, 127, 44, 148)(25, 129, 46, 150)(26, 130, 48, 152)(27, 131, 49, 153)(28, 132, 50, 154)(29, 133, 51, 155)(31, 135, 54, 158)(35, 139, 58, 162)(36, 140, 60, 164)(37, 141, 61, 165)(38, 142, 62, 166)(39, 143, 63, 167)(41, 145, 66, 170)(45, 149, 69, 173)(47, 151, 72, 176)(52, 156, 79, 183)(53, 157, 80, 184)(55, 159, 81, 185)(56, 160, 82, 186)(57, 161, 83, 187)(59, 163, 84, 188)(64, 168, 71, 175)(65, 169, 70, 174)(67, 171, 78, 182)(68, 172, 75, 179)(73, 177, 93, 197)(74, 178, 94, 198)(76, 180, 97, 201)(77, 181, 98, 202)(85, 189, 90, 194)(86, 190, 87, 191)(88, 192, 96, 200)(89, 193, 95, 199)(91, 195, 103, 207)(92, 196, 104, 208)(99, 203, 102, 206)(100, 204, 101, 205)(209, 210, 215, 213)(211, 216, 214, 218)(212, 220, 237, 222)(217, 228, 247, 230)(219, 233, 253, 235)(221, 227, 223, 239)(224, 236, 255, 234)(225, 231, 249, 229)(226, 243, 265, 245)(232, 246, 267, 244)(238, 256, 281, 261)(240, 263, 272, 252)(241, 264, 273, 248)(242, 257, 282, 260)(250, 275, 287, 270)(251, 276, 288, 266)(254, 268, 293, 279)(258, 269, 294, 278)(259, 283, 303, 285)(262, 286, 304, 284)(271, 295, 309, 297)(274, 298, 310, 296)(277, 289, 305, 300)(280, 290, 306, 299)(291, 301, 311, 308)(292, 302, 312, 307)(313, 315, 319, 318)(314, 320, 317, 322)(316, 325, 341, 327)(321, 333, 351, 335)(323, 338, 357, 340)(324, 331, 326, 343)(328, 339, 359, 337)(329, 334, 353, 332)(330, 348, 369, 350)(336, 349, 371, 347)(342, 364, 385, 361)(344, 352, 376, 368)(345, 356, 377, 367)(346, 365, 386, 360)(354, 370, 391, 380)(355, 374, 392, 379)(358, 382, 397, 373)(362, 383, 398, 372)(363, 388, 407, 390)(366, 389, 408, 387)(375, 400, 413, 402)(378, 401, 414, 399)(381, 403, 409, 394)(384, 404, 410, 393)(395, 411, 415, 406)(396, 412, 416, 405)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1986
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1980 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y2^-2, Y1^2 * Y2^2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1, Y2^-1), Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y1^2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 105, 4, 108)(2, 106, 9, 113)(3, 107, 11, 115)(5, 109, 16, 120)(6, 110, 17, 121)(7, 111, 18, 122)(8, 112, 19, 123)(10, 114, 24, 128)(12, 116, 30, 134)(13, 117, 32, 136)(14, 118, 33, 137)(15, 119, 34, 138)(20, 124, 40, 144)(21, 125, 42, 146)(22, 126, 43, 147)(23, 127, 44, 148)(25, 129, 46, 150)(26, 130, 48, 152)(27, 131, 49, 153)(28, 132, 50, 154)(29, 133, 51, 155)(31, 135, 54, 158)(35, 139, 58, 162)(36, 140, 60, 164)(37, 141, 61, 165)(38, 142, 62, 166)(39, 143, 63, 167)(41, 145, 66, 170)(45, 149, 69, 173)(47, 151, 72, 176)(52, 156, 79, 183)(53, 157, 80, 184)(55, 159, 81, 185)(56, 160, 82, 186)(57, 161, 83, 187)(59, 163, 86, 190)(64, 168, 89, 193)(65, 169, 90, 194)(67, 171, 73, 177)(68, 172, 74, 178)(70, 174, 76, 180)(71, 175, 77, 181)(75, 179, 96, 200)(78, 182, 98, 202)(84, 188, 92, 196)(85, 189, 93, 197)(87, 191, 101, 205)(88, 192, 102, 206)(91, 195, 95, 199)(94, 198, 97, 201)(99, 203, 103, 207)(100, 204, 104, 208)(209, 210, 215, 213)(211, 216, 214, 218)(212, 220, 237, 222)(217, 228, 247, 230)(219, 233, 253, 235)(221, 227, 223, 239)(224, 236, 255, 234)(225, 231, 249, 229)(226, 243, 265, 245)(232, 246, 267, 244)(238, 256, 281, 261)(240, 263, 272, 252)(241, 264, 273, 248)(242, 257, 282, 260)(250, 275, 292, 270)(251, 276, 293, 266)(254, 268, 290, 279)(258, 269, 289, 278)(259, 283, 303, 285)(262, 286, 305, 284)(271, 295, 306, 287)(274, 296, 304, 288)(277, 299, 311, 301)(280, 302, 312, 300)(291, 307, 310, 297)(294, 308, 309, 298)(313, 315, 319, 318)(314, 320, 317, 322)(316, 325, 341, 327)(321, 333, 351, 335)(323, 338, 357, 340)(324, 331, 326, 343)(328, 339, 359, 337)(329, 334, 353, 332)(330, 348, 369, 350)(336, 349, 371, 347)(342, 364, 385, 361)(344, 352, 376, 368)(345, 356, 377, 367)(346, 365, 386, 360)(354, 370, 396, 380)(355, 374, 397, 379)(358, 382, 394, 373)(362, 383, 393, 372)(363, 388, 407, 390)(366, 389, 409, 387)(375, 392, 410, 400)(378, 391, 408, 399)(381, 404, 415, 406)(384, 405, 416, 403)(395, 402, 414, 412)(398, 401, 413, 411)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1985
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1981 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^4, (Y2^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, Y1^-2 * Y2^2, R * Y1 * R * Y2, Y1^-2 * Y2^-2, (Y2 * Y1^-1)^2, (Y1 * Y3 * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1 * Y3 * Y1^-1 * Y3, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 4, 108)(2, 106, 9, 113)(3, 107, 11, 115)(5, 109, 16, 120)(6, 110, 17, 121)(7, 111, 18, 122)(8, 112, 19, 123)(10, 114, 24, 128)(12, 116, 30, 134)(13, 117, 32, 136)(14, 118, 33, 137)(15, 119, 34, 138)(20, 124, 40, 144)(21, 125, 42, 146)(22, 126, 43, 147)(23, 127, 44, 148)(25, 129, 46, 150)(26, 130, 48, 152)(27, 131, 49, 153)(28, 132, 50, 154)(29, 133, 51, 155)(31, 135, 54, 158)(35, 139, 58, 162)(36, 140, 60, 164)(37, 141, 61, 165)(38, 142, 62, 166)(39, 143, 63, 167)(41, 145, 66, 170)(45, 149, 69, 173)(47, 151, 72, 176)(52, 156, 79, 183)(53, 157, 80, 184)(55, 159, 81, 185)(56, 160, 82, 186)(57, 161, 83, 187)(59, 163, 84, 188)(64, 168, 70, 174)(65, 169, 71, 175)(67, 171, 75, 179)(68, 172, 78, 182)(73, 177, 93, 197)(74, 178, 94, 198)(76, 180, 97, 201)(77, 181, 98, 202)(85, 189, 87, 191)(86, 190, 90, 194)(88, 192, 95, 199)(89, 193, 96, 200)(91, 195, 103, 207)(92, 196, 104, 208)(99, 203, 101, 205)(100, 204, 102, 206)(209, 210, 215, 213)(211, 216, 214, 218)(212, 220, 237, 222)(217, 228, 247, 230)(219, 233, 253, 235)(221, 227, 223, 239)(224, 236, 255, 234)(225, 231, 249, 229)(226, 243, 265, 245)(232, 246, 267, 244)(238, 256, 281, 261)(240, 263, 272, 252)(241, 264, 273, 248)(242, 257, 282, 260)(250, 275, 288, 270)(251, 276, 287, 266)(254, 268, 293, 279)(258, 269, 294, 278)(259, 283, 303, 285)(262, 286, 304, 284)(271, 295, 309, 297)(274, 298, 310, 296)(277, 290, 306, 300)(280, 289, 305, 299)(291, 302, 312, 308)(292, 301, 311, 307)(313, 315, 319, 318)(314, 320, 317, 322)(316, 325, 341, 327)(321, 333, 351, 335)(323, 338, 357, 340)(324, 331, 326, 343)(328, 339, 359, 337)(329, 334, 353, 332)(330, 348, 369, 350)(336, 349, 371, 347)(342, 364, 385, 361)(344, 352, 376, 368)(345, 356, 377, 367)(346, 365, 386, 360)(354, 370, 392, 380)(355, 374, 391, 379)(358, 382, 397, 373)(362, 383, 398, 372)(363, 388, 407, 390)(366, 389, 408, 387)(375, 400, 413, 402)(378, 401, 414, 399)(381, 403, 410, 393)(384, 404, 409, 394)(395, 411, 416, 405)(396, 412, 415, 406)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1984
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1982 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = C2 x C2 x (C13 : C4) (small group id <208, 49>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2^-1 * Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^2 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 4, 108)(2, 106, 6, 110)(3, 107, 7, 111)(5, 109, 10, 114)(8, 112, 16, 120)(9, 113, 17, 121)(11, 115, 21, 125)(12, 116, 22, 126)(13, 117, 24, 128)(14, 118, 25, 129)(15, 119, 26, 130)(18, 122, 30, 134)(19, 123, 31, 135)(20, 124, 32, 136)(23, 127, 35, 139)(27, 131, 40, 144)(28, 132, 41, 145)(29, 133, 42, 146)(33, 137, 47, 151)(34, 138, 48, 152)(36, 140, 51, 155)(37, 141, 52, 156)(38, 142, 54, 158)(39, 143, 55, 159)(43, 147, 60, 164)(44, 148, 61, 165)(45, 149, 63, 167)(46, 150, 64, 168)(49, 153, 68, 172)(50, 154, 69, 173)(53, 157, 72, 176)(56, 160, 75, 179)(57, 161, 76, 180)(58, 162, 78, 182)(59, 163, 79, 183)(62, 166, 82, 186)(65, 169, 85, 189)(66, 170, 86, 190)(67, 171, 83, 187)(70, 174, 88, 192)(71, 175, 89, 193)(73, 177, 77, 181)(74, 178, 90, 194)(80, 184, 94, 198)(81, 185, 95, 199)(84, 188, 96, 200)(87, 191, 97, 201)(91, 195, 93, 197)(92, 196, 100, 204)(98, 202, 102, 206)(99, 203, 103, 207)(101, 205, 104, 208)(209, 210, 213, 211)(212, 216, 223, 217)(214, 219, 228, 220)(215, 221, 231, 222)(218, 226, 237, 227)(224, 233, 245, 235)(225, 236, 241, 229)(230, 242, 251, 238)(232, 239, 252, 244)(234, 246, 261, 247)(240, 253, 270, 254)(243, 257, 275, 258)(248, 264, 281, 262)(249, 263, 282, 265)(250, 266, 285, 267)(255, 273, 291, 271)(256, 272, 292, 274)(259, 278, 290, 276)(260, 277, 295, 279)(268, 288, 280, 286)(269, 287, 301, 289)(283, 297, 307, 299)(284, 300, 305, 293)(294, 306, 298, 302)(296, 303, 309, 304)(308, 310, 312, 311)(313, 315, 317, 314)(316, 321, 327, 320)(318, 324, 332, 323)(319, 326, 335, 325)(322, 331, 341, 330)(328, 339, 349, 337)(329, 333, 345, 340)(334, 342, 355, 346)(336, 348, 356, 343)(338, 351, 365, 350)(344, 358, 374, 357)(347, 362, 379, 361)(352, 366, 385, 368)(353, 369, 386, 367)(354, 371, 389, 370)(359, 375, 395, 377)(360, 378, 396, 376)(363, 380, 394, 382)(364, 383, 399, 381)(372, 390, 384, 392)(373, 393, 405, 391)(387, 403, 411, 401)(388, 397, 409, 404)(398, 406, 402, 410)(400, 408, 413, 407)(412, 415, 416, 414)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1989
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1983 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = C2 x C2 x (C13 : C4) (small group id <208, 49>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2 * Y1^-3, R * Y2 * R * Y1, Y2^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 4, 108)(2, 106, 6, 110)(3, 107, 7, 111)(5, 109, 10, 114)(8, 112, 16, 120)(9, 113, 17, 121)(11, 115, 21, 125)(12, 116, 22, 126)(13, 117, 24, 128)(14, 118, 25, 129)(15, 119, 26, 130)(18, 122, 30, 134)(19, 123, 31, 135)(20, 124, 32, 136)(23, 127, 35, 139)(27, 131, 40, 144)(28, 132, 41, 145)(29, 133, 42, 146)(33, 137, 47, 151)(34, 138, 48, 152)(36, 140, 51, 155)(37, 141, 52, 156)(38, 142, 54, 158)(39, 143, 55, 159)(43, 147, 60, 164)(44, 148, 61, 165)(45, 149, 63, 167)(46, 150, 64, 168)(49, 153, 68, 172)(50, 154, 69, 173)(53, 157, 72, 176)(56, 160, 75, 179)(57, 161, 76, 180)(58, 162, 78, 182)(59, 163, 79, 183)(62, 166, 82, 186)(65, 169, 85, 189)(66, 170, 86, 190)(67, 171, 84, 188)(70, 174, 88, 192)(71, 175, 89, 193)(73, 177, 90, 194)(74, 178, 77, 181)(80, 184, 94, 198)(81, 185, 95, 199)(83, 187, 96, 200)(87, 191, 98, 202)(91, 195, 100, 204)(92, 196, 93, 197)(97, 201, 102, 206)(99, 203, 103, 207)(101, 205, 104, 208)(209, 210, 213, 211)(212, 216, 223, 217)(214, 219, 228, 220)(215, 221, 231, 222)(218, 226, 237, 227)(224, 233, 245, 235)(225, 236, 241, 229)(230, 242, 251, 238)(232, 239, 252, 244)(234, 246, 261, 247)(240, 253, 270, 254)(243, 257, 275, 258)(248, 264, 281, 262)(249, 263, 282, 265)(250, 266, 285, 267)(255, 273, 291, 271)(256, 272, 292, 274)(259, 278, 295, 276)(260, 277, 290, 279)(268, 288, 301, 286)(269, 287, 280, 289)(283, 297, 304, 299)(284, 300, 305, 293)(294, 306, 309, 302)(296, 303, 298, 307)(308, 310, 312, 311)(313, 315, 317, 314)(316, 321, 327, 320)(318, 324, 332, 323)(319, 326, 335, 325)(322, 331, 341, 330)(328, 339, 349, 337)(329, 333, 345, 340)(334, 342, 355, 346)(336, 348, 356, 343)(338, 351, 365, 350)(344, 358, 374, 357)(347, 362, 379, 361)(352, 366, 385, 368)(353, 369, 386, 367)(354, 371, 389, 370)(359, 375, 395, 377)(360, 378, 396, 376)(363, 380, 399, 382)(364, 383, 394, 381)(372, 390, 405, 392)(373, 393, 384, 391)(387, 403, 408, 401)(388, 397, 409, 404)(398, 406, 413, 410)(400, 411, 402, 407)(412, 415, 416, 414)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.1988
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.1984 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, Y1^4, R * Y1 * R * Y2, (Y2, Y1^-1), (R * Y3)^2, Y2^4, Y2 * Y1 * Y3 * Y1^-1 * Y2^-1 * Y3, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2^2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 9, 113, 217, 321)(3, 107, 211, 315, 11, 115, 219, 323)(5, 109, 213, 317, 16, 120, 224, 328)(6, 110, 214, 318, 17, 121, 225, 329)(7, 111, 215, 319, 18, 122, 226, 330)(8, 112, 216, 320, 19, 123, 227, 331)(10, 114, 218, 322, 24, 128, 232, 336)(12, 116, 220, 324, 30, 134, 238, 342)(13, 117, 221, 325, 32, 136, 240, 344)(14, 118, 222, 326, 33, 137, 241, 345)(15, 119, 223, 327, 34, 138, 242, 346)(20, 124, 228, 332, 40, 144, 248, 352)(21, 125, 229, 333, 42, 146, 250, 354)(22, 126, 230, 334, 43, 147, 251, 355)(23, 127, 231, 335, 44, 148, 252, 356)(25, 129, 233, 337, 46, 150, 254, 358)(26, 130, 234, 338, 48, 152, 256, 360)(27, 131, 235, 339, 49, 153, 257, 361)(28, 132, 236, 340, 50, 154, 258, 362)(29, 133, 237, 341, 51, 155, 259, 363)(31, 135, 239, 343, 54, 158, 262, 366)(35, 139, 243, 347, 58, 162, 266, 370)(36, 140, 244, 348, 60, 164, 268, 372)(37, 141, 245, 349, 61, 165, 269, 373)(38, 142, 246, 350, 62, 166, 270, 374)(39, 143, 247, 351, 63, 167, 271, 375)(41, 145, 249, 353, 66, 170, 274, 378)(45, 149, 253, 357, 69, 173, 277, 381)(47, 151, 255, 359, 72, 176, 280, 384)(52, 156, 260, 364, 79, 183, 287, 391)(53, 157, 261, 365, 80, 184, 288, 392)(55, 159, 263, 367, 81, 185, 289, 393)(56, 160, 264, 368, 82, 186, 290, 394)(57, 161, 265, 369, 83, 187, 291, 395)(59, 163, 267, 371, 86, 190, 294, 398)(64, 168, 272, 376, 89, 193, 297, 401)(65, 169, 273, 377, 90, 194, 298, 402)(67, 171, 275, 379, 74, 178, 282, 386)(68, 172, 276, 380, 73, 177, 281, 385)(70, 174, 278, 382, 77, 181, 285, 389)(71, 175, 279, 383, 76, 180, 284, 388)(75, 179, 283, 387, 96, 200, 304, 408)(78, 182, 286, 390, 98, 202, 306, 410)(84, 188, 292, 396, 93, 197, 301, 405)(85, 189, 293, 397, 92, 196, 300, 404)(87, 191, 295, 399, 101, 205, 309, 413)(88, 192, 296, 400, 102, 206, 310, 414)(91, 195, 299, 403, 97, 201, 305, 409)(94, 198, 302, 406, 95, 199, 303, 407)(99, 203, 307, 411, 104, 208, 312, 416)(100, 204, 308, 412, 103, 207, 311, 415)
	L = (1, 106)(2, 111)(3, 112)(4, 116)(5, 105)(6, 114)(7, 109)(8, 110)(9, 124)(10, 107)(11, 129)(12, 133)(13, 123)(14, 108)(15, 135)(16, 132)(17, 127)(18, 139)(19, 119)(20, 143)(21, 121)(22, 113)(23, 145)(24, 142)(25, 149)(26, 120)(27, 115)(28, 151)(29, 118)(30, 152)(31, 117)(32, 159)(33, 160)(34, 153)(35, 161)(36, 128)(37, 122)(38, 163)(39, 126)(40, 137)(41, 125)(42, 171)(43, 172)(44, 136)(45, 131)(46, 164)(47, 130)(48, 177)(49, 178)(50, 165)(51, 179)(52, 138)(53, 134)(54, 182)(55, 168)(56, 169)(57, 141)(58, 147)(59, 140)(60, 185)(61, 186)(62, 146)(63, 191)(64, 148)(65, 144)(66, 192)(67, 188)(68, 189)(69, 195)(70, 154)(71, 150)(72, 198)(73, 157)(74, 156)(75, 199)(76, 158)(77, 155)(78, 201)(79, 170)(80, 167)(81, 175)(82, 174)(83, 203)(84, 166)(85, 162)(86, 204)(87, 200)(88, 202)(89, 190)(90, 187)(91, 207)(92, 176)(93, 173)(94, 208)(95, 181)(96, 184)(97, 180)(98, 183)(99, 205)(100, 206)(101, 194)(102, 193)(103, 197)(104, 196)(209, 315)(210, 320)(211, 319)(212, 325)(213, 322)(214, 313)(215, 318)(216, 317)(217, 333)(218, 314)(219, 338)(220, 331)(221, 341)(222, 343)(223, 316)(224, 339)(225, 334)(226, 348)(227, 326)(228, 329)(229, 351)(230, 353)(231, 321)(232, 349)(233, 328)(234, 357)(235, 359)(236, 323)(237, 327)(238, 364)(239, 324)(240, 352)(241, 356)(242, 365)(243, 336)(244, 369)(245, 371)(246, 330)(247, 335)(248, 376)(249, 332)(250, 370)(251, 374)(252, 377)(253, 340)(254, 382)(255, 337)(256, 346)(257, 342)(258, 383)(259, 388)(260, 385)(261, 386)(262, 389)(263, 345)(264, 344)(265, 350)(266, 396)(267, 347)(268, 362)(269, 358)(270, 397)(271, 391)(272, 368)(273, 367)(274, 392)(275, 355)(276, 354)(277, 404)(278, 393)(279, 394)(280, 405)(281, 361)(282, 360)(283, 366)(284, 407)(285, 409)(286, 363)(287, 408)(288, 410)(289, 373)(290, 372)(291, 401)(292, 380)(293, 379)(294, 402)(295, 378)(296, 375)(297, 413)(298, 414)(299, 384)(300, 415)(301, 416)(302, 381)(303, 390)(304, 400)(305, 387)(306, 399)(307, 398)(308, 395)(309, 412)(310, 411)(311, 406)(312, 403)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1981
Transitivity :: VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1985 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^4, (Y2^-1, Y1^-1), R * Y1 * R * Y2, Y2^2 * Y1^-2, (R * Y3)^2, Y1^2 * Y2^2, (Y1 * Y3 * Y2)^2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2, Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 9, 113, 217, 321)(3, 107, 211, 315, 11, 115, 219, 323)(5, 109, 213, 317, 16, 120, 224, 328)(6, 110, 214, 318, 17, 121, 225, 329)(7, 111, 215, 319, 18, 122, 226, 330)(8, 112, 216, 320, 19, 123, 227, 331)(10, 114, 218, 322, 24, 128, 232, 336)(12, 116, 220, 324, 30, 134, 238, 342)(13, 117, 221, 325, 32, 136, 240, 344)(14, 118, 222, 326, 33, 137, 241, 345)(15, 119, 223, 327, 34, 138, 242, 346)(20, 124, 228, 332, 40, 144, 248, 352)(21, 125, 229, 333, 42, 146, 250, 354)(22, 126, 230, 334, 43, 147, 251, 355)(23, 127, 231, 335, 44, 148, 252, 356)(25, 129, 233, 337, 46, 150, 254, 358)(26, 130, 234, 338, 48, 152, 256, 360)(27, 131, 235, 339, 49, 153, 257, 361)(28, 132, 236, 340, 50, 154, 258, 362)(29, 133, 237, 341, 51, 155, 259, 363)(31, 135, 239, 343, 54, 158, 262, 366)(35, 139, 243, 347, 58, 162, 266, 370)(36, 140, 244, 348, 60, 164, 268, 372)(37, 141, 245, 349, 61, 165, 269, 373)(38, 142, 246, 350, 62, 166, 270, 374)(39, 143, 247, 351, 63, 167, 271, 375)(41, 145, 249, 353, 66, 170, 274, 378)(45, 149, 253, 357, 69, 173, 277, 381)(47, 151, 255, 359, 72, 176, 280, 384)(52, 156, 260, 364, 79, 183, 287, 391)(53, 157, 261, 365, 80, 184, 288, 392)(55, 159, 263, 367, 81, 185, 289, 393)(56, 160, 264, 368, 82, 186, 290, 394)(57, 161, 265, 369, 83, 187, 291, 395)(59, 163, 267, 371, 84, 188, 292, 396)(64, 168, 272, 376, 71, 175, 279, 383)(65, 169, 273, 377, 70, 174, 278, 382)(67, 171, 275, 379, 78, 182, 286, 390)(68, 172, 276, 380, 75, 179, 283, 387)(73, 177, 281, 385, 93, 197, 301, 405)(74, 178, 282, 386, 94, 198, 302, 406)(76, 180, 284, 388, 97, 201, 305, 409)(77, 181, 285, 389, 98, 202, 306, 410)(85, 189, 293, 397, 90, 194, 298, 402)(86, 190, 294, 398, 87, 191, 295, 399)(88, 192, 296, 400, 96, 200, 304, 408)(89, 193, 297, 401, 95, 199, 303, 407)(91, 195, 299, 403, 103, 207, 311, 415)(92, 196, 300, 404, 104, 208, 312, 416)(99, 203, 307, 411, 102, 206, 310, 414)(100, 204, 308, 412, 101, 205, 309, 413)
	L = (1, 106)(2, 111)(3, 112)(4, 116)(5, 105)(6, 114)(7, 109)(8, 110)(9, 124)(10, 107)(11, 129)(12, 133)(13, 123)(14, 108)(15, 135)(16, 132)(17, 127)(18, 139)(19, 119)(20, 143)(21, 121)(22, 113)(23, 145)(24, 142)(25, 149)(26, 120)(27, 115)(28, 151)(29, 118)(30, 152)(31, 117)(32, 159)(33, 160)(34, 153)(35, 161)(36, 128)(37, 122)(38, 163)(39, 126)(40, 137)(41, 125)(42, 171)(43, 172)(44, 136)(45, 131)(46, 164)(47, 130)(48, 177)(49, 178)(50, 165)(51, 179)(52, 138)(53, 134)(54, 182)(55, 168)(56, 169)(57, 141)(58, 147)(59, 140)(60, 189)(61, 190)(62, 146)(63, 191)(64, 148)(65, 144)(66, 194)(67, 183)(68, 184)(69, 185)(70, 154)(71, 150)(72, 186)(73, 157)(74, 156)(75, 199)(76, 158)(77, 155)(78, 200)(79, 166)(80, 162)(81, 201)(82, 202)(83, 197)(84, 198)(85, 175)(86, 174)(87, 205)(88, 170)(89, 167)(90, 206)(91, 176)(92, 173)(93, 207)(94, 208)(95, 181)(96, 180)(97, 196)(98, 195)(99, 188)(100, 187)(101, 193)(102, 192)(103, 204)(104, 203)(209, 315)(210, 320)(211, 319)(212, 325)(213, 322)(214, 313)(215, 318)(216, 317)(217, 333)(218, 314)(219, 338)(220, 331)(221, 341)(222, 343)(223, 316)(224, 339)(225, 334)(226, 348)(227, 326)(228, 329)(229, 351)(230, 353)(231, 321)(232, 349)(233, 328)(234, 357)(235, 359)(236, 323)(237, 327)(238, 364)(239, 324)(240, 352)(241, 356)(242, 365)(243, 336)(244, 369)(245, 371)(246, 330)(247, 335)(248, 376)(249, 332)(250, 370)(251, 374)(252, 377)(253, 340)(254, 382)(255, 337)(256, 346)(257, 342)(258, 383)(259, 388)(260, 385)(261, 386)(262, 389)(263, 345)(264, 344)(265, 350)(266, 391)(267, 347)(268, 362)(269, 358)(270, 392)(271, 400)(272, 368)(273, 367)(274, 401)(275, 355)(276, 354)(277, 403)(278, 397)(279, 398)(280, 404)(281, 361)(282, 360)(283, 366)(284, 407)(285, 408)(286, 363)(287, 380)(288, 379)(289, 384)(290, 381)(291, 411)(292, 412)(293, 373)(294, 372)(295, 378)(296, 413)(297, 414)(298, 375)(299, 409)(300, 410)(301, 396)(302, 395)(303, 390)(304, 387)(305, 394)(306, 393)(307, 415)(308, 416)(309, 402)(310, 399)(311, 406)(312, 405)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1980
Transitivity :: VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1986 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y2^-2, Y1^2 * Y2^2, Y1^4, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1, Y2^-1), Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y1^2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 9, 113, 217, 321)(3, 107, 211, 315, 11, 115, 219, 323)(5, 109, 213, 317, 16, 120, 224, 328)(6, 110, 214, 318, 17, 121, 225, 329)(7, 111, 215, 319, 18, 122, 226, 330)(8, 112, 216, 320, 19, 123, 227, 331)(10, 114, 218, 322, 24, 128, 232, 336)(12, 116, 220, 324, 30, 134, 238, 342)(13, 117, 221, 325, 32, 136, 240, 344)(14, 118, 222, 326, 33, 137, 241, 345)(15, 119, 223, 327, 34, 138, 242, 346)(20, 124, 228, 332, 40, 144, 248, 352)(21, 125, 229, 333, 42, 146, 250, 354)(22, 126, 230, 334, 43, 147, 251, 355)(23, 127, 231, 335, 44, 148, 252, 356)(25, 129, 233, 337, 46, 150, 254, 358)(26, 130, 234, 338, 48, 152, 256, 360)(27, 131, 235, 339, 49, 153, 257, 361)(28, 132, 236, 340, 50, 154, 258, 362)(29, 133, 237, 341, 51, 155, 259, 363)(31, 135, 239, 343, 54, 158, 262, 366)(35, 139, 243, 347, 58, 162, 266, 370)(36, 140, 244, 348, 60, 164, 268, 372)(37, 141, 245, 349, 61, 165, 269, 373)(38, 142, 246, 350, 62, 166, 270, 374)(39, 143, 247, 351, 63, 167, 271, 375)(41, 145, 249, 353, 66, 170, 274, 378)(45, 149, 253, 357, 69, 173, 277, 381)(47, 151, 255, 359, 72, 176, 280, 384)(52, 156, 260, 364, 79, 183, 287, 391)(53, 157, 261, 365, 80, 184, 288, 392)(55, 159, 263, 367, 81, 185, 289, 393)(56, 160, 264, 368, 82, 186, 290, 394)(57, 161, 265, 369, 83, 187, 291, 395)(59, 163, 267, 371, 86, 190, 294, 398)(64, 168, 272, 376, 89, 193, 297, 401)(65, 169, 273, 377, 90, 194, 298, 402)(67, 171, 275, 379, 73, 177, 281, 385)(68, 172, 276, 380, 74, 178, 282, 386)(70, 174, 278, 382, 76, 180, 284, 388)(71, 175, 279, 383, 77, 181, 285, 389)(75, 179, 283, 387, 96, 200, 304, 408)(78, 182, 286, 390, 98, 202, 306, 410)(84, 188, 292, 396, 92, 196, 300, 404)(85, 189, 293, 397, 93, 197, 301, 405)(87, 191, 295, 399, 101, 205, 309, 413)(88, 192, 296, 400, 102, 206, 310, 414)(91, 195, 299, 403, 95, 199, 303, 407)(94, 198, 302, 406, 97, 201, 305, 409)(99, 203, 307, 411, 103, 207, 311, 415)(100, 204, 308, 412, 104, 208, 312, 416)
	L = (1, 106)(2, 111)(3, 112)(4, 116)(5, 105)(6, 114)(7, 109)(8, 110)(9, 124)(10, 107)(11, 129)(12, 133)(13, 123)(14, 108)(15, 135)(16, 132)(17, 127)(18, 139)(19, 119)(20, 143)(21, 121)(22, 113)(23, 145)(24, 142)(25, 149)(26, 120)(27, 115)(28, 151)(29, 118)(30, 152)(31, 117)(32, 159)(33, 160)(34, 153)(35, 161)(36, 128)(37, 122)(38, 163)(39, 126)(40, 137)(41, 125)(42, 171)(43, 172)(44, 136)(45, 131)(46, 164)(47, 130)(48, 177)(49, 178)(50, 165)(51, 179)(52, 138)(53, 134)(54, 182)(55, 168)(56, 169)(57, 141)(58, 147)(59, 140)(60, 186)(61, 185)(62, 146)(63, 191)(64, 148)(65, 144)(66, 192)(67, 188)(68, 189)(69, 195)(70, 154)(71, 150)(72, 198)(73, 157)(74, 156)(75, 199)(76, 158)(77, 155)(78, 201)(79, 167)(80, 170)(81, 174)(82, 175)(83, 203)(84, 166)(85, 162)(86, 204)(87, 202)(88, 200)(89, 187)(90, 190)(91, 207)(92, 176)(93, 173)(94, 208)(95, 181)(96, 184)(97, 180)(98, 183)(99, 206)(100, 205)(101, 194)(102, 193)(103, 197)(104, 196)(209, 315)(210, 320)(211, 319)(212, 325)(213, 322)(214, 313)(215, 318)(216, 317)(217, 333)(218, 314)(219, 338)(220, 331)(221, 341)(222, 343)(223, 316)(224, 339)(225, 334)(226, 348)(227, 326)(228, 329)(229, 351)(230, 353)(231, 321)(232, 349)(233, 328)(234, 357)(235, 359)(236, 323)(237, 327)(238, 364)(239, 324)(240, 352)(241, 356)(242, 365)(243, 336)(244, 369)(245, 371)(246, 330)(247, 335)(248, 376)(249, 332)(250, 370)(251, 374)(252, 377)(253, 340)(254, 382)(255, 337)(256, 346)(257, 342)(258, 383)(259, 388)(260, 385)(261, 386)(262, 389)(263, 345)(264, 344)(265, 350)(266, 396)(267, 347)(268, 362)(269, 358)(270, 397)(271, 392)(272, 368)(273, 367)(274, 391)(275, 355)(276, 354)(277, 404)(278, 394)(279, 393)(280, 405)(281, 361)(282, 360)(283, 366)(284, 407)(285, 409)(286, 363)(287, 408)(288, 410)(289, 372)(290, 373)(291, 402)(292, 380)(293, 379)(294, 401)(295, 378)(296, 375)(297, 413)(298, 414)(299, 384)(300, 415)(301, 416)(302, 381)(303, 390)(304, 399)(305, 387)(306, 400)(307, 398)(308, 395)(309, 411)(310, 412)(311, 406)(312, 403)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1979
Transitivity :: VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1987 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = (C2 x (C13 : C4)) : C2 (small group id <208, 34>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^4, (Y2^-1 * Y1^-1)^2, Y1^4, (R * Y3)^2, Y1^-2 * Y2^2, R * Y1 * R * Y2, Y1^-2 * Y2^-2, (Y2 * Y1^-1)^2, (Y1 * Y3 * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1 * Y3 * Y1^-1 * Y3, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 9, 113, 217, 321)(3, 107, 211, 315, 11, 115, 219, 323)(5, 109, 213, 317, 16, 120, 224, 328)(6, 110, 214, 318, 17, 121, 225, 329)(7, 111, 215, 319, 18, 122, 226, 330)(8, 112, 216, 320, 19, 123, 227, 331)(10, 114, 218, 322, 24, 128, 232, 336)(12, 116, 220, 324, 30, 134, 238, 342)(13, 117, 221, 325, 32, 136, 240, 344)(14, 118, 222, 326, 33, 137, 241, 345)(15, 119, 223, 327, 34, 138, 242, 346)(20, 124, 228, 332, 40, 144, 248, 352)(21, 125, 229, 333, 42, 146, 250, 354)(22, 126, 230, 334, 43, 147, 251, 355)(23, 127, 231, 335, 44, 148, 252, 356)(25, 129, 233, 337, 46, 150, 254, 358)(26, 130, 234, 338, 48, 152, 256, 360)(27, 131, 235, 339, 49, 153, 257, 361)(28, 132, 236, 340, 50, 154, 258, 362)(29, 133, 237, 341, 51, 155, 259, 363)(31, 135, 239, 343, 54, 158, 262, 366)(35, 139, 243, 347, 58, 162, 266, 370)(36, 140, 244, 348, 60, 164, 268, 372)(37, 141, 245, 349, 61, 165, 269, 373)(38, 142, 246, 350, 62, 166, 270, 374)(39, 143, 247, 351, 63, 167, 271, 375)(41, 145, 249, 353, 66, 170, 274, 378)(45, 149, 253, 357, 69, 173, 277, 381)(47, 151, 255, 359, 72, 176, 280, 384)(52, 156, 260, 364, 79, 183, 287, 391)(53, 157, 261, 365, 80, 184, 288, 392)(55, 159, 263, 367, 81, 185, 289, 393)(56, 160, 264, 368, 82, 186, 290, 394)(57, 161, 265, 369, 83, 187, 291, 395)(59, 163, 267, 371, 84, 188, 292, 396)(64, 168, 272, 376, 70, 174, 278, 382)(65, 169, 273, 377, 71, 175, 279, 383)(67, 171, 275, 379, 75, 179, 283, 387)(68, 172, 276, 380, 78, 182, 286, 390)(73, 177, 281, 385, 93, 197, 301, 405)(74, 178, 282, 386, 94, 198, 302, 406)(76, 180, 284, 388, 97, 201, 305, 409)(77, 181, 285, 389, 98, 202, 306, 410)(85, 189, 293, 397, 87, 191, 295, 399)(86, 190, 294, 398, 90, 194, 298, 402)(88, 192, 296, 400, 95, 199, 303, 407)(89, 193, 297, 401, 96, 200, 304, 408)(91, 195, 299, 403, 103, 207, 311, 415)(92, 196, 300, 404, 104, 208, 312, 416)(99, 203, 307, 411, 101, 205, 309, 413)(100, 204, 308, 412, 102, 206, 310, 414)
	L = (1, 106)(2, 111)(3, 112)(4, 116)(5, 105)(6, 114)(7, 109)(8, 110)(9, 124)(10, 107)(11, 129)(12, 133)(13, 123)(14, 108)(15, 135)(16, 132)(17, 127)(18, 139)(19, 119)(20, 143)(21, 121)(22, 113)(23, 145)(24, 142)(25, 149)(26, 120)(27, 115)(28, 151)(29, 118)(30, 152)(31, 117)(32, 159)(33, 160)(34, 153)(35, 161)(36, 128)(37, 122)(38, 163)(39, 126)(40, 137)(41, 125)(42, 171)(43, 172)(44, 136)(45, 131)(46, 164)(47, 130)(48, 177)(49, 178)(50, 165)(51, 179)(52, 138)(53, 134)(54, 182)(55, 168)(56, 169)(57, 141)(58, 147)(59, 140)(60, 189)(61, 190)(62, 146)(63, 191)(64, 148)(65, 144)(66, 194)(67, 184)(68, 183)(69, 186)(70, 154)(71, 150)(72, 185)(73, 157)(74, 156)(75, 199)(76, 158)(77, 155)(78, 200)(79, 162)(80, 166)(81, 201)(82, 202)(83, 198)(84, 197)(85, 175)(86, 174)(87, 205)(88, 170)(89, 167)(90, 206)(91, 176)(92, 173)(93, 207)(94, 208)(95, 181)(96, 180)(97, 195)(98, 196)(99, 188)(100, 187)(101, 193)(102, 192)(103, 203)(104, 204)(209, 315)(210, 320)(211, 319)(212, 325)(213, 322)(214, 313)(215, 318)(216, 317)(217, 333)(218, 314)(219, 338)(220, 331)(221, 341)(222, 343)(223, 316)(224, 339)(225, 334)(226, 348)(227, 326)(228, 329)(229, 351)(230, 353)(231, 321)(232, 349)(233, 328)(234, 357)(235, 359)(236, 323)(237, 327)(238, 364)(239, 324)(240, 352)(241, 356)(242, 365)(243, 336)(244, 369)(245, 371)(246, 330)(247, 335)(248, 376)(249, 332)(250, 370)(251, 374)(252, 377)(253, 340)(254, 382)(255, 337)(256, 346)(257, 342)(258, 383)(259, 388)(260, 385)(261, 386)(262, 389)(263, 345)(264, 344)(265, 350)(266, 392)(267, 347)(268, 362)(269, 358)(270, 391)(271, 400)(272, 368)(273, 367)(274, 401)(275, 355)(276, 354)(277, 403)(278, 397)(279, 398)(280, 404)(281, 361)(282, 360)(283, 366)(284, 407)(285, 408)(286, 363)(287, 379)(288, 380)(289, 381)(290, 384)(291, 411)(292, 412)(293, 373)(294, 372)(295, 378)(296, 413)(297, 414)(298, 375)(299, 410)(300, 409)(301, 395)(302, 396)(303, 390)(304, 387)(305, 394)(306, 393)(307, 416)(308, 415)(309, 402)(310, 399)(311, 406)(312, 405)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1978
Transitivity :: VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1988 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = C2 x C2 x (C13 : C4) (small group id <208, 49>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2^-1 * Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2^2 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 6, 110, 214, 318)(3, 107, 211, 315, 7, 111, 215, 319)(5, 109, 213, 317, 10, 114, 218, 322)(8, 112, 216, 320, 16, 120, 224, 328)(9, 113, 217, 321, 17, 121, 225, 329)(11, 115, 219, 323, 21, 125, 229, 333)(12, 116, 220, 324, 22, 126, 230, 334)(13, 117, 221, 325, 24, 128, 232, 336)(14, 118, 222, 326, 25, 129, 233, 337)(15, 119, 223, 327, 26, 130, 234, 338)(18, 122, 226, 330, 30, 134, 238, 342)(19, 123, 227, 331, 31, 135, 239, 343)(20, 124, 228, 332, 32, 136, 240, 344)(23, 127, 231, 335, 35, 139, 243, 347)(27, 131, 235, 339, 40, 144, 248, 352)(28, 132, 236, 340, 41, 145, 249, 353)(29, 133, 237, 341, 42, 146, 250, 354)(33, 137, 241, 345, 47, 151, 255, 359)(34, 138, 242, 346, 48, 152, 256, 360)(36, 140, 244, 348, 51, 155, 259, 363)(37, 141, 245, 349, 52, 156, 260, 364)(38, 142, 246, 350, 54, 158, 262, 366)(39, 143, 247, 351, 55, 159, 263, 367)(43, 147, 251, 355, 60, 164, 268, 372)(44, 148, 252, 356, 61, 165, 269, 373)(45, 149, 253, 357, 63, 167, 271, 375)(46, 150, 254, 358, 64, 168, 272, 376)(49, 153, 257, 361, 68, 172, 276, 380)(50, 154, 258, 362, 69, 173, 277, 381)(53, 157, 261, 365, 72, 176, 280, 384)(56, 160, 264, 368, 75, 179, 283, 387)(57, 161, 265, 369, 76, 180, 284, 388)(58, 162, 266, 370, 78, 182, 286, 390)(59, 163, 267, 371, 79, 183, 287, 391)(62, 166, 270, 374, 82, 186, 290, 394)(65, 169, 273, 377, 85, 189, 293, 397)(66, 170, 274, 378, 86, 190, 294, 398)(67, 171, 275, 379, 83, 187, 291, 395)(70, 174, 278, 382, 88, 192, 296, 400)(71, 175, 279, 383, 89, 193, 297, 401)(73, 177, 281, 385, 77, 181, 285, 389)(74, 178, 282, 386, 90, 194, 298, 402)(80, 184, 288, 392, 94, 198, 302, 406)(81, 185, 289, 393, 95, 199, 303, 407)(84, 188, 292, 396, 96, 200, 304, 408)(87, 191, 295, 399, 97, 201, 305, 409)(91, 195, 299, 403, 93, 197, 301, 405)(92, 196, 300, 404, 100, 204, 308, 412)(98, 202, 306, 410, 102, 206, 310, 414)(99, 203, 307, 411, 103, 207, 311, 415)(101, 205, 309, 413, 104, 208, 312, 416)
	L = (1, 106)(2, 109)(3, 105)(4, 112)(5, 107)(6, 115)(7, 117)(8, 119)(9, 108)(10, 122)(11, 124)(12, 110)(13, 127)(14, 111)(15, 113)(16, 129)(17, 132)(18, 133)(19, 114)(20, 116)(21, 121)(22, 138)(23, 118)(24, 135)(25, 141)(26, 142)(27, 120)(28, 137)(29, 123)(30, 126)(31, 148)(32, 149)(33, 125)(34, 147)(35, 153)(36, 128)(37, 131)(38, 157)(39, 130)(40, 160)(41, 159)(42, 162)(43, 134)(44, 140)(45, 166)(46, 136)(47, 169)(48, 168)(49, 171)(50, 139)(51, 174)(52, 173)(53, 143)(54, 144)(55, 178)(56, 177)(57, 145)(58, 181)(59, 146)(60, 184)(61, 183)(62, 150)(63, 151)(64, 188)(65, 187)(66, 152)(67, 154)(68, 155)(69, 191)(70, 186)(71, 156)(72, 182)(73, 158)(74, 161)(75, 193)(76, 196)(77, 163)(78, 164)(79, 197)(80, 176)(81, 165)(82, 172)(83, 167)(84, 170)(85, 180)(86, 202)(87, 175)(88, 199)(89, 203)(90, 198)(91, 179)(92, 201)(93, 185)(94, 190)(95, 205)(96, 192)(97, 189)(98, 194)(99, 195)(100, 206)(101, 200)(102, 208)(103, 204)(104, 207)(209, 315)(210, 313)(211, 317)(212, 321)(213, 314)(214, 324)(215, 326)(216, 316)(217, 327)(218, 331)(219, 318)(220, 332)(221, 319)(222, 335)(223, 320)(224, 339)(225, 333)(226, 322)(227, 341)(228, 323)(229, 345)(230, 342)(231, 325)(232, 348)(233, 328)(234, 351)(235, 349)(236, 329)(237, 330)(238, 355)(239, 336)(240, 358)(241, 340)(242, 334)(243, 362)(244, 356)(245, 337)(246, 338)(247, 365)(248, 366)(249, 369)(250, 371)(251, 346)(252, 343)(253, 344)(254, 374)(255, 375)(256, 378)(257, 347)(258, 379)(259, 380)(260, 383)(261, 350)(262, 385)(263, 353)(264, 352)(265, 386)(266, 354)(267, 389)(268, 390)(269, 393)(270, 357)(271, 395)(272, 360)(273, 359)(274, 396)(275, 361)(276, 394)(277, 364)(278, 363)(279, 399)(280, 392)(281, 368)(282, 367)(283, 403)(284, 397)(285, 370)(286, 384)(287, 373)(288, 372)(289, 405)(290, 382)(291, 377)(292, 376)(293, 409)(294, 406)(295, 381)(296, 408)(297, 387)(298, 410)(299, 411)(300, 388)(301, 391)(302, 402)(303, 400)(304, 413)(305, 404)(306, 398)(307, 401)(308, 415)(309, 407)(310, 412)(311, 416)(312, 414)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1983
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1989 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C2 x (C13 : C4) (small group id <104, 12>)
Aut   = C2 x C2 x (C13 : C4) (small group id <208, 49>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2 * Y1^-3, R * Y2 * R * Y1, Y2^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 105, 209, 313, 4, 108, 212, 316)(2, 106, 210, 314, 6, 110, 214, 318)(3, 107, 211, 315, 7, 111, 215, 319)(5, 109, 213, 317, 10, 114, 218, 322)(8, 112, 216, 320, 16, 120, 224, 328)(9, 113, 217, 321, 17, 121, 225, 329)(11, 115, 219, 323, 21, 125, 229, 333)(12, 116, 220, 324, 22, 126, 230, 334)(13, 117, 221, 325, 24, 128, 232, 336)(14, 118, 222, 326, 25, 129, 233, 337)(15, 119, 223, 327, 26, 130, 234, 338)(18, 122, 226, 330, 30, 134, 238, 342)(19, 123, 227, 331, 31, 135, 239, 343)(20, 124, 228, 332, 32, 136, 240, 344)(23, 127, 231, 335, 35, 139, 243, 347)(27, 131, 235, 339, 40, 144, 248, 352)(28, 132, 236, 340, 41, 145, 249, 353)(29, 133, 237, 341, 42, 146, 250, 354)(33, 137, 241, 345, 47, 151, 255, 359)(34, 138, 242, 346, 48, 152, 256, 360)(36, 140, 244, 348, 51, 155, 259, 363)(37, 141, 245, 349, 52, 156, 260, 364)(38, 142, 246, 350, 54, 158, 262, 366)(39, 143, 247, 351, 55, 159, 263, 367)(43, 147, 251, 355, 60, 164, 268, 372)(44, 148, 252, 356, 61, 165, 269, 373)(45, 149, 253, 357, 63, 167, 271, 375)(46, 150, 254, 358, 64, 168, 272, 376)(49, 153, 257, 361, 68, 172, 276, 380)(50, 154, 258, 362, 69, 173, 277, 381)(53, 157, 261, 365, 72, 176, 280, 384)(56, 160, 264, 368, 75, 179, 283, 387)(57, 161, 265, 369, 76, 180, 284, 388)(58, 162, 266, 370, 78, 182, 286, 390)(59, 163, 267, 371, 79, 183, 287, 391)(62, 166, 270, 374, 82, 186, 290, 394)(65, 169, 273, 377, 85, 189, 293, 397)(66, 170, 274, 378, 86, 190, 294, 398)(67, 171, 275, 379, 84, 188, 292, 396)(70, 174, 278, 382, 88, 192, 296, 400)(71, 175, 279, 383, 89, 193, 297, 401)(73, 177, 281, 385, 90, 194, 298, 402)(74, 178, 282, 386, 77, 181, 285, 389)(80, 184, 288, 392, 94, 198, 302, 406)(81, 185, 289, 393, 95, 199, 303, 407)(83, 187, 291, 395, 96, 200, 304, 408)(87, 191, 295, 399, 98, 202, 306, 410)(91, 195, 299, 403, 100, 204, 308, 412)(92, 196, 300, 404, 93, 197, 301, 405)(97, 201, 305, 409, 102, 206, 310, 414)(99, 203, 307, 411, 103, 207, 311, 415)(101, 205, 309, 413, 104, 208, 312, 416)
	L = (1, 106)(2, 109)(3, 105)(4, 112)(5, 107)(6, 115)(7, 117)(8, 119)(9, 108)(10, 122)(11, 124)(12, 110)(13, 127)(14, 111)(15, 113)(16, 129)(17, 132)(18, 133)(19, 114)(20, 116)(21, 121)(22, 138)(23, 118)(24, 135)(25, 141)(26, 142)(27, 120)(28, 137)(29, 123)(30, 126)(31, 148)(32, 149)(33, 125)(34, 147)(35, 153)(36, 128)(37, 131)(38, 157)(39, 130)(40, 160)(41, 159)(42, 162)(43, 134)(44, 140)(45, 166)(46, 136)(47, 169)(48, 168)(49, 171)(50, 139)(51, 174)(52, 173)(53, 143)(54, 144)(55, 178)(56, 177)(57, 145)(58, 181)(59, 146)(60, 184)(61, 183)(62, 150)(63, 151)(64, 188)(65, 187)(66, 152)(67, 154)(68, 155)(69, 186)(70, 191)(71, 156)(72, 185)(73, 158)(74, 161)(75, 193)(76, 196)(77, 163)(78, 164)(79, 176)(80, 197)(81, 165)(82, 175)(83, 167)(84, 170)(85, 180)(86, 202)(87, 172)(88, 199)(89, 200)(90, 203)(91, 179)(92, 201)(93, 182)(94, 190)(95, 194)(96, 195)(97, 189)(98, 205)(99, 192)(100, 206)(101, 198)(102, 208)(103, 204)(104, 207)(209, 315)(210, 313)(211, 317)(212, 321)(213, 314)(214, 324)(215, 326)(216, 316)(217, 327)(218, 331)(219, 318)(220, 332)(221, 319)(222, 335)(223, 320)(224, 339)(225, 333)(226, 322)(227, 341)(228, 323)(229, 345)(230, 342)(231, 325)(232, 348)(233, 328)(234, 351)(235, 349)(236, 329)(237, 330)(238, 355)(239, 336)(240, 358)(241, 340)(242, 334)(243, 362)(244, 356)(245, 337)(246, 338)(247, 365)(248, 366)(249, 369)(250, 371)(251, 346)(252, 343)(253, 344)(254, 374)(255, 375)(256, 378)(257, 347)(258, 379)(259, 380)(260, 383)(261, 350)(262, 385)(263, 353)(264, 352)(265, 386)(266, 354)(267, 389)(268, 390)(269, 393)(270, 357)(271, 395)(272, 360)(273, 359)(274, 396)(275, 361)(276, 399)(277, 364)(278, 363)(279, 394)(280, 391)(281, 368)(282, 367)(283, 403)(284, 397)(285, 370)(286, 405)(287, 373)(288, 372)(289, 384)(290, 381)(291, 377)(292, 376)(293, 409)(294, 406)(295, 382)(296, 411)(297, 387)(298, 407)(299, 408)(300, 388)(301, 392)(302, 413)(303, 400)(304, 401)(305, 404)(306, 398)(307, 402)(308, 415)(309, 410)(310, 412)(311, 416)(312, 414)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.1982
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.1990 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 8, 8})
Quotient :: edge
Aut^+ = C13 : C8 (small group id <104, 3>)
Aut   = C13 : C8 (small group id <104, 3>)
|r| :: 1
Presentation :: [ X1^4, X1^-2 * X2 * X1^2 * X2^-1, X1^-2 * X2^-4, X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1, X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^3 * X1, X2^2 * X1^-1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 ]
Map:: non-degenerate
	R = (1, 2, 6, 4)(3, 9, 17, 11)(5, 14, 18, 15)(7, 19, 12, 21)(8, 22, 13, 23)(10, 27, 16, 28)(20, 37, 24, 38)(25, 44, 29, 42)(26, 46, 30, 47)(31, 53, 33, 55)(32, 39, 34, 35)(36, 58, 40, 59)(41, 65, 43, 67)(45, 69, 48, 70)(49, 74, 51, 72)(50, 76, 52, 77)(54, 80, 56, 81)(57, 73, 60, 71)(61, 84, 63, 83)(62, 82, 64, 79)(66, 87, 68, 88)(75, 93, 78, 94)(85, 97, 86, 95)(89, 100, 90, 99)(91, 98, 92, 96)(101, 104, 102, 103)(105, 107, 114, 122, 110, 121, 120, 109)(106, 111, 124, 117, 108, 116, 128, 112)(113, 129, 149, 134, 115, 133, 152, 130)(118, 135, 158, 138, 119, 137, 160, 136)(123, 139, 161, 144, 125, 143, 164, 140)(126, 145, 170, 148, 127, 147, 172, 146)(131, 153, 179, 156, 132, 155, 182, 154)(141, 165, 189, 168, 142, 167, 190, 166)(150, 175, 195, 178, 151, 177, 196, 176)(157, 180, 169, 186, 159, 181, 171, 183)(162, 173, 193, 188, 163, 174, 194, 187)(184, 199, 207, 202, 185, 201, 208, 200)(191, 197, 205, 204, 192, 198, 206, 203)
	L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 16^4 ), ( 16^8 ) }
Outer automorphisms :: chiral
Dual of E27.1993
Transitivity :: ET+
Graph:: bipartite
	v = 39 e = 104 f = 13
	degree seq :: [ 4^26, 8^13 ]

E27.1991 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 8, 8})
Quotient :: edge
Aut^+ = C13 : C8 (small group id <104, 3>)
Aut   = C13 : C8 (small group id <104, 3>)
|r| :: 1
Presentation :: [ X1^4, X1 * X2^-4 * X1, X1^-1 * X2 * X1^2 * X2^-1 * X1^-1, X2^4 * X1^-2, X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1, X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2^-2 ]
Map:: non-degenerate
	R = (1, 2, 6, 4)(3, 9, 17, 11)(5, 14, 18, 15)(7, 19, 12, 21)(8, 22, 13, 23)(10, 27, 16, 28)(20, 37, 24, 38)(25, 44, 29, 42)(26, 46, 30, 47)(31, 53, 33, 55)(32, 39, 34, 35)(36, 58, 40, 59)(41, 65, 43, 67)(45, 69, 48, 70)(49, 74, 51, 72)(50, 76, 52, 77)(54, 80, 56, 81)(57, 83, 60, 84)(61, 71, 63, 73)(62, 86, 64, 87)(66, 79, 68, 82)(75, 93, 78, 94)(85, 90, 88, 92)(89, 95, 91, 96)(97, 100, 98, 99)(101, 103, 102, 104)(105, 107, 114, 122, 110, 121, 120, 109)(106, 111, 124, 117, 108, 116, 128, 112)(113, 129, 149, 134, 115, 133, 152, 130)(118, 135, 158, 138, 119, 137, 160, 136)(123, 139, 161, 144, 125, 143, 164, 140)(126, 145, 170, 148, 127, 147, 172, 146)(131, 153, 179, 156, 132, 155, 182, 154)(141, 165, 189, 168, 142, 167, 192, 166)(150, 175, 163, 178, 151, 177, 162, 176)(157, 180, 199, 186, 159, 181, 200, 183)(169, 190, 201, 184, 171, 191, 202, 185)(173, 193, 205, 196, 174, 195, 206, 194)(187, 203, 207, 197, 188, 204, 208, 198)
	L = (1, 105)(2, 106)(3, 107)(4, 108)(5, 109)(6, 110)(7, 111)(8, 112)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 128)(25, 129)(26, 130)(27, 131)(28, 132)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 142)(39, 143)(40, 144)(41, 145)(42, 146)(43, 147)(44, 148)(45, 149)(46, 150)(47, 151)(48, 152)(49, 153)(50, 154)(51, 155)(52, 156)(53, 157)(54, 158)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 164)(61, 165)(62, 166)(63, 167)(64, 168)(65, 169)(66, 170)(67, 171)(68, 172)(69, 173)(70, 174)(71, 175)(72, 176)(73, 177)(74, 178)(75, 179)(76, 180)(77, 181)(78, 182)(79, 183)(80, 184)(81, 185)(82, 186)(83, 187)(84, 188)(85, 189)(86, 190)(87, 191)(88, 192)(89, 193)(90, 194)(91, 195)(92, 196)(93, 197)(94, 198)(95, 199)(96, 200)(97, 201)(98, 202)(99, 203)(100, 204)(101, 205)(102, 206)(103, 207)(104, 208)
	local type(s) :: { ( 16^4 ), ( 16^8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: bipartite
	v = 39 e = 104 f = 13
	degree seq :: [ 4^26, 8^13 ]

E27.1992 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 8, 8})
Quotient :: loop
Aut^+ = C13 : C8 (small group id <104, 3>)
Aut   = C13 : C8 (small group id <104, 3>)
|r| :: 1
Presentation :: [ X1 * X2 * X1 * X2^-3, X1^2 * X2^-1 * X1^-1 * X2^-1 * X1, X1 * X2 * X1 * X2^5, X1^8, X1^-1 * X2^2 * X1^-2 * X2 * X1^-1 * X2^2 * X1^-1, X2 * X1 * X2^-1 * X1^2 * X2 * X1^-1 * X2^-2 * X1^-1 ]
Map:: non-degenerate
	R = (1, 105, 2, 106, 6, 110, 18, 122, 42, 146, 35, 139, 13, 117, 4, 108)(3, 107, 9, 113, 27, 131, 57, 161, 37, 141, 14, 118, 32, 136, 11, 115)(5, 109, 15, 119, 23, 127, 7, 111, 21, 125, 49, 153, 40, 144, 16, 120)(8, 112, 24, 128, 46, 150, 19, 123, 44, 148, 76, 180, 55, 159, 25, 129)(10, 114, 29, 133, 62, 166, 41, 145, 17, 121, 33, 137, 65, 169, 30, 134)(12, 116, 20, 124, 47, 151, 75, 179, 43, 147, 36, 140, 70, 174, 34, 138)(22, 126, 50, 154, 84, 188, 56, 160, 26, 130, 53, 157, 87, 191, 51, 155)(28, 132, 60, 164, 85, 189, 58, 162, 38, 142, 71, 175, 89, 193, 61, 165)(31, 135, 59, 163, 95, 199, 101, 205, 93, 197, 67, 171, 96, 200, 66, 170)(39, 143, 72, 176, 88, 192, 52, 156, 83, 187, 103, 207, 94, 198, 73, 177)(45, 149, 77, 181, 68, 172, 82, 186, 48, 152, 80, 184, 63, 167, 78, 182)(54, 158, 90, 194, 64, 168, 79, 183, 100, 204, 98, 202, 74, 178, 91, 195)(69, 173, 81, 185, 102, 206, 86, 190, 99, 203, 97, 201, 104, 208, 92, 196)
	L = (1, 107)(2, 111)(3, 114)(4, 116)(5, 105)(6, 123)(7, 126)(8, 106)(9, 122)(10, 125)(11, 135)(12, 132)(13, 129)(14, 108)(15, 134)(16, 130)(17, 109)(18, 147)(19, 149)(20, 110)(21, 146)(22, 148)(23, 156)(24, 155)(25, 152)(26, 112)(27, 162)(28, 113)(29, 161)(30, 168)(31, 167)(32, 165)(33, 115)(34, 173)(35, 120)(36, 117)(37, 121)(38, 118)(39, 119)(40, 177)(41, 178)(42, 141)(43, 142)(44, 139)(45, 140)(46, 183)(47, 182)(48, 124)(49, 145)(50, 144)(51, 190)(52, 189)(53, 127)(54, 128)(55, 195)(56, 196)(57, 197)(58, 198)(59, 131)(60, 179)(61, 192)(62, 181)(63, 133)(64, 187)(65, 184)(66, 185)(67, 136)(68, 137)(69, 191)(70, 186)(71, 138)(72, 194)(73, 193)(74, 143)(75, 203)(76, 160)(77, 159)(78, 205)(79, 166)(80, 150)(81, 151)(82, 170)(83, 153)(84, 175)(85, 154)(86, 204)(87, 164)(88, 163)(89, 157)(90, 206)(91, 169)(92, 158)(93, 172)(94, 171)(95, 207)(96, 176)(97, 174)(98, 208)(99, 188)(100, 180)(101, 201)(102, 199)(103, 202)(104, 200)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 104 f = 39
	degree seq :: [ 16^13 ]

E27.1993 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 8, 8})
Quotient :: loop
Aut^+ = C13 : C8 (small group id <104, 3>)
Aut   = C13 : C8 (small group id <104, 3>)
|r| :: 1
Presentation :: [ X2 * X1 * X2 * X1^-3, X1^-1 * X2^3 * X1^-1 * X2^-1, X1^-1 * X2^-1 * X1^-5 * X2^-1, X2^-1 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1 * X1^-2, X2 * X1 * X2^-1 * X1^2 * X2 * X1^-1 * X2^-1 * X1 * X2 ]
Map:: non-degenerate
	R = (1, 105, 2, 106, 6, 110, 18, 122, 42, 146, 35, 139, 13, 117, 4, 108)(3, 107, 9, 113, 27, 131, 57, 161, 37, 141, 14, 118, 32, 136, 11, 115)(5, 109, 15, 119, 23, 127, 7, 111, 21, 125, 49, 153, 40, 144, 16, 120)(8, 112, 24, 128, 46, 150, 19, 123, 44, 148, 76, 180, 55, 159, 25, 129)(10, 114, 29, 133, 62, 166, 41, 145, 17, 121, 33, 137, 65, 169, 30, 134)(12, 116, 20, 124, 47, 151, 75, 179, 43, 147, 36, 140, 70, 174, 34, 138)(22, 126, 50, 154, 84, 188, 56, 160, 26, 130, 53, 157, 87, 191, 51, 155)(28, 132, 60, 164, 89, 193, 58, 162, 38, 142, 71, 175, 85, 189, 61, 165)(31, 135, 59, 163, 94, 198, 102, 206, 93, 197, 67, 171, 98, 202, 66, 170)(39, 143, 72, 176, 88, 192, 52, 156, 83, 187, 103, 207, 95, 199, 73, 177)(45, 149, 77, 181, 63, 167, 82, 186, 48, 152, 80, 184, 68, 172, 78, 182)(54, 158, 90, 194, 74, 178, 79, 183, 100, 204, 96, 200, 64, 168, 91, 195)(69, 173, 81, 185, 101, 205, 92, 196, 99, 203, 97, 201, 104, 208, 86, 190)
	L = (1, 107)(2, 111)(3, 114)(4, 116)(5, 105)(6, 123)(7, 126)(8, 106)(9, 122)(10, 125)(11, 135)(12, 132)(13, 129)(14, 108)(15, 134)(16, 130)(17, 109)(18, 147)(19, 149)(20, 110)(21, 146)(22, 148)(23, 156)(24, 155)(25, 152)(26, 112)(27, 162)(28, 113)(29, 161)(30, 168)(31, 167)(32, 165)(33, 115)(34, 173)(35, 120)(36, 117)(37, 121)(38, 118)(39, 119)(40, 177)(41, 178)(42, 141)(43, 142)(44, 139)(45, 140)(46, 183)(47, 182)(48, 124)(49, 145)(50, 144)(51, 190)(52, 189)(53, 127)(54, 128)(55, 195)(56, 196)(57, 197)(58, 192)(59, 131)(60, 179)(61, 199)(62, 184)(63, 133)(64, 187)(65, 181)(66, 201)(67, 136)(68, 137)(69, 188)(70, 186)(71, 138)(72, 200)(73, 193)(74, 143)(75, 203)(76, 160)(77, 159)(78, 170)(79, 169)(80, 150)(81, 151)(82, 206)(83, 153)(84, 164)(85, 154)(86, 204)(87, 175)(88, 171)(89, 157)(90, 208)(91, 166)(92, 158)(93, 172)(94, 176)(95, 163)(96, 205)(97, 174)(98, 207)(99, 191)(100, 180)(101, 202)(102, 185)(103, 194)(104, 198)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: chiral
Dual of E27.1990
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 104 f = 39
	degree seq :: [ 16^13 ]

E27.1994 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 54})
Quotient :: dipole
Aut^+ = D108 (small group id <108, 4>)
Aut   = C2 x C2 x D54 (small group id <216, 23>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 109, 2, 110)(3, 111, 5, 113)(4, 112, 8, 116)(6, 114, 10, 118)(7, 115, 11, 119)(9, 117, 13, 121)(12, 120, 16, 124)(14, 122, 18, 126)(15, 123, 19, 127)(17, 125, 21, 129)(20, 128, 24, 132)(22, 130, 26, 134)(23, 131, 27, 135)(25, 133, 29, 137)(28, 136, 32, 140)(30, 138, 35, 143)(31, 139, 33, 141)(34, 142, 47, 155)(36, 144, 51, 159)(37, 145, 53, 161)(38, 146, 49, 157)(39, 147, 55, 163)(40, 148, 57, 165)(41, 149, 59, 167)(42, 150, 61, 169)(43, 151, 63, 171)(44, 152, 65, 173)(45, 153, 67, 175)(46, 154, 69, 177)(48, 156, 71, 179)(50, 158, 73, 181)(52, 160, 77, 185)(54, 162, 79, 187)(56, 164, 75, 183)(58, 166, 83, 191)(60, 168, 85, 193)(62, 170, 81, 189)(64, 172, 87, 195)(66, 174, 89, 197)(68, 176, 91, 199)(70, 178, 93, 201)(72, 180, 95, 203)(74, 182, 97, 205)(76, 184, 99, 207)(78, 186, 101, 209)(80, 188, 103, 211)(82, 190, 105, 213)(84, 192, 107, 215)(86, 194, 108, 216)(88, 196, 106, 214)(90, 198, 104, 212)(92, 200, 102, 210)(94, 202, 100, 208)(96, 204, 98, 206)(217, 325, 219, 327)(218, 326, 221, 329)(220, 328, 223, 331)(222, 330, 225, 333)(224, 332, 227, 335)(226, 334, 229, 337)(228, 336, 231, 339)(230, 338, 233, 341)(232, 340, 235, 343)(234, 342, 237, 345)(236, 344, 239, 347)(238, 346, 241, 349)(240, 348, 243, 351)(242, 350, 245, 353)(244, 352, 247, 355)(246, 354, 263, 371)(248, 356, 249, 357)(250, 358, 251, 359)(252, 360, 254, 362)(253, 361, 255, 363)(256, 364, 258, 366)(257, 365, 259, 367)(260, 368, 262, 370)(261, 369, 264, 372)(265, 373, 267, 375)(266, 374, 268, 376)(269, 377, 271, 379)(270, 378, 272, 380)(273, 381, 277, 385)(274, 382, 278, 386)(275, 383, 279, 387)(276, 384, 280, 388)(281, 389, 285, 393)(282, 390, 286, 394)(283, 391, 287, 395)(284, 392, 288, 396)(289, 397, 293, 401)(290, 398, 294, 402)(291, 399, 295, 403)(292, 400, 296, 404)(297, 405, 299, 407)(298, 406, 300, 408)(301, 409, 303, 411)(302, 410, 304, 412)(305, 413, 309, 417)(306, 414, 310, 418)(307, 415, 311, 419)(308, 416, 312, 420)(313, 421, 317, 425)(314, 422, 318, 426)(315, 423, 319, 427)(316, 424, 320, 428)(321, 429, 323, 431)(322, 430, 324, 432)
	L = (1, 220)(2, 222)(3, 223)(4, 217)(5, 225)(6, 218)(7, 219)(8, 228)(9, 221)(10, 230)(11, 231)(12, 224)(13, 233)(14, 226)(15, 227)(16, 236)(17, 229)(18, 238)(19, 239)(20, 232)(21, 241)(22, 234)(23, 235)(24, 244)(25, 237)(26, 246)(27, 247)(28, 240)(29, 263)(30, 242)(31, 243)(32, 265)(33, 267)(34, 269)(35, 271)(36, 273)(37, 275)(38, 277)(39, 279)(40, 281)(41, 283)(42, 285)(43, 287)(44, 289)(45, 291)(46, 293)(47, 245)(48, 295)(49, 248)(50, 297)(51, 249)(52, 299)(53, 250)(54, 301)(55, 251)(56, 303)(57, 252)(58, 305)(59, 253)(60, 307)(61, 254)(62, 309)(63, 255)(64, 311)(65, 256)(66, 313)(67, 257)(68, 315)(69, 258)(70, 317)(71, 259)(72, 319)(73, 260)(74, 321)(75, 261)(76, 322)(77, 262)(78, 323)(79, 264)(80, 324)(81, 266)(82, 316)(83, 268)(84, 320)(85, 270)(86, 318)(87, 272)(88, 314)(89, 274)(90, 312)(91, 276)(92, 310)(93, 278)(94, 308)(95, 280)(96, 306)(97, 282)(98, 304)(99, 284)(100, 298)(101, 286)(102, 302)(103, 288)(104, 300)(105, 290)(106, 292)(107, 294)(108, 296)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 4, 108, 4, 108 ) }
Outer automorphisms :: reflexible
Dual of E27.1995
Graph:: simple bipartite
	v = 108 e = 216 f = 56
	degree seq :: [ 4^108 ]

E27.1995 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 54})
Quotient :: dipole
Aut^+ = D108 (small group id <108, 4>)
Aut   = C2 x C2 x D54 (small group id <216, 23>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y3 * Y2)^2, Y1^14 * Y3 * Y1^-13 * Y2, Y1^2 * Y3 * Y1^-1 * Y2 * Y1^12 * Y3 * Y2 * Y1^12 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 109, 2, 110, 6, 114, 13, 121, 21, 129, 29, 137, 37, 145, 45, 153, 53, 161, 61, 169, 69, 177, 77, 185, 85, 193, 93, 201, 101, 209, 106, 214, 98, 206, 90, 198, 82, 190, 74, 182, 66, 174, 58, 166, 50, 158, 42, 150, 34, 142, 26, 134, 18, 126, 10, 118, 16, 124, 24, 132, 32, 140, 40, 148, 48, 156, 56, 164, 64, 172, 72, 180, 80, 188, 88, 196, 96, 204, 104, 212, 108, 216, 100, 208, 92, 200, 84, 192, 76, 184, 68, 176, 60, 168, 52, 160, 44, 152, 36, 144, 28, 136, 20, 128, 12, 120, 5, 113)(3, 111, 9, 117, 17, 125, 25, 133, 33, 141, 41, 149, 49, 157, 57, 165, 65, 173, 73, 181, 81, 189, 89, 197, 97, 205, 105, 213, 103, 211, 95, 203, 87, 195, 79, 187, 71, 179, 63, 171, 55, 163, 47, 155, 39, 147, 31, 139, 23, 131, 15, 123, 8, 116, 4, 112, 11, 119, 19, 127, 27, 135, 35, 143, 43, 151, 51, 159, 59, 167, 67, 175, 75, 183, 83, 191, 91, 199, 99, 207, 107, 215, 102, 210, 94, 202, 86, 194, 78, 186, 70, 178, 62, 170, 54, 162, 46, 154, 38, 146, 30, 138, 22, 130, 14, 122, 7, 115)(217, 325, 219, 327)(218, 326, 223, 331)(220, 328, 226, 334)(221, 329, 225, 333)(222, 330, 230, 338)(224, 332, 232, 340)(227, 335, 234, 342)(228, 336, 233, 341)(229, 337, 238, 346)(231, 339, 240, 348)(235, 343, 242, 350)(236, 344, 241, 349)(237, 345, 246, 354)(239, 347, 248, 356)(243, 351, 250, 358)(244, 352, 249, 357)(245, 353, 254, 362)(247, 355, 256, 364)(251, 359, 258, 366)(252, 360, 257, 365)(253, 361, 262, 370)(255, 363, 264, 372)(259, 367, 266, 374)(260, 368, 265, 373)(261, 369, 270, 378)(263, 371, 272, 380)(267, 375, 274, 382)(268, 376, 273, 381)(269, 377, 278, 386)(271, 379, 280, 388)(275, 383, 282, 390)(276, 384, 281, 389)(277, 385, 286, 394)(279, 387, 288, 396)(283, 391, 290, 398)(284, 392, 289, 397)(285, 393, 294, 402)(287, 395, 296, 404)(291, 399, 298, 406)(292, 400, 297, 405)(293, 401, 302, 410)(295, 403, 304, 412)(299, 407, 306, 414)(300, 408, 305, 413)(301, 409, 310, 418)(303, 411, 312, 420)(307, 415, 314, 422)(308, 416, 313, 421)(309, 417, 318, 426)(311, 419, 320, 428)(315, 423, 322, 430)(316, 424, 321, 429)(317, 425, 323, 431)(319, 427, 324, 432)
	L = (1, 220)(2, 224)(3, 226)(4, 217)(5, 227)(6, 231)(7, 232)(8, 218)(9, 234)(10, 219)(11, 221)(12, 235)(13, 239)(14, 240)(15, 222)(16, 223)(17, 242)(18, 225)(19, 228)(20, 243)(21, 247)(22, 248)(23, 229)(24, 230)(25, 250)(26, 233)(27, 236)(28, 251)(29, 255)(30, 256)(31, 237)(32, 238)(33, 258)(34, 241)(35, 244)(36, 259)(37, 263)(38, 264)(39, 245)(40, 246)(41, 266)(42, 249)(43, 252)(44, 267)(45, 271)(46, 272)(47, 253)(48, 254)(49, 274)(50, 257)(51, 260)(52, 275)(53, 279)(54, 280)(55, 261)(56, 262)(57, 282)(58, 265)(59, 268)(60, 283)(61, 287)(62, 288)(63, 269)(64, 270)(65, 290)(66, 273)(67, 276)(68, 291)(69, 295)(70, 296)(71, 277)(72, 278)(73, 298)(74, 281)(75, 284)(76, 299)(77, 303)(78, 304)(79, 285)(80, 286)(81, 306)(82, 289)(83, 292)(84, 307)(85, 311)(86, 312)(87, 293)(88, 294)(89, 314)(90, 297)(91, 300)(92, 315)(93, 319)(94, 320)(95, 301)(96, 302)(97, 322)(98, 305)(99, 308)(100, 323)(101, 321)(102, 324)(103, 309)(104, 310)(105, 317)(106, 313)(107, 316)(108, 318)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 4^4 ), ( 4^108 ) }
Outer automorphisms :: reflexible
Dual of E27.1994
Graph:: bipartite
	v = 56 e = 216 f = 108
	degree seq :: [ 4^54, 108^2 ]

E27.1996 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 54})
Quotient :: edge
Aut^+ = C27 : C4 (small group id <108, 1>)
Aut   = (C54 x C2) : C2 (small group id <216, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, T1^4, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^-2 * T2^27 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(109, 110, 114, 112)(111, 116, 121, 118)(113, 115, 122, 119)(117, 124, 129, 126)(120, 123, 130, 127)(125, 132, 137, 134)(128, 131, 138, 135)(133, 140, 145, 142)(136, 139, 146, 143)(141, 148, 153, 150)(144, 147, 154, 151)(149, 156, 161, 158)(152, 155, 162, 159)(157, 164, 169, 166)(160, 163, 170, 167)(165, 172, 177, 174)(168, 171, 178, 175)(173, 180, 185, 182)(176, 179, 186, 183)(181, 188, 193, 190)(184, 187, 194, 191)(189, 196, 201, 198)(192, 195, 202, 199)(197, 204, 209, 206)(200, 203, 210, 207)(205, 212, 216, 214)(208, 211, 213, 215)
	L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216)
	local type(s) :: { ( 8^4 ), ( 8^54 ) }
Outer automorphisms :: reflexible
Dual of E27.1997
Transitivity :: ET+
Graph:: bipartite
	v = 29 e = 108 f = 27
	degree seq :: [ 4^27, 54^2 ]

E27.1997 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 54})
Quotient :: loop
Aut^+ = C27 : C4 (small group id <108, 1>)
Aut   = (C54 x C2) : C2 (small group id <216, 8>)
|r| :: 2
Presentation :: [ F^2, T2^4, T1^2 * T2^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 109, 3, 111, 6, 114, 5, 113)(2, 110, 7, 115, 4, 112, 8, 116)(9, 117, 13, 121, 10, 118, 14, 122)(11, 119, 15, 123, 12, 120, 16, 124)(17, 125, 21, 129, 18, 126, 22, 130)(19, 127, 23, 131, 20, 128, 24, 132)(25, 133, 29, 137, 26, 134, 30, 138)(27, 135, 31, 139, 28, 136, 32, 140)(33, 141, 35, 143, 34, 142, 38, 146)(36, 144, 52, 160, 37, 145, 51, 159)(39, 147, 56, 164, 40, 148, 55, 163)(41, 149, 58, 166, 42, 150, 57, 165)(43, 151, 60, 168, 44, 152, 59, 167)(45, 153, 62, 170, 46, 154, 61, 169)(47, 155, 64, 172, 48, 156, 63, 171)(49, 157, 66, 174, 50, 158, 65, 173)(53, 161, 68, 176, 54, 162, 67, 175)(69, 177, 71, 179, 70, 178, 72, 180)(73, 181, 75, 183, 74, 182, 76, 184)(77, 185, 92, 200, 78, 186, 91, 199)(79, 187, 96, 204, 80, 188, 95, 203)(81, 189, 98, 206, 82, 190, 97, 205)(83, 191, 100, 208, 84, 192, 99, 207)(85, 193, 102, 210, 86, 194, 101, 209)(87, 195, 104, 212, 88, 196, 103, 211)(89, 197, 106, 214, 90, 198, 105, 213)(93, 201, 108, 216, 94, 202, 107, 215)
	L = (1, 110)(2, 114)(3, 117)(4, 109)(5, 118)(6, 112)(7, 119)(8, 120)(9, 113)(10, 111)(11, 116)(12, 115)(13, 125)(14, 126)(15, 127)(16, 128)(17, 122)(18, 121)(19, 124)(20, 123)(21, 133)(22, 134)(23, 135)(24, 136)(25, 130)(26, 129)(27, 132)(28, 131)(29, 141)(30, 142)(31, 159)(32, 160)(33, 138)(34, 137)(35, 163)(36, 165)(37, 166)(38, 164)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 140)(52, 139)(53, 181)(54, 182)(55, 146)(56, 143)(57, 145)(58, 144)(59, 148)(60, 147)(61, 150)(62, 149)(63, 152)(64, 151)(65, 154)(66, 153)(67, 156)(68, 155)(69, 158)(70, 157)(71, 199)(72, 200)(73, 162)(74, 161)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 201)(90, 202)(91, 180)(92, 179)(93, 198)(94, 197)(95, 184)(96, 183)(97, 186)(98, 185)(99, 188)(100, 187)(101, 190)(102, 189)(103, 192)(104, 191)(105, 194)(106, 193)(107, 196)(108, 195)
	local type(s) :: { ( 4, 54, 4, 54, 4, 54, 4, 54 ) }
Outer automorphisms :: reflexible
Dual of E27.1996
Transitivity :: ET+ VT+ AT
Graph::
	v = 27 e = 108 f = 29
	degree seq :: [ 8^27 ]

E27.1998 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 54})
Quotient :: dipole
Aut^+ = C27 : C4 (small group id <108, 1>)
Aut   = (C54 x C2) : C2 (small group id <216, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2^13 * Y1 * Y2^-13, Y2^54 ]
Map::
	R = (1, 109, 2, 110, 6, 114, 4, 112)(3, 111, 8, 116, 13, 121, 10, 118)(5, 113, 7, 115, 14, 122, 11, 119)(9, 117, 16, 124, 21, 129, 18, 126)(12, 120, 15, 123, 22, 130, 19, 127)(17, 125, 24, 132, 29, 137, 26, 134)(20, 128, 23, 131, 30, 138, 27, 135)(25, 133, 32, 140, 37, 145, 34, 142)(28, 136, 31, 139, 38, 146, 35, 143)(33, 141, 40, 148, 45, 153, 42, 150)(36, 144, 39, 147, 46, 154, 43, 151)(41, 149, 48, 156, 53, 161, 50, 158)(44, 152, 47, 155, 54, 162, 51, 159)(49, 157, 56, 164, 61, 169, 58, 166)(52, 160, 55, 163, 62, 170, 59, 167)(57, 165, 64, 172, 69, 177, 66, 174)(60, 168, 63, 171, 70, 178, 67, 175)(65, 173, 72, 180, 77, 185, 74, 182)(68, 176, 71, 179, 78, 186, 75, 183)(73, 181, 80, 188, 85, 193, 82, 190)(76, 184, 79, 187, 86, 194, 83, 191)(81, 189, 88, 196, 93, 201, 90, 198)(84, 192, 87, 195, 94, 202, 91, 199)(89, 197, 96, 204, 101, 209, 98, 206)(92, 200, 95, 203, 102, 210, 99, 207)(97, 205, 104, 212, 108, 216, 106, 214)(100, 208, 103, 211, 105, 213, 107, 215)(217, 325, 219, 327, 225, 333, 233, 341, 241, 349, 249, 357, 257, 365, 265, 373, 273, 381, 281, 389, 289, 397, 297, 405, 305, 413, 313, 421, 321, 429, 318, 426, 310, 418, 302, 410, 294, 402, 286, 394, 278, 386, 270, 378, 262, 370, 254, 362, 246, 354, 238, 346, 230, 338, 222, 330, 229, 337, 237, 345, 245, 353, 253, 361, 261, 369, 269, 377, 277, 385, 285, 393, 293, 401, 301, 409, 309, 417, 317, 425, 324, 432, 316, 424, 308, 416, 300, 408, 292, 400, 284, 392, 276, 384, 268, 376, 260, 368, 252, 360, 244, 352, 236, 344, 228, 336, 221, 329)(218, 326, 223, 331, 231, 339, 239, 347, 247, 355, 255, 363, 263, 371, 271, 379, 279, 387, 287, 395, 295, 403, 303, 411, 311, 419, 319, 427, 322, 430, 314, 422, 306, 414, 298, 406, 290, 398, 282, 390, 274, 382, 266, 374, 258, 366, 250, 358, 242, 350, 234, 342, 226, 334, 220, 328, 227, 335, 235, 343, 243, 351, 251, 359, 259, 367, 267, 375, 275, 383, 283, 391, 291, 399, 299, 407, 307, 415, 315, 423, 323, 431, 320, 428, 312, 420, 304, 412, 296, 404, 288, 396, 280, 388, 272, 380, 264, 372, 256, 364, 248, 356, 240, 348, 232, 340, 224, 332)
	L = (1, 219)(2, 223)(3, 225)(4, 227)(5, 217)(6, 229)(7, 231)(8, 218)(9, 233)(10, 220)(11, 235)(12, 221)(13, 237)(14, 222)(15, 239)(16, 224)(17, 241)(18, 226)(19, 243)(20, 228)(21, 245)(22, 230)(23, 247)(24, 232)(25, 249)(26, 234)(27, 251)(28, 236)(29, 253)(30, 238)(31, 255)(32, 240)(33, 257)(34, 242)(35, 259)(36, 244)(37, 261)(38, 246)(39, 263)(40, 248)(41, 265)(42, 250)(43, 267)(44, 252)(45, 269)(46, 254)(47, 271)(48, 256)(49, 273)(50, 258)(51, 275)(52, 260)(53, 277)(54, 262)(55, 279)(56, 264)(57, 281)(58, 266)(59, 283)(60, 268)(61, 285)(62, 270)(63, 287)(64, 272)(65, 289)(66, 274)(67, 291)(68, 276)(69, 293)(70, 278)(71, 295)(72, 280)(73, 297)(74, 282)(75, 299)(76, 284)(77, 301)(78, 286)(79, 303)(80, 288)(81, 305)(82, 290)(83, 307)(84, 292)(85, 309)(86, 294)(87, 311)(88, 296)(89, 313)(90, 298)(91, 315)(92, 300)(93, 317)(94, 302)(95, 319)(96, 304)(97, 321)(98, 306)(99, 323)(100, 308)(101, 324)(102, 310)(103, 322)(104, 312)(105, 318)(106, 314)(107, 320)(108, 316)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.1999
Graph:: bipartite
	v = 29 e = 216 f = 135
	degree seq :: [ 8^27, 108^2 ]

E27.1999 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 54})
Quotient :: dipole
Aut^+ = C27 : C4 (small group id <108, 1>)
Aut   = (C54 x C2) : C2 (small group id <216, 8>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^27, (Y3^-1 * Y1^-1)^54 ]
Map::
	R = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216)(217, 325, 218, 326, 222, 330, 220, 328)(219, 327, 224, 332, 229, 337, 226, 334)(221, 329, 223, 331, 230, 338, 227, 335)(225, 333, 232, 340, 237, 345, 234, 342)(228, 336, 231, 339, 238, 346, 235, 343)(233, 341, 240, 348, 245, 353, 242, 350)(236, 344, 239, 347, 246, 354, 243, 351)(241, 349, 248, 356, 253, 361, 250, 358)(244, 352, 247, 355, 254, 362, 251, 359)(249, 357, 256, 364, 261, 369, 258, 366)(252, 360, 255, 363, 262, 370, 259, 367)(257, 365, 264, 372, 269, 377, 266, 374)(260, 368, 263, 371, 270, 378, 267, 375)(265, 373, 272, 380, 277, 385, 274, 382)(268, 376, 271, 379, 278, 386, 275, 383)(273, 381, 280, 388, 285, 393, 282, 390)(276, 384, 279, 387, 286, 394, 283, 391)(281, 389, 288, 396, 293, 401, 290, 398)(284, 392, 287, 395, 294, 402, 291, 399)(289, 397, 296, 404, 301, 409, 298, 406)(292, 400, 295, 403, 302, 410, 299, 407)(297, 405, 304, 412, 309, 417, 306, 414)(300, 408, 303, 411, 310, 418, 307, 415)(305, 413, 312, 420, 317, 425, 314, 422)(308, 416, 311, 419, 318, 426, 315, 423)(313, 421, 320, 428, 324, 432, 322, 430)(316, 424, 319, 427, 321, 429, 323, 431)
	L = (1, 219)(2, 223)(3, 225)(4, 227)(5, 217)(6, 229)(7, 231)(8, 218)(9, 233)(10, 220)(11, 235)(12, 221)(13, 237)(14, 222)(15, 239)(16, 224)(17, 241)(18, 226)(19, 243)(20, 228)(21, 245)(22, 230)(23, 247)(24, 232)(25, 249)(26, 234)(27, 251)(28, 236)(29, 253)(30, 238)(31, 255)(32, 240)(33, 257)(34, 242)(35, 259)(36, 244)(37, 261)(38, 246)(39, 263)(40, 248)(41, 265)(42, 250)(43, 267)(44, 252)(45, 269)(46, 254)(47, 271)(48, 256)(49, 273)(50, 258)(51, 275)(52, 260)(53, 277)(54, 262)(55, 279)(56, 264)(57, 281)(58, 266)(59, 283)(60, 268)(61, 285)(62, 270)(63, 287)(64, 272)(65, 289)(66, 274)(67, 291)(68, 276)(69, 293)(70, 278)(71, 295)(72, 280)(73, 297)(74, 282)(75, 299)(76, 284)(77, 301)(78, 286)(79, 303)(80, 288)(81, 305)(82, 290)(83, 307)(84, 292)(85, 309)(86, 294)(87, 311)(88, 296)(89, 313)(90, 298)(91, 315)(92, 300)(93, 317)(94, 302)(95, 319)(96, 304)(97, 321)(98, 306)(99, 323)(100, 308)(101, 324)(102, 310)(103, 322)(104, 312)(105, 318)(106, 314)(107, 320)(108, 316)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 8, 108 ), ( 8, 108, 8, 108, 8, 108, 8, 108 ) }
Outer automorphisms :: reflexible
Dual of E27.1998
Graph:: simple bipartite
	v = 135 e = 216 f = 29
	degree seq :: [ 2^108, 8^27 ]

E27.2000 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 108, 108})
Quotient :: regular
Aut^+ = C108 (small group id <108, 2>)
Aut   = D216 (small group id <216, 6>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^54 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 40, 36, 33, 34, 37, 41, 44, 47, 49, 51, 53, 63, 59, 56, 57, 60, 64, 67, 70, 72, 74, 76, 86, 83, 80, 81, 79, 87, 90, 93, 95, 97, 99, 106, 104, 102, 78, 55, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 46, 43, 39, 35, 38, 42, 45, 48, 50, 52, 54, 69, 66, 62, 58, 61, 65, 68, 71, 73, 75, 77, 92, 89, 85, 82, 84, 88, 91, 94, 96, 98, 100, 108, 107, 105, 103, 101, 32, 28, 24, 20, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 46)(32, 55)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 45)(44, 48)(47, 50)(49, 52)(51, 54)(53, 69)(56, 58)(57, 61)(59, 62)(60, 65)(63, 66)(64, 68)(67, 71)(70, 73)(72, 75)(74, 77)(76, 92)(78, 101)(79, 88)(80, 82)(81, 84)(83, 85)(86, 89)(87, 91)(90, 94)(93, 96)(95, 98)(97, 100)(99, 108)(102, 103)(104, 105)(106, 107)
	local type(s) :: { ( 108^108 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 54 f = 1
	degree seq :: [ 108 ]

E27.2001 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 108, 108})
Quotient :: edge
Aut^+ = C108 (small group id <108, 2>)
Aut   = D216 (small group id <216, 6>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^54 * T1 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 36, 33, 35, 39, 42, 44, 46, 48, 50, 52, 57, 54, 56, 60, 63, 65, 67, 69, 71, 73, 79, 76, 78, 82, 85, 87, 89, 75, 92, 94, 100, 97, 99, 103, 106, 96, 74, 53, 30, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 29, 41, 38, 34, 37, 40, 43, 45, 47, 49, 51, 62, 59, 55, 58, 61, 64, 66, 68, 70, 72, 84, 81, 77, 80, 83, 86, 88, 90, 91, 93, 105, 102, 98, 101, 104, 107, 108, 95, 32, 28, 24, 20, 16, 12, 8, 4)(109, 110)(111, 113)(112, 114)(115, 117)(116, 118)(119, 121)(120, 122)(123, 125)(124, 126)(127, 129)(128, 130)(131, 133)(132, 134)(135, 137)(136, 138)(139, 149)(140, 161)(141, 142)(143, 145)(144, 146)(147, 148)(150, 151)(152, 153)(154, 155)(156, 157)(158, 159)(160, 170)(162, 163)(164, 166)(165, 167)(168, 169)(171, 172)(173, 174)(175, 176)(177, 178)(179, 180)(181, 192)(182, 203)(183, 199)(184, 185)(186, 188)(187, 189)(190, 191)(193, 194)(195, 196)(197, 198)(200, 201)(202, 213)(204, 216)(205, 206)(207, 209)(208, 210)(211, 212)(214, 215)
	L = (1, 109)(2, 110)(3, 111)(4, 112)(5, 113)(6, 114)(7, 115)(8, 116)(9, 117)(10, 118)(11, 119)(12, 120)(13, 121)(14, 122)(15, 123)(16, 124)(17, 125)(18, 126)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 134)(27, 135)(28, 136)(29, 137)(30, 138)(31, 139)(32, 140)(33, 141)(34, 142)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 165)(58, 166)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 173)(66, 174)(67, 175)(68, 176)(69, 177)(70, 178)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 185)(78, 186)(79, 187)(80, 188)(81, 189)(82, 190)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 197)(90, 198)(91, 199)(92, 200)(93, 201)(94, 202)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 209)(102, 210)(103, 211)(104, 212)(105, 213)(106, 214)(107, 215)(108, 216)
	local type(s) :: { ( 216, 216 ), ( 216^108 ) }
Outer automorphisms :: reflexible
Dual of E27.2002
Transitivity :: ET+
Graph:: bipartite
	v = 55 e = 108 f = 1
	degree seq :: [ 2^54, 108 ]

E27.2002 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 108, 108})
Quotient :: loop
Aut^+ = C108 (small group id <108, 2>)
Aut   = D216 (small group id <216, 6>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^54 * T1 ]
Map::
	R = (1, 109, 3, 111, 7, 115, 11, 119, 15, 123, 19, 127, 23, 131, 27, 135, 31, 139, 35, 143, 37, 145, 39, 147, 41, 149, 43, 151, 45, 153, 47, 155, 50, 158, 51, 159, 53, 161, 55, 163, 57, 165, 59, 167, 61, 169, 63, 171, 65, 173, 70, 178, 72, 180, 74, 182, 76, 184, 78, 186, 80, 188, 82, 190, 89, 197, 90, 198, 92, 200, 94, 202, 96, 204, 98, 206, 87, 195, 99, 207, 100, 208, 105, 213, 107, 215, 102, 210, 85, 193, 66, 174, 49, 157, 30, 138, 26, 134, 22, 130, 18, 126, 14, 122, 10, 118, 6, 114, 2, 110, 5, 113, 9, 117, 13, 121, 17, 125, 21, 129, 25, 133, 29, 137, 33, 141, 34, 142, 36, 144, 38, 146, 40, 148, 42, 150, 44, 152, 46, 154, 48, 156, 52, 160, 54, 162, 56, 164, 58, 166, 60, 168, 62, 170, 64, 172, 68, 176, 69, 177, 71, 179, 73, 181, 75, 183, 77, 185, 79, 187, 81, 189, 83, 191, 91, 199, 93, 201, 95, 203, 97, 205, 86, 194, 67, 175, 88, 196, 103, 211, 104, 212, 106, 214, 108, 216, 101, 209, 84, 192, 32, 140, 28, 136, 24, 132, 20, 128, 16, 124, 12, 120, 8, 116, 4, 112)
	L = (1, 110)(2, 109)(3, 113)(4, 114)(5, 111)(6, 112)(7, 117)(8, 118)(9, 115)(10, 116)(11, 121)(12, 122)(13, 119)(14, 120)(15, 125)(16, 126)(17, 123)(18, 124)(19, 129)(20, 130)(21, 127)(22, 128)(23, 133)(24, 134)(25, 131)(26, 132)(27, 137)(28, 138)(29, 135)(30, 136)(31, 141)(32, 157)(33, 139)(34, 143)(35, 142)(36, 145)(37, 144)(38, 147)(39, 146)(40, 149)(41, 148)(42, 151)(43, 150)(44, 153)(45, 152)(46, 155)(47, 154)(48, 158)(49, 140)(50, 156)(51, 160)(52, 159)(53, 162)(54, 161)(55, 164)(56, 163)(57, 166)(58, 165)(59, 168)(60, 167)(61, 170)(62, 169)(63, 172)(64, 171)(65, 176)(66, 192)(67, 195)(68, 173)(69, 178)(70, 177)(71, 180)(72, 179)(73, 182)(74, 181)(75, 184)(76, 183)(77, 186)(78, 185)(79, 188)(80, 187)(81, 190)(82, 189)(83, 197)(84, 174)(85, 209)(86, 206)(87, 175)(88, 207)(89, 191)(90, 199)(91, 198)(92, 201)(93, 200)(94, 203)(95, 202)(96, 205)(97, 204)(98, 194)(99, 196)(100, 211)(101, 193)(102, 216)(103, 208)(104, 213)(105, 212)(106, 215)(107, 214)(108, 210)
	local type(s) :: { ( 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108, 2, 108 ) }
Outer automorphisms :: reflexible
Dual of E27.2001
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 108 f = 55
	degree seq :: [ 216 ]

E27.2003 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 108, 108})
Quotient :: dipole
Aut^+ = C108 (small group id <108, 2>)
Aut   = D216 (small group id <216, 6>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^54 * Y1, (Y3 * Y2^-1)^108 ]
Map::
	R = (1, 109, 2, 110)(3, 111, 5, 113)(4, 112, 6, 114)(7, 115, 9, 117)(8, 116, 10, 118)(11, 119, 13, 121)(12, 120, 14, 122)(15, 123, 17, 125)(16, 124, 18, 126)(19, 127, 21, 129)(20, 128, 22, 130)(23, 131, 25, 133)(24, 132, 26, 134)(27, 135, 29, 137)(28, 136, 30, 138)(31, 139, 40, 148)(32, 140, 53, 161)(33, 141, 34, 142)(35, 143, 37, 145)(36, 144, 38, 146)(39, 147, 41, 149)(42, 150, 43, 151)(44, 152, 45, 153)(46, 154, 47, 155)(48, 156, 49, 157)(50, 158, 51, 159)(52, 160, 61, 169)(54, 162, 55, 163)(56, 164, 58, 166)(57, 165, 59, 167)(60, 168, 62, 170)(63, 171, 64, 172)(65, 173, 66, 174)(67, 175, 68, 176)(69, 177, 70, 178)(71, 179, 72, 180)(73, 181, 83, 191)(74, 182, 95, 203)(75, 183, 91, 199)(76, 184, 77, 185)(78, 186, 80, 188)(79, 187, 81, 189)(82, 190, 84, 192)(85, 193, 86, 194)(87, 195, 88, 196)(89, 197, 90, 198)(92, 200, 93, 201)(94, 202, 104, 212)(96, 204, 108, 216)(97, 205, 98, 206)(99, 207, 101, 209)(100, 208, 102, 210)(103, 211, 105, 213)(106, 214, 107, 215)(217, 325, 219, 327, 223, 331, 227, 335, 231, 339, 235, 343, 239, 347, 243, 351, 247, 355, 254, 362, 250, 358, 253, 361, 257, 365, 259, 367, 261, 369, 263, 371, 265, 373, 267, 375, 277, 385, 273, 381, 270, 378, 272, 380, 276, 384, 279, 387, 281, 389, 283, 391, 285, 393, 287, 395, 289, 397, 297, 405, 293, 401, 296, 404, 300, 408, 302, 410, 304, 412, 306, 414, 307, 415, 309, 417, 320, 428, 316, 424, 313, 421, 315, 423, 319, 427, 322, 430, 312, 420, 290, 398, 269, 377, 246, 354, 242, 350, 238, 346, 234, 342, 230, 338, 226, 334, 222, 330, 218, 326, 221, 329, 225, 333, 229, 337, 233, 341, 237, 345, 241, 349, 245, 353, 256, 364, 252, 360, 249, 357, 251, 359, 255, 363, 258, 366, 260, 368, 262, 370, 264, 372, 266, 374, 268, 376, 275, 383, 271, 379, 274, 382, 278, 386, 280, 388, 282, 390, 284, 392, 286, 394, 288, 396, 299, 407, 295, 403, 292, 400, 294, 402, 298, 406, 301, 409, 303, 411, 305, 413, 291, 399, 308, 416, 310, 418, 318, 426, 314, 422, 317, 425, 321, 429, 323, 431, 324, 432, 311, 419, 248, 356, 244, 352, 240, 348, 236, 344, 232, 340, 228, 336, 224, 332, 220, 328)
	L = (1, 218)(2, 217)(3, 221)(4, 222)(5, 219)(6, 220)(7, 225)(8, 226)(9, 223)(10, 224)(11, 229)(12, 230)(13, 227)(14, 228)(15, 233)(16, 234)(17, 231)(18, 232)(19, 237)(20, 238)(21, 235)(22, 236)(23, 241)(24, 242)(25, 239)(26, 240)(27, 245)(28, 246)(29, 243)(30, 244)(31, 256)(32, 269)(33, 250)(34, 249)(35, 253)(36, 254)(37, 251)(38, 252)(39, 257)(40, 247)(41, 255)(42, 259)(43, 258)(44, 261)(45, 260)(46, 263)(47, 262)(48, 265)(49, 264)(50, 267)(51, 266)(52, 277)(53, 248)(54, 271)(55, 270)(56, 274)(57, 275)(58, 272)(59, 273)(60, 278)(61, 268)(62, 276)(63, 280)(64, 279)(65, 282)(66, 281)(67, 284)(68, 283)(69, 286)(70, 285)(71, 288)(72, 287)(73, 299)(74, 311)(75, 307)(76, 293)(77, 292)(78, 296)(79, 297)(80, 294)(81, 295)(82, 300)(83, 289)(84, 298)(85, 302)(86, 301)(87, 304)(88, 303)(89, 306)(90, 305)(91, 291)(92, 309)(93, 308)(94, 320)(95, 290)(96, 324)(97, 314)(98, 313)(99, 317)(100, 318)(101, 315)(102, 316)(103, 321)(104, 310)(105, 319)(106, 323)(107, 322)(108, 312)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 2, 216, 2, 216 ), ( 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216, 2, 216 ) }
Outer automorphisms :: reflexible
Dual of E27.2004
Graph:: bipartite
	v = 55 e = 216 f = 109
	degree seq :: [ 4^54, 216 ]

E27.2004 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 108, 108})
Quotient :: dipole
Aut^+ = C108 (small group id <108, 2>)
Aut   = D216 (small group id <216, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y2^-1)^2, Y3 * Y1^54 ]
Map::
	R = (1, 109, 2, 110, 5, 113, 9, 117, 13, 121, 17, 125, 21, 129, 25, 133, 29, 137, 39, 147, 35, 143, 38, 146, 42, 150, 44, 152, 46, 154, 48, 156, 50, 158, 52, 160, 61, 169, 57, 165, 54, 162, 55, 163, 58, 166, 62, 170, 64, 172, 66, 174, 68, 176, 70, 178, 72, 180, 82, 190, 78, 186, 81, 189, 85, 193, 87, 195, 89, 197, 90, 198, 92, 200, 94, 202, 104, 212, 100, 208, 97, 205, 98, 206, 101, 209, 105, 213, 96, 204, 74, 182, 53, 161, 31, 139, 27, 135, 23, 131, 19, 127, 15, 123, 11, 119, 7, 115, 3, 111, 6, 114, 10, 118, 14, 122, 18, 126, 22, 130, 26, 134, 30, 138, 40, 148, 36, 144, 33, 141, 34, 142, 37, 145, 41, 149, 43, 151, 45, 153, 47, 155, 49, 157, 51, 159, 60, 168, 56, 164, 59, 167, 63, 171, 65, 173, 67, 175, 69, 177, 71, 179, 73, 181, 83, 191, 79, 187, 76, 184, 77, 185, 80, 188, 84, 192, 86, 194, 88, 196, 75, 183, 91, 199, 93, 201, 103, 211, 99, 207, 102, 210, 106, 214, 107, 215, 108, 216, 95, 203, 32, 140, 28, 136, 24, 132, 20, 128, 16, 124, 12, 120, 8, 116, 4, 112)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 335)(228, 336)(229, 337)(230, 338)(231, 339)(232, 340)(233, 341)(234, 342)(235, 343)(236, 344)(237, 345)(238, 346)(239, 347)(240, 348)(241, 349)(242, 350)(243, 351)(244, 352)(245, 353)(246, 354)(247, 355)(248, 356)(249, 357)(250, 358)(251, 359)(252, 360)(253, 361)(254, 362)(255, 363)(256, 364)(257, 365)(258, 366)(259, 367)(260, 368)(261, 369)(262, 370)(263, 371)(264, 372)(265, 373)(266, 374)(267, 375)(268, 376)(269, 377)(270, 378)(271, 379)(272, 380)(273, 381)(274, 382)(275, 383)(276, 384)(277, 385)(278, 386)(279, 387)(280, 388)(281, 389)(282, 390)(283, 391)(284, 392)(285, 393)(286, 394)(287, 395)(288, 396)(289, 397)(290, 398)(291, 399)(292, 400)(293, 401)(294, 402)(295, 403)(296, 404)(297, 405)(298, 406)(299, 407)(300, 408)(301, 409)(302, 410)(303, 411)(304, 412)(305, 413)(306, 414)(307, 415)(308, 416)(309, 417)(310, 418)(311, 419)(312, 420)(313, 421)(314, 422)(315, 423)(316, 424)(317, 425)(318, 426)(319, 427)(320, 428)(321, 429)(322, 430)(323, 431)(324, 432)
	L = (1, 219)(2, 222)(3, 217)(4, 223)(5, 226)(6, 218)(7, 220)(8, 227)(9, 230)(10, 221)(11, 224)(12, 231)(13, 234)(14, 225)(15, 228)(16, 235)(17, 238)(18, 229)(19, 232)(20, 239)(21, 242)(22, 233)(23, 236)(24, 243)(25, 246)(26, 237)(27, 240)(28, 247)(29, 256)(30, 241)(31, 244)(32, 269)(33, 251)(34, 254)(35, 249)(36, 255)(37, 258)(38, 250)(39, 252)(40, 245)(41, 260)(42, 253)(43, 262)(44, 257)(45, 264)(46, 259)(47, 266)(48, 261)(49, 268)(50, 263)(51, 277)(52, 265)(53, 248)(54, 272)(55, 275)(56, 270)(57, 276)(58, 279)(59, 271)(60, 273)(61, 267)(62, 281)(63, 274)(64, 283)(65, 278)(66, 285)(67, 280)(68, 287)(69, 282)(70, 289)(71, 284)(72, 299)(73, 286)(74, 311)(75, 308)(76, 294)(77, 297)(78, 292)(79, 298)(80, 301)(81, 293)(82, 295)(83, 288)(84, 303)(85, 296)(86, 305)(87, 300)(88, 306)(89, 302)(90, 304)(91, 310)(92, 291)(93, 320)(94, 307)(95, 290)(96, 324)(97, 315)(98, 318)(99, 313)(100, 319)(101, 322)(102, 314)(103, 316)(104, 309)(105, 323)(106, 317)(107, 321)(108, 312)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 4, 216 ), ( 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216, 4, 216 ) }
Outer automorphisms :: reflexible
Dual of E27.2003
Graph:: bipartite
	v = 109 e = 216 f = 55
	degree seq :: [ 2^108, 216 ]

E27.2005 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 55, 110})
Quotient :: regular
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-55 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 35, 38, 40, 42, 44, 46, 48, 50, 55, 52, 53, 56, 58, 60, 62, 64, 66, 68, 74, 77, 79, 81, 83, 85, 87, 89, 98, 95, 96, 94, 99, 100, 101, 103, 105, 107, 91, 70, 51, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 36, 33, 34, 37, 39, 41, 43, 45, 47, 49, 54, 57, 59, 61, 63, 65, 67, 69, 75, 72, 73, 76, 78, 80, 82, 84, 86, 88, 97, 92, 71, 93, 102, 104, 106, 108, 110, 109, 90, 32, 28, 24, 20, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 36)(32, 51)(33, 35)(34, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 55)(52, 54)(53, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 75)(70, 90)(71, 94)(72, 74)(73, 77)(76, 79)(78, 81)(80, 83)(82, 85)(84, 87)(86, 89)(88, 98)(91, 109)(92, 96)(93, 99)(95, 97)(100, 102)(101, 104)(103, 106)(105, 108)(107, 110)
	local type(s) :: { ( 55^110 ) }
Outer automorphisms :: reflexible
Dual of E27.2006
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 55 f = 2
	degree seq :: [ 110 ]

E27.2006 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 55, 110})
Quotient :: regular
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^55 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 39, 41, 43, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64, 66, 68, 72, 73, 75, 78, 80, 82, 84, 86, 88, 95, 96, 94, 99, 100, 101, 103, 105, 107, 109, 90, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 38, 35, 37, 40, 42, 44, 46, 48, 50, 57, 54, 56, 59, 61, 63, 65, 67, 69, 77, 74, 76, 79, 81, 83, 85, 87, 89, 98, 97, 92, 71, 93, 102, 104, 106, 108, 110, 91, 70, 51, 31, 27, 23, 19, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 38)(32, 51)(33, 35)(34, 37)(36, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 57)(52, 54)(53, 56)(55, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 77)(70, 90)(71, 94)(72, 74)(73, 76)(75, 79)(78, 81)(80, 83)(82, 85)(84, 87)(86, 89)(88, 98)(91, 109)(92, 96)(93, 99)(95, 97)(100, 102)(101, 104)(103, 106)(105, 108)(107, 110)
	local type(s) :: { ( 110^55 ) }
Outer automorphisms :: reflexible
Dual of E27.2005
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 55 f = 1
	degree seq :: [ 55^2 ]

E27.2007 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 55, 110})
Quotient :: edge
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^55 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 33, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 57, 59, 61, 63, 65, 67, 69, 72, 74, 77, 79, 81, 83, 85, 87, 89, 95, 97, 93, 99, 100, 102, 104, 106, 108, 109, 90, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 37, 34, 36, 39, 41, 43, 45, 47, 49, 56, 53, 55, 58, 60, 62, 64, 66, 68, 76, 73, 75, 78, 80, 82, 84, 86, 88, 98, 96, 92, 71, 94, 101, 103, 105, 107, 110, 91, 70, 51, 30, 26, 22, 18, 14, 10, 6)(111, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 123)(122, 124)(125, 127)(126, 128)(129, 131)(130, 132)(133, 135)(134, 136)(137, 139)(138, 140)(141, 147)(142, 161)(143, 144)(145, 146)(148, 149)(150, 151)(152, 153)(154, 155)(156, 157)(158, 159)(160, 166)(162, 163)(164, 165)(167, 168)(169, 170)(171, 172)(173, 174)(175, 176)(177, 178)(179, 186)(180, 200)(181, 203)(182, 183)(184, 185)(187, 188)(189, 190)(191, 192)(193, 194)(195, 196)(197, 198)(199, 208)(201, 219)(202, 207)(204, 209)(205, 206)(210, 211)(212, 213)(214, 215)(216, 217)(218, 220)
	L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 220, 220 ), ( 220^55 ) }
Outer automorphisms :: reflexible
Dual of E27.2011
Transitivity :: ET+
Graph:: simple bipartite
	v = 57 e = 110 f = 1
	degree seq :: [ 2^55, 55^2 ]

E27.2008 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 55, 110})
Quotient :: edge
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^25 * T2^-28, T2^-2 * T1^53 ]
Map:: non-degenerate
	R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 59, 85, 110, 107, 106, 103, 102, 97, 96, 90, 95, 92, 87, 100, 84, 81, 80, 77, 76, 71, 68, 62, 67, 64, 70, 74, 58, 55, 54, 51, 50, 45, 42, 36, 41, 38, 44, 48, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 60, 86, 109, 108, 105, 104, 101, 98, 94, 93, 89, 91, 88, 99, 83, 82, 79, 78, 75, 72, 66, 65, 61, 63, 69, 73, 57, 56, 53, 52, 49, 46, 40, 39, 35, 37, 43, 47, 31, 28, 23, 20, 15, 12, 6, 5)(111, 112, 116, 121, 125, 129, 133, 137, 141, 158, 153, 148, 145, 146, 150, 155, 159, 161, 163, 165, 167, 184, 179, 174, 171, 172, 176, 181, 185, 187, 189, 191, 193, 210, 198, 202, 199, 200, 204, 207, 211, 213, 215, 217, 219, 195, 170, 143, 140, 135, 132, 127, 124, 119, 114)(113, 117, 115, 118, 122, 126, 130, 134, 138, 142, 157, 154, 147, 151, 149, 152, 156, 160, 162, 164, 166, 168, 183, 180, 173, 177, 175, 178, 182, 186, 188, 190, 192, 194, 209, 197, 201, 205, 203, 206, 208, 212, 214, 216, 218, 220, 196, 169, 144, 139, 136, 131, 128, 123, 120)
	L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 4^55 ), ( 4^110 ) }
Outer automorphisms :: reflexible
Dual of E27.2012
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 110 f = 55
	degree seq :: [ 55^2, 110 ]

E27.2009 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 55, 110})
Quotient :: edge
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-55 ]
Map::
	R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 36)(32, 51)(33, 35)(34, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 55)(52, 54)(53, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 75)(70, 90)(71, 94)(72, 74)(73, 77)(76, 79)(78, 81)(80, 83)(82, 85)(84, 87)(86, 89)(88, 98)(91, 109)(92, 96)(93, 99)(95, 97)(100, 102)(101, 104)(103, 106)(105, 108)(107, 110)(111, 112, 115, 119, 123, 127, 131, 135, 139, 145, 148, 150, 152, 154, 156, 158, 160, 165, 162, 163, 166, 168, 170, 172, 174, 176, 178, 184, 187, 189, 191, 193, 195, 197, 199, 208, 205, 206, 204, 209, 210, 211, 213, 215, 217, 201, 180, 161, 141, 137, 133, 129, 125, 121, 117, 113, 116, 120, 124, 128, 132, 136, 140, 146, 143, 144, 147, 149, 151, 153, 155, 157, 159, 164, 167, 169, 171, 173, 175, 177, 179, 185, 182, 183, 186, 188, 190, 192, 194, 196, 198, 207, 202, 181, 203, 212, 214, 216, 218, 220, 219, 200, 142, 138, 134, 130, 126, 122, 118, 114)
	L = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)
	local type(s) :: { ( 110, 110 ), ( 110^110 ) }
Outer automorphisms :: reflexible
Dual of E27.2010
Transitivity :: ET+
Graph:: bipartite
	v = 56 e = 110 f = 2
	degree seq :: [ 2^55, 110 ]

E27.2010 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 55, 110})
Quotient :: loop
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^55 ]
Map::
	R = (1, 111, 3, 113, 7, 117, 11, 121, 15, 125, 19, 129, 23, 133, 27, 137, 31, 141, 35, 145, 37, 147, 39, 149, 41, 151, 43, 153, 45, 155, 47, 157, 50, 160, 51, 161, 53, 163, 55, 165, 57, 167, 59, 169, 61, 171, 63, 173, 65, 175, 70, 180, 72, 182, 74, 184, 76, 186, 78, 188, 80, 190, 82, 192, 89, 199, 90, 200, 92, 202, 94, 204, 96, 206, 98, 208, 86, 196, 67, 177, 88, 198, 104, 214, 107, 217, 109, 219, 110, 220, 101, 211, 84, 194, 32, 142, 28, 138, 24, 134, 20, 130, 16, 126, 12, 122, 8, 118, 4, 114)(2, 112, 5, 115, 9, 119, 13, 123, 17, 127, 21, 131, 25, 135, 29, 139, 33, 143, 34, 144, 36, 146, 38, 148, 40, 150, 42, 152, 44, 154, 46, 156, 48, 158, 52, 162, 54, 164, 56, 166, 58, 168, 60, 170, 62, 172, 64, 174, 68, 178, 69, 179, 71, 181, 73, 183, 75, 185, 77, 187, 79, 189, 81, 191, 83, 193, 91, 201, 93, 203, 95, 205, 97, 207, 99, 209, 100, 210, 87, 197, 103, 213, 105, 215, 106, 216, 108, 218, 102, 212, 85, 195, 66, 176, 49, 159, 30, 140, 26, 136, 22, 132, 18, 128, 14, 124, 10, 120, 6, 116)
	L = (1, 112)(2, 111)(3, 115)(4, 116)(5, 113)(6, 114)(7, 119)(8, 120)(9, 117)(10, 118)(11, 123)(12, 124)(13, 121)(14, 122)(15, 127)(16, 128)(17, 125)(18, 126)(19, 131)(20, 132)(21, 129)(22, 130)(23, 135)(24, 136)(25, 133)(26, 134)(27, 139)(28, 140)(29, 137)(30, 138)(31, 143)(32, 159)(33, 141)(34, 145)(35, 144)(36, 147)(37, 146)(38, 149)(39, 148)(40, 151)(41, 150)(42, 153)(43, 152)(44, 155)(45, 154)(46, 157)(47, 156)(48, 160)(49, 142)(50, 158)(51, 162)(52, 161)(53, 164)(54, 163)(55, 166)(56, 165)(57, 168)(58, 167)(59, 170)(60, 169)(61, 172)(62, 171)(63, 174)(64, 173)(65, 178)(66, 194)(67, 197)(68, 175)(69, 180)(70, 179)(71, 182)(72, 181)(73, 184)(74, 183)(75, 186)(76, 185)(77, 188)(78, 187)(79, 190)(80, 189)(81, 192)(82, 191)(83, 199)(84, 176)(85, 211)(86, 210)(87, 177)(88, 213)(89, 193)(90, 201)(91, 200)(92, 203)(93, 202)(94, 205)(95, 204)(96, 207)(97, 206)(98, 209)(99, 208)(100, 196)(101, 195)(102, 220)(103, 198)(104, 215)(105, 214)(106, 217)(107, 216)(108, 219)(109, 218)(110, 212)
	local type(s) :: { ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.2009
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 110 f = 56
	degree seq :: [ 110^2 ]

E27.2011 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 55, 110})
Quotient :: loop
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^25 * T2^-28, T2^-2 * T1^53 ]
Map::
	R = (1, 111, 3, 113, 9, 119, 13, 123, 17, 127, 21, 131, 25, 135, 29, 139, 33, 143, 57, 167, 81, 191, 105, 215, 108, 218, 110, 220, 103, 213, 102, 212, 99, 209, 98, 208, 95, 205, 94, 204, 84, 194, 89, 199, 85, 195, 87, 197, 91, 201, 80, 190, 77, 187, 76, 186, 73, 183, 72, 182, 69, 179, 66, 176, 60, 170, 65, 175, 62, 172, 68, 178, 55, 165, 54, 164, 51, 161, 50, 160, 47, 157, 46, 156, 40, 150, 39, 149, 35, 145, 37, 147, 43, 153, 32, 142, 27, 137, 24, 134, 19, 129, 16, 126, 11, 121, 8, 118, 2, 112, 7, 117, 4, 114, 10, 120, 14, 124, 18, 128, 22, 132, 26, 136, 30, 140, 34, 144, 58, 168, 82, 192, 106, 216, 107, 217, 109, 219, 104, 214, 101, 211, 100, 210, 97, 207, 96, 206, 93, 203, 83, 193, 86, 196, 90, 200, 88, 198, 92, 202, 79, 189, 78, 188, 75, 185, 74, 184, 71, 181, 70, 180, 64, 174, 63, 173, 59, 169, 61, 171, 67, 177, 56, 166, 53, 163, 52, 162, 49, 159, 48, 158, 45, 155, 42, 152, 36, 146, 41, 151, 38, 148, 44, 154, 31, 141, 28, 138, 23, 133, 20, 130, 15, 125, 12, 122, 6, 116, 5, 115)
	L = (1, 112)(2, 116)(3, 117)(4, 111)(5, 118)(6, 121)(7, 115)(8, 122)(9, 114)(10, 113)(11, 125)(12, 126)(13, 120)(14, 119)(15, 129)(16, 130)(17, 124)(18, 123)(19, 133)(20, 134)(21, 128)(22, 127)(23, 137)(24, 138)(25, 132)(26, 131)(27, 141)(28, 142)(29, 136)(30, 135)(31, 153)(32, 154)(33, 140)(34, 139)(35, 146)(36, 150)(37, 151)(38, 145)(39, 152)(40, 155)(41, 149)(42, 156)(43, 148)(44, 147)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 177)(56, 178)(57, 144)(58, 143)(59, 170)(60, 174)(61, 175)(62, 169)(63, 176)(64, 179)(65, 173)(66, 180)(67, 172)(68, 171)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 201)(80, 202)(81, 168)(82, 167)(83, 204)(84, 203)(85, 196)(86, 194)(87, 200)(88, 195)(89, 193)(90, 199)(91, 198)(92, 197)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 219)(104, 220)(105, 192)(106, 191)(107, 215)(108, 216)(109, 218)(110, 217)
	local type(s) :: { ( 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55, 2, 55 ) }
Outer automorphisms :: reflexible
Dual of E27.2007
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 110 f = 57
	degree seq :: [ 220 ]

E27.2012 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 55, 110})
Quotient :: loop
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-55 ]
Map:: non-degenerate
	R = (1, 111, 3, 113)(2, 112, 6, 116)(4, 114, 7, 117)(5, 115, 10, 120)(8, 118, 11, 121)(9, 119, 14, 124)(12, 122, 15, 125)(13, 123, 18, 128)(16, 126, 19, 129)(17, 127, 22, 132)(20, 130, 23, 133)(21, 131, 26, 136)(24, 134, 27, 137)(25, 135, 30, 140)(28, 138, 31, 141)(29, 139, 40, 150)(32, 142, 53, 163)(33, 143, 35, 145)(34, 144, 38, 148)(36, 146, 39, 149)(37, 147, 42, 152)(41, 151, 44, 154)(43, 153, 46, 156)(45, 155, 48, 158)(47, 157, 50, 160)(49, 159, 52, 162)(51, 161, 61, 171)(54, 164, 56, 166)(55, 165, 59, 169)(57, 167, 60, 170)(58, 168, 63, 173)(62, 172, 65, 175)(64, 174, 67, 177)(66, 176, 69, 179)(68, 178, 71, 181)(70, 180, 73, 183)(72, 182, 83, 193)(74, 184, 95, 205)(75, 185, 94, 204)(76, 186, 78, 188)(77, 187, 81, 191)(79, 189, 82, 192)(80, 190, 85, 195)(84, 194, 87, 197)(86, 196, 89, 199)(88, 198, 91, 201)(90, 200, 92, 202)(93, 203, 104, 214)(96, 206, 110, 220)(97, 207, 99, 209)(98, 208, 102, 212)(100, 210, 103, 213)(101, 211, 106, 216)(105, 215, 108, 218)(107, 217, 109, 219)
	L = (1, 112)(2, 115)(3, 116)(4, 111)(5, 119)(6, 120)(7, 113)(8, 114)(9, 123)(10, 124)(11, 117)(12, 118)(13, 127)(14, 128)(15, 121)(16, 122)(17, 131)(18, 132)(19, 125)(20, 126)(21, 135)(22, 136)(23, 129)(24, 130)(25, 139)(26, 140)(27, 133)(28, 134)(29, 149)(30, 150)(31, 137)(32, 138)(33, 144)(34, 147)(35, 148)(36, 143)(37, 151)(38, 152)(39, 145)(40, 146)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 170)(52, 171)(53, 141)(54, 165)(55, 168)(56, 169)(57, 164)(58, 172)(59, 173)(60, 166)(61, 167)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 192)(73, 193)(74, 163)(75, 203)(76, 187)(77, 190)(78, 191)(79, 186)(80, 194)(81, 195)(82, 188)(83, 189)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 185)(91, 202)(92, 204)(93, 213)(94, 214)(95, 142)(96, 184)(97, 208)(98, 211)(99, 212)(100, 207)(101, 215)(102, 216)(103, 209)(104, 210)(105, 217)(106, 218)(107, 206)(108, 219)(109, 220)(110, 205)
	local type(s) :: { ( 55, 110, 55, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.2008
Transitivity :: ET+ VT+ AT
Graph::
	v = 55 e = 110 f = 3
	degree seq :: [ 4^55 ]

E27.2013 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^55, (Y3 * Y2^-1)^110 ]
Map::
	R = (1, 111, 2, 112)(3, 113, 5, 115)(4, 114, 6, 116)(7, 117, 9, 119)(8, 118, 10, 120)(11, 121, 13, 123)(12, 122, 14, 124)(15, 125, 17, 127)(16, 126, 18, 128)(19, 129, 21, 131)(20, 130, 22, 132)(23, 133, 25, 135)(24, 134, 26, 136)(27, 137, 29, 139)(28, 138, 30, 140)(31, 141, 40, 150)(32, 142, 53, 163)(33, 143, 34, 144)(35, 145, 37, 147)(36, 146, 38, 148)(39, 149, 41, 151)(42, 152, 43, 153)(44, 154, 45, 155)(46, 156, 47, 157)(48, 158, 49, 159)(50, 160, 51, 161)(52, 162, 61, 171)(54, 164, 55, 165)(56, 166, 58, 168)(57, 167, 59, 169)(60, 170, 62, 172)(63, 173, 64, 174)(65, 175, 66, 176)(67, 177, 68, 178)(69, 179, 70, 180)(71, 181, 72, 182)(73, 183, 83, 193)(74, 184, 95, 205)(75, 185, 93, 203)(76, 186, 77, 187)(78, 188, 80, 190)(79, 189, 81, 191)(82, 192, 84, 194)(85, 195, 86, 196)(87, 197, 88, 198)(89, 199, 90, 200)(91, 201, 92, 202)(94, 204, 97, 207)(96, 206, 110, 220)(98, 208, 99, 209)(100, 210, 102, 212)(101, 211, 103, 213)(104, 214, 105, 215)(106, 216, 107, 217)(108, 218, 109, 219)(221, 331, 223, 333, 227, 337, 231, 341, 235, 345, 239, 349, 243, 353, 247, 357, 251, 361, 258, 368, 254, 364, 257, 367, 261, 371, 263, 373, 265, 375, 267, 377, 269, 379, 271, 381, 281, 391, 277, 387, 274, 384, 276, 386, 280, 390, 283, 393, 285, 395, 287, 397, 289, 399, 291, 401, 293, 403, 301, 411, 297, 407, 300, 410, 304, 414, 306, 416, 308, 418, 310, 420, 312, 422, 295, 405, 317, 427, 321, 431, 318, 428, 320, 430, 324, 434, 326, 436, 328, 438, 330, 440, 315, 425, 252, 362, 248, 358, 244, 354, 240, 350, 236, 346, 232, 342, 228, 338, 224, 334)(222, 332, 225, 335, 229, 339, 233, 343, 237, 347, 241, 351, 245, 355, 249, 359, 260, 370, 256, 366, 253, 363, 255, 365, 259, 369, 262, 372, 264, 374, 266, 376, 268, 378, 270, 380, 272, 382, 279, 389, 275, 385, 278, 388, 282, 392, 284, 394, 286, 396, 288, 398, 290, 400, 292, 402, 303, 413, 299, 409, 296, 406, 298, 408, 302, 412, 305, 415, 307, 417, 309, 419, 311, 421, 313, 423, 314, 424, 323, 433, 319, 429, 322, 432, 325, 435, 327, 437, 329, 439, 316, 426, 294, 404, 273, 383, 250, 360, 246, 356, 242, 352, 238, 348, 234, 344, 230, 340, 226, 336)
	L = (1, 222)(2, 221)(3, 225)(4, 226)(5, 223)(6, 224)(7, 229)(8, 230)(9, 227)(10, 228)(11, 233)(12, 234)(13, 231)(14, 232)(15, 237)(16, 238)(17, 235)(18, 236)(19, 241)(20, 242)(21, 239)(22, 240)(23, 245)(24, 246)(25, 243)(26, 244)(27, 249)(28, 250)(29, 247)(30, 248)(31, 260)(32, 273)(33, 254)(34, 253)(35, 257)(36, 258)(37, 255)(38, 256)(39, 261)(40, 251)(41, 259)(42, 263)(43, 262)(44, 265)(45, 264)(46, 267)(47, 266)(48, 269)(49, 268)(50, 271)(51, 270)(52, 281)(53, 252)(54, 275)(55, 274)(56, 278)(57, 279)(58, 276)(59, 277)(60, 282)(61, 272)(62, 280)(63, 284)(64, 283)(65, 286)(66, 285)(67, 288)(68, 287)(69, 290)(70, 289)(71, 292)(72, 291)(73, 303)(74, 315)(75, 313)(76, 297)(77, 296)(78, 300)(79, 301)(80, 298)(81, 299)(82, 304)(83, 293)(84, 302)(85, 306)(86, 305)(87, 308)(88, 307)(89, 310)(90, 309)(91, 312)(92, 311)(93, 295)(94, 317)(95, 294)(96, 330)(97, 314)(98, 319)(99, 318)(100, 322)(101, 323)(102, 320)(103, 321)(104, 325)(105, 324)(106, 327)(107, 326)(108, 329)(109, 328)(110, 316)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 2, 220, 2, 220 ), ( 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220, 2, 220 ) }
Outer automorphisms :: reflexible
Dual of E27.2016
Graph:: bipartite
	v = 57 e = 220 f = 111
	degree seq :: [ 4^55, 110^2 ]

E27.2014 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^26 * Y2^26, Y1^25 * Y2^-1 * Y1 * Y2^-27 * Y1, Y1^55, Y2^-466 * Y1^-26 ]
Map::
	R = (1, 111, 2, 112, 6, 116, 11, 121, 15, 125, 19, 129, 23, 133, 27, 137, 31, 141, 53, 163, 75, 185, 97, 207, 110, 220, 107, 217, 104, 214, 101, 211, 102, 212, 99, 209, 96, 206, 77, 187, 94, 204, 91, 201, 90, 200, 87, 197, 84, 194, 81, 191, 82, 192, 79, 189, 74, 184, 71, 181, 70, 180, 67, 177, 66, 176, 63, 173, 60, 170, 57, 167, 58, 168, 55, 165, 52, 162, 49, 159, 48, 158, 45, 155, 44, 154, 41, 151, 38, 148, 35, 145, 36, 146, 33, 143, 30, 140, 25, 135, 22, 132, 17, 127, 14, 124, 9, 119, 4, 114)(3, 113, 7, 117, 5, 115, 8, 118, 12, 122, 16, 126, 20, 130, 24, 134, 28, 138, 32, 142, 54, 164, 76, 186, 98, 208, 109, 219, 108, 218, 103, 213, 106, 216, 105, 215, 100, 210, 95, 205, 78, 188, 93, 203, 92, 202, 89, 199, 88, 198, 83, 193, 86, 196, 85, 195, 80, 190, 73, 183, 72, 182, 69, 179, 68, 178, 65, 175, 64, 174, 59, 169, 62, 172, 61, 171, 56, 166, 51, 161, 50, 160, 47, 157, 46, 156, 43, 153, 42, 152, 37, 147, 40, 150, 39, 149, 34, 144, 29, 139, 26, 136, 21, 131, 18, 128, 13, 123, 10, 120)(221, 331, 223, 333, 229, 339, 233, 343, 237, 347, 241, 351, 245, 355, 249, 359, 253, 363, 259, 369, 255, 365, 257, 367, 261, 371, 263, 373, 265, 375, 267, 377, 269, 379, 271, 381, 275, 385, 281, 391, 277, 387, 279, 389, 283, 393, 285, 395, 287, 397, 289, 399, 291, 401, 293, 403, 299, 409, 305, 415, 301, 411, 303, 413, 307, 417, 309, 419, 311, 421, 313, 423, 297, 407, 315, 425, 319, 429, 325, 435, 321, 431, 323, 433, 327, 437, 329, 439, 317, 427, 296, 406, 273, 383, 252, 362, 247, 357, 244, 354, 239, 349, 236, 346, 231, 341, 228, 338, 222, 332, 227, 337, 224, 334, 230, 340, 234, 344, 238, 348, 242, 352, 246, 356, 250, 360, 254, 364, 256, 366, 260, 370, 258, 368, 262, 372, 264, 374, 266, 376, 268, 378, 270, 380, 272, 382, 276, 386, 278, 388, 282, 392, 280, 390, 284, 394, 286, 396, 288, 398, 290, 400, 292, 402, 294, 404, 300, 410, 302, 412, 306, 416, 304, 414, 308, 418, 310, 420, 312, 422, 314, 424, 298, 408, 316, 426, 320, 430, 322, 432, 326, 436, 324, 434, 328, 438, 330, 440, 318, 428, 295, 405, 274, 384, 251, 361, 248, 358, 243, 353, 240, 350, 235, 345, 232, 342, 226, 336, 225, 335)
	L = (1, 223)(2, 227)(3, 229)(4, 230)(5, 221)(6, 225)(7, 224)(8, 222)(9, 233)(10, 234)(11, 228)(12, 226)(13, 237)(14, 238)(15, 232)(16, 231)(17, 241)(18, 242)(19, 236)(20, 235)(21, 245)(22, 246)(23, 240)(24, 239)(25, 249)(26, 250)(27, 244)(28, 243)(29, 253)(30, 254)(31, 248)(32, 247)(33, 259)(34, 256)(35, 257)(36, 260)(37, 261)(38, 262)(39, 255)(40, 258)(41, 263)(42, 264)(43, 265)(44, 266)(45, 267)(46, 268)(47, 269)(48, 270)(49, 271)(50, 272)(51, 275)(52, 276)(53, 252)(54, 251)(55, 281)(56, 278)(57, 279)(58, 282)(59, 283)(60, 284)(61, 277)(62, 280)(63, 285)(64, 286)(65, 287)(66, 288)(67, 289)(68, 290)(69, 291)(70, 292)(71, 293)(72, 294)(73, 299)(74, 300)(75, 274)(76, 273)(77, 315)(78, 316)(79, 305)(80, 302)(81, 303)(82, 306)(83, 307)(84, 308)(85, 301)(86, 304)(87, 309)(88, 310)(89, 311)(90, 312)(91, 313)(92, 314)(93, 297)(94, 298)(95, 319)(96, 320)(97, 296)(98, 295)(99, 325)(100, 322)(101, 323)(102, 326)(103, 327)(104, 328)(105, 321)(106, 324)(107, 329)(108, 330)(109, 317)(110, 318)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2015
Graph:: bipartite
	v = 3 e = 220 f = 165
	degree seq :: [ 110^2, 220 ]

E27.2015 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^55 * Y2, (Y3^-1 * Y1^-1)^110 ]
Map::
	R = (1, 111)(2, 112)(3, 113)(4, 114)(5, 115)(6, 116)(7, 117)(8, 118)(9, 119)(10, 120)(11, 121)(12, 122)(13, 123)(14, 124)(15, 125)(16, 126)(17, 127)(18, 128)(19, 129)(20, 130)(21, 131)(22, 132)(23, 133)(24, 134)(25, 135)(26, 136)(27, 137)(28, 138)(29, 139)(30, 140)(31, 141)(32, 142)(33, 143)(34, 144)(35, 145)(36, 146)(37, 147)(38, 148)(39, 149)(40, 150)(41, 151)(42, 152)(43, 153)(44, 154)(45, 155)(46, 156)(47, 157)(48, 158)(49, 159)(50, 160)(51, 161)(52, 162)(53, 163)(54, 164)(55, 165)(56, 166)(57, 167)(58, 168)(59, 169)(60, 170)(61, 171)(62, 172)(63, 173)(64, 174)(65, 175)(66, 176)(67, 177)(68, 178)(69, 179)(70, 180)(71, 181)(72, 182)(73, 183)(74, 184)(75, 185)(76, 186)(77, 187)(78, 188)(79, 189)(80, 190)(81, 191)(82, 192)(83, 193)(84, 194)(85, 195)(86, 196)(87, 197)(88, 198)(89, 199)(90, 200)(91, 201)(92, 202)(93, 203)(94, 204)(95, 205)(96, 206)(97, 207)(98, 208)(99, 209)(100, 210)(101, 211)(102, 212)(103, 213)(104, 214)(105, 215)(106, 216)(107, 217)(108, 218)(109, 219)(110, 220)(221, 331, 222, 332)(223, 333, 225, 335)(224, 334, 226, 336)(227, 337, 229, 339)(228, 338, 230, 340)(231, 341, 233, 343)(232, 342, 234, 344)(235, 345, 237, 347)(236, 346, 238, 348)(239, 349, 241, 351)(240, 350, 242, 352)(243, 353, 245, 355)(244, 354, 246, 356)(247, 357, 249, 359)(248, 358, 250, 360)(251, 361, 253, 363)(252, 362, 269, 379)(254, 364, 255, 365)(256, 366, 257, 367)(258, 368, 259, 369)(260, 370, 261, 371)(262, 372, 263, 373)(264, 374, 265, 375)(266, 376, 267, 377)(268, 378, 270, 380)(271, 381, 272, 382)(273, 383, 274, 384)(275, 385, 276, 386)(277, 387, 278, 388)(279, 389, 280, 390)(281, 391, 282, 392)(283, 393, 284, 394)(285, 395, 288, 398)(286, 396, 304, 414)(287, 397, 307, 417)(289, 399, 290, 400)(291, 401, 292, 402)(293, 403, 294, 404)(295, 405, 296, 406)(297, 407, 298, 408)(299, 409, 300, 410)(301, 411, 302, 412)(303, 413, 309, 419)(305, 415, 322, 432)(306, 416, 320, 430)(308, 418, 321, 431)(310, 420, 311, 421)(312, 422, 313, 423)(314, 424, 315, 425)(316, 426, 317, 427)(318, 428, 319, 429)(323, 433, 330, 440)(324, 434, 325, 435)(326, 436, 327, 437)(328, 438, 329, 439)
	L = (1, 223)(2, 225)(3, 227)(4, 221)(5, 229)(6, 222)(7, 231)(8, 224)(9, 233)(10, 226)(11, 235)(12, 228)(13, 237)(14, 230)(15, 239)(16, 232)(17, 241)(18, 234)(19, 243)(20, 236)(21, 245)(22, 238)(23, 247)(24, 240)(25, 249)(26, 242)(27, 251)(28, 244)(29, 253)(30, 246)(31, 255)(32, 248)(33, 254)(34, 256)(35, 257)(36, 258)(37, 259)(38, 260)(39, 261)(40, 262)(41, 263)(42, 264)(43, 265)(44, 266)(45, 267)(46, 268)(47, 270)(48, 272)(49, 250)(50, 271)(51, 273)(52, 274)(53, 275)(54, 276)(55, 277)(56, 278)(57, 279)(58, 280)(59, 281)(60, 282)(61, 283)(62, 284)(63, 285)(64, 288)(65, 290)(66, 269)(67, 308)(68, 289)(69, 291)(70, 292)(71, 293)(72, 294)(73, 295)(74, 296)(75, 297)(76, 298)(77, 299)(78, 300)(79, 301)(80, 302)(81, 303)(82, 309)(83, 311)(84, 252)(85, 286)(86, 287)(87, 321)(88, 324)(89, 310)(90, 312)(91, 313)(92, 314)(93, 315)(94, 316)(95, 317)(96, 318)(97, 319)(98, 320)(99, 306)(100, 307)(101, 325)(102, 304)(103, 305)(104, 326)(105, 327)(106, 328)(107, 329)(108, 330)(109, 323)(110, 322)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 110, 220 ), ( 110, 220, 110, 220 ) }
Outer automorphisms :: reflexible
Dual of E27.2014
Graph:: simple bipartite
	v = 165 e = 220 f = 3
	degree seq :: [ 2^110, 4^55 ]

E27.2016 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-55 ]
Map::
	R = (1, 111, 2, 112, 5, 115, 9, 119, 13, 123, 17, 127, 21, 131, 25, 135, 29, 139, 39, 149, 35, 145, 38, 148, 42, 152, 44, 154, 46, 156, 48, 158, 50, 160, 52, 162, 61, 171, 57, 167, 54, 164, 55, 165, 58, 168, 62, 172, 64, 174, 66, 176, 68, 178, 70, 180, 72, 182, 82, 192, 78, 188, 81, 191, 85, 195, 87, 197, 89, 199, 91, 201, 92, 202, 94, 204, 104, 214, 100, 210, 97, 207, 98, 208, 101, 211, 105, 215, 107, 217, 96, 206, 74, 184, 53, 163, 31, 141, 27, 137, 23, 133, 19, 129, 15, 125, 11, 121, 7, 117, 3, 113, 6, 116, 10, 120, 14, 124, 18, 128, 22, 132, 26, 136, 30, 140, 40, 150, 36, 146, 33, 143, 34, 144, 37, 147, 41, 151, 43, 153, 45, 155, 47, 157, 49, 159, 51, 161, 60, 170, 56, 166, 59, 169, 63, 173, 65, 175, 67, 177, 69, 179, 71, 181, 73, 183, 83, 193, 79, 189, 76, 186, 77, 187, 80, 190, 84, 194, 86, 196, 88, 198, 90, 200, 75, 185, 93, 203, 103, 213, 99, 209, 102, 212, 106, 216, 108, 218, 109, 219, 110, 220, 95, 205, 32, 142, 28, 138, 24, 134, 20, 130, 16, 126, 12, 122, 8, 118, 4, 114)(221, 331)(222, 332)(223, 333)(224, 334)(225, 335)(226, 336)(227, 337)(228, 338)(229, 339)(230, 340)(231, 341)(232, 342)(233, 343)(234, 344)(235, 345)(236, 346)(237, 347)(238, 348)(239, 349)(240, 350)(241, 351)(242, 352)(243, 353)(244, 354)(245, 355)(246, 356)(247, 357)(248, 358)(249, 359)(250, 360)(251, 361)(252, 362)(253, 363)(254, 364)(255, 365)(256, 366)(257, 367)(258, 368)(259, 369)(260, 370)(261, 371)(262, 372)(263, 373)(264, 374)(265, 375)(266, 376)(267, 377)(268, 378)(269, 379)(270, 380)(271, 381)(272, 382)(273, 383)(274, 384)(275, 385)(276, 386)(277, 387)(278, 388)(279, 389)(280, 390)(281, 391)(282, 392)(283, 393)(284, 394)(285, 395)(286, 396)(287, 397)(288, 398)(289, 399)(290, 400)(291, 401)(292, 402)(293, 403)(294, 404)(295, 405)(296, 406)(297, 407)(298, 408)(299, 409)(300, 410)(301, 411)(302, 412)(303, 413)(304, 414)(305, 415)(306, 416)(307, 417)(308, 418)(309, 419)(310, 420)(311, 421)(312, 422)(313, 423)(314, 424)(315, 425)(316, 426)(317, 427)(318, 428)(319, 429)(320, 430)(321, 431)(322, 432)(323, 433)(324, 434)(325, 435)(326, 436)(327, 437)(328, 438)(329, 439)(330, 440)
	L = (1, 223)(2, 226)(3, 221)(4, 227)(5, 230)(6, 222)(7, 224)(8, 231)(9, 234)(10, 225)(11, 228)(12, 235)(13, 238)(14, 229)(15, 232)(16, 239)(17, 242)(18, 233)(19, 236)(20, 243)(21, 246)(22, 237)(23, 240)(24, 247)(25, 250)(26, 241)(27, 244)(28, 251)(29, 260)(30, 245)(31, 248)(32, 273)(33, 255)(34, 258)(35, 253)(36, 259)(37, 262)(38, 254)(39, 256)(40, 249)(41, 264)(42, 257)(43, 266)(44, 261)(45, 268)(46, 263)(47, 270)(48, 265)(49, 272)(50, 267)(51, 281)(52, 269)(53, 252)(54, 276)(55, 279)(56, 274)(57, 280)(58, 283)(59, 275)(60, 277)(61, 271)(62, 285)(63, 278)(64, 287)(65, 282)(66, 289)(67, 284)(68, 291)(69, 286)(70, 293)(71, 288)(72, 303)(73, 290)(74, 315)(75, 314)(76, 298)(77, 301)(78, 296)(79, 302)(80, 305)(81, 297)(82, 299)(83, 292)(84, 307)(85, 300)(86, 309)(87, 304)(88, 311)(89, 306)(90, 312)(91, 308)(92, 310)(93, 324)(94, 295)(95, 294)(96, 330)(97, 319)(98, 322)(99, 317)(100, 323)(101, 326)(102, 318)(103, 320)(104, 313)(105, 328)(106, 321)(107, 329)(108, 325)(109, 327)(110, 316)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 4, 110 ), ( 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110, 4, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.2013
Graph:: bipartite
	v = 111 e = 220 f = 57
	degree seq :: [ 2^110, 220 ]

E27.2017 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^55 * Y1, (Y3 * Y2^-1)^55 ]
Map::
	R = (1, 111, 2, 112)(3, 113, 5, 115)(4, 114, 6, 116)(7, 117, 9, 119)(8, 118, 10, 120)(11, 121, 13, 123)(12, 122, 14, 124)(15, 125, 17, 127)(16, 126, 18, 128)(19, 129, 21, 131)(20, 130, 22, 132)(23, 133, 25, 135)(24, 134, 26, 136)(27, 137, 29, 139)(28, 138, 30, 140)(31, 141, 45, 155)(32, 142, 55, 165)(33, 143, 34, 144)(35, 145, 37, 147)(36, 146, 38, 148)(39, 149, 41, 151)(40, 150, 42, 152)(43, 153, 44, 154)(46, 156, 47, 157)(48, 158, 49, 159)(50, 160, 51, 161)(52, 162, 53, 163)(54, 164, 68, 178)(56, 166, 57, 167)(58, 168, 60, 170)(59, 169, 61, 171)(62, 172, 64, 174)(63, 173, 65, 175)(66, 176, 67, 177)(69, 179, 70, 180)(71, 181, 72, 182)(73, 183, 74, 184)(75, 185, 76, 186)(77, 187, 91, 201)(78, 188, 101, 211)(79, 189, 90, 200)(80, 190, 81, 191)(82, 192, 84, 194)(83, 193, 85, 195)(86, 196, 88, 198)(87, 197, 89, 199)(92, 202, 93, 203)(94, 204, 95, 205)(96, 206, 97, 207)(98, 208, 99, 209)(100, 210, 110, 220)(102, 212, 106, 216)(103, 213, 104, 214)(105, 215, 107, 217)(108, 218, 109, 219)(221, 331, 223, 333, 227, 337, 231, 341, 235, 345, 239, 349, 243, 353, 247, 357, 251, 361, 260, 370, 256, 366, 253, 363, 255, 365, 259, 369, 263, 373, 266, 376, 268, 378, 270, 380, 272, 382, 274, 384, 283, 393, 279, 389, 276, 386, 278, 388, 282, 392, 286, 396, 289, 399, 291, 401, 293, 403, 295, 405, 297, 407, 307, 417, 303, 413, 300, 410, 302, 412, 306, 416, 299, 409, 312, 422, 314, 424, 316, 426, 318, 428, 320, 430, 328, 438, 325, 435, 323, 433, 322, 432, 298, 408, 275, 385, 250, 360, 246, 356, 242, 352, 238, 348, 234, 344, 230, 340, 226, 336, 222, 332, 225, 335, 229, 339, 233, 343, 237, 347, 241, 351, 245, 355, 249, 359, 265, 375, 262, 372, 258, 368, 254, 364, 257, 367, 261, 371, 264, 374, 267, 377, 269, 379, 271, 381, 273, 383, 288, 398, 285, 395, 281, 391, 277, 387, 280, 390, 284, 394, 287, 397, 290, 400, 292, 402, 294, 404, 296, 406, 311, 421, 309, 419, 305, 415, 301, 411, 304, 414, 308, 418, 310, 420, 313, 423, 315, 425, 317, 427, 319, 429, 330, 440, 329, 439, 327, 437, 324, 434, 326, 436, 321, 431, 252, 362, 248, 358, 244, 354, 240, 350, 236, 346, 232, 342, 228, 338, 224, 334)
	L = (1, 222)(2, 221)(3, 225)(4, 226)(5, 223)(6, 224)(7, 229)(8, 230)(9, 227)(10, 228)(11, 233)(12, 234)(13, 231)(14, 232)(15, 237)(16, 238)(17, 235)(18, 236)(19, 241)(20, 242)(21, 239)(22, 240)(23, 245)(24, 246)(25, 243)(26, 244)(27, 249)(28, 250)(29, 247)(30, 248)(31, 265)(32, 275)(33, 254)(34, 253)(35, 257)(36, 258)(37, 255)(38, 256)(39, 261)(40, 262)(41, 259)(42, 260)(43, 264)(44, 263)(45, 251)(46, 267)(47, 266)(48, 269)(49, 268)(50, 271)(51, 270)(52, 273)(53, 272)(54, 288)(55, 252)(56, 277)(57, 276)(58, 280)(59, 281)(60, 278)(61, 279)(62, 284)(63, 285)(64, 282)(65, 283)(66, 287)(67, 286)(68, 274)(69, 290)(70, 289)(71, 292)(72, 291)(73, 294)(74, 293)(75, 296)(76, 295)(77, 311)(78, 321)(79, 310)(80, 301)(81, 300)(82, 304)(83, 305)(84, 302)(85, 303)(86, 308)(87, 309)(88, 306)(89, 307)(90, 299)(91, 297)(92, 313)(93, 312)(94, 315)(95, 314)(96, 317)(97, 316)(98, 319)(99, 318)(100, 330)(101, 298)(102, 326)(103, 324)(104, 323)(105, 327)(106, 322)(107, 325)(108, 329)(109, 328)(110, 320)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 2, 110, 2, 110 ), ( 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110, 2, 110 ) }
Outer automorphisms :: reflexible
Dual of E27.2018
Graph:: bipartite
	v = 56 e = 220 f = 112
	degree seq :: [ 4^55, 220 ]

E27.2018 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 55, 110})
Quotient :: dipole
Aut^+ = C110 (small group id <110, 6>)
Aut   = D220 (small group id <220, 14>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^25 * Y3^-28, Y3^-2 * Y1^53, (Y3 * Y2^-1)^110 ]
Map::
	R = (1, 111, 2, 112, 6, 116, 11, 121, 15, 125, 19, 129, 23, 133, 27, 137, 31, 141, 43, 153, 38, 148, 35, 145, 36, 146, 40, 150, 45, 155, 47, 157, 49, 159, 51, 161, 53, 163, 55, 165, 67, 177, 62, 172, 59, 169, 60, 170, 64, 174, 69, 179, 71, 181, 73, 183, 75, 185, 77, 187, 79, 189, 91, 201, 88, 198, 85, 195, 86, 196, 84, 194, 93, 203, 95, 205, 97, 207, 99, 209, 101, 211, 103, 213, 109, 219, 108, 218, 106, 216, 81, 191, 58, 168, 33, 143, 30, 140, 25, 135, 22, 132, 17, 127, 14, 124, 9, 119, 4, 114)(3, 113, 7, 117, 5, 115, 8, 118, 12, 122, 16, 126, 20, 130, 24, 134, 28, 138, 32, 142, 44, 154, 37, 147, 41, 151, 39, 149, 42, 152, 46, 156, 48, 158, 50, 160, 52, 162, 54, 164, 56, 166, 68, 178, 61, 171, 65, 175, 63, 173, 66, 176, 70, 180, 72, 182, 74, 184, 76, 186, 78, 188, 80, 190, 92, 202, 87, 197, 90, 200, 89, 199, 83, 193, 94, 204, 96, 206, 98, 208, 100, 210, 102, 212, 104, 214, 110, 220, 107, 217, 105, 215, 82, 192, 57, 167, 34, 144, 29, 139, 26, 136, 21, 131, 18, 128, 13, 123, 10, 120)(221, 331)(222, 332)(223, 333)(224, 334)(225, 335)(226, 336)(227, 337)(228, 338)(229, 339)(230, 340)(231, 341)(232, 342)(233, 343)(234, 344)(235, 345)(236, 346)(237, 347)(238, 348)(239, 349)(240, 350)(241, 351)(242, 352)(243, 353)(244, 354)(245, 355)(246, 356)(247, 357)(248, 358)(249, 359)(250, 360)(251, 361)(252, 362)(253, 363)(254, 364)(255, 365)(256, 366)(257, 367)(258, 368)(259, 369)(260, 370)(261, 371)(262, 372)(263, 373)(264, 374)(265, 375)(266, 376)(267, 377)(268, 378)(269, 379)(270, 380)(271, 381)(272, 382)(273, 383)(274, 384)(275, 385)(276, 386)(277, 387)(278, 388)(279, 389)(280, 390)(281, 391)(282, 392)(283, 393)(284, 394)(285, 395)(286, 396)(287, 397)(288, 398)(289, 399)(290, 400)(291, 401)(292, 402)(293, 403)(294, 404)(295, 405)(296, 406)(297, 407)(298, 408)(299, 409)(300, 410)(301, 411)(302, 412)(303, 413)(304, 414)(305, 415)(306, 416)(307, 417)(308, 418)(309, 419)(310, 420)(311, 421)(312, 422)(313, 423)(314, 424)(315, 425)(316, 426)(317, 427)(318, 428)(319, 429)(320, 430)(321, 431)(322, 432)(323, 433)(324, 434)(325, 435)(326, 436)(327, 437)(328, 438)(329, 439)(330, 440)
	L = (1, 223)(2, 227)(3, 229)(4, 230)(5, 221)(6, 225)(7, 224)(8, 222)(9, 233)(10, 234)(11, 228)(12, 226)(13, 237)(14, 238)(15, 232)(16, 231)(17, 241)(18, 242)(19, 236)(20, 235)(21, 245)(22, 246)(23, 240)(24, 239)(25, 249)(26, 250)(27, 244)(28, 243)(29, 253)(30, 254)(31, 248)(32, 247)(33, 277)(34, 278)(35, 257)(36, 261)(37, 263)(38, 264)(39, 255)(40, 259)(41, 258)(42, 256)(43, 252)(44, 251)(45, 262)(46, 260)(47, 266)(48, 265)(49, 268)(50, 267)(51, 270)(52, 269)(53, 272)(54, 271)(55, 274)(56, 273)(57, 301)(58, 302)(59, 281)(60, 285)(61, 287)(62, 288)(63, 279)(64, 283)(65, 282)(66, 280)(67, 276)(68, 275)(69, 286)(70, 284)(71, 290)(72, 289)(73, 292)(74, 291)(75, 294)(76, 293)(77, 296)(78, 295)(79, 298)(80, 297)(81, 325)(82, 326)(83, 306)(84, 309)(85, 307)(86, 310)(87, 311)(88, 312)(89, 305)(90, 308)(91, 300)(92, 299)(93, 303)(94, 304)(95, 314)(96, 313)(97, 316)(98, 315)(99, 318)(100, 317)(101, 320)(102, 319)(103, 322)(104, 321)(105, 328)(106, 327)(107, 329)(108, 330)(109, 324)(110, 323)(111, 331)(112, 332)(113, 333)(114, 334)(115, 335)(116, 336)(117, 337)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 346)(127, 347)(128, 348)(129, 349)(130, 350)(131, 351)(132, 352)(133, 353)(134, 354)(135, 355)(136, 356)(137, 357)(138, 358)(139, 359)(140, 360)(141, 361)(142, 362)(143, 363)(144, 364)(145, 365)(146, 366)(147, 367)(148, 368)(149, 369)(150, 370)(151, 371)(152, 372)(153, 373)(154, 374)(155, 375)(156, 376)(157, 377)(158, 378)(159, 379)(160, 380)(161, 381)(162, 382)(163, 383)(164, 384)(165, 385)(166, 386)(167, 387)(168, 388)(169, 389)(170, 390)(171, 391)(172, 392)(173, 393)(174, 394)(175, 395)(176, 396)(177, 397)(178, 398)(179, 399)(180, 400)(181, 401)(182, 402)(183, 403)(184, 404)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 429)(210, 430)(211, 431)(212, 432)(213, 433)(214, 434)(215, 435)(216, 436)(217, 437)(218, 438)(219, 439)(220, 440)
	local type(s) :: { ( 4, 220 ), ( 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220, 4, 220 ) }
Outer automorphisms :: reflexible
Dual of E27.2017
Graph:: simple bipartite
	v = 112 e = 220 f = 56
	degree seq :: [ 2^110, 110^2 ]

E27.2019 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = C2 x D56 (small group id <112, 29>)
Aut   = C2 x C2 x D56 (small group id <224, 176>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^28 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114)(3, 115, 5, 117)(4, 116, 8, 120)(6, 118, 10, 122)(7, 119, 11, 123)(9, 121, 13, 125)(12, 124, 16, 128)(14, 126, 18, 130)(15, 127, 19, 131)(17, 129, 21, 133)(20, 132, 24, 136)(22, 134, 26, 138)(23, 135, 27, 139)(25, 137, 29, 141)(28, 140, 32, 144)(30, 142, 36, 148)(31, 143, 40, 152)(33, 145, 53, 165)(34, 146, 57, 169)(35, 147, 60, 172)(37, 149, 64, 176)(38, 150, 51, 163)(39, 151, 55, 167)(41, 153, 58, 170)(42, 154, 61, 173)(43, 155, 65, 177)(44, 156, 68, 180)(45, 157, 71, 183)(46, 158, 73, 185)(47, 159, 75, 187)(48, 160, 77, 189)(49, 161, 79, 191)(50, 162, 81, 193)(52, 164, 83, 195)(54, 166, 85, 197)(56, 168, 93, 205)(59, 171, 97, 209)(62, 174, 100, 212)(63, 175, 87, 199)(66, 178, 104, 216)(67, 179, 91, 203)(69, 181, 95, 207)(70, 182, 89, 201)(72, 184, 98, 210)(74, 186, 101, 213)(76, 188, 105, 217)(78, 190, 108, 220)(80, 192, 109, 221)(82, 194, 111, 223)(84, 196, 112, 224)(86, 198, 99, 211)(88, 200, 96, 208)(90, 202, 106, 218)(92, 204, 102, 214)(94, 206, 103, 215)(107, 219, 110, 222)(225, 337, 227, 339)(226, 338, 229, 341)(228, 340, 231, 343)(230, 342, 233, 345)(232, 344, 235, 347)(234, 346, 237, 349)(236, 348, 239, 351)(238, 350, 241, 353)(240, 352, 243, 355)(242, 354, 245, 357)(244, 356, 247, 359)(246, 358, 249, 361)(248, 360, 251, 363)(250, 362, 253, 365)(252, 364, 255, 367)(254, 366, 275, 387)(256, 368, 264, 376)(257, 369, 259, 371)(258, 370, 261, 373)(260, 372, 262, 374)(263, 375, 266, 378)(265, 377, 267, 379)(268, 380, 270, 382)(269, 381, 271, 383)(272, 384, 274, 386)(273, 385, 276, 388)(277, 389, 284, 396)(278, 390, 294, 406)(279, 391, 285, 397)(280, 392, 286, 398)(281, 393, 288, 400)(282, 394, 289, 401)(283, 395, 290, 402)(287, 399, 291, 403)(292, 404, 297, 409)(293, 405, 298, 410)(295, 407, 299, 411)(296, 408, 300, 412)(301, 413, 305, 417)(302, 414, 306, 418)(303, 415, 307, 419)(304, 416, 308, 420)(309, 421, 313, 425)(310, 422, 314, 426)(311, 423, 315, 427)(312, 424, 316, 428)(317, 429, 324, 436)(318, 430, 334, 446)(319, 431, 325, 437)(320, 432, 326, 438)(321, 433, 328, 440)(322, 434, 329, 441)(323, 435, 330, 442)(327, 439, 331, 443)(332, 444, 335, 447)(333, 445, 336, 448)
	L = (1, 228)(2, 230)(3, 231)(4, 225)(5, 233)(6, 226)(7, 227)(8, 236)(9, 229)(10, 238)(11, 239)(12, 232)(13, 241)(14, 234)(15, 235)(16, 244)(17, 237)(18, 246)(19, 247)(20, 240)(21, 249)(22, 242)(23, 243)(24, 252)(25, 245)(26, 254)(27, 255)(28, 248)(29, 275)(30, 250)(31, 251)(32, 277)(33, 279)(34, 282)(35, 285)(36, 281)(37, 289)(38, 288)(39, 292)(40, 284)(41, 295)(42, 297)(43, 299)(44, 301)(45, 303)(46, 305)(47, 307)(48, 309)(49, 311)(50, 313)(51, 253)(52, 315)(53, 256)(54, 317)(55, 257)(56, 319)(57, 260)(58, 258)(59, 322)(60, 264)(61, 259)(62, 325)(63, 321)(64, 262)(65, 261)(66, 329)(67, 328)(68, 263)(69, 332)(70, 324)(71, 265)(72, 333)(73, 266)(74, 335)(75, 267)(76, 336)(77, 268)(78, 323)(79, 269)(80, 320)(81, 270)(82, 330)(83, 271)(84, 326)(85, 272)(86, 327)(87, 273)(88, 318)(89, 274)(90, 331)(91, 276)(92, 334)(93, 278)(94, 312)(95, 280)(96, 304)(97, 287)(98, 283)(99, 302)(100, 294)(101, 286)(102, 308)(103, 310)(104, 291)(105, 290)(106, 306)(107, 314)(108, 293)(109, 296)(110, 316)(111, 298)(112, 300)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2024
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2020 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1 * Y3 * Y1 * Y2)^2, (Y1 * Y2)^4, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 10, 122)(6, 118, 12, 124)(8, 120, 15, 127)(11, 123, 20, 132)(13, 125, 18, 130)(14, 126, 21, 133)(16, 128, 19, 131)(17, 129, 27, 139)(22, 134, 32, 144)(23, 135, 29, 141)(24, 136, 28, 140)(25, 137, 34, 146)(26, 138, 35, 147)(30, 142, 38, 150)(31, 143, 39, 151)(33, 145, 41, 153)(36, 148, 44, 156)(37, 149, 45, 157)(40, 152, 48, 160)(42, 154, 50, 162)(43, 155, 51, 163)(46, 158, 54, 166)(47, 159, 55, 167)(49, 161, 57, 169)(52, 164, 60, 172)(53, 165, 61, 173)(56, 168, 64, 176)(58, 170, 66, 178)(59, 171, 67, 179)(62, 174, 70, 182)(63, 175, 71, 183)(65, 177, 73, 185)(68, 180, 76, 188)(69, 181, 77, 189)(72, 184, 80, 192)(74, 186, 82, 194)(75, 187, 83, 195)(78, 190, 86, 198)(79, 191, 87, 199)(81, 193, 89, 201)(84, 196, 92, 204)(85, 197, 93, 205)(88, 200, 96, 208)(90, 202, 98, 210)(91, 203, 99, 211)(94, 206, 102, 214)(95, 207, 103, 215)(97, 209, 105, 217)(100, 212, 108, 220)(101, 213, 109, 221)(104, 216, 112, 224)(106, 218, 110, 222)(107, 219, 111, 223)(225, 337, 227, 339)(226, 338, 229, 341)(228, 340, 232, 344)(230, 342, 235, 347)(231, 343, 237, 349)(233, 345, 240, 352)(234, 346, 242, 354)(236, 348, 245, 357)(238, 350, 247, 359)(239, 351, 248, 360)(241, 353, 250, 362)(243, 355, 252, 364)(244, 356, 253, 365)(246, 358, 255, 367)(249, 361, 257, 369)(251, 363, 258, 370)(254, 366, 261, 373)(256, 368, 262, 374)(259, 371, 265, 377)(260, 372, 266, 378)(263, 375, 269, 381)(264, 376, 270, 382)(267, 379, 273, 385)(268, 380, 275, 387)(271, 383, 277, 389)(272, 384, 279, 391)(274, 386, 281, 393)(276, 388, 283, 395)(278, 390, 285, 397)(280, 392, 287, 399)(282, 394, 289, 401)(284, 396, 290, 402)(286, 398, 293, 405)(288, 400, 294, 406)(291, 403, 297, 409)(292, 404, 298, 410)(295, 407, 301, 413)(296, 408, 302, 414)(299, 411, 305, 417)(300, 412, 307, 419)(303, 415, 309, 421)(304, 416, 311, 423)(306, 418, 313, 425)(308, 420, 315, 427)(310, 422, 317, 429)(312, 424, 319, 431)(314, 426, 321, 433)(316, 428, 322, 434)(318, 430, 325, 437)(320, 432, 326, 438)(323, 435, 329, 441)(324, 436, 330, 442)(327, 439, 333, 445)(328, 440, 334, 446)(331, 443, 336, 448)(332, 444, 335, 447)
	L = (1, 228)(2, 230)(3, 232)(4, 225)(5, 235)(6, 226)(7, 238)(8, 227)(9, 241)(10, 243)(11, 229)(12, 246)(13, 247)(14, 231)(15, 249)(16, 250)(17, 233)(18, 252)(19, 234)(20, 254)(21, 255)(22, 236)(23, 237)(24, 257)(25, 239)(26, 240)(27, 260)(28, 242)(29, 261)(30, 244)(31, 245)(32, 264)(33, 248)(34, 266)(35, 267)(36, 251)(37, 253)(38, 270)(39, 271)(40, 256)(41, 273)(42, 258)(43, 259)(44, 276)(45, 277)(46, 262)(47, 263)(48, 280)(49, 265)(50, 282)(51, 283)(52, 268)(53, 269)(54, 286)(55, 287)(56, 272)(57, 289)(58, 274)(59, 275)(60, 292)(61, 293)(62, 278)(63, 279)(64, 296)(65, 281)(66, 298)(67, 299)(68, 284)(69, 285)(70, 302)(71, 303)(72, 288)(73, 305)(74, 290)(75, 291)(76, 308)(77, 309)(78, 294)(79, 295)(80, 312)(81, 297)(82, 314)(83, 315)(84, 300)(85, 301)(86, 318)(87, 319)(88, 304)(89, 321)(90, 306)(91, 307)(92, 324)(93, 325)(94, 310)(95, 311)(96, 328)(97, 313)(98, 330)(99, 331)(100, 316)(101, 317)(102, 334)(103, 335)(104, 320)(105, 336)(106, 322)(107, 323)(108, 333)(109, 332)(110, 326)(111, 327)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2026
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2021 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, (R * Y1)^2, (Y3 * Y2)^2, Y3^4, (R * Y3)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y1 * Y3^2 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114)(3, 115, 6, 118)(4, 116, 11, 123)(5, 117, 13, 125)(7, 119, 16, 128)(8, 120, 18, 130)(9, 121, 19, 131)(10, 122, 21, 133)(12, 124, 17, 129)(14, 126, 24, 136)(15, 127, 26, 138)(20, 132, 25, 137)(22, 134, 31, 143)(23, 135, 32, 144)(27, 139, 35, 147)(28, 140, 36, 148)(29, 141, 37, 149)(30, 142, 38, 150)(33, 145, 41, 153)(34, 146, 42, 154)(39, 151, 47, 159)(40, 152, 48, 160)(43, 155, 51, 163)(44, 156, 52, 164)(45, 157, 53, 165)(46, 158, 54, 166)(49, 161, 57, 169)(50, 162, 58, 170)(55, 167, 63, 175)(56, 168, 64, 176)(59, 171, 67, 179)(60, 172, 68, 180)(61, 173, 69, 181)(62, 174, 70, 182)(65, 177, 73, 185)(66, 178, 74, 186)(71, 183, 79, 191)(72, 184, 80, 192)(75, 187, 83, 195)(76, 188, 84, 196)(77, 189, 85, 197)(78, 190, 86, 198)(81, 193, 89, 201)(82, 194, 90, 202)(87, 199, 95, 207)(88, 200, 96, 208)(91, 203, 99, 211)(92, 204, 100, 212)(93, 205, 101, 213)(94, 206, 102, 214)(97, 209, 105, 217)(98, 210, 106, 218)(103, 215, 107, 219)(104, 216, 108, 220)(109, 221, 111, 223)(110, 222, 112, 224)(225, 337, 227, 339)(226, 338, 230, 342)(228, 340, 234, 346)(229, 341, 233, 345)(231, 343, 239, 351)(232, 344, 238, 350)(235, 347, 245, 357)(236, 348, 244, 356)(237, 349, 243, 355)(240, 352, 250, 362)(241, 353, 249, 361)(242, 354, 248, 360)(246, 358, 253, 365)(247, 359, 254, 366)(251, 363, 257, 369)(252, 364, 258, 370)(255, 367, 261, 373)(256, 368, 262, 374)(259, 371, 265, 377)(260, 372, 266, 378)(263, 375, 270, 382)(264, 376, 269, 381)(267, 379, 274, 386)(268, 380, 273, 385)(271, 383, 278, 390)(272, 384, 277, 389)(275, 387, 282, 394)(276, 388, 281, 393)(279, 391, 285, 397)(280, 392, 286, 398)(283, 395, 289, 401)(284, 396, 290, 402)(287, 399, 293, 405)(288, 400, 294, 406)(291, 403, 297, 409)(292, 404, 298, 410)(295, 407, 302, 414)(296, 408, 301, 413)(299, 411, 306, 418)(300, 412, 305, 417)(303, 415, 310, 422)(304, 416, 309, 421)(307, 419, 314, 426)(308, 420, 313, 425)(311, 423, 317, 429)(312, 424, 318, 430)(315, 427, 321, 433)(316, 428, 322, 434)(319, 431, 325, 437)(320, 432, 326, 438)(323, 435, 329, 441)(324, 436, 330, 442)(327, 439, 334, 446)(328, 440, 333, 445)(331, 443, 336, 448)(332, 444, 335, 447)
	L = (1, 228)(2, 231)(3, 233)(4, 236)(5, 225)(6, 238)(7, 241)(8, 226)(9, 244)(10, 227)(11, 246)(12, 229)(13, 247)(14, 249)(15, 230)(16, 251)(17, 232)(18, 252)(19, 253)(20, 234)(21, 254)(22, 237)(23, 235)(24, 257)(25, 239)(26, 258)(27, 242)(28, 240)(29, 245)(30, 243)(31, 263)(32, 264)(33, 250)(34, 248)(35, 267)(36, 268)(37, 269)(38, 270)(39, 256)(40, 255)(41, 273)(42, 274)(43, 260)(44, 259)(45, 262)(46, 261)(47, 279)(48, 280)(49, 266)(50, 265)(51, 283)(52, 284)(53, 285)(54, 286)(55, 272)(56, 271)(57, 289)(58, 290)(59, 276)(60, 275)(61, 278)(62, 277)(63, 295)(64, 296)(65, 282)(66, 281)(67, 299)(68, 300)(69, 301)(70, 302)(71, 288)(72, 287)(73, 305)(74, 306)(75, 292)(76, 291)(77, 294)(78, 293)(79, 311)(80, 312)(81, 298)(82, 297)(83, 315)(84, 316)(85, 317)(86, 318)(87, 304)(88, 303)(89, 321)(90, 322)(91, 308)(92, 307)(93, 310)(94, 309)(95, 327)(96, 328)(97, 314)(98, 313)(99, 331)(100, 332)(101, 333)(102, 334)(103, 320)(104, 319)(105, 335)(106, 336)(107, 324)(108, 323)(109, 326)(110, 325)(111, 330)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2027
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2022 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y3 * Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y1)^28 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 10, 122)(6, 118, 12, 124)(8, 120, 15, 127)(11, 123, 20, 132)(13, 125, 23, 135)(14, 126, 25, 137)(16, 128, 28, 140)(17, 129, 30, 142)(18, 130, 31, 143)(19, 131, 33, 145)(21, 133, 36, 148)(22, 134, 38, 150)(24, 136, 34, 146)(26, 138, 32, 144)(27, 139, 37, 149)(29, 141, 35, 147)(39, 151, 49, 161)(40, 152, 50, 162)(41, 153, 51, 163)(42, 154, 52, 164)(43, 155, 48, 160)(44, 156, 53, 165)(45, 157, 54, 166)(46, 158, 55, 167)(47, 159, 56, 168)(57, 169, 65, 177)(58, 170, 66, 178)(59, 171, 67, 179)(60, 172, 68, 180)(61, 173, 69, 181)(62, 174, 70, 182)(63, 175, 71, 183)(64, 176, 72, 184)(73, 185, 81, 193)(74, 186, 82, 194)(75, 187, 83, 195)(76, 188, 84, 196)(77, 189, 85, 197)(78, 190, 86, 198)(79, 191, 87, 199)(80, 192, 88, 200)(89, 201, 97, 209)(90, 202, 98, 210)(91, 203, 99, 211)(92, 204, 100, 212)(93, 205, 101, 213)(94, 206, 102, 214)(95, 207, 103, 215)(96, 208, 104, 216)(105, 217, 109, 221)(106, 218, 111, 223)(107, 219, 110, 222)(108, 220, 112, 224)(225, 337, 227, 339)(226, 338, 229, 341)(228, 340, 232, 344)(230, 342, 235, 347)(231, 343, 237, 349)(233, 345, 240, 352)(234, 346, 242, 354)(236, 348, 245, 357)(238, 350, 248, 360)(239, 351, 250, 362)(241, 353, 253, 365)(243, 355, 256, 368)(244, 356, 258, 370)(246, 358, 261, 373)(247, 359, 263, 375)(249, 361, 265, 377)(251, 363, 267, 379)(252, 364, 264, 376)(254, 366, 266, 378)(255, 367, 268, 380)(257, 369, 270, 382)(259, 371, 272, 384)(260, 372, 269, 381)(262, 374, 271, 383)(273, 385, 281, 393)(274, 386, 283, 395)(275, 387, 282, 394)(276, 388, 284, 396)(277, 389, 285, 397)(278, 390, 287, 399)(279, 391, 286, 398)(280, 392, 288, 400)(289, 401, 297, 409)(290, 402, 299, 411)(291, 403, 298, 410)(292, 404, 300, 412)(293, 405, 301, 413)(294, 406, 303, 415)(295, 407, 302, 414)(296, 408, 304, 416)(305, 417, 313, 425)(306, 418, 315, 427)(307, 419, 314, 426)(308, 420, 316, 428)(309, 421, 317, 429)(310, 422, 319, 431)(311, 423, 318, 430)(312, 424, 320, 432)(321, 433, 329, 441)(322, 434, 331, 443)(323, 435, 330, 442)(324, 436, 332, 444)(325, 437, 333, 445)(326, 438, 335, 447)(327, 439, 334, 446)(328, 440, 336, 448)
	L = (1, 228)(2, 230)(3, 232)(4, 225)(5, 235)(6, 226)(7, 238)(8, 227)(9, 241)(10, 243)(11, 229)(12, 246)(13, 248)(14, 231)(15, 251)(16, 253)(17, 233)(18, 256)(19, 234)(20, 259)(21, 261)(22, 236)(23, 264)(24, 237)(25, 266)(26, 267)(27, 239)(28, 263)(29, 240)(30, 265)(31, 269)(32, 242)(33, 271)(34, 272)(35, 244)(36, 268)(37, 245)(38, 270)(39, 252)(40, 247)(41, 254)(42, 249)(43, 250)(44, 260)(45, 255)(46, 262)(47, 257)(48, 258)(49, 282)(50, 284)(51, 281)(52, 283)(53, 286)(54, 288)(55, 285)(56, 287)(57, 275)(58, 273)(59, 276)(60, 274)(61, 279)(62, 277)(63, 280)(64, 278)(65, 298)(66, 300)(67, 297)(68, 299)(69, 302)(70, 304)(71, 301)(72, 303)(73, 291)(74, 289)(75, 292)(76, 290)(77, 295)(78, 293)(79, 296)(80, 294)(81, 314)(82, 316)(83, 313)(84, 315)(85, 318)(86, 320)(87, 317)(88, 319)(89, 307)(90, 305)(91, 308)(92, 306)(93, 311)(94, 309)(95, 312)(96, 310)(97, 330)(98, 332)(99, 329)(100, 331)(101, 334)(102, 336)(103, 333)(104, 335)(105, 323)(106, 321)(107, 324)(108, 322)(109, 327)(110, 325)(111, 328)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2025
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2023 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = (C28 x C2) : C2 (small group id <112, 30>)
Aut   = (D8 x D14) : C2 (small group id <224, 185>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y2 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114)(3, 115, 9, 121)(4, 116, 12, 124)(5, 117, 14, 126)(6, 118, 15, 127)(7, 119, 18, 130)(8, 120, 20, 132)(10, 122, 21, 133)(11, 123, 22, 134)(13, 125, 19, 131)(16, 128, 25, 137)(17, 129, 26, 138)(23, 135, 31, 143)(24, 136, 32, 144)(27, 139, 35, 147)(28, 140, 36, 148)(29, 141, 37, 149)(30, 142, 38, 150)(33, 145, 41, 153)(34, 146, 42, 154)(39, 151, 47, 159)(40, 152, 48, 160)(43, 155, 51, 163)(44, 156, 52, 164)(45, 157, 53, 165)(46, 158, 54, 166)(49, 161, 57, 169)(50, 162, 58, 170)(55, 167, 63, 175)(56, 168, 64, 176)(59, 171, 67, 179)(60, 172, 68, 180)(61, 173, 69, 181)(62, 174, 70, 182)(65, 177, 73, 185)(66, 178, 74, 186)(71, 183, 79, 191)(72, 184, 80, 192)(75, 187, 83, 195)(76, 188, 84, 196)(77, 189, 85, 197)(78, 190, 86, 198)(81, 193, 89, 201)(82, 194, 90, 202)(87, 199, 95, 207)(88, 200, 96, 208)(91, 203, 99, 211)(92, 204, 100, 212)(93, 205, 101, 213)(94, 206, 102, 214)(97, 209, 105, 217)(98, 210, 106, 218)(103, 215, 107, 219)(104, 216, 108, 220)(109, 221, 112, 224)(110, 222, 111, 223)(225, 337, 227, 339)(226, 338, 230, 342)(228, 340, 235, 347)(229, 341, 234, 346)(231, 343, 241, 353)(232, 344, 240, 352)(233, 345, 243, 355)(236, 348, 245, 357)(237, 349, 239, 351)(238, 350, 246, 358)(242, 354, 249, 361)(244, 356, 250, 362)(247, 359, 254, 366)(248, 360, 253, 365)(251, 363, 258, 370)(252, 364, 257, 369)(255, 367, 261, 373)(256, 368, 262, 374)(259, 371, 265, 377)(260, 372, 266, 378)(263, 375, 270, 382)(264, 376, 269, 381)(267, 379, 274, 386)(268, 380, 273, 385)(271, 383, 277, 389)(272, 384, 278, 390)(275, 387, 281, 393)(276, 388, 282, 394)(279, 391, 286, 398)(280, 392, 285, 397)(283, 395, 290, 402)(284, 396, 289, 401)(287, 399, 293, 405)(288, 400, 294, 406)(291, 403, 297, 409)(292, 404, 298, 410)(295, 407, 302, 414)(296, 408, 301, 413)(299, 411, 306, 418)(300, 412, 305, 417)(303, 415, 309, 421)(304, 416, 310, 422)(307, 419, 313, 425)(308, 420, 314, 426)(311, 423, 318, 430)(312, 424, 317, 429)(315, 427, 322, 434)(316, 428, 321, 433)(319, 431, 325, 437)(320, 432, 326, 438)(323, 435, 329, 441)(324, 436, 330, 442)(327, 439, 334, 446)(328, 440, 333, 445)(331, 443, 336, 448)(332, 444, 335, 447)
	L = (1, 228)(2, 231)(3, 234)(4, 237)(5, 225)(6, 240)(7, 243)(8, 226)(9, 241)(10, 239)(11, 227)(12, 247)(13, 229)(14, 248)(15, 235)(16, 233)(17, 230)(18, 251)(19, 232)(20, 252)(21, 253)(22, 254)(23, 238)(24, 236)(25, 257)(26, 258)(27, 244)(28, 242)(29, 246)(30, 245)(31, 263)(32, 264)(33, 250)(34, 249)(35, 267)(36, 268)(37, 269)(38, 270)(39, 256)(40, 255)(41, 273)(42, 274)(43, 260)(44, 259)(45, 262)(46, 261)(47, 279)(48, 280)(49, 266)(50, 265)(51, 283)(52, 284)(53, 285)(54, 286)(55, 272)(56, 271)(57, 289)(58, 290)(59, 276)(60, 275)(61, 278)(62, 277)(63, 295)(64, 296)(65, 282)(66, 281)(67, 299)(68, 300)(69, 301)(70, 302)(71, 288)(72, 287)(73, 305)(74, 306)(75, 292)(76, 291)(77, 294)(78, 293)(79, 311)(80, 312)(81, 298)(82, 297)(83, 315)(84, 316)(85, 317)(86, 318)(87, 304)(88, 303)(89, 321)(90, 322)(91, 308)(92, 307)(93, 310)(94, 309)(95, 327)(96, 328)(97, 314)(98, 313)(99, 331)(100, 332)(101, 333)(102, 334)(103, 320)(104, 319)(105, 335)(106, 336)(107, 324)(108, 323)(109, 326)(110, 325)(111, 330)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2028
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2024 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = C2 x D56 (small group id <112, 29>)
Aut   = C2 x C2 x D56 (small group id <224, 176>)
|r| :: 2
Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, Y1^28 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114, 6, 118, 13, 125, 21, 133, 29, 141, 37, 149, 45, 157, 53, 165, 61, 173, 69, 181, 77, 189, 85, 197, 93, 205, 101, 213, 100, 212, 92, 204, 84, 196, 76, 188, 68, 180, 60, 172, 52, 164, 44, 156, 36, 148, 28, 140, 20, 132, 12, 124, 5, 117)(3, 115, 9, 121, 17, 129, 25, 137, 33, 145, 41, 153, 49, 161, 57, 169, 65, 177, 73, 185, 81, 193, 89, 201, 97, 209, 105, 217, 108, 220, 102, 214, 94, 206, 86, 198, 78, 190, 70, 182, 62, 174, 54, 166, 46, 158, 38, 150, 30, 142, 22, 134, 14, 126, 7, 119)(4, 116, 11, 123, 19, 131, 27, 139, 35, 147, 43, 155, 51, 163, 59, 171, 67, 179, 75, 187, 83, 195, 91, 203, 99, 211, 107, 219, 109, 221, 103, 215, 95, 207, 87, 199, 79, 191, 71, 183, 63, 175, 55, 167, 47, 159, 39, 151, 31, 143, 23, 135, 15, 127, 8, 120)(10, 122, 16, 128, 24, 136, 32, 144, 40, 152, 48, 160, 56, 168, 64, 176, 72, 184, 80, 192, 88, 200, 96, 208, 104, 216, 110, 222, 112, 224, 111, 223, 106, 218, 98, 210, 90, 202, 82, 194, 74, 186, 66, 178, 58, 170, 50, 162, 42, 154, 34, 146, 26, 138, 18, 130)(225, 337, 227, 339)(226, 338, 231, 343)(228, 340, 234, 346)(229, 341, 233, 345)(230, 342, 238, 350)(232, 344, 240, 352)(235, 347, 242, 354)(236, 348, 241, 353)(237, 349, 246, 358)(239, 351, 248, 360)(243, 355, 250, 362)(244, 356, 249, 361)(245, 357, 254, 366)(247, 359, 256, 368)(251, 363, 258, 370)(252, 364, 257, 369)(253, 365, 262, 374)(255, 367, 264, 376)(259, 371, 266, 378)(260, 372, 265, 377)(261, 373, 270, 382)(263, 375, 272, 384)(267, 379, 274, 386)(268, 380, 273, 385)(269, 381, 278, 390)(271, 383, 280, 392)(275, 387, 282, 394)(276, 388, 281, 393)(277, 389, 286, 398)(279, 391, 288, 400)(283, 395, 290, 402)(284, 396, 289, 401)(285, 397, 294, 406)(287, 399, 296, 408)(291, 403, 298, 410)(292, 404, 297, 409)(293, 405, 302, 414)(295, 407, 304, 416)(299, 411, 306, 418)(300, 412, 305, 417)(301, 413, 310, 422)(303, 415, 312, 424)(307, 419, 314, 426)(308, 420, 313, 425)(309, 421, 318, 430)(311, 423, 320, 432)(315, 427, 322, 434)(316, 428, 321, 433)(317, 429, 326, 438)(319, 431, 328, 440)(323, 435, 330, 442)(324, 436, 329, 441)(325, 437, 332, 444)(327, 439, 334, 446)(331, 443, 335, 447)(333, 445, 336, 448)
	L = (1, 228)(2, 232)(3, 234)(4, 225)(5, 235)(6, 239)(7, 240)(8, 226)(9, 242)(10, 227)(11, 229)(12, 243)(13, 247)(14, 248)(15, 230)(16, 231)(17, 250)(18, 233)(19, 236)(20, 251)(21, 255)(22, 256)(23, 237)(24, 238)(25, 258)(26, 241)(27, 244)(28, 259)(29, 263)(30, 264)(31, 245)(32, 246)(33, 266)(34, 249)(35, 252)(36, 267)(37, 271)(38, 272)(39, 253)(40, 254)(41, 274)(42, 257)(43, 260)(44, 275)(45, 279)(46, 280)(47, 261)(48, 262)(49, 282)(50, 265)(51, 268)(52, 283)(53, 287)(54, 288)(55, 269)(56, 270)(57, 290)(58, 273)(59, 276)(60, 291)(61, 295)(62, 296)(63, 277)(64, 278)(65, 298)(66, 281)(67, 284)(68, 299)(69, 303)(70, 304)(71, 285)(72, 286)(73, 306)(74, 289)(75, 292)(76, 307)(77, 311)(78, 312)(79, 293)(80, 294)(81, 314)(82, 297)(83, 300)(84, 315)(85, 319)(86, 320)(87, 301)(88, 302)(89, 322)(90, 305)(91, 308)(92, 323)(93, 327)(94, 328)(95, 309)(96, 310)(97, 330)(98, 313)(99, 316)(100, 331)(101, 333)(102, 334)(103, 317)(104, 318)(105, 335)(106, 321)(107, 324)(108, 336)(109, 325)(110, 326)(111, 329)(112, 332)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2019
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2025 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-2 * Y2 * Y1, (Y1 * Y2 * Y1^-1 * Y2)^2, Y1^-2 * Y2 * Y1^-11 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114, 6, 118, 15, 127, 30, 142, 48, 160, 65, 177, 81, 193, 97, 209, 91, 203, 75, 187, 59, 171, 42, 154, 24, 136, 38, 150, 21, 133, 35, 147, 53, 165, 70, 182, 86, 198, 102, 214, 96, 208, 80, 192, 64, 176, 47, 159, 29, 141, 14, 126, 5, 117)(3, 115, 9, 121, 16, 128, 33, 145, 49, 161, 68, 180, 82, 194, 100, 212, 95, 207, 79, 191, 63, 175, 46, 158, 28, 140, 13, 125, 20, 132, 7, 119, 18, 130, 31, 143, 51, 163, 66, 178, 84, 196, 98, 210, 92, 204, 76, 188, 60, 172, 43, 155, 25, 137, 11, 123)(4, 116, 12, 124, 26, 138, 44, 156, 61, 173, 77, 189, 93, 205, 107, 219, 112, 224, 104, 216, 88, 200, 72, 184, 55, 167, 39, 151, 56, 168, 41, 153, 58, 170, 74, 186, 90, 202, 106, 218, 109, 221, 99, 211, 83, 195, 67, 179, 50, 162, 32, 144, 17, 129, 8, 120)(10, 122, 23, 135, 40, 152, 57, 169, 73, 185, 89, 201, 105, 217, 110, 222, 103, 215, 85, 197, 71, 183, 52, 164, 36, 148, 19, 131, 37, 149, 27, 139, 45, 157, 62, 174, 78, 190, 94, 206, 108, 220, 111, 223, 101, 213, 87, 199, 69, 181, 54, 166, 34, 146, 22, 134)(225, 337, 227, 339)(226, 338, 231, 343)(228, 340, 234, 346)(229, 341, 237, 349)(230, 342, 240, 352)(232, 344, 243, 355)(233, 345, 245, 357)(235, 347, 248, 360)(236, 348, 251, 363)(238, 350, 249, 361)(239, 351, 255, 367)(241, 353, 258, 370)(242, 354, 259, 371)(244, 356, 262, 374)(246, 358, 263, 375)(247, 359, 265, 377)(250, 362, 264, 376)(252, 364, 266, 378)(253, 365, 270, 382)(254, 366, 273, 385)(256, 368, 276, 388)(257, 369, 277, 389)(260, 372, 279, 391)(261, 373, 280, 392)(267, 379, 283, 395)(268, 380, 286, 398)(269, 381, 282, 394)(271, 383, 284, 396)(272, 384, 290, 402)(274, 386, 293, 405)(275, 387, 294, 406)(278, 390, 296, 408)(281, 393, 298, 410)(285, 397, 297, 409)(287, 399, 299, 411)(288, 400, 303, 415)(289, 401, 306, 418)(291, 403, 309, 421)(292, 404, 310, 422)(295, 407, 312, 424)(300, 412, 315, 427)(301, 413, 318, 430)(302, 414, 314, 426)(304, 416, 316, 428)(305, 417, 322, 434)(307, 419, 325, 437)(308, 420, 326, 438)(311, 423, 328, 440)(313, 425, 330, 442)(317, 429, 329, 441)(319, 431, 321, 433)(320, 432, 324, 436)(323, 435, 334, 446)(327, 439, 336, 448)(331, 443, 335, 447)(332, 444, 333, 445)
	L = (1, 228)(2, 232)(3, 234)(4, 225)(5, 236)(6, 241)(7, 243)(8, 226)(9, 246)(10, 227)(11, 247)(12, 229)(13, 251)(14, 250)(15, 256)(16, 258)(17, 230)(18, 260)(19, 231)(20, 261)(21, 263)(22, 233)(23, 235)(24, 265)(25, 264)(26, 238)(27, 237)(28, 269)(29, 268)(30, 274)(31, 276)(32, 239)(33, 278)(34, 240)(35, 279)(36, 242)(37, 244)(38, 280)(39, 245)(40, 249)(41, 248)(42, 282)(43, 281)(44, 253)(45, 252)(46, 286)(47, 285)(48, 291)(49, 293)(50, 254)(51, 295)(52, 255)(53, 296)(54, 257)(55, 259)(56, 262)(57, 267)(58, 266)(59, 298)(60, 297)(61, 271)(62, 270)(63, 302)(64, 301)(65, 307)(66, 309)(67, 272)(68, 311)(69, 273)(70, 312)(71, 275)(72, 277)(73, 284)(74, 283)(75, 314)(76, 313)(77, 288)(78, 287)(79, 318)(80, 317)(81, 323)(82, 325)(83, 289)(84, 327)(85, 290)(86, 328)(87, 292)(88, 294)(89, 300)(90, 299)(91, 330)(92, 329)(93, 304)(94, 303)(95, 332)(96, 331)(97, 333)(98, 334)(99, 305)(100, 335)(101, 306)(102, 336)(103, 308)(104, 310)(105, 316)(106, 315)(107, 320)(108, 319)(109, 321)(110, 322)(111, 324)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2022
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2026 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y1^-2 * Y2)^2, (Y2 * Y1)^4, Y1^-2 * Y2 * Y1^5 * Y2 * Y1^-7 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114, 6, 118, 15, 127, 30, 142, 48, 160, 65, 177, 81, 193, 97, 209, 90, 202, 76, 188, 58, 170, 42, 154, 22, 134, 35, 147, 25, 137, 38, 150, 54, 166, 71, 183, 87, 199, 103, 215, 96, 208, 80, 192, 64, 176, 47, 159, 29, 141, 14, 126, 5, 117)(3, 115, 9, 121, 21, 133, 39, 151, 57, 169, 73, 185, 89, 201, 98, 210, 85, 197, 66, 178, 52, 164, 31, 143, 20, 132, 7, 119, 18, 130, 13, 125, 28, 140, 46, 158, 63, 175, 79, 191, 95, 207, 101, 213, 82, 194, 69, 181, 49, 161, 34, 146, 16, 128, 11, 123)(4, 116, 12, 124, 26, 138, 44, 156, 61, 173, 77, 189, 93, 205, 107, 219, 112, 224, 104, 216, 88, 200, 72, 184, 56, 168, 43, 155, 55, 167, 41, 153, 60, 172, 75, 187, 92, 204, 106, 218, 109, 221, 99, 211, 83, 195, 67, 179, 50, 162, 32, 144, 17, 129, 8, 120)(10, 122, 24, 136, 33, 145, 53, 165, 68, 180, 86, 198, 100, 212, 111, 223, 108, 220, 94, 206, 78, 190, 62, 174, 45, 157, 27, 139, 36, 148, 19, 131, 37, 149, 51, 163, 70, 182, 84, 196, 102, 214, 110, 222, 105, 217, 91, 203, 74, 186, 59, 171, 40, 152, 23, 135)(225, 337, 227, 339)(226, 338, 231, 343)(228, 340, 234, 346)(229, 341, 237, 349)(230, 342, 240, 352)(232, 344, 243, 355)(233, 345, 246, 358)(235, 347, 249, 361)(236, 348, 251, 363)(238, 350, 245, 357)(239, 351, 255, 367)(241, 353, 257, 369)(242, 354, 259, 371)(244, 356, 262, 374)(247, 359, 265, 377)(248, 360, 267, 379)(250, 362, 264, 376)(252, 364, 266, 378)(253, 365, 270, 382)(254, 366, 273, 385)(256, 368, 275, 387)(258, 370, 278, 390)(260, 372, 279, 391)(261, 373, 280, 392)(263, 375, 282, 394)(268, 380, 286, 398)(269, 381, 284, 396)(271, 383, 281, 393)(272, 384, 290, 402)(274, 386, 292, 404)(276, 388, 295, 407)(277, 389, 296, 408)(283, 395, 299, 411)(285, 397, 298, 410)(287, 399, 300, 412)(288, 400, 303, 415)(289, 401, 306, 418)(291, 403, 308, 420)(293, 405, 311, 423)(294, 406, 312, 424)(297, 409, 314, 426)(301, 413, 318, 430)(302, 414, 316, 428)(304, 416, 313, 425)(305, 417, 322, 434)(307, 419, 324, 436)(309, 421, 327, 439)(310, 422, 328, 440)(315, 427, 330, 442)(317, 429, 329, 441)(319, 431, 321, 433)(320, 432, 325, 437)(323, 435, 334, 446)(326, 438, 336, 448)(331, 443, 335, 447)(332, 444, 333, 445)
	L = (1, 228)(2, 232)(3, 234)(4, 225)(5, 236)(6, 241)(7, 243)(8, 226)(9, 247)(10, 227)(11, 248)(12, 229)(13, 251)(14, 250)(15, 256)(16, 257)(17, 230)(18, 260)(19, 231)(20, 261)(21, 264)(22, 265)(23, 233)(24, 235)(25, 267)(26, 238)(27, 237)(28, 269)(29, 268)(30, 274)(31, 275)(32, 239)(33, 240)(34, 277)(35, 279)(36, 242)(37, 244)(38, 280)(39, 283)(40, 245)(41, 246)(42, 284)(43, 249)(44, 253)(45, 252)(46, 286)(47, 285)(48, 291)(49, 292)(50, 254)(51, 255)(52, 294)(53, 258)(54, 296)(55, 259)(56, 262)(57, 298)(58, 299)(59, 263)(60, 266)(61, 271)(62, 270)(63, 302)(64, 301)(65, 307)(66, 308)(67, 272)(68, 273)(69, 310)(70, 276)(71, 312)(72, 278)(73, 315)(74, 281)(75, 282)(76, 316)(77, 288)(78, 287)(79, 318)(80, 317)(81, 323)(82, 324)(83, 289)(84, 290)(85, 326)(86, 293)(87, 328)(88, 295)(89, 329)(90, 330)(91, 297)(92, 300)(93, 304)(94, 303)(95, 332)(96, 331)(97, 333)(98, 334)(99, 305)(100, 306)(101, 335)(102, 309)(103, 336)(104, 311)(105, 313)(106, 314)(107, 320)(108, 319)(109, 321)(110, 322)(111, 325)(112, 327)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2020
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2027 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = D8 x D14 (small group id <112, 31>)
Aut   = C2 x D8 x D14 (small group id <224, 178>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y3^-1 * Y1^-1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^14, Y1^-1 * Y3^-1 * Y1^6 * Y3^-1 * Y1^-7 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114, 7, 119, 18, 130, 33, 145, 49, 161, 65, 177, 81, 193, 97, 209, 94, 206, 78, 190, 62, 174, 46, 158, 30, 142, 15, 127, 24, 136, 39, 151, 55, 167, 71, 183, 87, 199, 103, 215, 96, 208, 80, 192, 64, 176, 48, 160, 32, 144, 17, 129, 5, 117)(3, 115, 11, 123, 25, 137, 41, 153, 57, 169, 73, 185, 89, 201, 105, 217, 112, 224, 104, 216, 88, 200, 72, 184, 56, 168, 40, 152, 28, 140, 44, 156, 60, 172, 76, 188, 92, 204, 108, 220, 109, 221, 98, 210, 82, 194, 66, 178, 50, 162, 34, 146, 19, 131, 8, 120)(4, 116, 14, 126, 29, 141, 45, 157, 61, 173, 77, 189, 93, 205, 99, 211, 84, 196, 67, 179, 52, 164, 35, 147, 21, 133, 9, 121, 6, 118, 16, 128, 31, 143, 47, 159, 63, 175, 79, 191, 95, 207, 100, 212, 83, 195, 68, 180, 51, 163, 36, 148, 20, 132, 10, 122)(12, 124, 23, 135, 37, 149, 54, 166, 69, 181, 86, 198, 101, 213, 111, 223, 107, 219, 90, 202, 75, 187, 58, 170, 43, 155, 26, 138, 13, 125, 22, 134, 38, 150, 53, 165, 70, 182, 85, 197, 102, 214, 110, 222, 106, 218, 91, 203, 74, 186, 59, 171, 42, 154, 27, 139)(225, 337, 227, 339)(226, 338, 232, 344)(228, 340, 237, 349)(229, 341, 235, 347)(230, 342, 236, 348)(231, 343, 243, 355)(233, 345, 247, 359)(234, 346, 246, 358)(238, 350, 250, 362)(239, 351, 252, 364)(240, 352, 251, 363)(241, 353, 249, 361)(242, 354, 258, 370)(244, 356, 262, 374)(245, 357, 261, 373)(248, 360, 264, 376)(253, 365, 267, 379)(254, 366, 268, 380)(255, 367, 266, 378)(256, 368, 265, 377)(257, 369, 274, 386)(259, 371, 278, 390)(260, 372, 277, 389)(263, 375, 280, 392)(269, 381, 282, 394)(270, 382, 284, 396)(271, 383, 283, 395)(272, 384, 281, 393)(273, 385, 290, 402)(275, 387, 294, 406)(276, 388, 293, 405)(279, 391, 296, 408)(285, 397, 299, 411)(286, 398, 300, 412)(287, 399, 298, 410)(288, 400, 297, 409)(289, 401, 306, 418)(291, 403, 310, 422)(292, 404, 309, 421)(295, 407, 312, 424)(301, 413, 314, 426)(302, 414, 316, 428)(303, 415, 315, 427)(304, 416, 313, 425)(305, 417, 322, 434)(307, 419, 326, 438)(308, 420, 325, 437)(311, 423, 328, 440)(317, 429, 331, 443)(318, 430, 332, 444)(319, 431, 330, 442)(320, 432, 329, 441)(321, 433, 333, 445)(323, 435, 335, 447)(324, 436, 334, 446)(327, 439, 336, 448)
	L = (1, 228)(2, 233)(3, 236)(4, 239)(5, 240)(6, 225)(7, 244)(8, 246)(9, 248)(10, 226)(11, 250)(12, 252)(13, 227)(14, 229)(15, 230)(16, 254)(17, 253)(18, 259)(19, 261)(20, 263)(21, 231)(22, 264)(23, 232)(24, 234)(25, 266)(26, 268)(27, 235)(28, 237)(29, 270)(30, 238)(31, 241)(32, 271)(33, 275)(34, 277)(35, 279)(36, 242)(37, 280)(38, 243)(39, 245)(40, 247)(41, 282)(42, 284)(43, 249)(44, 251)(45, 256)(46, 255)(47, 286)(48, 285)(49, 291)(50, 293)(51, 295)(52, 257)(53, 296)(54, 258)(55, 260)(56, 262)(57, 298)(58, 300)(59, 265)(60, 267)(61, 302)(62, 269)(63, 272)(64, 303)(65, 307)(66, 309)(67, 311)(68, 273)(69, 312)(70, 274)(71, 276)(72, 278)(73, 314)(74, 316)(75, 281)(76, 283)(77, 288)(78, 287)(79, 318)(80, 317)(81, 323)(82, 325)(83, 327)(84, 289)(85, 328)(86, 290)(87, 292)(88, 294)(89, 330)(90, 332)(91, 297)(92, 299)(93, 321)(94, 301)(95, 304)(96, 324)(97, 319)(98, 334)(99, 320)(100, 305)(101, 336)(102, 306)(103, 308)(104, 310)(105, 335)(106, 333)(107, 313)(108, 315)(109, 331)(110, 329)(111, 322)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2021
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2028 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 28})
Quotient :: dipole
Aut^+ = (C28 x C2) : C2 (small group id <112, 30>)
Aut   = (D8 x D14) : C2 (small group id <224, 185>)
|r| :: 2
Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1 * Y3^-1)^2, (R * Y1)^2, Y3^4, (Y3^-1 * Y1^-1)^2, Y1 * Y3^2 * Y2 * Y1 * Y2, Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y2, Y3^-2 * Y1 * Y2 * Y1 * Y2, (Y2 * Y1^-2)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^5 * Y2 * Y3 * Y1^-5 * Y3^-1, Y3^-2 * Y1^14, Y1^-1 * Y3^-1 * Y1^6 * Y3^-1 * Y1^-7 ]
Map:: polytopal non-degenerate
	R = (1, 113, 2, 114, 7, 119, 20, 132, 37, 149, 53, 165, 69, 181, 85, 197, 101, 213, 94, 206, 80, 192, 62, 174, 48, 160, 30, 142, 16, 128, 28, 140, 44, 156, 60, 172, 76, 188, 92, 204, 108, 220, 100, 212, 84, 196, 68, 180, 52, 164, 36, 148, 19, 131, 5, 117)(3, 115, 11, 123, 29, 141, 45, 157, 61, 173, 77, 189, 93, 205, 102, 214, 90, 202, 70, 182, 58, 170, 38, 150, 26, 138, 8, 120, 24, 136, 17, 129, 34, 146, 50, 162, 66, 178, 82, 194, 98, 210, 106, 218, 86, 198, 74, 186, 54, 166, 42, 154, 21, 133, 13, 125)(4, 116, 15, 127, 33, 145, 49, 161, 65, 177, 81, 193, 97, 209, 103, 215, 88, 200, 71, 183, 56, 168, 39, 151, 23, 135, 9, 121, 6, 118, 18, 130, 35, 147, 51, 163, 67, 179, 83, 195, 99, 211, 104, 216, 87, 199, 72, 184, 55, 167, 40, 152, 22, 134, 10, 122)(12, 124, 25, 137, 41, 153, 57, 169, 73, 185, 89, 201, 105, 217, 111, 223, 110, 222, 95, 207, 79, 191, 63, 175, 47, 159, 31, 143, 14, 126, 27, 139, 43, 155, 59, 171, 75, 187, 91, 203, 107, 219, 112, 224, 109, 221, 96, 208, 78, 190, 64, 176, 46, 158, 32, 144)(225, 337, 227, 339)(226, 338, 232, 344)(228, 340, 238, 350)(229, 341, 241, 353)(230, 342, 236, 348)(231, 343, 245, 357)(233, 345, 251, 363)(234, 346, 249, 361)(235, 347, 254, 366)(237, 349, 252, 364)(239, 351, 256, 368)(240, 352, 248, 360)(242, 354, 255, 367)(243, 355, 253, 365)(244, 356, 262, 374)(246, 358, 267, 379)(247, 359, 265, 377)(250, 362, 268, 380)(257, 369, 271, 383)(258, 370, 272, 384)(259, 371, 270, 382)(260, 372, 274, 386)(261, 373, 278, 390)(263, 375, 283, 395)(264, 376, 281, 393)(266, 378, 284, 396)(269, 381, 286, 398)(273, 385, 288, 400)(275, 387, 287, 399)(276, 388, 285, 397)(277, 389, 294, 406)(279, 391, 299, 411)(280, 392, 297, 409)(282, 394, 300, 412)(289, 401, 303, 415)(290, 402, 304, 416)(291, 403, 302, 414)(292, 404, 306, 418)(293, 405, 310, 422)(295, 407, 315, 427)(296, 408, 313, 425)(298, 410, 316, 428)(301, 413, 318, 430)(305, 417, 320, 432)(307, 419, 319, 431)(308, 420, 317, 429)(309, 421, 326, 438)(311, 423, 331, 443)(312, 424, 329, 441)(314, 426, 332, 444)(321, 433, 334, 446)(322, 434, 325, 437)(323, 435, 333, 445)(324, 436, 330, 442)(327, 439, 336, 448)(328, 440, 335, 447)
	L = (1, 228)(2, 233)(3, 236)(4, 240)(5, 242)(6, 225)(7, 246)(8, 249)(9, 252)(10, 226)(11, 255)(12, 248)(13, 251)(14, 227)(15, 229)(16, 230)(17, 256)(18, 254)(19, 257)(20, 263)(21, 265)(22, 268)(23, 231)(24, 238)(25, 237)(26, 267)(27, 232)(28, 234)(29, 270)(30, 239)(31, 241)(32, 235)(33, 272)(34, 271)(35, 243)(36, 275)(37, 279)(38, 281)(39, 284)(40, 244)(41, 250)(42, 283)(43, 245)(44, 247)(45, 287)(46, 258)(47, 253)(48, 259)(49, 260)(50, 288)(51, 286)(52, 289)(53, 295)(54, 297)(55, 300)(56, 261)(57, 266)(58, 299)(59, 262)(60, 264)(61, 302)(62, 273)(63, 274)(64, 269)(65, 304)(66, 303)(67, 276)(68, 307)(69, 311)(70, 313)(71, 316)(72, 277)(73, 282)(74, 315)(75, 278)(76, 280)(77, 319)(78, 290)(79, 285)(80, 291)(81, 292)(82, 320)(83, 318)(84, 321)(85, 327)(86, 329)(87, 332)(88, 293)(89, 298)(90, 331)(91, 294)(92, 296)(93, 333)(94, 305)(95, 306)(96, 301)(97, 325)(98, 334)(99, 308)(100, 328)(101, 323)(102, 335)(103, 324)(104, 309)(105, 314)(106, 336)(107, 310)(108, 312)(109, 322)(110, 317)(111, 330)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2023
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2029 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 28})
Quotient :: edge
Aut^+ = C4 x (C7 : C4) (small group id <112, 10>)
Aut   = (C14 x D8) : C2 (small group id <224, 135>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^2 * T1 * T2^2 * T1^-1, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^3 * T1 * T2^-11 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 27, 46, 62, 78, 94, 105, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 107, 100, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 104, 93, 77, 61, 45, 26, 9, 25, 14, 32, 50, 66, 82, 98, 108, 92, 76, 60, 44, 24, 8)(4, 12, 31, 49, 65, 81, 97, 109, 96, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 99, 110, 95, 80, 63, 48, 28, 13)(6, 17, 35, 53, 69, 85, 101, 111, 103, 87, 71, 55, 38, 19, 37, 22, 42, 58, 74, 90, 106, 112, 102, 86, 70, 54, 36, 18)(113, 114, 118, 116)(115, 121, 129, 123)(117, 126, 130, 127)(119, 131, 124, 133)(120, 134, 125, 135)(122, 136, 147, 140)(128, 132, 148, 143)(137, 149, 141, 152)(138, 154, 142, 155)(139, 157, 165, 159)(144, 150, 145, 153)(146, 162, 166, 163)(151, 167, 161, 169)(156, 170, 160, 171)(158, 172, 181, 175)(164, 168, 182, 177)(173, 186, 176, 187)(174, 189, 197, 191)(178, 183, 179, 185)(180, 194, 198, 195)(184, 199, 193, 201)(188, 202, 192, 203)(190, 204, 213, 207)(196, 200, 214, 209)(205, 218, 208, 219)(206, 216, 223, 221)(210, 215, 211, 217)(212, 220, 224, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.2030
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.2030 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 28})
Quotient :: loop
Aut^+ = C4 x (C7 : C4) (small group id <112, 10>)
Aut   = (C14 x D8) : C2 (small group id <224, 135>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^28 ]
Map:: polytopal non-degenerate
	R = (1, 113, 3, 115, 10, 122, 5, 117)(2, 114, 7, 119, 19, 131, 8, 120)(4, 116, 12, 124, 25, 137, 13, 125)(6, 118, 16, 128, 28, 140, 17, 129)(9, 121, 23, 135, 14, 126, 24, 136)(11, 123, 26, 138, 15, 127, 27, 139)(18, 130, 29, 141, 21, 133, 30, 142)(20, 132, 31, 143, 22, 134, 32, 144)(33, 145, 41, 153, 35, 147, 42, 154)(34, 146, 43, 155, 36, 148, 44, 156)(37, 149, 45, 157, 39, 151, 46, 158)(38, 150, 47, 159, 40, 152, 48, 160)(49, 161, 57, 169, 51, 163, 58, 170)(50, 162, 59, 171, 52, 164, 60, 172)(53, 165, 61, 173, 55, 167, 62, 174)(54, 166, 63, 175, 56, 168, 64, 176)(65, 177, 73, 185, 67, 179, 74, 186)(66, 178, 75, 187, 68, 180, 76, 188)(69, 181, 77, 189, 71, 183, 78, 190)(70, 182, 79, 191, 72, 184, 80, 192)(81, 193, 89, 201, 83, 195, 90, 202)(82, 194, 91, 203, 84, 196, 92, 204)(85, 197, 93, 205, 87, 199, 94, 206)(86, 198, 95, 207, 88, 200, 96, 208)(97, 209, 105, 217, 99, 211, 106, 218)(98, 210, 107, 219, 100, 212, 108, 220)(101, 213, 109, 221, 103, 215, 110, 222)(102, 214, 111, 223, 104, 216, 112, 224)
	L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 126)(6, 116)(7, 130)(8, 133)(9, 128)(10, 131)(11, 115)(12, 132)(13, 134)(14, 129)(15, 117)(16, 123)(17, 127)(18, 124)(19, 140)(20, 119)(21, 125)(22, 120)(23, 145)(24, 147)(25, 122)(26, 146)(27, 148)(28, 137)(29, 149)(30, 151)(31, 150)(32, 152)(33, 138)(34, 135)(35, 139)(36, 136)(37, 143)(38, 141)(39, 144)(40, 142)(41, 161)(42, 163)(43, 162)(44, 164)(45, 165)(46, 167)(47, 166)(48, 168)(49, 155)(50, 153)(51, 156)(52, 154)(53, 159)(54, 157)(55, 160)(56, 158)(57, 177)(58, 179)(59, 178)(60, 180)(61, 181)(62, 183)(63, 182)(64, 184)(65, 171)(66, 169)(67, 172)(68, 170)(69, 175)(70, 173)(71, 176)(72, 174)(73, 193)(74, 195)(75, 194)(76, 196)(77, 197)(78, 199)(79, 198)(80, 200)(81, 187)(82, 185)(83, 188)(84, 186)(85, 191)(86, 189)(87, 192)(88, 190)(89, 209)(90, 211)(91, 210)(92, 212)(93, 213)(94, 215)(95, 214)(96, 216)(97, 203)(98, 201)(99, 204)(100, 202)(101, 207)(102, 205)(103, 208)(104, 206)(105, 221)(106, 222)(107, 223)(108, 224)(109, 219)(110, 220)(111, 217)(112, 218)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2029
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.2031 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = C4 x (C7 : C4) (small group id <112, 10>)
Aut   = (C14 x D8) : C2 (small group id <224, 135>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^2 * Y1^-1 * Y2^2 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^3 * Y1 * Y2^-11 * Y1^-1 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 17, 129, 11, 123)(5, 117, 14, 126, 18, 130, 15, 127)(7, 119, 19, 131, 12, 124, 21, 133)(8, 120, 22, 134, 13, 125, 23, 135)(10, 122, 24, 136, 35, 147, 28, 140)(16, 128, 20, 132, 36, 148, 31, 143)(25, 137, 37, 149, 29, 141, 40, 152)(26, 138, 42, 154, 30, 142, 43, 155)(27, 139, 45, 157, 53, 165, 47, 159)(32, 144, 38, 150, 33, 145, 41, 153)(34, 146, 50, 162, 54, 166, 51, 163)(39, 151, 55, 167, 49, 161, 57, 169)(44, 156, 58, 170, 48, 160, 59, 171)(46, 158, 60, 172, 69, 181, 63, 175)(52, 164, 56, 168, 70, 182, 65, 177)(61, 173, 74, 186, 64, 176, 75, 187)(62, 174, 77, 189, 85, 197, 79, 191)(66, 178, 71, 183, 67, 179, 73, 185)(68, 180, 82, 194, 86, 198, 83, 195)(72, 184, 87, 199, 81, 193, 89, 201)(76, 188, 90, 202, 80, 192, 91, 203)(78, 190, 92, 204, 101, 213, 95, 207)(84, 196, 88, 200, 102, 214, 97, 209)(93, 205, 106, 218, 96, 208, 107, 219)(94, 206, 104, 216, 111, 223, 109, 221)(98, 210, 103, 215, 99, 211, 105, 217)(100, 212, 108, 220, 112, 224, 110, 222)(225, 337, 227, 339, 234, 346, 251, 363, 270, 382, 286, 398, 302, 414, 318, 430, 329, 441, 313, 425, 297, 409, 281, 393, 265, 377, 245, 357, 264, 376, 247, 359, 267, 379, 283, 395, 299, 411, 315, 427, 331, 443, 324, 436, 308, 420, 292, 404, 276, 388, 258, 370, 240, 352, 229, 341)(226, 338, 231, 343, 244, 356, 263, 375, 280, 392, 296, 408, 312, 424, 328, 440, 317, 429, 301, 413, 285, 397, 269, 381, 250, 362, 233, 345, 249, 361, 238, 350, 256, 368, 274, 386, 290, 402, 306, 418, 322, 434, 332, 444, 316, 428, 300, 412, 284, 396, 268, 380, 248, 360, 232, 344)(228, 340, 236, 348, 255, 367, 273, 385, 289, 401, 305, 417, 321, 433, 333, 445, 320, 432, 303, 415, 288, 400, 271, 383, 254, 366, 235, 347, 253, 365, 239, 351, 257, 369, 275, 387, 291, 403, 307, 419, 323, 435, 334, 446, 319, 431, 304, 416, 287, 399, 272, 384, 252, 364, 237, 349)(230, 342, 241, 353, 259, 371, 277, 389, 293, 405, 309, 421, 325, 437, 335, 447, 327, 439, 311, 423, 295, 407, 279, 391, 262, 374, 243, 355, 261, 373, 246, 358, 266, 378, 282, 394, 298, 410, 314, 426, 330, 442, 336, 448, 326, 438, 310, 422, 294, 406, 278, 390, 260, 372, 242, 354)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 329)(95, 304)(96, 303)(97, 333)(98, 332)(99, 334)(100, 308)(101, 335)(102, 310)(103, 311)(104, 317)(105, 313)(106, 336)(107, 324)(108, 316)(109, 320)(110, 319)(111, 327)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2032
Graph:: bipartite
	v = 32 e = 224 f = 140
	degree seq :: [ 8^28, 56^4 ]

E27.2032 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = C4 x (C7 : C4) (small group id <112, 10>)
Aut   = (C14 x D8) : C2 (small group id <224, 135>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2^-2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y3^2 * Y2^-1, (Y3 * Y2 * Y3 * Y2^-1)^2, (Y3^-1 * Y2^-1)^4, Y3^3 * Y2 * Y3^-11 * Y2^-1, (Y3^-1 * Y1^-1)^28 ]
Map:: polytopal
	R = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)(225, 337, 226, 338, 230, 342, 228, 340)(227, 339, 233, 345, 241, 353, 235, 347)(229, 341, 238, 350, 242, 354, 239, 351)(231, 343, 243, 355, 236, 348, 245, 357)(232, 344, 246, 358, 237, 349, 247, 359)(234, 346, 248, 360, 259, 371, 252, 364)(240, 352, 244, 356, 260, 372, 255, 367)(249, 361, 261, 373, 253, 365, 264, 376)(250, 362, 266, 378, 254, 366, 267, 379)(251, 363, 269, 381, 277, 389, 271, 383)(256, 368, 262, 374, 257, 369, 265, 377)(258, 370, 274, 386, 278, 390, 275, 387)(263, 375, 279, 391, 273, 385, 281, 393)(268, 380, 282, 394, 272, 384, 283, 395)(270, 382, 284, 396, 293, 405, 287, 399)(276, 388, 280, 392, 294, 406, 289, 401)(285, 397, 298, 410, 288, 400, 299, 411)(286, 398, 301, 413, 309, 421, 303, 415)(290, 402, 295, 407, 291, 403, 297, 409)(292, 404, 306, 418, 310, 422, 307, 419)(296, 408, 311, 423, 305, 417, 313, 425)(300, 412, 314, 426, 304, 416, 315, 427)(302, 414, 316, 428, 325, 437, 319, 431)(308, 420, 312, 424, 326, 438, 321, 433)(317, 429, 330, 442, 320, 432, 331, 443)(318, 430, 328, 440, 335, 447, 333, 445)(322, 434, 327, 439, 323, 435, 329, 441)(324, 436, 332, 444, 336, 448, 334, 446)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 329)(95, 304)(96, 303)(97, 333)(98, 332)(99, 334)(100, 308)(101, 335)(102, 310)(103, 311)(104, 317)(105, 313)(106, 336)(107, 324)(108, 316)(109, 320)(110, 319)(111, 327)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2031
Graph:: simple bipartite
	v = 140 e = 224 f = 32
	degree seq :: [ 2^112, 8^28 ]

E27.2033 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 28})
Quotient :: edge
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 14, 24)(11, 26, 15, 27)(18, 29, 21, 30)(20, 31, 22, 32)(33, 41, 35, 42)(34, 43, 36, 44)(37, 45, 39, 46)(38, 47, 40, 48)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 73, 67, 74)(66, 75, 68, 76)(69, 77, 71, 78)(70, 79, 72, 80)(81, 89, 83, 90)(82, 91, 84, 92)(85, 93, 87, 94)(86, 95, 88, 96)(97, 105, 99, 106)(98, 107, 100, 108)(101, 109, 103, 110)(102, 111, 104, 112)(113, 114, 118, 116)(115, 121, 128, 123)(117, 126, 129, 127)(119, 130, 124, 132)(120, 133, 125, 134)(122, 131, 140, 137)(135, 145, 138, 146)(136, 147, 139, 148)(141, 149, 143, 150)(142, 151, 144, 152)(153, 161, 155, 162)(154, 163, 156, 164)(157, 165, 159, 166)(158, 167, 160, 168)(169, 177, 171, 178)(170, 179, 172, 180)(173, 181, 175, 182)(174, 183, 176, 184)(185, 193, 187, 194)(186, 195, 188, 196)(189, 197, 191, 198)(190, 199, 192, 200)(201, 209, 203, 210)(202, 211, 204, 212)(205, 213, 207, 214)(206, 215, 208, 216)(217, 223, 219, 221)(218, 224, 220, 222)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 56^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2038
Transitivity :: ET+
Graph:: simple bipartite
	v = 56 e = 112 f = 4
	degree seq :: [ 4^56 ]

E27.2034 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 28})
Quotient :: edge
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^11 * T1^-1 * T2^-3 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 27, 46, 62, 78, 94, 103, 87, 71, 55, 38, 19, 37, 22, 42, 58, 74, 90, 106, 100, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 104, 96, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 99, 108, 92, 76, 60, 44, 24, 8)(4, 12, 31, 49, 65, 81, 97, 109, 93, 77, 61, 45, 26, 9, 25, 14, 32, 50, 66, 82, 98, 110, 95, 80, 63, 48, 28, 13)(6, 17, 35, 53, 69, 85, 101, 111, 105, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 107, 112, 102, 86, 70, 54, 36, 18)(113, 114, 118, 116)(115, 121, 129, 123)(117, 126, 130, 127)(119, 131, 124, 133)(120, 134, 125, 135)(122, 136, 147, 140)(128, 132, 148, 143)(137, 149, 141, 152)(138, 154, 142, 155)(139, 157, 165, 159)(144, 150, 145, 153)(146, 162, 166, 163)(151, 167, 161, 169)(156, 170, 160, 171)(158, 172, 181, 175)(164, 168, 182, 177)(173, 186, 176, 187)(174, 189, 197, 191)(178, 183, 179, 185)(180, 194, 198, 195)(184, 199, 193, 201)(188, 202, 192, 203)(190, 204, 213, 207)(196, 200, 214, 209)(205, 218, 208, 219)(206, 221, 223, 216)(210, 215, 211, 217)(212, 222, 224, 220)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.2036
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.2035 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 28})
Quotient :: edge
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^4 * T1^-1 * T2^-10 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 27, 46, 62, 78, 94, 102, 86, 70, 54, 36, 18, 6, 17, 35, 53, 69, 85, 101, 100, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 104, 95, 80, 63, 48, 28, 13, 4, 12, 31, 49, 65, 81, 97, 108, 92, 76, 60, 44, 24, 8)(9, 25, 14, 32, 50, 66, 82, 98, 110, 96, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 99, 109, 93, 77, 61, 45, 26)(19, 37, 22, 42, 58, 74, 90, 106, 112, 105, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 107, 111, 103, 87, 71, 55, 38)(113, 114, 118, 116)(115, 121, 129, 123)(117, 126, 130, 127)(119, 131, 124, 133)(120, 134, 125, 135)(122, 136, 147, 140)(128, 132, 148, 143)(137, 149, 141, 152)(138, 154, 142, 155)(139, 157, 165, 159)(144, 150, 145, 153)(146, 162, 166, 163)(151, 167, 161, 169)(156, 170, 160, 171)(158, 172, 181, 175)(164, 168, 182, 177)(173, 186, 176, 187)(174, 189, 197, 191)(178, 183, 179, 185)(180, 194, 198, 195)(184, 199, 193, 201)(188, 202, 192, 203)(190, 204, 213, 207)(196, 200, 214, 209)(205, 218, 208, 219)(206, 221, 212, 222)(210, 215, 211, 217)(216, 223, 220, 224)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.2037
Transitivity :: ET+
Graph:: bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.2036 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 28})
Quotient :: loop
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 113, 3, 115, 10, 122, 5, 117)(2, 114, 7, 119, 19, 131, 8, 120)(4, 116, 12, 124, 25, 137, 13, 125)(6, 118, 16, 128, 28, 140, 17, 129)(9, 121, 23, 135, 14, 126, 24, 136)(11, 123, 26, 138, 15, 127, 27, 139)(18, 130, 29, 141, 21, 133, 30, 142)(20, 132, 31, 143, 22, 134, 32, 144)(33, 145, 41, 153, 35, 147, 42, 154)(34, 146, 43, 155, 36, 148, 44, 156)(37, 149, 45, 157, 39, 151, 46, 158)(38, 150, 47, 159, 40, 152, 48, 160)(49, 161, 57, 169, 51, 163, 58, 170)(50, 162, 59, 171, 52, 164, 60, 172)(53, 165, 61, 173, 55, 167, 62, 174)(54, 166, 63, 175, 56, 168, 64, 176)(65, 177, 73, 185, 67, 179, 74, 186)(66, 178, 75, 187, 68, 180, 76, 188)(69, 181, 77, 189, 71, 183, 78, 190)(70, 182, 79, 191, 72, 184, 80, 192)(81, 193, 89, 201, 83, 195, 90, 202)(82, 194, 91, 203, 84, 196, 92, 204)(85, 197, 93, 205, 87, 199, 94, 206)(86, 198, 95, 207, 88, 200, 96, 208)(97, 209, 105, 217, 99, 211, 106, 218)(98, 210, 107, 219, 100, 212, 108, 220)(101, 213, 109, 221, 103, 215, 110, 222)(102, 214, 111, 223, 104, 216, 112, 224)
	L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 126)(6, 116)(7, 130)(8, 133)(9, 128)(10, 131)(11, 115)(12, 132)(13, 134)(14, 129)(15, 117)(16, 123)(17, 127)(18, 124)(19, 140)(20, 119)(21, 125)(22, 120)(23, 145)(24, 147)(25, 122)(26, 146)(27, 148)(28, 137)(29, 149)(30, 151)(31, 150)(32, 152)(33, 138)(34, 135)(35, 139)(36, 136)(37, 143)(38, 141)(39, 144)(40, 142)(41, 161)(42, 163)(43, 162)(44, 164)(45, 165)(46, 167)(47, 166)(48, 168)(49, 155)(50, 153)(51, 156)(52, 154)(53, 159)(54, 157)(55, 160)(56, 158)(57, 177)(58, 179)(59, 178)(60, 180)(61, 181)(62, 183)(63, 182)(64, 184)(65, 171)(66, 169)(67, 172)(68, 170)(69, 175)(70, 173)(71, 176)(72, 174)(73, 193)(74, 195)(75, 194)(76, 196)(77, 197)(78, 199)(79, 198)(80, 200)(81, 187)(82, 185)(83, 188)(84, 186)(85, 191)(86, 189)(87, 192)(88, 190)(89, 209)(90, 211)(91, 210)(92, 212)(93, 213)(94, 215)(95, 214)(96, 216)(97, 203)(98, 201)(99, 204)(100, 202)(101, 207)(102, 205)(103, 208)(104, 206)(105, 223)(106, 224)(107, 221)(108, 222)(109, 217)(110, 218)(111, 219)(112, 220)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2034
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.2037 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 28})
Quotient :: loop
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T1 * T2 * T1^2 * T2^-1 * T1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^28 ]
Map:: polytopal non-degenerate
	R = (1, 113, 3, 115, 10, 122, 5, 117)(2, 114, 7, 119, 19, 131, 8, 120)(4, 116, 12, 124, 25, 137, 13, 125)(6, 118, 16, 128, 28, 140, 17, 129)(9, 121, 23, 135, 14, 126, 24, 136)(11, 123, 26, 138, 15, 127, 27, 139)(18, 130, 29, 141, 21, 133, 30, 142)(20, 132, 31, 143, 22, 134, 32, 144)(33, 145, 41, 153, 35, 147, 42, 154)(34, 146, 43, 155, 36, 148, 44, 156)(37, 149, 45, 157, 39, 151, 46, 158)(38, 150, 47, 159, 40, 152, 48, 160)(49, 161, 57, 169, 51, 163, 58, 170)(50, 162, 59, 171, 52, 164, 60, 172)(53, 165, 61, 173, 55, 167, 62, 174)(54, 166, 63, 175, 56, 168, 64, 176)(65, 177, 73, 185, 67, 179, 74, 186)(66, 178, 75, 187, 68, 180, 76, 188)(69, 181, 77, 189, 71, 183, 78, 190)(70, 182, 79, 191, 72, 184, 80, 192)(81, 193, 89, 201, 83, 195, 90, 202)(82, 194, 91, 203, 84, 196, 92, 204)(85, 197, 93, 205, 87, 199, 94, 206)(86, 198, 95, 207, 88, 200, 96, 208)(97, 209, 105, 217, 99, 211, 106, 218)(98, 210, 107, 219, 100, 212, 108, 220)(101, 213, 109, 221, 103, 215, 110, 222)(102, 214, 111, 223, 104, 216, 112, 224)
	L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 126)(6, 116)(7, 130)(8, 133)(9, 128)(10, 131)(11, 115)(12, 132)(13, 134)(14, 129)(15, 117)(16, 123)(17, 127)(18, 124)(19, 140)(20, 119)(21, 125)(22, 120)(23, 145)(24, 147)(25, 122)(26, 146)(27, 148)(28, 137)(29, 149)(30, 151)(31, 150)(32, 152)(33, 138)(34, 135)(35, 139)(36, 136)(37, 143)(38, 141)(39, 144)(40, 142)(41, 161)(42, 163)(43, 162)(44, 164)(45, 165)(46, 167)(47, 166)(48, 168)(49, 155)(50, 153)(51, 156)(52, 154)(53, 159)(54, 157)(55, 160)(56, 158)(57, 177)(58, 179)(59, 178)(60, 180)(61, 181)(62, 183)(63, 182)(64, 184)(65, 171)(66, 169)(67, 172)(68, 170)(69, 175)(70, 173)(71, 176)(72, 174)(73, 193)(74, 195)(75, 194)(76, 196)(77, 197)(78, 199)(79, 198)(80, 200)(81, 187)(82, 185)(83, 188)(84, 186)(85, 191)(86, 189)(87, 192)(88, 190)(89, 209)(90, 211)(91, 210)(92, 212)(93, 213)(94, 215)(95, 214)(96, 216)(97, 203)(98, 201)(99, 204)(100, 202)(101, 207)(102, 205)(103, 208)(104, 206)(105, 222)(106, 221)(107, 224)(108, 223)(109, 220)(110, 219)(111, 218)(112, 217)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2035
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.2038 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 28})
Quotient :: loop
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^11 * T1^-1 * T2^-3 * T1^-1 ]
Map:: non-degenerate
	R = (1, 113, 3, 115, 10, 122, 27, 139, 46, 158, 62, 174, 78, 190, 94, 206, 103, 215, 87, 199, 71, 183, 55, 167, 38, 150, 19, 131, 37, 149, 22, 134, 42, 154, 58, 170, 74, 186, 90, 202, 106, 218, 100, 212, 84, 196, 68, 180, 52, 164, 34, 146, 16, 128, 5, 117)(2, 114, 7, 119, 20, 132, 39, 151, 56, 168, 72, 184, 88, 200, 104, 216, 96, 208, 79, 191, 64, 176, 47, 159, 30, 142, 11, 123, 29, 141, 15, 127, 33, 145, 51, 163, 67, 179, 83, 195, 99, 211, 108, 220, 92, 204, 76, 188, 60, 172, 44, 156, 24, 136, 8, 120)(4, 116, 12, 124, 31, 143, 49, 161, 65, 177, 81, 193, 97, 209, 109, 221, 93, 205, 77, 189, 61, 173, 45, 157, 26, 138, 9, 121, 25, 137, 14, 126, 32, 144, 50, 162, 66, 178, 82, 194, 98, 210, 110, 222, 95, 207, 80, 192, 63, 175, 48, 160, 28, 140, 13, 125)(6, 118, 17, 129, 35, 147, 53, 165, 69, 181, 85, 197, 101, 213, 111, 223, 105, 217, 89, 201, 73, 185, 57, 169, 41, 153, 21, 133, 40, 152, 23, 135, 43, 155, 59, 171, 75, 187, 91, 203, 107, 219, 112, 224, 102, 214, 86, 198, 70, 182, 54, 166, 36, 148, 18, 130)
	L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 126)(6, 116)(7, 131)(8, 134)(9, 129)(10, 136)(11, 115)(12, 133)(13, 135)(14, 130)(15, 117)(16, 132)(17, 123)(18, 127)(19, 124)(20, 148)(21, 119)(22, 125)(23, 120)(24, 147)(25, 149)(26, 154)(27, 157)(28, 122)(29, 152)(30, 155)(31, 128)(32, 150)(33, 153)(34, 162)(35, 140)(36, 143)(37, 141)(38, 145)(39, 167)(40, 137)(41, 144)(42, 142)(43, 138)(44, 170)(45, 165)(46, 172)(47, 139)(48, 171)(49, 169)(50, 166)(51, 146)(52, 168)(53, 159)(54, 163)(55, 161)(56, 182)(57, 151)(58, 160)(59, 156)(60, 181)(61, 186)(62, 189)(63, 158)(64, 187)(65, 164)(66, 183)(67, 185)(68, 194)(69, 175)(70, 177)(71, 179)(72, 199)(73, 178)(74, 176)(75, 173)(76, 202)(77, 197)(78, 204)(79, 174)(80, 203)(81, 201)(82, 198)(83, 180)(84, 200)(85, 191)(86, 195)(87, 193)(88, 214)(89, 184)(90, 192)(91, 188)(92, 213)(93, 218)(94, 221)(95, 190)(96, 219)(97, 196)(98, 215)(99, 217)(100, 222)(101, 207)(102, 209)(103, 211)(104, 206)(105, 210)(106, 208)(107, 205)(108, 212)(109, 223)(110, 224)(111, 216)(112, 220)
	local type(s) :: { ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2033
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 112 f = 56
	degree seq :: [ 56^4 ]

E27.2039 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, Y2^4, (R * Y3)^2, Y1^4, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y1 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y3^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^28 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 16, 128, 11, 123)(5, 117, 14, 126, 17, 129, 15, 127)(7, 119, 18, 130, 12, 124, 20, 132)(8, 120, 21, 133, 13, 125, 22, 134)(10, 122, 19, 131, 28, 140, 25, 137)(23, 135, 33, 145, 26, 138, 34, 146)(24, 136, 35, 147, 27, 139, 36, 148)(29, 141, 37, 149, 31, 143, 38, 150)(30, 142, 39, 151, 32, 144, 40, 152)(41, 153, 49, 161, 43, 155, 50, 162)(42, 154, 51, 163, 44, 156, 52, 164)(45, 157, 53, 165, 47, 159, 54, 166)(46, 158, 55, 167, 48, 160, 56, 168)(57, 169, 65, 177, 59, 171, 66, 178)(58, 170, 67, 179, 60, 172, 68, 180)(61, 173, 69, 181, 63, 175, 70, 182)(62, 174, 71, 183, 64, 176, 72, 184)(73, 185, 81, 193, 75, 187, 82, 194)(74, 186, 83, 195, 76, 188, 84, 196)(77, 189, 85, 197, 79, 191, 86, 198)(78, 190, 87, 199, 80, 192, 88, 200)(89, 201, 97, 209, 91, 203, 98, 210)(90, 202, 99, 211, 92, 204, 100, 212)(93, 205, 101, 213, 95, 207, 102, 214)(94, 206, 103, 215, 96, 208, 104, 216)(105, 217, 110, 222, 107, 219, 112, 224)(106, 218, 109, 221, 108, 220, 111, 223)(225, 337, 227, 339, 234, 346, 229, 341)(226, 338, 231, 343, 243, 355, 232, 344)(228, 340, 236, 348, 249, 361, 237, 349)(230, 342, 240, 352, 252, 364, 241, 353)(233, 345, 247, 359, 238, 350, 248, 360)(235, 347, 250, 362, 239, 351, 251, 363)(242, 354, 253, 365, 245, 357, 254, 366)(244, 356, 255, 367, 246, 358, 256, 368)(257, 369, 265, 377, 259, 371, 266, 378)(258, 370, 267, 379, 260, 372, 268, 380)(261, 373, 269, 381, 263, 375, 270, 382)(262, 374, 271, 383, 264, 376, 272, 384)(273, 385, 281, 393, 275, 387, 282, 394)(274, 386, 283, 395, 276, 388, 284, 396)(277, 389, 285, 397, 279, 391, 286, 398)(278, 390, 287, 399, 280, 392, 288, 400)(289, 401, 297, 409, 291, 403, 298, 410)(290, 402, 299, 411, 292, 404, 300, 412)(293, 405, 301, 413, 295, 407, 302, 414)(294, 406, 303, 415, 296, 408, 304, 416)(305, 417, 313, 425, 307, 419, 314, 426)(306, 418, 315, 427, 308, 420, 316, 428)(309, 421, 317, 429, 311, 423, 318, 430)(310, 422, 319, 431, 312, 424, 320, 432)(321, 433, 329, 441, 323, 435, 330, 442)(322, 434, 331, 443, 324, 436, 332, 444)(325, 437, 333, 445, 327, 439, 334, 446)(326, 438, 335, 447, 328, 440, 336, 448)
	L = (1, 228)(2, 225)(3, 235)(4, 230)(5, 239)(6, 226)(7, 244)(8, 246)(9, 227)(10, 249)(11, 240)(12, 242)(13, 245)(14, 229)(15, 241)(16, 233)(17, 238)(18, 231)(19, 234)(20, 236)(21, 232)(22, 237)(23, 258)(24, 260)(25, 252)(26, 257)(27, 259)(28, 243)(29, 262)(30, 264)(31, 261)(32, 263)(33, 247)(34, 250)(35, 248)(36, 251)(37, 253)(38, 255)(39, 254)(40, 256)(41, 274)(42, 276)(43, 273)(44, 275)(45, 278)(46, 280)(47, 277)(48, 279)(49, 265)(50, 267)(51, 266)(52, 268)(53, 269)(54, 271)(55, 270)(56, 272)(57, 290)(58, 292)(59, 289)(60, 291)(61, 294)(62, 296)(63, 293)(64, 295)(65, 281)(66, 283)(67, 282)(68, 284)(69, 285)(70, 287)(71, 286)(72, 288)(73, 306)(74, 308)(75, 305)(76, 307)(77, 310)(78, 312)(79, 309)(80, 311)(81, 297)(82, 299)(83, 298)(84, 300)(85, 301)(86, 303)(87, 302)(88, 304)(89, 322)(90, 324)(91, 321)(92, 323)(93, 326)(94, 328)(95, 325)(96, 327)(97, 313)(98, 315)(99, 314)(100, 316)(101, 317)(102, 319)(103, 318)(104, 320)(105, 336)(106, 335)(107, 334)(108, 333)(109, 330)(110, 329)(111, 332)(112, 331)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2044
Graph:: bipartite
	v = 56 e = 224 f = 116
	degree seq :: [ 8^56 ]

E27.2040 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^12 * Y1 * Y2^-2 * Y1 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 17, 129, 11, 123)(5, 117, 14, 126, 18, 130, 15, 127)(7, 119, 19, 131, 12, 124, 21, 133)(8, 120, 22, 134, 13, 125, 23, 135)(10, 122, 24, 136, 35, 147, 28, 140)(16, 128, 20, 132, 36, 148, 31, 143)(25, 137, 37, 149, 29, 141, 40, 152)(26, 138, 42, 154, 30, 142, 43, 155)(27, 139, 45, 157, 53, 165, 47, 159)(32, 144, 38, 150, 33, 145, 41, 153)(34, 146, 50, 162, 54, 166, 51, 163)(39, 151, 55, 167, 49, 161, 57, 169)(44, 156, 58, 170, 48, 160, 59, 171)(46, 158, 60, 172, 69, 181, 63, 175)(52, 164, 56, 168, 70, 182, 65, 177)(61, 173, 74, 186, 64, 176, 75, 187)(62, 174, 77, 189, 85, 197, 79, 191)(66, 178, 71, 183, 67, 179, 73, 185)(68, 180, 82, 194, 86, 198, 83, 195)(72, 184, 87, 199, 81, 193, 89, 201)(76, 188, 90, 202, 80, 192, 91, 203)(78, 190, 92, 204, 101, 213, 95, 207)(84, 196, 88, 200, 102, 214, 97, 209)(93, 205, 106, 218, 96, 208, 107, 219)(94, 206, 109, 221, 100, 212, 110, 222)(98, 210, 103, 215, 99, 211, 105, 217)(104, 216, 111, 223, 108, 220, 112, 224)(225, 337, 227, 339, 234, 346, 251, 363, 270, 382, 286, 398, 302, 414, 318, 430, 326, 438, 310, 422, 294, 406, 278, 390, 260, 372, 242, 354, 230, 342, 241, 353, 259, 371, 277, 389, 293, 405, 309, 421, 325, 437, 324, 436, 308, 420, 292, 404, 276, 388, 258, 370, 240, 352, 229, 341)(226, 338, 231, 343, 244, 356, 263, 375, 280, 392, 296, 408, 312, 424, 328, 440, 319, 431, 304, 416, 287, 399, 272, 384, 252, 364, 237, 349, 228, 340, 236, 348, 255, 367, 273, 385, 289, 401, 305, 417, 321, 433, 332, 444, 316, 428, 300, 412, 284, 396, 268, 380, 248, 360, 232, 344)(233, 345, 249, 361, 238, 350, 256, 368, 274, 386, 290, 402, 306, 418, 322, 434, 334, 446, 320, 432, 303, 415, 288, 400, 271, 383, 254, 366, 235, 347, 253, 365, 239, 351, 257, 369, 275, 387, 291, 403, 307, 419, 323, 435, 333, 445, 317, 429, 301, 413, 285, 397, 269, 381, 250, 362)(243, 355, 261, 373, 246, 358, 266, 378, 282, 394, 298, 410, 314, 426, 330, 442, 336, 448, 329, 441, 313, 425, 297, 409, 281, 393, 265, 377, 245, 357, 264, 376, 247, 359, 267, 379, 283, 395, 299, 411, 315, 427, 331, 443, 335, 447, 327, 439, 311, 423, 295, 407, 279, 391, 262, 374)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 326)(95, 304)(96, 303)(97, 332)(98, 334)(99, 333)(100, 308)(101, 324)(102, 310)(103, 311)(104, 319)(105, 313)(106, 336)(107, 335)(108, 316)(109, 317)(110, 320)(111, 327)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2042
Graph:: bipartite
	v = 32 e = 224 f = 140
	degree seq :: [ 8^28, 56^4 ]

E27.2041 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y1 * Y2^-13 * Y1 * Y2, Y2 * Y1 * Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-2 * Y1 * Y2^4 * Y1 * Y2^-1 * Y1 * Y2 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 9, 121, 17, 129, 11, 123)(5, 117, 14, 126, 18, 130, 15, 127)(7, 119, 19, 131, 12, 124, 21, 133)(8, 120, 22, 134, 13, 125, 23, 135)(10, 122, 24, 136, 35, 147, 28, 140)(16, 128, 20, 132, 36, 148, 31, 143)(25, 137, 37, 149, 29, 141, 40, 152)(26, 138, 42, 154, 30, 142, 43, 155)(27, 139, 45, 157, 53, 165, 47, 159)(32, 144, 38, 150, 33, 145, 41, 153)(34, 146, 50, 162, 54, 166, 51, 163)(39, 151, 55, 167, 49, 161, 57, 169)(44, 156, 58, 170, 48, 160, 59, 171)(46, 158, 60, 172, 69, 181, 63, 175)(52, 164, 56, 168, 70, 182, 65, 177)(61, 173, 74, 186, 64, 176, 75, 187)(62, 174, 77, 189, 85, 197, 79, 191)(66, 178, 71, 183, 67, 179, 73, 185)(68, 180, 82, 194, 86, 198, 83, 195)(72, 184, 87, 199, 81, 193, 89, 201)(76, 188, 90, 202, 80, 192, 91, 203)(78, 190, 92, 204, 101, 213, 95, 207)(84, 196, 88, 200, 102, 214, 97, 209)(93, 205, 106, 218, 96, 208, 107, 219)(94, 206, 109, 221, 111, 223, 104, 216)(98, 210, 103, 215, 99, 211, 105, 217)(100, 212, 110, 222, 112, 224, 108, 220)(225, 337, 227, 339, 234, 346, 251, 363, 270, 382, 286, 398, 302, 414, 318, 430, 327, 439, 311, 423, 295, 407, 279, 391, 262, 374, 243, 355, 261, 373, 246, 358, 266, 378, 282, 394, 298, 410, 314, 426, 330, 442, 324, 436, 308, 420, 292, 404, 276, 388, 258, 370, 240, 352, 229, 341)(226, 338, 231, 343, 244, 356, 263, 375, 280, 392, 296, 408, 312, 424, 328, 440, 320, 432, 303, 415, 288, 400, 271, 383, 254, 366, 235, 347, 253, 365, 239, 351, 257, 369, 275, 387, 291, 403, 307, 419, 323, 435, 332, 444, 316, 428, 300, 412, 284, 396, 268, 380, 248, 360, 232, 344)(228, 340, 236, 348, 255, 367, 273, 385, 289, 401, 305, 417, 321, 433, 333, 445, 317, 429, 301, 413, 285, 397, 269, 381, 250, 362, 233, 345, 249, 361, 238, 350, 256, 368, 274, 386, 290, 402, 306, 418, 322, 434, 334, 446, 319, 431, 304, 416, 287, 399, 272, 384, 252, 364, 237, 349)(230, 342, 241, 353, 259, 371, 277, 389, 293, 405, 309, 421, 325, 437, 335, 447, 329, 441, 313, 425, 297, 409, 281, 393, 265, 377, 245, 357, 264, 376, 247, 359, 267, 379, 283, 395, 299, 411, 315, 427, 331, 443, 336, 448, 326, 438, 310, 422, 294, 406, 278, 390, 260, 372, 242, 354)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 327)(95, 304)(96, 303)(97, 333)(98, 334)(99, 332)(100, 308)(101, 335)(102, 310)(103, 311)(104, 320)(105, 313)(106, 324)(107, 336)(108, 316)(109, 317)(110, 319)(111, 329)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2043
Graph:: bipartite
	v = 32 e = 224 f = 140
	degree seq :: [ 8^28, 56^4 ]

E27.2042 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^11 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^28 ]
Map:: polytopal
	R = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)(225, 337, 226, 338, 230, 342, 228, 340)(227, 339, 233, 345, 241, 353, 235, 347)(229, 341, 238, 350, 242, 354, 239, 351)(231, 343, 243, 355, 236, 348, 245, 357)(232, 344, 246, 358, 237, 349, 247, 359)(234, 346, 248, 360, 259, 371, 252, 364)(240, 352, 244, 356, 260, 372, 255, 367)(249, 361, 261, 373, 253, 365, 264, 376)(250, 362, 266, 378, 254, 366, 267, 379)(251, 363, 269, 381, 277, 389, 271, 383)(256, 368, 262, 374, 257, 369, 265, 377)(258, 370, 274, 386, 278, 390, 275, 387)(263, 375, 279, 391, 273, 385, 281, 393)(268, 380, 282, 394, 272, 384, 283, 395)(270, 382, 284, 396, 293, 405, 287, 399)(276, 388, 280, 392, 294, 406, 289, 401)(285, 397, 298, 410, 288, 400, 299, 411)(286, 398, 301, 413, 309, 421, 303, 415)(290, 402, 295, 407, 291, 403, 297, 409)(292, 404, 306, 418, 310, 422, 307, 419)(296, 408, 311, 423, 305, 417, 313, 425)(300, 412, 314, 426, 304, 416, 315, 427)(302, 414, 316, 428, 325, 437, 319, 431)(308, 420, 312, 424, 326, 438, 321, 433)(317, 429, 330, 442, 320, 432, 331, 443)(318, 430, 333, 445, 335, 447, 328, 440)(322, 434, 327, 439, 323, 435, 329, 441)(324, 436, 334, 446, 336, 448, 332, 444)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 327)(95, 304)(96, 303)(97, 333)(98, 334)(99, 332)(100, 308)(101, 335)(102, 310)(103, 311)(104, 320)(105, 313)(106, 324)(107, 336)(108, 316)(109, 317)(110, 319)(111, 329)(112, 326)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2040
Graph:: simple bipartite
	v = 140 e = 224 f = 32
	degree seq :: [ 2^112, 8^28 ]

E27.2043 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2^-2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y3^2 * Y2^-1, (Y3 * Y2 * Y3 * Y2^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^4 * Y2^-1 * Y3^-10 * Y2^-1, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)(225, 337, 226, 338, 230, 342, 228, 340)(227, 339, 233, 345, 241, 353, 235, 347)(229, 341, 238, 350, 242, 354, 239, 351)(231, 343, 243, 355, 236, 348, 245, 357)(232, 344, 246, 358, 237, 349, 247, 359)(234, 346, 248, 360, 259, 371, 252, 364)(240, 352, 244, 356, 260, 372, 255, 367)(249, 361, 261, 373, 253, 365, 264, 376)(250, 362, 266, 378, 254, 366, 267, 379)(251, 363, 269, 381, 277, 389, 271, 383)(256, 368, 262, 374, 257, 369, 265, 377)(258, 370, 274, 386, 278, 390, 275, 387)(263, 375, 279, 391, 273, 385, 281, 393)(268, 380, 282, 394, 272, 384, 283, 395)(270, 382, 284, 396, 293, 405, 287, 399)(276, 388, 280, 392, 294, 406, 289, 401)(285, 397, 298, 410, 288, 400, 299, 411)(286, 398, 301, 413, 309, 421, 303, 415)(290, 402, 295, 407, 291, 403, 297, 409)(292, 404, 306, 418, 310, 422, 307, 419)(296, 408, 311, 423, 305, 417, 313, 425)(300, 412, 314, 426, 304, 416, 315, 427)(302, 414, 316, 428, 325, 437, 319, 431)(308, 420, 312, 424, 326, 438, 321, 433)(317, 429, 330, 442, 320, 432, 331, 443)(318, 430, 333, 445, 324, 436, 334, 446)(322, 434, 327, 439, 323, 435, 329, 441)(328, 440, 335, 447, 332, 444, 336, 448)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 241)(7, 244)(8, 226)(9, 249)(10, 251)(11, 253)(12, 255)(13, 228)(14, 256)(15, 257)(16, 229)(17, 259)(18, 230)(19, 261)(20, 263)(21, 264)(22, 266)(23, 267)(24, 232)(25, 238)(26, 233)(27, 270)(28, 237)(29, 239)(30, 235)(31, 273)(32, 274)(33, 275)(34, 240)(35, 277)(36, 242)(37, 246)(38, 243)(39, 280)(40, 247)(41, 245)(42, 282)(43, 283)(44, 248)(45, 250)(46, 286)(47, 254)(48, 252)(49, 289)(50, 290)(51, 291)(52, 258)(53, 293)(54, 260)(55, 262)(56, 296)(57, 265)(58, 298)(59, 299)(60, 268)(61, 269)(62, 302)(63, 272)(64, 271)(65, 305)(66, 306)(67, 307)(68, 276)(69, 309)(70, 278)(71, 279)(72, 312)(73, 281)(74, 314)(75, 315)(76, 284)(77, 285)(78, 318)(79, 288)(80, 287)(81, 321)(82, 322)(83, 323)(84, 292)(85, 325)(86, 294)(87, 295)(88, 328)(89, 297)(90, 330)(91, 331)(92, 300)(93, 301)(94, 326)(95, 304)(96, 303)(97, 332)(98, 334)(99, 333)(100, 308)(101, 324)(102, 310)(103, 311)(104, 319)(105, 313)(106, 336)(107, 335)(108, 316)(109, 317)(110, 320)(111, 327)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2041
Graph:: simple bipartite
	v = 140 e = 224 f = 32
	degree seq :: [ 2^112, 8^28 ]

E27.2044 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = (C7 : C4) : C4 (small group id <112, 11>)
Aut   = (C2 x C4 x D14) : C2 (small group id <224, 79>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3^-1 * Y1)^4, (Y3 * Y2^-1)^4, Y1^-2 * Y3 * Y1^5 * Y3 * Y1^-7, Y1^3 * Y3^2 * Y1^5 * Y3^2 * Y1^5 * Y3 * Y1^-1 * Y3 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 17, 129, 35, 147, 53, 165, 69, 181, 85, 197, 101, 213, 94, 206, 79, 191, 62, 174, 47, 159, 26, 138, 41, 153, 29, 141, 43, 155, 59, 171, 75, 187, 91, 203, 107, 219, 98, 210, 82, 194, 66, 178, 50, 162, 32, 144, 13, 125, 4, 116)(3, 115, 9, 121, 25, 137, 45, 157, 61, 173, 77, 189, 93, 205, 103, 215, 90, 202, 71, 183, 58, 170, 37, 149, 24, 136, 8, 120, 23, 135, 14, 126, 34, 146, 51, 163, 68, 180, 83, 195, 100, 212, 105, 217, 86, 198, 73, 185, 54, 166, 39, 151, 18, 130, 11, 123)(5, 117, 15, 127, 33, 145, 52, 164, 67, 179, 84, 196, 99, 211, 102, 214, 89, 201, 70, 182, 57, 169, 36, 148, 22, 134, 7, 119, 20, 132, 12, 124, 31, 143, 49, 161, 65, 177, 81, 193, 97, 209, 106, 218, 87, 199, 74, 186, 55, 167, 40, 152, 19, 131, 16, 128)(10, 122, 21, 133, 38, 150, 56, 168, 72, 184, 88, 200, 104, 216, 111, 223, 110, 222, 95, 207, 80, 192, 63, 175, 48, 160, 27, 139, 42, 154, 30, 142, 44, 156, 60, 172, 76, 188, 92, 204, 108, 220, 112, 224, 109, 221, 96, 208, 78, 190, 64, 176, 46, 158, 28, 140)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448)
	L = (1, 227)(2, 231)(3, 234)(4, 236)(5, 225)(6, 242)(7, 245)(8, 226)(9, 250)(10, 229)(11, 253)(12, 252)(13, 249)(14, 228)(15, 251)(16, 254)(17, 260)(18, 262)(19, 230)(20, 265)(21, 232)(22, 267)(23, 266)(24, 268)(25, 270)(26, 239)(27, 233)(28, 238)(29, 240)(30, 235)(31, 271)(32, 273)(33, 237)(34, 272)(35, 278)(36, 280)(37, 241)(38, 243)(39, 283)(40, 284)(41, 247)(42, 244)(43, 248)(44, 246)(45, 286)(46, 257)(47, 258)(48, 255)(49, 288)(50, 285)(51, 256)(52, 287)(53, 294)(54, 296)(55, 259)(56, 261)(57, 299)(58, 300)(59, 264)(60, 263)(61, 302)(62, 276)(63, 269)(64, 275)(65, 303)(66, 305)(67, 274)(68, 304)(69, 310)(70, 312)(71, 277)(72, 279)(73, 315)(74, 316)(75, 282)(76, 281)(77, 318)(78, 291)(79, 292)(80, 289)(81, 320)(82, 317)(83, 290)(84, 319)(85, 326)(86, 328)(87, 293)(88, 295)(89, 331)(90, 332)(91, 298)(92, 297)(93, 333)(94, 308)(95, 301)(96, 307)(97, 325)(98, 330)(99, 306)(100, 334)(101, 324)(102, 335)(103, 309)(104, 311)(105, 322)(106, 336)(107, 314)(108, 313)(109, 323)(110, 321)(111, 327)(112, 329)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 8 ), ( 8^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2039
Graph:: simple bipartite
	v = 116 e = 224 f = 56
	degree seq :: [ 2^112, 56^4 ]

E27.2045 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 28})
Quotient :: edge
Aut^+ = C28 : C4 (small group id <112, 12>)
Aut   = (C28 x C2 x C2) : C2 (small group id <224, 125>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^4, T2^28 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 110, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 111, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 108, 112, 109, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14)(113, 114, 118, 116)(115, 120, 125, 122)(117, 119, 126, 123)(121, 128, 133, 130)(124, 127, 134, 131)(129, 136, 141, 138)(132, 135, 142, 139)(137, 144, 149, 146)(140, 143, 150, 147)(145, 152, 157, 154)(148, 151, 158, 155)(153, 160, 165, 162)(156, 159, 166, 163)(161, 168, 173, 170)(164, 167, 174, 171)(169, 176, 181, 178)(172, 175, 182, 179)(177, 184, 189, 186)(180, 183, 190, 187)(185, 192, 197, 194)(188, 191, 198, 195)(193, 200, 205, 202)(196, 199, 206, 203)(201, 208, 213, 210)(204, 207, 214, 211)(209, 216, 220, 218)(212, 215, 221, 219)(217, 222, 224, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8^4 ), ( 8^28 ) }
Outer automorphisms :: reflexible
Dual of E27.2046
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 112 f = 28
	degree seq :: [ 4^28, 28^4 ]

E27.2046 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 28})
Quotient :: loop
Aut^+ = C28 : C4 (small group id <112, 12>)
Aut   = (C28 x C2 x C2) : C2 (small group id <224, 125>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^-2 * T1^-1, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^28 ]
Map:: non-degenerate
	R = (1, 113, 3, 115, 6, 118, 5, 117)(2, 114, 7, 119, 4, 116, 8, 120)(9, 121, 13, 125, 10, 122, 14, 126)(11, 123, 15, 127, 12, 124, 16, 128)(17, 129, 21, 133, 18, 130, 22, 134)(19, 131, 23, 135, 20, 132, 24, 136)(25, 137, 29, 141, 26, 138, 30, 142)(27, 139, 31, 143, 28, 140, 32, 144)(33, 145, 57, 169, 34, 146, 58, 170)(35, 147, 60, 172, 40, 152, 62, 174)(36, 148, 63, 175, 38, 150, 64, 176)(37, 149, 65, 177, 39, 151, 66, 178)(41, 153, 67, 179, 42, 154, 68, 180)(43, 155, 61, 173, 44, 156, 59, 171)(45, 157, 69, 181, 46, 158, 70, 182)(47, 159, 71, 183, 48, 160, 72, 184)(49, 161, 73, 185, 50, 162, 74, 186)(51, 163, 75, 187, 52, 164, 76, 188)(53, 165, 77, 189, 54, 166, 78, 190)(55, 167, 79, 191, 56, 168, 80, 192)(81, 193, 105, 217, 82, 194, 106, 218)(83, 195, 107, 219, 84, 196, 108, 220)(85, 197, 109, 221, 86, 198, 110, 222)(87, 199, 111, 223, 88, 200, 112, 224)(89, 201, 104, 216, 90, 202, 103, 215)(91, 203, 101, 213, 92, 204, 102, 214)(93, 205, 100, 212, 94, 206, 99, 211)(95, 207, 97, 209, 96, 208, 98, 210)
	L = (1, 114)(2, 118)(3, 121)(4, 113)(5, 122)(6, 116)(7, 123)(8, 124)(9, 117)(10, 115)(11, 120)(12, 119)(13, 129)(14, 130)(15, 131)(16, 132)(17, 126)(18, 125)(19, 128)(20, 127)(21, 137)(22, 138)(23, 139)(24, 140)(25, 134)(26, 133)(27, 136)(28, 135)(29, 145)(30, 146)(31, 155)(32, 156)(33, 142)(34, 141)(35, 171)(36, 169)(37, 175)(38, 170)(39, 176)(40, 173)(41, 174)(42, 172)(43, 144)(44, 143)(45, 178)(46, 177)(47, 180)(48, 179)(49, 182)(50, 181)(51, 184)(52, 183)(53, 186)(54, 185)(55, 188)(56, 187)(57, 150)(58, 148)(59, 152)(60, 153)(61, 147)(62, 154)(63, 151)(64, 149)(65, 157)(66, 158)(67, 159)(68, 160)(69, 161)(70, 162)(71, 163)(72, 164)(73, 165)(74, 166)(75, 167)(76, 168)(77, 193)(78, 194)(79, 196)(80, 195)(81, 190)(82, 189)(83, 191)(84, 192)(85, 219)(86, 220)(87, 217)(88, 218)(89, 223)(90, 224)(91, 222)(92, 221)(93, 215)(94, 216)(95, 214)(96, 213)(97, 211)(98, 212)(99, 210)(100, 209)(101, 207)(102, 208)(103, 206)(104, 205)(105, 200)(106, 199)(107, 198)(108, 197)(109, 203)(110, 204)(111, 202)(112, 201)
	local type(s) :: { ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2045
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 28 e = 112 f = 32
	degree seq :: [ 8^28 ]

E27.2047 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = C28 : C4 (small group id <112, 12>)
Aut   = (C28 x C2 x C2) : C2 (small group id <224, 125>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (Y3^-1 * Y1^-1)^4, Y2^28 ]
Map::
	R = (1, 113, 2, 114, 6, 118, 4, 116)(3, 115, 8, 120, 13, 125, 10, 122)(5, 117, 7, 119, 14, 126, 11, 123)(9, 121, 16, 128, 21, 133, 18, 130)(12, 124, 15, 127, 22, 134, 19, 131)(17, 129, 24, 136, 29, 141, 26, 138)(20, 132, 23, 135, 30, 142, 27, 139)(25, 137, 32, 144, 37, 149, 34, 146)(28, 140, 31, 143, 38, 150, 35, 147)(33, 145, 40, 152, 45, 157, 42, 154)(36, 148, 39, 151, 46, 158, 43, 155)(41, 153, 48, 160, 53, 165, 50, 162)(44, 156, 47, 159, 54, 166, 51, 163)(49, 161, 56, 168, 61, 173, 58, 170)(52, 164, 55, 167, 62, 174, 59, 171)(57, 169, 64, 176, 69, 181, 66, 178)(60, 172, 63, 175, 70, 182, 67, 179)(65, 177, 72, 184, 77, 189, 74, 186)(68, 180, 71, 183, 78, 190, 75, 187)(73, 185, 80, 192, 85, 197, 82, 194)(76, 188, 79, 191, 86, 198, 83, 195)(81, 193, 88, 200, 93, 205, 90, 202)(84, 196, 87, 199, 94, 206, 91, 203)(89, 201, 96, 208, 101, 213, 98, 210)(92, 204, 95, 207, 102, 214, 99, 211)(97, 209, 104, 216, 108, 220, 106, 218)(100, 212, 103, 215, 109, 221, 107, 219)(105, 217, 110, 222, 112, 224, 111, 223)(225, 337, 227, 339, 233, 345, 241, 353, 249, 361, 257, 369, 265, 377, 273, 385, 281, 393, 289, 401, 297, 409, 305, 417, 313, 425, 321, 433, 329, 441, 324, 436, 316, 428, 308, 420, 300, 412, 292, 404, 284, 396, 276, 388, 268, 380, 260, 372, 252, 364, 244, 356, 236, 348, 229, 341)(226, 338, 231, 343, 239, 351, 247, 359, 255, 367, 263, 375, 271, 383, 279, 391, 287, 399, 295, 407, 303, 415, 311, 423, 319, 431, 327, 439, 334, 446, 328, 440, 320, 432, 312, 424, 304, 416, 296, 408, 288, 400, 280, 392, 272, 384, 264, 376, 256, 368, 248, 360, 240, 352, 232, 344)(228, 340, 235, 347, 243, 355, 251, 363, 259, 371, 267, 379, 275, 387, 283, 395, 291, 403, 299, 411, 307, 419, 315, 427, 323, 435, 331, 443, 335, 447, 330, 442, 322, 434, 314, 426, 306, 418, 298, 410, 290, 402, 282, 394, 274, 386, 266, 378, 258, 370, 250, 362, 242, 354, 234, 346)(230, 342, 237, 349, 245, 357, 253, 365, 261, 373, 269, 381, 277, 389, 285, 397, 293, 405, 301, 413, 309, 421, 317, 429, 325, 437, 332, 444, 336, 448, 333, 445, 326, 438, 318, 430, 310, 422, 302, 414, 294, 406, 286, 398, 278, 390, 270, 382, 262, 374, 254, 366, 246, 358, 238, 350)
	L = (1, 227)(2, 231)(3, 233)(4, 235)(5, 225)(6, 237)(7, 239)(8, 226)(9, 241)(10, 228)(11, 243)(12, 229)(13, 245)(14, 230)(15, 247)(16, 232)(17, 249)(18, 234)(19, 251)(20, 236)(21, 253)(22, 238)(23, 255)(24, 240)(25, 257)(26, 242)(27, 259)(28, 244)(29, 261)(30, 246)(31, 263)(32, 248)(33, 265)(34, 250)(35, 267)(36, 252)(37, 269)(38, 254)(39, 271)(40, 256)(41, 273)(42, 258)(43, 275)(44, 260)(45, 277)(46, 262)(47, 279)(48, 264)(49, 281)(50, 266)(51, 283)(52, 268)(53, 285)(54, 270)(55, 287)(56, 272)(57, 289)(58, 274)(59, 291)(60, 276)(61, 293)(62, 278)(63, 295)(64, 280)(65, 297)(66, 282)(67, 299)(68, 284)(69, 301)(70, 286)(71, 303)(72, 288)(73, 305)(74, 290)(75, 307)(76, 292)(77, 309)(78, 294)(79, 311)(80, 296)(81, 313)(82, 298)(83, 315)(84, 300)(85, 317)(86, 302)(87, 319)(88, 304)(89, 321)(90, 306)(91, 323)(92, 308)(93, 325)(94, 310)(95, 327)(96, 312)(97, 329)(98, 314)(99, 331)(100, 316)(101, 332)(102, 318)(103, 334)(104, 320)(105, 324)(106, 322)(107, 335)(108, 336)(109, 326)(110, 328)(111, 330)(112, 333)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2048
Graph:: bipartite
	v = 32 e = 224 f = 140
	degree seq :: [ 8^28, 56^4 ]

E27.2048 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 28})
Quotient :: dipole
Aut^+ = C28 : C4 (small group id <112, 12>)
Aut   = (C28 x C2 x C2) : C2 (small group id <224, 125>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^13 * Y2 * Y3^-15 * Y2^-1, (Y3^-1 * Y1^-1)^28 ]
Map::
	R = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)(225, 337, 226, 338, 230, 342, 228, 340)(227, 339, 232, 344, 237, 349, 234, 346)(229, 341, 231, 343, 238, 350, 235, 347)(233, 345, 240, 352, 245, 357, 242, 354)(236, 348, 239, 351, 246, 358, 243, 355)(241, 353, 248, 360, 253, 365, 250, 362)(244, 356, 247, 359, 254, 366, 251, 363)(249, 361, 256, 368, 261, 373, 258, 370)(252, 364, 255, 367, 262, 374, 259, 371)(257, 369, 264, 376, 269, 381, 266, 378)(260, 372, 263, 375, 270, 382, 267, 379)(265, 377, 272, 384, 277, 389, 274, 386)(268, 380, 271, 383, 278, 390, 275, 387)(273, 385, 280, 392, 285, 397, 282, 394)(276, 388, 279, 391, 286, 398, 283, 395)(281, 393, 288, 400, 293, 405, 290, 402)(284, 396, 287, 399, 294, 406, 291, 403)(289, 401, 296, 408, 301, 413, 298, 410)(292, 404, 295, 407, 302, 414, 299, 411)(297, 409, 304, 416, 309, 421, 306, 418)(300, 412, 303, 415, 310, 422, 307, 419)(305, 417, 312, 424, 317, 429, 314, 426)(308, 420, 311, 423, 318, 430, 315, 427)(313, 425, 320, 432, 325, 437, 322, 434)(316, 428, 319, 431, 326, 438, 323, 435)(321, 433, 328, 440, 332, 444, 330, 442)(324, 436, 327, 439, 333, 445, 331, 443)(329, 441, 334, 446, 336, 448, 335, 447)
	L = (1, 227)(2, 231)(3, 233)(4, 235)(5, 225)(6, 237)(7, 239)(8, 226)(9, 241)(10, 228)(11, 243)(12, 229)(13, 245)(14, 230)(15, 247)(16, 232)(17, 249)(18, 234)(19, 251)(20, 236)(21, 253)(22, 238)(23, 255)(24, 240)(25, 257)(26, 242)(27, 259)(28, 244)(29, 261)(30, 246)(31, 263)(32, 248)(33, 265)(34, 250)(35, 267)(36, 252)(37, 269)(38, 254)(39, 271)(40, 256)(41, 273)(42, 258)(43, 275)(44, 260)(45, 277)(46, 262)(47, 279)(48, 264)(49, 281)(50, 266)(51, 283)(52, 268)(53, 285)(54, 270)(55, 287)(56, 272)(57, 289)(58, 274)(59, 291)(60, 276)(61, 293)(62, 278)(63, 295)(64, 280)(65, 297)(66, 282)(67, 299)(68, 284)(69, 301)(70, 286)(71, 303)(72, 288)(73, 305)(74, 290)(75, 307)(76, 292)(77, 309)(78, 294)(79, 311)(80, 296)(81, 313)(82, 298)(83, 315)(84, 300)(85, 317)(86, 302)(87, 319)(88, 304)(89, 321)(90, 306)(91, 323)(92, 308)(93, 325)(94, 310)(95, 327)(96, 312)(97, 329)(98, 314)(99, 331)(100, 316)(101, 332)(102, 318)(103, 334)(104, 320)(105, 324)(106, 322)(107, 335)(108, 336)(109, 326)(110, 328)(111, 330)(112, 333)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 56 ), ( 8, 56, 8, 56, 8, 56, 8, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2047
Graph:: simple bipartite
	v = 140 e = 224 f = 32
	degree seq :: [ 2^112, 8^28 ]

E27.2049 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 56, 56})
Quotient :: regular
Aut^+ = C56 x C2 (small group id <112, 22>)
Aut   = C2 x D112 (small group id <224, 98>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^56 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 39, 41, 43, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64, 66, 68, 72, 73, 75, 78, 80, 82, 84, 86, 88, 95, 96, 98, 94, 101, 102, 103, 105, 107, 111, 109, 90, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 38, 35, 37, 40, 42, 44, 46, 48, 50, 57, 54, 56, 59, 61, 63, 65, 67, 69, 77, 74, 76, 79, 81, 83, 85, 87, 89, 100, 97, 99, 92, 71, 93, 104, 106, 108, 112, 110, 91, 70, 51, 31, 27, 23, 19, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 38)(32, 51)(33, 35)(34, 37)(36, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 57)(52, 54)(53, 56)(55, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 77)(70, 90)(71, 94)(72, 74)(73, 76)(75, 79)(78, 81)(80, 83)(82, 85)(84, 87)(86, 89)(88, 100)(91, 109)(92, 98)(93, 101)(95, 97)(96, 99)(102, 104)(103, 106)(105, 108)(107, 112)(110, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.2050 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 56, 56})
Quotient :: edge
Aut^+ = C56 x C2 (small group id <112, 22>)
Aut   = C2 x D112 (small group id <224, 98>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^56 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 46, 42, 38, 34, 37, 41, 45, 49, 51, 53, 55, 73, 69, 65, 61, 58, 60, 64, 68, 72, 75, 77, 79, 81, 96, 92, 88, 83, 87, 91, 95, 99, 101, 103, 105, 112, 110, 109, 107, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 48, 44, 40, 36, 33, 35, 39, 43, 47, 50, 52, 54, 56, 71, 67, 63, 59, 62, 66, 70, 74, 76, 78, 80, 98, 94, 90, 86, 84, 85, 89, 93, 97, 100, 102, 104, 106, 111, 108, 82, 57, 30, 26, 22, 18, 14, 10, 6)(113, 114)(115, 117)(116, 118)(119, 121)(120, 122)(123, 125)(124, 126)(127, 129)(128, 130)(131, 133)(132, 134)(135, 137)(136, 138)(139, 141)(140, 142)(143, 160)(144, 169)(145, 146)(147, 149)(148, 150)(151, 153)(152, 154)(155, 157)(156, 158)(159, 161)(162, 163)(164, 165)(166, 167)(168, 185)(170, 171)(172, 174)(173, 175)(176, 178)(177, 179)(180, 182)(181, 183)(184, 186)(187, 188)(189, 190)(191, 192)(193, 210)(194, 219)(195, 196)(197, 199)(198, 200)(201, 203)(202, 204)(205, 207)(206, 208)(209, 211)(212, 213)(214, 215)(216, 217)(218, 224)(220, 221)(222, 223)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2051
Transitivity :: ET+
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.2051 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 56, 56})
Quotient :: loop
Aut^+ = C56 x C2 (small group id <112, 22>)
Aut   = C2 x D112 (small group id <224, 98>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^56 ]
Map::
	R = (1, 113, 3, 115, 7, 119, 11, 123, 15, 127, 19, 131, 23, 135, 27, 139, 31, 143, 42, 154, 38, 150, 34, 146, 37, 149, 41, 153, 45, 157, 47, 159, 49, 161, 51, 163, 53, 165, 67, 179, 63, 175, 59, 171, 56, 168, 58, 170, 62, 174, 66, 178, 69, 181, 71, 183, 73, 185, 75, 187, 77, 189, 89, 201, 85, 197, 81, 193, 84, 196, 88, 200, 92, 204, 79, 191, 95, 207, 97, 209, 99, 211, 112, 224, 110, 222, 106, 218, 103, 215, 105, 217, 109, 221, 101, 213, 32, 144, 28, 140, 24, 136, 20, 132, 16, 128, 12, 124, 8, 120, 4, 116)(2, 114, 5, 117, 9, 121, 13, 125, 17, 129, 21, 133, 25, 137, 29, 141, 44, 156, 40, 152, 36, 148, 33, 145, 35, 147, 39, 151, 43, 155, 46, 158, 48, 160, 50, 162, 52, 164, 54, 166, 65, 177, 61, 173, 57, 169, 60, 172, 64, 176, 68, 180, 70, 182, 72, 184, 74, 186, 76, 188, 91, 203, 87, 199, 83, 195, 80, 192, 82, 194, 86, 198, 90, 202, 93, 205, 94, 206, 96, 208, 98, 210, 100, 212, 111, 223, 108, 220, 104, 216, 107, 219, 102, 214, 78, 190, 55, 167, 30, 142, 26, 138, 22, 134, 18, 130, 14, 126, 10, 122, 6, 118)
	L = (1, 114)(2, 113)(3, 117)(4, 118)(5, 115)(6, 116)(7, 121)(8, 122)(9, 119)(10, 120)(11, 125)(12, 126)(13, 123)(14, 124)(15, 129)(16, 130)(17, 127)(18, 128)(19, 133)(20, 134)(21, 131)(22, 132)(23, 137)(24, 138)(25, 135)(26, 136)(27, 141)(28, 142)(29, 139)(30, 140)(31, 156)(32, 167)(33, 146)(34, 145)(35, 149)(36, 150)(37, 147)(38, 148)(39, 153)(40, 154)(41, 151)(42, 152)(43, 157)(44, 143)(45, 155)(46, 159)(47, 158)(48, 161)(49, 160)(50, 163)(51, 162)(52, 165)(53, 164)(54, 179)(55, 144)(56, 169)(57, 168)(58, 172)(59, 173)(60, 170)(61, 171)(62, 176)(63, 177)(64, 174)(65, 175)(66, 180)(67, 166)(68, 178)(69, 182)(70, 181)(71, 184)(72, 183)(73, 186)(74, 185)(75, 188)(76, 187)(77, 203)(78, 213)(79, 205)(80, 193)(81, 192)(82, 196)(83, 197)(84, 194)(85, 195)(86, 200)(87, 201)(88, 198)(89, 199)(90, 204)(91, 189)(92, 202)(93, 191)(94, 207)(95, 206)(96, 209)(97, 208)(98, 211)(99, 210)(100, 224)(101, 190)(102, 221)(103, 216)(104, 215)(105, 219)(106, 220)(107, 217)(108, 218)(109, 214)(110, 223)(111, 222)(112, 212)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2050
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.2052 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 56, 56})
Quotient :: dipole
Aut^+ = C56 x C2 (small group id <112, 22>)
Aut   = C2 x D112 (small group id <224, 98>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^56, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 113, 2, 114)(3, 115, 5, 117)(4, 116, 6, 118)(7, 119, 9, 121)(8, 120, 10, 122)(11, 123, 13, 125)(12, 124, 14, 126)(15, 127, 17, 129)(16, 128, 18, 130)(19, 131, 21, 133)(20, 132, 22, 134)(23, 135, 25, 137)(24, 136, 26, 138)(27, 139, 29, 141)(28, 140, 30, 142)(31, 143, 44, 156)(32, 144, 55, 167)(33, 145, 34, 146)(35, 147, 37, 149)(36, 148, 38, 150)(39, 151, 41, 153)(40, 152, 42, 154)(43, 155, 45, 157)(46, 158, 47, 159)(48, 160, 49, 161)(50, 162, 51, 163)(52, 164, 53, 165)(54, 166, 67, 179)(56, 168, 57, 169)(58, 170, 60, 172)(59, 171, 61, 173)(62, 174, 64, 176)(63, 175, 65, 177)(66, 178, 68, 180)(69, 181, 70, 182)(71, 183, 72, 184)(73, 185, 74, 186)(75, 187, 76, 188)(77, 189, 91, 203)(78, 190, 101, 213)(79, 191, 93, 205)(80, 192, 81, 193)(82, 194, 84, 196)(83, 195, 85, 197)(86, 198, 88, 200)(87, 199, 89, 201)(90, 202, 92, 204)(94, 206, 95, 207)(96, 208, 97, 209)(98, 210, 99, 211)(100, 212, 112, 224)(102, 214, 109, 221)(103, 215, 104, 216)(105, 217, 107, 219)(106, 218, 108, 220)(110, 222, 111, 223)(225, 337, 227, 339, 231, 343, 235, 347, 239, 351, 243, 355, 247, 359, 251, 363, 255, 367, 266, 378, 262, 374, 258, 370, 261, 373, 265, 377, 269, 381, 271, 383, 273, 385, 275, 387, 277, 389, 291, 403, 287, 399, 283, 395, 280, 392, 282, 394, 286, 398, 290, 402, 293, 405, 295, 407, 297, 409, 299, 411, 301, 413, 313, 425, 309, 421, 305, 417, 308, 420, 312, 424, 316, 428, 303, 415, 319, 431, 321, 433, 323, 435, 336, 448, 334, 446, 330, 442, 327, 439, 329, 441, 333, 445, 325, 437, 256, 368, 252, 364, 248, 360, 244, 356, 240, 352, 236, 348, 232, 344, 228, 340)(226, 338, 229, 341, 233, 345, 237, 349, 241, 353, 245, 357, 249, 361, 253, 365, 268, 380, 264, 376, 260, 372, 257, 369, 259, 371, 263, 375, 267, 379, 270, 382, 272, 384, 274, 386, 276, 388, 278, 390, 289, 401, 285, 397, 281, 393, 284, 396, 288, 400, 292, 404, 294, 406, 296, 408, 298, 410, 300, 412, 315, 427, 311, 423, 307, 419, 304, 416, 306, 418, 310, 422, 314, 426, 317, 429, 318, 430, 320, 432, 322, 434, 324, 436, 335, 447, 332, 444, 328, 440, 331, 443, 326, 438, 302, 414, 279, 391, 254, 366, 250, 362, 246, 358, 242, 354, 238, 350, 234, 346, 230, 342)
	L = (1, 226)(2, 225)(3, 229)(4, 230)(5, 227)(6, 228)(7, 233)(8, 234)(9, 231)(10, 232)(11, 237)(12, 238)(13, 235)(14, 236)(15, 241)(16, 242)(17, 239)(18, 240)(19, 245)(20, 246)(21, 243)(22, 244)(23, 249)(24, 250)(25, 247)(26, 248)(27, 253)(28, 254)(29, 251)(30, 252)(31, 268)(32, 279)(33, 258)(34, 257)(35, 261)(36, 262)(37, 259)(38, 260)(39, 265)(40, 266)(41, 263)(42, 264)(43, 269)(44, 255)(45, 267)(46, 271)(47, 270)(48, 273)(49, 272)(50, 275)(51, 274)(52, 277)(53, 276)(54, 291)(55, 256)(56, 281)(57, 280)(58, 284)(59, 285)(60, 282)(61, 283)(62, 288)(63, 289)(64, 286)(65, 287)(66, 292)(67, 278)(68, 290)(69, 294)(70, 293)(71, 296)(72, 295)(73, 298)(74, 297)(75, 300)(76, 299)(77, 315)(78, 325)(79, 317)(80, 305)(81, 304)(82, 308)(83, 309)(84, 306)(85, 307)(86, 312)(87, 313)(88, 310)(89, 311)(90, 316)(91, 301)(92, 314)(93, 303)(94, 319)(95, 318)(96, 321)(97, 320)(98, 323)(99, 322)(100, 336)(101, 302)(102, 333)(103, 328)(104, 327)(105, 331)(106, 332)(107, 329)(108, 330)(109, 326)(110, 335)(111, 334)(112, 324)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2053
Graph:: bipartite
	v = 58 e = 224 f = 114
	degree seq :: [ 4^56, 112^2 ]

E27.2053 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 56, 56})
Quotient :: dipole
Aut^+ = C56 x C2 (small group id <112, 22>)
Aut   = C2 x D112 (small group id <224, 98>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-56, Y1^56 ]
Map::
	R = (1, 113, 2, 114, 5, 117, 9, 121, 13, 125, 17, 129, 21, 133, 25, 137, 29, 141, 36, 148, 38, 150, 40, 152, 42, 154, 44, 156, 46, 158, 48, 160, 50, 162, 51, 163, 52, 164, 54, 166, 56, 168, 58, 170, 60, 172, 62, 174, 64, 176, 71, 183, 73, 185, 75, 187, 77, 189, 79, 191, 81, 193, 83, 195, 89, 201, 90, 202, 91, 203, 93, 205, 95, 207, 97, 209, 99, 211, 86, 198, 67, 179, 87, 199, 105, 217, 110, 222, 111, 223, 112, 224, 103, 215, 84, 196, 32, 144, 28, 140, 24, 136, 20, 132, 16, 128, 12, 124, 8, 120, 4, 116)(3, 115, 6, 118, 10, 122, 14, 126, 18, 130, 22, 134, 26, 138, 30, 142, 33, 145, 34, 146, 35, 147, 37, 149, 39, 151, 41, 153, 43, 155, 45, 157, 47, 159, 53, 165, 55, 167, 57, 169, 59, 171, 61, 173, 63, 175, 65, 177, 68, 180, 69, 181, 70, 182, 72, 184, 74, 186, 76, 188, 78, 190, 80, 192, 82, 194, 92, 204, 94, 206, 96, 208, 98, 210, 100, 212, 101, 213, 102, 214, 88, 200, 106, 218, 107, 219, 108, 220, 109, 221, 104, 216, 85, 197, 66, 178, 49, 161, 31, 143, 27, 139, 23, 135, 19, 131, 15, 127, 11, 123, 7, 119)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448)
	L = (1, 227)(2, 230)(3, 225)(4, 231)(5, 234)(6, 226)(7, 228)(8, 235)(9, 238)(10, 229)(11, 232)(12, 239)(13, 242)(14, 233)(15, 236)(16, 243)(17, 246)(18, 237)(19, 240)(20, 247)(21, 250)(22, 241)(23, 244)(24, 251)(25, 254)(26, 245)(27, 248)(28, 255)(29, 257)(30, 249)(31, 252)(32, 273)(33, 253)(34, 260)(35, 262)(36, 258)(37, 264)(38, 259)(39, 266)(40, 261)(41, 268)(42, 263)(43, 270)(44, 265)(45, 272)(46, 267)(47, 274)(48, 269)(49, 256)(50, 271)(51, 277)(52, 279)(53, 275)(54, 281)(55, 276)(56, 283)(57, 278)(58, 285)(59, 280)(60, 287)(61, 282)(62, 289)(63, 284)(64, 292)(65, 286)(66, 308)(67, 312)(68, 288)(69, 295)(70, 297)(71, 293)(72, 299)(73, 294)(74, 301)(75, 296)(76, 303)(77, 298)(78, 305)(79, 300)(80, 307)(81, 302)(82, 313)(83, 304)(84, 290)(85, 327)(86, 326)(87, 330)(88, 291)(89, 306)(90, 316)(91, 318)(92, 314)(93, 320)(94, 315)(95, 322)(96, 317)(97, 324)(98, 319)(99, 325)(100, 321)(101, 323)(102, 310)(103, 309)(104, 336)(105, 331)(106, 311)(107, 329)(108, 334)(109, 335)(110, 332)(111, 333)(112, 328)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2052
Graph:: simple bipartite
	v = 114 e = 224 f = 58
	degree seq :: [ 2^112, 112^2 ]

E27.2054 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 56, 56})
Quotient :: regular
Aut^+ = C7 x (C8 : C2) (small group id <112, 23>)
Aut   = (C2 x D56) : C2 (small group id <224, 103>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2 * T1, (T1 * T2 * T1^-1 * T2)^2, T1^-11 * T2 * T1^12 * T2 * T1^-1, T2 * T1 * T2 * T1^27, T1^-1 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-4 * T2 * T1^2 * T2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 105, 97, 89, 81, 73, 65, 57, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 71, 78, 87, 94, 103, 110, 107, 99, 91, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 63, 70, 79, 86, 95, 102, 111, 106, 98, 90, 82, 74, 66, 58, 50, 42, 34, 26, 17, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 73)(68, 75)(69, 78)(71, 80)(74, 81)(76, 82)(77, 86)(79, 88)(83, 89)(84, 91)(85, 94)(87, 96)(90, 97)(92, 98)(93, 102)(95, 104)(99, 105)(100, 107)(101, 110)(103, 112)(106, 109)(108, 111)
	local type(s) :: { ( 56^56 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 56 f = 2
	degree seq :: [ 56^2 ]

E27.2055 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 56, 56})
Quotient :: edge
Aut^+ = C7 x (C8 : C2) (small group id <112, 23>)
Aut   = (C2 x D56) : C2 (small group id <224, 103>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^27 * T1 * T2 * T1, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-10 ]
Map::
	R = (1, 3, 8, 17, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 111, 103, 95, 87, 79, 71, 63, 55, 47, 39, 31, 23, 13, 21, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 107, 99, 91, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 16, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 14, 6)(113, 114)(115, 119)(116, 121)(117, 123)(118, 125)(120, 124)(122, 126)(127, 132)(128, 133)(129, 137)(130, 135)(131, 139)(134, 141)(136, 143)(138, 142)(140, 144)(145, 149)(146, 153)(147, 151)(148, 155)(150, 157)(152, 159)(154, 158)(156, 160)(161, 165)(162, 169)(163, 167)(164, 171)(166, 173)(168, 175)(170, 174)(172, 176)(177, 181)(178, 185)(179, 183)(180, 187)(182, 189)(184, 191)(186, 190)(188, 192)(193, 197)(194, 201)(195, 199)(196, 203)(198, 205)(200, 207)(202, 206)(204, 208)(209, 213)(210, 217)(211, 215)(212, 219)(214, 221)(216, 223)(218, 222)(220, 224)
	L = (1, 113)(2, 114)(3, 115)(4, 116)(5, 117)(6, 118)(7, 119)(8, 120)(9, 121)(10, 122)(11, 123)(12, 124)(13, 125)(14, 126)(15, 127)(16, 128)(17, 129)(18, 130)(19, 131)(20, 132)(21, 133)(22, 134)(23, 135)(24, 136)(25, 137)(26, 138)(27, 139)(28, 140)(29, 141)(30, 142)(31, 143)(32, 144)(33, 145)(34, 146)(35, 147)(36, 148)(37, 149)(38, 150)(39, 151)(40, 152)(41, 153)(42, 154)(43, 155)(44, 156)(45, 157)(46, 158)(47, 159)(48, 160)(49, 161)(50, 162)(51, 163)(52, 164)(53, 165)(54, 166)(55, 167)(56, 168)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 112, 112 ), ( 112^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2056
Transitivity :: ET+
Graph:: simple bipartite
	v = 58 e = 112 f = 2
	degree seq :: [ 2^56, 56^2 ]

E27.2056 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 56, 56})
Quotient :: loop
Aut^+ = C7 x (C8 : C2) (small group id <112, 23>)
Aut   = (C2 x D56) : C2 (small group id <224, 103>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^27 * T1 * T2 * T1, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-10 ]
Map::
	R = (1, 113, 3, 115, 8, 120, 17, 129, 26, 138, 34, 146, 42, 154, 50, 162, 58, 170, 66, 178, 74, 186, 82, 194, 90, 202, 98, 210, 106, 218, 111, 223, 103, 215, 95, 207, 87, 199, 79, 191, 71, 183, 63, 175, 55, 167, 47, 159, 39, 151, 31, 143, 23, 135, 13, 125, 21, 133, 11, 123, 20, 132, 29, 141, 37, 149, 45, 157, 53, 165, 61, 173, 69, 181, 77, 189, 85, 197, 93, 205, 101, 213, 109, 221, 108, 220, 100, 212, 92, 204, 84, 196, 76, 188, 68, 180, 60, 172, 52, 164, 44, 156, 36, 148, 28, 140, 19, 131, 10, 122, 4, 116)(2, 114, 5, 117, 12, 124, 22, 134, 30, 142, 38, 150, 46, 158, 54, 166, 62, 174, 70, 182, 78, 190, 86, 198, 94, 206, 102, 214, 110, 222, 107, 219, 99, 211, 91, 203, 83, 195, 75, 187, 67, 179, 59, 171, 51, 163, 43, 155, 35, 147, 27, 139, 18, 130, 9, 121, 16, 128, 7, 119, 15, 127, 25, 137, 33, 145, 41, 153, 49, 161, 57, 169, 65, 177, 73, 185, 81, 193, 89, 201, 97, 209, 105, 217, 112, 224, 104, 216, 96, 208, 88, 200, 80, 192, 72, 184, 64, 176, 56, 168, 48, 160, 40, 152, 32, 144, 24, 136, 14, 126, 6, 118)
	L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 124)(9, 116)(10, 126)(11, 117)(12, 120)(13, 118)(14, 122)(15, 132)(16, 133)(17, 137)(18, 135)(19, 139)(20, 127)(21, 128)(22, 141)(23, 130)(24, 143)(25, 129)(26, 142)(27, 131)(28, 144)(29, 134)(30, 138)(31, 136)(32, 140)(33, 149)(34, 153)(35, 151)(36, 155)(37, 145)(38, 157)(39, 147)(40, 159)(41, 146)(42, 158)(43, 148)(44, 160)(45, 150)(46, 154)(47, 152)(48, 156)(49, 165)(50, 169)(51, 167)(52, 171)(53, 161)(54, 173)(55, 163)(56, 175)(57, 162)(58, 174)(59, 164)(60, 176)(61, 166)(62, 170)(63, 168)(64, 172)(65, 181)(66, 185)(67, 183)(68, 187)(69, 177)(70, 189)(71, 179)(72, 191)(73, 178)(74, 190)(75, 180)(76, 192)(77, 182)(78, 186)(79, 184)(80, 188)(81, 197)(82, 201)(83, 199)(84, 203)(85, 193)(86, 205)(87, 195)(88, 207)(89, 194)(90, 206)(91, 196)(92, 208)(93, 198)(94, 202)(95, 200)(96, 204)(97, 213)(98, 217)(99, 215)(100, 219)(101, 209)(102, 221)(103, 211)(104, 223)(105, 210)(106, 222)(107, 212)(108, 224)(109, 214)(110, 218)(111, 216)(112, 220)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2055
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 112 f = 58
	degree seq :: [ 112^2 ]

E27.2057 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 56, 56})
Quotient :: dipole
Aut^+ = C7 x (C8 : C2) (small group id <112, 23>)
Aut   = (C2 x D56) : C2 (small group id <224, 103>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^27 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 113, 2, 114)(3, 115, 7, 119)(4, 116, 9, 121)(5, 117, 11, 123)(6, 118, 13, 125)(8, 120, 12, 124)(10, 122, 14, 126)(15, 127, 20, 132)(16, 128, 21, 133)(17, 129, 25, 137)(18, 130, 23, 135)(19, 131, 27, 139)(22, 134, 29, 141)(24, 136, 31, 143)(26, 138, 30, 142)(28, 140, 32, 144)(33, 145, 37, 149)(34, 146, 41, 153)(35, 147, 39, 151)(36, 148, 43, 155)(38, 150, 45, 157)(40, 152, 47, 159)(42, 154, 46, 158)(44, 156, 48, 160)(49, 161, 53, 165)(50, 162, 57, 169)(51, 163, 55, 167)(52, 164, 59, 171)(54, 166, 61, 173)(56, 168, 63, 175)(58, 170, 62, 174)(60, 172, 64, 176)(65, 177, 69, 181)(66, 178, 73, 185)(67, 179, 71, 183)(68, 180, 75, 187)(70, 182, 77, 189)(72, 184, 79, 191)(74, 186, 78, 190)(76, 188, 80, 192)(81, 193, 85, 197)(82, 194, 89, 201)(83, 195, 87, 199)(84, 196, 91, 203)(86, 198, 93, 205)(88, 200, 95, 207)(90, 202, 94, 206)(92, 204, 96, 208)(97, 209, 101, 213)(98, 210, 105, 217)(99, 211, 103, 215)(100, 212, 107, 219)(102, 214, 109, 221)(104, 216, 111, 223)(106, 218, 110, 222)(108, 220, 112, 224)(225, 337, 227, 339, 232, 344, 241, 353, 250, 362, 258, 370, 266, 378, 274, 386, 282, 394, 290, 402, 298, 410, 306, 418, 314, 426, 322, 434, 330, 442, 335, 447, 327, 439, 319, 431, 311, 423, 303, 415, 295, 407, 287, 399, 279, 391, 271, 383, 263, 375, 255, 367, 247, 359, 237, 349, 245, 357, 235, 347, 244, 356, 253, 365, 261, 373, 269, 381, 277, 389, 285, 397, 293, 405, 301, 413, 309, 421, 317, 429, 325, 437, 333, 445, 332, 444, 324, 436, 316, 428, 308, 420, 300, 412, 292, 404, 284, 396, 276, 388, 268, 380, 260, 372, 252, 364, 243, 355, 234, 346, 228, 340)(226, 338, 229, 341, 236, 348, 246, 358, 254, 366, 262, 374, 270, 382, 278, 390, 286, 398, 294, 406, 302, 414, 310, 422, 318, 430, 326, 438, 334, 446, 331, 443, 323, 435, 315, 427, 307, 419, 299, 411, 291, 403, 283, 395, 275, 387, 267, 379, 259, 371, 251, 363, 242, 354, 233, 345, 240, 352, 231, 343, 239, 351, 249, 361, 257, 369, 265, 377, 273, 385, 281, 393, 289, 401, 297, 409, 305, 417, 313, 425, 321, 433, 329, 441, 336, 448, 328, 440, 320, 432, 312, 424, 304, 416, 296, 408, 288, 400, 280, 392, 272, 384, 264, 376, 256, 368, 248, 360, 238, 350, 230, 342)
	L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 235)(6, 237)(7, 227)(8, 236)(9, 228)(10, 238)(11, 229)(12, 232)(13, 230)(14, 234)(15, 244)(16, 245)(17, 249)(18, 247)(19, 251)(20, 239)(21, 240)(22, 253)(23, 242)(24, 255)(25, 241)(26, 254)(27, 243)(28, 256)(29, 246)(30, 250)(31, 248)(32, 252)(33, 261)(34, 265)(35, 263)(36, 267)(37, 257)(38, 269)(39, 259)(40, 271)(41, 258)(42, 270)(43, 260)(44, 272)(45, 262)(46, 266)(47, 264)(48, 268)(49, 277)(50, 281)(51, 279)(52, 283)(53, 273)(54, 285)(55, 275)(56, 287)(57, 274)(58, 286)(59, 276)(60, 288)(61, 278)(62, 282)(63, 280)(64, 284)(65, 293)(66, 297)(67, 295)(68, 299)(69, 289)(70, 301)(71, 291)(72, 303)(73, 290)(74, 302)(75, 292)(76, 304)(77, 294)(78, 298)(79, 296)(80, 300)(81, 309)(82, 313)(83, 311)(84, 315)(85, 305)(86, 317)(87, 307)(88, 319)(89, 306)(90, 318)(91, 308)(92, 320)(93, 310)(94, 314)(95, 312)(96, 316)(97, 325)(98, 329)(99, 327)(100, 331)(101, 321)(102, 333)(103, 323)(104, 335)(105, 322)(106, 334)(107, 324)(108, 336)(109, 326)(110, 330)(111, 328)(112, 332)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2058
Graph:: bipartite
	v = 58 e = 224 f = 114
	degree seq :: [ 4^56, 112^2 ]

E27.2058 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 56, 56})
Quotient :: dipole
Aut^+ = C7 x (C8 : C2) (small group id <112, 23>)
Aut   = (C2 x D56) : C2 (small group id <224, 103>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y3 * Y1^-1 * Y3 * Y1)^2, Y1^-2 * Y3 * Y1^-25 * Y3 * Y1^-1, Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^-11 ]
Map::
	R = (1, 113, 2, 114, 5, 117, 11, 123, 20, 132, 29, 141, 37, 149, 45, 157, 53, 165, 61, 173, 69, 181, 77, 189, 85, 197, 93, 205, 101, 213, 109, 221, 105, 217, 97, 209, 89, 201, 81, 193, 73, 185, 65, 177, 57, 169, 49, 161, 41, 153, 33, 145, 25, 137, 16, 128, 24, 136, 15, 127, 23, 135, 32, 144, 40, 152, 48, 160, 56, 168, 64, 176, 72, 184, 80, 192, 88, 200, 96, 208, 104, 216, 112, 224, 108, 220, 100, 212, 92, 204, 84, 196, 76, 188, 68, 180, 60, 172, 52, 164, 44, 156, 36, 148, 28, 140, 19, 131, 10, 122, 4, 116)(3, 115, 7, 119, 12, 124, 22, 134, 30, 142, 39, 151, 46, 158, 55, 167, 62, 174, 71, 183, 78, 190, 87, 199, 94, 206, 103, 215, 110, 222, 107, 219, 99, 211, 91, 203, 83, 195, 75, 187, 67, 179, 59, 171, 51, 163, 43, 155, 35, 147, 27, 139, 18, 130, 9, 121, 14, 126, 6, 118, 13, 125, 21, 133, 31, 143, 38, 150, 47, 159, 54, 166, 63, 175, 70, 182, 79, 191, 86, 198, 95, 207, 102, 214, 111, 223, 106, 218, 98, 210, 90, 202, 82, 194, 74, 186, 66, 178, 58, 170, 50, 162, 42, 154, 34, 146, 26, 138, 17, 129, 8, 120)(225, 337)(226, 338)(227, 339)(228, 340)(229, 341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237, 349)(238, 350)(239, 351)(240, 352)(241, 353)(242, 354)(243, 355)(244, 356)(245, 357)(246, 358)(247, 359)(248, 360)(249, 361)(250, 362)(251, 363)(252, 364)(253, 365)(254, 366)(255, 367)(256, 368)(257, 369)(258, 370)(259, 371)(260, 372)(261, 373)(262, 374)(263, 375)(264, 376)(265, 377)(266, 378)(267, 379)(268, 380)(269, 381)(270, 382)(271, 383)(272, 384)(273, 385)(274, 386)(275, 387)(276, 388)(277, 389)(278, 390)(279, 391)(280, 392)(281, 393)(282, 394)(283, 395)(284, 396)(285, 397)(286, 398)(287, 399)(288, 400)(289, 401)(290, 402)(291, 403)(292, 404)(293, 405)(294, 406)(295, 407)(296, 408)(297, 409)(298, 410)(299, 411)(300, 412)(301, 413)(302, 414)(303, 415)(304, 416)(305, 417)(306, 418)(307, 419)(308, 420)(309, 421)(310, 422)(311, 423)(312, 424)(313, 425)(314, 426)(315, 427)(316, 428)(317, 429)(318, 430)(319, 431)(320, 432)(321, 433)(322, 434)(323, 435)(324, 436)(325, 437)(326, 438)(327, 439)(328, 440)(329, 441)(330, 442)(331, 443)(332, 444)(333, 445)(334, 446)(335, 447)(336, 448)
	L = (1, 227)(2, 230)(3, 225)(4, 233)(5, 236)(6, 226)(7, 239)(8, 240)(9, 228)(10, 241)(11, 245)(12, 229)(13, 247)(14, 248)(15, 231)(16, 232)(17, 234)(18, 249)(19, 251)(20, 254)(21, 235)(22, 256)(23, 237)(24, 238)(25, 242)(26, 257)(27, 243)(28, 258)(29, 262)(30, 244)(31, 264)(32, 246)(33, 250)(34, 252)(35, 265)(36, 267)(37, 270)(38, 253)(39, 272)(40, 255)(41, 259)(42, 273)(43, 260)(44, 274)(45, 278)(46, 261)(47, 280)(48, 263)(49, 266)(50, 268)(51, 281)(52, 283)(53, 286)(54, 269)(55, 288)(56, 271)(57, 275)(58, 289)(59, 276)(60, 290)(61, 294)(62, 277)(63, 296)(64, 279)(65, 282)(66, 284)(67, 297)(68, 299)(69, 302)(70, 285)(71, 304)(72, 287)(73, 291)(74, 305)(75, 292)(76, 306)(77, 310)(78, 293)(79, 312)(80, 295)(81, 298)(82, 300)(83, 313)(84, 315)(85, 318)(86, 301)(87, 320)(88, 303)(89, 307)(90, 321)(91, 308)(92, 322)(93, 326)(94, 309)(95, 328)(96, 311)(97, 314)(98, 316)(99, 329)(100, 331)(101, 334)(102, 317)(103, 336)(104, 319)(105, 323)(106, 333)(107, 324)(108, 335)(109, 330)(110, 325)(111, 332)(112, 327)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112, 4, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2057
Graph:: simple bipartite
	v = 114 e = 224 f = 58
	degree seq :: [ 2^112, 112^2 ]

E27.2059 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 38, 57})
Quotient :: regular
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^3 * T2 * T1^11 * T2 * T1^5 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 101, 108, 96, 84, 72, 60, 48, 34, 46, 32, 16, 28, 43, 57, 69, 81, 93, 105, 113, 114, 107, 95, 83, 71, 59, 47, 33, 17, 29, 44, 31, 45, 58, 70, 82, 94, 106, 112, 100, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 24, 41, 56, 66, 79, 92, 102, 111, 99, 87, 75, 63, 51, 37, 21, 30, 14, 6, 13, 27, 40, 55, 68, 78, 91, 104, 110, 98, 86, 74, 62, 50, 36, 20, 9, 19, 26, 12, 25, 42, 54, 67, 80, 90, 103, 109, 97, 85, 73, 61, 49, 35, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 66)(55, 69)(56, 70)(61, 72)(62, 71)(64, 73)(65, 78)(67, 81)(68, 82)(74, 84)(75, 83)(76, 86)(77, 90)(79, 93)(80, 94)(85, 95)(87, 96)(88, 99)(89, 102)(91, 105)(92, 106)(97, 108)(98, 107)(100, 109)(101, 110)(103, 113)(104, 112)(111, 114)
	local type(s) :: { ( 38^57 ) }
Outer automorphisms :: reflexible
Dual of E27.2060
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 57 f = 3
	degree seq :: [ 57^2 ]

E27.2060 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 38, 57})
Quotient :: regular
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2, T2 * T1 * T2 * T1^17 * T2 * T1, T1^-2 * T2 * T1^-5 * T2 * T1^-11 * T2 * T1^-1, T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 32, 47, 61, 73, 85, 97, 109, 103, 91, 79, 67, 55, 41, 54, 40, 53, 39, 52, 66, 78, 90, 102, 114, 108, 96, 84, 72, 60, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 62, 75, 86, 99, 110, 106, 94, 82, 70, 58, 44, 29, 38, 24, 37, 23, 36, 50, 65, 76, 89, 100, 113, 105, 93, 81, 69, 57, 43, 28, 17, 8)(6, 13, 21, 34, 48, 63, 74, 87, 98, 111, 104, 92, 80, 68, 56, 42, 27, 16, 26, 15, 25, 35, 51, 64, 77, 88, 101, 112, 107, 95, 83, 71, 59, 45, 30, 18, 9, 14)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 55)(45, 58)(46, 59)(47, 62)(49, 64)(51, 66)(56, 67)(57, 68)(60, 69)(61, 74)(63, 76)(65, 78)(70, 79)(71, 82)(72, 83)(73, 86)(75, 88)(77, 90)(80, 91)(81, 92)(84, 93)(85, 98)(87, 100)(89, 102)(94, 103)(95, 106)(96, 107)(97, 110)(99, 112)(101, 114)(104, 109)(105, 111)(108, 113)
	local type(s) :: { ( 57^38 ) }
Outer automorphisms :: reflexible
Dual of E27.2059
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 3 e = 57 f = 2
	degree seq :: [ 38^3 ]

E27.2061 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 38, 57})
Quotient :: edge
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^17 * T1 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-5 ]
Map::
	R = (1, 3, 8, 17, 28, 43, 57, 69, 81, 93, 105, 112, 100, 88, 76, 64, 52, 36, 50, 34, 48, 32, 47, 61, 73, 85, 97, 109, 108, 96, 84, 72, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 63, 75, 87, 99, 111, 106, 94, 82, 70, 58, 44, 29, 42, 27, 40, 25, 39, 55, 67, 79, 91, 103, 114, 102, 90, 78, 66, 54, 38, 24, 14, 6)(7, 15, 26, 41, 56, 68, 80, 92, 104, 113, 101, 89, 77, 65, 53, 37, 23, 13, 21, 11, 20, 33, 49, 62, 74, 86, 98, 110, 107, 95, 83, 71, 59, 45, 30, 18, 9, 16)(115, 116)(117, 121)(118, 123)(119, 125)(120, 127)(122, 126)(124, 128)(129, 139)(130, 141)(131, 140)(132, 143)(133, 144)(134, 146)(135, 148)(136, 147)(137, 150)(138, 151)(142, 149)(145, 152)(153, 161)(154, 162)(155, 169)(156, 164)(157, 170)(158, 166)(159, 172)(160, 173)(163, 175)(165, 176)(167, 178)(168, 179)(171, 177)(174, 180)(181, 187)(182, 193)(183, 194)(184, 190)(185, 196)(186, 197)(188, 199)(189, 200)(191, 202)(192, 203)(195, 201)(198, 204)(205, 211)(206, 217)(207, 218)(208, 214)(209, 220)(210, 221)(212, 223)(213, 224)(215, 226)(216, 227)(219, 225)(222, 228)
	L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 114, 114 ), ( 114^38 ) }
Outer automorphisms :: reflexible
Dual of E27.2065
Transitivity :: ET+
Graph:: simple bipartite
	v = 60 e = 114 f = 2
	degree seq :: [ 2^57, 38^3 ]

E27.2062 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 38, 57})
Quotient :: edge
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^4 * T1 * T2^-1, T2^-1 * T1 * T2^-1 * T1^6 * T2^-3 * T1^2 * T2^-2 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1^35, T2^7 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^4 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 47, 61, 73, 85, 97, 109, 105, 95, 84, 70, 54, 34, 21, 42, 60, 39, 20, 13, 28, 50, 64, 76, 88, 100, 112, 104, 91, 81, 71, 59, 38, 18, 6, 17, 36, 57, 41, 30, 52, 66, 78, 90, 102, 114, 108, 94, 80, 67, 55, 43, 33, 15, 5)(2, 7, 19, 40, 26, 49, 65, 74, 87, 101, 110, 107, 96, 82, 68, 53, 37, 32, 45, 23, 9, 4, 12, 29, 48, 63, 77, 86, 99, 113, 103, 93, 83, 72, 56, 35, 16, 14, 31, 46, 24, 11, 27, 51, 62, 75, 89, 98, 111, 106, 92, 79, 69, 58, 44, 22, 8)(115, 116, 120, 130, 148, 167, 181, 193, 205, 217, 223, 215, 204, 189, 178, 162, 139, 154, 171, 160, 174, 159, 147, 158, 173, 186, 198, 210, 222, 225, 214, 200, 187, 179, 166, 141, 127, 118)(117, 123, 131, 122, 135, 149, 169, 182, 195, 206, 219, 227, 216, 201, 190, 176, 161, 143, 155, 133, 153, 145, 129, 146, 152, 172, 184, 197, 208, 221, 226, 212, 199, 191, 180, 163, 142, 125)(119, 128, 132, 151, 168, 183, 194, 207, 218, 224, 211, 203, 192, 177, 164, 140, 124, 138, 150, 137, 156, 136, 157, 170, 185, 196, 209, 220, 228, 213, 202, 188, 175, 165, 144, 126, 134, 121)
	L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 4^38 ), ( 4^57 ) }
Outer automorphisms :: reflexible
Dual of E27.2066
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 114 f = 57
	degree seq :: [ 38^3, 57^2 ]

E27.2063 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 38, 57})
Quotient :: edge
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^3 * T2 * T1^11 * T2 * T1^5 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 66)(55, 69)(56, 70)(61, 72)(62, 71)(64, 73)(65, 78)(67, 81)(68, 82)(74, 84)(75, 83)(76, 86)(77, 90)(79, 93)(80, 94)(85, 95)(87, 96)(88, 99)(89, 102)(91, 105)(92, 106)(97, 108)(98, 107)(100, 109)(101, 110)(103, 113)(104, 112)(111, 114)(115, 116, 119, 125, 137, 153, 167, 179, 191, 203, 215, 222, 210, 198, 186, 174, 162, 148, 160, 146, 130, 142, 157, 171, 183, 195, 207, 219, 227, 228, 221, 209, 197, 185, 173, 161, 147, 131, 143, 158, 145, 159, 172, 184, 196, 208, 220, 226, 214, 202, 190, 178, 166, 152, 136, 124, 118)(117, 121, 129, 138, 155, 170, 180, 193, 206, 216, 225, 213, 201, 189, 177, 165, 151, 135, 144, 128, 120, 127, 141, 154, 169, 182, 192, 205, 218, 224, 212, 200, 188, 176, 164, 150, 134, 123, 133, 140, 126, 139, 156, 168, 181, 194, 204, 217, 223, 211, 199, 187, 175, 163, 149, 132, 122)
	L = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)
	local type(s) :: { ( 76, 76 ), ( 76^57 ) }
Outer automorphisms :: reflexible
Dual of E27.2064
Transitivity :: ET+
Graph:: simple bipartite
	v = 59 e = 114 f = 3
	degree seq :: [ 2^57, 57^2 ]

E27.2064 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 38, 57})
Quotient :: loop
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^17 * T1 * T2 * T1 * T2 * T1, T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-1 * T1 * T2^-3 * T1 * T2^-5 ]
Map::
	R = (1, 115, 3, 117, 8, 122, 17, 131, 28, 142, 43, 157, 57, 171, 69, 183, 81, 195, 93, 207, 105, 219, 112, 226, 100, 214, 88, 202, 76, 190, 64, 178, 52, 166, 36, 150, 50, 164, 34, 148, 48, 162, 32, 146, 47, 161, 61, 175, 73, 187, 85, 199, 97, 211, 109, 223, 108, 222, 96, 210, 84, 198, 72, 186, 60, 174, 46, 160, 31, 145, 19, 133, 10, 124, 4, 118)(2, 116, 5, 119, 12, 126, 22, 136, 35, 149, 51, 165, 63, 177, 75, 189, 87, 201, 99, 213, 111, 225, 106, 220, 94, 208, 82, 196, 70, 184, 58, 172, 44, 158, 29, 143, 42, 156, 27, 141, 40, 154, 25, 139, 39, 153, 55, 169, 67, 181, 79, 193, 91, 205, 103, 217, 114, 228, 102, 216, 90, 204, 78, 192, 66, 180, 54, 168, 38, 152, 24, 138, 14, 128, 6, 120)(7, 121, 15, 129, 26, 140, 41, 155, 56, 170, 68, 182, 80, 194, 92, 206, 104, 218, 113, 227, 101, 215, 89, 203, 77, 191, 65, 179, 53, 167, 37, 151, 23, 137, 13, 127, 21, 135, 11, 125, 20, 134, 33, 147, 49, 163, 62, 176, 74, 188, 86, 200, 98, 212, 110, 224, 107, 221, 95, 209, 83, 197, 71, 185, 59, 173, 45, 159, 30, 144, 18, 132, 9, 123, 16, 130)
	L = (1, 116)(2, 115)(3, 121)(4, 123)(5, 125)(6, 127)(7, 117)(8, 126)(9, 118)(10, 128)(11, 119)(12, 122)(13, 120)(14, 124)(15, 139)(16, 141)(17, 140)(18, 143)(19, 144)(20, 146)(21, 148)(22, 147)(23, 150)(24, 151)(25, 129)(26, 131)(27, 130)(28, 149)(29, 132)(30, 133)(31, 152)(32, 134)(33, 136)(34, 135)(35, 142)(36, 137)(37, 138)(38, 145)(39, 161)(40, 162)(41, 169)(42, 164)(43, 170)(44, 166)(45, 172)(46, 173)(47, 153)(48, 154)(49, 175)(50, 156)(51, 176)(52, 158)(53, 178)(54, 179)(55, 155)(56, 157)(57, 177)(58, 159)(59, 160)(60, 180)(61, 163)(62, 165)(63, 171)(64, 167)(65, 168)(66, 174)(67, 187)(68, 193)(69, 194)(70, 190)(71, 196)(72, 197)(73, 181)(74, 199)(75, 200)(76, 184)(77, 202)(78, 203)(79, 182)(80, 183)(81, 201)(82, 185)(83, 186)(84, 204)(85, 188)(86, 189)(87, 195)(88, 191)(89, 192)(90, 198)(91, 211)(92, 217)(93, 218)(94, 214)(95, 220)(96, 221)(97, 205)(98, 223)(99, 224)(100, 208)(101, 226)(102, 227)(103, 206)(104, 207)(105, 225)(106, 209)(107, 210)(108, 228)(109, 212)(110, 213)(111, 219)(112, 215)(113, 216)(114, 222)
	local type(s) :: { ( 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.2063
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 114 f = 59
	degree seq :: [ 76^3 ]

E27.2065 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 38, 57})
Quotient :: loop
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-1 * T1^-3, T2^-1 * T1 * T2^4 * T1 * T2^-1, T2^-1 * T1 * T2^-1 * T1^6 * T2^-3 * T1^2 * T2^-2 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1^35, T2^7 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^2 * T1^-2 * T2^4 ]
Map::
	R = (1, 115, 3, 117, 10, 124, 25, 139, 47, 161, 61, 175, 73, 187, 85, 199, 97, 211, 109, 223, 105, 219, 95, 209, 84, 198, 70, 184, 54, 168, 34, 148, 21, 135, 42, 156, 60, 174, 39, 153, 20, 134, 13, 127, 28, 142, 50, 164, 64, 178, 76, 190, 88, 202, 100, 214, 112, 226, 104, 218, 91, 205, 81, 195, 71, 185, 59, 173, 38, 152, 18, 132, 6, 120, 17, 131, 36, 150, 57, 171, 41, 155, 30, 144, 52, 166, 66, 180, 78, 192, 90, 204, 102, 216, 114, 228, 108, 222, 94, 208, 80, 194, 67, 181, 55, 169, 43, 157, 33, 147, 15, 129, 5, 119)(2, 116, 7, 121, 19, 133, 40, 154, 26, 140, 49, 163, 65, 179, 74, 188, 87, 201, 101, 215, 110, 224, 107, 221, 96, 210, 82, 196, 68, 182, 53, 167, 37, 151, 32, 146, 45, 159, 23, 137, 9, 123, 4, 118, 12, 126, 29, 143, 48, 162, 63, 177, 77, 191, 86, 200, 99, 213, 113, 227, 103, 217, 93, 207, 83, 197, 72, 186, 56, 170, 35, 149, 16, 130, 14, 128, 31, 145, 46, 160, 24, 138, 11, 125, 27, 141, 51, 165, 62, 176, 75, 189, 89, 203, 98, 212, 111, 225, 106, 220, 92, 206, 79, 193, 69, 183, 58, 172, 44, 158, 22, 136, 8, 122)
	L = (1, 116)(2, 120)(3, 123)(4, 115)(5, 128)(6, 130)(7, 119)(8, 135)(9, 131)(10, 138)(11, 117)(12, 134)(13, 118)(14, 132)(15, 146)(16, 148)(17, 122)(18, 151)(19, 153)(20, 121)(21, 149)(22, 157)(23, 156)(24, 150)(25, 154)(26, 124)(27, 127)(28, 125)(29, 155)(30, 126)(31, 129)(32, 152)(33, 158)(34, 167)(35, 169)(36, 137)(37, 168)(38, 172)(39, 145)(40, 171)(41, 133)(42, 136)(43, 170)(44, 173)(45, 147)(46, 174)(47, 143)(48, 139)(49, 142)(50, 140)(51, 144)(52, 141)(53, 181)(54, 183)(55, 182)(56, 185)(57, 160)(58, 184)(59, 186)(60, 159)(61, 165)(62, 161)(63, 164)(64, 162)(65, 166)(66, 163)(67, 193)(68, 195)(69, 194)(70, 197)(71, 196)(72, 198)(73, 179)(74, 175)(75, 178)(76, 176)(77, 180)(78, 177)(79, 205)(80, 207)(81, 206)(82, 209)(83, 208)(84, 210)(85, 191)(86, 187)(87, 190)(88, 188)(89, 192)(90, 189)(91, 217)(92, 219)(93, 218)(94, 221)(95, 220)(96, 222)(97, 203)(98, 199)(99, 202)(100, 200)(101, 204)(102, 201)(103, 223)(104, 224)(105, 227)(106, 228)(107, 226)(108, 225)(109, 215)(110, 211)(111, 214)(112, 212)(113, 216)(114, 213)
	local type(s) :: { ( 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38, 2, 38 ) }
Outer automorphisms :: reflexible
Dual of E27.2061
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 114 f = 60
	degree seq :: [ 114^2 ]

E27.2066 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 38, 57})
Quotient :: loop
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^3 * T2 * T1^-3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^3 * T2 * T1^11 * T2 * T1^5 ]
Map:: polytopal non-degenerate
	R = (1, 115, 3, 117)(2, 116, 6, 120)(4, 118, 9, 123)(5, 119, 12, 126)(7, 121, 16, 130)(8, 122, 17, 131)(10, 124, 21, 135)(11, 125, 24, 138)(13, 127, 28, 142)(14, 128, 29, 143)(15, 129, 31, 145)(18, 132, 34, 148)(19, 133, 32, 146)(20, 134, 33, 147)(22, 136, 35, 149)(23, 137, 40, 154)(25, 139, 43, 157)(26, 140, 44, 158)(27, 141, 45, 159)(30, 144, 46, 160)(36, 150, 48, 162)(37, 151, 47, 161)(38, 152, 50, 164)(39, 153, 54, 168)(41, 155, 57, 171)(42, 156, 58, 172)(49, 163, 59, 173)(51, 165, 60, 174)(52, 166, 63, 177)(53, 167, 66, 180)(55, 169, 69, 183)(56, 170, 70, 184)(61, 175, 72, 186)(62, 176, 71, 185)(64, 178, 73, 187)(65, 179, 78, 192)(67, 181, 81, 195)(68, 182, 82, 196)(74, 188, 84, 198)(75, 189, 83, 197)(76, 190, 86, 200)(77, 191, 90, 204)(79, 193, 93, 207)(80, 194, 94, 208)(85, 199, 95, 209)(87, 201, 96, 210)(88, 202, 99, 213)(89, 203, 102, 216)(91, 205, 105, 219)(92, 206, 106, 220)(97, 211, 108, 222)(98, 212, 107, 221)(100, 214, 109, 223)(101, 215, 110, 224)(103, 217, 113, 227)(104, 218, 112, 226)(111, 225, 114, 228)
	L = (1, 116)(2, 119)(3, 121)(4, 115)(5, 125)(6, 127)(7, 129)(8, 117)(9, 133)(10, 118)(11, 137)(12, 139)(13, 141)(14, 120)(15, 138)(16, 142)(17, 143)(18, 122)(19, 140)(20, 123)(21, 144)(22, 124)(23, 153)(24, 155)(25, 156)(26, 126)(27, 154)(28, 157)(29, 158)(30, 128)(31, 159)(32, 130)(33, 131)(34, 160)(35, 132)(36, 134)(37, 135)(38, 136)(39, 167)(40, 169)(41, 170)(42, 168)(43, 171)(44, 145)(45, 172)(46, 146)(47, 147)(48, 148)(49, 149)(50, 150)(51, 151)(52, 152)(53, 179)(54, 181)(55, 182)(56, 180)(57, 183)(58, 184)(59, 161)(60, 162)(61, 163)(62, 164)(63, 165)(64, 166)(65, 191)(66, 193)(67, 194)(68, 192)(69, 195)(70, 196)(71, 173)(72, 174)(73, 175)(74, 176)(75, 177)(76, 178)(77, 203)(78, 205)(79, 206)(80, 204)(81, 207)(82, 208)(83, 185)(84, 186)(85, 187)(86, 188)(87, 189)(88, 190)(89, 215)(90, 217)(91, 218)(92, 216)(93, 219)(94, 220)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 222)(102, 225)(103, 223)(104, 224)(105, 227)(106, 226)(107, 209)(108, 210)(109, 211)(110, 212)(111, 213)(112, 214)(113, 228)(114, 221)
	local type(s) :: { ( 38, 57, 38, 57 ) }
Outer automorphisms :: reflexible
Dual of E27.2062
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 57 e = 114 f = 5
	degree seq :: [ 4^57 ]

E27.2067 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^3 * Y1 * Y2^15 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^57 ]
Map::
	R = (1, 115, 2, 116)(3, 117, 7, 121)(4, 118, 9, 123)(5, 119, 11, 125)(6, 120, 13, 127)(8, 122, 12, 126)(10, 124, 14, 128)(15, 129, 25, 139)(16, 130, 27, 141)(17, 131, 26, 140)(18, 132, 29, 143)(19, 133, 30, 144)(20, 134, 32, 146)(21, 135, 34, 148)(22, 136, 33, 147)(23, 137, 36, 150)(24, 138, 37, 151)(28, 142, 35, 149)(31, 145, 38, 152)(39, 153, 47, 161)(40, 154, 48, 162)(41, 155, 55, 169)(42, 156, 50, 164)(43, 157, 56, 170)(44, 158, 52, 166)(45, 159, 58, 172)(46, 160, 59, 173)(49, 163, 61, 175)(51, 165, 62, 176)(53, 167, 64, 178)(54, 168, 65, 179)(57, 171, 63, 177)(60, 174, 66, 180)(67, 181, 73, 187)(68, 182, 79, 193)(69, 183, 80, 194)(70, 184, 76, 190)(71, 185, 82, 196)(72, 186, 83, 197)(74, 188, 85, 199)(75, 189, 86, 200)(77, 191, 88, 202)(78, 192, 89, 203)(81, 195, 87, 201)(84, 198, 90, 204)(91, 205, 97, 211)(92, 206, 103, 217)(93, 207, 104, 218)(94, 208, 100, 214)(95, 209, 106, 220)(96, 210, 107, 221)(98, 212, 109, 223)(99, 213, 110, 224)(101, 215, 112, 226)(102, 216, 113, 227)(105, 219, 111, 225)(108, 222, 114, 228)(229, 343, 231, 345, 236, 350, 245, 359, 256, 370, 271, 385, 285, 399, 297, 411, 309, 423, 321, 435, 333, 447, 340, 454, 328, 442, 316, 430, 304, 418, 292, 406, 280, 394, 264, 378, 278, 392, 262, 376, 276, 390, 260, 374, 275, 389, 289, 403, 301, 415, 313, 427, 325, 439, 337, 451, 336, 450, 324, 438, 312, 426, 300, 414, 288, 402, 274, 388, 259, 373, 247, 361, 238, 352, 232, 346)(230, 344, 233, 347, 240, 354, 250, 364, 263, 377, 279, 393, 291, 405, 303, 417, 315, 429, 327, 441, 339, 453, 334, 448, 322, 436, 310, 424, 298, 412, 286, 400, 272, 386, 257, 371, 270, 384, 255, 369, 268, 382, 253, 367, 267, 381, 283, 397, 295, 409, 307, 421, 319, 433, 331, 445, 342, 456, 330, 444, 318, 432, 306, 420, 294, 408, 282, 396, 266, 380, 252, 366, 242, 356, 234, 348)(235, 349, 243, 357, 254, 368, 269, 383, 284, 398, 296, 410, 308, 422, 320, 434, 332, 446, 341, 455, 329, 443, 317, 431, 305, 419, 293, 407, 281, 395, 265, 379, 251, 365, 241, 355, 249, 363, 239, 353, 248, 362, 261, 375, 277, 391, 290, 404, 302, 416, 314, 428, 326, 440, 338, 452, 335, 449, 323, 437, 311, 425, 299, 413, 287, 401, 273, 387, 258, 372, 246, 360, 237, 351, 244, 358)
	L = (1, 230)(2, 229)(3, 235)(4, 237)(5, 239)(6, 241)(7, 231)(8, 240)(9, 232)(10, 242)(11, 233)(12, 236)(13, 234)(14, 238)(15, 253)(16, 255)(17, 254)(18, 257)(19, 258)(20, 260)(21, 262)(22, 261)(23, 264)(24, 265)(25, 243)(26, 245)(27, 244)(28, 263)(29, 246)(30, 247)(31, 266)(32, 248)(33, 250)(34, 249)(35, 256)(36, 251)(37, 252)(38, 259)(39, 275)(40, 276)(41, 283)(42, 278)(43, 284)(44, 280)(45, 286)(46, 287)(47, 267)(48, 268)(49, 289)(50, 270)(51, 290)(52, 272)(53, 292)(54, 293)(55, 269)(56, 271)(57, 291)(58, 273)(59, 274)(60, 294)(61, 277)(62, 279)(63, 285)(64, 281)(65, 282)(66, 288)(67, 301)(68, 307)(69, 308)(70, 304)(71, 310)(72, 311)(73, 295)(74, 313)(75, 314)(76, 298)(77, 316)(78, 317)(79, 296)(80, 297)(81, 315)(82, 299)(83, 300)(84, 318)(85, 302)(86, 303)(87, 309)(88, 305)(89, 306)(90, 312)(91, 325)(92, 331)(93, 332)(94, 328)(95, 334)(96, 335)(97, 319)(98, 337)(99, 338)(100, 322)(101, 340)(102, 341)(103, 320)(104, 321)(105, 339)(106, 323)(107, 324)(108, 342)(109, 326)(110, 327)(111, 333)(112, 329)(113, 330)(114, 336)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 2, 114, 2, 114 ), ( 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114, 2, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.2070
Graph:: bipartite
	v = 60 e = 228 f = 116
	degree seq :: [ 4^57, 76^3 ]

E27.2068 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y1 * Y2)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y2^-2 * Y1 * Y2^3 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2^3, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^23 * Y1^-1 * Y2 * Y1 * Y2^-1 ]
Map::
	R = (1, 115, 2, 116, 6, 120, 16, 130, 34, 148, 53, 167, 67, 181, 79, 193, 91, 205, 103, 217, 109, 223, 101, 215, 90, 204, 75, 189, 64, 178, 48, 162, 25, 139, 40, 154, 57, 171, 46, 160, 60, 174, 45, 159, 33, 147, 44, 158, 59, 173, 72, 186, 84, 198, 96, 210, 108, 222, 111, 225, 100, 214, 86, 200, 73, 187, 65, 179, 52, 166, 27, 141, 13, 127, 4, 118)(3, 117, 9, 123, 17, 131, 8, 122, 21, 135, 35, 149, 55, 169, 68, 182, 81, 195, 92, 206, 105, 219, 113, 227, 102, 216, 87, 201, 76, 190, 62, 176, 47, 161, 29, 143, 41, 155, 19, 133, 39, 153, 31, 145, 15, 129, 32, 146, 38, 152, 58, 172, 70, 184, 83, 197, 94, 208, 107, 221, 112, 226, 98, 212, 85, 199, 77, 191, 66, 180, 49, 163, 28, 142, 11, 125)(5, 119, 14, 128, 18, 132, 37, 151, 54, 168, 69, 183, 80, 194, 93, 207, 104, 218, 110, 224, 97, 211, 89, 203, 78, 192, 63, 177, 50, 164, 26, 140, 10, 124, 24, 138, 36, 150, 23, 137, 42, 156, 22, 136, 43, 157, 56, 170, 71, 185, 82, 196, 95, 209, 106, 220, 114, 228, 99, 213, 88, 202, 74, 188, 61, 175, 51, 165, 30, 144, 12, 126, 20, 134, 7, 121)(229, 343, 231, 345, 238, 352, 253, 367, 275, 389, 289, 403, 301, 415, 313, 427, 325, 439, 337, 451, 333, 447, 323, 437, 312, 426, 298, 412, 282, 396, 262, 376, 249, 363, 270, 384, 288, 402, 267, 381, 248, 362, 241, 355, 256, 370, 278, 392, 292, 406, 304, 418, 316, 430, 328, 442, 340, 454, 332, 446, 319, 433, 309, 423, 299, 413, 287, 401, 266, 380, 246, 360, 234, 348, 245, 359, 264, 378, 285, 399, 269, 383, 258, 372, 280, 394, 294, 408, 306, 420, 318, 432, 330, 444, 342, 456, 336, 450, 322, 436, 308, 422, 295, 409, 283, 397, 271, 385, 261, 375, 243, 357, 233, 347)(230, 344, 235, 349, 247, 361, 268, 382, 254, 368, 277, 391, 293, 407, 302, 416, 315, 429, 329, 443, 338, 452, 335, 449, 324, 438, 310, 424, 296, 410, 281, 395, 265, 379, 260, 374, 273, 387, 251, 365, 237, 351, 232, 346, 240, 354, 257, 371, 276, 390, 291, 405, 305, 419, 314, 428, 327, 441, 341, 455, 331, 445, 321, 435, 311, 425, 300, 414, 284, 398, 263, 377, 244, 358, 242, 356, 259, 373, 274, 388, 252, 366, 239, 353, 255, 369, 279, 393, 290, 404, 303, 417, 317, 431, 326, 440, 339, 453, 334, 448, 320, 434, 307, 421, 297, 411, 286, 400, 272, 386, 250, 364, 236, 350)
	L = (1, 231)(2, 235)(3, 238)(4, 240)(5, 229)(6, 245)(7, 247)(8, 230)(9, 232)(10, 253)(11, 255)(12, 257)(13, 256)(14, 259)(15, 233)(16, 242)(17, 264)(18, 234)(19, 268)(20, 241)(21, 270)(22, 236)(23, 237)(24, 239)(25, 275)(26, 277)(27, 279)(28, 278)(29, 276)(30, 280)(31, 274)(32, 273)(33, 243)(34, 249)(35, 244)(36, 285)(37, 260)(38, 246)(39, 248)(40, 254)(41, 258)(42, 288)(43, 261)(44, 250)(45, 251)(46, 252)(47, 289)(48, 291)(49, 293)(50, 292)(51, 290)(52, 294)(53, 265)(54, 262)(55, 271)(56, 263)(57, 269)(58, 272)(59, 266)(60, 267)(61, 301)(62, 303)(63, 305)(64, 304)(65, 302)(66, 306)(67, 283)(68, 281)(69, 286)(70, 282)(71, 287)(72, 284)(73, 313)(74, 315)(75, 317)(76, 316)(77, 314)(78, 318)(79, 297)(80, 295)(81, 299)(82, 296)(83, 300)(84, 298)(85, 325)(86, 327)(87, 329)(88, 328)(89, 326)(90, 330)(91, 309)(92, 307)(93, 311)(94, 308)(95, 312)(96, 310)(97, 337)(98, 339)(99, 341)(100, 340)(101, 338)(102, 342)(103, 321)(104, 319)(105, 323)(106, 320)(107, 324)(108, 322)(109, 333)(110, 335)(111, 334)(112, 332)(113, 331)(114, 336)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2069
Graph:: bipartite
	v = 5 e = 228 f = 171
	degree seq :: [ 76^3, 114^2 ]

E27.2069 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-3 * Y2, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3, Y3^-3 * Y2 * Y3^-14 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^57 ]
Map:: polytopal
	R = (1, 115)(2, 116)(3, 117)(4, 118)(5, 119)(6, 120)(7, 121)(8, 122)(9, 123)(10, 124)(11, 125)(12, 126)(13, 127)(14, 128)(15, 129)(16, 130)(17, 131)(18, 132)(19, 133)(20, 134)(21, 135)(22, 136)(23, 137)(24, 138)(25, 139)(26, 140)(27, 141)(28, 142)(29, 143)(30, 144)(31, 145)(32, 146)(33, 147)(34, 148)(35, 149)(36, 150)(37, 151)(38, 152)(39, 153)(40, 154)(41, 155)(42, 156)(43, 157)(44, 158)(45, 159)(46, 160)(47, 161)(48, 162)(49, 163)(50, 164)(51, 165)(52, 166)(53, 167)(54, 168)(55, 169)(56, 170)(57, 171)(58, 172)(59, 173)(60, 174)(61, 175)(62, 176)(63, 177)(64, 178)(65, 179)(66, 180)(67, 181)(68, 182)(69, 183)(70, 184)(71, 185)(72, 186)(73, 187)(74, 188)(75, 189)(76, 190)(77, 191)(78, 192)(79, 193)(80, 194)(81, 195)(82, 196)(83, 197)(84, 198)(85, 199)(86, 200)(87, 201)(88, 202)(89, 203)(90, 204)(91, 205)(92, 206)(93, 207)(94, 208)(95, 209)(96, 210)(97, 211)(98, 212)(99, 213)(100, 214)(101, 215)(102, 216)(103, 217)(104, 218)(105, 219)(106, 220)(107, 221)(108, 222)(109, 223)(110, 224)(111, 225)(112, 226)(113, 227)(114, 228)(229, 343, 230, 344)(231, 345, 235, 349)(232, 346, 237, 351)(233, 347, 239, 353)(234, 348, 241, 355)(236, 350, 245, 359)(238, 352, 249, 363)(240, 354, 253, 367)(242, 356, 257, 371)(243, 357, 251, 365)(244, 358, 255, 369)(246, 360, 254, 368)(247, 361, 252, 366)(248, 362, 256, 370)(250, 364, 258, 372)(259, 373, 269, 383)(260, 374, 268, 382)(261, 375, 267, 381)(262, 376, 270, 384)(263, 377, 275, 389)(264, 378, 273, 387)(265, 379, 272, 386)(266, 380, 278, 392)(271, 385, 281, 395)(274, 388, 284, 398)(276, 390, 282, 396)(277, 391, 288, 402)(279, 393, 285, 399)(280, 394, 291, 405)(283, 397, 294, 408)(286, 400, 297, 411)(287, 401, 293, 407)(289, 403, 295, 409)(290, 404, 296, 410)(292, 406, 298, 412)(299, 413, 306, 420)(300, 414, 305, 419)(301, 415, 311, 425)(302, 416, 309, 423)(303, 417, 308, 422)(304, 418, 314, 428)(307, 421, 317, 431)(310, 424, 320, 434)(312, 426, 318, 432)(313, 427, 324, 438)(315, 429, 321, 435)(316, 430, 327, 441)(319, 433, 330, 444)(322, 436, 333, 447)(323, 437, 329, 443)(325, 439, 331, 445)(326, 440, 332, 446)(328, 442, 334, 448)(335, 449, 340, 454)(336, 450, 341, 455)(337, 451, 338, 452)(339, 453, 342, 456)
	L = (1, 231)(2, 233)(3, 236)(4, 229)(5, 240)(6, 230)(7, 243)(8, 246)(9, 247)(10, 232)(11, 251)(12, 254)(13, 255)(14, 234)(15, 259)(16, 235)(17, 261)(18, 263)(19, 262)(20, 237)(21, 260)(22, 238)(23, 267)(24, 239)(25, 269)(26, 271)(27, 270)(28, 241)(29, 268)(30, 242)(31, 275)(32, 244)(33, 276)(34, 245)(35, 277)(36, 248)(37, 249)(38, 250)(39, 281)(40, 252)(41, 282)(42, 253)(43, 283)(44, 256)(45, 257)(46, 258)(47, 287)(48, 288)(49, 289)(50, 264)(51, 265)(52, 266)(53, 293)(54, 294)(55, 295)(56, 272)(57, 273)(58, 274)(59, 299)(60, 300)(61, 301)(62, 278)(63, 279)(64, 280)(65, 305)(66, 306)(67, 307)(68, 284)(69, 285)(70, 286)(71, 311)(72, 312)(73, 313)(74, 290)(75, 291)(76, 292)(77, 317)(78, 318)(79, 319)(80, 296)(81, 297)(82, 298)(83, 323)(84, 324)(85, 325)(86, 302)(87, 303)(88, 304)(89, 329)(90, 330)(91, 331)(92, 308)(93, 309)(94, 310)(95, 335)(96, 336)(97, 337)(98, 314)(99, 315)(100, 316)(101, 341)(102, 340)(103, 339)(104, 320)(105, 321)(106, 322)(107, 338)(108, 334)(109, 333)(110, 326)(111, 327)(112, 328)(113, 342)(114, 332)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 76, 114 ), ( 76, 114, 76, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.2068
Graph:: simple bipartite
	v = 171 e = 228 f = 5
	degree seq :: [ 2^114, 4^57 ]

E27.2070 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1^3 * Y3 * Y1^-3, Y1^11 * Y3 * Y1^5 * Y3 * Y1^3 ]
Map::
	R = (1, 115, 2, 116, 5, 119, 11, 125, 23, 137, 39, 153, 53, 167, 65, 179, 77, 191, 89, 203, 101, 215, 108, 222, 96, 210, 84, 198, 72, 186, 60, 174, 48, 162, 34, 148, 46, 160, 32, 146, 16, 130, 28, 142, 43, 157, 57, 171, 69, 183, 81, 195, 93, 207, 105, 219, 113, 227, 114, 228, 107, 221, 95, 209, 83, 197, 71, 185, 59, 173, 47, 161, 33, 147, 17, 131, 29, 143, 44, 158, 31, 145, 45, 159, 58, 172, 70, 184, 82, 196, 94, 208, 106, 220, 112, 226, 100, 214, 88, 202, 76, 190, 64, 178, 52, 166, 38, 152, 22, 136, 10, 124, 4, 118)(3, 117, 7, 121, 15, 129, 24, 138, 41, 155, 56, 170, 66, 180, 79, 193, 92, 206, 102, 216, 111, 225, 99, 213, 87, 201, 75, 189, 63, 177, 51, 165, 37, 151, 21, 135, 30, 144, 14, 128, 6, 120, 13, 127, 27, 141, 40, 154, 55, 169, 68, 182, 78, 192, 91, 205, 104, 218, 110, 224, 98, 212, 86, 200, 74, 188, 62, 176, 50, 164, 36, 150, 20, 134, 9, 123, 19, 133, 26, 140, 12, 126, 25, 139, 42, 156, 54, 168, 67, 181, 80, 194, 90, 204, 103, 217, 109, 223, 97, 211, 85, 199, 73, 187, 61, 175, 49, 163, 35, 149, 18, 132, 8, 122)(229, 343)(230, 344)(231, 345)(232, 346)(233, 347)(234, 348)(235, 349)(236, 350)(237, 351)(238, 352)(239, 353)(240, 354)(241, 355)(242, 356)(243, 357)(244, 358)(245, 359)(246, 360)(247, 361)(248, 362)(249, 363)(250, 364)(251, 365)(252, 366)(253, 367)(254, 368)(255, 369)(256, 370)(257, 371)(258, 372)(259, 373)(260, 374)(261, 375)(262, 376)(263, 377)(264, 378)(265, 379)(266, 380)(267, 381)(268, 382)(269, 383)(270, 384)(271, 385)(272, 386)(273, 387)(274, 388)(275, 389)(276, 390)(277, 391)(278, 392)(279, 393)(280, 394)(281, 395)(282, 396)(283, 397)(284, 398)(285, 399)(286, 400)(287, 401)(288, 402)(289, 403)(290, 404)(291, 405)(292, 406)(293, 407)(294, 408)(295, 409)(296, 410)(297, 411)(298, 412)(299, 413)(300, 414)(301, 415)(302, 416)(303, 417)(304, 418)(305, 419)(306, 420)(307, 421)(308, 422)(309, 423)(310, 424)(311, 425)(312, 426)(313, 427)(314, 428)(315, 429)(316, 430)(317, 431)(318, 432)(319, 433)(320, 434)(321, 435)(322, 436)(323, 437)(324, 438)(325, 439)(326, 440)(327, 441)(328, 442)(329, 443)(330, 444)(331, 445)(332, 446)(333, 447)(334, 448)(335, 449)(336, 450)(337, 451)(338, 452)(339, 453)(340, 454)(341, 455)(342, 456)
	L = (1, 231)(2, 234)(3, 229)(4, 237)(5, 240)(6, 230)(7, 244)(8, 245)(9, 232)(10, 249)(11, 252)(12, 233)(13, 256)(14, 257)(15, 259)(16, 235)(17, 236)(18, 262)(19, 260)(20, 261)(21, 238)(22, 263)(23, 268)(24, 239)(25, 271)(26, 272)(27, 273)(28, 241)(29, 242)(30, 274)(31, 243)(32, 247)(33, 248)(34, 246)(35, 250)(36, 276)(37, 275)(38, 278)(39, 282)(40, 251)(41, 285)(42, 286)(43, 253)(44, 254)(45, 255)(46, 258)(47, 265)(48, 264)(49, 287)(50, 266)(51, 288)(52, 291)(53, 294)(54, 267)(55, 297)(56, 298)(57, 269)(58, 270)(59, 277)(60, 279)(61, 300)(62, 299)(63, 280)(64, 301)(65, 306)(66, 281)(67, 309)(68, 310)(69, 283)(70, 284)(71, 290)(72, 289)(73, 292)(74, 312)(75, 311)(76, 314)(77, 318)(78, 293)(79, 321)(80, 322)(81, 295)(82, 296)(83, 303)(84, 302)(85, 323)(86, 304)(87, 324)(88, 327)(89, 330)(90, 305)(91, 333)(92, 334)(93, 307)(94, 308)(95, 313)(96, 315)(97, 336)(98, 335)(99, 316)(100, 337)(101, 338)(102, 317)(103, 341)(104, 340)(105, 319)(106, 320)(107, 326)(108, 325)(109, 328)(110, 329)(111, 342)(112, 332)(113, 331)(114, 339)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 4, 76 ), ( 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76, 4, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.2067
Graph:: simple bipartite
	v = 116 e = 228 f = 60
	degree seq :: [ 2^114, 114^2 ]

E27.2071 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-3 * Y1 * Y2^3 * Y1, Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, (Y2^-1 * R * Y2^-2)^2, Y2^15 * Y1 * Y2^2 * Y1 * Y2^2, (Y3 * Y2^-1)^38 ]
Map::
	R = (1, 115, 2, 116)(3, 117, 7, 121)(4, 118, 9, 123)(5, 119, 11, 125)(6, 120, 13, 127)(8, 122, 17, 131)(10, 124, 21, 135)(12, 126, 25, 139)(14, 128, 29, 143)(15, 129, 23, 137)(16, 130, 27, 141)(18, 132, 26, 140)(19, 133, 24, 138)(20, 134, 28, 142)(22, 136, 30, 144)(31, 145, 41, 155)(32, 146, 40, 154)(33, 147, 39, 153)(34, 148, 42, 156)(35, 149, 47, 161)(36, 150, 45, 159)(37, 151, 44, 158)(38, 152, 50, 164)(43, 157, 53, 167)(46, 160, 56, 170)(48, 162, 54, 168)(49, 163, 60, 174)(51, 165, 57, 171)(52, 166, 63, 177)(55, 169, 66, 180)(58, 172, 69, 183)(59, 173, 65, 179)(61, 175, 67, 181)(62, 176, 68, 182)(64, 178, 70, 184)(71, 185, 78, 192)(72, 186, 77, 191)(73, 187, 83, 197)(74, 188, 81, 195)(75, 189, 80, 194)(76, 190, 86, 200)(79, 193, 89, 203)(82, 196, 92, 206)(84, 198, 90, 204)(85, 199, 96, 210)(87, 201, 93, 207)(88, 202, 99, 213)(91, 205, 102, 216)(94, 208, 105, 219)(95, 209, 101, 215)(97, 211, 103, 217)(98, 212, 104, 218)(100, 214, 106, 220)(107, 221, 112, 226)(108, 222, 113, 227)(109, 223, 110, 224)(111, 225, 114, 228)(229, 343, 231, 345, 236, 350, 246, 360, 263, 377, 277, 391, 289, 403, 301, 415, 313, 427, 325, 439, 337, 451, 333, 447, 321, 435, 309, 423, 297, 411, 285, 399, 273, 387, 257, 371, 268, 382, 252, 366, 239, 353, 251, 365, 267, 381, 281, 395, 293, 407, 305, 419, 317, 431, 329, 443, 341, 455, 342, 456, 332, 446, 320, 434, 308, 422, 296, 410, 284, 398, 272, 386, 256, 370, 241, 355, 255, 369, 270, 384, 253, 367, 269, 383, 282, 396, 294, 408, 306, 420, 318, 432, 330, 444, 340, 454, 328, 442, 316, 430, 304, 418, 292, 406, 280, 394, 266, 380, 250, 364, 238, 352, 232, 346)(230, 344, 233, 347, 240, 354, 254, 368, 271, 385, 283, 397, 295, 409, 307, 421, 319, 433, 331, 445, 339, 453, 327, 441, 315, 429, 303, 417, 291, 405, 279, 393, 265, 379, 249, 363, 260, 374, 244, 358, 235, 349, 243, 357, 259, 373, 275, 389, 287, 401, 299, 413, 311, 425, 323, 437, 335, 449, 338, 452, 326, 440, 314, 428, 302, 416, 290, 404, 278, 392, 264, 378, 248, 362, 237, 351, 247, 361, 262, 376, 245, 359, 261, 375, 276, 390, 288, 402, 300, 414, 312, 426, 324, 438, 336, 450, 334, 448, 322, 436, 310, 424, 298, 412, 286, 400, 274, 388, 258, 372, 242, 356, 234, 348)
	L = (1, 230)(2, 229)(3, 235)(4, 237)(5, 239)(6, 241)(7, 231)(8, 245)(9, 232)(10, 249)(11, 233)(12, 253)(13, 234)(14, 257)(15, 251)(16, 255)(17, 236)(18, 254)(19, 252)(20, 256)(21, 238)(22, 258)(23, 243)(24, 247)(25, 240)(26, 246)(27, 244)(28, 248)(29, 242)(30, 250)(31, 269)(32, 268)(33, 267)(34, 270)(35, 275)(36, 273)(37, 272)(38, 278)(39, 261)(40, 260)(41, 259)(42, 262)(43, 281)(44, 265)(45, 264)(46, 284)(47, 263)(48, 282)(49, 288)(50, 266)(51, 285)(52, 291)(53, 271)(54, 276)(55, 294)(56, 274)(57, 279)(58, 297)(59, 293)(60, 277)(61, 295)(62, 296)(63, 280)(64, 298)(65, 287)(66, 283)(67, 289)(68, 290)(69, 286)(70, 292)(71, 306)(72, 305)(73, 311)(74, 309)(75, 308)(76, 314)(77, 300)(78, 299)(79, 317)(80, 303)(81, 302)(82, 320)(83, 301)(84, 318)(85, 324)(86, 304)(87, 321)(88, 327)(89, 307)(90, 312)(91, 330)(92, 310)(93, 315)(94, 333)(95, 329)(96, 313)(97, 331)(98, 332)(99, 316)(100, 334)(101, 323)(102, 319)(103, 325)(104, 326)(105, 322)(106, 328)(107, 340)(108, 341)(109, 338)(110, 337)(111, 342)(112, 335)(113, 336)(114, 339)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 2, 76, 2, 76 ), ( 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76, 2, 76 ) }
Outer automorphisms :: reflexible
Dual of E27.2072
Graph:: bipartite
	v = 59 e = 228 f = 117
	degree seq :: [ 4^57, 114^2 ]

E27.2072 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 38, 57})
Quotient :: dipole
Aut^+ = C19 x S3 (small group id <114, 3>)
Aut   = S3 x D38 (small group id <228, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^4 * Y1 * Y3^-1, Y3^-1 * Y1 * Y3^-1 * Y1^6 * Y3^-9 * Y1, Y1^28 * Y3^9, (Y3 * Y2^-1)^57 ]
Map::
	R = (1, 115, 2, 116, 6, 120, 16, 130, 34, 148, 53, 167, 67, 181, 79, 193, 91, 205, 103, 217, 109, 223, 101, 215, 90, 204, 75, 189, 64, 178, 48, 162, 25, 139, 40, 154, 57, 171, 46, 160, 60, 174, 45, 159, 33, 147, 44, 158, 59, 173, 72, 186, 84, 198, 96, 210, 108, 222, 111, 225, 100, 214, 86, 200, 73, 187, 65, 179, 52, 166, 27, 141, 13, 127, 4, 118)(3, 117, 9, 123, 17, 131, 8, 122, 21, 135, 35, 149, 55, 169, 68, 182, 81, 195, 92, 206, 105, 219, 113, 227, 102, 216, 87, 201, 76, 190, 62, 176, 47, 161, 29, 143, 41, 155, 19, 133, 39, 153, 31, 145, 15, 129, 32, 146, 38, 152, 58, 172, 70, 184, 83, 197, 94, 208, 107, 221, 112, 226, 98, 212, 85, 199, 77, 191, 66, 180, 49, 163, 28, 142, 11, 125)(5, 119, 14, 128, 18, 132, 37, 151, 54, 168, 69, 183, 80, 194, 93, 207, 104, 218, 110, 224, 97, 211, 89, 203, 78, 192, 63, 177, 50, 164, 26, 140, 10, 124, 24, 138, 36, 150, 23, 137, 42, 156, 22, 136, 43, 157, 56, 170, 71, 185, 82, 196, 95, 209, 106, 220, 114, 228, 99, 213, 88, 202, 74, 188, 61, 175, 51, 165, 30, 144, 12, 126, 20, 134, 7, 121)(229, 343)(230, 344)(231, 345)(232, 346)(233, 347)(234, 348)(235, 349)(236, 350)(237, 351)(238, 352)(239, 353)(240, 354)(241, 355)(242, 356)(243, 357)(244, 358)(245, 359)(246, 360)(247, 361)(248, 362)(249, 363)(250, 364)(251, 365)(252, 366)(253, 367)(254, 368)(255, 369)(256, 370)(257, 371)(258, 372)(259, 373)(260, 374)(261, 375)(262, 376)(263, 377)(264, 378)(265, 379)(266, 380)(267, 381)(268, 382)(269, 383)(270, 384)(271, 385)(272, 386)(273, 387)(274, 388)(275, 389)(276, 390)(277, 391)(278, 392)(279, 393)(280, 394)(281, 395)(282, 396)(283, 397)(284, 398)(285, 399)(286, 400)(287, 401)(288, 402)(289, 403)(290, 404)(291, 405)(292, 406)(293, 407)(294, 408)(295, 409)(296, 410)(297, 411)(298, 412)(299, 413)(300, 414)(301, 415)(302, 416)(303, 417)(304, 418)(305, 419)(306, 420)(307, 421)(308, 422)(309, 423)(310, 424)(311, 425)(312, 426)(313, 427)(314, 428)(315, 429)(316, 430)(317, 431)(318, 432)(319, 433)(320, 434)(321, 435)(322, 436)(323, 437)(324, 438)(325, 439)(326, 440)(327, 441)(328, 442)(329, 443)(330, 444)(331, 445)(332, 446)(333, 447)(334, 448)(335, 449)(336, 450)(337, 451)(338, 452)(339, 453)(340, 454)(341, 455)(342, 456)
	L = (1, 231)(2, 235)(3, 238)(4, 240)(5, 229)(6, 245)(7, 247)(8, 230)(9, 232)(10, 253)(11, 255)(12, 257)(13, 256)(14, 259)(15, 233)(16, 242)(17, 264)(18, 234)(19, 268)(20, 241)(21, 270)(22, 236)(23, 237)(24, 239)(25, 275)(26, 277)(27, 279)(28, 278)(29, 276)(30, 280)(31, 274)(32, 273)(33, 243)(34, 249)(35, 244)(36, 285)(37, 260)(38, 246)(39, 248)(40, 254)(41, 258)(42, 288)(43, 261)(44, 250)(45, 251)(46, 252)(47, 289)(48, 291)(49, 293)(50, 292)(51, 290)(52, 294)(53, 265)(54, 262)(55, 271)(56, 263)(57, 269)(58, 272)(59, 266)(60, 267)(61, 301)(62, 303)(63, 305)(64, 304)(65, 302)(66, 306)(67, 283)(68, 281)(69, 286)(70, 282)(71, 287)(72, 284)(73, 313)(74, 315)(75, 317)(76, 316)(77, 314)(78, 318)(79, 297)(80, 295)(81, 299)(82, 296)(83, 300)(84, 298)(85, 325)(86, 327)(87, 329)(88, 328)(89, 326)(90, 330)(91, 309)(92, 307)(93, 311)(94, 308)(95, 312)(96, 310)(97, 337)(98, 339)(99, 341)(100, 340)(101, 338)(102, 342)(103, 321)(104, 319)(105, 323)(106, 320)(107, 324)(108, 322)(109, 333)(110, 335)(111, 334)(112, 332)(113, 331)(114, 336)(115, 343)(116, 344)(117, 345)(118, 346)(119, 347)(120, 348)(121, 349)(122, 350)(123, 351)(124, 352)(125, 353)(126, 354)(127, 355)(128, 356)(129, 357)(130, 358)(131, 359)(132, 360)(133, 361)(134, 362)(135, 363)(136, 364)(137, 365)(138, 366)(139, 367)(140, 368)(141, 369)(142, 370)(143, 371)(144, 372)(145, 373)(146, 374)(147, 375)(148, 376)(149, 377)(150, 378)(151, 379)(152, 380)(153, 381)(154, 382)(155, 383)(156, 384)(157, 385)(158, 386)(159, 387)(160, 388)(161, 389)(162, 390)(163, 391)(164, 392)(165, 393)(166, 394)(167, 395)(168, 396)(169, 397)(170, 398)(171, 399)(172, 400)(173, 401)(174, 402)(175, 403)(176, 404)(177, 405)(178, 406)(179, 407)(180, 408)(181, 409)(182, 410)(183, 411)(184, 412)(185, 413)(186, 414)(187, 415)(188, 416)(189, 417)(190, 418)(191, 419)(192, 420)(193, 421)(194, 422)(195, 423)(196, 424)(197, 425)(198, 426)(199, 427)(200, 428)(201, 429)(202, 430)(203, 431)(204, 432)(205, 433)(206, 434)(207, 435)(208, 436)(209, 437)(210, 438)(211, 439)(212, 440)(213, 441)(214, 442)(215, 443)(216, 444)(217, 445)(218, 446)(219, 447)(220, 448)(221, 449)(222, 450)(223, 451)(224, 452)(225, 453)(226, 454)(227, 455)(228, 456)
	local type(s) :: { ( 4, 114 ), ( 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114, 4, 114 ) }
Outer automorphisms :: reflexible
Dual of E27.2071
Graph:: simple bipartite
	v = 117 e = 228 f = 59
	degree seq :: [ 2^114, 76^3 ]

E27.2073 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 5, 6})
Quotient :: edge
Aut^+ = SL(2,5) (small group id <120, 5>)
Aut   = SL(2,5) : C2 (small group id <240, 93>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1 * T2^-1 * T1, T1^5, T2^6, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^2 * T2, (T2^-1 * T1^-1)^5 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 26, 17, 5)(2, 7, 11, 28, 23, 8)(4, 12, 31, 37, 15, 14)(6, 18, 21, 47, 44, 19)(9, 25, 27, 40, 39, 16)(13, 32, 42, 62, 34, 33)(20, 46, 29, 51, 50, 22)(24, 52, 55, 49, 75, 53)(30, 57, 58, 36, 64, 35)(38, 54, 80, 56, 66, 65)(41, 68, 48, 72, 71, 43)(45, 73, 76, 70, 93, 74)(59, 84, 69, 61, 86, 60)(63, 82, 104, 83, 88, 87)(67, 91, 94, 85, 105, 92)(77, 99, 81, 97, 100, 78)(79, 101, 102, 90, 108, 89)(95, 113, 98, 111, 114, 96)(103, 115, 116, 107, 118, 106)(109, 119, 112, 117, 120, 110)(121, 122, 126, 133, 124)(123, 129, 144, 149, 131)(125, 135, 156, 158, 136)(127, 140, 165, 168, 141)(128, 137, 160, 169, 142)(130, 132, 150, 176, 147)(134, 154, 181, 183, 155)(138, 161, 187, 189, 162)(139, 143, 171, 190, 163)(145, 174, 199, 201, 175)(146, 148, 167, 182, 157)(151, 152, 179, 203, 178)(153, 164, 192, 205, 180)(159, 186, 210, 198, 173)(166, 195, 217, 218, 196)(170, 172, 197, 216, 194)(177, 202, 223, 209, 185)(184, 208, 227, 222, 200)(188, 213, 231, 232, 214)(191, 193, 215, 230, 212)(204, 225, 237, 226, 207)(206, 211, 229, 236, 224)(219, 228, 238, 239, 233)(220, 221, 235, 240, 234)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 10^5 ), ( 10^6 ) }
Outer automorphisms :: reflexible
Dual of E27.2074
Transitivity :: ET+
Graph:: simple bipartite
	v = 44 e = 120 f = 24
	degree seq :: [ 5^24, 6^20 ]

E27.2074 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 5, 6})
Quotient :: loop
Aut^+ = SL(2,5) (small group id <120, 5>)
Aut   = SL(2,5) : C2 (small group id <240, 93>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, T2^5, T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1, T1^-1 * T2^-1 * T1 * T2^-4 * T1 * T2^-1, T2 * T1^-4 * T2 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^2, (T1^2 * T2^-1)^3, (T1^-1 * T2^2)^3, T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 121, 3, 123, 10, 130, 17, 137, 5, 125)(2, 122, 7, 127, 21, 141, 25, 145, 8, 128)(4, 124, 12, 132, 33, 153, 38, 158, 14, 134)(6, 126, 18, 138, 45, 165, 49, 169, 19, 139)(9, 129, 20, 140, 44, 164, 63, 183, 27, 147)(11, 131, 30, 150, 69, 189, 73, 193, 32, 152)(13, 133, 35, 155, 78, 198, 81, 201, 36, 156)(15, 135, 22, 142, 53, 173, 87, 207, 40, 160)(16, 136, 24, 144, 48, 168, 80, 200, 37, 157)(23, 143, 46, 166, 91, 211, 106, 226, 56, 176)(26, 146, 60, 180, 57, 177, 98, 218, 61, 181)(28, 148, 50, 170, 99, 219, 96, 216, 65, 185)(29, 149, 66, 186, 58, 178, 94, 214, 68, 188)(31, 151, 71, 191, 114, 234, 115, 235, 72, 192)(34, 154, 75, 195, 110, 230, 64, 184, 77, 197)(39, 159, 52, 172, 100, 220, 97, 217, 84, 204)(41, 161, 59, 179, 105, 225, 62, 182, 88, 208)(42, 162, 54, 174, 103, 223, 74, 194, 90, 210)(43, 163, 86, 206, 109, 229, 117, 237, 82, 202)(47, 167, 79, 199, 108, 228, 120, 240, 95, 215)(51, 171, 92, 212, 118, 238, 116, 236, 83, 203)(55, 175, 93, 213, 119, 239, 113, 233, 76, 196)(67, 187, 111, 231, 104, 224, 85, 205, 101, 221)(70, 190, 112, 232, 107, 227, 89, 209, 102, 222)
	L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 135)(6, 133)(7, 140)(8, 143)(9, 146)(10, 148)(11, 123)(12, 147)(13, 124)(14, 152)(15, 159)(16, 125)(17, 162)(18, 164)(19, 167)(20, 170)(21, 171)(22, 127)(23, 175)(24, 128)(25, 178)(26, 151)(27, 182)(28, 184)(29, 130)(30, 185)(31, 131)(32, 188)(33, 181)(34, 132)(35, 183)(36, 197)(37, 134)(38, 192)(39, 161)(40, 205)(41, 136)(42, 209)(43, 137)(44, 212)(45, 206)(46, 138)(47, 191)(48, 139)(49, 217)(50, 174)(51, 193)(52, 141)(53, 203)(54, 142)(55, 177)(56, 224)(57, 144)(58, 227)(59, 145)(60, 219)(61, 215)(62, 196)(63, 229)(64, 187)(65, 201)(66, 210)(67, 149)(68, 202)(69, 230)(70, 150)(71, 216)(72, 222)(73, 221)(74, 153)(75, 218)(76, 154)(77, 223)(78, 225)(79, 155)(80, 156)(81, 233)(82, 157)(83, 158)(84, 199)(85, 213)(86, 160)(87, 189)(88, 180)(89, 211)(90, 235)(91, 163)(92, 214)(93, 165)(94, 166)(95, 231)(96, 168)(97, 232)(98, 169)(99, 238)(100, 186)(101, 172)(102, 173)(103, 236)(104, 234)(105, 176)(106, 207)(107, 228)(108, 179)(109, 204)(110, 240)(111, 194)(112, 195)(113, 190)(114, 198)(115, 239)(116, 200)(117, 208)(118, 237)(119, 220)(120, 226)
	local type(s) :: { ( 5, 6, 5, 6, 5, 6, 5, 6, 5, 6 ) }
Outer automorphisms :: reflexible
Dual of E27.2073
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 24 e = 120 f = 44
	degree seq :: [ 10^24 ]

E27.2075 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 5, 6})
Quotient :: dipole
Aut^+ = SL(2,5) (small group id <120, 5>)
Aut   = SL(2,5) : C2 (small group id <240, 93>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y2^2, Y1^5, Y2^6, Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^5 ]
Map::
	R = (1, 121, 2, 122, 6, 126, 13, 133, 4, 124)(3, 123, 9, 129, 24, 144, 29, 149, 11, 131)(5, 125, 15, 135, 36, 156, 38, 158, 16, 136)(7, 127, 20, 140, 45, 165, 48, 168, 21, 141)(8, 128, 17, 137, 40, 160, 49, 169, 22, 142)(10, 130, 12, 132, 30, 150, 56, 176, 27, 147)(14, 134, 34, 154, 61, 181, 63, 183, 35, 155)(18, 138, 41, 161, 67, 187, 69, 189, 42, 162)(19, 139, 23, 143, 51, 171, 70, 190, 43, 163)(25, 145, 54, 174, 79, 199, 81, 201, 55, 175)(26, 146, 28, 148, 47, 167, 62, 182, 37, 157)(31, 151, 32, 152, 59, 179, 83, 203, 58, 178)(33, 153, 44, 164, 72, 192, 85, 205, 60, 180)(39, 159, 66, 186, 90, 210, 78, 198, 53, 173)(46, 166, 75, 195, 97, 217, 98, 218, 76, 196)(50, 170, 52, 172, 77, 197, 96, 216, 74, 194)(57, 177, 82, 202, 103, 223, 89, 209, 65, 185)(64, 184, 88, 208, 107, 227, 102, 222, 80, 200)(68, 188, 93, 213, 111, 231, 112, 232, 94, 214)(71, 191, 73, 193, 95, 215, 110, 230, 92, 212)(84, 204, 105, 225, 117, 237, 106, 226, 87, 207)(86, 206, 91, 211, 109, 229, 116, 236, 104, 224)(99, 219, 108, 228, 118, 238, 119, 239, 113, 233)(100, 220, 101, 221, 115, 235, 120, 240, 114, 234)(241, 361, 243, 363, 250, 370, 266, 386, 257, 377, 245, 365)(242, 362, 247, 367, 251, 371, 268, 388, 263, 383, 248, 368)(244, 364, 252, 372, 271, 391, 277, 397, 255, 375, 254, 374)(246, 366, 258, 378, 261, 381, 287, 407, 284, 404, 259, 379)(249, 369, 265, 385, 267, 387, 280, 400, 279, 399, 256, 376)(253, 373, 272, 392, 282, 402, 302, 422, 274, 394, 273, 393)(260, 380, 286, 406, 269, 389, 291, 411, 290, 410, 262, 382)(264, 384, 292, 412, 295, 415, 289, 409, 315, 435, 293, 413)(270, 390, 297, 417, 298, 418, 276, 396, 304, 424, 275, 395)(278, 398, 294, 414, 320, 440, 296, 416, 306, 426, 305, 425)(281, 401, 308, 428, 288, 408, 312, 432, 311, 431, 283, 403)(285, 405, 313, 433, 316, 436, 310, 430, 333, 453, 314, 434)(299, 419, 324, 444, 309, 429, 301, 421, 326, 446, 300, 420)(303, 423, 322, 442, 344, 464, 323, 443, 328, 448, 327, 447)(307, 427, 331, 451, 334, 454, 325, 445, 345, 465, 332, 452)(317, 437, 339, 459, 321, 441, 337, 457, 340, 460, 318, 438)(319, 439, 341, 461, 342, 462, 330, 450, 348, 468, 329, 449)(335, 455, 353, 473, 338, 458, 351, 471, 354, 474, 336, 456)(343, 463, 355, 475, 356, 476, 347, 467, 358, 478, 346, 466)(349, 469, 359, 479, 352, 472, 357, 477, 360, 480, 350, 470)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 258)(7, 251)(8, 242)(9, 265)(10, 266)(11, 268)(12, 271)(13, 272)(14, 244)(15, 254)(16, 249)(17, 245)(18, 261)(19, 246)(20, 286)(21, 287)(22, 260)(23, 248)(24, 292)(25, 267)(26, 257)(27, 280)(28, 263)(29, 291)(30, 297)(31, 277)(32, 282)(33, 253)(34, 273)(35, 270)(36, 304)(37, 255)(38, 294)(39, 256)(40, 279)(41, 308)(42, 302)(43, 281)(44, 259)(45, 313)(46, 269)(47, 284)(48, 312)(49, 315)(50, 262)(51, 290)(52, 295)(53, 264)(54, 320)(55, 289)(56, 306)(57, 298)(58, 276)(59, 324)(60, 299)(61, 326)(62, 274)(63, 322)(64, 275)(65, 278)(66, 305)(67, 331)(68, 288)(69, 301)(70, 333)(71, 283)(72, 311)(73, 316)(74, 285)(75, 293)(76, 310)(77, 339)(78, 317)(79, 341)(80, 296)(81, 337)(82, 344)(83, 328)(84, 309)(85, 345)(86, 300)(87, 303)(88, 327)(89, 319)(90, 348)(91, 334)(92, 307)(93, 314)(94, 325)(95, 353)(96, 335)(97, 340)(98, 351)(99, 321)(100, 318)(101, 342)(102, 330)(103, 355)(104, 323)(105, 332)(106, 343)(107, 358)(108, 329)(109, 359)(110, 349)(111, 354)(112, 357)(113, 338)(114, 336)(115, 356)(116, 347)(117, 360)(118, 346)(119, 352)(120, 350)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.2076
Graph:: bipartite
	v = 44 e = 240 f = 144
	degree seq :: [ 10^24, 12^20 ]

E27.2076 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 5, 6})
Quotient :: dipole
Aut^+ = SL(2,5) (small group id <120, 5>)
Aut   = SL(2,5) : C2 (small group id <240, 93>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y2^5, Y3^6, Y3^-1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^5, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362, 246, 366, 253, 373, 244, 364)(243, 363, 249, 369, 264, 384, 269, 389, 251, 371)(245, 365, 255, 375, 276, 396, 278, 398, 256, 376)(247, 367, 250, 370, 266, 386, 287, 407, 261, 381)(248, 368, 262, 382, 288, 408, 290, 410, 263, 383)(252, 372, 270, 390, 299, 419, 300, 420, 271, 391)(254, 374, 274, 394, 303, 423, 280, 400, 257, 377)(258, 378, 260, 380, 285, 405, 309, 429, 282, 402)(259, 379, 283, 403, 310, 430, 312, 432, 284, 404)(265, 385, 267, 387, 279, 399, 291, 411, 294, 414)(268, 388, 295, 415, 320, 440, 321, 441, 296, 416)(272, 392, 281, 401, 307, 427, 327, 447, 301, 421)(273, 393, 302, 422, 317, 437, 292, 412, 275, 395)(277, 397, 298, 418, 323, 443, 330, 450, 306, 426)(286, 406, 305, 425, 329, 449, 335, 455, 313, 433)(289, 409, 314, 434, 336, 456, 338, 458, 316, 436)(293, 413, 318, 438, 340, 460, 341, 461, 319, 439)(297, 417, 304, 424, 326, 446, 344, 464, 322, 442)(308, 428, 315, 435, 337, 457, 349, 469, 331, 451)(311, 431, 332, 452, 350, 470, 352, 472, 334, 454)(324, 444, 333, 453, 351, 471, 355, 475, 339, 459)(325, 445, 328, 448, 347, 467, 358, 478, 346, 466)(342, 462, 356, 476, 360, 480, 354, 474, 348, 468)(343, 463, 345, 465, 357, 477, 359, 479, 353, 473)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 258)(7, 260)(8, 242)(9, 265)(10, 267)(11, 268)(12, 249)(13, 272)(14, 244)(15, 251)(16, 248)(17, 245)(18, 281)(19, 246)(20, 279)(21, 286)(22, 261)(23, 259)(24, 292)(25, 275)(26, 280)(27, 257)(28, 266)(29, 297)(30, 294)(31, 293)(32, 270)(33, 253)(34, 271)(35, 254)(36, 296)(37, 255)(38, 289)(39, 256)(40, 277)(41, 291)(42, 308)(43, 282)(44, 273)(45, 278)(46, 285)(47, 306)(48, 313)(49, 262)(50, 311)(51, 263)(52, 304)(53, 264)(54, 284)(55, 303)(56, 314)(57, 295)(58, 269)(59, 312)(60, 325)(61, 324)(62, 301)(63, 319)(64, 274)(65, 276)(66, 305)(67, 290)(68, 307)(69, 316)(70, 331)(71, 283)(72, 328)(73, 332)(74, 287)(75, 288)(76, 315)(77, 339)(78, 317)(79, 298)(80, 341)(81, 343)(82, 342)(83, 322)(84, 299)(85, 318)(86, 300)(87, 334)(88, 302)(89, 321)(90, 348)(91, 347)(92, 309)(93, 310)(94, 333)(95, 353)(96, 330)(97, 335)(98, 354)(99, 326)(100, 355)(101, 345)(102, 320)(103, 336)(104, 346)(105, 323)(106, 356)(107, 327)(108, 329)(109, 359)(110, 338)(111, 349)(112, 360)(113, 350)(114, 337)(115, 357)(116, 340)(117, 344)(118, 352)(119, 358)(120, 351)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2075
Graph:: simple bipartite
	v = 144 e = 240 f = 44
	degree seq :: [ 2^120, 10^24 ]

E27.2077 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2)^4, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y3 * Y1)^15 ]
Map:: polytopal non-degenerate
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 18, 138)(14, 134, 24, 144)(16, 136, 27, 147)(17, 137, 29, 149)(19, 139, 25, 145)(21, 141, 23, 143)(22, 142, 32, 152)(26, 146, 35, 155)(28, 148, 36, 156)(30, 150, 39, 159)(31, 151, 40, 160)(33, 153, 41, 161)(34, 154, 37, 157)(38, 158, 46, 166)(42, 162, 50, 170)(43, 163, 51, 171)(44, 164, 52, 172)(45, 165, 53, 173)(47, 167, 55, 175)(48, 168, 56, 176)(49, 169, 57, 177)(54, 174, 62, 182)(58, 178, 66, 186)(59, 179, 67, 187)(60, 180, 68, 188)(61, 181, 69, 189)(63, 183, 71, 191)(64, 184, 72, 192)(65, 185, 73, 193)(70, 190, 78, 198)(74, 194, 82, 202)(75, 195, 83, 203)(76, 196, 84, 204)(77, 197, 85, 205)(79, 199, 87, 207)(80, 200, 88, 208)(81, 201, 89, 209)(86, 206, 94, 214)(90, 210, 98, 218)(91, 211, 99, 219)(92, 212, 100, 220)(93, 213, 101, 221)(95, 215, 103, 223)(96, 216, 104, 224)(97, 217, 105, 225)(102, 222, 110, 230)(106, 226, 114, 234)(107, 227, 115, 235)(108, 228, 116, 236)(109, 229, 117, 237)(111, 231, 118, 238)(112, 232, 119, 239)(113, 233, 120, 240)(241, 361, 243, 363)(242, 362, 245, 365)(244, 364, 248, 368)(246, 366, 251, 371)(247, 367, 253, 373)(249, 369, 256, 376)(250, 370, 258, 378)(252, 372, 261, 381)(254, 374, 263, 383)(255, 375, 265, 385)(257, 377, 268, 388)(259, 379, 267, 387)(260, 380, 264, 384)(262, 382, 271, 391)(266, 386, 274, 394)(269, 389, 277, 397)(270, 390, 273, 393)(272, 392, 281, 401)(275, 395, 276, 396)(278, 398, 285, 405)(279, 399, 280, 400)(282, 402, 289, 409)(283, 403, 284, 404)(286, 406, 291, 411)(287, 407, 288, 408)(290, 410, 295, 415)(292, 412, 293, 413)(294, 414, 299, 419)(296, 416, 297, 417)(298, 418, 303, 423)(300, 420, 301, 421)(302, 422, 308, 428)(304, 424, 305, 425)(306, 426, 312, 432)(307, 427, 309, 429)(310, 430, 316, 436)(311, 431, 313, 433)(314, 434, 320, 440)(315, 435, 317, 437)(318, 438, 325, 445)(319, 439, 321, 441)(322, 442, 329, 449)(323, 443, 324, 444)(326, 446, 333, 453)(327, 447, 328, 448)(330, 450, 337, 457)(331, 451, 332, 452)(334, 454, 339, 459)(335, 455, 336, 456)(338, 458, 343, 463)(340, 460, 341, 461)(342, 462, 347, 467)(344, 464, 345, 465)(346, 466, 351, 471)(348, 468, 349, 469)(350, 470, 356, 476)(352, 472, 353, 473)(354, 474, 359, 479)(355, 475, 357, 477)(358, 478, 360, 480)
	L = (1, 244)(2, 246)(3, 248)(4, 241)(5, 251)(6, 242)(7, 254)(8, 243)(9, 257)(10, 259)(11, 245)(12, 262)(13, 263)(14, 247)(15, 266)(16, 268)(17, 249)(18, 267)(19, 250)(20, 270)(21, 271)(22, 252)(23, 253)(24, 273)(25, 274)(26, 255)(27, 258)(28, 256)(29, 278)(30, 260)(31, 261)(32, 282)(33, 264)(34, 265)(35, 283)(36, 284)(37, 285)(38, 269)(39, 287)(40, 288)(41, 289)(42, 272)(43, 275)(44, 276)(45, 277)(46, 294)(47, 279)(48, 280)(49, 281)(50, 298)(51, 299)(52, 300)(53, 301)(54, 286)(55, 303)(56, 304)(57, 305)(58, 290)(59, 291)(60, 292)(61, 293)(62, 310)(63, 295)(64, 296)(65, 297)(66, 314)(67, 315)(68, 316)(69, 317)(70, 302)(71, 319)(72, 320)(73, 321)(74, 306)(75, 307)(76, 308)(77, 309)(78, 326)(79, 311)(80, 312)(81, 313)(82, 330)(83, 331)(84, 332)(85, 333)(86, 318)(87, 335)(88, 336)(89, 337)(90, 322)(91, 323)(92, 324)(93, 325)(94, 342)(95, 327)(96, 328)(97, 329)(98, 346)(99, 347)(100, 348)(101, 349)(102, 334)(103, 351)(104, 352)(105, 353)(106, 338)(107, 339)(108, 340)(109, 341)(110, 354)(111, 343)(112, 344)(113, 345)(114, 350)(115, 360)(116, 359)(117, 358)(118, 357)(119, 356)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 30, 4, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2080
Graph:: simple bipartite
	v = 120 e = 240 f = 68
	degree seq :: [ 4^120 ]

E27.2078 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (Y3 * Y1)^15, (Y2 * Y1)^15 ]
Map:: polytopal non-degenerate
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 23, 143)(14, 134, 25, 145)(16, 136, 28, 148)(17, 137, 30, 150)(18, 138, 31, 151)(19, 139, 33, 153)(21, 141, 36, 156)(22, 142, 38, 158)(24, 144, 35, 155)(26, 146, 37, 157)(27, 147, 32, 152)(29, 149, 34, 154)(39, 159, 49, 169)(40, 160, 50, 170)(41, 161, 51, 171)(42, 162, 52, 172)(43, 163, 48, 168)(44, 164, 53, 173)(45, 165, 54, 174)(46, 166, 55, 175)(47, 167, 56, 176)(57, 177, 65, 185)(58, 178, 66, 186)(59, 179, 67, 187)(60, 180, 68, 188)(61, 181, 69, 189)(62, 182, 70, 190)(63, 183, 71, 191)(64, 184, 72, 192)(73, 193, 81, 201)(74, 194, 82, 202)(75, 195, 83, 203)(76, 196, 84, 204)(77, 197, 85, 205)(78, 198, 86, 206)(79, 199, 87, 207)(80, 200, 88, 208)(89, 209, 97, 217)(90, 210, 98, 218)(91, 211, 99, 219)(92, 212, 100, 220)(93, 213, 101, 221)(94, 214, 102, 222)(95, 215, 103, 223)(96, 216, 104, 224)(105, 225, 113, 233)(106, 226, 114, 234)(107, 227, 115, 235)(108, 228, 116, 236)(109, 229, 117, 237)(110, 230, 118, 238)(111, 231, 119, 239)(112, 232, 120, 240)(241, 361, 243, 363)(242, 362, 245, 365)(244, 364, 248, 368)(246, 366, 251, 371)(247, 367, 253, 373)(249, 369, 256, 376)(250, 370, 258, 378)(252, 372, 261, 381)(254, 374, 264, 384)(255, 375, 266, 386)(257, 377, 269, 389)(259, 379, 272, 392)(260, 380, 274, 394)(262, 382, 277, 397)(263, 383, 279, 399)(265, 385, 281, 401)(267, 387, 283, 403)(268, 388, 282, 402)(270, 390, 280, 400)(271, 391, 284, 404)(273, 393, 286, 406)(275, 395, 288, 408)(276, 396, 287, 407)(278, 398, 285, 405)(289, 409, 297, 417)(290, 410, 299, 419)(291, 411, 300, 420)(292, 412, 298, 418)(293, 413, 301, 421)(294, 414, 303, 423)(295, 415, 304, 424)(296, 416, 302, 422)(305, 425, 313, 433)(306, 426, 315, 435)(307, 427, 316, 436)(308, 428, 314, 434)(309, 429, 317, 437)(310, 430, 319, 439)(311, 431, 320, 440)(312, 432, 318, 438)(321, 441, 329, 449)(322, 442, 331, 451)(323, 443, 332, 452)(324, 444, 330, 450)(325, 445, 333, 453)(326, 446, 335, 455)(327, 447, 336, 456)(328, 448, 334, 454)(337, 457, 345, 465)(338, 458, 347, 467)(339, 459, 348, 468)(340, 460, 346, 466)(341, 461, 349, 469)(342, 462, 351, 471)(343, 463, 352, 472)(344, 464, 350, 470)(353, 473, 357, 477)(354, 474, 359, 479)(355, 475, 358, 478)(356, 476, 360, 480)
	L = (1, 244)(2, 246)(3, 248)(4, 241)(5, 251)(6, 242)(7, 254)(8, 243)(9, 257)(10, 259)(11, 245)(12, 262)(13, 264)(14, 247)(15, 267)(16, 269)(17, 249)(18, 272)(19, 250)(20, 275)(21, 277)(22, 252)(23, 280)(24, 253)(25, 282)(26, 283)(27, 255)(28, 281)(29, 256)(30, 279)(31, 285)(32, 258)(33, 287)(34, 288)(35, 260)(36, 286)(37, 261)(38, 284)(39, 270)(40, 263)(41, 268)(42, 265)(43, 266)(44, 278)(45, 271)(46, 276)(47, 273)(48, 274)(49, 298)(50, 300)(51, 299)(52, 297)(53, 302)(54, 304)(55, 303)(56, 301)(57, 292)(58, 289)(59, 291)(60, 290)(61, 296)(62, 293)(63, 295)(64, 294)(65, 314)(66, 316)(67, 315)(68, 313)(69, 318)(70, 320)(71, 319)(72, 317)(73, 308)(74, 305)(75, 307)(76, 306)(77, 312)(78, 309)(79, 311)(80, 310)(81, 330)(82, 332)(83, 331)(84, 329)(85, 334)(86, 336)(87, 335)(88, 333)(89, 324)(90, 321)(91, 323)(92, 322)(93, 328)(94, 325)(95, 327)(96, 326)(97, 346)(98, 348)(99, 347)(100, 345)(101, 350)(102, 352)(103, 351)(104, 349)(105, 340)(106, 337)(107, 339)(108, 338)(109, 344)(110, 341)(111, 343)(112, 342)(113, 360)(114, 358)(115, 359)(116, 357)(117, 356)(118, 354)(119, 355)(120, 353)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 30, 4, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2079
Graph:: simple bipartite
	v = 120 e = 240 f = 68
	degree seq :: [ 4^120 ]

E27.2079 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1 * Y2 * Y1^-2 * Y2, Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1 * Y3 * Y1, Y1^15 ]
Map:: polytopal non-degenerate
	R = (1, 121, 2, 122, 6, 126, 15, 135, 33, 153, 53, 173, 69, 189, 85, 205, 100, 220, 84, 204, 68, 188, 52, 172, 32, 152, 14, 134, 5, 125)(3, 123, 9, 129, 21, 141, 34, 154, 56, 176, 74, 194, 86, 206, 103, 223, 109, 229, 94, 214, 78, 198, 62, 182, 45, 165, 26, 146, 11, 131)(4, 124, 12, 132, 27, 147, 46, 166, 63, 183, 79, 199, 95, 215, 110, 230, 102, 222, 87, 207, 71, 191, 55, 175, 35, 155, 17, 137, 8, 128)(7, 127, 18, 138, 38, 158, 54, 174, 72, 192, 90, 210, 101, 221, 114, 234, 99, 219, 83, 203, 67, 187, 51, 171, 31, 151, 25, 145, 20, 140)(10, 130, 24, 144, 43, 163, 61, 181, 77, 197, 93, 213, 108, 228, 118, 238, 116, 236, 104, 224, 92, 212, 75, 195, 57, 177, 41, 161, 23, 143)(13, 133, 29, 149, 22, 142, 16, 136, 36, 156, 58, 178, 70, 190, 88, 208, 105, 225, 113, 233, 98, 218, 82, 202, 66, 186, 50, 170, 30, 150)(19, 139, 40, 160, 44, 164, 47, 167, 64, 184, 81, 201, 96, 216, 111, 231, 120, 240, 115, 235, 107, 227, 91, 211, 73, 193, 60, 180, 39, 159)(28, 148, 48, 168, 65, 185, 80, 200, 97, 217, 112, 232, 119, 239, 117, 237, 106, 226, 89, 209, 76, 196, 59, 179, 37, 157, 42, 162, 49, 169)(241, 361, 243, 363)(242, 362, 247, 367)(244, 364, 250, 370)(245, 365, 253, 373)(246, 366, 256, 376)(248, 368, 259, 379)(249, 369, 262, 382)(251, 371, 265, 385)(252, 372, 268, 388)(254, 374, 271, 391)(255, 375, 274, 394)(257, 377, 277, 397)(258, 378, 261, 381)(260, 380, 269, 389)(263, 383, 282, 402)(264, 384, 284, 404)(266, 386, 270, 390)(267, 387, 287, 407)(272, 392, 285, 405)(273, 393, 294, 414)(275, 395, 297, 417)(276, 396, 278, 398)(279, 399, 281, 401)(280, 400, 289, 409)(283, 403, 288, 408)(286, 406, 301, 421)(290, 410, 291, 411)(292, 412, 306, 426)(293, 413, 310, 430)(295, 415, 313, 433)(296, 416, 298, 418)(299, 419, 300, 420)(302, 422, 307, 427)(303, 423, 320, 440)(304, 424, 305, 425)(308, 428, 323, 443)(309, 429, 326, 446)(311, 431, 329, 449)(312, 432, 314, 434)(315, 435, 316, 436)(317, 437, 321, 441)(318, 438, 322, 442)(319, 439, 336, 456)(324, 444, 334, 454)(325, 445, 341, 461)(327, 447, 344, 464)(328, 448, 330, 450)(331, 451, 332, 452)(333, 453, 337, 457)(335, 455, 348, 468)(338, 458, 339, 459)(340, 460, 353, 473)(342, 462, 355, 475)(343, 463, 345, 465)(346, 466, 347, 467)(349, 469, 354, 474)(350, 470, 359, 479)(351, 471, 352, 472)(356, 476, 357, 477)(358, 478, 360, 480)
	L = (1, 244)(2, 248)(3, 250)(4, 241)(5, 252)(6, 257)(7, 259)(8, 242)(9, 263)(10, 243)(11, 264)(12, 245)(13, 268)(14, 267)(15, 275)(16, 277)(17, 246)(18, 279)(19, 247)(20, 280)(21, 281)(22, 282)(23, 249)(24, 251)(25, 284)(26, 283)(27, 254)(28, 253)(29, 289)(30, 288)(31, 287)(32, 286)(33, 295)(34, 297)(35, 255)(36, 299)(37, 256)(38, 300)(39, 258)(40, 260)(41, 261)(42, 262)(43, 266)(44, 265)(45, 301)(46, 272)(47, 271)(48, 270)(49, 269)(50, 305)(51, 304)(52, 303)(53, 311)(54, 313)(55, 273)(56, 315)(57, 274)(58, 316)(59, 276)(60, 278)(61, 285)(62, 317)(63, 292)(64, 291)(65, 290)(66, 320)(67, 321)(68, 319)(69, 327)(70, 329)(71, 293)(72, 331)(73, 294)(74, 332)(75, 296)(76, 298)(77, 302)(78, 333)(79, 308)(80, 306)(81, 307)(82, 337)(83, 336)(84, 335)(85, 342)(86, 344)(87, 309)(88, 346)(89, 310)(90, 347)(91, 312)(92, 314)(93, 318)(94, 348)(95, 324)(96, 323)(97, 322)(98, 352)(99, 351)(100, 350)(101, 355)(102, 325)(103, 356)(104, 326)(105, 357)(106, 328)(107, 330)(108, 334)(109, 358)(110, 340)(111, 339)(112, 338)(113, 359)(114, 360)(115, 341)(116, 343)(117, 345)(118, 349)(119, 353)(120, 354)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4^4 ), ( 4^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2078
Graph:: simple bipartite
	v = 68 e = 240 f = 120
	degree seq :: [ 4^60, 30^8 ]

E27.2080 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (Y2 * Y1^-3)^2, Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1^2, Y3 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^15 ]
Map:: polytopal non-degenerate
	R = (1, 121, 2, 122, 6, 126, 15, 135, 33, 153, 53, 173, 69, 189, 85, 205, 100, 220, 84, 204, 68, 188, 52, 172, 32, 152, 14, 134, 5, 125)(3, 123, 9, 129, 21, 141, 45, 165, 61, 181, 77, 197, 93, 213, 108, 228, 104, 224, 86, 206, 76, 196, 57, 177, 34, 154, 26, 146, 11, 131)(4, 124, 12, 132, 27, 147, 49, 169, 65, 185, 81, 201, 97, 217, 112, 232, 102, 222, 87, 207, 71, 191, 55, 175, 35, 155, 17, 137, 8, 128)(7, 127, 18, 138, 39, 159, 31, 151, 51, 171, 67, 187, 83, 203, 99, 219, 114, 234, 101, 221, 92, 212, 73, 193, 54, 174, 44, 164, 20, 140)(10, 130, 24, 144, 43, 163, 56, 176, 74, 194, 91, 211, 103, 223, 116, 236, 119, 239, 109, 229, 95, 215, 79, 199, 62, 182, 47, 167, 23, 143)(13, 133, 29, 149, 50, 170, 66, 186, 82, 202, 98, 218, 113, 233, 107, 227, 89, 209, 70, 190, 60, 180, 38, 158, 16, 136, 36, 156, 30, 150)(19, 139, 42, 162, 59, 179, 72, 192, 90, 210, 106, 226, 115, 235, 118, 238, 111, 231, 96, 216, 78, 198, 64, 184, 48, 168, 22, 142, 41, 161)(25, 145, 37, 157, 58, 178, 75, 195, 88, 208, 105, 225, 117, 237, 120, 240, 110, 230, 94, 214, 80, 200, 63, 183, 46, 166, 28, 148, 40, 160)(241, 361, 243, 363)(242, 362, 247, 367)(244, 364, 250, 370)(245, 365, 253, 373)(246, 366, 256, 376)(248, 368, 259, 379)(249, 369, 262, 382)(251, 371, 265, 385)(252, 372, 268, 388)(254, 374, 271, 391)(255, 375, 274, 394)(257, 377, 277, 397)(258, 378, 280, 400)(260, 380, 283, 403)(261, 381, 286, 406)(263, 383, 279, 399)(264, 384, 276, 396)(266, 386, 282, 402)(267, 387, 288, 408)(269, 389, 287, 407)(270, 390, 281, 401)(272, 392, 285, 405)(273, 393, 294, 414)(275, 395, 296, 416)(278, 398, 299, 419)(284, 404, 298, 418)(289, 409, 302, 422)(290, 410, 304, 424)(291, 411, 303, 423)(292, 412, 306, 426)(293, 413, 310, 430)(295, 415, 312, 432)(297, 417, 315, 435)(300, 420, 314, 434)(301, 421, 318, 438)(305, 425, 320, 440)(307, 427, 319, 439)(308, 428, 323, 443)(309, 429, 326, 446)(311, 431, 328, 448)(313, 433, 331, 451)(316, 436, 330, 450)(317, 437, 334, 454)(321, 441, 336, 456)(322, 442, 335, 455)(324, 444, 333, 453)(325, 445, 341, 461)(327, 447, 343, 463)(329, 449, 346, 466)(332, 452, 345, 465)(337, 457, 349, 469)(338, 458, 351, 471)(339, 459, 350, 470)(340, 460, 353, 473)(342, 462, 355, 475)(344, 464, 357, 477)(347, 467, 356, 476)(348, 468, 358, 478)(352, 472, 360, 480)(354, 474, 359, 479)
	L = (1, 244)(2, 248)(3, 250)(4, 241)(5, 252)(6, 257)(7, 259)(8, 242)(9, 263)(10, 243)(11, 264)(12, 245)(13, 268)(14, 267)(15, 275)(16, 277)(17, 246)(18, 281)(19, 247)(20, 282)(21, 287)(22, 279)(23, 249)(24, 251)(25, 276)(26, 283)(27, 254)(28, 253)(29, 286)(30, 280)(31, 288)(32, 289)(33, 295)(34, 296)(35, 255)(36, 265)(37, 256)(38, 298)(39, 262)(40, 270)(41, 258)(42, 260)(43, 266)(44, 299)(45, 302)(46, 269)(47, 261)(48, 271)(49, 272)(50, 303)(51, 304)(52, 305)(53, 311)(54, 312)(55, 273)(56, 274)(57, 314)(58, 278)(59, 284)(60, 315)(61, 319)(62, 285)(63, 290)(64, 291)(65, 292)(66, 320)(67, 318)(68, 321)(69, 327)(70, 328)(71, 293)(72, 294)(73, 330)(74, 297)(75, 300)(76, 331)(77, 335)(78, 307)(79, 301)(80, 306)(81, 308)(82, 334)(83, 336)(84, 337)(85, 342)(86, 343)(87, 309)(88, 310)(89, 345)(90, 313)(91, 316)(92, 346)(93, 349)(94, 322)(95, 317)(96, 323)(97, 324)(98, 350)(99, 351)(100, 352)(101, 355)(102, 325)(103, 326)(104, 356)(105, 329)(106, 332)(107, 357)(108, 359)(109, 333)(110, 338)(111, 339)(112, 340)(113, 360)(114, 358)(115, 341)(116, 344)(117, 347)(118, 354)(119, 348)(120, 353)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4^4 ), ( 4^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2077
Graph:: simple bipartite
	v = 68 e = 240 f = 120
	degree seq :: [ 4^60, 30^8 ]

E27.2081 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 15})
Quotient :: edge
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1)^2, (F * T1)^2, T1^4, (F * T2)^2, (T2^-2 * T1^-1)^2, T2^15 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 24, 43, 60, 76, 92, 96, 80, 64, 47, 29, 14, 5)(2, 7, 18, 36, 54, 70, 86, 102, 104, 88, 72, 56, 38, 20, 8)(4, 11, 26, 45, 62, 78, 94, 109, 107, 91, 75, 59, 42, 23, 12)(6, 15, 31, 50, 66, 82, 98, 112, 114, 100, 84, 68, 52, 33, 16)(9, 21, 13, 28, 46, 63, 79, 95, 110, 106, 90, 74, 58, 41, 22)(17, 34, 19, 37, 55, 71, 87, 103, 116, 115, 101, 85, 69, 53, 35)(25, 39, 27, 40, 57, 73, 89, 105, 117, 118, 108, 93, 77, 61, 44)(30, 48, 32, 51, 67, 83, 99, 113, 120, 119, 111, 97, 81, 65, 49)(121, 122, 126, 124)(123, 129, 139, 128)(125, 131, 145, 133)(127, 137, 152, 136)(130, 143, 160, 142)(132, 135, 150, 147)(134, 148, 155, 138)(140, 157, 169, 151)(141, 159, 168, 154)(144, 158, 170, 162)(146, 153, 171, 164)(149, 156, 172, 165)(161, 177, 185, 175)(163, 178, 191, 176)(166, 181, 187, 173)(167, 182, 197, 183)(174, 189, 203, 188)(179, 186, 201, 193)(180, 195, 209, 194)(184, 199, 205, 190)(192, 207, 217, 202)(196, 208, 218, 211)(198, 204, 219, 213)(200, 206, 220, 214)(210, 225, 231, 223)(212, 226, 236, 224)(215, 228, 233, 221)(216, 229, 238, 230)(222, 235, 240, 234)(227, 232, 239, 237)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 8^4 ), ( 8^15 ) }
Outer automorphisms :: reflexible
Dual of E27.2082
Transitivity :: ET+
Graph:: simple bipartite
	v = 38 e = 120 f = 30
	degree seq :: [ 4^30, 15^8 ]

E27.2082 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 15})
Quotient :: loop
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1^-2)^2, (T2^-1 * T1^-1)^15 ]
Map:: polytopal non-degenerate
	R = (1, 121, 3, 123, 10, 130, 5, 125)(2, 122, 7, 127, 19, 139, 8, 128)(4, 124, 12, 132, 25, 145, 13, 133)(6, 126, 16, 136, 28, 148, 17, 137)(9, 129, 23, 143, 15, 135, 24, 144)(11, 131, 26, 146, 14, 134, 27, 147)(18, 138, 29, 149, 22, 142, 30, 150)(20, 140, 31, 151, 21, 141, 32, 152)(33, 153, 41, 161, 36, 156, 42, 162)(34, 154, 43, 163, 35, 155, 44, 164)(37, 157, 45, 165, 40, 160, 46, 166)(38, 158, 47, 167, 39, 159, 48, 168)(49, 169, 57, 177, 52, 172, 58, 178)(50, 170, 59, 179, 51, 171, 60, 180)(53, 173, 61, 181, 56, 176, 62, 182)(54, 174, 63, 183, 55, 175, 64, 184)(65, 185, 73, 193, 68, 188, 74, 194)(66, 186, 75, 195, 67, 187, 76, 196)(69, 189, 77, 197, 72, 192, 78, 198)(70, 190, 79, 199, 71, 191, 80, 200)(81, 201, 89, 209, 84, 204, 90, 210)(82, 202, 91, 211, 83, 203, 92, 212)(85, 205, 93, 213, 88, 208, 94, 214)(86, 206, 95, 215, 87, 207, 96, 216)(97, 217, 105, 225, 100, 220, 106, 226)(98, 218, 107, 227, 99, 219, 108, 228)(101, 221, 109, 229, 104, 224, 110, 230)(102, 222, 111, 231, 103, 223, 112, 232)(113, 233, 117, 237, 116, 236, 120, 240)(114, 234, 119, 239, 115, 235, 118, 238)
	L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 124)(7, 138)(8, 141)(9, 137)(10, 145)(11, 123)(12, 142)(13, 140)(14, 136)(15, 125)(16, 135)(17, 131)(18, 133)(19, 130)(20, 127)(21, 132)(22, 128)(23, 153)(24, 155)(25, 148)(26, 156)(27, 154)(28, 139)(29, 157)(30, 159)(31, 160)(32, 158)(33, 147)(34, 143)(35, 146)(36, 144)(37, 152)(38, 149)(39, 151)(40, 150)(41, 169)(42, 171)(43, 172)(44, 170)(45, 173)(46, 175)(47, 176)(48, 174)(49, 164)(50, 161)(51, 163)(52, 162)(53, 168)(54, 165)(55, 167)(56, 166)(57, 185)(58, 187)(59, 188)(60, 186)(61, 189)(62, 191)(63, 192)(64, 190)(65, 180)(66, 177)(67, 179)(68, 178)(69, 184)(70, 181)(71, 183)(72, 182)(73, 201)(74, 203)(75, 204)(76, 202)(77, 205)(78, 207)(79, 208)(80, 206)(81, 196)(82, 193)(83, 195)(84, 194)(85, 200)(86, 197)(87, 199)(88, 198)(89, 217)(90, 219)(91, 220)(92, 218)(93, 221)(94, 223)(95, 224)(96, 222)(97, 212)(98, 209)(99, 211)(100, 210)(101, 216)(102, 213)(103, 215)(104, 214)(105, 233)(106, 235)(107, 236)(108, 234)(109, 237)(110, 239)(111, 240)(112, 238)(113, 228)(114, 225)(115, 227)(116, 226)(117, 232)(118, 229)(119, 231)(120, 230)
	local type(s) :: { ( 4, 15, 4, 15, 4, 15, 4, 15 ) }
Outer automorphisms :: reflexible
Dual of E27.2081
Transitivity :: ET+ VT+ AT
Graph::
	v = 30 e = 120 f = 38
	degree seq :: [ 8^30 ]

E27.2083 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2^-2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^15 ]
Map::
	R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 19, 139, 8, 128)(5, 125, 11, 131, 25, 145, 13, 133)(7, 127, 17, 137, 32, 152, 16, 136)(10, 130, 23, 143, 40, 160, 22, 142)(12, 132, 15, 135, 30, 150, 27, 147)(14, 134, 28, 148, 35, 155, 18, 138)(20, 140, 37, 157, 49, 169, 31, 151)(21, 141, 39, 159, 48, 168, 34, 154)(24, 144, 38, 158, 50, 170, 42, 162)(26, 146, 33, 153, 51, 171, 44, 164)(29, 149, 36, 156, 52, 172, 45, 165)(41, 161, 57, 177, 65, 185, 55, 175)(43, 163, 58, 178, 71, 191, 56, 176)(46, 166, 61, 181, 67, 187, 53, 173)(47, 167, 62, 182, 77, 197, 63, 183)(54, 174, 69, 189, 83, 203, 68, 188)(59, 179, 66, 186, 81, 201, 73, 193)(60, 180, 75, 195, 89, 209, 74, 194)(64, 184, 79, 199, 85, 205, 70, 190)(72, 192, 87, 207, 97, 217, 82, 202)(76, 196, 88, 208, 98, 218, 91, 211)(78, 198, 84, 204, 99, 219, 93, 213)(80, 200, 86, 206, 100, 220, 94, 214)(90, 210, 105, 225, 111, 231, 103, 223)(92, 212, 106, 226, 116, 236, 104, 224)(95, 215, 108, 228, 113, 233, 101, 221)(96, 216, 109, 229, 118, 238, 110, 230)(102, 222, 115, 235, 120, 240, 114, 234)(107, 227, 112, 232, 119, 239, 117, 237)(241, 361, 243, 363, 250, 370, 264, 384, 283, 403, 300, 420, 316, 436, 332, 452, 336, 456, 320, 440, 304, 424, 287, 407, 269, 389, 254, 374, 245, 365)(242, 362, 247, 367, 258, 378, 276, 396, 294, 414, 310, 430, 326, 446, 342, 462, 344, 464, 328, 448, 312, 432, 296, 416, 278, 398, 260, 380, 248, 368)(244, 364, 251, 371, 266, 386, 285, 405, 302, 422, 318, 438, 334, 454, 349, 469, 347, 467, 331, 451, 315, 435, 299, 419, 282, 402, 263, 383, 252, 372)(246, 366, 255, 375, 271, 391, 290, 410, 306, 426, 322, 442, 338, 458, 352, 472, 354, 474, 340, 460, 324, 444, 308, 428, 292, 412, 273, 393, 256, 376)(249, 369, 261, 381, 253, 373, 268, 388, 286, 406, 303, 423, 319, 439, 335, 455, 350, 470, 346, 466, 330, 450, 314, 434, 298, 418, 281, 401, 262, 382)(257, 377, 274, 394, 259, 379, 277, 397, 295, 415, 311, 431, 327, 447, 343, 463, 356, 476, 355, 475, 341, 461, 325, 445, 309, 429, 293, 413, 275, 395)(265, 385, 279, 399, 267, 387, 280, 400, 297, 417, 313, 433, 329, 449, 345, 465, 357, 477, 358, 478, 348, 468, 333, 453, 317, 437, 301, 421, 284, 404)(270, 390, 288, 408, 272, 392, 291, 411, 307, 427, 323, 443, 339, 459, 353, 473, 360, 480, 359, 479, 351, 471, 337, 457, 321, 441, 305, 425, 289, 409)
	L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 255)(7, 258)(8, 242)(9, 261)(10, 264)(11, 266)(12, 244)(13, 268)(14, 245)(15, 271)(16, 246)(17, 274)(18, 276)(19, 277)(20, 248)(21, 253)(22, 249)(23, 252)(24, 283)(25, 279)(26, 285)(27, 280)(28, 286)(29, 254)(30, 288)(31, 290)(32, 291)(33, 256)(34, 259)(35, 257)(36, 294)(37, 295)(38, 260)(39, 267)(40, 297)(41, 262)(42, 263)(43, 300)(44, 265)(45, 302)(46, 303)(47, 269)(48, 272)(49, 270)(50, 306)(51, 307)(52, 273)(53, 275)(54, 310)(55, 311)(56, 278)(57, 313)(58, 281)(59, 282)(60, 316)(61, 284)(62, 318)(63, 319)(64, 287)(65, 289)(66, 322)(67, 323)(68, 292)(69, 293)(70, 326)(71, 327)(72, 296)(73, 329)(74, 298)(75, 299)(76, 332)(77, 301)(78, 334)(79, 335)(80, 304)(81, 305)(82, 338)(83, 339)(84, 308)(85, 309)(86, 342)(87, 343)(88, 312)(89, 345)(90, 314)(91, 315)(92, 336)(93, 317)(94, 349)(95, 350)(96, 320)(97, 321)(98, 352)(99, 353)(100, 324)(101, 325)(102, 344)(103, 356)(104, 328)(105, 357)(106, 330)(107, 331)(108, 333)(109, 347)(110, 346)(111, 337)(112, 354)(113, 360)(114, 340)(115, 341)(116, 355)(117, 358)(118, 348)(119, 351)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2084
Graph:: bipartite
	v = 38 e = 240 f = 150
	degree seq :: [ 8^30, 30^8 ]

E27.2084 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 15})
Quotient :: dipole
Aut^+ = (C5 x A4) : C2 (small group id <120, 38>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2^-1)^2, (Y3^-1 * Y1^-1)^15 ]
Map:: polytopal
	R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362, 246, 366, 244, 364)(243, 363, 249, 369, 261, 381, 251, 371)(245, 365, 253, 373, 258, 378, 247, 367)(248, 368, 259, 379, 271, 391, 255, 375)(250, 370, 263, 383, 277, 397, 260, 380)(252, 372, 256, 376, 272, 392, 267, 387)(254, 374, 266, 386, 284, 404, 268, 388)(257, 377, 274, 394, 291, 411, 273, 393)(262, 382, 270, 390, 288, 408, 279, 399)(264, 384, 278, 398, 289, 409, 281, 401)(265, 385, 280, 400, 290, 410, 276, 396)(269, 389, 275, 395, 292, 412, 285, 405)(282, 402, 297, 417, 305, 425, 295, 415)(283, 403, 298, 418, 313, 433, 299, 419)(286, 406, 301, 421, 307, 427, 293, 413)(287, 407, 303, 423, 309, 429, 294, 414)(296, 416, 311, 431, 321, 441, 306, 426)(300, 420, 315, 435, 327, 447, 312, 432)(302, 422, 308, 428, 323, 443, 317, 437)(304, 424, 318, 438, 333, 453, 319, 439)(310, 430, 325, 445, 339, 459, 324, 444)(314, 434, 322, 442, 337, 457, 329, 449)(316, 436, 328, 448, 338, 458, 330, 450)(320, 440, 326, 446, 340, 460, 334, 454)(331, 451, 345, 465, 351, 471, 343, 463)(332, 452, 346, 466, 357, 477, 347, 467)(335, 455, 348, 468, 353, 473, 341, 461)(336, 456, 350, 470, 355, 475, 342, 462)(344, 464, 356, 476, 359, 479, 352, 472)(349, 469, 354, 474, 360, 480, 358, 478)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 264)(11, 265)(12, 266)(13, 268)(14, 245)(15, 270)(16, 246)(17, 275)(18, 276)(19, 277)(20, 248)(21, 279)(22, 249)(23, 251)(24, 283)(25, 253)(26, 285)(27, 280)(28, 286)(29, 254)(30, 289)(31, 290)(32, 291)(33, 256)(34, 258)(35, 294)(36, 259)(37, 295)(38, 260)(39, 297)(40, 261)(41, 262)(42, 263)(43, 300)(44, 267)(45, 302)(46, 303)(47, 269)(48, 271)(49, 306)(50, 272)(51, 307)(52, 273)(53, 274)(54, 310)(55, 311)(56, 278)(57, 313)(58, 281)(59, 282)(60, 316)(61, 284)(62, 318)(63, 319)(64, 287)(65, 288)(66, 322)(67, 323)(68, 292)(69, 293)(70, 326)(71, 327)(72, 296)(73, 329)(74, 298)(75, 299)(76, 332)(77, 301)(78, 334)(79, 335)(80, 304)(81, 305)(82, 338)(83, 339)(84, 308)(85, 309)(86, 342)(87, 343)(88, 312)(89, 345)(90, 314)(91, 315)(92, 336)(93, 317)(94, 349)(95, 350)(96, 320)(97, 321)(98, 352)(99, 353)(100, 324)(101, 325)(102, 344)(103, 356)(104, 328)(105, 357)(106, 330)(107, 331)(108, 333)(109, 346)(110, 347)(111, 337)(112, 354)(113, 360)(114, 340)(115, 341)(116, 355)(117, 358)(118, 348)(119, 351)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 8, 30 ), ( 8, 30, 8, 30, 8, 30, 8, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2083
Graph:: simple bipartite
	v = 150 e = 240 f = 38
	degree seq :: [ 2^120, 8^30 ]

E27.2085 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 30, 30})
Quotient :: regular
Aut^+ = C10 x A4 (small group id <120, 43>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2 * T1^-2 * T2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^30, T1^-1 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-3 * T2 * T1^-2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 110, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 10, 4)(3, 7, 15, 24, 33, 42, 48, 57, 66, 72, 81, 90, 96, 105, 114, 118, 115, 107, 99, 91, 83, 75, 67, 59, 51, 43, 35, 27, 18, 8)(6, 13, 26, 32, 41, 50, 56, 65, 74, 80, 89, 98, 104, 113, 120, 117, 109, 101, 93, 85, 77, 69, 61, 53, 45, 37, 29, 21, 17, 14)(9, 19, 16, 12, 25, 34, 40, 49, 58, 64, 73, 82, 88, 97, 106, 112, 119, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 15)(14, 19)(18, 20)(22, 27)(23, 32)(25, 26)(28, 29)(30, 36)(31, 40)(33, 34)(35, 37)(38, 45)(39, 48)(41, 42)(43, 44)(46, 51)(47, 56)(49, 50)(52, 53)(54, 60)(55, 64)(57, 58)(59, 61)(62, 69)(63, 72)(65, 66)(67, 68)(70, 75)(71, 80)(73, 74)(76, 77)(78, 84)(79, 88)(81, 82)(83, 85)(86, 93)(87, 96)(89, 90)(91, 92)(94, 99)(95, 104)(97, 98)(100, 101)(102, 108)(103, 112)(105, 106)(107, 109)(110, 117)(111, 118)(113, 114)(115, 116)(119, 120)
	local type(s) :: { ( 30^30 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 4 e = 60 f = 4
	degree seq :: [ 30^4 ]

E27.2086 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 30, 30})
Quotient :: edge
Aut^+ = C10 x A4 (small group id <120, 43>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2^2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2^-2, T2^30, T2^-1 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 * T1 * T2^-2 ]
Map::
	R = (1, 3, 8, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 107, 115, 110, 102, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 10, 4)(2, 5, 12, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 118, 112, 104, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 119, 117, 109, 101, 93, 85, 77, 69, 61, 53, 45, 37, 29, 21, 13, 16)(9, 19, 11, 17, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 120, 116, 108, 100, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 137)(130, 141)(132, 135)(134, 140)(136, 139)(138, 143)(142, 144)(145, 146)(147, 153)(148, 149)(150, 156)(151, 154)(152, 157)(155, 162)(158, 165)(159, 161)(160, 164)(163, 167)(166, 168)(169, 170)(171, 177)(172, 173)(174, 180)(175, 178)(176, 181)(179, 186)(182, 189)(183, 185)(184, 188)(187, 191)(190, 192)(193, 194)(195, 201)(196, 197)(198, 204)(199, 202)(200, 205)(203, 210)(206, 213)(207, 209)(208, 212)(211, 215)(214, 216)(217, 218)(219, 225)(220, 221)(222, 228)(223, 226)(224, 229)(227, 234)(230, 237)(231, 233)(232, 236)(235, 238)(239, 240)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 60, 60 ), ( 60^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2087
Transitivity :: ET+
Graph:: simple bipartite
	v = 64 e = 120 f = 4
	degree seq :: [ 2^60, 30^4 ]

E27.2087 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 30, 30})
Quotient :: loop
Aut^+ = C10 x A4 (small group id <120, 43>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2^2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2^-2, T2^30, T2^-1 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 * T1 * T2^-2 ]
Map::
	R = (1, 121, 3, 123, 8, 128, 18, 138, 27, 147, 35, 155, 43, 163, 51, 171, 59, 179, 67, 187, 75, 195, 83, 203, 91, 211, 99, 219, 107, 227, 115, 235, 110, 230, 102, 222, 94, 214, 86, 206, 78, 198, 70, 190, 62, 182, 54, 174, 46, 166, 38, 158, 30, 150, 22, 142, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 23, 143, 31, 151, 39, 159, 47, 167, 55, 175, 63, 183, 71, 191, 79, 199, 87, 207, 95, 215, 103, 223, 111, 231, 118, 238, 112, 232, 104, 224, 96, 216, 88, 208, 80, 200, 72, 192, 64, 184, 56, 176, 48, 168, 40, 160, 32, 152, 24, 144, 14, 134, 6, 126)(7, 127, 15, 135, 25, 145, 33, 153, 41, 161, 49, 169, 57, 177, 65, 185, 73, 193, 81, 201, 89, 209, 97, 217, 105, 225, 113, 233, 119, 239, 117, 237, 109, 229, 101, 221, 93, 213, 85, 205, 77, 197, 69, 189, 61, 181, 53, 173, 45, 165, 37, 157, 29, 149, 21, 141, 13, 133, 16, 136)(9, 129, 19, 139, 11, 131, 17, 137, 26, 146, 34, 154, 42, 162, 50, 170, 58, 178, 66, 186, 74, 194, 82, 202, 90, 210, 98, 218, 106, 226, 114, 234, 120, 240, 116, 236, 108, 228, 100, 220, 92, 212, 84, 204, 76, 196, 68, 188, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 20, 140)
	L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 137)(9, 124)(10, 141)(11, 125)(12, 135)(13, 126)(14, 140)(15, 132)(16, 139)(17, 128)(18, 143)(19, 136)(20, 134)(21, 130)(22, 144)(23, 138)(24, 142)(25, 146)(26, 145)(27, 153)(28, 149)(29, 148)(30, 156)(31, 154)(32, 157)(33, 147)(34, 151)(35, 162)(36, 150)(37, 152)(38, 165)(39, 161)(40, 164)(41, 159)(42, 155)(43, 167)(44, 160)(45, 158)(46, 168)(47, 163)(48, 166)(49, 170)(50, 169)(51, 177)(52, 173)(53, 172)(54, 180)(55, 178)(56, 181)(57, 171)(58, 175)(59, 186)(60, 174)(61, 176)(62, 189)(63, 185)(64, 188)(65, 183)(66, 179)(67, 191)(68, 184)(69, 182)(70, 192)(71, 187)(72, 190)(73, 194)(74, 193)(75, 201)(76, 197)(77, 196)(78, 204)(79, 202)(80, 205)(81, 195)(82, 199)(83, 210)(84, 198)(85, 200)(86, 213)(87, 209)(88, 212)(89, 207)(90, 203)(91, 215)(92, 208)(93, 206)(94, 216)(95, 211)(96, 214)(97, 218)(98, 217)(99, 225)(100, 221)(101, 220)(102, 228)(103, 226)(104, 229)(105, 219)(106, 223)(107, 234)(108, 222)(109, 224)(110, 237)(111, 233)(112, 236)(113, 231)(114, 227)(115, 238)(116, 232)(117, 230)(118, 235)(119, 240)(120, 239)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2086
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 120 f = 64
	degree seq :: [ 60^4 ]

E27.2088 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 30, 30})
Quotient :: dipole
Aut^+ = C10 x A4 (small group id <120, 43>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * R * Y2^2 * R * Y2, Y2^30, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 15, 135)(14, 134, 20, 140)(16, 136, 19, 139)(18, 138, 23, 143)(22, 142, 24, 144)(25, 145, 26, 146)(27, 147, 33, 153)(28, 148, 29, 149)(30, 150, 36, 156)(31, 151, 34, 154)(32, 152, 37, 157)(35, 155, 42, 162)(38, 158, 45, 165)(39, 159, 41, 161)(40, 160, 44, 164)(43, 163, 47, 167)(46, 166, 48, 168)(49, 169, 50, 170)(51, 171, 57, 177)(52, 172, 53, 173)(54, 174, 60, 180)(55, 175, 58, 178)(56, 176, 61, 181)(59, 179, 66, 186)(62, 182, 69, 189)(63, 183, 65, 185)(64, 184, 68, 188)(67, 187, 71, 191)(70, 190, 72, 192)(73, 193, 74, 194)(75, 195, 81, 201)(76, 196, 77, 197)(78, 198, 84, 204)(79, 199, 82, 202)(80, 200, 85, 205)(83, 203, 90, 210)(86, 206, 93, 213)(87, 207, 89, 209)(88, 208, 92, 212)(91, 211, 95, 215)(94, 214, 96, 216)(97, 217, 98, 218)(99, 219, 105, 225)(100, 220, 101, 221)(102, 222, 108, 228)(103, 223, 106, 226)(104, 224, 109, 229)(107, 227, 114, 234)(110, 230, 117, 237)(111, 231, 113, 233)(112, 232, 116, 236)(115, 235, 118, 238)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 267, 387, 275, 395, 283, 403, 291, 411, 299, 419, 307, 427, 315, 435, 323, 443, 331, 451, 339, 459, 347, 467, 355, 475, 350, 470, 342, 462, 334, 454, 326, 446, 318, 438, 310, 430, 302, 422, 294, 414, 286, 406, 278, 398, 270, 390, 262, 382, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 263, 383, 271, 391, 279, 399, 287, 407, 295, 415, 303, 423, 311, 431, 319, 439, 327, 447, 335, 455, 343, 463, 351, 471, 358, 478, 352, 472, 344, 464, 336, 456, 328, 448, 320, 440, 312, 432, 304, 424, 296, 416, 288, 408, 280, 400, 272, 392, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 265, 385, 273, 393, 281, 401, 289, 409, 297, 417, 305, 425, 313, 433, 321, 441, 329, 449, 337, 457, 345, 465, 353, 473, 359, 479, 357, 477, 349, 469, 341, 461, 333, 453, 325, 445, 317, 437, 309, 429, 301, 421, 293, 413, 285, 405, 277, 397, 269, 389, 261, 381, 253, 373, 256, 376)(249, 369, 259, 379, 251, 371, 257, 377, 266, 386, 274, 394, 282, 402, 290, 410, 298, 418, 306, 426, 314, 434, 322, 442, 330, 450, 338, 458, 346, 466, 354, 474, 360, 480, 356, 476, 348, 468, 340, 460, 332, 452, 324, 444, 316, 436, 308, 428, 300, 420, 292, 412, 284, 404, 276, 396, 268, 388, 260, 380)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 255)(13, 246)(14, 260)(15, 252)(16, 259)(17, 248)(18, 263)(19, 256)(20, 254)(21, 250)(22, 264)(23, 258)(24, 262)(25, 266)(26, 265)(27, 273)(28, 269)(29, 268)(30, 276)(31, 274)(32, 277)(33, 267)(34, 271)(35, 282)(36, 270)(37, 272)(38, 285)(39, 281)(40, 284)(41, 279)(42, 275)(43, 287)(44, 280)(45, 278)(46, 288)(47, 283)(48, 286)(49, 290)(50, 289)(51, 297)(52, 293)(53, 292)(54, 300)(55, 298)(56, 301)(57, 291)(58, 295)(59, 306)(60, 294)(61, 296)(62, 309)(63, 305)(64, 308)(65, 303)(66, 299)(67, 311)(68, 304)(69, 302)(70, 312)(71, 307)(72, 310)(73, 314)(74, 313)(75, 321)(76, 317)(77, 316)(78, 324)(79, 322)(80, 325)(81, 315)(82, 319)(83, 330)(84, 318)(85, 320)(86, 333)(87, 329)(88, 332)(89, 327)(90, 323)(91, 335)(92, 328)(93, 326)(94, 336)(95, 331)(96, 334)(97, 338)(98, 337)(99, 345)(100, 341)(101, 340)(102, 348)(103, 346)(104, 349)(105, 339)(106, 343)(107, 354)(108, 342)(109, 344)(110, 357)(111, 353)(112, 356)(113, 351)(114, 347)(115, 358)(116, 352)(117, 350)(118, 355)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2089
Graph:: bipartite
	v = 64 e = 240 f = 124
	degree seq :: [ 4^60, 60^4 ]

E27.2089 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 30, 30})
Quotient :: dipole
Aut^+ = C10 x A4 (small group id <120, 43>)
Aut   = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^30, Y1^-3 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-3 * Y3 ]
Map::
	R = (1, 121, 2, 122, 5, 125, 11, 131, 23, 143, 31, 151, 39, 159, 47, 167, 55, 175, 63, 183, 71, 191, 79, 199, 87, 207, 95, 215, 103, 223, 111, 231, 110, 230, 102, 222, 94, 214, 86, 206, 78, 198, 70, 190, 62, 182, 54, 174, 46, 166, 38, 158, 30, 150, 22, 142, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 24, 144, 33, 153, 42, 162, 48, 168, 57, 177, 66, 186, 72, 192, 81, 201, 90, 210, 96, 216, 105, 225, 114, 234, 118, 238, 115, 235, 107, 227, 99, 219, 91, 211, 83, 203, 75, 195, 67, 187, 59, 179, 51, 171, 43, 163, 35, 155, 27, 147, 18, 138, 8, 128)(6, 126, 13, 133, 26, 146, 32, 152, 41, 161, 50, 170, 56, 176, 65, 185, 74, 194, 80, 200, 89, 209, 98, 218, 104, 224, 113, 233, 120, 240, 117, 237, 109, 229, 101, 221, 93, 213, 85, 205, 77, 197, 69, 189, 61, 181, 53, 173, 45, 165, 37, 157, 29, 149, 21, 141, 17, 137, 14, 134)(9, 129, 19, 139, 16, 136, 12, 132, 25, 145, 34, 154, 40, 160, 49, 169, 58, 178, 64, 184, 73, 193, 82, 202, 88, 208, 97, 217, 106, 226, 112, 232, 119, 239, 116, 236, 108, 228, 100, 220, 92, 212, 84, 204, 76, 196, 68, 188, 60, 180, 52, 172, 44, 164, 36, 156, 28, 148, 20, 140)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480)
	L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 261)(11, 264)(12, 245)(13, 255)(14, 259)(15, 253)(16, 247)(17, 248)(18, 260)(19, 254)(20, 258)(21, 250)(22, 267)(23, 272)(24, 251)(25, 266)(26, 265)(27, 262)(28, 269)(29, 268)(30, 276)(31, 280)(32, 263)(33, 274)(34, 273)(35, 277)(36, 270)(37, 275)(38, 285)(39, 288)(40, 271)(41, 282)(42, 281)(43, 284)(44, 283)(45, 278)(46, 291)(47, 296)(48, 279)(49, 290)(50, 289)(51, 286)(52, 293)(53, 292)(54, 300)(55, 304)(56, 287)(57, 298)(58, 297)(59, 301)(60, 294)(61, 299)(62, 309)(63, 312)(64, 295)(65, 306)(66, 305)(67, 308)(68, 307)(69, 302)(70, 315)(71, 320)(72, 303)(73, 314)(74, 313)(75, 310)(76, 317)(77, 316)(78, 324)(79, 328)(80, 311)(81, 322)(82, 321)(83, 325)(84, 318)(85, 323)(86, 333)(87, 336)(88, 319)(89, 330)(90, 329)(91, 332)(92, 331)(93, 326)(94, 339)(95, 344)(96, 327)(97, 338)(98, 337)(99, 334)(100, 341)(101, 340)(102, 348)(103, 352)(104, 335)(105, 346)(106, 345)(107, 349)(108, 342)(109, 347)(110, 357)(111, 358)(112, 343)(113, 354)(114, 353)(115, 356)(116, 355)(117, 350)(118, 351)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2088
Graph:: simple bipartite
	v = 124 e = 240 f = 64
	degree seq :: [ 2^120, 60^4 ]

E27.2090 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 20, 60})
Quotient :: regular
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-13 * T2 * T1^-4 * T2 * T1^-3 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 101, 113, 107, 95, 83, 71, 59, 47, 33, 17, 29, 44, 31, 45, 58, 70, 82, 94, 106, 118, 120, 119, 108, 96, 84, 72, 60, 48, 34, 46, 32, 16, 28, 43, 57, 69, 81, 93, 105, 117, 112, 100, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 24, 41, 56, 66, 79, 92, 102, 115, 110, 98, 86, 74, 62, 50, 36, 20, 9, 19, 26, 12, 25, 42, 54, 67, 80, 90, 103, 116, 111, 99, 87, 75, 63, 51, 37, 21, 30, 14, 6, 13, 27, 40, 55, 68, 78, 91, 104, 114, 109, 97, 85, 73, 61, 49, 35, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 66)(55, 69)(56, 70)(61, 72)(62, 71)(64, 73)(65, 78)(67, 81)(68, 82)(74, 84)(75, 83)(76, 86)(77, 90)(79, 93)(80, 94)(85, 95)(87, 96)(88, 99)(89, 102)(91, 105)(92, 106)(97, 108)(98, 107)(100, 109)(101, 114)(103, 117)(104, 118)(110, 119)(111, 113)(112, 115)(116, 120)
	local type(s) :: { ( 20^60 ) }
Outer automorphisms :: reflexible
Dual of E27.2091
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 60 f = 6
	degree seq :: [ 60^2 ]

E27.2091 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 20, 60})
Quotient :: regular
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2, T1^20, (T2 * T1^-1 * T2 * T1^-3)^15 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 32, 47, 61, 73, 85, 97, 96, 84, 72, 60, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 62, 75, 86, 99, 108, 105, 93, 81, 69, 57, 43, 28, 17, 8)(6, 13, 21, 34, 48, 63, 74, 87, 98, 109, 107, 95, 83, 71, 59, 45, 30, 18, 9, 14)(15, 25, 35, 51, 64, 77, 88, 101, 110, 117, 114, 104, 92, 80, 68, 56, 42, 27, 16, 26)(23, 36, 50, 65, 76, 89, 100, 111, 116, 115, 106, 94, 82, 70, 58, 44, 29, 38, 24, 37)(39, 52, 66, 78, 90, 102, 112, 118, 120, 119, 113, 103, 91, 79, 67, 55, 41, 54, 40, 53)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 55)(45, 58)(46, 59)(47, 62)(49, 64)(51, 66)(56, 67)(57, 68)(60, 69)(61, 74)(63, 76)(65, 78)(70, 79)(71, 82)(72, 83)(73, 86)(75, 88)(77, 90)(80, 91)(81, 92)(84, 93)(85, 98)(87, 100)(89, 102)(94, 103)(95, 106)(96, 107)(97, 108)(99, 110)(101, 112)(104, 113)(105, 114)(109, 116)(111, 118)(115, 119)(117, 120)
	local type(s) :: { ( 60^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2090
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 6 e = 60 f = 2
	degree seq :: [ 20^6 ]

E27.2092 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 20, 60})
Quotient :: edge
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^20, (T1 * T2^-1 * T1 * T2^-3)^15 ]
Map::
	R = (1, 3, 8, 17, 28, 43, 57, 69, 81, 93, 105, 96, 84, 72, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 63, 75, 87, 99, 110, 102, 90, 78, 66, 54, 38, 24, 14, 6)(7, 15, 26, 41, 56, 68, 80, 92, 104, 114, 107, 95, 83, 71, 59, 45, 30, 18, 9, 16)(11, 20, 33, 49, 62, 74, 86, 98, 109, 117, 112, 101, 89, 77, 65, 53, 37, 23, 13, 21)(25, 39, 55, 67, 79, 91, 103, 113, 119, 115, 106, 94, 82, 70, 58, 44, 29, 42, 27, 40)(32, 47, 61, 73, 85, 97, 108, 116, 120, 118, 111, 100, 88, 76, 64, 52, 36, 50, 34, 48)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 132)(130, 134)(135, 145)(136, 147)(137, 146)(138, 149)(139, 150)(140, 152)(141, 154)(142, 153)(143, 156)(144, 157)(148, 155)(151, 158)(159, 167)(160, 168)(161, 175)(162, 170)(163, 176)(164, 172)(165, 178)(166, 179)(169, 181)(171, 182)(173, 184)(174, 185)(177, 183)(180, 186)(187, 193)(188, 199)(189, 200)(190, 196)(191, 202)(192, 203)(194, 205)(195, 206)(197, 208)(198, 209)(201, 207)(204, 210)(211, 217)(212, 223)(213, 224)(214, 220)(215, 226)(216, 227)(218, 228)(219, 229)(221, 231)(222, 232)(225, 230)(233, 236)(234, 239)(235, 238)(237, 240)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 120, 120 ), ( 120^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2096
Transitivity :: ET+
Graph:: simple bipartite
	v = 66 e = 120 f = 2
	degree seq :: [ 2^60, 20^6 ]

E27.2093 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 20, 60})
Quotient :: edge
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-1 * T2^3 * T1 * T2^-3, T2^10 * T1^-1 * T2^5 * T1^-1 * T2 * T1^-2, T2^-1 * T1 * T2^-1 * T1^17 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 47, 61, 73, 85, 97, 109, 118, 104, 91, 81, 71, 59, 38, 18, 6, 17, 36, 57, 41, 30, 52, 66, 78, 90, 102, 114, 115, 105, 95, 84, 70, 54, 34, 21, 42, 60, 39, 20, 13, 28, 50, 64, 76, 88, 100, 112, 119, 108, 94, 80, 67, 55, 43, 33, 15, 5)(2, 7, 19, 40, 26, 49, 65, 74, 87, 101, 110, 116, 103, 93, 83, 72, 56, 35, 16, 14, 31, 46, 24, 11, 27, 51, 62, 75, 89, 98, 111, 117, 107, 96, 82, 68, 53, 37, 32, 45, 23, 9, 4, 12, 29, 48, 63, 77, 86, 99, 113, 120, 106, 92, 79, 69, 58, 44, 22, 8)(121, 122, 126, 136, 154, 173, 187, 199, 211, 223, 235, 231, 220, 206, 193, 185, 172, 147, 133, 124)(123, 129, 137, 128, 141, 155, 175, 188, 201, 212, 225, 236, 232, 218, 205, 197, 186, 169, 148, 131)(125, 134, 138, 157, 174, 189, 200, 213, 224, 237, 234, 219, 208, 194, 181, 171, 150, 132, 140, 127)(130, 144, 156, 143, 162, 142, 163, 176, 191, 202, 215, 226, 239, 230, 217, 209, 198, 183, 170, 146)(135, 152, 158, 178, 190, 203, 214, 227, 238, 233, 222, 207, 196, 182, 167, 149, 161, 139, 159, 151)(145, 160, 177, 166, 180, 165, 153, 164, 179, 192, 204, 216, 228, 240, 229, 221, 210, 195, 184, 168)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4^20 ), ( 4^60 ) }
Outer automorphisms :: reflexible
Dual of E27.2097
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 120 f = 60
	degree seq :: [ 20^6, 60^2 ]

E27.2094 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 20, 60})
Quotient :: edge
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-19 * T2 * T1^-1 * T2 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 32)(20, 33)(22, 35)(23, 40)(25, 43)(26, 44)(27, 45)(30, 46)(36, 48)(37, 47)(38, 50)(39, 54)(41, 57)(42, 58)(49, 59)(51, 60)(52, 63)(53, 66)(55, 69)(56, 70)(61, 72)(62, 71)(64, 73)(65, 78)(67, 81)(68, 82)(74, 84)(75, 83)(76, 86)(77, 90)(79, 93)(80, 94)(85, 95)(87, 96)(88, 99)(89, 102)(91, 105)(92, 106)(97, 108)(98, 107)(100, 109)(101, 114)(103, 117)(104, 118)(110, 119)(111, 113)(112, 115)(116, 120)(121, 122, 125, 131, 143, 159, 173, 185, 197, 209, 221, 233, 227, 215, 203, 191, 179, 167, 153, 137, 149, 164, 151, 165, 178, 190, 202, 214, 226, 238, 240, 239, 228, 216, 204, 192, 180, 168, 154, 166, 152, 136, 148, 163, 177, 189, 201, 213, 225, 237, 232, 220, 208, 196, 184, 172, 158, 142, 130, 124)(123, 127, 135, 144, 161, 176, 186, 199, 212, 222, 235, 230, 218, 206, 194, 182, 170, 156, 140, 129, 139, 146, 132, 145, 162, 174, 187, 200, 210, 223, 236, 231, 219, 207, 195, 183, 171, 157, 141, 150, 134, 126, 133, 147, 160, 175, 188, 198, 211, 224, 234, 229, 217, 205, 193, 181, 169, 155, 138, 128)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 40, 40 ), ( 40^60 ) }
Outer automorphisms :: reflexible
Dual of E27.2095
Transitivity :: ET+
Graph:: simple bipartite
	v = 62 e = 120 f = 6
	degree seq :: [ 2^60, 60^2 ]

E27.2095 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 20, 60})
Quotient :: loop
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, T2^20, (T1 * T2^-1 * T1 * T2^-3)^15 ]
Map::
	R = (1, 121, 3, 123, 8, 128, 17, 137, 28, 148, 43, 163, 57, 177, 69, 189, 81, 201, 93, 213, 105, 225, 96, 216, 84, 204, 72, 192, 60, 180, 46, 166, 31, 151, 19, 139, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 22, 142, 35, 155, 51, 171, 63, 183, 75, 195, 87, 207, 99, 219, 110, 230, 102, 222, 90, 210, 78, 198, 66, 186, 54, 174, 38, 158, 24, 144, 14, 134, 6, 126)(7, 127, 15, 135, 26, 146, 41, 161, 56, 176, 68, 188, 80, 200, 92, 212, 104, 224, 114, 234, 107, 227, 95, 215, 83, 203, 71, 191, 59, 179, 45, 165, 30, 150, 18, 138, 9, 129, 16, 136)(11, 131, 20, 140, 33, 153, 49, 169, 62, 182, 74, 194, 86, 206, 98, 218, 109, 229, 117, 237, 112, 232, 101, 221, 89, 209, 77, 197, 65, 185, 53, 173, 37, 157, 23, 143, 13, 133, 21, 141)(25, 145, 39, 159, 55, 175, 67, 187, 79, 199, 91, 211, 103, 223, 113, 233, 119, 239, 115, 235, 106, 226, 94, 214, 82, 202, 70, 190, 58, 178, 44, 164, 29, 149, 42, 162, 27, 147, 40, 160)(32, 152, 47, 167, 61, 181, 73, 193, 85, 205, 97, 217, 108, 228, 116, 236, 120, 240, 118, 238, 111, 231, 100, 220, 88, 208, 76, 196, 64, 184, 52, 172, 36, 156, 50, 170, 34, 154, 48, 168)
	L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 132)(9, 124)(10, 134)(11, 125)(12, 128)(13, 126)(14, 130)(15, 145)(16, 147)(17, 146)(18, 149)(19, 150)(20, 152)(21, 154)(22, 153)(23, 156)(24, 157)(25, 135)(26, 137)(27, 136)(28, 155)(29, 138)(30, 139)(31, 158)(32, 140)(33, 142)(34, 141)(35, 148)(36, 143)(37, 144)(38, 151)(39, 167)(40, 168)(41, 175)(42, 170)(43, 176)(44, 172)(45, 178)(46, 179)(47, 159)(48, 160)(49, 181)(50, 162)(51, 182)(52, 164)(53, 184)(54, 185)(55, 161)(56, 163)(57, 183)(58, 165)(59, 166)(60, 186)(61, 169)(62, 171)(63, 177)(64, 173)(65, 174)(66, 180)(67, 193)(68, 199)(69, 200)(70, 196)(71, 202)(72, 203)(73, 187)(74, 205)(75, 206)(76, 190)(77, 208)(78, 209)(79, 188)(80, 189)(81, 207)(82, 191)(83, 192)(84, 210)(85, 194)(86, 195)(87, 201)(88, 197)(89, 198)(90, 204)(91, 217)(92, 223)(93, 224)(94, 220)(95, 226)(96, 227)(97, 211)(98, 228)(99, 229)(100, 214)(101, 231)(102, 232)(103, 212)(104, 213)(105, 230)(106, 215)(107, 216)(108, 218)(109, 219)(110, 225)(111, 221)(112, 222)(113, 236)(114, 239)(115, 238)(116, 233)(117, 240)(118, 235)(119, 234)(120, 237)
	local type(s) :: { ( 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2094
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 120 f = 62
	degree seq :: [ 40^6 ]

E27.2096 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 20, 60})
Quotient :: loop
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-1 * T2^3 * T1 * T2^-3, T2^10 * T1^-1 * T2^5 * T1^-1 * T2 * T1^-2, T2^-1 * T1 * T2^-1 * T1^17 ]
Map::
	R = (1, 121, 3, 123, 10, 130, 25, 145, 47, 167, 61, 181, 73, 193, 85, 205, 97, 217, 109, 229, 118, 238, 104, 224, 91, 211, 81, 201, 71, 191, 59, 179, 38, 158, 18, 138, 6, 126, 17, 137, 36, 156, 57, 177, 41, 161, 30, 150, 52, 172, 66, 186, 78, 198, 90, 210, 102, 222, 114, 234, 115, 235, 105, 225, 95, 215, 84, 204, 70, 190, 54, 174, 34, 154, 21, 141, 42, 162, 60, 180, 39, 159, 20, 140, 13, 133, 28, 148, 50, 170, 64, 184, 76, 196, 88, 208, 100, 220, 112, 232, 119, 239, 108, 228, 94, 214, 80, 200, 67, 187, 55, 175, 43, 163, 33, 153, 15, 135, 5, 125)(2, 122, 7, 127, 19, 139, 40, 160, 26, 146, 49, 169, 65, 185, 74, 194, 87, 207, 101, 221, 110, 230, 116, 236, 103, 223, 93, 213, 83, 203, 72, 192, 56, 176, 35, 155, 16, 136, 14, 134, 31, 151, 46, 166, 24, 144, 11, 131, 27, 147, 51, 171, 62, 182, 75, 195, 89, 209, 98, 218, 111, 231, 117, 237, 107, 227, 96, 216, 82, 202, 68, 188, 53, 173, 37, 157, 32, 152, 45, 165, 23, 143, 9, 129, 4, 124, 12, 132, 29, 149, 48, 168, 63, 183, 77, 197, 86, 206, 99, 219, 113, 233, 120, 240, 106, 226, 92, 212, 79, 199, 69, 189, 58, 178, 44, 164, 22, 142, 8, 128)
	L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 125)(8, 141)(9, 137)(10, 144)(11, 123)(12, 140)(13, 124)(14, 138)(15, 152)(16, 154)(17, 128)(18, 157)(19, 159)(20, 127)(21, 155)(22, 163)(23, 162)(24, 156)(25, 160)(26, 130)(27, 133)(28, 131)(29, 161)(30, 132)(31, 135)(32, 158)(33, 164)(34, 173)(35, 175)(36, 143)(37, 174)(38, 178)(39, 151)(40, 177)(41, 139)(42, 142)(43, 176)(44, 179)(45, 153)(46, 180)(47, 149)(48, 145)(49, 148)(50, 146)(51, 150)(52, 147)(53, 187)(54, 189)(55, 188)(56, 191)(57, 166)(58, 190)(59, 192)(60, 165)(61, 171)(62, 167)(63, 170)(64, 168)(65, 172)(66, 169)(67, 199)(68, 201)(69, 200)(70, 203)(71, 202)(72, 204)(73, 185)(74, 181)(75, 184)(76, 182)(77, 186)(78, 183)(79, 211)(80, 213)(81, 212)(82, 215)(83, 214)(84, 216)(85, 197)(86, 193)(87, 196)(88, 194)(89, 198)(90, 195)(91, 223)(92, 225)(93, 224)(94, 227)(95, 226)(96, 228)(97, 209)(98, 205)(99, 208)(100, 206)(101, 210)(102, 207)(103, 235)(104, 237)(105, 236)(106, 239)(107, 238)(108, 240)(109, 221)(110, 217)(111, 220)(112, 218)(113, 222)(114, 219)(115, 231)(116, 232)(117, 234)(118, 233)(119, 230)(120, 229)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.2092
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 120 f = 66
	degree seq :: [ 120^2 ]

E27.2097 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 20, 60})
Quotient :: loop
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-19 * T2 * T1^-1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 21, 141)(11, 131, 24, 144)(13, 133, 28, 148)(14, 134, 29, 149)(15, 135, 31, 151)(18, 138, 34, 154)(19, 139, 32, 152)(20, 140, 33, 153)(22, 142, 35, 155)(23, 143, 40, 160)(25, 145, 43, 163)(26, 146, 44, 164)(27, 147, 45, 165)(30, 150, 46, 166)(36, 156, 48, 168)(37, 157, 47, 167)(38, 158, 50, 170)(39, 159, 54, 174)(41, 161, 57, 177)(42, 162, 58, 178)(49, 169, 59, 179)(51, 171, 60, 180)(52, 172, 63, 183)(53, 173, 66, 186)(55, 175, 69, 189)(56, 176, 70, 190)(61, 181, 72, 192)(62, 182, 71, 191)(64, 184, 73, 193)(65, 185, 78, 198)(67, 187, 81, 201)(68, 188, 82, 202)(74, 194, 84, 204)(75, 195, 83, 203)(76, 196, 86, 206)(77, 197, 90, 210)(79, 199, 93, 213)(80, 200, 94, 214)(85, 205, 95, 215)(87, 207, 96, 216)(88, 208, 99, 219)(89, 209, 102, 222)(91, 211, 105, 225)(92, 212, 106, 226)(97, 217, 108, 228)(98, 218, 107, 227)(100, 220, 109, 229)(101, 221, 114, 234)(103, 223, 117, 237)(104, 224, 118, 238)(110, 230, 119, 239)(111, 231, 113, 233)(112, 232, 115, 235)(116, 236, 120, 240)
	L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 139)(10, 124)(11, 143)(12, 145)(13, 147)(14, 126)(15, 144)(16, 148)(17, 149)(18, 128)(19, 146)(20, 129)(21, 150)(22, 130)(23, 159)(24, 161)(25, 162)(26, 132)(27, 160)(28, 163)(29, 164)(30, 134)(31, 165)(32, 136)(33, 137)(34, 166)(35, 138)(36, 140)(37, 141)(38, 142)(39, 173)(40, 175)(41, 176)(42, 174)(43, 177)(44, 151)(45, 178)(46, 152)(47, 153)(48, 154)(49, 155)(50, 156)(51, 157)(52, 158)(53, 185)(54, 187)(55, 188)(56, 186)(57, 189)(58, 190)(59, 167)(60, 168)(61, 169)(62, 170)(63, 171)(64, 172)(65, 197)(66, 199)(67, 200)(68, 198)(69, 201)(70, 202)(71, 179)(72, 180)(73, 181)(74, 182)(75, 183)(76, 184)(77, 209)(78, 211)(79, 212)(80, 210)(81, 213)(82, 214)(83, 191)(84, 192)(85, 193)(86, 194)(87, 195)(88, 196)(89, 221)(90, 223)(91, 224)(92, 222)(93, 225)(94, 226)(95, 203)(96, 204)(97, 205)(98, 206)(99, 207)(100, 208)(101, 233)(102, 235)(103, 236)(104, 234)(105, 237)(106, 238)(107, 215)(108, 216)(109, 217)(110, 218)(111, 219)(112, 220)(113, 227)(114, 229)(115, 230)(116, 231)(117, 232)(118, 240)(119, 228)(120, 239)
	local type(s) :: { ( 20, 60, 20, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2093
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 60 e = 120 f = 8
	degree seq :: [ 4^60 ]

E27.2098 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^20, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 12, 132)(10, 130, 14, 134)(15, 135, 25, 145)(16, 136, 27, 147)(17, 137, 26, 146)(18, 138, 29, 149)(19, 139, 30, 150)(20, 140, 32, 152)(21, 141, 34, 154)(22, 142, 33, 153)(23, 143, 36, 156)(24, 144, 37, 157)(28, 148, 35, 155)(31, 151, 38, 158)(39, 159, 47, 167)(40, 160, 48, 168)(41, 161, 55, 175)(42, 162, 50, 170)(43, 163, 56, 176)(44, 164, 52, 172)(45, 165, 58, 178)(46, 166, 59, 179)(49, 169, 61, 181)(51, 171, 62, 182)(53, 173, 64, 184)(54, 174, 65, 185)(57, 177, 63, 183)(60, 180, 66, 186)(67, 187, 73, 193)(68, 188, 79, 199)(69, 189, 80, 200)(70, 190, 76, 196)(71, 191, 82, 202)(72, 192, 83, 203)(74, 194, 85, 205)(75, 195, 86, 206)(77, 197, 88, 208)(78, 198, 89, 209)(81, 201, 87, 207)(84, 204, 90, 210)(91, 211, 97, 217)(92, 212, 103, 223)(93, 213, 104, 224)(94, 214, 100, 220)(95, 215, 106, 226)(96, 216, 107, 227)(98, 218, 108, 228)(99, 219, 109, 229)(101, 221, 111, 231)(102, 222, 112, 232)(105, 225, 110, 230)(113, 233, 116, 236)(114, 234, 119, 239)(115, 235, 118, 238)(117, 237, 120, 240)(241, 361, 243, 363, 248, 368, 257, 377, 268, 388, 283, 403, 297, 417, 309, 429, 321, 441, 333, 453, 345, 465, 336, 456, 324, 444, 312, 432, 300, 420, 286, 406, 271, 391, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 275, 395, 291, 411, 303, 423, 315, 435, 327, 447, 339, 459, 350, 470, 342, 462, 330, 450, 318, 438, 306, 426, 294, 414, 278, 398, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 266, 386, 281, 401, 296, 416, 308, 428, 320, 440, 332, 452, 344, 464, 354, 474, 347, 467, 335, 455, 323, 443, 311, 431, 299, 419, 285, 405, 270, 390, 258, 378, 249, 369, 256, 376)(251, 371, 260, 380, 273, 393, 289, 409, 302, 422, 314, 434, 326, 446, 338, 458, 349, 469, 357, 477, 352, 472, 341, 461, 329, 449, 317, 437, 305, 425, 293, 413, 277, 397, 263, 383, 253, 373, 261, 381)(265, 385, 279, 399, 295, 415, 307, 427, 319, 439, 331, 451, 343, 463, 353, 473, 359, 479, 355, 475, 346, 466, 334, 454, 322, 442, 310, 430, 298, 418, 284, 404, 269, 389, 282, 402, 267, 387, 280, 400)(272, 392, 287, 407, 301, 421, 313, 433, 325, 445, 337, 457, 348, 468, 356, 476, 360, 480, 358, 478, 351, 471, 340, 460, 328, 448, 316, 436, 304, 424, 292, 412, 276, 396, 290, 410, 274, 394, 288, 408)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 252)(9, 244)(10, 254)(11, 245)(12, 248)(13, 246)(14, 250)(15, 265)(16, 267)(17, 266)(18, 269)(19, 270)(20, 272)(21, 274)(22, 273)(23, 276)(24, 277)(25, 255)(26, 257)(27, 256)(28, 275)(29, 258)(30, 259)(31, 278)(32, 260)(33, 262)(34, 261)(35, 268)(36, 263)(37, 264)(38, 271)(39, 287)(40, 288)(41, 295)(42, 290)(43, 296)(44, 292)(45, 298)(46, 299)(47, 279)(48, 280)(49, 301)(50, 282)(51, 302)(52, 284)(53, 304)(54, 305)(55, 281)(56, 283)(57, 303)(58, 285)(59, 286)(60, 306)(61, 289)(62, 291)(63, 297)(64, 293)(65, 294)(66, 300)(67, 313)(68, 319)(69, 320)(70, 316)(71, 322)(72, 323)(73, 307)(74, 325)(75, 326)(76, 310)(77, 328)(78, 329)(79, 308)(80, 309)(81, 327)(82, 311)(83, 312)(84, 330)(85, 314)(86, 315)(87, 321)(88, 317)(89, 318)(90, 324)(91, 337)(92, 343)(93, 344)(94, 340)(95, 346)(96, 347)(97, 331)(98, 348)(99, 349)(100, 334)(101, 351)(102, 352)(103, 332)(104, 333)(105, 350)(106, 335)(107, 336)(108, 338)(109, 339)(110, 345)(111, 341)(112, 342)(113, 356)(114, 359)(115, 358)(116, 353)(117, 360)(118, 355)(119, 354)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 120, 2, 120 ), ( 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120, 2, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.2101
Graph:: bipartite
	v = 66 e = 240 f = 122
	degree seq :: [ 4^60, 40^6 ]

E27.2099 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y2^3 * Y1^-1 * Y2^-3 * Y1, Y2 * Y1^-1 * Y2^3 * Y1^-1 * Y2^-1 * Y1^5 * Y2^-1 * Y1 * Y2^2, Y2^-1 * Y1 * Y2^-1 * Y1^17, Y2^60 ]
Map::
	R = (1, 121, 2, 122, 6, 126, 16, 136, 34, 154, 53, 173, 67, 187, 79, 199, 91, 211, 103, 223, 115, 235, 111, 231, 100, 220, 86, 206, 73, 193, 65, 185, 52, 172, 27, 147, 13, 133, 4, 124)(3, 123, 9, 129, 17, 137, 8, 128, 21, 141, 35, 155, 55, 175, 68, 188, 81, 201, 92, 212, 105, 225, 116, 236, 112, 232, 98, 218, 85, 205, 77, 197, 66, 186, 49, 169, 28, 148, 11, 131)(5, 125, 14, 134, 18, 138, 37, 157, 54, 174, 69, 189, 80, 200, 93, 213, 104, 224, 117, 237, 114, 234, 99, 219, 88, 208, 74, 194, 61, 181, 51, 171, 30, 150, 12, 132, 20, 140, 7, 127)(10, 130, 24, 144, 36, 156, 23, 143, 42, 162, 22, 142, 43, 163, 56, 176, 71, 191, 82, 202, 95, 215, 106, 226, 119, 239, 110, 230, 97, 217, 89, 209, 78, 198, 63, 183, 50, 170, 26, 146)(15, 135, 32, 152, 38, 158, 58, 178, 70, 190, 83, 203, 94, 214, 107, 227, 118, 238, 113, 233, 102, 222, 87, 207, 76, 196, 62, 182, 47, 167, 29, 149, 41, 161, 19, 139, 39, 159, 31, 151)(25, 145, 40, 160, 57, 177, 46, 166, 60, 180, 45, 165, 33, 153, 44, 164, 59, 179, 72, 192, 84, 204, 96, 216, 108, 228, 120, 240, 109, 229, 101, 221, 90, 210, 75, 195, 64, 184, 48, 168)(241, 361, 243, 363, 250, 370, 265, 385, 287, 407, 301, 421, 313, 433, 325, 445, 337, 457, 349, 469, 358, 478, 344, 464, 331, 451, 321, 441, 311, 431, 299, 419, 278, 398, 258, 378, 246, 366, 257, 377, 276, 396, 297, 417, 281, 401, 270, 390, 292, 412, 306, 426, 318, 438, 330, 450, 342, 462, 354, 474, 355, 475, 345, 465, 335, 455, 324, 444, 310, 430, 294, 414, 274, 394, 261, 381, 282, 402, 300, 420, 279, 399, 260, 380, 253, 373, 268, 388, 290, 410, 304, 424, 316, 436, 328, 448, 340, 460, 352, 472, 359, 479, 348, 468, 334, 454, 320, 440, 307, 427, 295, 415, 283, 403, 273, 393, 255, 375, 245, 365)(242, 362, 247, 367, 259, 379, 280, 400, 266, 386, 289, 409, 305, 425, 314, 434, 327, 447, 341, 461, 350, 470, 356, 476, 343, 463, 333, 453, 323, 443, 312, 432, 296, 416, 275, 395, 256, 376, 254, 374, 271, 391, 286, 406, 264, 384, 251, 371, 267, 387, 291, 411, 302, 422, 315, 435, 329, 449, 338, 458, 351, 471, 357, 477, 347, 467, 336, 456, 322, 442, 308, 428, 293, 413, 277, 397, 272, 392, 285, 405, 263, 383, 249, 369, 244, 364, 252, 372, 269, 389, 288, 408, 303, 423, 317, 437, 326, 446, 339, 459, 353, 473, 360, 480, 346, 466, 332, 452, 319, 439, 309, 429, 298, 418, 284, 404, 262, 382, 248, 368)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 265)(11, 267)(12, 269)(13, 268)(14, 271)(15, 245)(16, 254)(17, 276)(18, 246)(19, 280)(20, 253)(21, 282)(22, 248)(23, 249)(24, 251)(25, 287)(26, 289)(27, 291)(28, 290)(29, 288)(30, 292)(31, 286)(32, 285)(33, 255)(34, 261)(35, 256)(36, 297)(37, 272)(38, 258)(39, 260)(40, 266)(41, 270)(42, 300)(43, 273)(44, 262)(45, 263)(46, 264)(47, 301)(48, 303)(49, 305)(50, 304)(51, 302)(52, 306)(53, 277)(54, 274)(55, 283)(56, 275)(57, 281)(58, 284)(59, 278)(60, 279)(61, 313)(62, 315)(63, 317)(64, 316)(65, 314)(66, 318)(67, 295)(68, 293)(69, 298)(70, 294)(71, 299)(72, 296)(73, 325)(74, 327)(75, 329)(76, 328)(77, 326)(78, 330)(79, 309)(80, 307)(81, 311)(82, 308)(83, 312)(84, 310)(85, 337)(86, 339)(87, 341)(88, 340)(89, 338)(90, 342)(91, 321)(92, 319)(93, 323)(94, 320)(95, 324)(96, 322)(97, 349)(98, 351)(99, 353)(100, 352)(101, 350)(102, 354)(103, 333)(104, 331)(105, 335)(106, 332)(107, 336)(108, 334)(109, 358)(110, 356)(111, 357)(112, 359)(113, 360)(114, 355)(115, 345)(116, 343)(117, 347)(118, 344)(119, 348)(120, 346)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2100
Graph:: bipartite
	v = 8 e = 240 f = 180
	degree seq :: [ 40^6, 120^2 ]

E27.2100 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^3 * Y2 * Y3^-2, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3, Y3^13 * Y2 * Y3^4 * Y2 * Y3^3, (Y3^-1 * Y1^-1)^60 ]
Map:: polytopal
	R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 257, 377)(250, 370, 261, 381)(252, 372, 265, 385)(254, 374, 269, 389)(255, 375, 263, 383)(256, 376, 267, 387)(258, 378, 266, 386)(259, 379, 264, 384)(260, 380, 268, 388)(262, 382, 270, 390)(271, 391, 281, 401)(272, 392, 280, 400)(273, 393, 279, 399)(274, 394, 282, 402)(275, 395, 287, 407)(276, 396, 285, 405)(277, 397, 284, 404)(278, 398, 290, 410)(283, 403, 293, 413)(286, 406, 296, 416)(288, 408, 294, 414)(289, 409, 300, 420)(291, 411, 297, 417)(292, 412, 303, 423)(295, 415, 306, 426)(298, 418, 309, 429)(299, 419, 305, 425)(301, 421, 307, 427)(302, 422, 308, 428)(304, 424, 310, 430)(311, 431, 318, 438)(312, 432, 317, 437)(313, 433, 323, 443)(314, 434, 321, 441)(315, 435, 320, 440)(316, 436, 326, 446)(319, 439, 329, 449)(322, 442, 332, 452)(324, 444, 330, 450)(325, 445, 336, 456)(327, 447, 333, 453)(328, 448, 339, 459)(331, 451, 342, 462)(334, 454, 345, 465)(335, 455, 341, 461)(337, 457, 343, 463)(338, 458, 344, 464)(340, 460, 346, 466)(347, 467, 354, 474)(348, 468, 353, 473)(349, 469, 358, 478)(350, 470, 357, 477)(351, 471, 356, 476)(352, 472, 355, 475)(359, 479, 360, 480)
	L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 258)(9, 259)(10, 244)(11, 263)(12, 266)(13, 267)(14, 246)(15, 271)(16, 247)(17, 273)(18, 275)(19, 274)(20, 249)(21, 272)(22, 250)(23, 279)(24, 251)(25, 281)(26, 283)(27, 282)(28, 253)(29, 280)(30, 254)(31, 287)(32, 256)(33, 288)(34, 257)(35, 289)(36, 260)(37, 261)(38, 262)(39, 293)(40, 264)(41, 294)(42, 265)(43, 295)(44, 268)(45, 269)(46, 270)(47, 299)(48, 300)(49, 301)(50, 276)(51, 277)(52, 278)(53, 305)(54, 306)(55, 307)(56, 284)(57, 285)(58, 286)(59, 311)(60, 312)(61, 313)(62, 290)(63, 291)(64, 292)(65, 317)(66, 318)(67, 319)(68, 296)(69, 297)(70, 298)(71, 323)(72, 324)(73, 325)(74, 302)(75, 303)(76, 304)(77, 329)(78, 330)(79, 331)(80, 308)(81, 309)(82, 310)(83, 335)(84, 336)(85, 337)(86, 314)(87, 315)(88, 316)(89, 341)(90, 342)(91, 343)(92, 320)(93, 321)(94, 322)(95, 347)(96, 348)(97, 349)(98, 326)(99, 327)(100, 328)(101, 353)(102, 354)(103, 355)(104, 332)(105, 333)(106, 334)(107, 358)(108, 359)(109, 356)(110, 338)(111, 339)(112, 340)(113, 352)(114, 360)(115, 350)(116, 344)(117, 345)(118, 346)(119, 351)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 40, 120 ), ( 40, 120, 40, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.2099
Graph:: simple bipartite
	v = 180 e = 240 f = 8
	degree seq :: [ 2^120, 4^60 ]

E27.2101 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3, Y3 * Y1^3 * Y3 * Y1^-3, Y1^-19 * Y3 * Y1^-1 * Y3 ]
Map::
	R = (1, 121, 2, 122, 5, 125, 11, 131, 23, 143, 39, 159, 53, 173, 65, 185, 77, 197, 89, 209, 101, 221, 113, 233, 107, 227, 95, 215, 83, 203, 71, 191, 59, 179, 47, 167, 33, 153, 17, 137, 29, 149, 44, 164, 31, 151, 45, 165, 58, 178, 70, 190, 82, 202, 94, 214, 106, 226, 118, 238, 120, 240, 119, 239, 108, 228, 96, 216, 84, 204, 72, 192, 60, 180, 48, 168, 34, 154, 46, 166, 32, 152, 16, 136, 28, 148, 43, 163, 57, 177, 69, 189, 81, 201, 93, 213, 105, 225, 117, 237, 112, 232, 100, 220, 88, 208, 76, 196, 64, 184, 52, 172, 38, 158, 22, 142, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 24, 144, 41, 161, 56, 176, 66, 186, 79, 199, 92, 212, 102, 222, 115, 235, 110, 230, 98, 218, 86, 206, 74, 194, 62, 182, 50, 170, 36, 156, 20, 140, 9, 129, 19, 139, 26, 146, 12, 132, 25, 145, 42, 162, 54, 174, 67, 187, 80, 200, 90, 210, 103, 223, 116, 236, 111, 231, 99, 219, 87, 207, 75, 195, 63, 183, 51, 171, 37, 157, 21, 141, 30, 150, 14, 134, 6, 126, 13, 133, 27, 147, 40, 160, 55, 175, 68, 188, 78, 198, 91, 211, 104, 224, 114, 234, 109, 229, 97, 217, 85, 205, 73, 193, 61, 181, 49, 169, 35, 155, 18, 138, 8, 128)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480)
	L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 261)(11, 264)(12, 245)(13, 268)(14, 269)(15, 271)(16, 247)(17, 248)(18, 274)(19, 272)(20, 273)(21, 250)(22, 275)(23, 280)(24, 251)(25, 283)(26, 284)(27, 285)(28, 253)(29, 254)(30, 286)(31, 255)(32, 259)(33, 260)(34, 258)(35, 262)(36, 288)(37, 287)(38, 290)(39, 294)(40, 263)(41, 297)(42, 298)(43, 265)(44, 266)(45, 267)(46, 270)(47, 277)(48, 276)(49, 299)(50, 278)(51, 300)(52, 303)(53, 306)(54, 279)(55, 309)(56, 310)(57, 281)(58, 282)(59, 289)(60, 291)(61, 312)(62, 311)(63, 292)(64, 313)(65, 318)(66, 293)(67, 321)(68, 322)(69, 295)(70, 296)(71, 302)(72, 301)(73, 304)(74, 324)(75, 323)(76, 326)(77, 330)(78, 305)(79, 333)(80, 334)(81, 307)(82, 308)(83, 315)(84, 314)(85, 335)(86, 316)(87, 336)(88, 339)(89, 342)(90, 317)(91, 345)(92, 346)(93, 319)(94, 320)(95, 325)(96, 327)(97, 348)(98, 347)(99, 328)(100, 349)(101, 354)(102, 329)(103, 357)(104, 358)(105, 331)(106, 332)(107, 338)(108, 337)(109, 340)(110, 359)(111, 353)(112, 355)(113, 351)(114, 341)(115, 352)(116, 360)(117, 343)(118, 344)(119, 350)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2098
Graph:: simple bipartite
	v = 122 e = 240 f = 66
	degree seq :: [ 2^120, 120^2 ]

E27.2102 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-3 * Y1 * Y2^3 * Y1, Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, (Y2^-1 * R * Y2^-2)^2, Y2^19 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 25, 145)(14, 134, 29, 149)(15, 135, 23, 143)(16, 136, 27, 147)(18, 138, 26, 146)(19, 139, 24, 144)(20, 140, 28, 148)(22, 142, 30, 150)(31, 151, 41, 161)(32, 152, 40, 160)(33, 153, 39, 159)(34, 154, 42, 162)(35, 155, 47, 167)(36, 156, 45, 165)(37, 157, 44, 164)(38, 158, 50, 170)(43, 163, 53, 173)(46, 166, 56, 176)(48, 168, 54, 174)(49, 169, 60, 180)(51, 171, 57, 177)(52, 172, 63, 183)(55, 175, 66, 186)(58, 178, 69, 189)(59, 179, 65, 185)(61, 181, 67, 187)(62, 182, 68, 188)(64, 184, 70, 190)(71, 191, 78, 198)(72, 192, 77, 197)(73, 193, 83, 203)(74, 194, 81, 201)(75, 195, 80, 200)(76, 196, 86, 206)(79, 199, 89, 209)(82, 202, 92, 212)(84, 204, 90, 210)(85, 205, 96, 216)(87, 207, 93, 213)(88, 208, 99, 219)(91, 211, 102, 222)(94, 214, 105, 225)(95, 215, 101, 221)(97, 217, 103, 223)(98, 218, 104, 224)(100, 220, 106, 226)(107, 227, 114, 234)(108, 228, 113, 233)(109, 229, 118, 238)(110, 230, 117, 237)(111, 231, 116, 236)(112, 232, 115, 235)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 275, 395, 289, 409, 301, 421, 313, 433, 325, 445, 337, 457, 349, 469, 356, 476, 344, 464, 332, 452, 320, 440, 308, 428, 296, 416, 284, 404, 268, 388, 253, 373, 267, 387, 282, 402, 265, 385, 281, 401, 294, 414, 306, 426, 318, 438, 330, 450, 342, 462, 354, 474, 360, 480, 357, 477, 345, 465, 333, 453, 321, 441, 309, 429, 297, 417, 285, 405, 269, 389, 280, 400, 264, 384, 251, 371, 263, 383, 279, 399, 293, 413, 305, 425, 317, 437, 329, 449, 341, 461, 353, 473, 352, 472, 340, 460, 328, 448, 316, 436, 304, 424, 292, 412, 278, 398, 262, 382, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 266, 386, 283, 403, 295, 415, 307, 427, 319, 439, 331, 451, 343, 463, 355, 475, 350, 470, 338, 458, 326, 446, 314, 434, 302, 422, 290, 410, 276, 396, 260, 380, 249, 369, 259, 379, 274, 394, 257, 377, 273, 393, 288, 408, 300, 420, 312, 432, 324, 444, 336, 456, 348, 468, 359, 479, 351, 471, 339, 459, 327, 447, 315, 435, 303, 423, 291, 411, 277, 397, 261, 381, 272, 392, 256, 376, 247, 367, 255, 375, 271, 391, 287, 407, 299, 419, 311, 431, 323, 443, 335, 455, 347, 467, 358, 478, 346, 466, 334, 454, 322, 442, 310, 430, 298, 418, 286, 406, 270, 390, 254, 374, 246, 366)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 265)(13, 246)(14, 269)(15, 263)(16, 267)(17, 248)(18, 266)(19, 264)(20, 268)(21, 250)(22, 270)(23, 255)(24, 259)(25, 252)(26, 258)(27, 256)(28, 260)(29, 254)(30, 262)(31, 281)(32, 280)(33, 279)(34, 282)(35, 287)(36, 285)(37, 284)(38, 290)(39, 273)(40, 272)(41, 271)(42, 274)(43, 293)(44, 277)(45, 276)(46, 296)(47, 275)(48, 294)(49, 300)(50, 278)(51, 297)(52, 303)(53, 283)(54, 288)(55, 306)(56, 286)(57, 291)(58, 309)(59, 305)(60, 289)(61, 307)(62, 308)(63, 292)(64, 310)(65, 299)(66, 295)(67, 301)(68, 302)(69, 298)(70, 304)(71, 318)(72, 317)(73, 323)(74, 321)(75, 320)(76, 326)(77, 312)(78, 311)(79, 329)(80, 315)(81, 314)(82, 332)(83, 313)(84, 330)(85, 336)(86, 316)(87, 333)(88, 339)(89, 319)(90, 324)(91, 342)(92, 322)(93, 327)(94, 345)(95, 341)(96, 325)(97, 343)(98, 344)(99, 328)(100, 346)(101, 335)(102, 331)(103, 337)(104, 338)(105, 334)(106, 340)(107, 354)(108, 353)(109, 358)(110, 357)(111, 356)(112, 355)(113, 348)(114, 347)(115, 352)(116, 351)(117, 350)(118, 349)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2103
Graph:: bipartite
	v = 62 e = 240 f = 126
	degree seq :: [ 4^60, 120^2 ]

E27.2103 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 20, 60})
Quotient :: dipole
Aut^+ = C20 x S3 (small group id <120, 22>)
Aut   = S3 x D40 (small group id <240, 137>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1 * Y3^-3, Y3^-1 * Y1 * Y3^-1 * Y1^17, Y3^10 * Y1^-1 * Y3^5 * Y1^-1 * Y3 * Y1^-2, (Y3 * Y2^-1)^60 ]
Map::
	R = (1, 121, 2, 122, 6, 126, 16, 136, 34, 154, 53, 173, 67, 187, 79, 199, 91, 211, 103, 223, 115, 235, 111, 231, 100, 220, 86, 206, 73, 193, 65, 185, 52, 172, 27, 147, 13, 133, 4, 124)(3, 123, 9, 129, 17, 137, 8, 128, 21, 141, 35, 155, 55, 175, 68, 188, 81, 201, 92, 212, 105, 225, 116, 236, 112, 232, 98, 218, 85, 205, 77, 197, 66, 186, 49, 169, 28, 148, 11, 131)(5, 125, 14, 134, 18, 138, 37, 157, 54, 174, 69, 189, 80, 200, 93, 213, 104, 224, 117, 237, 114, 234, 99, 219, 88, 208, 74, 194, 61, 181, 51, 171, 30, 150, 12, 132, 20, 140, 7, 127)(10, 130, 24, 144, 36, 156, 23, 143, 42, 162, 22, 142, 43, 163, 56, 176, 71, 191, 82, 202, 95, 215, 106, 226, 119, 239, 110, 230, 97, 217, 89, 209, 78, 198, 63, 183, 50, 170, 26, 146)(15, 135, 32, 152, 38, 158, 58, 178, 70, 190, 83, 203, 94, 214, 107, 227, 118, 238, 113, 233, 102, 222, 87, 207, 76, 196, 62, 182, 47, 167, 29, 149, 41, 161, 19, 139, 39, 159, 31, 151)(25, 145, 40, 160, 57, 177, 46, 166, 60, 180, 45, 165, 33, 153, 44, 164, 59, 179, 72, 192, 84, 204, 96, 216, 108, 228, 120, 240, 109, 229, 101, 221, 90, 210, 75, 195, 64, 184, 48, 168)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 257)(7, 259)(8, 242)(9, 244)(10, 265)(11, 267)(12, 269)(13, 268)(14, 271)(15, 245)(16, 254)(17, 276)(18, 246)(19, 280)(20, 253)(21, 282)(22, 248)(23, 249)(24, 251)(25, 287)(26, 289)(27, 291)(28, 290)(29, 288)(30, 292)(31, 286)(32, 285)(33, 255)(34, 261)(35, 256)(36, 297)(37, 272)(38, 258)(39, 260)(40, 266)(41, 270)(42, 300)(43, 273)(44, 262)(45, 263)(46, 264)(47, 301)(48, 303)(49, 305)(50, 304)(51, 302)(52, 306)(53, 277)(54, 274)(55, 283)(56, 275)(57, 281)(58, 284)(59, 278)(60, 279)(61, 313)(62, 315)(63, 317)(64, 316)(65, 314)(66, 318)(67, 295)(68, 293)(69, 298)(70, 294)(71, 299)(72, 296)(73, 325)(74, 327)(75, 329)(76, 328)(77, 326)(78, 330)(79, 309)(80, 307)(81, 311)(82, 308)(83, 312)(84, 310)(85, 337)(86, 339)(87, 341)(88, 340)(89, 338)(90, 342)(91, 321)(92, 319)(93, 323)(94, 320)(95, 324)(96, 322)(97, 349)(98, 351)(99, 353)(100, 352)(101, 350)(102, 354)(103, 333)(104, 331)(105, 335)(106, 332)(107, 336)(108, 334)(109, 358)(110, 356)(111, 357)(112, 359)(113, 360)(114, 355)(115, 345)(116, 343)(117, 347)(118, 344)(119, 348)(120, 346)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 120 ), ( 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120, 4, 120 ) }
Outer automorphisms :: reflexible
Dual of E27.2102
Graph:: simple bipartite
	v = 126 e = 240 f = 62
	degree seq :: [ 2^120, 40^6 ]

E27.2104 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 14, 63})
Quotient :: regular
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1, T1^2 * T2 * T1^-1 * T2 * T1^6, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2, T1^-3 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^3 * T2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 43, 58, 33, 16, 28, 48, 73, 96, 106, 84, 57, 32, 52, 76, 98, 116, 121, 105, 83, 56, 80, 102, 118, 125, 124, 110, 88, 82, 104, 120, 126, 123, 109, 87, 61, 81, 103, 119, 122, 108, 86, 60, 35, 53, 77, 99, 107, 85, 59, 34, 17, 29, 49, 70, 42, 22, 10, 4)(3, 7, 15, 31, 55, 54, 30, 14, 6, 13, 27, 51, 79, 78, 50, 26, 12, 25, 47, 75, 101, 100, 74, 46, 24, 45, 72, 97, 117, 114, 94, 69, 44, 71, 95, 115, 113, 93, 68, 41, 67, 92, 112, 111, 91, 66, 40, 21, 39, 65, 90, 89, 64, 38, 20, 9, 19, 37, 63, 62, 36, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 69)(43, 67)(45, 73)(46, 70)(47, 76)(50, 77)(51, 80)(54, 81)(55, 82)(62, 88)(63, 83)(64, 87)(65, 84)(66, 86)(68, 85)(71, 96)(72, 98)(74, 99)(75, 102)(78, 103)(79, 104)(89, 110)(90, 105)(91, 109)(92, 106)(93, 108)(94, 107)(95, 116)(97, 118)(100, 119)(101, 120)(111, 124)(112, 121)(113, 123)(114, 122)(115, 125)(117, 126)
	local type(s) :: { ( 14^63 ) }
Outer automorphisms :: reflexible
Dual of E27.2105
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 63 f = 9
	degree seq :: [ 63^2 ]

E27.2105 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 14, 63})
Quotient :: regular
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^14, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 32, 47, 65, 64, 46, 31, 19, 10, 4)(3, 7, 12, 22, 33, 49, 66, 86, 81, 60, 43, 28, 17, 8)(6, 13, 21, 34, 48, 67, 85, 84, 63, 45, 30, 18, 9, 14)(15, 25, 35, 51, 68, 88, 105, 101, 80, 59, 42, 27, 16, 26)(23, 36, 50, 69, 87, 106, 104, 83, 62, 44, 29, 38, 24, 37)(39, 55, 70, 90, 107, 121, 118, 100, 79, 58, 41, 57, 40, 56)(52, 71, 89, 108, 120, 119, 103, 82, 61, 74, 54, 73, 53, 72)(75, 95, 109, 123, 126, 124, 117, 99, 78, 98, 77, 97, 76, 96)(91, 110, 122, 116, 125, 115, 102, 114, 94, 113, 93, 112, 92, 111)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 41)(28, 42)(31, 43)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 61)(45, 62)(46, 63)(47, 66)(49, 68)(51, 70)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)(64, 81)(65, 85)(67, 87)(69, 89)(71, 91)(72, 92)(73, 93)(74, 94)(82, 102)(83, 103)(84, 104)(86, 105)(88, 107)(90, 109)(95, 114)(96, 115)(97, 116)(98, 110)(99, 111)(100, 117)(101, 118)(106, 120)(108, 122)(112, 124)(113, 123)(119, 125)(121, 126)
	local type(s) :: { ( 63^14 ) }
Outer automorphisms :: reflexible
Dual of E27.2104
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 9 e = 63 f = 2
	degree seq :: [ 14^9 ]

E27.2106 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 14, 63})
Quotient :: edge
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^14, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ]
Map::
	R = (1, 3, 8, 17, 28, 43, 60, 81, 64, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 70, 91, 74, 54, 38, 24, 14, 6)(7, 15, 26, 41, 58, 79, 100, 84, 63, 45, 30, 18, 9, 16)(11, 20, 33, 49, 68, 89, 110, 94, 73, 53, 37, 23, 13, 21)(25, 39, 56, 77, 98, 117, 104, 83, 62, 44, 29, 42, 27, 40)(32, 47, 66, 87, 108, 122, 114, 93, 72, 52, 36, 50, 34, 48)(55, 75, 96, 115, 125, 119, 103, 82, 61, 80, 59, 78, 57, 76)(65, 85, 106, 120, 126, 124, 113, 92, 71, 90, 69, 88, 67, 86)(95, 111, 123, 109, 121, 107, 102, 105, 101, 118, 99, 116, 97, 112)(127, 128)(129, 133)(130, 135)(131, 137)(132, 139)(134, 138)(136, 140)(141, 151)(142, 153)(143, 152)(144, 155)(145, 156)(146, 158)(147, 160)(148, 159)(149, 162)(150, 163)(154, 161)(157, 164)(165, 181)(166, 183)(167, 182)(168, 185)(169, 184)(170, 187)(171, 188)(172, 189)(173, 191)(174, 193)(175, 192)(176, 195)(177, 194)(178, 197)(179, 198)(180, 199)(186, 196)(190, 200)(201, 221)(202, 223)(203, 222)(204, 225)(205, 224)(206, 227)(207, 226)(208, 228)(209, 229)(210, 230)(211, 231)(212, 233)(213, 232)(214, 235)(215, 234)(216, 237)(217, 236)(218, 238)(219, 239)(220, 240)(241, 249)(242, 250)(243, 251)(244, 246)(245, 247)(248, 252)
	L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 145)(20, 146)(21, 147)(22, 148)(23, 149)(24, 150)(25, 151)(26, 152)(27, 153)(28, 154)(29, 155)(30, 156)(31, 157)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 169)(44, 170)(45, 171)(46, 172)(47, 173)(48, 174)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 181)(56, 182)(57, 183)(58, 184)(59, 185)(60, 186)(61, 187)(62, 188)(63, 189)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 126, 126 ), ( 126^14 ) }
Outer automorphisms :: reflexible
Dual of E27.2110
Transitivity :: ET+
Graph:: simple bipartite
	v = 72 e = 126 f = 2
	degree seq :: [ 2^63, 14^9 ]

E27.2107 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 14, 63})
Quotient :: edge
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^2 * T2^3 * T1, T2^-1 * T1 * T2 * T1^-3 * T2 * T1 * T2^-1 * T1, T1 * T2^-7 * T1 * T2^2, T1^-1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1^-1 * T2^2, T2^2 * T1^-3 * T2^2 * T1^-7 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 48, 79, 67, 39, 20, 13, 28, 51, 82, 111, 102, 68, 41, 30, 53, 84, 113, 126, 108, 103, 70, 55, 86, 115, 122, 98, 73, 107, 104, 88, 117, 121, 94, 62, 43, 72, 106, 118, 125, 97, 61, 34, 21, 42, 71, 105, 101, 66, 38, 18, 6, 17, 36, 64, 93, 59, 33, 15, 5)(2, 7, 19, 40, 69, 75, 45, 23, 9, 4, 12, 29, 54, 87, 76, 46, 24, 11, 27, 52, 85, 116, 109, 77, 47, 26, 50, 83, 114, 124, 100, 92, 78, 49, 81, 112, 120, 96, 65, 58, 91, 80, 110, 123, 95, 60, 37, 32, 57, 90, 119, 99, 63, 35, 16, 14, 31, 56, 89, 74, 44, 22, 8)(127, 128, 132, 142, 160, 186, 220, 246, 241, 209, 179, 153, 139, 130)(129, 135, 143, 134, 147, 161, 188, 221, 248, 238, 210, 176, 154, 137)(131, 140, 144, 163, 187, 222, 247, 240, 212, 178, 156, 138, 146, 133)(136, 150, 162, 149, 168, 148, 169, 189, 224, 249, 239, 207, 177, 152)(141, 158, 164, 191, 223, 250, 243, 211, 181, 155, 167, 145, 165, 157)(151, 173, 190, 172, 197, 171, 198, 170, 199, 225, 252, 236, 208, 175)(159, 184, 192, 226, 251, 242, 214, 180, 196, 166, 194, 182, 193, 183)(174, 204, 219, 203, 231, 202, 232, 201, 233, 200, 234, 245, 237, 206)(185, 218, 227, 235, 244, 213, 230, 195, 229, 215, 228, 216, 205, 217)
	L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 145)(20, 146)(21, 147)(22, 148)(23, 149)(24, 150)(25, 151)(26, 152)(27, 153)(28, 154)(29, 155)(30, 156)(31, 157)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 169)(44, 170)(45, 171)(46, 172)(47, 173)(48, 174)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 181)(56, 182)(57, 183)(58, 184)(59, 185)(60, 186)(61, 187)(62, 188)(63, 189)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 4^14 ), ( 4^63 ) }
Outer automorphisms :: reflexible
Dual of E27.2111
Transitivity :: ET+
Graph:: bipartite
	v = 11 e = 126 f = 63
	degree seq :: [ 14^9, 63^2 ]

E27.2108 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 14, 63})
Quotient :: edge
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^2 * T2 * T1^-1 * T2 * T1^6, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1, T1^-3 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^3 * T2 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 69)(43, 67)(45, 73)(46, 70)(47, 76)(50, 77)(51, 80)(54, 81)(55, 82)(62, 88)(63, 83)(64, 87)(65, 84)(66, 86)(68, 85)(71, 96)(72, 98)(74, 99)(75, 102)(78, 103)(79, 104)(89, 110)(90, 105)(91, 109)(92, 106)(93, 108)(94, 107)(95, 116)(97, 118)(100, 119)(101, 120)(111, 124)(112, 121)(113, 123)(114, 122)(115, 125)(117, 126)(127, 128, 131, 137, 149, 169, 184, 159, 142, 154, 174, 199, 222, 232, 210, 183, 158, 178, 202, 224, 242, 247, 231, 209, 182, 206, 228, 244, 251, 250, 236, 214, 208, 230, 246, 252, 249, 235, 213, 187, 207, 229, 245, 248, 234, 212, 186, 161, 179, 203, 225, 233, 211, 185, 160, 143, 155, 175, 196, 168, 148, 136, 130)(129, 133, 141, 157, 181, 180, 156, 140, 132, 139, 153, 177, 205, 204, 176, 152, 138, 151, 173, 201, 227, 226, 200, 172, 150, 171, 198, 223, 243, 240, 220, 195, 170, 197, 221, 241, 239, 219, 194, 167, 193, 218, 238, 237, 217, 192, 166, 147, 165, 191, 216, 215, 190, 164, 146, 135, 145, 163, 189, 188, 162, 144, 134)
	L = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 145)(20, 146)(21, 147)(22, 148)(23, 149)(24, 150)(25, 151)(26, 152)(27, 153)(28, 154)(29, 155)(30, 156)(31, 157)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 169)(44, 170)(45, 171)(46, 172)(47, 173)(48, 174)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 181)(56, 182)(57, 183)(58, 184)(59, 185)(60, 186)(61, 187)(62, 188)(63, 189)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)
	local type(s) :: { ( 28, 28 ), ( 28^63 ) }
Outer automorphisms :: reflexible
Dual of E27.2109
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 126 f = 9
	degree seq :: [ 2^63, 63^2 ]

E27.2109 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 14, 63})
Quotient :: loop
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^14, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ]
Map::
	R = (1, 127, 3, 129, 8, 134, 17, 143, 28, 154, 43, 169, 60, 186, 81, 207, 64, 190, 46, 172, 31, 157, 19, 145, 10, 136, 4, 130)(2, 128, 5, 131, 12, 138, 22, 148, 35, 161, 51, 177, 70, 196, 91, 217, 74, 200, 54, 180, 38, 164, 24, 150, 14, 140, 6, 132)(7, 133, 15, 141, 26, 152, 41, 167, 58, 184, 79, 205, 100, 226, 84, 210, 63, 189, 45, 171, 30, 156, 18, 144, 9, 135, 16, 142)(11, 137, 20, 146, 33, 159, 49, 175, 68, 194, 89, 215, 110, 236, 94, 220, 73, 199, 53, 179, 37, 163, 23, 149, 13, 139, 21, 147)(25, 151, 39, 165, 56, 182, 77, 203, 98, 224, 117, 243, 104, 230, 83, 209, 62, 188, 44, 170, 29, 155, 42, 168, 27, 153, 40, 166)(32, 158, 47, 173, 66, 192, 87, 213, 108, 234, 122, 248, 114, 240, 93, 219, 72, 198, 52, 178, 36, 162, 50, 176, 34, 160, 48, 174)(55, 181, 75, 201, 96, 222, 115, 241, 125, 251, 119, 245, 103, 229, 82, 208, 61, 187, 80, 206, 59, 185, 78, 204, 57, 183, 76, 202)(65, 191, 85, 211, 106, 232, 120, 246, 126, 252, 124, 250, 113, 239, 92, 218, 71, 197, 90, 216, 69, 195, 88, 214, 67, 193, 86, 212)(95, 221, 111, 237, 123, 249, 109, 235, 121, 247, 107, 233, 102, 228, 105, 231, 101, 227, 118, 244, 99, 225, 116, 242, 97, 223, 112, 238)
	L = (1, 128)(2, 127)(3, 133)(4, 135)(5, 137)(6, 139)(7, 129)(8, 138)(9, 130)(10, 140)(11, 131)(12, 134)(13, 132)(14, 136)(15, 151)(16, 153)(17, 152)(18, 155)(19, 156)(20, 158)(21, 160)(22, 159)(23, 162)(24, 163)(25, 141)(26, 143)(27, 142)(28, 161)(29, 144)(30, 145)(31, 164)(32, 146)(33, 148)(34, 147)(35, 154)(36, 149)(37, 150)(38, 157)(39, 181)(40, 183)(41, 182)(42, 185)(43, 184)(44, 187)(45, 188)(46, 189)(47, 191)(48, 193)(49, 192)(50, 195)(51, 194)(52, 197)(53, 198)(54, 199)(55, 165)(56, 167)(57, 166)(58, 169)(59, 168)(60, 196)(61, 170)(62, 171)(63, 172)(64, 200)(65, 173)(66, 175)(67, 174)(68, 177)(69, 176)(70, 186)(71, 178)(72, 179)(73, 180)(74, 190)(75, 221)(76, 223)(77, 222)(78, 225)(79, 224)(80, 227)(81, 226)(82, 228)(83, 229)(84, 230)(85, 231)(86, 233)(87, 232)(88, 235)(89, 234)(90, 237)(91, 236)(92, 238)(93, 239)(94, 240)(95, 201)(96, 203)(97, 202)(98, 205)(99, 204)(100, 207)(101, 206)(102, 208)(103, 209)(104, 210)(105, 211)(106, 213)(107, 212)(108, 215)(109, 214)(110, 217)(111, 216)(112, 218)(113, 219)(114, 220)(115, 249)(116, 250)(117, 251)(118, 246)(119, 247)(120, 244)(121, 245)(122, 252)(123, 241)(124, 242)(125, 243)(126, 248)
	local type(s) :: { ( 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63, 2, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.2108
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 126 f = 65
	degree seq :: [ 28^9 ]

E27.2110 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 14, 63})
Quotient :: loop
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ F^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^2 * T2^3 * T1, T2^-1 * T1 * T2 * T1^-3 * T2 * T1 * T2^-1 * T1, T1 * T2^-7 * T1 * T2^2, T1^-1 * T2^2 * T1 * T2^-2 * T1 * T2^-2 * T1^-1 * T2^2, T2^2 * T1^-3 * T2^2 * T1^-7 ]
Map::
	R = (1, 127, 3, 129, 10, 136, 25, 151, 48, 174, 79, 205, 67, 193, 39, 165, 20, 146, 13, 139, 28, 154, 51, 177, 82, 208, 111, 237, 102, 228, 68, 194, 41, 167, 30, 156, 53, 179, 84, 210, 113, 239, 126, 252, 108, 234, 103, 229, 70, 196, 55, 181, 86, 212, 115, 241, 122, 248, 98, 224, 73, 199, 107, 233, 104, 230, 88, 214, 117, 243, 121, 247, 94, 220, 62, 188, 43, 169, 72, 198, 106, 232, 118, 244, 125, 251, 97, 223, 61, 187, 34, 160, 21, 147, 42, 168, 71, 197, 105, 231, 101, 227, 66, 192, 38, 164, 18, 144, 6, 132, 17, 143, 36, 162, 64, 190, 93, 219, 59, 185, 33, 159, 15, 141, 5, 131)(2, 128, 7, 133, 19, 145, 40, 166, 69, 195, 75, 201, 45, 171, 23, 149, 9, 135, 4, 130, 12, 138, 29, 155, 54, 180, 87, 213, 76, 202, 46, 172, 24, 150, 11, 137, 27, 153, 52, 178, 85, 211, 116, 242, 109, 235, 77, 203, 47, 173, 26, 152, 50, 176, 83, 209, 114, 240, 124, 250, 100, 226, 92, 218, 78, 204, 49, 175, 81, 207, 112, 238, 120, 246, 96, 222, 65, 191, 58, 184, 91, 217, 80, 206, 110, 236, 123, 249, 95, 221, 60, 186, 37, 163, 32, 158, 57, 183, 90, 216, 119, 245, 99, 225, 63, 189, 35, 161, 16, 142, 14, 140, 31, 157, 56, 182, 89, 215, 74, 200, 44, 170, 22, 148, 8, 134)
	L = (1, 128)(2, 132)(3, 135)(4, 127)(5, 140)(6, 142)(7, 131)(8, 147)(9, 143)(10, 150)(11, 129)(12, 146)(13, 130)(14, 144)(15, 158)(16, 160)(17, 134)(18, 163)(19, 165)(20, 133)(21, 161)(22, 169)(23, 168)(24, 162)(25, 173)(26, 136)(27, 139)(28, 137)(29, 167)(30, 138)(31, 141)(32, 164)(33, 184)(34, 186)(35, 188)(36, 149)(37, 187)(38, 191)(39, 157)(40, 194)(41, 145)(42, 148)(43, 189)(44, 199)(45, 198)(46, 197)(47, 190)(48, 204)(49, 151)(50, 154)(51, 152)(52, 156)(53, 153)(54, 196)(55, 155)(56, 193)(57, 159)(58, 192)(59, 218)(60, 220)(61, 222)(62, 221)(63, 224)(64, 172)(65, 223)(66, 226)(67, 183)(68, 182)(69, 229)(70, 166)(71, 171)(72, 170)(73, 225)(74, 234)(75, 233)(76, 232)(77, 231)(78, 219)(79, 217)(80, 174)(81, 177)(82, 175)(83, 179)(84, 176)(85, 181)(86, 178)(87, 230)(88, 180)(89, 228)(90, 205)(91, 185)(92, 227)(93, 203)(94, 246)(95, 248)(96, 247)(97, 250)(98, 249)(99, 252)(100, 251)(101, 235)(102, 216)(103, 215)(104, 195)(105, 202)(106, 201)(107, 200)(108, 245)(109, 244)(110, 208)(111, 206)(112, 210)(113, 207)(114, 212)(115, 209)(116, 214)(117, 211)(118, 213)(119, 237)(120, 241)(121, 240)(122, 238)(123, 239)(124, 243)(125, 242)(126, 236)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E27.2106
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 126 f = 72
	degree seq :: [ 126^2 ]

E27.2111 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 14, 63})
Quotient :: loop
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^2 * T2 * T1^-1 * T2 * T1^6, T1^-1 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1, T1^-3 * T2 * T1^-3 * T2 * T1^3 * T2 * T1^3 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 127, 3, 129)(2, 128, 6, 132)(4, 130, 9, 135)(5, 131, 12, 138)(7, 133, 16, 142)(8, 134, 17, 143)(10, 136, 21, 147)(11, 137, 24, 150)(13, 139, 28, 154)(14, 140, 29, 155)(15, 141, 32, 158)(18, 144, 35, 161)(19, 145, 33, 159)(20, 146, 34, 160)(22, 148, 41, 167)(23, 149, 44, 170)(25, 151, 48, 174)(26, 152, 49, 175)(27, 153, 52, 178)(30, 156, 53, 179)(31, 157, 56, 182)(36, 162, 61, 187)(37, 163, 57, 183)(38, 164, 60, 186)(39, 165, 58, 184)(40, 166, 59, 185)(42, 168, 69, 195)(43, 169, 67, 193)(45, 171, 73, 199)(46, 172, 70, 196)(47, 173, 76, 202)(50, 176, 77, 203)(51, 177, 80, 206)(54, 180, 81, 207)(55, 181, 82, 208)(62, 188, 88, 214)(63, 189, 83, 209)(64, 190, 87, 213)(65, 191, 84, 210)(66, 192, 86, 212)(68, 194, 85, 211)(71, 197, 96, 222)(72, 198, 98, 224)(74, 200, 99, 225)(75, 201, 102, 228)(78, 204, 103, 229)(79, 205, 104, 230)(89, 215, 110, 236)(90, 216, 105, 231)(91, 217, 109, 235)(92, 218, 106, 232)(93, 219, 108, 234)(94, 220, 107, 233)(95, 221, 116, 242)(97, 223, 118, 244)(100, 226, 119, 245)(101, 227, 120, 246)(111, 237, 124, 250)(112, 238, 121, 247)(113, 239, 123, 249)(114, 240, 122, 248)(115, 241, 125, 251)(117, 243, 126, 252)
	L = (1, 128)(2, 131)(3, 133)(4, 127)(5, 137)(6, 139)(7, 141)(8, 129)(9, 145)(10, 130)(11, 149)(12, 151)(13, 153)(14, 132)(15, 157)(16, 154)(17, 155)(18, 134)(19, 163)(20, 135)(21, 165)(22, 136)(23, 169)(24, 171)(25, 173)(26, 138)(27, 177)(28, 174)(29, 175)(30, 140)(31, 181)(32, 178)(33, 142)(34, 143)(35, 179)(36, 144)(37, 189)(38, 146)(39, 191)(40, 147)(41, 193)(42, 148)(43, 184)(44, 197)(45, 198)(46, 150)(47, 201)(48, 199)(49, 196)(50, 152)(51, 205)(52, 202)(53, 203)(54, 156)(55, 180)(56, 206)(57, 158)(58, 159)(59, 160)(60, 161)(61, 207)(62, 162)(63, 188)(64, 164)(65, 216)(66, 166)(67, 218)(68, 167)(69, 170)(70, 168)(71, 221)(72, 223)(73, 222)(74, 172)(75, 227)(76, 224)(77, 225)(78, 176)(79, 204)(80, 228)(81, 229)(82, 230)(83, 182)(84, 183)(85, 185)(86, 186)(87, 187)(88, 208)(89, 190)(90, 215)(91, 192)(92, 238)(93, 194)(94, 195)(95, 241)(96, 232)(97, 243)(98, 242)(99, 233)(100, 200)(101, 226)(102, 244)(103, 245)(104, 246)(105, 209)(106, 210)(107, 211)(108, 212)(109, 213)(110, 214)(111, 217)(112, 237)(113, 219)(114, 220)(115, 239)(116, 247)(117, 240)(118, 251)(119, 248)(120, 252)(121, 231)(122, 234)(123, 235)(124, 236)(125, 250)(126, 249)
	local type(s) :: { ( 14, 63, 14, 63 ) }
Outer automorphisms :: reflexible
Dual of E27.2107
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 63 e = 126 f = 11
	degree seq :: [ 4^63 ]

E27.2112 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^14, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^63 ]
Map::
	R = (1, 127, 2, 128)(3, 129, 7, 133)(4, 130, 9, 135)(5, 131, 11, 137)(6, 132, 13, 139)(8, 134, 12, 138)(10, 136, 14, 140)(15, 141, 25, 151)(16, 142, 27, 153)(17, 143, 26, 152)(18, 144, 29, 155)(19, 145, 30, 156)(20, 146, 32, 158)(21, 147, 34, 160)(22, 148, 33, 159)(23, 149, 36, 162)(24, 150, 37, 163)(28, 154, 35, 161)(31, 157, 38, 164)(39, 165, 55, 181)(40, 166, 57, 183)(41, 167, 56, 182)(42, 168, 59, 185)(43, 169, 58, 184)(44, 170, 61, 187)(45, 171, 62, 188)(46, 172, 63, 189)(47, 173, 65, 191)(48, 174, 67, 193)(49, 175, 66, 192)(50, 176, 69, 195)(51, 177, 68, 194)(52, 178, 71, 197)(53, 179, 72, 198)(54, 180, 73, 199)(60, 186, 70, 196)(64, 190, 74, 200)(75, 201, 95, 221)(76, 202, 97, 223)(77, 203, 96, 222)(78, 204, 99, 225)(79, 205, 98, 224)(80, 206, 101, 227)(81, 207, 100, 226)(82, 208, 102, 228)(83, 209, 103, 229)(84, 210, 104, 230)(85, 211, 105, 231)(86, 212, 107, 233)(87, 213, 106, 232)(88, 214, 109, 235)(89, 215, 108, 234)(90, 216, 111, 237)(91, 217, 110, 236)(92, 218, 112, 238)(93, 219, 113, 239)(94, 220, 114, 240)(115, 241, 123, 249)(116, 242, 124, 250)(117, 243, 125, 251)(118, 244, 120, 246)(119, 245, 121, 247)(122, 248, 126, 252)(253, 379, 255, 381, 260, 386, 269, 395, 280, 406, 295, 421, 312, 438, 333, 459, 316, 442, 298, 424, 283, 409, 271, 397, 262, 388, 256, 382)(254, 380, 257, 383, 264, 390, 274, 400, 287, 413, 303, 429, 322, 448, 343, 469, 326, 452, 306, 432, 290, 416, 276, 402, 266, 392, 258, 384)(259, 385, 267, 393, 278, 404, 293, 419, 310, 436, 331, 457, 352, 478, 336, 462, 315, 441, 297, 423, 282, 408, 270, 396, 261, 387, 268, 394)(263, 389, 272, 398, 285, 411, 301, 427, 320, 446, 341, 467, 362, 488, 346, 472, 325, 451, 305, 431, 289, 415, 275, 401, 265, 391, 273, 399)(277, 403, 291, 417, 308, 434, 329, 455, 350, 476, 369, 495, 356, 482, 335, 461, 314, 440, 296, 422, 281, 407, 294, 420, 279, 405, 292, 418)(284, 410, 299, 425, 318, 444, 339, 465, 360, 486, 374, 500, 366, 492, 345, 471, 324, 450, 304, 430, 288, 414, 302, 428, 286, 412, 300, 426)(307, 433, 327, 453, 348, 474, 367, 493, 377, 503, 371, 497, 355, 481, 334, 460, 313, 439, 332, 458, 311, 437, 330, 456, 309, 435, 328, 454)(317, 443, 337, 463, 358, 484, 372, 498, 378, 504, 376, 502, 365, 491, 344, 470, 323, 449, 342, 468, 321, 447, 340, 466, 319, 445, 338, 464)(347, 473, 363, 489, 375, 501, 361, 487, 373, 499, 359, 485, 354, 480, 357, 483, 353, 479, 370, 496, 351, 477, 368, 494, 349, 475, 364, 490)
	L = (1, 254)(2, 253)(3, 259)(4, 261)(5, 263)(6, 265)(7, 255)(8, 264)(9, 256)(10, 266)(11, 257)(12, 260)(13, 258)(14, 262)(15, 277)(16, 279)(17, 278)(18, 281)(19, 282)(20, 284)(21, 286)(22, 285)(23, 288)(24, 289)(25, 267)(26, 269)(27, 268)(28, 287)(29, 270)(30, 271)(31, 290)(32, 272)(33, 274)(34, 273)(35, 280)(36, 275)(37, 276)(38, 283)(39, 307)(40, 309)(41, 308)(42, 311)(43, 310)(44, 313)(45, 314)(46, 315)(47, 317)(48, 319)(49, 318)(50, 321)(51, 320)(52, 323)(53, 324)(54, 325)(55, 291)(56, 293)(57, 292)(58, 295)(59, 294)(60, 322)(61, 296)(62, 297)(63, 298)(64, 326)(65, 299)(66, 301)(67, 300)(68, 303)(69, 302)(70, 312)(71, 304)(72, 305)(73, 306)(74, 316)(75, 347)(76, 349)(77, 348)(78, 351)(79, 350)(80, 353)(81, 352)(82, 354)(83, 355)(84, 356)(85, 357)(86, 359)(87, 358)(88, 361)(89, 360)(90, 363)(91, 362)(92, 364)(93, 365)(94, 366)(95, 327)(96, 329)(97, 328)(98, 331)(99, 330)(100, 333)(101, 332)(102, 334)(103, 335)(104, 336)(105, 337)(106, 339)(107, 338)(108, 341)(109, 340)(110, 343)(111, 342)(112, 344)(113, 345)(114, 346)(115, 375)(116, 376)(117, 377)(118, 372)(119, 373)(120, 370)(121, 371)(122, 378)(123, 367)(124, 368)(125, 369)(126, 374)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 2, 126, 2, 126 ), ( 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126, 2, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.2115
Graph:: bipartite
	v = 72 e = 252 f = 128
	degree seq :: [ 4^63, 28^9 ]

E27.2113 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, (Y1 * Y2)^2, (R * Y1)^2, R * Y2 * R * Y3, Y1^-3 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1^-2 * Y2 * Y1^2, Y1^-2 * Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-2 * Y1^2 * Y2^3 * Y1, Y2 * Y1^-3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2^-7 * Y1 * Y2^2, Y1 * Y2^-2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y2^-1 * Y1 * Y2^-1 * Y1^11 ]
Map::
	R = (1, 127, 2, 128, 6, 132, 16, 142, 34, 160, 60, 186, 94, 220, 120, 246, 115, 241, 83, 209, 53, 179, 27, 153, 13, 139, 4, 130)(3, 129, 9, 135, 17, 143, 8, 134, 21, 147, 35, 161, 62, 188, 95, 221, 122, 248, 112, 238, 84, 210, 50, 176, 28, 154, 11, 137)(5, 131, 14, 140, 18, 144, 37, 163, 61, 187, 96, 222, 121, 247, 114, 240, 86, 212, 52, 178, 30, 156, 12, 138, 20, 146, 7, 133)(10, 136, 24, 150, 36, 162, 23, 149, 42, 168, 22, 148, 43, 169, 63, 189, 98, 224, 123, 249, 113, 239, 81, 207, 51, 177, 26, 152)(15, 141, 32, 158, 38, 164, 65, 191, 97, 223, 124, 250, 117, 243, 85, 211, 55, 181, 29, 155, 41, 167, 19, 145, 39, 165, 31, 157)(25, 151, 47, 173, 64, 190, 46, 172, 71, 197, 45, 171, 72, 198, 44, 170, 73, 199, 99, 225, 126, 252, 110, 236, 82, 208, 49, 175)(33, 159, 58, 184, 66, 192, 100, 226, 125, 251, 116, 242, 88, 214, 54, 180, 70, 196, 40, 166, 68, 194, 56, 182, 67, 193, 57, 183)(48, 174, 78, 204, 93, 219, 77, 203, 105, 231, 76, 202, 106, 232, 75, 201, 107, 233, 74, 200, 108, 234, 119, 245, 111, 237, 80, 206)(59, 185, 92, 218, 101, 227, 109, 235, 118, 244, 87, 213, 104, 230, 69, 195, 103, 229, 89, 215, 102, 228, 90, 216, 79, 205, 91, 217)(253, 379, 255, 381, 262, 388, 277, 403, 300, 426, 331, 457, 319, 445, 291, 417, 272, 398, 265, 391, 280, 406, 303, 429, 334, 460, 363, 489, 354, 480, 320, 446, 293, 419, 282, 408, 305, 431, 336, 462, 365, 491, 378, 504, 360, 486, 355, 481, 322, 448, 307, 433, 338, 464, 367, 493, 374, 500, 350, 476, 325, 451, 359, 485, 356, 482, 340, 466, 369, 495, 373, 499, 346, 472, 314, 440, 295, 421, 324, 450, 358, 484, 370, 496, 377, 503, 349, 475, 313, 439, 286, 412, 273, 399, 294, 420, 323, 449, 357, 483, 353, 479, 318, 444, 290, 416, 270, 396, 258, 384, 269, 395, 288, 414, 316, 442, 345, 471, 311, 437, 285, 411, 267, 393, 257, 383)(254, 380, 259, 385, 271, 397, 292, 418, 321, 447, 327, 453, 297, 423, 275, 401, 261, 387, 256, 382, 264, 390, 281, 407, 306, 432, 339, 465, 328, 454, 298, 424, 276, 402, 263, 389, 279, 405, 304, 430, 337, 463, 368, 494, 361, 487, 329, 455, 299, 425, 278, 404, 302, 428, 335, 461, 366, 492, 376, 502, 352, 478, 344, 470, 330, 456, 301, 427, 333, 459, 364, 490, 372, 498, 348, 474, 317, 443, 310, 436, 343, 469, 332, 458, 362, 488, 375, 501, 347, 473, 312, 438, 289, 415, 284, 410, 309, 435, 342, 468, 371, 497, 351, 477, 315, 441, 287, 413, 268, 394, 266, 392, 283, 409, 308, 434, 341, 467, 326, 452, 296, 422, 274, 400, 260, 386)
	L = (1, 255)(2, 259)(3, 262)(4, 264)(5, 253)(6, 269)(7, 271)(8, 254)(9, 256)(10, 277)(11, 279)(12, 281)(13, 280)(14, 283)(15, 257)(16, 266)(17, 288)(18, 258)(19, 292)(20, 265)(21, 294)(22, 260)(23, 261)(24, 263)(25, 300)(26, 302)(27, 304)(28, 303)(29, 306)(30, 305)(31, 308)(32, 309)(33, 267)(34, 273)(35, 268)(36, 316)(37, 284)(38, 270)(39, 272)(40, 321)(41, 282)(42, 323)(43, 324)(44, 274)(45, 275)(46, 276)(47, 278)(48, 331)(49, 333)(50, 335)(51, 334)(52, 337)(53, 336)(54, 339)(55, 338)(56, 341)(57, 342)(58, 343)(59, 285)(60, 289)(61, 286)(62, 295)(63, 287)(64, 345)(65, 310)(66, 290)(67, 291)(68, 293)(69, 327)(70, 307)(71, 357)(72, 358)(73, 359)(74, 296)(75, 297)(76, 298)(77, 299)(78, 301)(79, 319)(80, 362)(81, 364)(82, 363)(83, 366)(84, 365)(85, 368)(86, 367)(87, 328)(88, 369)(89, 326)(90, 371)(91, 332)(92, 330)(93, 311)(94, 314)(95, 312)(96, 317)(97, 313)(98, 325)(99, 315)(100, 344)(101, 318)(102, 320)(103, 322)(104, 340)(105, 353)(106, 370)(107, 356)(108, 355)(109, 329)(110, 375)(111, 354)(112, 372)(113, 378)(114, 376)(115, 374)(116, 361)(117, 373)(118, 377)(119, 351)(120, 348)(121, 346)(122, 350)(123, 347)(124, 352)(125, 349)(126, 360)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2114
Graph:: bipartite
	v = 11 e = 252 f = 189
	degree seq :: [ 28^9, 126^2 ]

E27.2114 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1, Y3^7 * Y2 * Y3^-1 * Y2 * Y3, Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2, Y3^3 * Y2 * Y3^3 * Y2 * Y3^-3 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^63 ]
Map:: polytopal
	R = (1, 127)(2, 128)(3, 129)(4, 130)(5, 131)(6, 132)(7, 133)(8, 134)(9, 135)(10, 136)(11, 137)(12, 138)(13, 139)(14, 140)(15, 141)(16, 142)(17, 143)(18, 144)(19, 145)(20, 146)(21, 147)(22, 148)(23, 149)(24, 150)(25, 151)(26, 152)(27, 153)(28, 154)(29, 155)(30, 156)(31, 157)(32, 158)(33, 159)(34, 160)(35, 161)(36, 162)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 169)(44, 170)(45, 171)(46, 172)(47, 173)(48, 174)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 181)(56, 182)(57, 183)(58, 184)(59, 185)(60, 186)(61, 187)(62, 188)(63, 189)(64, 190)(65, 191)(66, 192)(67, 193)(68, 194)(69, 195)(70, 196)(71, 197)(72, 198)(73, 199)(74, 200)(75, 201)(76, 202)(77, 203)(78, 204)(79, 205)(80, 206)(81, 207)(82, 208)(83, 209)(84, 210)(85, 211)(86, 212)(87, 213)(88, 214)(89, 215)(90, 216)(91, 217)(92, 218)(93, 219)(94, 220)(95, 221)(96, 222)(97, 223)(98, 224)(99, 225)(100, 226)(101, 227)(102, 228)(103, 229)(104, 230)(105, 231)(106, 232)(107, 233)(108, 234)(109, 235)(110, 236)(111, 237)(112, 238)(113, 239)(114, 240)(115, 241)(116, 242)(117, 243)(118, 244)(119, 245)(120, 246)(121, 247)(122, 248)(123, 249)(124, 250)(125, 251)(126, 252)(253, 379, 254, 380)(255, 381, 259, 385)(256, 382, 261, 387)(257, 383, 263, 389)(258, 384, 265, 391)(260, 386, 269, 395)(262, 388, 273, 399)(264, 390, 277, 403)(266, 392, 281, 407)(267, 393, 275, 401)(268, 394, 279, 405)(270, 396, 287, 413)(271, 397, 276, 402)(272, 398, 280, 406)(274, 400, 293, 419)(278, 404, 299, 425)(282, 408, 305, 431)(283, 409, 297, 423)(284, 410, 303, 429)(285, 411, 295, 421)(286, 412, 301, 427)(288, 414, 313, 439)(289, 415, 298, 424)(290, 416, 304, 430)(291, 417, 296, 422)(292, 418, 302, 428)(294, 420, 321, 447)(300, 426, 328, 454)(306, 432, 334, 460)(307, 433, 326, 452)(308, 434, 332, 458)(309, 435, 324, 450)(310, 436, 330, 456)(311, 437, 323, 449)(312, 438, 322, 448)(314, 440, 319, 445)(315, 441, 327, 453)(316, 442, 333, 459)(317, 443, 325, 451)(318, 444, 331, 457)(320, 446, 329, 455)(335, 461, 352, 478)(336, 462, 350, 476)(337, 463, 356, 482)(338, 464, 348, 474)(339, 465, 354, 480)(340, 466, 347, 473)(341, 467, 358, 484)(342, 468, 351, 477)(343, 469, 357, 483)(344, 470, 349, 475)(345, 471, 355, 481)(346, 472, 353, 479)(359, 485, 370, 496)(360, 486, 368, 494)(361, 487, 372, 498)(362, 488, 367, 493)(363, 489, 374, 500)(364, 490, 369, 495)(365, 491, 373, 499)(366, 492, 371, 497)(375, 501, 378, 504)(376, 502, 377, 503)
	L = (1, 255)(2, 257)(3, 260)(4, 253)(5, 264)(6, 254)(7, 267)(8, 270)(9, 271)(10, 256)(11, 275)(12, 278)(13, 279)(14, 258)(15, 283)(16, 259)(17, 285)(18, 288)(19, 289)(20, 261)(21, 291)(22, 262)(23, 295)(24, 263)(25, 297)(26, 300)(27, 301)(28, 265)(29, 303)(30, 266)(31, 307)(32, 268)(33, 309)(34, 269)(35, 311)(36, 314)(37, 315)(38, 272)(39, 317)(40, 273)(41, 319)(42, 274)(43, 323)(44, 276)(45, 324)(46, 277)(47, 326)(48, 308)(49, 322)(50, 280)(51, 330)(52, 281)(53, 332)(54, 282)(55, 335)(56, 284)(57, 336)(58, 286)(59, 338)(60, 287)(61, 340)(62, 296)(63, 306)(64, 290)(65, 342)(66, 292)(67, 344)(68, 293)(69, 313)(70, 294)(71, 347)(72, 348)(73, 298)(74, 350)(75, 299)(76, 352)(77, 302)(78, 354)(79, 304)(80, 356)(81, 305)(82, 328)(83, 337)(84, 359)(85, 310)(86, 360)(87, 312)(88, 362)(89, 316)(90, 341)(91, 318)(92, 364)(93, 320)(94, 321)(95, 349)(96, 367)(97, 325)(98, 368)(99, 327)(100, 370)(101, 329)(102, 353)(103, 331)(104, 372)(105, 333)(106, 334)(107, 361)(108, 375)(109, 339)(110, 376)(111, 343)(112, 363)(113, 345)(114, 346)(115, 369)(116, 377)(117, 351)(118, 378)(119, 355)(120, 371)(121, 357)(122, 358)(123, 366)(124, 365)(125, 374)(126, 373)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 28, 126 ), ( 28, 126, 28, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.2113
Graph:: simple bipartite
	v = 189 e = 252 f = 11
	degree seq :: [ 2^126, 4^63 ]

E27.2115 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y1^6 * Y3 * Y1^-1 * Y3 * Y1^2, Y1^-2 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3, (Y1^-4 * Y3 * Y1^-3)^2, Y1^-3 * Y3 * Y1^-3 * Y3 * Y1^3 * Y3 * Y1^3 * Y3 ]
Map::
	R = (1, 127, 2, 128, 5, 131, 11, 137, 23, 149, 43, 169, 58, 184, 33, 159, 16, 142, 28, 154, 48, 174, 73, 199, 96, 222, 106, 232, 84, 210, 57, 183, 32, 158, 52, 178, 76, 202, 98, 224, 116, 242, 121, 247, 105, 231, 83, 209, 56, 182, 80, 206, 102, 228, 118, 244, 125, 251, 124, 250, 110, 236, 88, 214, 82, 208, 104, 230, 120, 246, 126, 252, 123, 249, 109, 235, 87, 213, 61, 187, 81, 207, 103, 229, 119, 245, 122, 248, 108, 234, 86, 212, 60, 186, 35, 161, 53, 179, 77, 203, 99, 225, 107, 233, 85, 211, 59, 185, 34, 160, 17, 143, 29, 155, 49, 175, 70, 196, 42, 168, 22, 148, 10, 136, 4, 130)(3, 129, 7, 133, 15, 141, 31, 157, 55, 181, 54, 180, 30, 156, 14, 140, 6, 132, 13, 139, 27, 153, 51, 177, 79, 205, 78, 204, 50, 176, 26, 152, 12, 138, 25, 151, 47, 173, 75, 201, 101, 227, 100, 226, 74, 200, 46, 172, 24, 150, 45, 171, 72, 198, 97, 223, 117, 243, 114, 240, 94, 220, 69, 195, 44, 170, 71, 197, 95, 221, 115, 241, 113, 239, 93, 219, 68, 194, 41, 167, 67, 193, 92, 218, 112, 238, 111, 237, 91, 217, 66, 192, 40, 166, 21, 147, 39, 165, 65, 191, 90, 216, 89, 215, 64, 190, 38, 164, 20, 146, 9, 135, 19, 145, 37, 163, 63, 189, 62, 188, 36, 162, 18, 144, 8, 134)(253, 379)(254, 380)(255, 381)(256, 382)(257, 383)(258, 384)(259, 385)(260, 386)(261, 387)(262, 388)(263, 389)(264, 390)(265, 391)(266, 392)(267, 393)(268, 394)(269, 395)(270, 396)(271, 397)(272, 398)(273, 399)(274, 400)(275, 401)(276, 402)(277, 403)(278, 404)(279, 405)(280, 406)(281, 407)(282, 408)(283, 409)(284, 410)(285, 411)(286, 412)(287, 413)(288, 414)(289, 415)(290, 416)(291, 417)(292, 418)(293, 419)(294, 420)(295, 421)(296, 422)(297, 423)(298, 424)(299, 425)(300, 426)(301, 427)(302, 428)(303, 429)(304, 430)(305, 431)(306, 432)(307, 433)(308, 434)(309, 435)(310, 436)(311, 437)(312, 438)(313, 439)(314, 440)(315, 441)(316, 442)(317, 443)(318, 444)(319, 445)(320, 446)(321, 447)(322, 448)(323, 449)(324, 450)(325, 451)(326, 452)(327, 453)(328, 454)(329, 455)(330, 456)(331, 457)(332, 458)(333, 459)(334, 460)(335, 461)(336, 462)(337, 463)(338, 464)(339, 465)(340, 466)(341, 467)(342, 468)(343, 469)(344, 470)(345, 471)(346, 472)(347, 473)(348, 474)(349, 475)(350, 476)(351, 477)(352, 478)(353, 479)(354, 480)(355, 481)(356, 482)(357, 483)(358, 484)(359, 485)(360, 486)(361, 487)(362, 488)(363, 489)(364, 490)(365, 491)(366, 492)(367, 493)(368, 494)(369, 495)(370, 496)(371, 497)(372, 498)(373, 499)(374, 500)(375, 501)(376, 502)(377, 503)(378, 504)
	L = (1, 255)(2, 258)(3, 253)(4, 261)(5, 264)(6, 254)(7, 268)(8, 269)(9, 256)(10, 273)(11, 276)(12, 257)(13, 280)(14, 281)(15, 284)(16, 259)(17, 260)(18, 287)(19, 285)(20, 286)(21, 262)(22, 293)(23, 296)(24, 263)(25, 300)(26, 301)(27, 304)(28, 265)(29, 266)(30, 305)(31, 308)(32, 267)(33, 271)(34, 272)(35, 270)(36, 313)(37, 309)(38, 312)(39, 310)(40, 311)(41, 274)(42, 321)(43, 319)(44, 275)(45, 325)(46, 322)(47, 328)(48, 277)(49, 278)(50, 329)(51, 332)(52, 279)(53, 282)(54, 333)(55, 334)(56, 283)(57, 289)(58, 291)(59, 292)(60, 290)(61, 288)(62, 340)(63, 335)(64, 339)(65, 336)(66, 338)(67, 295)(68, 337)(69, 294)(70, 298)(71, 348)(72, 350)(73, 297)(74, 351)(75, 354)(76, 299)(77, 302)(78, 355)(79, 356)(80, 303)(81, 306)(82, 307)(83, 315)(84, 317)(85, 320)(86, 318)(87, 316)(88, 314)(89, 362)(90, 357)(91, 361)(92, 358)(93, 360)(94, 359)(95, 368)(96, 323)(97, 370)(98, 324)(99, 326)(100, 371)(101, 372)(102, 327)(103, 330)(104, 331)(105, 342)(106, 344)(107, 346)(108, 345)(109, 343)(110, 341)(111, 376)(112, 373)(113, 375)(114, 374)(115, 377)(116, 347)(117, 378)(118, 349)(119, 352)(120, 353)(121, 364)(122, 366)(123, 365)(124, 363)(125, 367)(126, 369)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2112
Graph:: simple bipartite
	v = 128 e = 252 f = 72
	degree seq :: [ 2^126, 126^2 ]

E27.2116 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^7 * Y1 * Y2^-1 * Y1 * Y2, Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1, Y2^3 * Y1 * Y2^3 * Y1 * Y2^-3 * Y1 * Y2^-3 * Y1, (Y3 * Y2^-1)^14 ]
Map::
	R = (1, 127, 2, 128)(3, 129, 7, 133)(4, 130, 9, 135)(5, 131, 11, 137)(6, 132, 13, 139)(8, 134, 17, 143)(10, 136, 21, 147)(12, 138, 25, 151)(14, 140, 29, 155)(15, 141, 23, 149)(16, 142, 27, 153)(18, 144, 35, 161)(19, 145, 24, 150)(20, 146, 28, 154)(22, 148, 41, 167)(26, 152, 47, 173)(30, 156, 53, 179)(31, 157, 45, 171)(32, 158, 51, 177)(33, 159, 43, 169)(34, 160, 49, 175)(36, 162, 61, 187)(37, 163, 46, 172)(38, 164, 52, 178)(39, 165, 44, 170)(40, 166, 50, 176)(42, 168, 69, 195)(48, 174, 76, 202)(54, 180, 82, 208)(55, 181, 74, 200)(56, 182, 80, 206)(57, 183, 72, 198)(58, 184, 78, 204)(59, 185, 71, 197)(60, 186, 70, 196)(62, 188, 67, 193)(63, 189, 75, 201)(64, 190, 81, 207)(65, 191, 73, 199)(66, 192, 79, 205)(68, 194, 77, 203)(83, 209, 100, 226)(84, 210, 98, 224)(85, 211, 104, 230)(86, 212, 96, 222)(87, 213, 102, 228)(88, 214, 95, 221)(89, 215, 106, 232)(90, 216, 99, 225)(91, 217, 105, 231)(92, 218, 97, 223)(93, 219, 103, 229)(94, 220, 101, 227)(107, 233, 118, 244)(108, 234, 116, 242)(109, 235, 120, 246)(110, 236, 115, 241)(111, 237, 122, 248)(112, 238, 117, 243)(113, 239, 121, 247)(114, 240, 119, 245)(123, 249, 126, 252)(124, 250, 125, 251)(253, 379, 255, 381, 260, 386, 270, 396, 288, 414, 314, 440, 296, 422, 276, 402, 263, 389, 275, 401, 295, 421, 323, 449, 347, 473, 349, 475, 325, 451, 298, 424, 277, 403, 297, 423, 324, 450, 348, 474, 367, 493, 369, 495, 351, 477, 327, 453, 299, 425, 326, 452, 350, 476, 368, 494, 377, 503, 374, 500, 358, 484, 334, 460, 328, 454, 352, 478, 370, 496, 378, 504, 373, 499, 357, 483, 333, 459, 305, 431, 332, 458, 356, 482, 372, 498, 371, 497, 355, 481, 331, 457, 304, 430, 281, 407, 303, 429, 330, 456, 354, 480, 353, 479, 329, 455, 302, 428, 280, 406, 265, 391, 279, 405, 301, 427, 322, 448, 294, 420, 274, 400, 262, 388, 256, 382)(254, 380, 257, 383, 264, 390, 278, 404, 300, 426, 308, 434, 284, 410, 268, 394, 259, 385, 267, 393, 283, 409, 307, 433, 335, 461, 337, 463, 310, 436, 286, 412, 269, 395, 285, 411, 309, 435, 336, 462, 359, 485, 361, 487, 339, 465, 312, 438, 287, 413, 311, 437, 338, 464, 360, 486, 375, 501, 366, 492, 346, 472, 321, 447, 313, 439, 340, 466, 362, 488, 376, 502, 365, 491, 345, 471, 320, 446, 293, 419, 319, 445, 344, 470, 364, 490, 363, 489, 343, 469, 318, 444, 292, 418, 273, 399, 291, 417, 317, 443, 342, 468, 341, 467, 316, 442, 290, 416, 272, 398, 261, 387, 271, 397, 289, 415, 315, 441, 306, 432, 282, 408, 266, 392, 258, 384)
	L = (1, 254)(2, 253)(3, 259)(4, 261)(5, 263)(6, 265)(7, 255)(8, 269)(9, 256)(10, 273)(11, 257)(12, 277)(13, 258)(14, 281)(15, 275)(16, 279)(17, 260)(18, 287)(19, 276)(20, 280)(21, 262)(22, 293)(23, 267)(24, 271)(25, 264)(26, 299)(27, 268)(28, 272)(29, 266)(30, 305)(31, 297)(32, 303)(33, 295)(34, 301)(35, 270)(36, 313)(37, 298)(38, 304)(39, 296)(40, 302)(41, 274)(42, 321)(43, 285)(44, 291)(45, 283)(46, 289)(47, 278)(48, 328)(49, 286)(50, 292)(51, 284)(52, 290)(53, 282)(54, 334)(55, 326)(56, 332)(57, 324)(58, 330)(59, 323)(60, 322)(61, 288)(62, 319)(63, 327)(64, 333)(65, 325)(66, 331)(67, 314)(68, 329)(69, 294)(70, 312)(71, 311)(72, 309)(73, 317)(74, 307)(75, 315)(76, 300)(77, 320)(78, 310)(79, 318)(80, 308)(81, 316)(82, 306)(83, 352)(84, 350)(85, 356)(86, 348)(87, 354)(88, 347)(89, 358)(90, 351)(91, 357)(92, 349)(93, 355)(94, 353)(95, 340)(96, 338)(97, 344)(98, 336)(99, 342)(100, 335)(101, 346)(102, 339)(103, 345)(104, 337)(105, 343)(106, 341)(107, 370)(108, 368)(109, 372)(110, 367)(111, 374)(112, 369)(113, 373)(114, 371)(115, 362)(116, 360)(117, 364)(118, 359)(119, 366)(120, 361)(121, 365)(122, 363)(123, 378)(124, 377)(125, 376)(126, 375)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E27.2117
Graph:: bipartite
	v = 65 e = 252 f = 135
	degree seq :: [ 4^63, 126^2 ]

E27.2117 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 63})
Quotient :: dipole
Aut^+ = C7 x D18 (small group id <126, 3>)
Aut   = D14 x D18 (small group id <252, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-2 * Y1^2 * Y3^3 * Y1, Y3^-1 * Y1 * Y3 * Y1^-3 * Y3 * Y1 * Y3^-1 * Y1, Y1 * Y3^-7 * Y1 * Y3^2, Y1^-1 * Y3^2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1^-1 * Y3^2, Y3^2 * Y1^-3 * Y3^2 * Y1^-7, (Y3 * Y2^-1)^63 ]
Map::
	R = (1, 127, 2, 128, 6, 132, 16, 142, 34, 160, 60, 186, 94, 220, 120, 246, 115, 241, 83, 209, 53, 179, 27, 153, 13, 139, 4, 130)(3, 129, 9, 135, 17, 143, 8, 134, 21, 147, 35, 161, 62, 188, 95, 221, 122, 248, 112, 238, 84, 210, 50, 176, 28, 154, 11, 137)(5, 131, 14, 140, 18, 144, 37, 163, 61, 187, 96, 222, 121, 247, 114, 240, 86, 212, 52, 178, 30, 156, 12, 138, 20, 146, 7, 133)(10, 136, 24, 150, 36, 162, 23, 149, 42, 168, 22, 148, 43, 169, 63, 189, 98, 224, 123, 249, 113, 239, 81, 207, 51, 177, 26, 152)(15, 141, 32, 158, 38, 164, 65, 191, 97, 223, 124, 250, 117, 243, 85, 211, 55, 181, 29, 155, 41, 167, 19, 145, 39, 165, 31, 157)(25, 151, 47, 173, 64, 190, 46, 172, 71, 197, 45, 171, 72, 198, 44, 170, 73, 199, 99, 225, 126, 252, 110, 236, 82, 208, 49, 175)(33, 159, 58, 184, 66, 192, 100, 226, 125, 251, 116, 242, 88, 214, 54, 180, 70, 196, 40, 166, 68, 194, 56, 182, 67, 193, 57, 183)(48, 174, 78, 204, 93, 219, 77, 203, 105, 231, 76, 202, 106, 232, 75, 201, 107, 233, 74, 200, 108, 234, 119, 245, 111, 237, 80, 206)(59, 185, 92, 218, 101, 227, 109, 235, 118, 244, 87, 213, 104, 230, 69, 195, 103, 229, 89, 215, 102, 228, 90, 216, 79, 205, 91, 217)(253, 379)(254, 380)(255, 381)(256, 382)(257, 383)(258, 384)(259, 385)(260, 386)(261, 387)(262, 388)(263, 389)(264, 390)(265, 391)(266, 392)(267, 393)(268, 394)(269, 395)(270, 396)(271, 397)(272, 398)(273, 399)(274, 400)(275, 401)(276, 402)(277, 403)(278, 404)(279, 405)(280, 406)(281, 407)(282, 408)(283, 409)(284, 410)(285, 411)(286, 412)(287, 413)(288, 414)(289, 415)(290, 416)(291, 417)(292, 418)(293, 419)(294, 420)(295, 421)(296, 422)(297, 423)(298, 424)(299, 425)(300, 426)(301, 427)(302, 428)(303, 429)(304, 430)(305, 431)(306, 432)(307, 433)(308, 434)(309, 435)(310, 436)(311, 437)(312, 438)(313, 439)(314, 440)(315, 441)(316, 442)(317, 443)(318, 444)(319, 445)(320, 446)(321, 447)(322, 448)(323, 449)(324, 450)(325, 451)(326, 452)(327, 453)(328, 454)(329, 455)(330, 456)(331, 457)(332, 458)(333, 459)(334, 460)(335, 461)(336, 462)(337, 463)(338, 464)(339, 465)(340, 466)(341, 467)(342, 468)(343, 469)(344, 470)(345, 471)(346, 472)(347, 473)(348, 474)(349, 475)(350, 476)(351, 477)(352, 478)(353, 479)(354, 480)(355, 481)(356, 482)(357, 483)(358, 484)(359, 485)(360, 486)(361, 487)(362, 488)(363, 489)(364, 490)(365, 491)(366, 492)(367, 493)(368, 494)(369, 495)(370, 496)(371, 497)(372, 498)(373, 499)(374, 500)(375, 501)(376, 502)(377, 503)(378, 504)
	L = (1, 255)(2, 259)(3, 262)(4, 264)(5, 253)(6, 269)(7, 271)(8, 254)(9, 256)(10, 277)(11, 279)(12, 281)(13, 280)(14, 283)(15, 257)(16, 266)(17, 288)(18, 258)(19, 292)(20, 265)(21, 294)(22, 260)(23, 261)(24, 263)(25, 300)(26, 302)(27, 304)(28, 303)(29, 306)(30, 305)(31, 308)(32, 309)(33, 267)(34, 273)(35, 268)(36, 316)(37, 284)(38, 270)(39, 272)(40, 321)(41, 282)(42, 323)(43, 324)(44, 274)(45, 275)(46, 276)(47, 278)(48, 331)(49, 333)(50, 335)(51, 334)(52, 337)(53, 336)(54, 339)(55, 338)(56, 341)(57, 342)(58, 343)(59, 285)(60, 289)(61, 286)(62, 295)(63, 287)(64, 345)(65, 310)(66, 290)(67, 291)(68, 293)(69, 327)(70, 307)(71, 357)(72, 358)(73, 359)(74, 296)(75, 297)(76, 298)(77, 299)(78, 301)(79, 319)(80, 362)(81, 364)(82, 363)(83, 366)(84, 365)(85, 368)(86, 367)(87, 328)(88, 369)(89, 326)(90, 371)(91, 332)(92, 330)(93, 311)(94, 314)(95, 312)(96, 317)(97, 313)(98, 325)(99, 315)(100, 344)(101, 318)(102, 320)(103, 322)(104, 340)(105, 353)(106, 370)(107, 356)(108, 355)(109, 329)(110, 375)(111, 354)(112, 372)(113, 378)(114, 376)(115, 374)(116, 361)(117, 373)(118, 377)(119, 351)(120, 348)(121, 346)(122, 350)(123, 347)(124, 352)(125, 349)(126, 360)(127, 379)(128, 380)(129, 381)(130, 382)(131, 383)(132, 384)(133, 385)(134, 386)(135, 387)(136, 388)(137, 389)(138, 390)(139, 391)(140, 392)(141, 393)(142, 394)(143, 395)(144, 396)(145, 397)(146, 398)(147, 399)(148, 400)(149, 401)(150, 402)(151, 403)(152, 404)(153, 405)(154, 406)(155, 407)(156, 408)(157, 409)(158, 410)(159, 411)(160, 412)(161, 413)(162, 414)(163, 415)(164, 416)(165, 417)(166, 418)(167, 419)(168, 420)(169, 421)(170, 422)(171, 423)(172, 424)(173, 425)(174, 426)(175, 427)(176, 428)(177, 429)(178, 430)(179, 431)(180, 432)(181, 433)(182, 434)(183, 435)(184, 436)(185, 437)(186, 438)(187, 439)(188, 440)(189, 441)(190, 442)(191, 443)(192, 444)(193, 445)(194, 446)(195, 447)(196, 448)(197, 449)(198, 450)(199, 451)(200, 452)(201, 453)(202, 454)(203, 455)(204, 456)(205, 457)(206, 458)(207, 459)(208, 460)(209, 461)(210, 462)(211, 463)(212, 464)(213, 465)(214, 466)(215, 467)(216, 468)(217, 469)(218, 470)(219, 471)(220, 472)(221, 473)(222, 474)(223, 475)(224, 476)(225, 477)(226, 478)(227, 479)(228, 480)(229, 481)(230, 482)(231, 483)(232, 484)(233, 485)(234, 486)(235, 487)(236, 488)(237, 489)(238, 490)(239, 491)(240, 492)(241, 493)(242, 494)(243, 495)(244, 496)(245, 497)(246, 498)(247, 499)(248, 500)(249, 501)(250, 502)(251, 503)(252, 504)
	local type(s) :: { ( 4, 126 ), ( 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126, 4, 126 ) }
Outer automorphisms :: reflexible
Dual of E27.2116
Graph:: simple bipartite
	v = 135 e = 252 f = 65
	degree seq :: [ 2^126, 28^9 ]

E27.2118 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 9, 36})
Quotient :: regular
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-5 * T2 * T1^-2 * T2 * T1^-2 * T2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^36 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 43, 75, 113, 102, 127, 99, 58, 88, 119, 137, 143, 142, 134, 140, 132, 139, 144, 141, 135, 104, 62, 92, 122, 97, 124, 112, 74, 42, 22, 10, 4)(3, 7, 15, 24, 45, 78, 114, 94, 54, 90, 51, 28, 50, 87, 115, 136, 129, 108, 128, 91, 120, 138, 123, 110, 69, 39, 68, 84, 48, 83, 117, 80, 65, 37, 18, 8)(6, 13, 27, 44, 77, 70, 109, 67, 38, 66, 82, 47, 81, 118, 107, 133, 101, 59, 100, 121, 98, 131, 106, 63, 35, 17, 34, 56, 31, 55, 95, 73, 41, 21, 30, 14)(9, 19, 26, 12, 25, 46, 76, 64, 36, 60, 33, 16, 32, 57, 79, 116, 105, 130, 103, 61, 89, 126, 96, 125, 111, 72, 93, 53, 29, 52, 86, 49, 85, 71, 40, 20)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 58)(33, 59)(34, 61)(35, 62)(40, 70)(41, 72)(42, 71)(43, 76)(45, 79)(46, 80)(50, 88)(51, 89)(52, 91)(53, 92)(55, 96)(56, 97)(57, 98)(60, 102)(63, 105)(64, 107)(65, 106)(66, 99)(67, 108)(68, 101)(69, 104)(73, 78)(74, 95)(75, 114)(77, 115)(81, 119)(82, 120)(83, 121)(84, 122)(85, 123)(86, 124)(87, 125)(90, 127)(93, 129)(94, 130)(100, 132)(103, 134)(109, 113)(110, 118)(111, 135)(112, 117)(116, 137)(126, 139)(128, 140)(131, 141)(133, 142)(136, 143)(138, 144)
	local type(s) :: { ( 9^36 ) }
Outer automorphisms :: reflexible
Dual of E27.2119
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 4 e = 72 f = 16
	degree seq :: [ 36^4 ]

E27.2119 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 9, 36})
Quotient :: regular
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, T1^9, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T2 * T1 * T2 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 42, 22, 10, 4)(3, 7, 15, 24, 44, 64, 37, 18, 8)(6, 13, 27, 43, 72, 41, 21, 30, 14)(9, 19, 26, 12, 25, 45, 70, 40, 20)(16, 32, 56, 73, 102, 63, 36, 59, 33)(17, 34, 55, 31, 54, 89, 100, 62, 35)(28, 49, 81, 108, 122, 88, 53, 84, 50)(29, 51, 80, 48, 79, 107, 71, 87, 52)(38, 65, 76, 46, 75, 106, 69, 104, 66)(39, 67, 78, 47, 77, 109, 74, 105, 68)(57, 82, 110, 132, 139, 127, 96, 118, 93)(58, 94, 112, 92, 124, 131, 101, 126, 95)(60, 83, 117, 90, 116, 130, 99, 121, 97)(61, 86, 113, 91, 115, 134, 123, 129, 98)(85, 111, 135, 114, 133, 138, 120, 103, 119)(125, 136, 143, 140, 142, 144, 141, 128, 137)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 43)(25, 46)(26, 47)(27, 48)(30, 53)(32, 57)(33, 58)(34, 60)(35, 61)(40, 69)(41, 71)(42, 70)(44, 73)(45, 74)(49, 82)(50, 83)(51, 85)(52, 86)(54, 90)(55, 91)(56, 92)(59, 96)(62, 99)(63, 101)(64, 100)(65, 93)(66, 103)(67, 95)(68, 98)(72, 108)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(84, 118)(87, 120)(88, 121)(89, 123)(94, 125)(97, 128)(102, 132)(104, 127)(105, 131)(106, 133)(107, 129)(109, 134)(117, 136)(119, 137)(122, 139)(124, 140)(126, 141)(130, 142)(135, 143)(138, 144)
	local type(s) :: { ( 36^9 ) }
Outer automorphisms :: reflexible
Dual of E27.2118
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 16 e = 72 f = 4
	degree seq :: [ 9^16 ]

E27.2120 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 36})
Quotient :: edge
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^3 * T1 * T2^-1, T2^9, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1, (T2 * T1 * T2^-1 * T1)^4 ]
Map::
	R = (1, 3, 8, 18, 37, 42, 22, 10, 4)(2, 5, 12, 26, 49, 54, 30, 14, 6)(7, 15, 32, 58, 72, 41, 21, 34, 16)(9, 19, 36, 17, 35, 63, 70, 40, 20)(11, 23, 44, 76, 90, 53, 29, 46, 24)(13, 27, 48, 25, 47, 81, 88, 52, 28)(31, 55, 91, 108, 131, 97, 61, 92, 56)(33, 59, 94, 57, 93, 107, 71, 96, 60)(38, 65, 99, 62, 98, 106, 69, 104, 66)(39, 67, 102, 64, 101, 132, 100, 105, 68)(43, 73, 109, 126, 138, 115, 79, 110, 74)(45, 77, 112, 75, 111, 125, 89, 114, 78)(50, 83, 117, 80, 116, 124, 87, 122, 84)(51, 85, 120, 82, 119, 139, 118, 123, 86)(95, 128, 141, 127, 133, 142, 130, 103, 129)(113, 135, 143, 134, 140, 144, 137, 121, 136)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 175)(160, 177)(162, 170)(163, 182)(164, 183)(166, 174)(167, 187)(168, 189)(171, 194)(172, 195)(176, 201)(178, 205)(179, 206)(180, 208)(181, 202)(184, 213)(185, 215)(186, 214)(188, 219)(190, 223)(191, 224)(192, 226)(193, 220)(196, 231)(197, 233)(198, 232)(199, 217)(200, 227)(203, 239)(204, 229)(207, 244)(209, 218)(210, 247)(211, 222)(212, 230)(216, 252)(221, 257)(225, 262)(228, 265)(234, 270)(235, 260)(236, 254)(237, 271)(238, 263)(240, 274)(241, 266)(242, 253)(243, 272)(245, 256)(246, 264)(248, 259)(249, 269)(250, 277)(251, 267)(255, 278)(258, 281)(261, 279)(268, 284)(273, 280)(275, 282)(276, 283)(285, 287)(286, 288)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 72, 72 ), ( 72^9 ) }
Outer automorphisms :: reflexible
Dual of E27.2124
Transitivity :: ET+
Graph:: simple bipartite
	v = 88 e = 144 f = 4
	degree seq :: [ 2^72, 9^16 ]

E27.2121 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 36})
Quotient :: edge
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1 * T2^-1 * T1^-4 * T2^-1 * T1, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2^-1 * T1^-4 * T2^-1 * T1^2, T2 * T1^-2 * T2^2 * T1^-2 * T2 * T1^-1, T1^-1 * T2^2 * T1^-1 * T2^32 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 26, 63, 111, 138, 129, 100, 130, 96, 51, 34, 71, 114, 139, 122, 140, 144, 141, 126, 121, 85, 42, 16, 41, 84, 120, 88, 124, 132, 101, 55, 39, 15, 5)(2, 7, 19, 48, 27, 65, 113, 107, 59, 106, 72, 30, 13, 33, 76, 112, 104, 135, 143, 133, 103, 134, 117, 75, 40, 35, 78, 109, 61, 108, 136, 116, 69, 56, 22, 8)(4, 12, 31, 64, 80, 118, 137, 110, 79, 115, 67, 29, 70, 52, 99, 128, 92, 127, 142, 131, 98, 91, 46, 18, 6, 17, 43, 87, 49, 94, 119, 83, 38, 60, 24, 9)(11, 28, 68, 54, 21, 53, 93, 47, 20, 50, 97, 66, 45, 90, 123, 86, 44, 89, 125, 95, 77, 82, 105, 58, 23, 57, 102, 73, 32, 74, 81, 37, 14, 36, 62, 25)(145, 146, 150, 160, 184, 214, 178, 157, 148)(147, 153, 167, 185, 162, 189, 215, 173, 155)(149, 158, 179, 186, 221, 177, 195, 164, 151)(152, 165, 196, 219, 176, 156, 174, 188, 161)(154, 169, 205, 228, 202, 248, 258, 210, 171)(159, 182, 226, 229, 242, 194, 240, 223, 180)(163, 191, 236, 222, 181, 224, 220, 239, 193)(166, 199, 218, 261, 270, 233, 216, 244, 197)(168, 203, 234, 190, 213, 172, 211, 247, 201)(170, 192, 231, 264, 253, 272, 283, 256, 208)(175, 217, 232, 187, 230, 266, 243, 198, 207)(183, 200, 235, 265, 278, 259, 274, 250, 204)(206, 254, 279, 249, 227, 209, 241, 275, 252)(212, 260, 268, 246, 277, 284, 267, 251, 255)(225, 245, 238, 269, 285, 271, 237, 273, 262)(257, 263, 276, 280, 286, 288, 287, 281, 282)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4^9 ), ( 4^36 ) }
Outer automorphisms :: reflexible
Dual of E27.2125
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 144 f = 72
	degree seq :: [ 9^16, 36^4 ]

E27.2122 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 36})
Quotient :: edge
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-1 * T2 * T1^-5 * T2 * T1^-2 * T2 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^36 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 58)(33, 59)(34, 61)(35, 62)(40, 70)(41, 72)(42, 71)(43, 76)(45, 79)(46, 80)(50, 88)(51, 89)(52, 91)(53, 92)(55, 96)(56, 97)(57, 98)(60, 102)(63, 105)(64, 107)(65, 106)(66, 99)(67, 108)(68, 101)(69, 104)(73, 78)(74, 95)(75, 114)(77, 115)(81, 119)(82, 120)(83, 121)(84, 122)(85, 123)(86, 124)(87, 125)(90, 127)(93, 129)(94, 130)(100, 132)(103, 134)(109, 113)(110, 118)(111, 135)(112, 117)(116, 137)(126, 139)(128, 140)(131, 141)(133, 142)(136, 143)(138, 144)(145, 146, 149, 155, 167, 187, 219, 257, 246, 271, 243, 202, 232, 263, 281, 287, 286, 278, 284, 276, 283, 288, 285, 279, 248, 206, 236, 266, 241, 268, 256, 218, 186, 166, 154, 148)(147, 151, 159, 168, 189, 222, 258, 238, 198, 234, 195, 172, 194, 231, 259, 280, 273, 252, 272, 235, 264, 282, 267, 254, 213, 183, 212, 228, 192, 227, 261, 224, 209, 181, 162, 152)(150, 157, 171, 188, 221, 214, 253, 211, 182, 210, 226, 191, 225, 262, 251, 277, 245, 203, 244, 265, 242, 275, 250, 207, 179, 161, 178, 200, 175, 199, 239, 217, 185, 165, 174, 158)(153, 163, 170, 156, 169, 190, 220, 208, 180, 204, 177, 160, 176, 201, 223, 260, 249, 274, 247, 205, 233, 270, 240, 269, 255, 216, 237, 197, 173, 196, 230, 193, 229, 215, 184, 164)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 18, 18 ), ( 18^36 ) }
Outer automorphisms :: reflexible
Dual of E27.2123
Transitivity :: ET+
Graph:: simple bipartite
	v = 76 e = 144 f = 16
	degree seq :: [ 2^72, 36^4 ]

E27.2123 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 36})
Quotient :: loop
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^3 * T1 * T2^-1, T2^9, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1, (T2 * T1 * T2^-1 * T1)^4 ]
Map::
	R = (1, 145, 3, 147, 8, 152, 18, 162, 37, 181, 42, 186, 22, 166, 10, 154, 4, 148)(2, 146, 5, 149, 12, 156, 26, 170, 49, 193, 54, 198, 30, 174, 14, 158, 6, 150)(7, 151, 15, 159, 32, 176, 58, 202, 72, 216, 41, 185, 21, 165, 34, 178, 16, 160)(9, 153, 19, 163, 36, 180, 17, 161, 35, 179, 63, 207, 70, 214, 40, 184, 20, 164)(11, 155, 23, 167, 44, 188, 76, 220, 90, 234, 53, 197, 29, 173, 46, 190, 24, 168)(13, 157, 27, 171, 48, 192, 25, 169, 47, 191, 81, 225, 88, 232, 52, 196, 28, 172)(31, 175, 55, 199, 91, 235, 108, 252, 131, 275, 97, 241, 61, 205, 92, 236, 56, 200)(33, 177, 59, 203, 94, 238, 57, 201, 93, 237, 107, 251, 71, 215, 96, 240, 60, 204)(38, 182, 65, 209, 99, 243, 62, 206, 98, 242, 106, 250, 69, 213, 104, 248, 66, 210)(39, 183, 67, 211, 102, 246, 64, 208, 101, 245, 132, 276, 100, 244, 105, 249, 68, 212)(43, 187, 73, 217, 109, 253, 126, 270, 138, 282, 115, 259, 79, 223, 110, 254, 74, 218)(45, 189, 77, 221, 112, 256, 75, 219, 111, 255, 125, 269, 89, 233, 114, 258, 78, 222)(50, 194, 83, 227, 117, 261, 80, 224, 116, 260, 124, 268, 87, 231, 122, 266, 84, 228)(51, 195, 85, 229, 120, 264, 82, 226, 119, 263, 139, 283, 118, 262, 123, 267, 86, 230)(95, 239, 128, 272, 141, 285, 127, 271, 133, 277, 142, 286, 130, 274, 103, 247, 129, 273)(113, 257, 135, 279, 143, 287, 134, 278, 140, 284, 144, 288, 137, 281, 121, 265, 136, 280)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 169)(13, 150)(14, 173)(15, 175)(16, 177)(17, 152)(18, 170)(19, 182)(20, 183)(21, 154)(22, 174)(23, 187)(24, 189)(25, 156)(26, 162)(27, 194)(28, 195)(29, 158)(30, 166)(31, 159)(32, 201)(33, 160)(34, 205)(35, 206)(36, 208)(37, 202)(38, 163)(39, 164)(40, 213)(41, 215)(42, 214)(43, 167)(44, 219)(45, 168)(46, 223)(47, 224)(48, 226)(49, 220)(50, 171)(51, 172)(52, 231)(53, 233)(54, 232)(55, 217)(56, 227)(57, 176)(58, 181)(59, 239)(60, 229)(61, 178)(62, 179)(63, 244)(64, 180)(65, 218)(66, 247)(67, 222)(68, 230)(69, 184)(70, 186)(71, 185)(72, 252)(73, 199)(74, 209)(75, 188)(76, 193)(77, 257)(78, 211)(79, 190)(80, 191)(81, 262)(82, 192)(83, 200)(84, 265)(85, 204)(86, 212)(87, 196)(88, 198)(89, 197)(90, 270)(91, 260)(92, 254)(93, 271)(94, 263)(95, 203)(96, 274)(97, 266)(98, 253)(99, 272)(100, 207)(101, 256)(102, 264)(103, 210)(104, 259)(105, 269)(106, 277)(107, 267)(108, 216)(109, 242)(110, 236)(111, 278)(112, 245)(113, 221)(114, 281)(115, 248)(116, 235)(117, 279)(118, 225)(119, 238)(120, 246)(121, 228)(122, 241)(123, 251)(124, 284)(125, 249)(126, 234)(127, 237)(128, 243)(129, 280)(130, 240)(131, 282)(132, 283)(133, 250)(134, 255)(135, 261)(136, 273)(137, 258)(138, 275)(139, 276)(140, 268)(141, 287)(142, 288)(143, 285)(144, 286)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.2122
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 16 e = 144 f = 76
	degree seq :: [ 18^16 ]

E27.2124 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 36})
Quotient :: loop
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1 * T2^-1 * T1^-4 * T2^-1 * T1, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2^-1 * T1^-4 * T2^-1 * T1^2, T2 * T1^-2 * T2^2 * T1^-2 * T2 * T1^-1, T1^-1 * T2^2 * T1^-1 * T2^32 ]
Map::
	R = (1, 145, 3, 147, 10, 154, 26, 170, 63, 207, 111, 255, 138, 282, 129, 273, 100, 244, 130, 274, 96, 240, 51, 195, 34, 178, 71, 215, 114, 258, 139, 283, 122, 266, 140, 284, 144, 288, 141, 285, 126, 270, 121, 265, 85, 229, 42, 186, 16, 160, 41, 185, 84, 228, 120, 264, 88, 232, 124, 268, 132, 276, 101, 245, 55, 199, 39, 183, 15, 159, 5, 149)(2, 146, 7, 151, 19, 163, 48, 192, 27, 171, 65, 209, 113, 257, 107, 251, 59, 203, 106, 250, 72, 216, 30, 174, 13, 157, 33, 177, 76, 220, 112, 256, 104, 248, 135, 279, 143, 287, 133, 277, 103, 247, 134, 278, 117, 261, 75, 219, 40, 184, 35, 179, 78, 222, 109, 253, 61, 205, 108, 252, 136, 280, 116, 260, 69, 213, 56, 200, 22, 166, 8, 152)(4, 148, 12, 156, 31, 175, 64, 208, 80, 224, 118, 262, 137, 281, 110, 254, 79, 223, 115, 259, 67, 211, 29, 173, 70, 214, 52, 196, 99, 243, 128, 272, 92, 236, 127, 271, 142, 286, 131, 275, 98, 242, 91, 235, 46, 190, 18, 162, 6, 150, 17, 161, 43, 187, 87, 231, 49, 193, 94, 238, 119, 263, 83, 227, 38, 182, 60, 204, 24, 168, 9, 153)(11, 155, 28, 172, 68, 212, 54, 198, 21, 165, 53, 197, 93, 237, 47, 191, 20, 164, 50, 194, 97, 241, 66, 210, 45, 189, 90, 234, 123, 267, 86, 230, 44, 188, 89, 233, 125, 269, 95, 239, 77, 221, 82, 226, 105, 249, 58, 202, 23, 167, 57, 201, 102, 246, 73, 217, 32, 176, 74, 218, 81, 225, 37, 181, 14, 158, 36, 180, 62, 206, 25, 169)
	L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 158)(6, 160)(7, 149)(8, 165)(9, 167)(10, 169)(11, 147)(12, 174)(13, 148)(14, 179)(15, 182)(16, 184)(17, 152)(18, 189)(19, 191)(20, 151)(21, 196)(22, 199)(23, 185)(24, 203)(25, 205)(26, 192)(27, 154)(28, 211)(29, 155)(30, 188)(31, 217)(32, 156)(33, 195)(34, 157)(35, 186)(36, 159)(37, 224)(38, 226)(39, 200)(40, 214)(41, 162)(42, 221)(43, 230)(44, 161)(45, 215)(46, 213)(47, 236)(48, 231)(49, 163)(50, 240)(51, 164)(52, 219)(53, 166)(54, 207)(55, 218)(56, 235)(57, 168)(58, 248)(59, 234)(60, 183)(61, 228)(62, 254)(63, 175)(64, 170)(65, 241)(66, 171)(67, 247)(68, 260)(69, 172)(70, 178)(71, 173)(72, 244)(73, 232)(74, 261)(75, 176)(76, 239)(77, 177)(78, 181)(79, 180)(80, 220)(81, 245)(82, 229)(83, 209)(84, 202)(85, 242)(86, 266)(87, 264)(88, 187)(89, 216)(90, 190)(91, 265)(92, 222)(93, 273)(94, 269)(95, 193)(96, 223)(97, 275)(98, 194)(99, 198)(100, 197)(101, 238)(102, 277)(103, 201)(104, 258)(105, 227)(106, 204)(107, 255)(108, 206)(109, 272)(110, 279)(111, 212)(112, 208)(113, 263)(114, 210)(115, 274)(116, 268)(117, 270)(118, 225)(119, 276)(120, 253)(121, 278)(122, 243)(123, 251)(124, 246)(125, 285)(126, 233)(127, 237)(128, 283)(129, 262)(130, 250)(131, 252)(132, 280)(133, 284)(134, 259)(135, 249)(136, 286)(137, 282)(138, 257)(139, 256)(140, 267)(141, 271)(142, 288)(143, 281)(144, 287)
	local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) }
Outer automorphisms :: reflexible
Dual of E27.2120
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 144 f = 88
	degree seq :: [ 72^4 ]

E27.2125 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 36})
Quotient :: loop
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-1 * T2 * T1^-5 * T2 * T1^-2 * T2 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^36 ]
Map:: polytopal non-degenerate
	R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 17, 161)(10, 154, 21, 165)(11, 155, 24, 168)(13, 157, 28, 172)(14, 158, 29, 173)(15, 159, 31, 175)(18, 162, 36, 180)(19, 163, 38, 182)(20, 164, 39, 183)(22, 166, 37, 181)(23, 167, 44, 188)(25, 169, 47, 191)(26, 170, 48, 192)(27, 171, 49, 193)(30, 174, 54, 198)(32, 176, 58, 202)(33, 177, 59, 203)(34, 178, 61, 205)(35, 179, 62, 206)(40, 184, 70, 214)(41, 185, 72, 216)(42, 186, 71, 215)(43, 187, 76, 220)(45, 189, 79, 223)(46, 190, 80, 224)(50, 194, 88, 232)(51, 195, 89, 233)(52, 196, 91, 235)(53, 197, 92, 236)(55, 199, 96, 240)(56, 200, 97, 241)(57, 201, 98, 242)(60, 204, 102, 246)(63, 207, 105, 249)(64, 208, 107, 251)(65, 209, 106, 250)(66, 210, 99, 243)(67, 211, 108, 252)(68, 212, 101, 245)(69, 213, 104, 248)(73, 217, 78, 222)(74, 218, 95, 239)(75, 219, 114, 258)(77, 221, 115, 259)(81, 225, 119, 263)(82, 226, 120, 264)(83, 227, 121, 265)(84, 228, 122, 266)(85, 229, 123, 267)(86, 230, 124, 268)(87, 231, 125, 269)(90, 234, 127, 271)(93, 237, 129, 273)(94, 238, 130, 274)(100, 244, 132, 276)(103, 247, 134, 278)(109, 253, 113, 257)(110, 254, 118, 262)(111, 255, 135, 279)(112, 256, 117, 261)(116, 260, 137, 281)(126, 270, 139, 283)(128, 272, 140, 284)(131, 275, 141, 285)(133, 277, 142, 286)(136, 280, 143, 287)(138, 282, 144, 288)
	L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 168)(16, 176)(17, 178)(18, 152)(19, 170)(20, 153)(21, 174)(22, 154)(23, 187)(24, 189)(25, 190)(26, 156)(27, 188)(28, 194)(29, 196)(30, 158)(31, 199)(32, 201)(33, 160)(34, 200)(35, 161)(36, 204)(37, 162)(38, 210)(39, 212)(40, 164)(41, 165)(42, 166)(43, 219)(44, 221)(45, 222)(46, 220)(47, 225)(48, 227)(49, 229)(50, 231)(51, 172)(52, 230)(53, 173)(54, 234)(55, 239)(56, 175)(57, 223)(58, 232)(59, 244)(60, 177)(61, 233)(62, 236)(63, 179)(64, 180)(65, 181)(66, 226)(67, 182)(68, 228)(69, 183)(70, 253)(71, 184)(72, 237)(73, 185)(74, 186)(75, 257)(76, 208)(77, 214)(78, 258)(79, 260)(80, 209)(81, 262)(82, 191)(83, 261)(84, 192)(85, 215)(86, 193)(87, 259)(88, 263)(89, 270)(90, 195)(91, 264)(92, 266)(93, 197)(94, 198)(95, 217)(96, 269)(97, 268)(98, 275)(99, 202)(100, 265)(101, 203)(102, 271)(103, 205)(104, 206)(105, 274)(106, 207)(107, 277)(108, 272)(109, 211)(110, 213)(111, 216)(112, 218)(113, 246)(114, 238)(115, 280)(116, 249)(117, 224)(118, 251)(119, 281)(120, 282)(121, 242)(122, 241)(123, 254)(124, 256)(125, 255)(126, 240)(127, 243)(128, 235)(129, 252)(130, 247)(131, 250)(132, 283)(133, 245)(134, 284)(135, 248)(136, 273)(137, 287)(138, 267)(139, 288)(140, 276)(141, 279)(142, 278)(143, 286)(144, 285)
	local type(s) :: { ( 9, 36, 9, 36 ) }
Outer automorphisms :: reflexible
Dual of E27.2121
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 72 e = 144 f = 20
	degree seq :: [ 4^72 ]

E27.2126 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (R * Y2^-2 * Y1)^2, Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-1, (Y2^-2 * R * Y2^-1)^2, Y2^9, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y2 * Y1 * Y2^-1 * Y1)^4, (Y3 * Y2^-1)^36 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 31, 175)(16, 160, 33, 177)(18, 162, 26, 170)(19, 163, 38, 182)(20, 164, 39, 183)(22, 166, 30, 174)(23, 167, 43, 187)(24, 168, 45, 189)(27, 171, 50, 194)(28, 172, 51, 195)(32, 176, 57, 201)(34, 178, 61, 205)(35, 179, 62, 206)(36, 180, 64, 208)(37, 181, 58, 202)(40, 184, 69, 213)(41, 185, 71, 215)(42, 186, 70, 214)(44, 188, 75, 219)(46, 190, 79, 223)(47, 191, 80, 224)(48, 192, 82, 226)(49, 193, 76, 220)(52, 196, 87, 231)(53, 197, 89, 233)(54, 198, 88, 232)(55, 199, 73, 217)(56, 200, 83, 227)(59, 203, 95, 239)(60, 204, 85, 229)(63, 207, 100, 244)(65, 209, 74, 218)(66, 210, 103, 247)(67, 211, 78, 222)(68, 212, 86, 230)(72, 216, 108, 252)(77, 221, 113, 257)(81, 225, 118, 262)(84, 228, 121, 265)(90, 234, 126, 270)(91, 235, 116, 260)(92, 236, 110, 254)(93, 237, 127, 271)(94, 238, 119, 263)(96, 240, 130, 274)(97, 241, 122, 266)(98, 242, 109, 253)(99, 243, 128, 272)(101, 245, 112, 256)(102, 246, 120, 264)(104, 248, 115, 259)(105, 249, 125, 269)(106, 250, 133, 277)(107, 251, 123, 267)(111, 255, 134, 278)(114, 258, 137, 281)(117, 261, 135, 279)(124, 268, 140, 284)(129, 273, 136, 280)(131, 275, 138, 282)(132, 276, 139, 283)(141, 285, 143, 287)(142, 286, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 325, 469, 330, 474, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 337, 481, 342, 486, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 320, 464, 346, 490, 360, 504, 329, 473, 309, 453, 322, 466, 304, 448)(297, 441, 307, 451, 324, 468, 305, 449, 323, 467, 351, 495, 358, 502, 328, 472, 308, 452)(299, 443, 311, 455, 332, 476, 364, 508, 378, 522, 341, 485, 317, 461, 334, 478, 312, 456)(301, 445, 315, 459, 336, 480, 313, 457, 335, 479, 369, 513, 376, 520, 340, 484, 316, 460)(319, 463, 343, 487, 379, 523, 396, 540, 419, 563, 385, 529, 349, 493, 380, 524, 344, 488)(321, 465, 347, 491, 382, 526, 345, 489, 381, 525, 395, 539, 359, 503, 384, 528, 348, 492)(326, 470, 353, 497, 387, 531, 350, 494, 386, 530, 394, 538, 357, 501, 392, 536, 354, 498)(327, 471, 355, 499, 390, 534, 352, 496, 389, 533, 420, 564, 388, 532, 393, 537, 356, 500)(331, 475, 361, 505, 397, 541, 414, 558, 426, 570, 403, 547, 367, 511, 398, 542, 362, 506)(333, 477, 365, 509, 400, 544, 363, 507, 399, 543, 413, 557, 377, 521, 402, 546, 366, 510)(338, 482, 371, 515, 405, 549, 368, 512, 404, 548, 412, 556, 375, 519, 410, 554, 372, 516)(339, 483, 373, 517, 408, 552, 370, 514, 407, 551, 427, 571, 406, 550, 411, 555, 374, 518)(383, 527, 416, 560, 429, 573, 415, 559, 421, 565, 430, 574, 418, 562, 391, 535, 417, 561)(401, 545, 423, 567, 431, 575, 422, 566, 428, 572, 432, 576, 425, 569, 409, 553, 424, 568)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 319)(16, 321)(17, 296)(18, 314)(19, 326)(20, 327)(21, 298)(22, 318)(23, 331)(24, 333)(25, 300)(26, 306)(27, 338)(28, 339)(29, 302)(30, 310)(31, 303)(32, 345)(33, 304)(34, 349)(35, 350)(36, 352)(37, 346)(38, 307)(39, 308)(40, 357)(41, 359)(42, 358)(43, 311)(44, 363)(45, 312)(46, 367)(47, 368)(48, 370)(49, 364)(50, 315)(51, 316)(52, 375)(53, 377)(54, 376)(55, 361)(56, 371)(57, 320)(58, 325)(59, 383)(60, 373)(61, 322)(62, 323)(63, 388)(64, 324)(65, 362)(66, 391)(67, 366)(68, 374)(69, 328)(70, 330)(71, 329)(72, 396)(73, 343)(74, 353)(75, 332)(76, 337)(77, 401)(78, 355)(79, 334)(80, 335)(81, 406)(82, 336)(83, 344)(84, 409)(85, 348)(86, 356)(87, 340)(88, 342)(89, 341)(90, 414)(91, 404)(92, 398)(93, 415)(94, 407)(95, 347)(96, 418)(97, 410)(98, 397)(99, 416)(100, 351)(101, 400)(102, 408)(103, 354)(104, 403)(105, 413)(106, 421)(107, 411)(108, 360)(109, 386)(110, 380)(111, 422)(112, 389)(113, 365)(114, 425)(115, 392)(116, 379)(117, 423)(118, 369)(119, 382)(120, 390)(121, 372)(122, 385)(123, 395)(124, 428)(125, 393)(126, 378)(127, 381)(128, 387)(129, 424)(130, 384)(131, 426)(132, 427)(133, 394)(134, 399)(135, 405)(136, 417)(137, 402)(138, 419)(139, 420)(140, 412)(141, 431)(142, 432)(143, 429)(144, 430)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2129
Graph:: bipartite
	v = 88 e = 288 f = 148
	degree seq :: [ 4^72, 18^16 ]

E27.2127 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1, Y2^-1 * Y1^3 * Y2 * Y1^-3, Y1 * Y2^-1 * Y1^2 * Y2^-2 * Y1^2 * Y2^-1, Y1^9, Y1^-1 * Y2^2 * Y1^-1 * Y2^32 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 40, 184, 70, 214, 34, 178, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 41, 185, 18, 162, 45, 189, 71, 215, 29, 173, 11, 155)(5, 149, 14, 158, 35, 179, 42, 186, 77, 221, 33, 177, 51, 195, 20, 164, 7, 151)(8, 152, 21, 165, 52, 196, 75, 219, 32, 176, 12, 156, 30, 174, 44, 188, 17, 161)(10, 154, 25, 169, 61, 205, 84, 228, 58, 202, 104, 248, 114, 258, 66, 210, 27, 171)(15, 159, 38, 182, 82, 226, 85, 229, 98, 242, 50, 194, 96, 240, 79, 223, 36, 180)(19, 163, 47, 191, 92, 236, 78, 222, 37, 181, 80, 224, 76, 220, 95, 239, 49, 193)(22, 166, 55, 199, 74, 218, 117, 261, 126, 270, 89, 233, 72, 216, 100, 244, 53, 197)(24, 168, 59, 203, 90, 234, 46, 190, 69, 213, 28, 172, 67, 211, 103, 247, 57, 201)(26, 170, 48, 192, 87, 231, 120, 264, 109, 253, 128, 272, 139, 283, 112, 256, 64, 208)(31, 175, 73, 217, 88, 232, 43, 187, 86, 230, 122, 266, 99, 243, 54, 198, 63, 207)(39, 183, 56, 200, 91, 235, 121, 265, 134, 278, 115, 259, 130, 274, 106, 250, 60, 204)(62, 206, 110, 254, 135, 279, 105, 249, 83, 227, 65, 209, 97, 241, 131, 275, 108, 252)(68, 212, 116, 260, 124, 268, 102, 246, 133, 277, 140, 284, 123, 267, 107, 251, 111, 255)(81, 225, 101, 245, 94, 238, 125, 269, 141, 285, 127, 271, 93, 237, 129, 273, 118, 262)(113, 257, 119, 263, 132, 276, 136, 280, 142, 286, 144, 288, 143, 287, 137, 281, 138, 282)(289, 433, 291, 435, 298, 442, 314, 458, 351, 495, 399, 543, 426, 570, 417, 561, 388, 532, 418, 562, 384, 528, 339, 483, 322, 466, 359, 503, 402, 546, 427, 571, 410, 554, 428, 572, 432, 576, 429, 573, 414, 558, 409, 553, 373, 517, 330, 474, 304, 448, 329, 473, 372, 516, 408, 552, 376, 520, 412, 556, 420, 564, 389, 533, 343, 487, 327, 471, 303, 447, 293, 437)(290, 434, 295, 439, 307, 451, 336, 480, 315, 459, 353, 497, 401, 545, 395, 539, 347, 491, 394, 538, 360, 504, 318, 462, 301, 445, 321, 465, 364, 508, 400, 544, 392, 536, 423, 567, 431, 575, 421, 565, 391, 535, 422, 566, 405, 549, 363, 507, 328, 472, 323, 467, 366, 510, 397, 541, 349, 493, 396, 540, 424, 568, 404, 548, 357, 501, 344, 488, 310, 454, 296, 440)(292, 436, 300, 444, 319, 463, 352, 496, 368, 512, 406, 550, 425, 569, 398, 542, 367, 511, 403, 547, 355, 499, 317, 461, 358, 502, 340, 484, 387, 531, 416, 560, 380, 524, 415, 559, 430, 574, 419, 563, 386, 530, 379, 523, 334, 478, 306, 450, 294, 438, 305, 449, 331, 475, 375, 519, 337, 481, 382, 526, 407, 551, 371, 515, 326, 470, 348, 492, 312, 456, 297, 441)(299, 443, 316, 460, 356, 500, 342, 486, 309, 453, 341, 485, 381, 525, 335, 479, 308, 452, 338, 482, 385, 529, 354, 498, 333, 477, 378, 522, 411, 555, 374, 518, 332, 476, 377, 521, 413, 557, 383, 527, 365, 509, 370, 514, 393, 537, 346, 490, 311, 455, 345, 489, 390, 534, 361, 505, 320, 464, 362, 506, 369, 513, 325, 469, 302, 446, 324, 468, 350, 494, 313, 457)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 316)(12, 319)(13, 321)(14, 324)(15, 293)(16, 329)(17, 331)(18, 294)(19, 336)(20, 338)(21, 341)(22, 296)(23, 345)(24, 297)(25, 299)(26, 351)(27, 353)(28, 356)(29, 358)(30, 301)(31, 352)(32, 362)(33, 364)(34, 359)(35, 366)(36, 350)(37, 302)(38, 348)(39, 303)(40, 323)(41, 372)(42, 304)(43, 375)(44, 377)(45, 378)(46, 306)(47, 308)(48, 315)(49, 382)(50, 385)(51, 322)(52, 387)(53, 381)(54, 309)(55, 327)(56, 310)(57, 390)(58, 311)(59, 394)(60, 312)(61, 396)(62, 313)(63, 399)(64, 368)(65, 401)(66, 333)(67, 317)(68, 342)(69, 344)(70, 340)(71, 402)(72, 318)(73, 320)(74, 369)(75, 328)(76, 400)(77, 370)(78, 397)(79, 403)(80, 406)(81, 325)(82, 393)(83, 326)(84, 408)(85, 330)(86, 332)(87, 337)(88, 412)(89, 413)(90, 411)(91, 334)(92, 415)(93, 335)(94, 407)(95, 365)(96, 339)(97, 354)(98, 379)(99, 416)(100, 418)(101, 343)(102, 361)(103, 422)(104, 423)(105, 346)(106, 360)(107, 347)(108, 424)(109, 349)(110, 367)(111, 426)(112, 392)(113, 395)(114, 427)(115, 355)(116, 357)(117, 363)(118, 425)(119, 371)(120, 376)(121, 373)(122, 428)(123, 374)(124, 420)(125, 383)(126, 409)(127, 430)(128, 380)(129, 388)(130, 384)(131, 386)(132, 389)(133, 391)(134, 405)(135, 431)(136, 404)(137, 398)(138, 417)(139, 410)(140, 432)(141, 414)(142, 419)(143, 421)(144, 429)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2128
Graph:: bipartite
	v = 20 e = 288 f = 216
	degree seq :: [ 18^16, 72^4 ]

E27.2128 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-3 * Y2 * Y3^3 * Y2, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3, Y3^5 * Y2 * Y3^2 * Y2 * Y3^2 * Y2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^36 ]
Map:: polytopal
	R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 319, 463)(304, 448, 321, 465)(306, 450, 314, 458)(307, 451, 326, 470)(308, 452, 327, 471)(310, 454, 318, 462)(311, 455, 331, 475)(312, 456, 333, 477)(315, 459, 338, 482)(316, 460, 339, 483)(320, 464, 345, 489)(322, 466, 349, 493)(323, 467, 350, 494)(324, 468, 352, 496)(325, 469, 346, 490)(328, 472, 358, 502)(329, 473, 360, 504)(330, 474, 359, 503)(332, 476, 365, 509)(334, 478, 369, 513)(335, 479, 370, 514)(336, 480, 372, 516)(337, 481, 366, 510)(340, 484, 378, 522)(341, 485, 380, 524)(342, 486, 379, 523)(343, 487, 363, 507)(344, 488, 374, 518)(347, 491, 388, 532)(348, 492, 376, 520)(351, 495, 382, 526)(353, 497, 381, 525)(354, 498, 364, 508)(355, 499, 396, 540)(356, 500, 368, 512)(357, 501, 377, 521)(361, 505, 373, 517)(362, 506, 371, 515)(367, 511, 406, 550)(375, 519, 414, 558)(383, 527, 409, 553)(384, 528, 402, 546)(385, 529, 420, 564)(386, 530, 411, 555)(387, 531, 419, 563)(389, 533, 423, 567)(390, 534, 415, 559)(391, 535, 401, 545)(392, 536, 421, 565)(393, 537, 404, 548)(394, 538, 412, 556)(395, 539, 413, 557)(397, 541, 408, 552)(398, 542, 417, 561)(399, 543, 416, 560)(400, 544, 418, 562)(403, 547, 425, 569)(405, 549, 424, 568)(407, 551, 428, 572)(410, 554, 426, 570)(422, 566, 427, 571)(429, 573, 431, 575)(430, 574, 432, 576)
	L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 320)(16, 295)(17, 323)(18, 325)(19, 324)(20, 297)(21, 322)(22, 298)(23, 332)(24, 299)(25, 335)(26, 337)(27, 336)(28, 301)(29, 334)(30, 302)(31, 343)(32, 346)(33, 347)(34, 304)(35, 351)(36, 305)(37, 353)(38, 354)(39, 356)(40, 308)(41, 309)(42, 310)(43, 363)(44, 366)(45, 367)(46, 312)(47, 371)(48, 313)(49, 373)(50, 374)(51, 376)(52, 316)(53, 317)(54, 318)(55, 383)(56, 319)(57, 385)(58, 387)(59, 386)(60, 321)(61, 384)(62, 391)(63, 381)(64, 393)(65, 395)(66, 392)(67, 326)(68, 394)(69, 327)(70, 397)(71, 328)(72, 389)(73, 329)(74, 330)(75, 401)(76, 331)(77, 403)(78, 405)(79, 404)(80, 333)(81, 402)(82, 409)(83, 361)(84, 411)(85, 413)(86, 410)(87, 338)(88, 412)(89, 339)(90, 415)(91, 340)(92, 407)(93, 341)(94, 342)(95, 419)(96, 344)(97, 359)(98, 345)(99, 358)(100, 421)(101, 348)(102, 349)(103, 417)(104, 350)(105, 418)(106, 352)(107, 408)(108, 422)(109, 355)(110, 357)(111, 360)(112, 362)(113, 424)(114, 364)(115, 379)(116, 365)(117, 378)(118, 426)(119, 368)(120, 369)(121, 399)(122, 370)(123, 400)(124, 372)(125, 390)(126, 427)(127, 375)(128, 377)(129, 380)(130, 382)(131, 429)(132, 398)(133, 430)(134, 388)(135, 396)(136, 431)(137, 416)(138, 432)(139, 406)(140, 414)(141, 423)(142, 420)(143, 428)(144, 425)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 18, 72 ), ( 18, 72, 18, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2127
Graph:: simple bipartite
	v = 216 e = 288 f = 20
	degree seq :: [ 2^144, 4^72 ]

E27.2129 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y1^-4 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3, Y1^36 ]
Map::
	R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 43, 187, 75, 219, 113, 257, 102, 246, 127, 271, 99, 243, 58, 202, 88, 232, 119, 263, 137, 281, 143, 287, 142, 286, 134, 278, 140, 284, 132, 276, 139, 283, 144, 288, 141, 285, 135, 279, 104, 248, 62, 206, 92, 236, 122, 266, 97, 241, 124, 268, 112, 256, 74, 218, 42, 186, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 24, 168, 45, 189, 78, 222, 114, 258, 94, 238, 54, 198, 90, 234, 51, 195, 28, 172, 50, 194, 87, 231, 115, 259, 136, 280, 129, 273, 108, 252, 128, 272, 91, 235, 120, 264, 138, 282, 123, 267, 110, 254, 69, 213, 39, 183, 68, 212, 84, 228, 48, 192, 83, 227, 117, 261, 80, 224, 65, 209, 37, 181, 18, 162, 8, 152)(6, 150, 13, 157, 27, 171, 44, 188, 77, 221, 70, 214, 109, 253, 67, 211, 38, 182, 66, 210, 82, 226, 47, 191, 81, 225, 118, 262, 107, 251, 133, 277, 101, 245, 59, 203, 100, 244, 121, 265, 98, 242, 131, 275, 106, 250, 63, 207, 35, 179, 17, 161, 34, 178, 56, 200, 31, 175, 55, 199, 95, 239, 73, 217, 41, 185, 21, 165, 30, 174, 14, 158)(9, 153, 19, 163, 26, 170, 12, 156, 25, 169, 46, 190, 76, 220, 64, 208, 36, 180, 60, 204, 33, 177, 16, 160, 32, 176, 57, 201, 79, 223, 116, 260, 105, 249, 130, 274, 103, 247, 61, 205, 89, 233, 126, 270, 96, 240, 125, 269, 111, 255, 72, 216, 93, 237, 53, 197, 29, 173, 52, 196, 86, 230, 49, 193, 85, 229, 71, 215, 40, 184, 20, 164)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 305)(9, 292)(10, 309)(11, 312)(12, 293)(13, 316)(14, 317)(15, 319)(16, 295)(17, 296)(18, 324)(19, 326)(20, 327)(21, 298)(22, 325)(23, 332)(24, 299)(25, 335)(26, 336)(27, 337)(28, 301)(29, 302)(30, 342)(31, 303)(32, 346)(33, 347)(34, 349)(35, 350)(36, 306)(37, 310)(38, 307)(39, 308)(40, 358)(41, 360)(42, 359)(43, 364)(44, 311)(45, 367)(46, 368)(47, 313)(48, 314)(49, 315)(50, 376)(51, 377)(52, 379)(53, 380)(54, 318)(55, 384)(56, 385)(57, 386)(58, 320)(59, 321)(60, 390)(61, 322)(62, 323)(63, 393)(64, 395)(65, 394)(66, 387)(67, 396)(68, 389)(69, 392)(70, 328)(71, 330)(72, 329)(73, 366)(74, 383)(75, 402)(76, 331)(77, 403)(78, 361)(79, 333)(80, 334)(81, 407)(82, 408)(83, 409)(84, 410)(85, 411)(86, 412)(87, 413)(88, 338)(89, 339)(90, 415)(91, 340)(92, 341)(93, 417)(94, 418)(95, 362)(96, 343)(97, 344)(98, 345)(99, 354)(100, 420)(101, 356)(102, 348)(103, 422)(104, 357)(105, 351)(106, 353)(107, 352)(108, 355)(109, 401)(110, 406)(111, 423)(112, 405)(113, 397)(114, 363)(115, 365)(116, 425)(117, 400)(118, 398)(119, 369)(120, 370)(121, 371)(122, 372)(123, 373)(124, 374)(125, 375)(126, 427)(127, 378)(128, 428)(129, 381)(130, 382)(131, 429)(132, 388)(133, 430)(134, 391)(135, 399)(136, 431)(137, 404)(138, 432)(139, 414)(140, 416)(141, 419)(142, 421)(143, 424)(144, 426)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.2126
Graph:: simple bipartite
	v = 148 e = 288 f = 88
	degree seq :: [ 2^144, 72^4 ]

E27.2130 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (R * Y2^-2 * Y1)^2, Y2^-3 * Y1 * Y2^3 * Y1, (Y2^-2 * R * Y2^-1)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, Y2^5 * Y1 * Y2^2 * Y1 * Y2^2 * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, (Y3 * Y2^-1)^9, Y2^36 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 31, 175)(16, 160, 33, 177)(18, 162, 26, 170)(19, 163, 38, 182)(20, 164, 39, 183)(22, 166, 30, 174)(23, 167, 43, 187)(24, 168, 45, 189)(27, 171, 50, 194)(28, 172, 51, 195)(32, 176, 57, 201)(34, 178, 61, 205)(35, 179, 62, 206)(36, 180, 64, 208)(37, 181, 58, 202)(40, 184, 70, 214)(41, 185, 72, 216)(42, 186, 71, 215)(44, 188, 77, 221)(46, 190, 81, 225)(47, 191, 82, 226)(48, 192, 84, 228)(49, 193, 78, 222)(52, 196, 90, 234)(53, 197, 92, 236)(54, 198, 91, 235)(55, 199, 75, 219)(56, 200, 86, 230)(59, 203, 100, 244)(60, 204, 88, 232)(63, 207, 94, 238)(65, 209, 93, 237)(66, 210, 76, 220)(67, 211, 108, 252)(68, 212, 80, 224)(69, 213, 89, 233)(73, 217, 85, 229)(74, 218, 83, 227)(79, 223, 118, 262)(87, 231, 126, 270)(95, 239, 121, 265)(96, 240, 114, 258)(97, 241, 132, 276)(98, 242, 123, 267)(99, 243, 131, 275)(101, 245, 135, 279)(102, 246, 127, 271)(103, 247, 113, 257)(104, 248, 133, 277)(105, 249, 116, 260)(106, 250, 124, 268)(107, 251, 125, 269)(109, 253, 120, 264)(110, 254, 129, 273)(111, 255, 128, 272)(112, 256, 130, 274)(115, 259, 137, 281)(117, 261, 136, 280)(119, 263, 140, 284)(122, 266, 138, 282)(134, 278, 139, 283)(141, 285, 143, 287)(142, 286, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 325, 469, 353, 497, 395, 539, 408, 552, 369, 513, 402, 546, 364, 508, 331, 475, 363, 507, 401, 545, 424, 568, 431, 575, 428, 572, 414, 558, 427, 571, 406, 550, 426, 570, 432, 576, 425, 569, 416, 560, 377, 521, 339, 483, 376, 520, 412, 556, 372, 516, 411, 555, 400, 544, 362, 506, 330, 474, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 337, 481, 373, 517, 413, 557, 390, 534, 349, 493, 384, 528, 344, 488, 319, 463, 343, 487, 383, 527, 419, 563, 429, 573, 423, 567, 396, 540, 422, 566, 388, 532, 421, 565, 430, 574, 420, 564, 398, 542, 357, 501, 327, 471, 356, 500, 394, 538, 352, 496, 393, 537, 418, 562, 382, 526, 342, 486, 318, 462, 302, 446, 294, 438)(295, 439, 303, 447, 320, 464, 346, 490, 387, 531, 358, 502, 397, 541, 355, 499, 326, 470, 354, 498, 392, 536, 350, 494, 391, 535, 417, 561, 380, 524, 407, 551, 368, 512, 333, 477, 367, 511, 404, 548, 365, 509, 403, 547, 379, 523, 340, 484, 316, 460, 301, 445, 315, 459, 336, 480, 313, 457, 335, 479, 371, 515, 361, 505, 329, 473, 309, 453, 322, 466, 304, 448)(297, 441, 307, 451, 324, 468, 305, 449, 323, 467, 351, 495, 381, 525, 341, 485, 317, 461, 334, 478, 312, 456, 299, 443, 311, 455, 332, 476, 366, 510, 405, 549, 378, 522, 415, 559, 375, 519, 338, 482, 374, 518, 410, 554, 370, 514, 409, 553, 399, 543, 360, 504, 389, 533, 348, 492, 321, 465, 347, 491, 386, 530, 345, 489, 385, 529, 359, 503, 328, 472, 308, 452)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 319)(16, 321)(17, 296)(18, 314)(19, 326)(20, 327)(21, 298)(22, 318)(23, 331)(24, 333)(25, 300)(26, 306)(27, 338)(28, 339)(29, 302)(30, 310)(31, 303)(32, 345)(33, 304)(34, 349)(35, 350)(36, 352)(37, 346)(38, 307)(39, 308)(40, 358)(41, 360)(42, 359)(43, 311)(44, 365)(45, 312)(46, 369)(47, 370)(48, 372)(49, 366)(50, 315)(51, 316)(52, 378)(53, 380)(54, 379)(55, 363)(56, 374)(57, 320)(58, 325)(59, 388)(60, 376)(61, 322)(62, 323)(63, 382)(64, 324)(65, 381)(66, 364)(67, 396)(68, 368)(69, 377)(70, 328)(71, 330)(72, 329)(73, 373)(74, 371)(75, 343)(76, 354)(77, 332)(78, 337)(79, 406)(80, 356)(81, 334)(82, 335)(83, 362)(84, 336)(85, 361)(86, 344)(87, 414)(88, 348)(89, 357)(90, 340)(91, 342)(92, 341)(93, 353)(94, 351)(95, 409)(96, 402)(97, 420)(98, 411)(99, 419)(100, 347)(101, 423)(102, 415)(103, 401)(104, 421)(105, 404)(106, 412)(107, 413)(108, 355)(109, 408)(110, 417)(111, 416)(112, 418)(113, 391)(114, 384)(115, 425)(116, 393)(117, 424)(118, 367)(119, 428)(120, 397)(121, 383)(122, 426)(123, 386)(124, 394)(125, 395)(126, 375)(127, 390)(128, 399)(129, 398)(130, 400)(131, 387)(132, 385)(133, 392)(134, 427)(135, 389)(136, 405)(137, 403)(138, 410)(139, 422)(140, 407)(141, 431)(142, 432)(143, 429)(144, 430)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E27.2131
Graph:: bipartite
	v = 76 e = 288 f = 160
	degree seq :: [ 4^72, 72^4 ]

E27.2131 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 36})
Quotient :: dipole
Aut^+ = (Q8 : C9) : C2 (small group id <144, 36>)
Aut   = $<288, 340>$ (small group id <288, 340>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^3 * Y3 * Y1^-3, Y3 * Y1^-1 * Y3^-4 * Y1^-1 * Y3, Y3 * Y1^-2 * Y3^2 * Y1^-2 * Y3 * Y1^-1, Y1^9, (Y3 * Y2^-1)^36 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 40, 184, 70, 214, 34, 178, 13, 157, 4, 148)(3, 147, 9, 153, 23, 167, 41, 185, 18, 162, 45, 189, 71, 215, 29, 173, 11, 155)(5, 149, 14, 158, 35, 179, 42, 186, 77, 221, 33, 177, 51, 195, 20, 164, 7, 151)(8, 152, 21, 165, 52, 196, 75, 219, 32, 176, 12, 156, 30, 174, 44, 188, 17, 161)(10, 154, 25, 169, 61, 205, 84, 228, 58, 202, 104, 248, 114, 258, 66, 210, 27, 171)(15, 159, 38, 182, 82, 226, 85, 229, 98, 242, 50, 194, 96, 240, 79, 223, 36, 180)(19, 163, 47, 191, 92, 236, 78, 222, 37, 181, 80, 224, 76, 220, 95, 239, 49, 193)(22, 166, 55, 199, 74, 218, 117, 261, 126, 270, 89, 233, 72, 216, 100, 244, 53, 197)(24, 168, 59, 203, 90, 234, 46, 190, 69, 213, 28, 172, 67, 211, 103, 247, 57, 201)(26, 170, 48, 192, 87, 231, 120, 264, 109, 253, 128, 272, 139, 283, 112, 256, 64, 208)(31, 175, 73, 217, 88, 232, 43, 187, 86, 230, 122, 266, 99, 243, 54, 198, 63, 207)(39, 183, 56, 200, 91, 235, 121, 265, 134, 278, 115, 259, 130, 274, 106, 250, 60, 204)(62, 206, 110, 254, 135, 279, 105, 249, 83, 227, 65, 209, 97, 241, 131, 275, 108, 252)(68, 212, 116, 260, 124, 268, 102, 246, 133, 277, 140, 284, 123, 267, 107, 251, 111, 255)(81, 225, 101, 245, 94, 238, 125, 269, 141, 285, 127, 271, 93, 237, 129, 273, 118, 262)(113, 257, 119, 263, 132, 276, 136, 280, 142, 286, 144, 288, 143, 287, 137, 281, 138, 282)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 314)(11, 316)(12, 319)(13, 321)(14, 324)(15, 293)(16, 329)(17, 331)(18, 294)(19, 336)(20, 338)(21, 341)(22, 296)(23, 345)(24, 297)(25, 299)(26, 351)(27, 353)(28, 356)(29, 358)(30, 301)(31, 352)(32, 362)(33, 364)(34, 359)(35, 366)(36, 350)(37, 302)(38, 348)(39, 303)(40, 323)(41, 372)(42, 304)(43, 375)(44, 377)(45, 378)(46, 306)(47, 308)(48, 315)(49, 382)(50, 385)(51, 322)(52, 387)(53, 381)(54, 309)(55, 327)(56, 310)(57, 390)(58, 311)(59, 394)(60, 312)(61, 396)(62, 313)(63, 399)(64, 368)(65, 401)(66, 333)(67, 317)(68, 342)(69, 344)(70, 340)(71, 402)(72, 318)(73, 320)(74, 369)(75, 328)(76, 400)(77, 370)(78, 397)(79, 403)(80, 406)(81, 325)(82, 393)(83, 326)(84, 408)(85, 330)(86, 332)(87, 337)(88, 412)(89, 413)(90, 411)(91, 334)(92, 415)(93, 335)(94, 407)(95, 365)(96, 339)(97, 354)(98, 379)(99, 416)(100, 418)(101, 343)(102, 361)(103, 422)(104, 423)(105, 346)(106, 360)(107, 347)(108, 424)(109, 349)(110, 367)(111, 426)(112, 392)(113, 395)(114, 427)(115, 355)(116, 357)(117, 363)(118, 425)(119, 371)(120, 376)(121, 373)(122, 428)(123, 374)(124, 420)(125, 383)(126, 409)(127, 430)(128, 380)(129, 388)(130, 384)(131, 386)(132, 389)(133, 391)(134, 405)(135, 431)(136, 404)(137, 398)(138, 417)(139, 410)(140, 432)(141, 414)(142, 419)(143, 421)(144, 429)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 72 ), ( 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72, 4, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2130
Graph:: simple bipartite
	v = 160 e = 288 f = 76
	degree seq :: [ 2^144, 18^16 ]

E27.2132 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 72})
Quotient :: regular
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^4 * T2)^2, (T2 * T1^2)^4, T1^-4 * T2 * T1^5 * T2 * T1^-9 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 43, 66, 85, 101, 117, 133, 128, 111, 94, 80, 58, 33, 16, 28, 48, 69, 61, 76, 92, 108, 124, 140, 144, 142, 127, 110, 96, 79, 57, 32, 52, 72, 60, 35, 53, 73, 90, 106, 122, 138, 143, 141, 126, 112, 95, 78, 56, 75, 59, 34, 17, 29, 49, 70, 88, 104, 120, 136, 132, 116, 100, 84, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 77, 93, 109, 125, 134, 123, 105, 87, 67, 54, 30, 14, 6, 13, 27, 51, 41, 64, 83, 99, 115, 131, 139, 121, 103, 86, 74, 50, 26, 12, 25, 47, 40, 21, 39, 63, 82, 98, 114, 130, 137, 119, 102, 91, 71, 46, 24, 45, 38, 20, 9, 19, 37, 62, 81, 97, 113, 129, 135, 118, 107, 89, 68, 44, 36, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 141)(130, 142)(131, 133)(132, 135)(137, 143)(139, 144)
	local type(s) :: { ( 8^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2133
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 72 f = 18
	degree seq :: [ 72^2 ]

E27.2133 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 72})
Quotient :: regular
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, (T1 * T2 * T1^3)^2, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 31, 28, 17, 8)(6, 13, 21, 32, 30, 18, 9, 14)(15, 25, 33, 43, 40, 27, 16, 26)(23, 34, 42, 41, 29, 36, 24, 35)(37, 47, 52, 50, 39, 49, 38, 48)(44, 53, 51, 56, 46, 55, 45, 54)(57, 65, 60, 68, 59, 67, 58, 66)(61, 69, 64, 72, 63, 71, 62, 70)(73, 81, 76, 84, 75, 83, 74, 82)(77, 85, 80, 88, 79, 87, 78, 86)(89, 97, 92, 100, 91, 99, 90, 98)(93, 101, 96, 104, 95, 103, 94, 102)(105, 113, 108, 116, 107, 115, 106, 114)(109, 117, 112, 120, 111, 119, 110, 118)(121, 129, 124, 132, 123, 131, 122, 130)(125, 133, 128, 136, 127, 135, 126, 134)(137, 141, 140, 144, 139, 143, 138, 142)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128)(129, 137)(130, 138)(131, 139)(132, 140)(133, 141)(134, 142)(135, 143)(136, 144)
	local type(s) :: { ( 72^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2132
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 18 e = 72 f = 2
	degree seq :: [ 8^18 ]

E27.2134 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^72 ]
Map::
	R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 26, 39, 30, 18, 9, 16)(11, 20, 32, 44, 36, 23, 13, 21)(25, 37, 48, 41, 29, 40, 27, 38)(31, 42, 53, 46, 35, 45, 33, 43)(47, 57, 51, 60, 50, 59, 49, 58)(52, 61, 56, 64, 55, 63, 54, 62)(65, 73, 68, 76, 67, 75, 66, 74)(69, 77, 72, 80, 71, 79, 70, 78)(81, 89, 84, 92, 83, 91, 82, 90)(85, 93, 88, 96, 87, 95, 86, 94)(97, 105, 100, 108, 99, 107, 98, 106)(101, 109, 104, 112, 103, 111, 102, 110)(113, 121, 116, 124, 115, 123, 114, 122)(117, 125, 120, 128, 119, 127, 118, 126)(129, 137, 132, 140, 131, 139, 130, 138)(133, 141, 136, 144, 135, 143, 134, 142)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 156)(154, 158)(159, 169)(160, 171)(161, 170)(162, 173)(163, 174)(164, 175)(165, 177)(166, 176)(167, 179)(168, 180)(172, 178)(181, 191)(182, 193)(183, 192)(184, 194)(185, 195)(186, 196)(187, 198)(188, 197)(189, 199)(190, 200)(201, 209)(202, 210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 241)(234, 242)(235, 243)(236, 244)(237, 245)(238, 246)(239, 247)(240, 248)(249, 257)(250, 258)(251, 259)(252, 260)(253, 261)(254, 262)(255, 263)(256, 264)(265, 273)(266, 274)(267, 275)(268, 276)(269, 277)(270, 278)(271, 279)(272, 280)(281, 285)(282, 286)(283, 287)(284, 288)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 144, 144 ), ( 144^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2138
Transitivity :: ET+
Graph:: simple bipartite
	v = 90 e = 144 f = 2
	degree seq :: [ 2^72, 8^18 ]

E27.2135 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2^-1 * T1, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^8, T2^18 * T1^2 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 48, 64, 80, 96, 112, 128, 135, 119, 103, 87, 71, 55, 39, 20, 13, 28, 43, 59, 75, 91, 107, 123, 139, 144, 136, 120, 104, 88, 72, 56, 41, 30, 34, 21, 42, 58, 74, 90, 106, 122, 138, 143, 134, 118, 102, 86, 70, 54, 38, 18, 6, 17, 36, 53, 69, 85, 101, 117, 133, 132, 116, 100, 84, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 89, 105, 121, 137, 125, 109, 93, 77, 61, 45, 23, 9, 4, 12, 29, 49, 65, 81, 97, 113, 129, 141, 126, 110, 94, 78, 62, 46, 24, 11, 27, 37, 32, 51, 67, 83, 99, 115, 131, 142, 127, 111, 95, 79, 63, 47, 26, 35, 16, 14, 31, 50, 66, 82, 98, 114, 130, 140, 124, 108, 92, 76, 60, 44, 22, 8)(145, 146, 150, 160, 178, 171, 157, 148)(147, 153, 161, 152, 165, 179, 172, 155)(149, 158, 162, 181, 174, 156, 164, 151)(154, 168, 180, 167, 186, 166, 187, 170)(159, 176, 182, 173, 185, 163, 183, 175)(169, 191, 197, 190, 202, 189, 203, 188)(177, 193, 198, 184, 200, 194, 199, 195)(192, 204, 213, 207, 218, 206, 219, 205)(196, 201, 214, 210, 216, 211, 215, 209)(208, 221, 229, 220, 234, 223, 235, 222)(212, 226, 230, 227, 232, 225, 231, 217)(224, 238, 245, 237, 250, 236, 251, 239)(228, 243, 246, 241, 248, 233, 247, 242)(240, 255, 261, 254, 266, 253, 267, 252)(244, 257, 262, 249, 264, 258, 263, 259)(256, 268, 277, 271, 282, 270, 283, 269)(260, 265, 278, 274, 280, 275, 279, 273)(272, 281, 276, 284, 287, 286, 288, 285)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4^8 ), ( 4^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2139
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 144 f = 72
	degree seq :: [ 8^18, 72^2 ]

E27.2136 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^4 * T2)^2, (T2 * T1^2)^4, T1^-4 * T2 * T1^5 * T2 * T1^-9 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 141)(130, 142)(131, 133)(132, 135)(137, 143)(139, 144)(145, 146, 149, 155, 167, 187, 210, 229, 245, 261, 277, 272, 255, 238, 224, 202, 177, 160, 172, 192, 213, 205, 220, 236, 252, 268, 284, 288, 286, 271, 254, 240, 223, 201, 176, 196, 216, 204, 179, 197, 217, 234, 250, 266, 282, 287, 285, 270, 256, 239, 222, 200, 219, 203, 178, 161, 173, 193, 214, 232, 248, 264, 280, 276, 260, 244, 228, 209, 186, 166, 154, 148)(147, 151, 159, 175, 199, 221, 237, 253, 269, 278, 267, 249, 231, 211, 198, 174, 158, 150, 157, 171, 195, 185, 208, 227, 243, 259, 275, 283, 265, 247, 230, 218, 194, 170, 156, 169, 191, 184, 165, 183, 207, 226, 242, 258, 274, 281, 263, 246, 235, 215, 190, 168, 189, 182, 164, 153, 163, 181, 206, 225, 241, 257, 273, 279, 262, 251, 233, 212, 188, 180, 162, 152)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 16, 16 ), ( 16^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2137
Transitivity :: ET+
Graph:: simple bipartite
	v = 74 e = 144 f = 18
	degree seq :: [ 2^72, 72^2 ]

E27.2137 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^72 ]
Map::
	R = (1, 145, 3, 147, 8, 152, 17, 161, 28, 172, 19, 163, 10, 154, 4, 148)(2, 146, 5, 149, 12, 156, 22, 166, 34, 178, 24, 168, 14, 158, 6, 150)(7, 151, 15, 159, 26, 170, 39, 183, 30, 174, 18, 162, 9, 153, 16, 160)(11, 155, 20, 164, 32, 176, 44, 188, 36, 180, 23, 167, 13, 157, 21, 165)(25, 169, 37, 181, 48, 192, 41, 185, 29, 173, 40, 184, 27, 171, 38, 182)(31, 175, 42, 186, 53, 197, 46, 190, 35, 179, 45, 189, 33, 177, 43, 187)(47, 191, 57, 201, 51, 195, 60, 204, 50, 194, 59, 203, 49, 193, 58, 202)(52, 196, 61, 205, 56, 200, 64, 208, 55, 199, 63, 207, 54, 198, 62, 206)(65, 209, 73, 217, 68, 212, 76, 220, 67, 211, 75, 219, 66, 210, 74, 218)(69, 213, 77, 221, 72, 216, 80, 224, 71, 215, 79, 223, 70, 214, 78, 222)(81, 225, 89, 233, 84, 228, 92, 236, 83, 227, 91, 235, 82, 226, 90, 234)(85, 229, 93, 237, 88, 232, 96, 240, 87, 231, 95, 239, 86, 230, 94, 238)(97, 241, 105, 249, 100, 244, 108, 252, 99, 243, 107, 251, 98, 242, 106, 250)(101, 245, 109, 253, 104, 248, 112, 256, 103, 247, 111, 255, 102, 246, 110, 254)(113, 257, 121, 265, 116, 260, 124, 268, 115, 259, 123, 267, 114, 258, 122, 266)(117, 261, 125, 269, 120, 264, 128, 272, 119, 263, 127, 271, 118, 262, 126, 270)(129, 273, 137, 281, 132, 276, 140, 284, 131, 275, 139, 283, 130, 274, 138, 282)(133, 277, 141, 285, 136, 280, 144, 288, 135, 279, 143, 287, 134, 278, 142, 286)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 156)(9, 148)(10, 158)(11, 149)(12, 152)(13, 150)(14, 154)(15, 169)(16, 171)(17, 170)(18, 173)(19, 174)(20, 175)(21, 177)(22, 176)(23, 179)(24, 180)(25, 159)(26, 161)(27, 160)(28, 178)(29, 162)(30, 163)(31, 164)(32, 166)(33, 165)(34, 172)(35, 167)(36, 168)(37, 191)(38, 193)(39, 192)(40, 194)(41, 195)(42, 196)(43, 198)(44, 197)(45, 199)(46, 200)(47, 181)(48, 183)(49, 182)(50, 184)(51, 185)(52, 186)(53, 188)(54, 187)(55, 189)(56, 190)(57, 209)(58, 210)(59, 211)(60, 212)(61, 213)(62, 214)(63, 215)(64, 216)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 225)(74, 226)(75, 227)(76, 228)(77, 229)(78, 230)(79, 231)(80, 232)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272)(137, 285)(138, 286)(139, 287)(140, 288)(141, 281)(142, 282)(143, 283)(144, 284)
	local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2136
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 18 e = 144 f = 74
	degree seq :: [ 16^18 ]

E27.2138 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2^-1 * T1, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^8, T2^18 * T1^2 ]
Map::
	R = (1, 145, 3, 147, 10, 154, 25, 169, 48, 192, 64, 208, 80, 224, 96, 240, 112, 256, 128, 272, 135, 279, 119, 263, 103, 247, 87, 231, 71, 215, 55, 199, 39, 183, 20, 164, 13, 157, 28, 172, 43, 187, 59, 203, 75, 219, 91, 235, 107, 251, 123, 267, 139, 283, 144, 288, 136, 280, 120, 264, 104, 248, 88, 232, 72, 216, 56, 200, 41, 185, 30, 174, 34, 178, 21, 165, 42, 186, 58, 202, 74, 218, 90, 234, 106, 250, 122, 266, 138, 282, 143, 287, 134, 278, 118, 262, 102, 246, 86, 230, 70, 214, 54, 198, 38, 182, 18, 162, 6, 150, 17, 161, 36, 180, 53, 197, 69, 213, 85, 229, 101, 245, 117, 261, 133, 277, 132, 276, 116, 260, 100, 244, 84, 228, 68, 212, 52, 196, 33, 177, 15, 159, 5, 149)(2, 146, 7, 151, 19, 163, 40, 184, 57, 201, 73, 217, 89, 233, 105, 249, 121, 265, 137, 281, 125, 269, 109, 253, 93, 237, 77, 221, 61, 205, 45, 189, 23, 167, 9, 153, 4, 148, 12, 156, 29, 173, 49, 193, 65, 209, 81, 225, 97, 241, 113, 257, 129, 273, 141, 285, 126, 270, 110, 254, 94, 238, 78, 222, 62, 206, 46, 190, 24, 168, 11, 155, 27, 171, 37, 181, 32, 176, 51, 195, 67, 211, 83, 227, 99, 243, 115, 259, 131, 275, 142, 286, 127, 271, 111, 255, 95, 239, 79, 223, 63, 207, 47, 191, 26, 170, 35, 179, 16, 160, 14, 158, 31, 175, 50, 194, 66, 210, 82, 226, 98, 242, 114, 258, 130, 274, 140, 284, 124, 268, 108, 252, 92, 236, 76, 220, 60, 204, 44, 188, 22, 166, 8, 152)
	L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 158)(6, 160)(7, 149)(8, 165)(9, 161)(10, 168)(11, 147)(12, 164)(13, 148)(14, 162)(15, 176)(16, 178)(17, 152)(18, 181)(19, 183)(20, 151)(21, 179)(22, 187)(23, 186)(24, 180)(25, 191)(26, 154)(27, 157)(28, 155)(29, 185)(30, 156)(31, 159)(32, 182)(33, 193)(34, 171)(35, 172)(36, 167)(37, 174)(38, 173)(39, 175)(40, 200)(41, 163)(42, 166)(43, 170)(44, 169)(45, 203)(46, 202)(47, 197)(48, 204)(49, 198)(50, 199)(51, 177)(52, 201)(53, 190)(54, 184)(55, 195)(56, 194)(57, 214)(58, 189)(59, 188)(60, 213)(61, 192)(62, 219)(63, 218)(64, 221)(65, 196)(66, 216)(67, 215)(68, 226)(69, 207)(70, 210)(71, 209)(72, 211)(73, 212)(74, 206)(75, 205)(76, 234)(77, 229)(78, 208)(79, 235)(80, 238)(81, 231)(82, 230)(83, 232)(84, 243)(85, 220)(86, 227)(87, 217)(88, 225)(89, 247)(90, 223)(91, 222)(92, 251)(93, 250)(94, 245)(95, 224)(96, 255)(97, 248)(98, 228)(99, 246)(100, 257)(101, 237)(102, 241)(103, 242)(104, 233)(105, 264)(106, 236)(107, 239)(108, 240)(109, 267)(110, 266)(111, 261)(112, 268)(113, 262)(114, 263)(115, 244)(116, 265)(117, 254)(118, 249)(119, 259)(120, 258)(121, 278)(122, 253)(123, 252)(124, 277)(125, 256)(126, 283)(127, 282)(128, 281)(129, 260)(130, 280)(131, 279)(132, 284)(133, 271)(134, 274)(135, 273)(136, 275)(137, 276)(138, 270)(139, 269)(140, 287)(141, 272)(142, 288)(143, 286)(144, 285)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2134
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 144 f = 90
	degree seq :: [ 144^2 ]

E27.2139 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^4 * T2)^2, (T2 * T1^2)^4, T1^-4 * T2 * T1^5 * T2 * T1^-9 ]
Map:: polytopal non-degenerate
	R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 17, 161)(10, 154, 21, 165)(11, 155, 24, 168)(13, 157, 28, 172)(14, 158, 29, 173)(15, 159, 32, 176)(18, 162, 35, 179)(19, 163, 33, 177)(20, 164, 34, 178)(22, 166, 41, 185)(23, 167, 44, 188)(25, 169, 48, 192)(26, 170, 49, 193)(27, 171, 52, 196)(30, 174, 53, 197)(31, 175, 56, 200)(36, 180, 61, 205)(37, 181, 57, 201)(38, 182, 60, 204)(39, 183, 58, 202)(40, 184, 59, 203)(42, 186, 55, 199)(43, 187, 67, 211)(45, 189, 69, 213)(46, 190, 70, 214)(47, 191, 72, 216)(50, 194, 73, 217)(51, 195, 75, 219)(54, 198, 76, 220)(62, 206, 78, 222)(63, 207, 79, 223)(64, 208, 80, 224)(65, 209, 81, 225)(66, 210, 86, 230)(68, 212, 88, 232)(71, 215, 90, 234)(74, 218, 92, 236)(77, 221, 94, 238)(82, 226, 95, 239)(83, 227, 96, 240)(84, 228, 98, 242)(85, 229, 102, 246)(87, 231, 104, 248)(89, 233, 106, 250)(91, 235, 108, 252)(93, 237, 110, 254)(97, 241, 111, 255)(99, 243, 112, 256)(100, 244, 115, 259)(101, 245, 118, 262)(103, 247, 120, 264)(105, 249, 122, 266)(107, 251, 124, 268)(109, 253, 126, 270)(113, 257, 127, 271)(114, 258, 128, 272)(116, 260, 125, 269)(117, 261, 134, 278)(119, 263, 136, 280)(121, 265, 138, 282)(123, 267, 140, 284)(129, 273, 141, 285)(130, 274, 142, 286)(131, 275, 133, 277)(132, 276, 135, 279)(137, 281, 143, 287)(139, 283, 144, 288)
	L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 175)(16, 172)(17, 173)(18, 152)(19, 181)(20, 153)(21, 183)(22, 154)(23, 187)(24, 189)(25, 191)(26, 156)(27, 195)(28, 192)(29, 193)(30, 158)(31, 199)(32, 196)(33, 160)(34, 161)(35, 197)(36, 162)(37, 206)(38, 164)(39, 207)(40, 165)(41, 208)(42, 166)(43, 210)(44, 180)(45, 182)(46, 168)(47, 184)(48, 213)(49, 214)(50, 170)(51, 185)(52, 216)(53, 217)(54, 174)(55, 221)(56, 219)(57, 176)(58, 177)(59, 178)(60, 179)(61, 220)(62, 225)(63, 226)(64, 227)(65, 186)(66, 229)(67, 198)(68, 188)(69, 205)(70, 232)(71, 190)(72, 204)(73, 234)(74, 194)(75, 203)(76, 236)(77, 237)(78, 200)(79, 201)(80, 202)(81, 241)(82, 242)(83, 243)(84, 209)(85, 245)(86, 218)(87, 211)(88, 248)(89, 212)(90, 250)(91, 215)(92, 252)(93, 253)(94, 224)(95, 222)(96, 223)(97, 257)(98, 258)(99, 259)(100, 228)(101, 261)(102, 235)(103, 230)(104, 264)(105, 231)(106, 266)(107, 233)(108, 268)(109, 269)(110, 240)(111, 238)(112, 239)(113, 273)(114, 274)(115, 275)(116, 244)(117, 277)(118, 251)(119, 246)(120, 280)(121, 247)(122, 282)(123, 249)(124, 284)(125, 278)(126, 256)(127, 254)(128, 255)(129, 279)(130, 281)(131, 283)(132, 260)(133, 272)(134, 267)(135, 262)(136, 276)(137, 263)(138, 287)(139, 265)(140, 288)(141, 270)(142, 271)(143, 285)(144, 286)
	local type(s) :: { ( 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2135
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 72 e = 144 f = 20
	degree seq :: [ 4^72 ]

E27.2140 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^72 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 12, 156)(10, 154, 14, 158)(15, 159, 25, 169)(16, 160, 27, 171)(17, 161, 26, 170)(18, 162, 29, 173)(19, 163, 30, 174)(20, 164, 31, 175)(21, 165, 33, 177)(22, 166, 32, 176)(23, 167, 35, 179)(24, 168, 36, 180)(28, 172, 34, 178)(37, 181, 47, 191)(38, 182, 49, 193)(39, 183, 48, 192)(40, 184, 50, 194)(41, 185, 51, 195)(42, 186, 52, 196)(43, 187, 54, 198)(44, 188, 53, 197)(45, 189, 55, 199)(46, 190, 56, 200)(57, 201, 65, 209)(58, 202, 66, 210)(59, 203, 67, 211)(60, 204, 68, 212)(61, 205, 69, 213)(62, 206, 70, 214)(63, 207, 71, 215)(64, 208, 72, 216)(73, 217, 81, 225)(74, 218, 82, 226)(75, 219, 83, 227)(76, 220, 84, 228)(77, 221, 85, 229)(78, 222, 86, 230)(79, 223, 87, 231)(80, 224, 88, 232)(89, 233, 97, 241)(90, 234, 98, 242)(91, 235, 99, 243)(92, 236, 100, 244)(93, 237, 101, 245)(94, 238, 102, 246)(95, 239, 103, 247)(96, 240, 104, 248)(105, 249, 113, 257)(106, 250, 114, 258)(107, 251, 115, 259)(108, 252, 116, 260)(109, 253, 117, 261)(110, 254, 118, 262)(111, 255, 119, 263)(112, 256, 120, 264)(121, 265, 129, 273)(122, 266, 130, 274)(123, 267, 131, 275)(124, 268, 132, 276)(125, 269, 133, 277)(126, 270, 134, 278)(127, 271, 135, 279)(128, 272, 136, 280)(137, 281, 141, 285)(138, 282, 142, 286)(139, 283, 143, 287)(140, 284, 144, 288)(289, 433, 291, 435, 296, 440, 305, 449, 316, 460, 307, 451, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 310, 454, 322, 466, 312, 456, 302, 446, 294, 438)(295, 439, 303, 447, 314, 458, 327, 471, 318, 462, 306, 450, 297, 441, 304, 448)(299, 443, 308, 452, 320, 464, 332, 476, 324, 468, 311, 455, 301, 445, 309, 453)(313, 457, 325, 469, 336, 480, 329, 473, 317, 461, 328, 472, 315, 459, 326, 470)(319, 463, 330, 474, 341, 485, 334, 478, 323, 467, 333, 477, 321, 465, 331, 475)(335, 479, 345, 489, 339, 483, 348, 492, 338, 482, 347, 491, 337, 481, 346, 490)(340, 484, 349, 493, 344, 488, 352, 496, 343, 487, 351, 495, 342, 486, 350, 494)(353, 497, 361, 505, 356, 500, 364, 508, 355, 499, 363, 507, 354, 498, 362, 506)(357, 501, 365, 509, 360, 504, 368, 512, 359, 503, 367, 511, 358, 502, 366, 510)(369, 513, 377, 521, 372, 516, 380, 524, 371, 515, 379, 523, 370, 514, 378, 522)(373, 517, 381, 525, 376, 520, 384, 528, 375, 519, 383, 527, 374, 518, 382, 526)(385, 529, 393, 537, 388, 532, 396, 540, 387, 531, 395, 539, 386, 530, 394, 538)(389, 533, 397, 541, 392, 536, 400, 544, 391, 535, 399, 543, 390, 534, 398, 542)(401, 545, 409, 553, 404, 548, 412, 556, 403, 547, 411, 555, 402, 546, 410, 554)(405, 549, 413, 557, 408, 552, 416, 560, 407, 551, 415, 559, 406, 550, 414, 558)(417, 561, 425, 569, 420, 564, 428, 572, 419, 563, 427, 571, 418, 562, 426, 570)(421, 565, 429, 573, 424, 568, 432, 576, 423, 567, 431, 575, 422, 566, 430, 574)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 300)(9, 292)(10, 302)(11, 293)(12, 296)(13, 294)(14, 298)(15, 313)(16, 315)(17, 314)(18, 317)(19, 318)(20, 319)(21, 321)(22, 320)(23, 323)(24, 324)(25, 303)(26, 305)(27, 304)(28, 322)(29, 306)(30, 307)(31, 308)(32, 310)(33, 309)(34, 316)(35, 311)(36, 312)(37, 335)(38, 337)(39, 336)(40, 338)(41, 339)(42, 340)(43, 342)(44, 341)(45, 343)(46, 344)(47, 325)(48, 327)(49, 326)(50, 328)(51, 329)(52, 330)(53, 332)(54, 331)(55, 333)(56, 334)(57, 353)(58, 354)(59, 355)(60, 356)(61, 357)(62, 358)(63, 359)(64, 360)(65, 345)(66, 346)(67, 347)(68, 348)(69, 349)(70, 350)(71, 351)(72, 352)(73, 369)(74, 370)(75, 371)(76, 372)(77, 373)(78, 374)(79, 375)(80, 376)(81, 361)(82, 362)(83, 363)(84, 364)(85, 365)(86, 366)(87, 367)(88, 368)(89, 385)(90, 386)(91, 387)(92, 388)(93, 389)(94, 390)(95, 391)(96, 392)(97, 377)(98, 378)(99, 379)(100, 380)(101, 381)(102, 382)(103, 383)(104, 384)(105, 401)(106, 402)(107, 403)(108, 404)(109, 405)(110, 406)(111, 407)(112, 408)(113, 393)(114, 394)(115, 395)(116, 396)(117, 397)(118, 398)(119, 399)(120, 400)(121, 417)(122, 418)(123, 419)(124, 420)(125, 421)(126, 422)(127, 423)(128, 424)(129, 409)(130, 410)(131, 411)(132, 412)(133, 413)(134, 414)(135, 415)(136, 416)(137, 429)(138, 430)(139, 431)(140, 432)(141, 425)(142, 426)(143, 427)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 144, 2, 144 ), ( 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2143
Graph:: bipartite
	v = 90 e = 288 f = 146
	degree seq :: [ 4^72, 16^18 ]

E27.2141 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y2^-1 * Y1^-2 * Y2 * Y1^2, (Y2^-2 * Y1 * Y2^-1)^2, Y1^8, Y1 * Y2^14 * Y1 * Y2^-4 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 34, 178, 27, 171, 13, 157, 4, 148)(3, 147, 9, 153, 17, 161, 8, 152, 21, 165, 35, 179, 28, 172, 11, 155)(5, 149, 14, 158, 18, 162, 37, 181, 30, 174, 12, 156, 20, 164, 7, 151)(10, 154, 24, 168, 36, 180, 23, 167, 42, 186, 22, 166, 43, 187, 26, 170)(15, 159, 32, 176, 38, 182, 29, 173, 41, 185, 19, 163, 39, 183, 31, 175)(25, 169, 47, 191, 53, 197, 46, 190, 58, 202, 45, 189, 59, 203, 44, 188)(33, 177, 49, 193, 54, 198, 40, 184, 56, 200, 50, 194, 55, 199, 51, 195)(48, 192, 60, 204, 69, 213, 63, 207, 74, 218, 62, 206, 75, 219, 61, 205)(52, 196, 57, 201, 70, 214, 66, 210, 72, 216, 67, 211, 71, 215, 65, 209)(64, 208, 77, 221, 85, 229, 76, 220, 90, 234, 79, 223, 91, 235, 78, 222)(68, 212, 82, 226, 86, 230, 83, 227, 88, 232, 81, 225, 87, 231, 73, 217)(80, 224, 94, 238, 101, 245, 93, 237, 106, 250, 92, 236, 107, 251, 95, 239)(84, 228, 99, 243, 102, 246, 97, 241, 104, 248, 89, 233, 103, 247, 98, 242)(96, 240, 111, 255, 117, 261, 110, 254, 122, 266, 109, 253, 123, 267, 108, 252)(100, 244, 113, 257, 118, 262, 105, 249, 120, 264, 114, 258, 119, 263, 115, 259)(112, 256, 124, 268, 133, 277, 127, 271, 138, 282, 126, 270, 139, 283, 125, 269)(116, 260, 121, 265, 134, 278, 130, 274, 136, 280, 131, 275, 135, 279, 129, 273)(128, 272, 137, 281, 132, 276, 140, 284, 143, 287, 142, 286, 144, 288, 141, 285)(289, 433, 291, 435, 298, 442, 313, 457, 336, 480, 352, 496, 368, 512, 384, 528, 400, 544, 416, 560, 423, 567, 407, 551, 391, 535, 375, 519, 359, 503, 343, 487, 327, 471, 308, 452, 301, 445, 316, 460, 331, 475, 347, 491, 363, 507, 379, 523, 395, 539, 411, 555, 427, 571, 432, 576, 424, 568, 408, 552, 392, 536, 376, 520, 360, 504, 344, 488, 329, 473, 318, 462, 322, 466, 309, 453, 330, 474, 346, 490, 362, 506, 378, 522, 394, 538, 410, 554, 426, 570, 431, 575, 422, 566, 406, 550, 390, 534, 374, 518, 358, 502, 342, 486, 326, 470, 306, 450, 294, 438, 305, 449, 324, 468, 341, 485, 357, 501, 373, 517, 389, 533, 405, 549, 421, 565, 420, 564, 404, 548, 388, 532, 372, 516, 356, 500, 340, 484, 321, 465, 303, 447, 293, 437)(290, 434, 295, 439, 307, 451, 328, 472, 345, 489, 361, 505, 377, 521, 393, 537, 409, 553, 425, 569, 413, 557, 397, 541, 381, 525, 365, 509, 349, 493, 333, 477, 311, 455, 297, 441, 292, 436, 300, 444, 317, 461, 337, 481, 353, 497, 369, 513, 385, 529, 401, 545, 417, 561, 429, 573, 414, 558, 398, 542, 382, 526, 366, 510, 350, 494, 334, 478, 312, 456, 299, 443, 315, 459, 325, 469, 320, 464, 339, 483, 355, 499, 371, 515, 387, 531, 403, 547, 419, 563, 430, 574, 415, 559, 399, 543, 383, 527, 367, 511, 351, 495, 335, 479, 314, 458, 323, 467, 304, 448, 302, 446, 319, 463, 338, 482, 354, 498, 370, 514, 386, 530, 402, 546, 418, 562, 428, 572, 412, 556, 396, 540, 380, 524, 364, 508, 348, 492, 332, 476, 310, 454, 296, 440)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 313)(11, 315)(12, 317)(13, 316)(14, 319)(15, 293)(16, 302)(17, 324)(18, 294)(19, 328)(20, 301)(21, 330)(22, 296)(23, 297)(24, 299)(25, 336)(26, 323)(27, 325)(28, 331)(29, 337)(30, 322)(31, 338)(32, 339)(33, 303)(34, 309)(35, 304)(36, 341)(37, 320)(38, 306)(39, 308)(40, 345)(41, 318)(42, 346)(43, 347)(44, 310)(45, 311)(46, 312)(47, 314)(48, 352)(49, 353)(50, 354)(51, 355)(52, 321)(53, 357)(54, 326)(55, 327)(56, 329)(57, 361)(58, 362)(59, 363)(60, 332)(61, 333)(62, 334)(63, 335)(64, 368)(65, 369)(66, 370)(67, 371)(68, 340)(69, 373)(70, 342)(71, 343)(72, 344)(73, 377)(74, 378)(75, 379)(76, 348)(77, 349)(78, 350)(79, 351)(80, 384)(81, 385)(82, 386)(83, 387)(84, 356)(85, 389)(86, 358)(87, 359)(88, 360)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 405)(102, 374)(103, 375)(104, 376)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 421)(118, 390)(119, 391)(120, 392)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 423)(129, 429)(130, 428)(131, 430)(132, 404)(133, 420)(134, 406)(135, 407)(136, 408)(137, 413)(138, 431)(139, 432)(140, 412)(141, 414)(142, 415)(143, 422)(144, 424)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2142
Graph:: bipartite
	v = 20 e = 288 f = 216
	degree seq :: [ 16^18, 144^2 ]

E27.2142 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^4 * Y2)^2, (Y3^-2 * Y2)^4, Y3^-3 * Y2 * Y3^13 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^72 ]
Map:: polytopal
	R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 311, 455)(304, 448, 315, 459)(306, 450, 323, 467)(307, 451, 312, 456)(308, 452, 316, 460)(310, 454, 329, 473)(314, 458, 335, 479)(318, 462, 341, 485)(319, 463, 333, 477)(320, 464, 339, 483)(321, 465, 331, 475)(322, 466, 337, 481)(324, 468, 342, 486)(325, 469, 334, 478)(326, 470, 340, 484)(327, 471, 332, 476)(328, 472, 338, 482)(330, 474, 336, 480)(343, 487, 358, 502)(344, 488, 363, 507)(345, 489, 356, 500)(346, 490, 362, 506)(347, 491, 354, 498)(348, 492, 361, 505)(349, 493, 365, 509)(350, 494, 359, 503)(351, 495, 357, 501)(352, 496, 355, 499)(353, 497, 369, 513)(360, 504, 373, 517)(364, 508, 377, 521)(366, 510, 379, 523)(367, 511, 378, 522)(368, 512, 382, 526)(370, 514, 375, 519)(371, 515, 374, 518)(372, 516, 386, 530)(376, 520, 390, 534)(380, 524, 394, 538)(381, 525, 393, 537)(383, 527, 395, 539)(384, 528, 399, 543)(385, 529, 389, 533)(387, 531, 391, 535)(388, 532, 403, 547)(392, 536, 407, 551)(396, 540, 411, 555)(397, 541, 410, 554)(398, 542, 409, 553)(400, 544, 412, 556)(401, 545, 406, 550)(402, 546, 405, 549)(404, 548, 408, 552)(413, 557, 427, 571)(414, 558, 426, 570)(415, 559, 425, 569)(416, 560, 424, 568)(417, 561, 423, 567)(418, 562, 422, 566)(419, 563, 421, 565)(420, 564, 428, 572)(429, 573, 431, 575)(430, 574, 432, 576)
	L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 319)(16, 295)(17, 321)(18, 324)(19, 325)(20, 297)(21, 327)(22, 298)(23, 331)(24, 299)(25, 333)(26, 336)(27, 337)(28, 301)(29, 339)(30, 302)(31, 343)(32, 304)(33, 345)(34, 305)(35, 347)(36, 349)(37, 350)(38, 308)(39, 351)(40, 309)(41, 352)(42, 310)(43, 354)(44, 312)(45, 356)(46, 313)(47, 358)(48, 360)(49, 361)(50, 316)(51, 362)(52, 317)(53, 363)(54, 318)(55, 329)(56, 320)(57, 328)(58, 322)(59, 326)(60, 323)(61, 368)(62, 369)(63, 370)(64, 371)(65, 330)(66, 341)(67, 332)(68, 340)(69, 334)(70, 338)(71, 335)(72, 376)(73, 377)(74, 378)(75, 379)(76, 342)(77, 344)(78, 346)(79, 348)(80, 384)(81, 385)(82, 386)(83, 387)(84, 353)(85, 355)(86, 357)(87, 359)(88, 392)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 373)(102, 374)(103, 375)(104, 408)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 389)(118, 390)(119, 391)(120, 424)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 421)(129, 428)(130, 430)(131, 429)(132, 404)(133, 405)(134, 406)(135, 407)(136, 413)(137, 420)(138, 432)(139, 431)(140, 412)(141, 414)(142, 415)(143, 422)(144, 423)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 16, 144 ), ( 16, 144, 16, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2141
Graph:: simple bipartite
	v = 216 e = 288 f = 20
	degree seq :: [ 2^144, 4^72 ]

E27.2143 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y1^4 * Y3)^2, (Y3 * Y1^-2)^4, Y1^-4 * Y3 * Y1^5 * Y3 * Y1^-9 ]
Map::
	R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 43, 187, 66, 210, 85, 229, 101, 245, 117, 261, 133, 277, 128, 272, 111, 255, 94, 238, 80, 224, 58, 202, 33, 177, 16, 160, 28, 172, 48, 192, 69, 213, 61, 205, 76, 220, 92, 236, 108, 252, 124, 268, 140, 284, 144, 288, 142, 286, 127, 271, 110, 254, 96, 240, 79, 223, 57, 201, 32, 176, 52, 196, 72, 216, 60, 204, 35, 179, 53, 197, 73, 217, 90, 234, 106, 250, 122, 266, 138, 282, 143, 287, 141, 285, 126, 270, 112, 256, 95, 239, 78, 222, 56, 200, 75, 219, 59, 203, 34, 178, 17, 161, 29, 173, 49, 193, 70, 214, 88, 232, 104, 248, 120, 264, 136, 280, 132, 276, 116, 260, 100, 244, 84, 228, 65, 209, 42, 186, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 31, 175, 55, 199, 77, 221, 93, 237, 109, 253, 125, 269, 134, 278, 123, 267, 105, 249, 87, 231, 67, 211, 54, 198, 30, 174, 14, 158, 6, 150, 13, 157, 27, 171, 51, 195, 41, 185, 64, 208, 83, 227, 99, 243, 115, 259, 131, 275, 139, 283, 121, 265, 103, 247, 86, 230, 74, 218, 50, 194, 26, 170, 12, 156, 25, 169, 47, 191, 40, 184, 21, 165, 39, 183, 63, 207, 82, 226, 98, 242, 114, 258, 130, 274, 137, 281, 119, 263, 102, 246, 91, 235, 71, 215, 46, 190, 24, 168, 45, 189, 38, 182, 20, 164, 9, 153, 19, 163, 37, 181, 62, 206, 81, 225, 97, 241, 113, 257, 129, 273, 135, 279, 118, 262, 107, 251, 89, 233, 68, 212, 44, 188, 36, 180, 18, 162, 8, 152)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 305)(9, 292)(10, 309)(11, 312)(12, 293)(13, 316)(14, 317)(15, 320)(16, 295)(17, 296)(18, 323)(19, 321)(20, 322)(21, 298)(22, 329)(23, 332)(24, 299)(25, 336)(26, 337)(27, 340)(28, 301)(29, 302)(30, 341)(31, 344)(32, 303)(33, 307)(34, 308)(35, 306)(36, 349)(37, 345)(38, 348)(39, 346)(40, 347)(41, 310)(42, 343)(43, 355)(44, 311)(45, 357)(46, 358)(47, 360)(48, 313)(49, 314)(50, 361)(51, 363)(52, 315)(53, 318)(54, 364)(55, 330)(56, 319)(57, 325)(58, 327)(59, 328)(60, 326)(61, 324)(62, 366)(63, 367)(64, 368)(65, 369)(66, 374)(67, 331)(68, 376)(69, 333)(70, 334)(71, 378)(72, 335)(73, 338)(74, 380)(75, 339)(76, 342)(77, 382)(78, 350)(79, 351)(80, 352)(81, 353)(82, 383)(83, 384)(84, 386)(85, 390)(86, 354)(87, 392)(88, 356)(89, 394)(90, 359)(91, 396)(92, 362)(93, 398)(94, 365)(95, 370)(96, 371)(97, 399)(98, 372)(99, 400)(100, 403)(101, 406)(102, 373)(103, 408)(104, 375)(105, 410)(106, 377)(107, 412)(108, 379)(109, 414)(110, 381)(111, 385)(112, 387)(113, 415)(114, 416)(115, 388)(116, 413)(117, 422)(118, 389)(119, 424)(120, 391)(121, 426)(122, 393)(123, 428)(124, 395)(125, 404)(126, 397)(127, 401)(128, 402)(129, 429)(130, 430)(131, 421)(132, 423)(133, 419)(134, 405)(135, 420)(136, 407)(137, 431)(138, 409)(139, 432)(140, 411)(141, 417)(142, 418)(143, 425)(144, 427)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2140
Graph:: simple bipartite
	v = 146 e = 288 f = 90
	degree seq :: [ 2^144, 144^2 ]

E27.2144 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^4 * Y1)^2, (Y2^2 * Y1)^4, (Y3 * Y2^-1)^8, Y2^-3 * Y1 * Y2^13 * Y1 * Y2^-2, (Y2^-2 * R * Y2^-7)^2 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 23, 167)(16, 160, 27, 171)(18, 162, 35, 179)(19, 163, 24, 168)(20, 164, 28, 172)(22, 166, 41, 185)(26, 170, 47, 191)(30, 174, 53, 197)(31, 175, 45, 189)(32, 176, 51, 195)(33, 177, 43, 187)(34, 178, 49, 193)(36, 180, 54, 198)(37, 181, 46, 190)(38, 182, 52, 196)(39, 183, 44, 188)(40, 184, 50, 194)(42, 186, 48, 192)(55, 199, 70, 214)(56, 200, 75, 219)(57, 201, 68, 212)(58, 202, 74, 218)(59, 203, 66, 210)(60, 204, 73, 217)(61, 205, 77, 221)(62, 206, 71, 215)(63, 207, 69, 213)(64, 208, 67, 211)(65, 209, 81, 225)(72, 216, 85, 229)(76, 220, 89, 233)(78, 222, 91, 235)(79, 223, 90, 234)(80, 224, 94, 238)(82, 226, 87, 231)(83, 227, 86, 230)(84, 228, 98, 242)(88, 232, 102, 246)(92, 236, 106, 250)(93, 237, 105, 249)(95, 239, 107, 251)(96, 240, 111, 255)(97, 241, 101, 245)(99, 243, 103, 247)(100, 244, 115, 259)(104, 248, 119, 263)(108, 252, 123, 267)(109, 253, 122, 266)(110, 254, 121, 265)(112, 256, 124, 268)(113, 257, 118, 262)(114, 258, 117, 261)(116, 260, 120, 264)(125, 269, 139, 283)(126, 270, 138, 282)(127, 271, 137, 281)(128, 272, 136, 280)(129, 273, 135, 279)(130, 274, 134, 278)(131, 275, 133, 277)(132, 276, 140, 284)(141, 285, 143, 287)(142, 286, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 324, 468, 349, 493, 368, 512, 384, 528, 400, 544, 416, 560, 421, 565, 405, 549, 389, 533, 373, 517, 355, 499, 332, 476, 312, 456, 299, 443, 311, 455, 331, 475, 354, 498, 341, 485, 363, 507, 379, 523, 395, 539, 411, 555, 427, 571, 431, 575, 422, 566, 406, 550, 390, 534, 374, 518, 357, 501, 334, 478, 313, 457, 333, 477, 356, 500, 340, 484, 317, 461, 339, 483, 362, 506, 378, 522, 394, 538, 410, 554, 426, 570, 432, 576, 423, 567, 407, 551, 391, 535, 375, 519, 359, 503, 335, 479, 358, 502, 338, 482, 316, 460, 301, 445, 315, 459, 337, 481, 361, 505, 377, 521, 393, 537, 409, 553, 425, 569, 420, 564, 404, 548, 388, 532, 372, 516, 353, 497, 330, 474, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 336, 480, 360, 504, 376, 520, 392, 536, 408, 552, 424, 568, 413, 557, 397, 541, 381, 525, 365, 509, 344, 488, 320, 464, 304, 448, 295, 439, 303, 447, 319, 463, 343, 487, 329, 473, 352, 496, 371, 515, 387, 531, 403, 547, 419, 563, 429, 573, 414, 558, 398, 542, 382, 526, 366, 510, 346, 490, 322, 466, 305, 449, 321, 465, 345, 489, 328, 472, 309, 453, 327, 471, 351, 495, 370, 514, 386, 530, 402, 546, 418, 562, 430, 574, 415, 559, 399, 543, 383, 527, 367, 511, 348, 492, 323, 467, 347, 491, 326, 470, 308, 452, 297, 441, 307, 451, 325, 469, 350, 494, 369, 513, 385, 529, 401, 545, 417, 561, 428, 572, 412, 556, 396, 540, 380, 524, 364, 508, 342, 486, 318, 462, 302, 446, 294, 438)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 311)(16, 315)(17, 296)(18, 323)(19, 312)(20, 316)(21, 298)(22, 329)(23, 303)(24, 307)(25, 300)(26, 335)(27, 304)(28, 308)(29, 302)(30, 341)(31, 333)(32, 339)(33, 331)(34, 337)(35, 306)(36, 342)(37, 334)(38, 340)(39, 332)(40, 338)(41, 310)(42, 336)(43, 321)(44, 327)(45, 319)(46, 325)(47, 314)(48, 330)(49, 322)(50, 328)(51, 320)(52, 326)(53, 318)(54, 324)(55, 358)(56, 363)(57, 356)(58, 362)(59, 354)(60, 361)(61, 365)(62, 359)(63, 357)(64, 355)(65, 369)(66, 347)(67, 352)(68, 345)(69, 351)(70, 343)(71, 350)(72, 373)(73, 348)(74, 346)(75, 344)(76, 377)(77, 349)(78, 379)(79, 378)(80, 382)(81, 353)(82, 375)(83, 374)(84, 386)(85, 360)(86, 371)(87, 370)(88, 390)(89, 364)(90, 367)(91, 366)(92, 394)(93, 393)(94, 368)(95, 395)(96, 399)(97, 389)(98, 372)(99, 391)(100, 403)(101, 385)(102, 376)(103, 387)(104, 407)(105, 381)(106, 380)(107, 383)(108, 411)(109, 410)(110, 409)(111, 384)(112, 412)(113, 406)(114, 405)(115, 388)(116, 408)(117, 402)(118, 401)(119, 392)(120, 404)(121, 398)(122, 397)(123, 396)(124, 400)(125, 427)(126, 426)(127, 425)(128, 424)(129, 423)(130, 422)(131, 421)(132, 428)(133, 419)(134, 418)(135, 417)(136, 416)(137, 415)(138, 414)(139, 413)(140, 420)(141, 431)(142, 432)(143, 429)(144, 430)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2145
Graph:: bipartite
	v = 74 e = 288 f = 162
	degree seq :: [ 4^72, 144^2 ]

E27.2145 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C8 x D18 (small group id <144, 5>)
Aut   = $<288, 120>$ (small group id <288, 120>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y1^-1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^2, Y3^-1 * Y1^-2 * Y3 * Y1^2, (R * Y2 * Y3^-1)^2, (Y3^-3 * Y1)^2, Y1^8, Y3^-15 * Y1 * Y3 * Y1^-1 * Y3^-2, (Y3 * Y2^-1)^72 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 34, 178, 27, 171, 13, 157, 4, 148)(3, 147, 9, 153, 17, 161, 8, 152, 21, 165, 35, 179, 28, 172, 11, 155)(5, 149, 14, 158, 18, 162, 37, 181, 30, 174, 12, 156, 20, 164, 7, 151)(10, 154, 24, 168, 36, 180, 23, 167, 42, 186, 22, 166, 43, 187, 26, 170)(15, 159, 32, 176, 38, 182, 29, 173, 41, 185, 19, 163, 39, 183, 31, 175)(25, 169, 47, 191, 53, 197, 46, 190, 58, 202, 45, 189, 59, 203, 44, 188)(33, 177, 49, 193, 54, 198, 40, 184, 56, 200, 50, 194, 55, 199, 51, 195)(48, 192, 60, 204, 69, 213, 63, 207, 74, 218, 62, 206, 75, 219, 61, 205)(52, 196, 57, 201, 70, 214, 66, 210, 72, 216, 67, 211, 71, 215, 65, 209)(64, 208, 77, 221, 85, 229, 76, 220, 90, 234, 79, 223, 91, 235, 78, 222)(68, 212, 82, 226, 86, 230, 83, 227, 88, 232, 81, 225, 87, 231, 73, 217)(80, 224, 94, 238, 101, 245, 93, 237, 106, 250, 92, 236, 107, 251, 95, 239)(84, 228, 99, 243, 102, 246, 97, 241, 104, 248, 89, 233, 103, 247, 98, 242)(96, 240, 111, 255, 117, 261, 110, 254, 122, 266, 109, 253, 123, 267, 108, 252)(100, 244, 113, 257, 118, 262, 105, 249, 120, 264, 114, 258, 119, 263, 115, 259)(112, 256, 124, 268, 133, 277, 127, 271, 138, 282, 126, 270, 139, 283, 125, 269)(116, 260, 121, 265, 134, 278, 130, 274, 136, 280, 131, 275, 135, 279, 129, 273)(128, 272, 137, 281, 132, 276, 140, 284, 143, 287, 142, 286, 144, 288, 141, 285)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 313)(11, 315)(12, 317)(13, 316)(14, 319)(15, 293)(16, 302)(17, 324)(18, 294)(19, 328)(20, 301)(21, 330)(22, 296)(23, 297)(24, 299)(25, 336)(26, 323)(27, 325)(28, 331)(29, 337)(30, 322)(31, 338)(32, 339)(33, 303)(34, 309)(35, 304)(36, 341)(37, 320)(38, 306)(39, 308)(40, 345)(41, 318)(42, 346)(43, 347)(44, 310)(45, 311)(46, 312)(47, 314)(48, 352)(49, 353)(50, 354)(51, 355)(52, 321)(53, 357)(54, 326)(55, 327)(56, 329)(57, 361)(58, 362)(59, 363)(60, 332)(61, 333)(62, 334)(63, 335)(64, 368)(65, 369)(66, 370)(67, 371)(68, 340)(69, 373)(70, 342)(71, 343)(72, 344)(73, 377)(74, 378)(75, 379)(76, 348)(77, 349)(78, 350)(79, 351)(80, 384)(81, 385)(82, 386)(83, 387)(84, 356)(85, 389)(86, 358)(87, 359)(88, 360)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 405)(102, 374)(103, 375)(104, 376)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 421)(118, 390)(119, 391)(120, 392)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 423)(129, 429)(130, 428)(131, 430)(132, 404)(133, 420)(134, 406)(135, 407)(136, 408)(137, 413)(138, 431)(139, 432)(140, 412)(141, 414)(142, 415)(143, 422)(144, 424)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 144 ), ( 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2144
Graph:: simple bipartite
	v = 162 e = 288 f = 74
	degree seq :: [ 2^144, 16^18 ]

E27.2146 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 72})
Quotient :: regular
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^-5 * T2 * T1^7 * T2 * T1^-6 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 43, 66, 85, 101, 117, 133, 126, 112, 95, 78, 56, 75, 59, 34, 17, 29, 49, 70, 88, 104, 120, 136, 143, 141, 127, 110, 96, 79, 57, 32, 52, 72, 60, 35, 53, 73, 90, 106, 122, 138, 144, 142, 128, 111, 94, 80, 58, 33, 16, 28, 48, 69, 61, 76, 92, 108, 124, 140, 132, 116, 100, 84, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 77, 93, 109, 125, 137, 119, 102, 91, 71, 46, 24, 45, 38, 20, 9, 19, 37, 62, 81, 97, 113, 129, 139, 121, 103, 86, 74, 50, 26, 12, 25, 47, 40, 21, 39, 63, 82, 98, 114, 130, 134, 123, 105, 87, 67, 54, 30, 14, 6, 13, 27, 51, 41, 64, 83, 99, 115, 131, 135, 118, 107, 89, 68, 44, 36, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 133)(130, 141)(131, 142)(132, 139)(135, 143)(137, 144)
	local type(s) :: { ( 8^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2147
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 72 f = 18
	degree seq :: [ 72^2 ]

E27.2147 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 72})
Quotient :: regular
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-4 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-3 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 31, 28, 17, 8)(6, 13, 21, 32, 30, 18, 9, 14)(15, 25, 33, 43, 40, 27, 16, 26)(23, 34, 42, 41, 29, 36, 24, 35)(37, 47, 52, 50, 39, 49, 38, 48)(44, 53, 51, 56, 46, 55, 45, 54)(57, 65, 60, 68, 59, 67, 58, 66)(61, 69, 64, 72, 63, 71, 62, 70)(73, 81, 76, 84, 75, 83, 74, 82)(77, 85, 80, 88, 79, 87, 78, 86)(89, 97, 92, 100, 91, 99, 90, 98)(93, 101, 96, 104, 95, 103, 94, 102)(105, 113, 108, 116, 107, 115, 106, 114)(109, 117, 112, 120, 111, 119, 110, 118)(121, 129, 124, 132, 123, 131, 122, 130)(125, 133, 128, 136, 127, 135, 126, 134)(137, 143, 140, 142, 139, 141, 138, 144)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128)(129, 137)(130, 138)(131, 139)(132, 140)(133, 141)(134, 142)(135, 143)(136, 144)
	local type(s) :: { ( 72^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2146
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 18 e = 72 f = 2
	degree seq :: [ 8^18 ]

E27.2148 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^72 ]
Map::
	R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 26, 39, 30, 18, 9, 16)(11, 20, 32, 44, 36, 23, 13, 21)(25, 37, 48, 41, 29, 40, 27, 38)(31, 42, 53, 46, 35, 45, 33, 43)(47, 57, 51, 60, 50, 59, 49, 58)(52, 61, 56, 64, 55, 63, 54, 62)(65, 73, 68, 76, 67, 75, 66, 74)(69, 77, 72, 80, 71, 79, 70, 78)(81, 89, 84, 92, 83, 91, 82, 90)(85, 93, 88, 96, 87, 95, 86, 94)(97, 105, 100, 108, 99, 107, 98, 106)(101, 109, 104, 112, 103, 111, 102, 110)(113, 121, 116, 124, 115, 123, 114, 122)(117, 125, 120, 128, 119, 127, 118, 126)(129, 137, 132, 140, 131, 139, 130, 138)(133, 141, 136, 144, 135, 143, 134, 142)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 156)(154, 158)(159, 169)(160, 171)(161, 170)(162, 173)(163, 174)(164, 175)(165, 177)(166, 176)(167, 179)(168, 180)(172, 178)(181, 191)(182, 193)(183, 192)(184, 194)(185, 195)(186, 196)(187, 198)(188, 197)(189, 199)(190, 200)(201, 209)(202, 210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 241)(234, 242)(235, 243)(236, 244)(237, 245)(238, 246)(239, 247)(240, 248)(249, 257)(250, 258)(251, 259)(252, 260)(253, 261)(254, 262)(255, 263)(256, 264)(265, 273)(266, 274)(267, 275)(268, 276)(269, 277)(270, 278)(271, 279)(272, 280)(281, 287)(282, 288)(283, 285)(284, 286)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 144, 144 ), ( 144^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2152
Transitivity :: ET+
Graph:: simple bipartite
	v = 90 e = 144 f = 2
	degree seq :: [ 2^72, 8^18 ]

E27.2149 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-2 * T2^-1 * T1^2, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^8, T2^14 * T1^-1 * T2^-3 * T1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 48, 64, 80, 96, 112, 128, 134, 118, 102, 86, 70, 54, 38, 18, 6, 17, 36, 53, 69, 85, 101, 117, 133, 143, 136, 120, 104, 88, 72, 56, 41, 30, 34, 21, 42, 58, 74, 90, 106, 122, 138, 144, 135, 119, 103, 87, 71, 55, 39, 20, 13, 28, 43, 59, 75, 91, 107, 123, 139, 132, 116, 100, 84, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 89, 105, 121, 137, 127, 111, 95, 79, 63, 47, 26, 35, 16, 14, 31, 50, 66, 82, 98, 114, 130, 142, 126, 110, 94, 78, 62, 46, 24, 11, 27, 37, 32, 51, 67, 83, 99, 115, 131, 141, 125, 109, 93, 77, 61, 45, 23, 9, 4, 12, 29, 49, 65, 81, 97, 113, 129, 140, 124, 108, 92, 76, 60, 44, 22, 8)(145, 146, 150, 160, 178, 171, 157, 148)(147, 153, 161, 152, 165, 179, 172, 155)(149, 158, 162, 181, 174, 156, 164, 151)(154, 168, 180, 167, 186, 166, 187, 170)(159, 176, 182, 173, 185, 163, 183, 175)(169, 191, 197, 190, 202, 189, 203, 188)(177, 193, 198, 184, 200, 194, 199, 195)(192, 204, 213, 207, 218, 206, 219, 205)(196, 201, 214, 210, 216, 211, 215, 209)(208, 221, 229, 220, 234, 223, 235, 222)(212, 226, 230, 227, 232, 225, 231, 217)(224, 238, 245, 237, 250, 236, 251, 239)(228, 243, 246, 241, 248, 233, 247, 242)(240, 255, 261, 254, 266, 253, 267, 252)(244, 257, 262, 249, 264, 258, 263, 259)(256, 268, 277, 271, 282, 270, 283, 269)(260, 265, 278, 274, 280, 275, 279, 273)(272, 285, 287, 284, 288, 281, 276, 286)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4^8 ), ( 4^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2153
Transitivity :: ET+
Graph:: bipartite
	v = 20 e = 144 f = 72
	degree seq :: [ 8^18, 72^2 ]

E27.2150 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 72})
Quotient :: edge
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^-5 * T2 * T1^7 * T2 * T1^-6 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 133)(130, 141)(131, 142)(132, 139)(135, 143)(137, 144)(145, 146, 149, 155, 167, 187, 210, 229, 245, 261, 277, 270, 256, 239, 222, 200, 219, 203, 178, 161, 173, 193, 214, 232, 248, 264, 280, 287, 285, 271, 254, 240, 223, 201, 176, 196, 216, 204, 179, 197, 217, 234, 250, 266, 282, 288, 286, 272, 255, 238, 224, 202, 177, 160, 172, 192, 213, 205, 220, 236, 252, 268, 284, 276, 260, 244, 228, 209, 186, 166, 154, 148)(147, 151, 159, 175, 199, 221, 237, 253, 269, 281, 263, 246, 235, 215, 190, 168, 189, 182, 164, 153, 163, 181, 206, 225, 241, 257, 273, 283, 265, 247, 230, 218, 194, 170, 156, 169, 191, 184, 165, 183, 207, 226, 242, 258, 274, 278, 267, 249, 231, 211, 198, 174, 158, 150, 157, 171, 195, 185, 208, 227, 243, 259, 275, 279, 262, 251, 233, 212, 188, 180, 162, 152)
	L = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 16, 16 ), ( 16^72 ) }
Outer automorphisms :: reflexible
Dual of E27.2151
Transitivity :: ET+
Graph:: simple bipartite
	v = 74 e = 144 f = 18
	degree seq :: [ 2^72, 72^2 ]

E27.2151 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^72 ]
Map::
	R = (1, 145, 3, 147, 8, 152, 17, 161, 28, 172, 19, 163, 10, 154, 4, 148)(2, 146, 5, 149, 12, 156, 22, 166, 34, 178, 24, 168, 14, 158, 6, 150)(7, 151, 15, 159, 26, 170, 39, 183, 30, 174, 18, 162, 9, 153, 16, 160)(11, 155, 20, 164, 32, 176, 44, 188, 36, 180, 23, 167, 13, 157, 21, 165)(25, 169, 37, 181, 48, 192, 41, 185, 29, 173, 40, 184, 27, 171, 38, 182)(31, 175, 42, 186, 53, 197, 46, 190, 35, 179, 45, 189, 33, 177, 43, 187)(47, 191, 57, 201, 51, 195, 60, 204, 50, 194, 59, 203, 49, 193, 58, 202)(52, 196, 61, 205, 56, 200, 64, 208, 55, 199, 63, 207, 54, 198, 62, 206)(65, 209, 73, 217, 68, 212, 76, 220, 67, 211, 75, 219, 66, 210, 74, 218)(69, 213, 77, 221, 72, 216, 80, 224, 71, 215, 79, 223, 70, 214, 78, 222)(81, 225, 89, 233, 84, 228, 92, 236, 83, 227, 91, 235, 82, 226, 90, 234)(85, 229, 93, 237, 88, 232, 96, 240, 87, 231, 95, 239, 86, 230, 94, 238)(97, 241, 105, 249, 100, 244, 108, 252, 99, 243, 107, 251, 98, 242, 106, 250)(101, 245, 109, 253, 104, 248, 112, 256, 103, 247, 111, 255, 102, 246, 110, 254)(113, 257, 121, 265, 116, 260, 124, 268, 115, 259, 123, 267, 114, 258, 122, 266)(117, 261, 125, 269, 120, 264, 128, 272, 119, 263, 127, 271, 118, 262, 126, 270)(129, 273, 137, 281, 132, 276, 140, 284, 131, 275, 139, 283, 130, 274, 138, 282)(133, 277, 141, 285, 136, 280, 144, 288, 135, 279, 143, 287, 134, 278, 142, 286)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 156)(9, 148)(10, 158)(11, 149)(12, 152)(13, 150)(14, 154)(15, 169)(16, 171)(17, 170)(18, 173)(19, 174)(20, 175)(21, 177)(22, 176)(23, 179)(24, 180)(25, 159)(26, 161)(27, 160)(28, 178)(29, 162)(30, 163)(31, 164)(32, 166)(33, 165)(34, 172)(35, 167)(36, 168)(37, 191)(38, 193)(39, 192)(40, 194)(41, 195)(42, 196)(43, 198)(44, 197)(45, 199)(46, 200)(47, 181)(48, 183)(49, 182)(50, 184)(51, 185)(52, 186)(53, 188)(54, 187)(55, 189)(56, 190)(57, 209)(58, 210)(59, 211)(60, 212)(61, 213)(62, 214)(63, 215)(64, 216)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 225)(74, 226)(75, 227)(76, 228)(77, 229)(78, 230)(79, 231)(80, 232)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(89, 241)(90, 242)(91, 243)(92, 244)(93, 245)(94, 246)(95, 247)(96, 248)(97, 233)(98, 234)(99, 235)(100, 236)(101, 237)(102, 238)(103, 239)(104, 240)(105, 257)(106, 258)(107, 259)(108, 260)(109, 261)(110, 262)(111, 263)(112, 264)(113, 249)(114, 250)(115, 251)(116, 252)(117, 253)(118, 254)(119, 255)(120, 256)(121, 273)(122, 274)(123, 275)(124, 276)(125, 277)(126, 278)(127, 279)(128, 280)(129, 265)(130, 266)(131, 267)(132, 268)(133, 269)(134, 270)(135, 271)(136, 272)(137, 287)(138, 288)(139, 285)(140, 286)(141, 283)(142, 284)(143, 281)(144, 282)
	local type(s) :: { ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2150
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 18 e = 144 f = 74
	degree seq :: [ 16^18 ]

E27.2152 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2 * T1^-2 * T2^-1 * T1^2, T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-2, T1^8, T2^14 * T1^-1 * T2^-3 * T1 * T2 ]
Map::
	R = (1, 145, 3, 147, 10, 154, 25, 169, 48, 192, 64, 208, 80, 224, 96, 240, 112, 256, 128, 272, 134, 278, 118, 262, 102, 246, 86, 230, 70, 214, 54, 198, 38, 182, 18, 162, 6, 150, 17, 161, 36, 180, 53, 197, 69, 213, 85, 229, 101, 245, 117, 261, 133, 277, 143, 287, 136, 280, 120, 264, 104, 248, 88, 232, 72, 216, 56, 200, 41, 185, 30, 174, 34, 178, 21, 165, 42, 186, 58, 202, 74, 218, 90, 234, 106, 250, 122, 266, 138, 282, 144, 288, 135, 279, 119, 263, 103, 247, 87, 231, 71, 215, 55, 199, 39, 183, 20, 164, 13, 157, 28, 172, 43, 187, 59, 203, 75, 219, 91, 235, 107, 251, 123, 267, 139, 283, 132, 276, 116, 260, 100, 244, 84, 228, 68, 212, 52, 196, 33, 177, 15, 159, 5, 149)(2, 146, 7, 151, 19, 163, 40, 184, 57, 201, 73, 217, 89, 233, 105, 249, 121, 265, 137, 281, 127, 271, 111, 255, 95, 239, 79, 223, 63, 207, 47, 191, 26, 170, 35, 179, 16, 160, 14, 158, 31, 175, 50, 194, 66, 210, 82, 226, 98, 242, 114, 258, 130, 274, 142, 286, 126, 270, 110, 254, 94, 238, 78, 222, 62, 206, 46, 190, 24, 168, 11, 155, 27, 171, 37, 181, 32, 176, 51, 195, 67, 211, 83, 227, 99, 243, 115, 259, 131, 275, 141, 285, 125, 269, 109, 253, 93, 237, 77, 221, 61, 205, 45, 189, 23, 167, 9, 153, 4, 148, 12, 156, 29, 173, 49, 193, 65, 209, 81, 225, 97, 241, 113, 257, 129, 273, 140, 284, 124, 268, 108, 252, 92, 236, 76, 220, 60, 204, 44, 188, 22, 166, 8, 152)
	L = (1, 146)(2, 150)(3, 153)(4, 145)(5, 158)(6, 160)(7, 149)(8, 165)(9, 161)(10, 168)(11, 147)(12, 164)(13, 148)(14, 162)(15, 176)(16, 178)(17, 152)(18, 181)(19, 183)(20, 151)(21, 179)(22, 187)(23, 186)(24, 180)(25, 191)(26, 154)(27, 157)(28, 155)(29, 185)(30, 156)(31, 159)(32, 182)(33, 193)(34, 171)(35, 172)(36, 167)(37, 174)(38, 173)(39, 175)(40, 200)(41, 163)(42, 166)(43, 170)(44, 169)(45, 203)(46, 202)(47, 197)(48, 204)(49, 198)(50, 199)(51, 177)(52, 201)(53, 190)(54, 184)(55, 195)(56, 194)(57, 214)(58, 189)(59, 188)(60, 213)(61, 192)(62, 219)(63, 218)(64, 221)(65, 196)(66, 216)(67, 215)(68, 226)(69, 207)(70, 210)(71, 209)(72, 211)(73, 212)(74, 206)(75, 205)(76, 234)(77, 229)(78, 208)(79, 235)(80, 238)(81, 231)(82, 230)(83, 232)(84, 243)(85, 220)(86, 227)(87, 217)(88, 225)(89, 247)(90, 223)(91, 222)(92, 251)(93, 250)(94, 245)(95, 224)(96, 255)(97, 248)(98, 228)(99, 246)(100, 257)(101, 237)(102, 241)(103, 242)(104, 233)(105, 264)(106, 236)(107, 239)(108, 240)(109, 267)(110, 266)(111, 261)(112, 268)(113, 262)(114, 263)(115, 244)(116, 265)(117, 254)(118, 249)(119, 259)(120, 258)(121, 278)(122, 253)(123, 252)(124, 277)(125, 256)(126, 283)(127, 282)(128, 285)(129, 260)(130, 280)(131, 279)(132, 286)(133, 271)(134, 274)(135, 273)(136, 275)(137, 276)(138, 270)(139, 269)(140, 288)(141, 287)(142, 272)(143, 284)(144, 281)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2148
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 144 f = 90
	degree seq :: [ 144^2 ]

E27.2153 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 72})
Quotient :: loop
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^-5 * T2 * T1^7 * T2 * T1^-6 ]
Map:: polytopal non-degenerate
	R = (1, 145, 3, 147)(2, 146, 6, 150)(4, 148, 9, 153)(5, 149, 12, 156)(7, 151, 16, 160)(8, 152, 17, 161)(10, 154, 21, 165)(11, 155, 24, 168)(13, 157, 28, 172)(14, 158, 29, 173)(15, 159, 32, 176)(18, 162, 35, 179)(19, 163, 33, 177)(20, 164, 34, 178)(22, 166, 41, 185)(23, 167, 44, 188)(25, 169, 48, 192)(26, 170, 49, 193)(27, 171, 52, 196)(30, 174, 53, 197)(31, 175, 56, 200)(36, 180, 61, 205)(37, 181, 57, 201)(38, 182, 60, 204)(39, 183, 58, 202)(40, 184, 59, 203)(42, 186, 55, 199)(43, 187, 67, 211)(45, 189, 69, 213)(46, 190, 70, 214)(47, 191, 72, 216)(50, 194, 73, 217)(51, 195, 75, 219)(54, 198, 76, 220)(62, 206, 78, 222)(63, 207, 79, 223)(64, 208, 80, 224)(65, 209, 81, 225)(66, 210, 86, 230)(68, 212, 88, 232)(71, 215, 90, 234)(74, 218, 92, 236)(77, 221, 94, 238)(82, 226, 95, 239)(83, 227, 96, 240)(84, 228, 98, 242)(85, 229, 102, 246)(87, 231, 104, 248)(89, 233, 106, 250)(91, 235, 108, 252)(93, 237, 110, 254)(97, 241, 111, 255)(99, 243, 112, 256)(100, 244, 115, 259)(101, 245, 118, 262)(103, 247, 120, 264)(105, 249, 122, 266)(107, 251, 124, 268)(109, 253, 126, 270)(113, 257, 127, 271)(114, 258, 128, 272)(116, 260, 125, 269)(117, 261, 134, 278)(119, 263, 136, 280)(121, 265, 138, 282)(123, 267, 140, 284)(129, 273, 133, 277)(130, 274, 141, 285)(131, 275, 142, 286)(132, 276, 139, 283)(135, 279, 143, 287)(137, 281, 144, 288)
	L = (1, 146)(2, 149)(3, 151)(4, 145)(5, 155)(6, 157)(7, 159)(8, 147)(9, 163)(10, 148)(11, 167)(12, 169)(13, 171)(14, 150)(15, 175)(16, 172)(17, 173)(18, 152)(19, 181)(20, 153)(21, 183)(22, 154)(23, 187)(24, 189)(25, 191)(26, 156)(27, 195)(28, 192)(29, 193)(30, 158)(31, 199)(32, 196)(33, 160)(34, 161)(35, 197)(36, 162)(37, 206)(38, 164)(39, 207)(40, 165)(41, 208)(42, 166)(43, 210)(44, 180)(45, 182)(46, 168)(47, 184)(48, 213)(49, 214)(50, 170)(51, 185)(52, 216)(53, 217)(54, 174)(55, 221)(56, 219)(57, 176)(58, 177)(59, 178)(60, 179)(61, 220)(62, 225)(63, 226)(64, 227)(65, 186)(66, 229)(67, 198)(68, 188)(69, 205)(70, 232)(71, 190)(72, 204)(73, 234)(74, 194)(75, 203)(76, 236)(77, 237)(78, 200)(79, 201)(80, 202)(81, 241)(82, 242)(83, 243)(84, 209)(85, 245)(86, 218)(87, 211)(88, 248)(89, 212)(90, 250)(91, 215)(92, 252)(93, 253)(94, 224)(95, 222)(96, 223)(97, 257)(98, 258)(99, 259)(100, 228)(101, 261)(102, 235)(103, 230)(104, 264)(105, 231)(106, 266)(107, 233)(108, 268)(109, 269)(110, 240)(111, 238)(112, 239)(113, 273)(114, 274)(115, 275)(116, 244)(117, 277)(118, 251)(119, 246)(120, 280)(121, 247)(122, 282)(123, 249)(124, 284)(125, 281)(126, 256)(127, 254)(128, 255)(129, 283)(130, 278)(131, 279)(132, 260)(133, 270)(134, 267)(135, 262)(136, 287)(137, 263)(138, 288)(139, 265)(140, 276)(141, 271)(142, 272)(143, 285)(144, 286)
	local type(s) :: { ( 8, 72, 8, 72 ) }
Outer automorphisms :: reflexible
Dual of E27.2149
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 72 e = 144 f = 20
	degree seq :: [ 4^72 ]

E27.2154 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^72 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 12, 156)(10, 154, 14, 158)(15, 159, 25, 169)(16, 160, 27, 171)(17, 161, 26, 170)(18, 162, 29, 173)(19, 163, 30, 174)(20, 164, 31, 175)(21, 165, 33, 177)(22, 166, 32, 176)(23, 167, 35, 179)(24, 168, 36, 180)(28, 172, 34, 178)(37, 181, 47, 191)(38, 182, 49, 193)(39, 183, 48, 192)(40, 184, 50, 194)(41, 185, 51, 195)(42, 186, 52, 196)(43, 187, 54, 198)(44, 188, 53, 197)(45, 189, 55, 199)(46, 190, 56, 200)(57, 201, 65, 209)(58, 202, 66, 210)(59, 203, 67, 211)(60, 204, 68, 212)(61, 205, 69, 213)(62, 206, 70, 214)(63, 207, 71, 215)(64, 208, 72, 216)(73, 217, 81, 225)(74, 218, 82, 226)(75, 219, 83, 227)(76, 220, 84, 228)(77, 221, 85, 229)(78, 222, 86, 230)(79, 223, 87, 231)(80, 224, 88, 232)(89, 233, 97, 241)(90, 234, 98, 242)(91, 235, 99, 243)(92, 236, 100, 244)(93, 237, 101, 245)(94, 238, 102, 246)(95, 239, 103, 247)(96, 240, 104, 248)(105, 249, 113, 257)(106, 250, 114, 258)(107, 251, 115, 259)(108, 252, 116, 260)(109, 253, 117, 261)(110, 254, 118, 262)(111, 255, 119, 263)(112, 256, 120, 264)(121, 265, 129, 273)(122, 266, 130, 274)(123, 267, 131, 275)(124, 268, 132, 276)(125, 269, 133, 277)(126, 270, 134, 278)(127, 271, 135, 279)(128, 272, 136, 280)(137, 281, 143, 287)(138, 282, 144, 288)(139, 283, 141, 285)(140, 284, 142, 286)(289, 433, 291, 435, 296, 440, 305, 449, 316, 460, 307, 451, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 310, 454, 322, 466, 312, 456, 302, 446, 294, 438)(295, 439, 303, 447, 314, 458, 327, 471, 318, 462, 306, 450, 297, 441, 304, 448)(299, 443, 308, 452, 320, 464, 332, 476, 324, 468, 311, 455, 301, 445, 309, 453)(313, 457, 325, 469, 336, 480, 329, 473, 317, 461, 328, 472, 315, 459, 326, 470)(319, 463, 330, 474, 341, 485, 334, 478, 323, 467, 333, 477, 321, 465, 331, 475)(335, 479, 345, 489, 339, 483, 348, 492, 338, 482, 347, 491, 337, 481, 346, 490)(340, 484, 349, 493, 344, 488, 352, 496, 343, 487, 351, 495, 342, 486, 350, 494)(353, 497, 361, 505, 356, 500, 364, 508, 355, 499, 363, 507, 354, 498, 362, 506)(357, 501, 365, 509, 360, 504, 368, 512, 359, 503, 367, 511, 358, 502, 366, 510)(369, 513, 377, 521, 372, 516, 380, 524, 371, 515, 379, 523, 370, 514, 378, 522)(373, 517, 381, 525, 376, 520, 384, 528, 375, 519, 383, 527, 374, 518, 382, 526)(385, 529, 393, 537, 388, 532, 396, 540, 387, 531, 395, 539, 386, 530, 394, 538)(389, 533, 397, 541, 392, 536, 400, 544, 391, 535, 399, 543, 390, 534, 398, 542)(401, 545, 409, 553, 404, 548, 412, 556, 403, 547, 411, 555, 402, 546, 410, 554)(405, 549, 413, 557, 408, 552, 416, 560, 407, 551, 415, 559, 406, 550, 414, 558)(417, 561, 425, 569, 420, 564, 428, 572, 419, 563, 427, 571, 418, 562, 426, 570)(421, 565, 429, 573, 424, 568, 432, 576, 423, 567, 431, 575, 422, 566, 430, 574)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 300)(9, 292)(10, 302)(11, 293)(12, 296)(13, 294)(14, 298)(15, 313)(16, 315)(17, 314)(18, 317)(19, 318)(20, 319)(21, 321)(22, 320)(23, 323)(24, 324)(25, 303)(26, 305)(27, 304)(28, 322)(29, 306)(30, 307)(31, 308)(32, 310)(33, 309)(34, 316)(35, 311)(36, 312)(37, 335)(38, 337)(39, 336)(40, 338)(41, 339)(42, 340)(43, 342)(44, 341)(45, 343)(46, 344)(47, 325)(48, 327)(49, 326)(50, 328)(51, 329)(52, 330)(53, 332)(54, 331)(55, 333)(56, 334)(57, 353)(58, 354)(59, 355)(60, 356)(61, 357)(62, 358)(63, 359)(64, 360)(65, 345)(66, 346)(67, 347)(68, 348)(69, 349)(70, 350)(71, 351)(72, 352)(73, 369)(74, 370)(75, 371)(76, 372)(77, 373)(78, 374)(79, 375)(80, 376)(81, 361)(82, 362)(83, 363)(84, 364)(85, 365)(86, 366)(87, 367)(88, 368)(89, 385)(90, 386)(91, 387)(92, 388)(93, 389)(94, 390)(95, 391)(96, 392)(97, 377)(98, 378)(99, 379)(100, 380)(101, 381)(102, 382)(103, 383)(104, 384)(105, 401)(106, 402)(107, 403)(108, 404)(109, 405)(110, 406)(111, 407)(112, 408)(113, 393)(114, 394)(115, 395)(116, 396)(117, 397)(118, 398)(119, 399)(120, 400)(121, 417)(122, 418)(123, 419)(124, 420)(125, 421)(126, 422)(127, 423)(128, 424)(129, 409)(130, 410)(131, 411)(132, 412)(133, 413)(134, 414)(135, 415)(136, 416)(137, 431)(138, 432)(139, 429)(140, 430)(141, 427)(142, 428)(143, 425)(144, 426)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 144, 2, 144 ), ( 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144, 2, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2157
Graph:: bipartite
	v = 90 e = 288 f = 146
	degree seq :: [ 4^72, 16^18 ]

E27.2155 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-2 * Y2^-1 * Y1, Y1^-2 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1, Y1^8, Y2^15 * Y1 * Y2^-2 * Y1 * Y2 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 34, 178, 27, 171, 13, 157, 4, 148)(3, 147, 9, 153, 17, 161, 8, 152, 21, 165, 35, 179, 28, 172, 11, 155)(5, 149, 14, 158, 18, 162, 37, 181, 30, 174, 12, 156, 20, 164, 7, 151)(10, 154, 24, 168, 36, 180, 23, 167, 42, 186, 22, 166, 43, 187, 26, 170)(15, 159, 32, 176, 38, 182, 29, 173, 41, 185, 19, 163, 39, 183, 31, 175)(25, 169, 47, 191, 53, 197, 46, 190, 58, 202, 45, 189, 59, 203, 44, 188)(33, 177, 49, 193, 54, 198, 40, 184, 56, 200, 50, 194, 55, 199, 51, 195)(48, 192, 60, 204, 69, 213, 63, 207, 74, 218, 62, 206, 75, 219, 61, 205)(52, 196, 57, 201, 70, 214, 66, 210, 72, 216, 67, 211, 71, 215, 65, 209)(64, 208, 77, 221, 85, 229, 76, 220, 90, 234, 79, 223, 91, 235, 78, 222)(68, 212, 82, 226, 86, 230, 83, 227, 88, 232, 81, 225, 87, 231, 73, 217)(80, 224, 94, 238, 101, 245, 93, 237, 106, 250, 92, 236, 107, 251, 95, 239)(84, 228, 99, 243, 102, 246, 97, 241, 104, 248, 89, 233, 103, 247, 98, 242)(96, 240, 111, 255, 117, 261, 110, 254, 122, 266, 109, 253, 123, 267, 108, 252)(100, 244, 113, 257, 118, 262, 105, 249, 120, 264, 114, 258, 119, 263, 115, 259)(112, 256, 124, 268, 133, 277, 127, 271, 138, 282, 126, 270, 139, 283, 125, 269)(116, 260, 121, 265, 134, 278, 130, 274, 136, 280, 131, 275, 135, 279, 129, 273)(128, 272, 141, 285, 143, 287, 140, 284, 144, 288, 137, 281, 132, 276, 142, 286)(289, 433, 291, 435, 298, 442, 313, 457, 336, 480, 352, 496, 368, 512, 384, 528, 400, 544, 416, 560, 422, 566, 406, 550, 390, 534, 374, 518, 358, 502, 342, 486, 326, 470, 306, 450, 294, 438, 305, 449, 324, 468, 341, 485, 357, 501, 373, 517, 389, 533, 405, 549, 421, 565, 431, 575, 424, 568, 408, 552, 392, 536, 376, 520, 360, 504, 344, 488, 329, 473, 318, 462, 322, 466, 309, 453, 330, 474, 346, 490, 362, 506, 378, 522, 394, 538, 410, 554, 426, 570, 432, 576, 423, 567, 407, 551, 391, 535, 375, 519, 359, 503, 343, 487, 327, 471, 308, 452, 301, 445, 316, 460, 331, 475, 347, 491, 363, 507, 379, 523, 395, 539, 411, 555, 427, 571, 420, 564, 404, 548, 388, 532, 372, 516, 356, 500, 340, 484, 321, 465, 303, 447, 293, 437)(290, 434, 295, 439, 307, 451, 328, 472, 345, 489, 361, 505, 377, 521, 393, 537, 409, 553, 425, 569, 415, 559, 399, 543, 383, 527, 367, 511, 351, 495, 335, 479, 314, 458, 323, 467, 304, 448, 302, 446, 319, 463, 338, 482, 354, 498, 370, 514, 386, 530, 402, 546, 418, 562, 430, 574, 414, 558, 398, 542, 382, 526, 366, 510, 350, 494, 334, 478, 312, 456, 299, 443, 315, 459, 325, 469, 320, 464, 339, 483, 355, 499, 371, 515, 387, 531, 403, 547, 419, 563, 429, 573, 413, 557, 397, 541, 381, 525, 365, 509, 349, 493, 333, 477, 311, 455, 297, 441, 292, 436, 300, 444, 317, 461, 337, 481, 353, 497, 369, 513, 385, 529, 401, 545, 417, 561, 428, 572, 412, 556, 396, 540, 380, 524, 364, 508, 348, 492, 332, 476, 310, 454, 296, 440)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 313)(11, 315)(12, 317)(13, 316)(14, 319)(15, 293)(16, 302)(17, 324)(18, 294)(19, 328)(20, 301)(21, 330)(22, 296)(23, 297)(24, 299)(25, 336)(26, 323)(27, 325)(28, 331)(29, 337)(30, 322)(31, 338)(32, 339)(33, 303)(34, 309)(35, 304)(36, 341)(37, 320)(38, 306)(39, 308)(40, 345)(41, 318)(42, 346)(43, 347)(44, 310)(45, 311)(46, 312)(47, 314)(48, 352)(49, 353)(50, 354)(51, 355)(52, 321)(53, 357)(54, 326)(55, 327)(56, 329)(57, 361)(58, 362)(59, 363)(60, 332)(61, 333)(62, 334)(63, 335)(64, 368)(65, 369)(66, 370)(67, 371)(68, 340)(69, 373)(70, 342)(71, 343)(72, 344)(73, 377)(74, 378)(75, 379)(76, 348)(77, 349)(78, 350)(79, 351)(80, 384)(81, 385)(82, 386)(83, 387)(84, 356)(85, 389)(86, 358)(87, 359)(88, 360)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 405)(102, 374)(103, 375)(104, 376)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 421)(118, 390)(119, 391)(120, 392)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 422)(129, 428)(130, 430)(131, 429)(132, 404)(133, 431)(134, 406)(135, 407)(136, 408)(137, 415)(138, 432)(139, 420)(140, 412)(141, 413)(142, 414)(143, 424)(144, 423)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2156
Graph:: bipartite
	v = 20 e = 288 f = 216
	degree seq :: [ 16^18, 144^2 ]

E27.2156 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^4 * Y2)^2, (Y3^-2 * Y2)^4, Y3^-13 * Y2 * Y3^3 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^72 ]
Map:: polytopal
	R = (1, 145)(2, 146)(3, 147)(4, 148)(5, 149)(6, 150)(7, 151)(8, 152)(9, 153)(10, 154)(11, 155)(12, 156)(13, 157)(14, 158)(15, 159)(16, 160)(17, 161)(18, 162)(19, 163)(20, 164)(21, 165)(22, 166)(23, 167)(24, 168)(25, 169)(26, 170)(27, 171)(28, 172)(29, 173)(30, 174)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 181)(38, 182)(39, 183)(40, 184)(41, 185)(42, 186)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 193)(50, 194)(51, 195)(52, 196)(53, 197)(54, 198)(55, 199)(56, 200)(57, 201)(58, 202)(59, 203)(60, 204)(61, 205)(62, 206)(63, 207)(64, 208)(65, 209)(66, 210)(67, 211)(68, 212)(69, 213)(70, 214)(71, 215)(72, 216)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)(289, 433, 290, 434)(291, 435, 295, 439)(292, 436, 297, 441)(293, 437, 299, 443)(294, 438, 301, 445)(296, 440, 305, 449)(298, 442, 309, 453)(300, 444, 313, 457)(302, 446, 317, 461)(303, 447, 311, 455)(304, 448, 315, 459)(306, 450, 323, 467)(307, 451, 312, 456)(308, 452, 316, 460)(310, 454, 329, 473)(314, 458, 335, 479)(318, 462, 341, 485)(319, 463, 333, 477)(320, 464, 339, 483)(321, 465, 331, 475)(322, 466, 337, 481)(324, 468, 342, 486)(325, 469, 334, 478)(326, 470, 340, 484)(327, 471, 332, 476)(328, 472, 338, 482)(330, 474, 336, 480)(343, 487, 358, 502)(344, 488, 363, 507)(345, 489, 356, 500)(346, 490, 362, 506)(347, 491, 354, 498)(348, 492, 361, 505)(349, 493, 365, 509)(350, 494, 359, 503)(351, 495, 357, 501)(352, 496, 355, 499)(353, 497, 369, 513)(360, 504, 373, 517)(364, 508, 377, 521)(366, 510, 379, 523)(367, 511, 378, 522)(368, 512, 382, 526)(370, 514, 375, 519)(371, 515, 374, 518)(372, 516, 386, 530)(376, 520, 390, 534)(380, 524, 394, 538)(381, 525, 393, 537)(383, 527, 395, 539)(384, 528, 399, 543)(385, 529, 389, 533)(387, 531, 391, 535)(388, 532, 403, 547)(392, 536, 407, 551)(396, 540, 411, 555)(397, 541, 410, 554)(398, 542, 409, 553)(400, 544, 412, 556)(401, 545, 406, 550)(402, 546, 405, 549)(404, 548, 408, 552)(413, 557, 427, 571)(414, 558, 426, 570)(415, 559, 425, 569)(416, 560, 429, 573)(417, 561, 423, 567)(418, 562, 422, 566)(419, 563, 421, 565)(420, 564, 430, 574)(424, 568, 431, 575)(428, 572, 432, 576)
	L = (1, 291)(2, 293)(3, 296)(4, 289)(5, 300)(6, 290)(7, 303)(8, 306)(9, 307)(10, 292)(11, 311)(12, 314)(13, 315)(14, 294)(15, 319)(16, 295)(17, 321)(18, 324)(19, 325)(20, 297)(21, 327)(22, 298)(23, 331)(24, 299)(25, 333)(26, 336)(27, 337)(28, 301)(29, 339)(30, 302)(31, 343)(32, 304)(33, 345)(34, 305)(35, 347)(36, 349)(37, 350)(38, 308)(39, 351)(40, 309)(41, 352)(42, 310)(43, 354)(44, 312)(45, 356)(46, 313)(47, 358)(48, 360)(49, 361)(50, 316)(51, 362)(52, 317)(53, 363)(54, 318)(55, 329)(56, 320)(57, 328)(58, 322)(59, 326)(60, 323)(61, 368)(62, 369)(63, 370)(64, 371)(65, 330)(66, 341)(67, 332)(68, 340)(69, 334)(70, 338)(71, 335)(72, 376)(73, 377)(74, 378)(75, 379)(76, 342)(77, 344)(78, 346)(79, 348)(80, 384)(81, 385)(82, 386)(83, 387)(84, 353)(85, 355)(86, 357)(87, 359)(88, 392)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 373)(102, 374)(103, 375)(104, 408)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 389)(118, 390)(119, 391)(120, 424)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 423)(129, 430)(130, 429)(131, 428)(132, 404)(133, 405)(134, 406)(135, 407)(136, 415)(137, 432)(138, 431)(139, 420)(140, 412)(141, 413)(142, 414)(143, 421)(144, 422)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 16, 144 ), ( 16, 144, 16, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2155
Graph:: simple bipartite
	v = 216 e = 288 f = 20
	degree seq :: [ 2^144, 4^72 ]

E27.2157 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1^-4)^2, (Y1^-2 * Y3)^4, Y1^-4 * Y3 * Y1^7 * Y3 * Y1^-7 ]
Map::
	R = (1, 145, 2, 146, 5, 149, 11, 155, 23, 167, 43, 187, 66, 210, 85, 229, 101, 245, 117, 261, 133, 277, 126, 270, 112, 256, 95, 239, 78, 222, 56, 200, 75, 219, 59, 203, 34, 178, 17, 161, 29, 173, 49, 193, 70, 214, 88, 232, 104, 248, 120, 264, 136, 280, 143, 287, 141, 285, 127, 271, 110, 254, 96, 240, 79, 223, 57, 201, 32, 176, 52, 196, 72, 216, 60, 204, 35, 179, 53, 197, 73, 217, 90, 234, 106, 250, 122, 266, 138, 282, 144, 288, 142, 286, 128, 272, 111, 255, 94, 238, 80, 224, 58, 202, 33, 177, 16, 160, 28, 172, 48, 192, 69, 213, 61, 205, 76, 220, 92, 236, 108, 252, 124, 268, 140, 284, 132, 276, 116, 260, 100, 244, 84, 228, 65, 209, 42, 186, 22, 166, 10, 154, 4, 148)(3, 147, 7, 151, 15, 159, 31, 175, 55, 199, 77, 221, 93, 237, 109, 253, 125, 269, 137, 281, 119, 263, 102, 246, 91, 235, 71, 215, 46, 190, 24, 168, 45, 189, 38, 182, 20, 164, 9, 153, 19, 163, 37, 181, 62, 206, 81, 225, 97, 241, 113, 257, 129, 273, 139, 283, 121, 265, 103, 247, 86, 230, 74, 218, 50, 194, 26, 170, 12, 156, 25, 169, 47, 191, 40, 184, 21, 165, 39, 183, 63, 207, 82, 226, 98, 242, 114, 258, 130, 274, 134, 278, 123, 267, 105, 249, 87, 231, 67, 211, 54, 198, 30, 174, 14, 158, 6, 150, 13, 157, 27, 171, 51, 195, 41, 185, 64, 208, 83, 227, 99, 243, 115, 259, 131, 275, 135, 279, 118, 262, 107, 251, 89, 233, 68, 212, 44, 188, 36, 180, 18, 162, 8, 152)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 294)(3, 289)(4, 297)(5, 300)(6, 290)(7, 304)(8, 305)(9, 292)(10, 309)(11, 312)(12, 293)(13, 316)(14, 317)(15, 320)(16, 295)(17, 296)(18, 323)(19, 321)(20, 322)(21, 298)(22, 329)(23, 332)(24, 299)(25, 336)(26, 337)(27, 340)(28, 301)(29, 302)(30, 341)(31, 344)(32, 303)(33, 307)(34, 308)(35, 306)(36, 349)(37, 345)(38, 348)(39, 346)(40, 347)(41, 310)(42, 343)(43, 355)(44, 311)(45, 357)(46, 358)(47, 360)(48, 313)(49, 314)(50, 361)(51, 363)(52, 315)(53, 318)(54, 364)(55, 330)(56, 319)(57, 325)(58, 327)(59, 328)(60, 326)(61, 324)(62, 366)(63, 367)(64, 368)(65, 369)(66, 374)(67, 331)(68, 376)(69, 333)(70, 334)(71, 378)(72, 335)(73, 338)(74, 380)(75, 339)(76, 342)(77, 382)(78, 350)(79, 351)(80, 352)(81, 353)(82, 383)(83, 384)(84, 386)(85, 390)(86, 354)(87, 392)(88, 356)(89, 394)(90, 359)(91, 396)(92, 362)(93, 398)(94, 365)(95, 370)(96, 371)(97, 399)(98, 372)(99, 400)(100, 403)(101, 406)(102, 373)(103, 408)(104, 375)(105, 410)(106, 377)(107, 412)(108, 379)(109, 414)(110, 381)(111, 385)(112, 387)(113, 415)(114, 416)(115, 388)(116, 413)(117, 422)(118, 389)(119, 424)(120, 391)(121, 426)(122, 393)(123, 428)(124, 395)(125, 404)(126, 397)(127, 401)(128, 402)(129, 421)(130, 429)(131, 430)(132, 427)(133, 417)(134, 405)(135, 431)(136, 407)(137, 432)(138, 409)(139, 420)(140, 411)(141, 418)(142, 419)(143, 423)(144, 425)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2154
Graph:: simple bipartite
	v = 146 e = 288 f = 90
	degree seq :: [ 2^144, 144^2 ]

E27.2158 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^4 * Y1)^2, (Y2^2 * Y1)^4, (Y3 * Y2^-1)^8, (Y2^-1 * Y1 * R * Y2^-6)^2, Y2^-13 * Y1 * Y2^3 * Y1 * Y2^-2 ]
Map::
	R = (1, 145, 2, 146)(3, 147, 7, 151)(4, 148, 9, 153)(5, 149, 11, 155)(6, 150, 13, 157)(8, 152, 17, 161)(10, 154, 21, 165)(12, 156, 25, 169)(14, 158, 29, 173)(15, 159, 23, 167)(16, 160, 27, 171)(18, 162, 35, 179)(19, 163, 24, 168)(20, 164, 28, 172)(22, 166, 41, 185)(26, 170, 47, 191)(30, 174, 53, 197)(31, 175, 45, 189)(32, 176, 51, 195)(33, 177, 43, 187)(34, 178, 49, 193)(36, 180, 54, 198)(37, 181, 46, 190)(38, 182, 52, 196)(39, 183, 44, 188)(40, 184, 50, 194)(42, 186, 48, 192)(55, 199, 70, 214)(56, 200, 75, 219)(57, 201, 68, 212)(58, 202, 74, 218)(59, 203, 66, 210)(60, 204, 73, 217)(61, 205, 77, 221)(62, 206, 71, 215)(63, 207, 69, 213)(64, 208, 67, 211)(65, 209, 81, 225)(72, 216, 85, 229)(76, 220, 89, 233)(78, 222, 91, 235)(79, 223, 90, 234)(80, 224, 94, 238)(82, 226, 87, 231)(83, 227, 86, 230)(84, 228, 98, 242)(88, 232, 102, 246)(92, 236, 106, 250)(93, 237, 105, 249)(95, 239, 107, 251)(96, 240, 111, 255)(97, 241, 101, 245)(99, 243, 103, 247)(100, 244, 115, 259)(104, 248, 119, 263)(108, 252, 123, 267)(109, 253, 122, 266)(110, 254, 121, 265)(112, 256, 124, 268)(113, 257, 118, 262)(114, 258, 117, 261)(116, 260, 120, 264)(125, 269, 139, 283)(126, 270, 138, 282)(127, 271, 137, 281)(128, 272, 141, 285)(129, 273, 135, 279)(130, 274, 134, 278)(131, 275, 133, 277)(132, 276, 142, 286)(136, 280, 143, 287)(140, 284, 144, 288)(289, 433, 291, 435, 296, 440, 306, 450, 324, 468, 349, 493, 368, 512, 384, 528, 400, 544, 416, 560, 423, 567, 407, 551, 391, 535, 375, 519, 359, 503, 335, 479, 358, 502, 338, 482, 316, 460, 301, 445, 315, 459, 337, 481, 361, 505, 377, 521, 393, 537, 409, 553, 425, 569, 432, 576, 422, 566, 406, 550, 390, 534, 374, 518, 357, 501, 334, 478, 313, 457, 333, 477, 356, 500, 340, 484, 317, 461, 339, 483, 362, 506, 378, 522, 394, 538, 410, 554, 426, 570, 431, 575, 421, 565, 405, 549, 389, 533, 373, 517, 355, 499, 332, 476, 312, 456, 299, 443, 311, 455, 331, 475, 354, 498, 341, 485, 363, 507, 379, 523, 395, 539, 411, 555, 427, 571, 420, 564, 404, 548, 388, 532, 372, 516, 353, 497, 330, 474, 310, 454, 298, 442, 292, 436)(290, 434, 293, 437, 300, 444, 314, 458, 336, 480, 360, 504, 376, 520, 392, 536, 408, 552, 424, 568, 415, 559, 399, 543, 383, 527, 367, 511, 348, 492, 323, 467, 347, 491, 326, 470, 308, 452, 297, 441, 307, 451, 325, 469, 350, 494, 369, 513, 385, 529, 401, 545, 417, 561, 430, 574, 414, 558, 398, 542, 382, 526, 366, 510, 346, 490, 322, 466, 305, 449, 321, 465, 345, 489, 328, 472, 309, 453, 327, 471, 351, 495, 370, 514, 386, 530, 402, 546, 418, 562, 429, 573, 413, 557, 397, 541, 381, 525, 365, 509, 344, 488, 320, 464, 304, 448, 295, 439, 303, 447, 319, 463, 343, 487, 329, 473, 352, 496, 371, 515, 387, 531, 403, 547, 419, 563, 428, 572, 412, 556, 396, 540, 380, 524, 364, 508, 342, 486, 318, 462, 302, 446, 294, 438)
	L = (1, 290)(2, 289)(3, 295)(4, 297)(5, 299)(6, 301)(7, 291)(8, 305)(9, 292)(10, 309)(11, 293)(12, 313)(13, 294)(14, 317)(15, 311)(16, 315)(17, 296)(18, 323)(19, 312)(20, 316)(21, 298)(22, 329)(23, 303)(24, 307)(25, 300)(26, 335)(27, 304)(28, 308)(29, 302)(30, 341)(31, 333)(32, 339)(33, 331)(34, 337)(35, 306)(36, 342)(37, 334)(38, 340)(39, 332)(40, 338)(41, 310)(42, 336)(43, 321)(44, 327)(45, 319)(46, 325)(47, 314)(48, 330)(49, 322)(50, 328)(51, 320)(52, 326)(53, 318)(54, 324)(55, 358)(56, 363)(57, 356)(58, 362)(59, 354)(60, 361)(61, 365)(62, 359)(63, 357)(64, 355)(65, 369)(66, 347)(67, 352)(68, 345)(69, 351)(70, 343)(71, 350)(72, 373)(73, 348)(74, 346)(75, 344)(76, 377)(77, 349)(78, 379)(79, 378)(80, 382)(81, 353)(82, 375)(83, 374)(84, 386)(85, 360)(86, 371)(87, 370)(88, 390)(89, 364)(90, 367)(91, 366)(92, 394)(93, 393)(94, 368)(95, 395)(96, 399)(97, 389)(98, 372)(99, 391)(100, 403)(101, 385)(102, 376)(103, 387)(104, 407)(105, 381)(106, 380)(107, 383)(108, 411)(109, 410)(110, 409)(111, 384)(112, 412)(113, 406)(114, 405)(115, 388)(116, 408)(117, 402)(118, 401)(119, 392)(120, 404)(121, 398)(122, 397)(123, 396)(124, 400)(125, 427)(126, 426)(127, 425)(128, 429)(129, 423)(130, 422)(131, 421)(132, 430)(133, 419)(134, 418)(135, 417)(136, 431)(137, 415)(138, 414)(139, 413)(140, 432)(141, 416)(142, 420)(143, 424)(144, 428)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2159
Graph:: bipartite
	v = 74 e = 288 f = 162
	degree seq :: [ 4^72, 144^2 ]

E27.2159 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 72})
Quotient :: dipole
Aut^+ = C72 : C2 (small group id <144, 6>)
Aut   = $<288, 124>$ (small group id <288, 124>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-3 * Y3^2 * Y1^-1, Y1^8, Y1 * Y3^-18 * Y1, (Y3 * Y2^-1)^72 ]
Map::
	R = (1, 145, 2, 146, 6, 150, 16, 160, 34, 178, 27, 171, 13, 157, 4, 148)(3, 147, 9, 153, 17, 161, 8, 152, 21, 165, 35, 179, 28, 172, 11, 155)(5, 149, 14, 158, 18, 162, 37, 181, 30, 174, 12, 156, 20, 164, 7, 151)(10, 154, 24, 168, 36, 180, 23, 167, 42, 186, 22, 166, 43, 187, 26, 170)(15, 159, 32, 176, 38, 182, 29, 173, 41, 185, 19, 163, 39, 183, 31, 175)(25, 169, 47, 191, 53, 197, 46, 190, 58, 202, 45, 189, 59, 203, 44, 188)(33, 177, 49, 193, 54, 198, 40, 184, 56, 200, 50, 194, 55, 199, 51, 195)(48, 192, 60, 204, 69, 213, 63, 207, 74, 218, 62, 206, 75, 219, 61, 205)(52, 196, 57, 201, 70, 214, 66, 210, 72, 216, 67, 211, 71, 215, 65, 209)(64, 208, 77, 221, 85, 229, 76, 220, 90, 234, 79, 223, 91, 235, 78, 222)(68, 212, 82, 226, 86, 230, 83, 227, 88, 232, 81, 225, 87, 231, 73, 217)(80, 224, 94, 238, 101, 245, 93, 237, 106, 250, 92, 236, 107, 251, 95, 239)(84, 228, 99, 243, 102, 246, 97, 241, 104, 248, 89, 233, 103, 247, 98, 242)(96, 240, 111, 255, 117, 261, 110, 254, 122, 266, 109, 253, 123, 267, 108, 252)(100, 244, 113, 257, 118, 262, 105, 249, 120, 264, 114, 258, 119, 263, 115, 259)(112, 256, 124, 268, 133, 277, 127, 271, 138, 282, 126, 270, 139, 283, 125, 269)(116, 260, 121, 265, 134, 278, 130, 274, 136, 280, 131, 275, 135, 279, 129, 273)(128, 272, 141, 285, 143, 287, 140, 284, 144, 288, 137, 281, 132, 276, 142, 286)(289, 433)(290, 434)(291, 435)(292, 436)(293, 437)(294, 438)(295, 439)(296, 440)(297, 441)(298, 442)(299, 443)(300, 444)(301, 445)(302, 446)(303, 447)(304, 448)(305, 449)(306, 450)(307, 451)(308, 452)(309, 453)(310, 454)(311, 455)(312, 456)(313, 457)(314, 458)(315, 459)(316, 460)(317, 461)(318, 462)(319, 463)(320, 464)(321, 465)(322, 466)(323, 467)(324, 468)(325, 469)(326, 470)(327, 471)(328, 472)(329, 473)(330, 474)(331, 475)(332, 476)(333, 477)(334, 478)(335, 479)(336, 480)(337, 481)(338, 482)(339, 483)(340, 484)(341, 485)(342, 486)(343, 487)(344, 488)(345, 489)(346, 490)(347, 491)(348, 492)(349, 493)(350, 494)(351, 495)(352, 496)(353, 497)(354, 498)(355, 499)(356, 500)(357, 501)(358, 502)(359, 503)(360, 504)(361, 505)(362, 506)(363, 507)(364, 508)(365, 509)(366, 510)(367, 511)(368, 512)(369, 513)(370, 514)(371, 515)(372, 516)(373, 517)(374, 518)(375, 519)(376, 520)(377, 521)(378, 522)(379, 523)(380, 524)(381, 525)(382, 526)(383, 527)(384, 528)(385, 529)(386, 530)(387, 531)(388, 532)(389, 533)(390, 534)(391, 535)(392, 536)(393, 537)(394, 538)(395, 539)(396, 540)(397, 541)(398, 542)(399, 543)(400, 544)(401, 545)(402, 546)(403, 547)(404, 548)(405, 549)(406, 550)(407, 551)(408, 552)(409, 553)(410, 554)(411, 555)(412, 556)(413, 557)(414, 558)(415, 559)(416, 560)(417, 561)(418, 562)(419, 563)(420, 564)(421, 565)(422, 566)(423, 567)(424, 568)(425, 569)(426, 570)(427, 571)(428, 572)(429, 573)(430, 574)(431, 575)(432, 576)
	L = (1, 291)(2, 295)(3, 298)(4, 300)(5, 289)(6, 305)(7, 307)(8, 290)(9, 292)(10, 313)(11, 315)(12, 317)(13, 316)(14, 319)(15, 293)(16, 302)(17, 324)(18, 294)(19, 328)(20, 301)(21, 330)(22, 296)(23, 297)(24, 299)(25, 336)(26, 323)(27, 325)(28, 331)(29, 337)(30, 322)(31, 338)(32, 339)(33, 303)(34, 309)(35, 304)(36, 341)(37, 320)(38, 306)(39, 308)(40, 345)(41, 318)(42, 346)(43, 347)(44, 310)(45, 311)(46, 312)(47, 314)(48, 352)(49, 353)(50, 354)(51, 355)(52, 321)(53, 357)(54, 326)(55, 327)(56, 329)(57, 361)(58, 362)(59, 363)(60, 332)(61, 333)(62, 334)(63, 335)(64, 368)(65, 369)(66, 370)(67, 371)(68, 340)(69, 373)(70, 342)(71, 343)(72, 344)(73, 377)(74, 378)(75, 379)(76, 348)(77, 349)(78, 350)(79, 351)(80, 384)(81, 385)(82, 386)(83, 387)(84, 356)(85, 389)(86, 358)(87, 359)(88, 360)(89, 393)(90, 394)(91, 395)(92, 364)(93, 365)(94, 366)(95, 367)(96, 400)(97, 401)(98, 402)(99, 403)(100, 372)(101, 405)(102, 374)(103, 375)(104, 376)(105, 409)(106, 410)(107, 411)(108, 380)(109, 381)(110, 382)(111, 383)(112, 416)(113, 417)(114, 418)(115, 419)(116, 388)(117, 421)(118, 390)(119, 391)(120, 392)(121, 425)(122, 426)(123, 427)(124, 396)(125, 397)(126, 398)(127, 399)(128, 422)(129, 428)(130, 430)(131, 429)(132, 404)(133, 431)(134, 406)(135, 407)(136, 408)(137, 415)(138, 432)(139, 420)(140, 412)(141, 413)(142, 414)(143, 424)(144, 423)(145, 433)(146, 434)(147, 435)(148, 436)(149, 437)(150, 438)(151, 439)(152, 440)(153, 441)(154, 442)(155, 443)(156, 444)(157, 445)(158, 446)(159, 447)(160, 448)(161, 449)(162, 450)(163, 451)(164, 452)(165, 453)(166, 454)(167, 455)(168, 456)(169, 457)(170, 458)(171, 459)(172, 460)(173, 461)(174, 462)(175, 463)(176, 464)(177, 465)(178, 466)(179, 467)(180, 468)(181, 469)(182, 470)(183, 471)(184, 472)(185, 473)(186, 474)(187, 475)(188, 476)(189, 477)(190, 478)(191, 479)(192, 480)(193, 481)(194, 482)(195, 483)(196, 484)(197, 485)(198, 486)(199, 487)(200, 488)(201, 489)(202, 490)(203, 491)(204, 492)(205, 493)(206, 494)(207, 495)(208, 496)(209, 497)(210, 498)(211, 499)(212, 500)(213, 501)(214, 502)(215, 503)(216, 504)(217, 505)(218, 506)(219, 507)(220, 508)(221, 509)(222, 510)(223, 511)(224, 512)(225, 513)(226, 514)(227, 515)(228, 516)(229, 517)(230, 518)(231, 519)(232, 520)(233, 521)(234, 522)(235, 523)(236, 524)(237, 525)(238, 526)(239, 527)(240, 528)(241, 529)(242, 530)(243, 531)(244, 532)(245, 533)(246, 534)(247, 535)(248, 536)(249, 537)(250, 538)(251, 539)(252, 540)(253, 541)(254, 542)(255, 543)(256, 544)(257, 545)(258, 546)(259, 547)(260, 548)(261, 549)(262, 550)(263, 551)(264, 552)(265, 553)(266, 554)(267, 555)(268, 556)(269, 557)(270, 558)(271, 559)(272, 560)(273, 561)(274, 562)(275, 563)(276, 564)(277, 565)(278, 566)(279, 567)(280, 568)(281, 569)(282, 570)(283, 571)(284, 572)(285, 573)(286, 574)(287, 575)(288, 576)
	local type(s) :: { ( 4, 144 ), ( 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144, 4, 144 ) }
Outer automorphisms :: reflexible
Dual of E27.2158
Graph:: simple bipartite
	v = 162 e = 288 f = 74
	degree seq :: [ 2^144, 16^18 ]

E27.2160 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 6})
Quotient :: halfedge^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y2)^3, (Y3 * Y1)^26 ]
Map:: non-degenerate
	R = (1, 158, 2, 157)(3, 163, 7, 159)(4, 165, 9, 160)(5, 167, 11, 161)(6, 169, 13, 162)(8, 168, 12, 164)(10, 170, 14, 166)(15, 179, 23, 171)(16, 180, 24, 172)(17, 181, 25, 173)(18, 182, 26, 174)(19, 183, 27, 175)(20, 184, 28, 176)(21, 185, 29, 177)(22, 186, 30, 178)(31, 193, 37, 187)(32, 194, 38, 188)(33, 195, 39, 189)(34, 196, 40, 190)(35, 197, 41, 191)(36, 198, 42, 192)(43, 205, 49, 199)(44, 206, 50, 200)(45, 207, 51, 201)(46, 208, 52, 202)(47, 209, 53, 203)(48, 210, 54, 204)(55, 247, 91, 211)(56, 248, 92, 212)(57, 249, 93, 213)(58, 250, 94, 214)(59, 251, 95, 215)(60, 252, 96, 216)(61, 253, 97, 217)(62, 254, 98, 218)(63, 255, 99, 219)(64, 256, 100, 220)(65, 257, 101, 221)(66, 258, 102, 222)(67, 259, 103, 223)(68, 261, 105, 224)(69, 262, 106, 225)(70, 260, 104, 226)(71, 263, 107, 227)(72, 264, 108, 228)(73, 265, 109, 229)(74, 266, 110, 230)(75, 267, 111, 231)(76, 268, 112, 232)(77, 269, 113, 233)(78, 270, 114, 234)(79, 271, 115, 235)(80, 272, 116, 236)(81, 273, 117, 237)(82, 274, 118, 238)(83, 275, 119, 239)(84, 276, 120, 240)(85, 277, 121, 241)(86, 278, 122, 242)(87, 279, 123, 243)(88, 280, 124, 244)(89, 281, 125, 245)(90, 282, 126, 246)(127, 310, 154, 283)(128, 311, 155, 284)(129, 312, 156, 285)(130, 303, 147, 286)(131, 299, 143, 287)(132, 307, 151, 288)(133, 308, 152, 289)(134, 294, 138, 290)(135, 304, 148, 291)(136, 297, 141, 292)(137, 306, 150, 293)(139, 300, 144, 295)(140, 309, 153, 296)(142, 302, 146, 298)(145, 305, 149, 301)
	L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 19)(12, 21)(13, 22)(16, 25)(20, 29)(23, 31)(24, 33)(26, 32)(27, 34)(28, 36)(30, 35)(37, 43)(38, 45)(39, 44)(40, 46)(41, 48)(42, 47)(49, 55)(50, 57)(51, 56)(52, 60)(53, 70)(54, 61)(58, 91)(59, 96)(62, 94)(63, 93)(64, 101)(65, 92)(66, 95)(67, 104)(68, 106)(69, 97)(71, 98)(72, 109)(73, 99)(74, 100)(75, 102)(76, 113)(77, 103)(78, 105)(79, 107)(80, 110)(81, 108)(82, 111)(83, 114)(84, 112)(85, 115)(86, 117)(87, 116)(88, 118)(89, 120)(90, 119)(121, 127)(122, 129)(123, 128)(124, 132)(125, 140)(126, 133)(130, 154)(131, 151)(134, 147)(135, 156)(136, 150)(137, 155)(138, 143)(139, 153)(141, 146)(142, 152)(144, 149)(145, 148)(157, 160)(158, 162)(159, 164)(161, 168)(163, 172)(165, 171)(166, 173)(167, 176)(169, 175)(170, 177)(174, 181)(178, 185)(179, 188)(180, 187)(182, 189)(183, 191)(184, 190)(186, 192)(193, 200)(194, 199)(195, 201)(196, 203)(197, 202)(198, 204)(205, 212)(206, 211)(207, 213)(208, 217)(209, 216)(210, 226)(214, 248)(215, 253)(218, 255)(219, 247)(220, 250)(221, 249)(222, 259)(223, 252)(224, 251)(225, 260)(227, 256)(228, 254)(229, 257)(230, 265)(231, 261)(232, 258)(233, 262)(234, 269)(235, 264)(236, 263)(237, 266)(238, 268)(239, 267)(240, 270)(241, 272)(242, 271)(243, 273)(244, 275)(245, 274)(246, 276)(277, 284)(278, 283)(279, 285)(280, 289)(281, 288)(282, 296)(286, 311)(287, 308)(290, 304)(291, 310)(292, 303)(293, 312)(294, 300)(295, 307)(297, 299)(298, 309)(301, 306)(302, 305)
	local type(s) :: { ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2161
Transitivity :: VT+ AT
Graph:: simple bipartite
	v = 78 e = 156 f = 26
	degree seq :: [ 4^78 ]

E27.2161 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 6})
Quotient :: halfedge^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y2 * Y1^-1, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y2)^3, Y1^6, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 158, 2, 162, 6, 170, 14, 166, 10, 161, 5, 157)(3, 165, 9, 171, 15, 168, 12, 160, 4, 167, 11, 159)(7, 172, 16, 169, 13, 174, 18, 164, 8, 173, 17, 163)(19, 181, 25, 177, 21, 183, 27, 176, 20, 182, 26, 175)(22, 184, 28, 180, 24, 186, 30, 179, 23, 185, 29, 178)(31, 193, 37, 189, 33, 195, 39, 188, 32, 194, 38, 187)(34, 196, 40, 192, 36, 198, 42, 191, 35, 197, 41, 190)(43, 205, 49, 201, 45, 207, 51, 200, 44, 206, 50, 199)(46, 208, 52, 204, 48, 210, 54, 203, 47, 209, 53, 202)(55, 241, 85, 213, 57, 245, 89, 212, 56, 243, 87, 211)(58, 247, 91, 220, 64, 256, 100, 217, 61, 249, 93, 214)(59, 250, 94, 216, 60, 253, 97, 222, 66, 252, 96, 215)(62, 257, 101, 219, 63, 260, 104, 221, 65, 259, 103, 218)(67, 265, 109, 224, 68, 268, 112, 225, 69, 267, 111, 223)(70, 271, 115, 227, 71, 274, 118, 228, 72, 273, 117, 226)(73, 277, 121, 230, 74, 280, 124, 231, 75, 279, 123, 229)(76, 283, 127, 233, 77, 286, 130, 234, 78, 285, 129, 232)(79, 289, 133, 236, 80, 292, 136, 237, 81, 291, 135, 235)(82, 295, 139, 239, 83, 298, 142, 240, 84, 297, 141, 238)(86, 302, 146, 244, 88, 304, 148, 246, 90, 301, 145, 242)(92, 308, 152, 255, 99, 312, 156, 262, 106, 307, 151, 248)(95, 310, 154, 264, 108, 311, 155, 254, 98, 309, 153, 251)(102, 303, 147, 263, 107, 306, 150, 261, 105, 305, 149, 258)(110, 296, 140, 270, 114, 300, 144, 269, 113, 299, 143, 266)(116, 294, 138, 276, 120, 293, 137, 275, 119, 290, 134, 272)(122, 288, 132, 282, 126, 287, 131, 281, 125, 284, 128, 278)
	L = (1, 3)(2, 7)(4, 6)(5, 13)(8, 14)(9, 19)(10, 15)(11, 21)(12, 20)(16, 22)(17, 24)(18, 23)(25, 31)(26, 33)(27, 32)(28, 34)(29, 36)(30, 35)(37, 43)(38, 45)(39, 44)(40, 46)(41, 48)(42, 47)(49, 55)(50, 57)(51, 56)(52, 58)(53, 64)(54, 61)(59, 85)(60, 87)(62, 91)(63, 93)(65, 100)(66, 89)(67, 94)(68, 96)(69, 97)(70, 101)(71, 103)(72, 104)(73, 109)(74, 111)(75, 112)(76, 115)(77, 117)(78, 118)(79, 121)(80, 123)(81, 124)(82, 127)(83, 129)(84, 130)(86, 133)(88, 135)(90, 136)(92, 139)(95, 146)(98, 148)(99, 141)(102, 152)(105, 156)(106, 142)(107, 151)(108, 145)(110, 154)(113, 155)(114, 153)(116, 147)(119, 150)(120, 149)(122, 140)(125, 144)(126, 143)(128, 138)(131, 137)(132, 134)(157, 160)(158, 164)(159, 166)(161, 163)(162, 171)(165, 176)(167, 175)(168, 177)(169, 170)(172, 179)(173, 178)(174, 180)(181, 188)(182, 187)(183, 189)(184, 191)(185, 190)(186, 192)(193, 200)(194, 199)(195, 201)(196, 203)(197, 202)(198, 204)(205, 212)(206, 211)(207, 213)(208, 217)(209, 214)(210, 220)(215, 243)(216, 245)(218, 249)(219, 256)(221, 247)(222, 241)(223, 252)(224, 253)(225, 250)(226, 259)(227, 260)(228, 257)(229, 267)(230, 268)(231, 265)(232, 273)(233, 274)(234, 271)(235, 279)(236, 280)(237, 277)(238, 285)(239, 286)(240, 283)(242, 291)(244, 292)(246, 289)(248, 297)(251, 301)(254, 302)(255, 298)(258, 307)(261, 308)(262, 295)(263, 312)(264, 304)(266, 309)(269, 310)(270, 311)(272, 305)(275, 303)(276, 306)(278, 299)(281, 296)(282, 300)(284, 290)(287, 294)(288, 293)
	local type(s) :: { ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2160
Transitivity :: VT+ AT
Graph:: bipartite
	v = 26 e = 156 f = 78
	degree seq :: [ 12^26 ]

E27.2162 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 6})
Quotient :: edge^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y3 * Y2)^26 ]
Map::
	R = (1, 157, 4, 160)(2, 158, 6, 162)(3, 159, 8, 164)(5, 161, 12, 168)(7, 163, 15, 171)(9, 165, 17, 173)(10, 166, 18, 174)(11, 167, 19, 175)(13, 169, 21, 177)(14, 170, 22, 178)(16, 172, 23, 179)(20, 176, 27, 183)(24, 180, 31, 187)(25, 181, 32, 188)(26, 182, 33, 189)(28, 184, 34, 190)(29, 185, 35, 191)(30, 186, 36, 192)(37, 193, 43, 199)(38, 194, 44, 200)(39, 195, 45, 201)(40, 196, 46, 202)(41, 197, 47, 203)(42, 198, 48, 204)(49, 205, 55, 211)(50, 206, 56, 212)(51, 207, 57, 213)(52, 208, 91, 247)(53, 209, 93, 249)(54, 210, 95, 251)(58, 214, 99, 255)(59, 215, 103, 259)(60, 216, 106, 262)(61, 217, 105, 261)(62, 218, 110, 266)(63, 219, 109, 265)(64, 220, 113, 269)(65, 221, 97, 253)(66, 222, 116, 272)(67, 223, 118, 274)(68, 224, 120, 276)(69, 225, 101, 257)(70, 226, 123, 279)(71, 227, 125, 281)(72, 228, 102, 258)(73, 229, 128, 284)(74, 230, 98, 254)(75, 231, 131, 287)(76, 232, 133, 289)(77, 233, 135, 291)(78, 234, 137, 293)(79, 235, 139, 295)(80, 236, 141, 297)(81, 237, 143, 299)(82, 238, 145, 301)(83, 239, 147, 303)(84, 240, 149, 305)(85, 241, 151, 307)(86, 242, 153, 309)(87, 243, 155, 311)(88, 244, 156, 312)(89, 245, 152, 308)(90, 246, 154, 310)(92, 248, 150, 306)(94, 250, 146, 302)(96, 252, 148, 304)(100, 256, 124, 280)(104, 260, 117, 273)(107, 263, 119, 275)(108, 264, 134, 290)(111, 267, 126, 282)(112, 268, 140, 296)(114, 270, 129, 285)(115, 271, 142, 298)(121, 277, 132, 288)(122, 278, 136, 292)(127, 283, 138, 294)(130, 286, 144, 300)(313, 314)(315, 319)(316, 321)(317, 323)(318, 325)(320, 328)(322, 327)(324, 332)(326, 331)(329, 336)(330, 338)(333, 340)(334, 342)(335, 341)(337, 339)(343, 349)(344, 351)(345, 350)(346, 352)(347, 354)(348, 353)(355, 361)(356, 363)(357, 362)(358, 364)(359, 366)(360, 365)(367, 386)(368, 377)(369, 375)(370, 409)(371, 413)(372, 417)(373, 407)(374, 421)(376, 410)(378, 422)(379, 411)(380, 414)(381, 405)(382, 418)(383, 415)(384, 403)(385, 432)(387, 425)(388, 430)(389, 428)(390, 443)(391, 437)(392, 435)(393, 440)(394, 447)(395, 445)(396, 449)(397, 453)(398, 451)(399, 455)(400, 459)(401, 457)(402, 461)(404, 465)(406, 463)(408, 467)(412, 456)(416, 450)(419, 448)(420, 462)(423, 454)(424, 468)(426, 452)(427, 466)(429, 441)(431, 438)(433, 446)(434, 460)(436, 444)(439, 458)(442, 464)(469, 471)(470, 473)(472, 478)(474, 482)(475, 479)(476, 481)(477, 480)(483, 488)(484, 487)(485, 493)(486, 492)(489, 497)(490, 496)(491, 498)(494, 495)(499, 506)(500, 505)(501, 507)(502, 509)(503, 508)(504, 510)(511, 518)(512, 517)(513, 519)(514, 521)(515, 520)(516, 522)(523, 531)(524, 542)(525, 533)(526, 566)(527, 570)(528, 569)(529, 559)(530, 565)(532, 577)(534, 581)(535, 578)(536, 573)(537, 563)(538, 588)(539, 574)(540, 561)(541, 571)(543, 567)(544, 599)(545, 586)(546, 584)(547, 596)(548, 593)(549, 591)(550, 605)(551, 603)(552, 601)(553, 611)(554, 609)(555, 607)(556, 617)(557, 615)(558, 613)(560, 623)(562, 621)(564, 619)(568, 608)(572, 602)(575, 606)(576, 614)(579, 612)(580, 620)(582, 610)(583, 624)(585, 592)(587, 597)(589, 604)(590, 618)(594, 600)(595, 616)(598, 622)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 24, 24 ), ( 24^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2165
Graph:: simple bipartite
	v = 234 e = 312 f = 26
	degree seq :: [ 2^156, 4^78 ]

E27.2163 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 6})
Quotient :: edge^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y2 * Y3^4, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 157, 4, 160, 6, 162, 15, 171, 9, 165, 5, 161)(2, 158, 7, 163, 3, 159, 10, 166, 14, 170, 8, 164)(11, 167, 19, 175, 12, 168, 21, 177, 13, 169, 20, 176)(16, 172, 22, 178, 17, 173, 24, 180, 18, 174, 23, 179)(25, 181, 31, 187, 26, 182, 33, 189, 27, 183, 32, 188)(28, 184, 34, 190, 29, 185, 36, 192, 30, 186, 35, 191)(37, 193, 43, 199, 38, 194, 45, 201, 39, 195, 44, 200)(40, 196, 46, 202, 41, 197, 48, 204, 42, 198, 47, 203)(49, 205, 55, 211, 50, 206, 57, 213, 51, 207, 56, 212)(52, 208, 109, 265, 53, 209, 111, 267, 54, 210, 113, 269)(58, 214, 97, 253, 66, 222, 99, 255, 63, 219, 98, 254)(59, 215, 94, 250, 71, 227, 96, 252, 60, 216, 95, 251)(61, 217, 106, 262, 62, 218, 108, 264, 72, 228, 107, 263)(64, 220, 110, 266, 65, 221, 114, 270, 67, 223, 112, 268)(68, 224, 87, 243, 70, 226, 86, 242, 69, 225, 85, 241)(73, 229, 84, 240, 75, 231, 83, 239, 74, 230, 82, 238)(76, 232, 121, 277, 77, 233, 122, 278, 78, 234, 123, 279)(79, 235, 124, 280, 80, 236, 125, 281, 81, 237, 126, 282)(88, 244, 127, 283, 89, 245, 128, 284, 90, 246, 130, 286)(91, 247, 133, 289, 92, 248, 134, 290, 93, 249, 136, 292)(100, 256, 139, 295, 101, 257, 140, 296, 102, 258, 142, 298)(103, 259, 145, 301, 104, 260, 146, 302, 105, 261, 148, 304)(115, 271, 129, 285, 116, 272, 132, 288, 118, 274, 131, 287)(117, 273, 150, 306, 119, 275, 149, 305, 120, 276, 147, 303)(135, 291, 152, 308, 138, 294, 154, 310, 137, 293, 151, 307)(141, 297, 153, 309, 144, 300, 156, 312, 143, 299, 155, 311)(313, 314)(315, 321)(316, 323)(317, 324)(318, 326)(319, 328)(320, 329)(322, 330)(325, 327)(331, 337)(332, 338)(333, 339)(334, 340)(335, 341)(336, 342)(343, 349)(344, 350)(345, 351)(346, 352)(347, 353)(348, 354)(355, 361)(356, 362)(357, 363)(358, 364)(359, 365)(360, 366)(367, 427)(368, 428)(369, 430)(370, 422)(371, 418)(372, 420)(373, 433)(374, 435)(375, 426)(376, 436)(377, 438)(378, 424)(379, 437)(380, 410)(381, 409)(382, 411)(383, 419)(384, 434)(385, 407)(386, 406)(387, 408)(388, 439)(389, 442)(390, 440)(391, 445)(392, 448)(393, 446)(394, 397)(395, 399)(396, 398)(400, 451)(401, 454)(402, 452)(403, 457)(404, 460)(405, 458)(412, 462)(413, 459)(414, 461)(415, 456)(416, 453)(417, 455)(421, 463)(423, 466)(425, 464)(429, 449)(431, 450)(432, 447)(441, 467)(443, 465)(444, 468)(469, 471)(470, 474)(472, 480)(473, 481)(475, 485)(476, 486)(477, 482)(478, 484)(479, 483)(487, 494)(488, 495)(489, 493)(490, 497)(491, 498)(492, 496)(499, 506)(500, 507)(501, 505)(502, 509)(503, 510)(504, 508)(511, 518)(512, 519)(513, 517)(514, 521)(515, 522)(516, 520)(523, 584)(524, 586)(525, 583)(526, 582)(527, 576)(528, 575)(529, 590)(530, 589)(531, 580)(532, 593)(533, 592)(534, 578)(535, 594)(536, 565)(537, 567)(538, 566)(539, 574)(540, 591)(541, 562)(542, 564)(543, 563)(544, 596)(545, 595)(546, 598)(547, 602)(548, 601)(549, 604)(550, 555)(551, 554)(552, 553)(556, 608)(557, 607)(558, 610)(559, 614)(560, 613)(561, 616)(568, 617)(569, 618)(570, 615)(571, 611)(572, 612)(573, 609)(577, 620)(579, 619)(581, 622)(585, 603)(587, 605)(588, 606)(597, 621)(599, 624)(600, 623)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 8, 8 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2164
Graph:: simple bipartite
	v = 182 e = 312 f = 78
	degree seq :: [ 2^156, 12^26 ]

E27.2164 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 6})
Quotient :: loop^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^3, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y3 * Y2)^26 ]
Map::
	R = (1, 157, 313, 469, 4, 160, 316, 472)(2, 158, 314, 470, 6, 162, 318, 474)(3, 159, 315, 471, 8, 164, 320, 476)(5, 161, 317, 473, 12, 168, 324, 480)(7, 163, 319, 475, 15, 171, 327, 483)(9, 165, 321, 477, 17, 173, 329, 485)(10, 166, 322, 478, 18, 174, 330, 486)(11, 167, 323, 479, 19, 175, 331, 487)(13, 169, 325, 481, 21, 177, 333, 489)(14, 170, 326, 482, 22, 178, 334, 490)(16, 172, 328, 484, 23, 179, 335, 491)(20, 176, 332, 488, 27, 183, 339, 495)(24, 180, 336, 492, 31, 187, 343, 499)(25, 181, 337, 493, 32, 188, 344, 500)(26, 182, 338, 494, 33, 189, 345, 501)(28, 184, 340, 496, 34, 190, 346, 502)(29, 185, 341, 497, 35, 191, 347, 503)(30, 186, 342, 498, 36, 192, 348, 504)(37, 193, 349, 505, 43, 199, 355, 511)(38, 194, 350, 506, 44, 200, 356, 512)(39, 195, 351, 507, 45, 201, 357, 513)(40, 196, 352, 508, 46, 202, 358, 514)(41, 197, 353, 509, 47, 203, 359, 515)(42, 198, 354, 510, 48, 204, 360, 516)(49, 205, 361, 517, 55, 211, 367, 523)(50, 206, 362, 518, 56, 212, 368, 524)(51, 207, 363, 519, 57, 213, 369, 525)(52, 208, 364, 520, 91, 247, 403, 559)(53, 209, 365, 521, 93, 249, 405, 561)(54, 210, 366, 522, 95, 251, 407, 563)(58, 214, 370, 526, 99, 255, 411, 567)(59, 215, 371, 527, 103, 259, 415, 571)(60, 216, 372, 528, 106, 262, 418, 574)(61, 217, 373, 529, 101, 257, 413, 569)(62, 218, 374, 530, 110, 266, 422, 578)(63, 219, 375, 531, 97, 253, 409, 565)(64, 220, 376, 532, 113, 269, 425, 581)(65, 221, 377, 533, 98, 254, 410, 566)(66, 222, 378, 534, 116, 272, 428, 584)(67, 223, 379, 535, 118, 274, 430, 586)(68, 224, 380, 536, 120, 276, 432, 588)(69, 225, 381, 537, 102, 258, 414, 570)(70, 226, 382, 538, 123, 279, 435, 591)(71, 227, 383, 539, 125, 281, 437, 593)(72, 228, 384, 540, 105, 261, 417, 573)(73, 229, 385, 541, 128, 284, 440, 596)(74, 230, 386, 542, 109, 265, 421, 577)(75, 231, 387, 543, 131, 287, 443, 599)(76, 232, 388, 544, 133, 289, 445, 601)(77, 233, 389, 545, 135, 291, 447, 603)(78, 234, 390, 546, 137, 293, 449, 605)(79, 235, 391, 547, 139, 295, 451, 607)(80, 236, 392, 548, 141, 297, 453, 609)(81, 237, 393, 549, 143, 299, 455, 611)(82, 238, 394, 550, 145, 301, 457, 613)(83, 239, 395, 551, 147, 303, 459, 615)(84, 240, 396, 552, 149, 305, 461, 617)(85, 241, 397, 553, 151, 307, 463, 619)(86, 242, 398, 554, 153, 309, 465, 621)(87, 243, 399, 555, 155, 311, 467, 623)(88, 244, 400, 556, 152, 308, 464, 620)(89, 245, 401, 557, 154, 310, 466, 622)(90, 246, 402, 558, 156, 312, 468, 624)(92, 248, 404, 560, 146, 302, 458, 614)(94, 250, 406, 562, 148, 304, 460, 616)(96, 252, 408, 564, 150, 306, 462, 618)(100, 256, 412, 568, 124, 280, 436, 592)(104, 260, 416, 572, 117, 273, 429, 585)(107, 263, 419, 575, 119, 275, 431, 587)(108, 264, 420, 576, 134, 290, 446, 602)(111, 267, 423, 579, 126, 282, 438, 594)(112, 268, 424, 580, 140, 296, 452, 608)(114, 270, 426, 582, 129, 285, 441, 597)(115, 271, 427, 583, 142, 298, 454, 610)(121, 277, 433, 589, 132, 288, 444, 600)(122, 278, 434, 590, 136, 292, 448, 604)(127, 283, 439, 595, 138, 294, 450, 606)(130, 286, 442, 598, 144, 300, 456, 612)
	L = (1, 158)(2, 157)(3, 163)(4, 165)(5, 167)(6, 169)(7, 159)(8, 172)(9, 160)(10, 171)(11, 161)(12, 176)(13, 162)(14, 175)(15, 166)(16, 164)(17, 180)(18, 182)(19, 170)(20, 168)(21, 184)(22, 186)(23, 185)(24, 173)(25, 183)(26, 174)(27, 181)(28, 177)(29, 179)(30, 178)(31, 193)(32, 195)(33, 194)(34, 196)(35, 198)(36, 197)(37, 187)(38, 189)(39, 188)(40, 190)(41, 192)(42, 191)(43, 205)(44, 207)(45, 206)(46, 208)(47, 210)(48, 209)(49, 199)(50, 201)(51, 200)(52, 202)(53, 204)(54, 203)(55, 219)(56, 230)(57, 221)(58, 253)(59, 257)(60, 261)(61, 247)(62, 265)(63, 211)(64, 254)(65, 213)(66, 255)(67, 269)(68, 258)(69, 251)(70, 259)(71, 276)(72, 249)(73, 262)(74, 212)(75, 266)(76, 272)(77, 287)(78, 274)(79, 279)(80, 284)(81, 281)(82, 289)(83, 293)(84, 291)(85, 295)(86, 299)(87, 297)(88, 301)(89, 305)(90, 303)(91, 217)(92, 307)(93, 228)(94, 311)(95, 225)(96, 309)(97, 214)(98, 220)(99, 222)(100, 296)(101, 215)(102, 224)(103, 226)(104, 290)(105, 216)(106, 229)(107, 294)(108, 302)(109, 218)(110, 231)(111, 300)(112, 308)(113, 223)(114, 298)(115, 312)(116, 232)(117, 280)(118, 234)(119, 285)(120, 227)(121, 292)(122, 306)(123, 235)(124, 273)(125, 237)(126, 288)(127, 304)(128, 236)(129, 275)(130, 310)(131, 233)(132, 282)(133, 238)(134, 260)(135, 240)(136, 277)(137, 239)(138, 263)(139, 241)(140, 256)(141, 243)(142, 270)(143, 242)(144, 267)(145, 244)(146, 264)(147, 246)(148, 283)(149, 245)(150, 278)(151, 248)(152, 268)(153, 252)(154, 286)(155, 250)(156, 271)(313, 471)(314, 473)(315, 469)(316, 478)(317, 470)(318, 482)(319, 479)(320, 481)(321, 480)(322, 472)(323, 475)(324, 477)(325, 476)(326, 474)(327, 488)(328, 487)(329, 493)(330, 492)(331, 484)(332, 483)(333, 497)(334, 496)(335, 498)(336, 486)(337, 485)(338, 495)(339, 494)(340, 490)(341, 489)(342, 491)(343, 506)(344, 505)(345, 507)(346, 509)(347, 508)(348, 510)(349, 500)(350, 499)(351, 501)(352, 503)(353, 502)(354, 504)(355, 518)(356, 517)(357, 519)(358, 521)(359, 520)(360, 522)(361, 512)(362, 511)(363, 513)(364, 515)(365, 514)(366, 516)(367, 533)(368, 531)(369, 542)(370, 566)(371, 570)(372, 569)(373, 561)(374, 565)(375, 524)(376, 577)(377, 523)(378, 578)(379, 567)(380, 573)(381, 559)(382, 574)(383, 571)(384, 563)(385, 588)(386, 525)(387, 581)(388, 586)(389, 584)(390, 599)(391, 593)(392, 591)(393, 596)(394, 603)(395, 601)(396, 605)(397, 609)(398, 607)(399, 611)(400, 615)(401, 613)(402, 617)(403, 537)(404, 621)(405, 529)(406, 619)(407, 540)(408, 623)(409, 530)(410, 526)(411, 535)(412, 610)(413, 528)(414, 527)(415, 539)(416, 604)(417, 536)(418, 538)(419, 602)(420, 616)(421, 532)(422, 534)(423, 608)(424, 622)(425, 543)(426, 612)(427, 620)(428, 545)(429, 594)(430, 544)(431, 592)(432, 541)(433, 606)(434, 614)(435, 548)(436, 587)(437, 547)(438, 585)(439, 618)(440, 549)(441, 600)(442, 624)(443, 546)(444, 597)(445, 551)(446, 575)(447, 550)(448, 572)(449, 552)(450, 589)(451, 554)(452, 579)(453, 553)(454, 568)(455, 555)(456, 582)(457, 557)(458, 590)(459, 556)(460, 576)(461, 558)(462, 595)(463, 562)(464, 583)(465, 560)(466, 580)(467, 564)(468, 598)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2163
Transitivity :: VT+
Graph:: bipartite
	v = 78 e = 312 f = 182
	degree seq :: [ 8^78 ]

E27.2165 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 6})
Quotient :: loop^2
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y2 * Y3^4, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 157, 313, 469, 4, 160, 316, 472, 6, 162, 318, 474, 15, 171, 327, 483, 9, 165, 321, 477, 5, 161, 317, 473)(2, 158, 314, 470, 7, 163, 319, 475, 3, 159, 315, 471, 10, 166, 322, 478, 14, 170, 326, 482, 8, 164, 320, 476)(11, 167, 323, 479, 19, 175, 331, 487, 12, 168, 324, 480, 21, 177, 333, 489, 13, 169, 325, 481, 20, 176, 332, 488)(16, 172, 328, 484, 22, 178, 334, 490, 17, 173, 329, 485, 24, 180, 336, 492, 18, 174, 330, 486, 23, 179, 335, 491)(25, 181, 337, 493, 31, 187, 343, 499, 26, 182, 338, 494, 33, 189, 345, 501, 27, 183, 339, 495, 32, 188, 344, 500)(28, 184, 340, 496, 34, 190, 346, 502, 29, 185, 341, 497, 36, 192, 348, 504, 30, 186, 342, 498, 35, 191, 347, 503)(37, 193, 349, 505, 43, 199, 355, 511, 38, 194, 350, 506, 45, 201, 357, 513, 39, 195, 351, 507, 44, 200, 356, 512)(40, 196, 352, 508, 46, 202, 358, 514, 41, 197, 353, 509, 48, 204, 360, 516, 42, 198, 354, 510, 47, 203, 359, 515)(49, 205, 361, 517, 55, 211, 367, 523, 50, 206, 362, 518, 57, 213, 369, 525, 51, 207, 363, 519, 56, 212, 368, 524)(52, 208, 364, 520, 101, 257, 413, 569, 53, 209, 365, 521, 100, 256, 412, 568, 54, 210, 366, 522, 102, 258, 414, 570)(58, 214, 370, 526, 114, 270, 426, 582, 63, 219, 375, 531, 126, 282, 438, 594, 66, 222, 378, 534, 115, 271, 427, 583)(59, 215, 371, 527, 118, 274, 430, 586, 60, 216, 372, 528, 121, 277, 433, 589, 71, 227, 383, 539, 119, 275, 431, 587)(61, 217, 373, 529, 122, 278, 434, 590, 72, 228, 384, 540, 124, 280, 436, 592, 62, 218, 374, 530, 123, 279, 435, 591)(64, 220, 376, 532, 127, 283, 439, 595, 67, 223, 379, 535, 129, 285, 441, 597, 65, 221, 377, 533, 128, 284, 440, 596)(68, 224, 380, 536, 112, 268, 424, 580, 69, 225, 381, 537, 113, 269, 425, 581, 70, 226, 382, 538, 125, 281, 437, 593)(73, 229, 385, 541, 116, 272, 428, 584, 74, 230, 386, 542, 117, 273, 429, 585, 75, 231, 387, 543, 120, 276, 432, 588)(76, 232, 388, 544, 136, 292, 448, 604, 78, 234, 390, 546, 138, 294, 450, 606, 77, 233, 389, 545, 137, 293, 449, 605)(79, 235, 391, 547, 139, 295, 451, 607, 81, 237, 393, 549, 141, 297, 453, 609, 80, 236, 392, 548, 140, 296, 452, 608)(82, 238, 394, 550, 130, 286, 442, 598, 83, 239, 395, 551, 131, 287, 443, 599, 84, 240, 396, 552, 132, 288, 444, 600)(85, 241, 397, 553, 133, 289, 445, 601, 86, 242, 398, 554, 134, 290, 446, 602, 87, 243, 399, 555, 135, 291, 447, 603)(88, 244, 400, 556, 148, 304, 460, 616, 90, 246, 402, 558, 150, 306, 462, 618, 89, 245, 401, 557, 149, 305, 461, 617)(91, 247, 403, 559, 109, 265, 421, 577, 93, 249, 405, 561, 110, 266, 422, 578, 92, 248, 404, 560, 111, 267, 423, 579)(94, 250, 406, 562, 142, 298, 454, 610, 95, 251, 407, 563, 143, 299, 455, 611, 96, 252, 408, 564, 144, 300, 456, 612)(97, 253, 409, 565, 145, 301, 457, 613, 98, 254, 410, 566, 146, 302, 458, 614, 99, 255, 411, 567, 147, 303, 459, 615)(103, 259, 415, 571, 151, 307, 463, 619, 104, 260, 416, 572, 152, 308, 464, 620, 105, 261, 417, 573, 153, 309, 465, 621)(106, 262, 418, 574, 154, 310, 466, 622, 107, 263, 419, 575, 155, 311, 467, 623, 108, 264, 420, 576, 156, 312, 468, 624)
	L = (1, 158)(2, 157)(3, 165)(4, 167)(5, 168)(6, 170)(7, 172)(8, 173)(9, 159)(10, 174)(11, 160)(12, 161)(13, 171)(14, 162)(15, 169)(16, 163)(17, 164)(18, 166)(19, 181)(20, 182)(21, 183)(22, 184)(23, 185)(24, 186)(25, 175)(26, 176)(27, 177)(28, 178)(29, 179)(30, 180)(31, 193)(32, 194)(33, 195)(34, 196)(35, 197)(36, 198)(37, 187)(38, 188)(39, 189)(40, 190)(41, 191)(42, 192)(43, 205)(44, 206)(45, 207)(46, 208)(47, 209)(48, 210)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 265)(56, 266)(57, 267)(58, 268)(59, 272)(60, 276)(61, 275)(62, 274)(63, 281)(64, 271)(65, 270)(66, 269)(67, 282)(68, 286)(69, 288)(70, 287)(71, 273)(72, 277)(73, 289)(74, 291)(75, 290)(76, 279)(77, 278)(78, 280)(79, 284)(80, 283)(81, 285)(82, 298)(83, 300)(84, 299)(85, 301)(86, 303)(87, 302)(88, 293)(89, 292)(90, 294)(91, 296)(92, 295)(93, 297)(94, 307)(95, 309)(96, 308)(97, 310)(98, 312)(99, 311)(100, 305)(101, 304)(102, 306)(103, 262)(104, 264)(105, 263)(106, 259)(107, 261)(108, 260)(109, 211)(110, 212)(111, 213)(112, 214)(113, 222)(114, 221)(115, 220)(116, 215)(117, 227)(118, 218)(119, 217)(120, 216)(121, 228)(122, 233)(123, 232)(124, 234)(125, 219)(126, 223)(127, 236)(128, 235)(129, 237)(130, 224)(131, 226)(132, 225)(133, 229)(134, 231)(135, 230)(136, 245)(137, 244)(138, 246)(139, 248)(140, 247)(141, 249)(142, 238)(143, 240)(144, 239)(145, 241)(146, 243)(147, 242)(148, 257)(149, 256)(150, 258)(151, 250)(152, 252)(153, 251)(154, 253)(155, 255)(156, 254)(313, 471)(314, 474)(315, 469)(316, 480)(317, 481)(318, 470)(319, 485)(320, 486)(321, 482)(322, 484)(323, 483)(324, 472)(325, 473)(326, 477)(327, 479)(328, 478)(329, 475)(330, 476)(331, 494)(332, 495)(333, 493)(334, 497)(335, 498)(336, 496)(337, 489)(338, 487)(339, 488)(340, 492)(341, 490)(342, 491)(343, 506)(344, 507)(345, 505)(346, 509)(347, 510)(348, 508)(349, 501)(350, 499)(351, 500)(352, 504)(353, 502)(354, 503)(355, 518)(356, 519)(357, 517)(358, 521)(359, 522)(360, 520)(361, 513)(362, 511)(363, 512)(364, 516)(365, 514)(366, 515)(367, 578)(368, 579)(369, 577)(370, 581)(371, 585)(372, 584)(373, 586)(374, 589)(375, 580)(376, 582)(377, 594)(378, 593)(379, 583)(380, 599)(381, 598)(382, 600)(383, 588)(384, 587)(385, 602)(386, 601)(387, 603)(388, 590)(389, 592)(390, 591)(391, 595)(392, 597)(393, 596)(394, 611)(395, 610)(396, 612)(397, 614)(398, 613)(399, 615)(400, 604)(401, 606)(402, 605)(403, 607)(404, 609)(405, 608)(406, 620)(407, 619)(408, 621)(409, 623)(410, 622)(411, 624)(412, 616)(413, 618)(414, 617)(415, 575)(416, 574)(417, 576)(418, 572)(419, 571)(420, 573)(421, 525)(422, 523)(423, 524)(424, 531)(425, 526)(426, 532)(427, 535)(428, 528)(429, 527)(430, 529)(431, 540)(432, 539)(433, 530)(434, 544)(435, 546)(436, 545)(437, 534)(438, 533)(439, 547)(440, 549)(441, 548)(442, 537)(443, 536)(444, 538)(445, 542)(446, 541)(447, 543)(448, 556)(449, 558)(450, 557)(451, 559)(452, 561)(453, 560)(454, 551)(455, 550)(456, 552)(457, 554)(458, 553)(459, 555)(460, 568)(461, 570)(462, 569)(463, 563)(464, 562)(465, 564)(466, 566)(467, 565)(468, 567)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2162
Transitivity :: VT+
Graph:: bipartite
	v = 26 e = 312 f = 234
	degree seq :: [ 24^26 ]

E27.2166 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1 * Y3 * Y1 * Y2)^2, (Y3 * Y1)^6, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158)(3, 159, 7, 163)(4, 160, 9, 165)(5, 161, 10, 166)(6, 162, 12, 168)(8, 164, 15, 171)(11, 167, 20, 176)(13, 169, 23, 179)(14, 170, 21, 177)(16, 172, 19, 175)(17, 173, 28, 184)(18, 174, 29, 185)(22, 178, 34, 190)(24, 180, 37, 193)(25, 181, 36, 192)(26, 182, 39, 195)(27, 183, 40, 196)(30, 186, 44, 200)(31, 187, 43, 199)(32, 188, 46, 202)(33, 189, 47, 203)(35, 191, 49, 205)(38, 194, 53, 209)(41, 197, 48, 204)(42, 198, 57, 213)(45, 201, 61, 217)(50, 206, 67, 223)(51, 207, 66, 222)(52, 208, 63, 219)(54, 210, 64, 220)(55, 211, 60, 216)(56, 212, 62, 218)(58, 214, 74, 230)(59, 215, 73, 229)(65, 221, 79, 235)(68, 224, 83, 239)(69, 225, 82, 238)(70, 226, 78, 234)(71, 227, 77, 233)(72, 228, 85, 241)(75, 231, 89, 245)(76, 232, 88, 244)(80, 236, 93, 249)(81, 237, 92, 248)(84, 240, 96, 252)(86, 242, 99, 255)(87, 243, 98, 254)(90, 246, 102, 258)(91, 247, 103, 259)(94, 250, 107, 263)(95, 251, 106, 262)(97, 253, 109, 265)(100, 256, 113, 269)(101, 257, 112, 268)(104, 260, 117, 273)(105, 261, 116, 272)(108, 264, 120, 276)(110, 266, 123, 279)(111, 267, 122, 278)(114, 270, 126, 282)(115, 271, 127, 283)(118, 274, 131, 287)(119, 275, 130, 286)(121, 277, 133, 289)(124, 280, 137, 293)(125, 281, 136, 292)(128, 284, 141, 297)(129, 285, 140, 296)(132, 288, 144, 300)(134, 290, 147, 303)(135, 291, 146, 302)(138, 294, 150, 306)(139, 295, 151, 307)(142, 298, 155, 311)(143, 299, 154, 310)(145, 301, 156, 312)(148, 304, 152, 308)(149, 305, 153, 309)(313, 469, 315, 471)(314, 470, 317, 473)(316, 472, 320, 476)(318, 474, 323, 479)(319, 475, 325, 481)(321, 477, 328, 484)(322, 478, 330, 486)(324, 480, 333, 489)(326, 482, 336, 492)(327, 483, 337, 493)(329, 485, 339, 495)(331, 487, 342, 498)(332, 488, 343, 499)(334, 490, 345, 501)(335, 491, 347, 503)(338, 494, 350, 506)(340, 496, 351, 507)(341, 497, 354, 510)(344, 500, 357, 513)(346, 502, 358, 514)(348, 504, 362, 518)(349, 505, 363, 519)(352, 508, 367, 523)(353, 509, 366, 522)(355, 511, 370, 526)(356, 512, 371, 527)(359, 515, 375, 531)(360, 516, 374, 530)(361, 517, 377, 533)(364, 520, 380, 536)(365, 521, 381, 537)(368, 524, 383, 539)(369, 525, 384, 540)(372, 528, 387, 543)(373, 529, 388, 544)(376, 532, 390, 546)(378, 534, 392, 548)(379, 535, 393, 549)(382, 538, 396, 552)(385, 541, 398, 554)(386, 542, 399, 555)(389, 545, 402, 558)(391, 547, 403, 559)(394, 550, 406, 562)(395, 551, 407, 563)(397, 553, 409, 565)(400, 556, 412, 568)(401, 557, 413, 569)(404, 560, 416, 572)(405, 561, 417, 573)(408, 564, 420, 576)(410, 566, 422, 578)(411, 567, 423, 579)(414, 570, 426, 582)(415, 571, 427, 583)(418, 574, 430, 586)(419, 575, 431, 587)(421, 577, 433, 589)(424, 580, 436, 592)(425, 581, 437, 593)(428, 584, 440, 596)(429, 585, 441, 597)(432, 588, 444, 600)(434, 590, 446, 602)(435, 591, 447, 603)(438, 594, 450, 606)(439, 595, 451, 607)(442, 598, 454, 610)(443, 599, 455, 611)(445, 601, 457, 613)(448, 604, 460, 616)(449, 605, 461, 617)(452, 608, 464, 620)(453, 609, 465, 621)(456, 612, 468, 624)(458, 614, 467, 623)(459, 615, 466, 622)(462, 618, 463, 619)
	L = (1, 316)(2, 318)(3, 320)(4, 313)(5, 323)(6, 314)(7, 326)(8, 315)(9, 329)(10, 331)(11, 317)(12, 334)(13, 336)(14, 319)(15, 338)(16, 339)(17, 321)(18, 342)(19, 322)(20, 344)(21, 345)(22, 324)(23, 348)(24, 325)(25, 350)(26, 327)(27, 328)(28, 353)(29, 355)(30, 330)(31, 357)(32, 332)(33, 333)(34, 360)(35, 362)(36, 335)(37, 364)(38, 337)(39, 366)(40, 368)(41, 340)(42, 370)(43, 341)(44, 372)(45, 343)(46, 374)(47, 376)(48, 346)(49, 378)(50, 347)(51, 380)(52, 349)(53, 382)(54, 351)(55, 383)(56, 352)(57, 385)(58, 354)(59, 387)(60, 356)(61, 389)(62, 358)(63, 390)(64, 359)(65, 392)(66, 361)(67, 394)(68, 363)(69, 396)(70, 365)(71, 367)(72, 398)(73, 369)(74, 400)(75, 371)(76, 402)(77, 373)(78, 375)(79, 404)(80, 377)(81, 406)(82, 379)(83, 408)(84, 381)(85, 410)(86, 384)(87, 412)(88, 386)(89, 414)(90, 388)(91, 416)(92, 391)(93, 418)(94, 393)(95, 420)(96, 395)(97, 422)(98, 397)(99, 424)(100, 399)(101, 426)(102, 401)(103, 428)(104, 403)(105, 430)(106, 405)(107, 432)(108, 407)(109, 434)(110, 409)(111, 436)(112, 411)(113, 438)(114, 413)(115, 440)(116, 415)(117, 442)(118, 417)(119, 444)(120, 419)(121, 446)(122, 421)(123, 448)(124, 423)(125, 450)(126, 425)(127, 452)(128, 427)(129, 454)(130, 429)(131, 456)(132, 431)(133, 458)(134, 433)(135, 460)(136, 435)(137, 462)(138, 437)(139, 464)(140, 439)(141, 466)(142, 441)(143, 468)(144, 443)(145, 467)(146, 445)(147, 465)(148, 447)(149, 463)(150, 449)(151, 461)(152, 451)(153, 459)(154, 453)(155, 457)(156, 455)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2170
Graph:: simple bipartite
	v = 156 e = 312 f = 104
	degree seq :: [ 4^156 ]

E27.2167 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2, (Y3^2 * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y3, Y3^26, Y3^-12 * Y2 * Y3^2 * Y1 * Y3^-10 * Y2 * Y1 ]
Map:: non-degenerate
	R = (1, 157, 2, 158)(3, 159, 9, 165)(4, 160, 12, 168)(5, 161, 14, 170)(6, 162, 16, 172)(7, 163, 19, 175)(8, 164, 21, 177)(10, 166, 24, 180)(11, 167, 26, 182)(13, 169, 22, 178)(15, 171, 20, 176)(17, 173, 29, 185)(18, 174, 28, 184)(23, 179, 31, 187)(25, 181, 37, 193)(27, 183, 33, 189)(30, 186, 42, 198)(32, 188, 38, 194)(34, 190, 45, 201)(35, 191, 39, 195)(36, 192, 41, 197)(40, 196, 51, 207)(43, 199, 48, 204)(44, 200, 47, 203)(46, 202, 54, 210)(49, 205, 50, 206)(52, 208, 61, 217)(53, 209, 57, 213)(55, 211, 66, 222)(56, 212, 62, 218)(58, 214, 69, 225)(59, 215, 63, 219)(60, 216, 65, 221)(64, 220, 75, 231)(67, 223, 72, 228)(68, 224, 71, 227)(70, 226, 78, 234)(73, 229, 74, 230)(76, 232, 85, 241)(77, 233, 81, 237)(79, 235, 90, 246)(80, 236, 86, 242)(82, 238, 93, 249)(83, 239, 87, 243)(84, 240, 89, 245)(88, 244, 99, 255)(91, 247, 96, 252)(92, 248, 95, 251)(94, 250, 102, 258)(97, 253, 98, 254)(100, 256, 109, 265)(101, 257, 105, 261)(103, 259, 114, 270)(104, 260, 110, 266)(106, 262, 117, 273)(107, 263, 111, 267)(108, 264, 113, 269)(112, 268, 123, 279)(115, 271, 120, 276)(116, 272, 119, 275)(118, 274, 126, 282)(121, 277, 122, 278)(124, 280, 133, 289)(125, 281, 129, 285)(127, 283, 138, 294)(128, 284, 134, 290)(130, 286, 141, 297)(131, 287, 135, 291)(132, 288, 137, 293)(136, 292, 147, 303)(139, 295, 144, 300)(140, 296, 143, 299)(142, 298, 150, 306)(145, 301, 146, 302)(148, 304, 153, 309)(149, 305, 152, 308)(151, 307, 155, 311)(154, 310, 156, 312)(313, 469, 315, 471)(314, 470, 318, 474)(316, 472, 323, 479)(317, 473, 322, 478)(319, 475, 330, 486)(320, 476, 329, 485)(321, 477, 332, 488)(324, 480, 339, 495)(325, 481, 328, 484)(326, 482, 338, 494)(327, 483, 337, 493)(331, 487, 343, 499)(333, 489, 340, 496)(334, 490, 346, 502)(335, 491, 347, 503)(336, 492, 350, 506)(341, 497, 353, 509)(342, 498, 345, 501)(344, 500, 352, 508)(348, 504, 358, 514)(349, 505, 359, 515)(351, 507, 362, 518)(354, 510, 365, 521)(355, 511, 357, 513)(356, 512, 364, 520)(360, 516, 370, 526)(361, 517, 371, 527)(363, 519, 374, 530)(366, 522, 377, 533)(367, 523, 369, 525)(368, 524, 376, 532)(372, 528, 382, 538)(373, 529, 383, 539)(375, 531, 386, 542)(378, 534, 389, 545)(379, 535, 381, 537)(380, 536, 388, 544)(384, 540, 394, 550)(385, 541, 395, 551)(387, 543, 398, 554)(390, 546, 401, 557)(391, 547, 393, 549)(392, 548, 400, 556)(396, 552, 406, 562)(397, 553, 407, 563)(399, 555, 410, 566)(402, 558, 413, 569)(403, 559, 405, 561)(404, 560, 412, 568)(408, 564, 418, 574)(409, 565, 419, 575)(411, 567, 422, 578)(414, 570, 425, 581)(415, 571, 417, 573)(416, 572, 424, 580)(420, 576, 430, 586)(421, 577, 431, 587)(423, 579, 434, 590)(426, 582, 437, 593)(427, 583, 429, 585)(428, 584, 436, 592)(432, 588, 442, 598)(433, 589, 443, 599)(435, 591, 446, 602)(438, 594, 449, 605)(439, 595, 441, 597)(440, 596, 448, 604)(444, 600, 454, 610)(445, 601, 455, 611)(447, 603, 458, 614)(450, 606, 461, 617)(451, 607, 453, 609)(452, 608, 460, 616)(456, 612, 465, 621)(457, 613, 466, 622)(459, 615, 467, 623)(462, 618, 468, 624)(463, 619, 464, 620)
	L = (1, 316)(2, 319)(3, 322)(4, 325)(5, 313)(6, 329)(7, 332)(8, 314)(9, 330)(10, 337)(11, 315)(12, 340)(13, 342)(14, 343)(15, 317)(16, 323)(17, 346)(18, 318)(19, 338)(20, 347)(21, 339)(22, 320)(23, 321)(24, 331)(25, 352)(26, 333)(27, 353)(28, 326)(29, 324)(30, 355)(31, 350)(32, 327)(33, 328)(34, 358)(35, 359)(36, 334)(37, 335)(38, 362)(39, 336)(40, 364)(41, 365)(42, 341)(43, 367)(44, 344)(45, 345)(46, 370)(47, 371)(48, 348)(49, 349)(50, 374)(51, 351)(52, 376)(53, 377)(54, 354)(55, 379)(56, 356)(57, 357)(58, 382)(59, 383)(60, 360)(61, 361)(62, 386)(63, 363)(64, 388)(65, 389)(66, 366)(67, 391)(68, 368)(69, 369)(70, 394)(71, 395)(72, 372)(73, 373)(74, 398)(75, 375)(76, 400)(77, 401)(78, 378)(79, 403)(80, 380)(81, 381)(82, 406)(83, 407)(84, 384)(85, 385)(86, 410)(87, 387)(88, 412)(89, 413)(90, 390)(91, 415)(92, 392)(93, 393)(94, 418)(95, 419)(96, 396)(97, 397)(98, 422)(99, 399)(100, 424)(101, 425)(102, 402)(103, 427)(104, 404)(105, 405)(106, 430)(107, 431)(108, 408)(109, 409)(110, 434)(111, 411)(112, 436)(113, 437)(114, 414)(115, 439)(116, 416)(117, 417)(118, 442)(119, 443)(120, 420)(121, 421)(122, 446)(123, 423)(124, 448)(125, 449)(126, 426)(127, 451)(128, 428)(129, 429)(130, 454)(131, 455)(132, 432)(133, 433)(134, 458)(135, 435)(136, 460)(137, 461)(138, 438)(139, 463)(140, 440)(141, 441)(142, 465)(143, 466)(144, 444)(145, 445)(146, 467)(147, 447)(148, 464)(149, 468)(150, 450)(151, 452)(152, 453)(153, 457)(154, 456)(155, 462)(156, 459)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2171
Graph:: simple bipartite
	v = 156 e = 312 f = 104
	degree seq :: [ 4^156 ]

E27.2168 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158)(3, 159, 7, 163)(4, 160, 9, 165)(5, 161, 10, 166)(6, 162, 12, 168)(8, 164, 15, 171)(11, 167, 20, 176)(13, 169, 23, 179)(14, 170, 25, 181)(16, 172, 28, 184)(17, 173, 30, 186)(18, 174, 31, 187)(19, 175, 33, 189)(21, 177, 36, 192)(22, 178, 38, 194)(24, 180, 41, 197)(26, 182, 44, 200)(27, 183, 37, 193)(29, 185, 35, 191)(32, 188, 50, 206)(34, 190, 53, 209)(39, 195, 57, 213)(40, 196, 55, 211)(42, 198, 51, 207)(43, 199, 56, 212)(45, 201, 60, 216)(46, 202, 49, 205)(47, 203, 52, 208)(48, 204, 64, 220)(54, 210, 67, 223)(58, 214, 73, 229)(59, 215, 74, 230)(61, 217, 72, 228)(62, 218, 70, 226)(63, 219, 69, 225)(65, 221, 79, 235)(66, 222, 80, 236)(68, 224, 78, 234)(71, 227, 83, 239)(75, 231, 86, 242)(76, 232, 88, 244)(77, 233, 89, 245)(81, 237, 92, 248)(82, 238, 94, 250)(84, 240, 97, 253)(85, 241, 98, 254)(87, 243, 96, 252)(90, 246, 103, 259)(91, 247, 104, 260)(93, 249, 102, 258)(95, 251, 107, 263)(99, 255, 110, 266)(100, 256, 112, 268)(101, 257, 113, 269)(105, 261, 116, 272)(106, 262, 118, 274)(108, 264, 121, 277)(109, 265, 122, 278)(111, 267, 120, 276)(114, 270, 127, 283)(115, 271, 128, 284)(117, 273, 126, 282)(119, 275, 131, 287)(123, 279, 134, 290)(124, 280, 136, 292)(125, 281, 137, 293)(129, 285, 140, 296)(130, 286, 142, 298)(132, 288, 145, 301)(133, 289, 146, 302)(135, 291, 144, 300)(138, 294, 151, 307)(139, 295, 152, 308)(141, 297, 150, 306)(143, 299, 154, 310)(147, 303, 155, 311)(148, 304, 149, 305)(153, 309, 156, 312)(313, 469, 315, 471)(314, 470, 317, 473)(316, 472, 320, 476)(318, 474, 323, 479)(319, 475, 325, 481)(321, 477, 328, 484)(322, 478, 330, 486)(324, 480, 333, 489)(326, 482, 336, 492)(327, 483, 338, 494)(329, 485, 341, 497)(331, 487, 344, 500)(332, 488, 346, 502)(334, 490, 349, 505)(335, 491, 351, 507)(337, 493, 354, 510)(339, 495, 357, 513)(340, 496, 358, 514)(342, 498, 355, 511)(343, 499, 360, 516)(345, 501, 363, 519)(347, 503, 366, 522)(348, 504, 367, 523)(350, 506, 364, 520)(352, 508, 370, 526)(353, 509, 371, 527)(356, 512, 373, 529)(359, 515, 375, 531)(361, 517, 377, 533)(362, 518, 378, 534)(365, 521, 380, 536)(368, 524, 382, 538)(369, 525, 383, 539)(372, 528, 387, 543)(374, 530, 388, 544)(376, 532, 389, 545)(379, 535, 393, 549)(381, 537, 394, 550)(384, 540, 396, 552)(385, 541, 397, 553)(386, 542, 399, 555)(390, 546, 402, 558)(391, 547, 403, 559)(392, 548, 405, 561)(395, 551, 407, 563)(398, 554, 411, 567)(400, 556, 412, 568)(401, 557, 413, 569)(404, 560, 417, 573)(406, 562, 418, 574)(408, 564, 420, 576)(409, 565, 421, 577)(410, 566, 423, 579)(414, 570, 426, 582)(415, 571, 427, 583)(416, 572, 429, 585)(419, 575, 431, 587)(422, 578, 435, 591)(424, 580, 436, 592)(425, 581, 437, 593)(428, 584, 441, 597)(430, 586, 442, 598)(432, 588, 444, 600)(433, 589, 445, 601)(434, 590, 447, 603)(438, 594, 450, 606)(439, 595, 451, 607)(440, 596, 453, 609)(443, 599, 455, 611)(446, 602, 459, 615)(448, 604, 460, 616)(449, 605, 461, 617)(452, 608, 465, 621)(454, 610, 466, 622)(456, 612, 464, 620)(457, 613, 463, 619)(458, 614, 462, 618)(467, 623, 468, 624)
	L = (1, 316)(2, 318)(3, 320)(4, 313)(5, 323)(6, 314)(7, 326)(8, 315)(9, 329)(10, 331)(11, 317)(12, 334)(13, 336)(14, 319)(15, 339)(16, 341)(17, 321)(18, 344)(19, 322)(20, 347)(21, 349)(22, 324)(23, 352)(24, 325)(25, 355)(26, 357)(27, 327)(28, 359)(29, 328)(30, 354)(31, 361)(32, 330)(33, 364)(34, 366)(35, 332)(36, 368)(37, 333)(38, 363)(39, 370)(40, 335)(41, 372)(42, 342)(43, 337)(44, 374)(45, 338)(46, 375)(47, 340)(48, 377)(49, 343)(50, 379)(51, 350)(52, 345)(53, 381)(54, 346)(55, 382)(56, 348)(57, 384)(58, 351)(59, 387)(60, 353)(61, 388)(62, 356)(63, 358)(64, 390)(65, 360)(66, 393)(67, 362)(68, 394)(69, 365)(70, 367)(71, 396)(72, 369)(73, 398)(74, 400)(75, 371)(76, 373)(77, 402)(78, 376)(79, 404)(80, 406)(81, 378)(82, 380)(83, 408)(84, 383)(85, 411)(86, 385)(87, 412)(88, 386)(89, 414)(90, 389)(91, 417)(92, 391)(93, 418)(94, 392)(95, 420)(96, 395)(97, 422)(98, 424)(99, 397)(100, 399)(101, 426)(102, 401)(103, 428)(104, 430)(105, 403)(106, 405)(107, 432)(108, 407)(109, 435)(110, 409)(111, 436)(112, 410)(113, 438)(114, 413)(115, 441)(116, 415)(117, 442)(118, 416)(119, 444)(120, 419)(121, 446)(122, 448)(123, 421)(124, 423)(125, 450)(126, 425)(127, 452)(128, 454)(129, 427)(130, 429)(131, 456)(132, 431)(133, 459)(134, 433)(135, 460)(136, 434)(137, 462)(138, 437)(139, 465)(140, 439)(141, 466)(142, 440)(143, 464)(144, 443)(145, 467)(146, 461)(147, 445)(148, 447)(149, 458)(150, 449)(151, 468)(152, 455)(153, 451)(154, 453)(155, 457)(156, 463)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2169
Graph:: simple bipartite
	v = 156 e = 312 f = 104
	degree seq :: [ 4^156 ]

E27.2169 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 15, 171, 14, 170, 5, 161)(3, 159, 9, 165, 16, 172, 31, 187, 25, 181, 11, 167)(4, 160, 12, 168, 26, 182, 30, 186, 17, 173, 8, 164)(7, 163, 18, 174, 29, 185, 28, 184, 13, 169, 20, 176)(10, 166, 23, 179, 40, 196, 47, 203, 32, 188, 22, 178)(19, 175, 35, 191, 27, 183, 43, 199, 45, 201, 34, 190)(21, 177, 37, 193, 46, 202, 42, 198, 24, 180, 39, 195)(33, 189, 48, 204, 44, 200, 52, 208, 36, 192, 50, 206)(38, 194, 55, 211, 41, 197, 57, 213, 60, 216, 54, 210)(49, 205, 63, 219, 51, 207, 65, 221, 59, 215, 62, 218)(53, 209, 67, 223, 58, 214, 71, 227, 56, 212, 69, 225)(61, 217, 73, 229, 66, 222, 77, 233, 64, 220, 75, 231)(68, 224, 81, 237, 70, 226, 83, 239, 72, 228, 80, 236)(74, 230, 87, 243, 76, 232, 89, 245, 78, 234, 86, 242)(79, 235, 91, 247, 84, 240, 95, 251, 82, 238, 93, 249)(85, 241, 97, 253, 90, 246, 101, 257, 88, 244, 99, 255)(92, 248, 105, 261, 94, 250, 107, 263, 96, 252, 104, 260)(98, 254, 111, 267, 100, 256, 113, 269, 102, 258, 110, 266)(103, 259, 115, 271, 108, 264, 119, 275, 106, 262, 117, 273)(109, 265, 121, 277, 114, 270, 125, 281, 112, 268, 123, 279)(116, 272, 129, 285, 118, 274, 131, 287, 120, 276, 128, 284)(122, 278, 135, 291, 124, 280, 137, 293, 126, 282, 134, 290)(127, 283, 139, 295, 132, 288, 143, 299, 130, 286, 141, 297)(133, 289, 145, 301, 138, 294, 149, 305, 136, 292, 147, 303)(140, 296, 152, 308, 142, 298, 153, 309, 144, 300, 151, 307)(146, 302, 155, 311, 148, 304, 156, 312, 150, 306, 154, 310)(313, 469, 315, 471)(314, 470, 319, 475)(316, 472, 322, 478)(317, 473, 325, 481)(318, 474, 328, 484)(320, 476, 331, 487)(321, 477, 333, 489)(323, 479, 336, 492)(324, 480, 339, 495)(326, 482, 337, 493)(327, 483, 341, 497)(329, 485, 344, 500)(330, 486, 345, 501)(332, 488, 348, 504)(334, 490, 350, 506)(335, 491, 353, 509)(338, 494, 352, 508)(340, 496, 356, 512)(342, 498, 357, 513)(343, 499, 358, 514)(346, 502, 361, 517)(347, 503, 363, 519)(349, 505, 365, 521)(351, 507, 368, 524)(354, 510, 370, 526)(355, 511, 371, 527)(359, 515, 372, 528)(360, 516, 373, 529)(362, 518, 376, 532)(364, 520, 378, 534)(366, 522, 380, 536)(367, 523, 382, 538)(369, 525, 384, 540)(374, 530, 386, 542)(375, 531, 388, 544)(377, 533, 390, 546)(379, 535, 391, 547)(381, 537, 394, 550)(383, 539, 396, 552)(385, 541, 397, 553)(387, 543, 400, 556)(389, 545, 402, 558)(392, 548, 404, 560)(393, 549, 406, 562)(395, 551, 408, 564)(398, 554, 410, 566)(399, 555, 412, 568)(401, 557, 414, 570)(403, 559, 415, 571)(405, 561, 418, 574)(407, 563, 420, 576)(409, 565, 421, 577)(411, 567, 424, 580)(413, 569, 426, 582)(416, 572, 428, 584)(417, 573, 430, 586)(419, 575, 432, 588)(422, 578, 434, 590)(423, 579, 436, 592)(425, 581, 438, 594)(427, 583, 439, 595)(429, 585, 442, 598)(431, 587, 444, 600)(433, 589, 445, 601)(435, 591, 448, 604)(437, 593, 450, 606)(440, 596, 452, 608)(441, 597, 454, 610)(443, 599, 456, 612)(446, 602, 458, 614)(447, 603, 460, 616)(449, 605, 462, 618)(451, 607, 461, 617)(453, 609, 457, 613)(455, 611, 459, 615)(463, 619, 468, 624)(464, 620, 466, 622)(465, 621, 467, 623)
	L = (1, 316)(2, 320)(3, 322)(4, 313)(5, 324)(6, 329)(7, 331)(8, 314)(9, 334)(10, 315)(11, 335)(12, 317)(13, 339)(14, 338)(15, 342)(16, 344)(17, 318)(18, 346)(19, 319)(20, 347)(21, 350)(22, 321)(23, 323)(24, 353)(25, 352)(26, 326)(27, 325)(28, 355)(29, 357)(30, 327)(31, 359)(32, 328)(33, 361)(34, 330)(35, 332)(36, 363)(37, 366)(38, 333)(39, 367)(40, 337)(41, 336)(42, 369)(43, 340)(44, 371)(45, 341)(46, 372)(47, 343)(48, 374)(49, 345)(50, 375)(51, 348)(52, 377)(53, 380)(54, 349)(55, 351)(56, 382)(57, 354)(58, 384)(59, 356)(60, 358)(61, 386)(62, 360)(63, 362)(64, 388)(65, 364)(66, 390)(67, 392)(68, 365)(69, 393)(70, 368)(71, 395)(72, 370)(73, 398)(74, 373)(75, 399)(76, 376)(77, 401)(78, 378)(79, 404)(80, 379)(81, 381)(82, 406)(83, 383)(84, 408)(85, 410)(86, 385)(87, 387)(88, 412)(89, 389)(90, 414)(91, 416)(92, 391)(93, 417)(94, 394)(95, 419)(96, 396)(97, 422)(98, 397)(99, 423)(100, 400)(101, 425)(102, 402)(103, 428)(104, 403)(105, 405)(106, 430)(107, 407)(108, 432)(109, 434)(110, 409)(111, 411)(112, 436)(113, 413)(114, 438)(115, 440)(116, 415)(117, 441)(118, 418)(119, 443)(120, 420)(121, 446)(122, 421)(123, 447)(124, 424)(125, 449)(126, 426)(127, 452)(128, 427)(129, 429)(130, 454)(131, 431)(132, 456)(133, 458)(134, 433)(135, 435)(136, 460)(137, 437)(138, 462)(139, 463)(140, 439)(141, 464)(142, 442)(143, 465)(144, 444)(145, 466)(146, 445)(147, 467)(148, 448)(149, 468)(150, 450)(151, 451)(152, 453)(153, 455)(154, 457)(155, 459)(156, 461)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4^4 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2168
Graph:: simple bipartite
	v = 104 e = 312 f = 156
	degree seq :: [ 4^78, 12^26 ]

E27.2170 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y1^6, Y1^-1 * Y3 * Y1^2 * Y2 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 15, 171, 14, 170, 5, 161)(3, 159, 9, 165, 21, 177, 32, 188, 16, 172, 11, 167)(4, 160, 12, 168, 26, 182, 30, 186, 17, 173, 8, 164)(7, 163, 18, 174, 13, 169, 28, 184, 29, 185, 20, 176)(10, 166, 24, 180, 31, 187, 46, 202, 37, 193, 23, 179)(19, 175, 35, 191, 45, 201, 43, 199, 27, 183, 34, 190)(22, 178, 38, 194, 25, 181, 42, 198, 47, 203, 40, 196)(33, 189, 48, 204, 36, 192, 52, 208, 44, 200, 50, 206)(39, 195, 55, 211, 60, 216, 57, 213, 41, 197, 54, 210)(49, 205, 63, 219, 59, 215, 65, 221, 51, 207, 62, 218)(53, 209, 67, 223, 56, 212, 71, 227, 58, 214, 69, 225)(61, 217, 73, 229, 64, 220, 77, 233, 66, 222, 75, 231)(68, 224, 81, 237, 72, 228, 83, 239, 70, 226, 80, 236)(74, 230, 87, 243, 78, 234, 89, 245, 76, 232, 86, 242)(79, 235, 91, 247, 82, 238, 95, 251, 84, 240, 93, 249)(85, 241, 97, 253, 88, 244, 101, 257, 90, 246, 99, 255)(92, 248, 105, 261, 96, 252, 107, 263, 94, 250, 104, 260)(98, 254, 111, 267, 102, 258, 113, 269, 100, 256, 110, 266)(103, 259, 115, 271, 106, 262, 119, 275, 108, 264, 117, 273)(109, 265, 121, 277, 112, 268, 125, 281, 114, 270, 123, 279)(116, 272, 129, 285, 120, 276, 131, 287, 118, 274, 128, 284)(122, 278, 135, 291, 126, 282, 137, 293, 124, 280, 134, 290)(127, 283, 139, 295, 130, 286, 143, 299, 132, 288, 141, 297)(133, 289, 145, 301, 136, 292, 149, 305, 138, 294, 147, 303)(140, 296, 153, 309, 144, 300, 155, 311, 142, 298, 152, 308)(146, 302, 156, 312, 150, 306, 151, 307, 148, 304, 154, 310)(313, 469, 315, 471)(314, 470, 319, 475)(316, 472, 322, 478)(317, 473, 325, 481)(318, 474, 328, 484)(320, 476, 331, 487)(321, 477, 334, 490)(323, 479, 337, 493)(324, 480, 339, 495)(326, 482, 333, 489)(327, 483, 341, 497)(329, 485, 343, 499)(330, 486, 345, 501)(332, 488, 348, 504)(335, 491, 351, 507)(336, 492, 353, 509)(338, 494, 349, 505)(340, 496, 356, 512)(342, 498, 357, 513)(344, 500, 359, 515)(346, 502, 361, 517)(347, 503, 363, 519)(350, 506, 365, 521)(352, 508, 368, 524)(354, 510, 370, 526)(355, 511, 371, 527)(358, 514, 372, 528)(360, 516, 373, 529)(362, 518, 376, 532)(364, 520, 378, 534)(366, 522, 380, 536)(367, 523, 382, 538)(369, 525, 384, 540)(374, 530, 386, 542)(375, 531, 388, 544)(377, 533, 390, 546)(379, 535, 391, 547)(381, 537, 394, 550)(383, 539, 396, 552)(385, 541, 397, 553)(387, 543, 400, 556)(389, 545, 402, 558)(392, 548, 404, 560)(393, 549, 406, 562)(395, 551, 408, 564)(398, 554, 410, 566)(399, 555, 412, 568)(401, 557, 414, 570)(403, 559, 415, 571)(405, 561, 418, 574)(407, 563, 420, 576)(409, 565, 421, 577)(411, 567, 424, 580)(413, 569, 426, 582)(416, 572, 428, 584)(417, 573, 430, 586)(419, 575, 432, 588)(422, 578, 434, 590)(423, 579, 436, 592)(425, 581, 438, 594)(427, 583, 439, 595)(429, 585, 442, 598)(431, 587, 444, 600)(433, 589, 445, 601)(435, 591, 448, 604)(437, 593, 450, 606)(440, 596, 452, 608)(441, 597, 454, 610)(443, 599, 456, 612)(446, 602, 458, 614)(447, 603, 460, 616)(449, 605, 462, 618)(451, 607, 463, 619)(453, 609, 466, 622)(455, 611, 468, 624)(457, 613, 465, 621)(459, 615, 467, 623)(461, 617, 464, 620)
	L = (1, 316)(2, 320)(3, 322)(4, 313)(5, 324)(6, 329)(7, 331)(8, 314)(9, 335)(10, 315)(11, 336)(12, 317)(13, 339)(14, 338)(15, 342)(16, 343)(17, 318)(18, 346)(19, 319)(20, 347)(21, 349)(22, 351)(23, 321)(24, 323)(25, 353)(26, 326)(27, 325)(28, 355)(29, 357)(30, 327)(31, 328)(32, 358)(33, 361)(34, 330)(35, 332)(36, 363)(37, 333)(38, 366)(39, 334)(40, 367)(41, 337)(42, 369)(43, 340)(44, 371)(45, 341)(46, 344)(47, 372)(48, 374)(49, 345)(50, 375)(51, 348)(52, 377)(53, 380)(54, 350)(55, 352)(56, 382)(57, 354)(58, 384)(59, 356)(60, 359)(61, 386)(62, 360)(63, 362)(64, 388)(65, 364)(66, 390)(67, 392)(68, 365)(69, 393)(70, 368)(71, 395)(72, 370)(73, 398)(74, 373)(75, 399)(76, 376)(77, 401)(78, 378)(79, 404)(80, 379)(81, 381)(82, 406)(83, 383)(84, 408)(85, 410)(86, 385)(87, 387)(88, 412)(89, 389)(90, 414)(91, 416)(92, 391)(93, 417)(94, 394)(95, 419)(96, 396)(97, 422)(98, 397)(99, 423)(100, 400)(101, 425)(102, 402)(103, 428)(104, 403)(105, 405)(106, 430)(107, 407)(108, 432)(109, 434)(110, 409)(111, 411)(112, 436)(113, 413)(114, 438)(115, 440)(116, 415)(117, 441)(118, 418)(119, 443)(120, 420)(121, 446)(122, 421)(123, 447)(124, 424)(125, 449)(126, 426)(127, 452)(128, 427)(129, 429)(130, 454)(131, 431)(132, 456)(133, 458)(134, 433)(135, 435)(136, 460)(137, 437)(138, 462)(139, 464)(140, 439)(141, 465)(142, 442)(143, 467)(144, 444)(145, 466)(146, 445)(147, 468)(148, 448)(149, 463)(150, 450)(151, 461)(152, 451)(153, 453)(154, 457)(155, 455)(156, 459)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4^4 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2166
Graph:: simple bipartite
	v = 104 e = 312 f = 156
	degree seq :: [ 4^78, 12^26 ]

E27.2171 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 6})
Quotient :: dipole
Aut^+ = S3 x D26 (small group id <156, 11>)
Aut   = C2 x S3 x D26 (small group id <312, 54>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^3, Y1^2 * Y3^-1, (Y2 * Y3^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 157, 2, 158, 4, 160, 8, 164, 6, 162, 5, 161)(3, 159, 9, 165, 10, 166, 18, 174, 12, 168, 11, 167)(7, 163, 14, 170, 13, 169, 20, 176, 16, 172, 15, 171)(17, 173, 23, 179, 19, 175, 26, 182, 25, 181, 24, 180)(21, 177, 28, 184, 22, 178, 30, 186, 27, 183, 29, 185)(31, 187, 37, 193, 32, 188, 39, 195, 33, 189, 38, 194)(34, 190, 40, 196, 35, 191, 42, 198, 36, 192, 41, 197)(43, 199, 49, 205, 44, 200, 51, 207, 45, 201, 50, 206)(46, 202, 52, 208, 47, 203, 54, 210, 48, 204, 53, 209)(55, 211, 91, 247, 56, 212, 92, 248, 57, 213, 93, 249)(58, 214, 94, 250, 61, 217, 101, 257, 63, 219, 95, 251)(59, 215, 96, 252, 64, 220, 102, 258, 62, 218, 98, 254)(60, 216, 99, 255, 66, 222, 97, 253, 68, 224, 100, 256)(65, 221, 103, 259, 71, 227, 105, 261, 67, 223, 104, 260)(69, 225, 106, 262, 72, 228, 108, 264, 70, 226, 107, 263)(73, 229, 109, 265, 75, 231, 111, 267, 74, 230, 110, 266)(76, 232, 112, 268, 78, 234, 114, 270, 77, 233, 113, 269)(79, 235, 115, 271, 81, 237, 117, 273, 80, 236, 116, 272)(82, 238, 118, 274, 84, 240, 120, 276, 83, 239, 119, 275)(85, 241, 121, 277, 87, 243, 123, 279, 86, 242, 122, 278)(88, 244, 124, 280, 90, 246, 126, 282, 89, 245, 125, 281)(127, 283, 154, 310, 129, 285, 156, 312, 128, 284, 155, 311)(130, 286, 148, 304, 132, 288, 150, 306, 131, 287, 149, 305)(133, 289, 147, 303, 137, 293, 146, 302, 134, 290, 145, 301)(135, 291, 153, 309, 138, 294, 152, 308, 136, 292, 151, 307)(139, 295, 144, 300, 141, 297, 143, 299, 140, 296, 142, 298)(313, 469, 315, 471)(314, 470, 319, 475)(316, 472, 324, 480)(317, 473, 325, 481)(318, 474, 322, 478)(320, 476, 328, 484)(321, 477, 329, 485)(323, 479, 331, 487)(326, 482, 333, 489)(327, 483, 334, 490)(330, 486, 337, 493)(332, 488, 339, 495)(335, 491, 343, 499)(336, 492, 344, 500)(338, 494, 345, 501)(340, 496, 346, 502)(341, 497, 347, 503)(342, 498, 348, 504)(349, 505, 355, 511)(350, 506, 356, 512)(351, 507, 357, 513)(352, 508, 358, 514)(353, 509, 359, 515)(354, 510, 360, 516)(361, 517, 367, 523)(362, 518, 368, 524)(363, 519, 369, 525)(364, 520, 380, 536)(365, 521, 372, 528)(366, 522, 378, 534)(370, 526, 405, 561)(371, 527, 409, 565)(373, 529, 404, 560)(374, 530, 412, 568)(375, 531, 403, 559)(376, 532, 411, 567)(377, 533, 413, 569)(379, 535, 407, 563)(381, 537, 414, 570)(382, 538, 410, 566)(383, 539, 406, 562)(384, 540, 408, 564)(385, 541, 417, 573)(386, 542, 416, 572)(387, 543, 415, 571)(388, 544, 420, 576)(389, 545, 419, 575)(390, 546, 418, 574)(391, 547, 423, 579)(392, 548, 422, 578)(393, 549, 421, 577)(394, 550, 426, 582)(395, 551, 425, 581)(396, 552, 424, 580)(397, 553, 429, 585)(398, 554, 428, 584)(399, 555, 427, 583)(400, 556, 432, 588)(401, 557, 431, 587)(402, 558, 430, 586)(433, 589, 441, 597)(434, 590, 440, 596)(435, 591, 439, 595)(436, 592, 448, 604)(437, 593, 447, 603)(438, 594, 450, 606)(442, 598, 466, 622)(443, 599, 468, 624)(444, 600, 467, 623)(445, 601, 464, 620)(446, 602, 463, 619)(449, 605, 465, 621)(451, 607, 461, 617)(452, 608, 460, 616)(453, 609, 462, 618)(454, 610, 457, 613)(455, 611, 459, 615)(456, 612, 458, 614)
	L = (1, 316)(2, 320)(3, 322)(4, 318)(5, 314)(6, 313)(7, 325)(8, 317)(9, 330)(10, 324)(11, 321)(12, 315)(13, 328)(14, 332)(15, 326)(16, 319)(17, 331)(18, 323)(19, 337)(20, 327)(21, 334)(22, 339)(23, 338)(24, 335)(25, 329)(26, 336)(27, 333)(28, 342)(29, 340)(30, 341)(31, 344)(32, 345)(33, 343)(34, 347)(35, 348)(36, 346)(37, 351)(38, 349)(39, 350)(40, 354)(41, 352)(42, 353)(43, 356)(44, 357)(45, 355)(46, 359)(47, 360)(48, 358)(49, 363)(50, 361)(51, 362)(52, 366)(53, 364)(54, 365)(55, 368)(56, 369)(57, 367)(58, 373)(59, 376)(60, 378)(61, 375)(62, 371)(63, 370)(64, 374)(65, 383)(66, 380)(67, 377)(68, 372)(69, 384)(70, 381)(71, 379)(72, 382)(73, 387)(74, 385)(75, 386)(76, 390)(77, 388)(78, 389)(79, 393)(80, 391)(81, 392)(82, 396)(83, 394)(84, 395)(85, 399)(86, 397)(87, 398)(88, 402)(89, 400)(90, 401)(91, 404)(92, 405)(93, 403)(94, 413)(95, 406)(96, 414)(97, 412)(98, 408)(99, 409)(100, 411)(101, 407)(102, 410)(103, 417)(104, 415)(105, 416)(106, 420)(107, 418)(108, 419)(109, 423)(110, 421)(111, 422)(112, 426)(113, 424)(114, 425)(115, 429)(116, 427)(117, 428)(118, 432)(119, 430)(120, 431)(121, 435)(122, 433)(123, 434)(124, 438)(125, 436)(126, 437)(127, 441)(128, 439)(129, 440)(130, 444)(131, 442)(132, 443)(133, 449)(134, 445)(135, 450)(136, 447)(137, 446)(138, 448)(139, 453)(140, 451)(141, 452)(142, 456)(143, 454)(144, 455)(145, 459)(146, 457)(147, 458)(148, 462)(149, 460)(150, 461)(151, 465)(152, 463)(153, 464)(154, 468)(155, 466)(156, 467)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4^4 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2167
Graph:: bipartite
	v = 104 e = 312 f = 156
	degree seq :: [ 4^78, 12^26 ]

E27.2172 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 4, 6})
Quotient :: edge
Aut^+ = C39 : C4 (small group id <156, 10>)
Aut   = C39 : C4 (small group id <156, 10>)
|r| :: 1
Presentation :: [ X1^4, X2 * X1 * X2^2 * X1^-1 * X2, X2^6, (X2^-1 * X1^-1)^4, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1, X1^-2 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 25, 11)(5, 14, 37, 15)(7, 19, 46, 21)(8, 22, 52, 23)(10, 24, 41, 29)(12, 32, 66, 34)(13, 35, 70, 36)(16, 20, 45, 33)(17, 40, 75, 42)(18, 43, 81, 44)(26, 57, 100, 58)(27, 59, 103, 60)(28, 61, 96, 62)(30, 64, 86, 47)(31, 65, 93, 53)(38, 69, 114, 73)(39, 74, 87, 48)(49, 88, 128, 89)(50, 90, 105, 76)(51, 91, 101, 82)(54, 94, 102, 77)(55, 95, 134, 97)(56, 98, 137, 99)(63, 106, 142, 104)(67, 79, 123, 112)(68, 83, 126, 113)(71, 80, 124, 116)(72, 117, 146, 118)(78, 121, 147, 122)(84, 127, 151, 129)(85, 130, 152, 131)(92, 132, 153, 133)(107, 135, 143, 110)(108, 138, 145, 115)(109, 136, 144, 111)(119, 139, 154, 148)(120, 141, 156, 149)(125, 140, 155, 150)(157, 159, 166, 184, 172, 161)(158, 163, 176, 205, 180, 164)(160, 168, 189, 219, 185, 169)(162, 173, 197, 234, 201, 174)(165, 182, 170, 194, 217, 183)(167, 186, 171, 195, 218, 187)(175, 203, 178, 209, 244, 204)(177, 206, 179, 210, 245, 207)(181, 211, 252, 228, 193, 212)(188, 223, 191, 227, 262, 224)(190, 213, 192, 215, 260, 225)(196, 232, 199, 238, 277, 233)(198, 235, 200, 239, 278, 236)(202, 240, 284, 248, 208, 241)(214, 257, 216, 261, 229, 258)(220, 263, 221, 265, 230, 264)(222, 266, 298, 271, 226, 267)(231, 275, 303, 281, 237, 276)(242, 272, 243, 268, 249, 269)(246, 251, 247, 254, 250, 273)(253, 291, 255, 294, 274, 292)(256, 295, 270, 297, 259, 296)(279, 283, 280, 286, 282, 288)(285, 290, 287, 302, 289, 293)(299, 310, 300, 311, 301, 312)(304, 307, 305, 309, 306, 308)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^4 ), ( 8^6 ) }
Outer automorphisms :: chiral
Dual of E27.2173
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 4^39, 6^26 ]

E27.2173 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 4, 6})
Quotient :: loop
Aut^+ = C39 : C4 (small group id <156, 10>)
Aut   = C39 : C4 (small group id <156, 10>)
|r| :: 1
Presentation :: [ X1^4, X2^4, X2^-2 * X1^-1 * X2^-1 * X1^2 * X2^-1 * X1^-1, X2 * X1 * X2^-1 * X1^2 * X2^2 * X1^-1 * X2 * X1^-1, X2^-1 * X1 * X2^2 * X1^2 * X2^-1 * X1 * X2 * X1^-1, X2^-2 * X1 * X2^-1 * X1 * X2^-1 * X1^-2 * X2 * X1^-1 * X2 * X1^-1, X1 * X2^-1 * X1^2 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1, (X2^-1 * X1^-1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 4, 160)(3, 159, 9, 165, 23, 179, 11, 167)(5, 161, 14, 170, 35, 191, 15, 171)(7, 163, 18, 174, 45, 201, 20, 176)(8, 164, 21, 177, 52, 208, 22, 178)(10, 166, 26, 182, 63, 219, 27, 183)(12, 168, 30, 186, 72, 228, 32, 188)(13, 169, 33, 189, 64, 220, 34, 190)(16, 172, 40, 196, 84, 240, 42, 198)(17, 173, 43, 199, 89, 245, 44, 200)(19, 175, 48, 204, 97, 253, 49, 205)(24, 180, 59, 215, 39, 195, 60, 216)(25, 181, 61, 217, 106, 262, 62, 218)(28, 184, 67, 223, 101, 257, 69, 225)(29, 185, 70, 226, 36, 192, 71, 227)(31, 187, 73, 229, 111, 267, 57, 213)(37, 193, 80, 236, 131, 287, 81, 237)(38, 194, 82, 238, 129, 285, 83, 239)(41, 197, 85, 241, 135, 291, 86, 242)(46, 202, 93, 249, 56, 212, 94, 250)(47, 203, 95, 251, 141, 297, 96, 252)(50, 206, 100, 256, 137, 293, 102, 258)(51, 207, 103, 259, 53, 209, 104, 260)(54, 210, 107, 263, 154, 310, 108, 264)(55, 211, 109, 265, 79, 235, 110, 266)(58, 214, 112, 268, 153, 309, 113, 269)(65, 221, 122, 278, 142, 298, 91, 247)(66, 222, 90, 246, 139, 295, 88, 244)(68, 224, 123, 279, 74, 230, 121, 277)(75, 231, 99, 255, 76, 232, 128, 284)(77, 233, 98, 254, 151, 307, 130, 286)(78, 234, 92, 248, 143, 299, 124, 280)(87, 243, 136, 292, 127, 283, 138, 294)(105, 261, 134, 290, 119, 275, 152, 308)(114, 270, 147, 303, 120, 276, 148, 304)(115, 271, 150, 306, 132, 288, 144, 300)(116, 272, 145, 301, 133, 289, 155, 311)(117, 273, 156, 312, 118, 274, 146, 302)(125, 281, 140, 296, 126, 282, 149, 305)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 172)(7, 175)(8, 158)(9, 180)(10, 161)(11, 184)(12, 187)(13, 160)(14, 192)(15, 194)(16, 197)(17, 162)(18, 202)(19, 164)(20, 206)(21, 209)(22, 211)(23, 213)(24, 200)(25, 165)(26, 220)(27, 222)(28, 224)(29, 167)(30, 212)(31, 169)(32, 230)(33, 232)(34, 203)(35, 234)(36, 235)(37, 170)(38, 196)(39, 171)(40, 195)(41, 173)(42, 243)(43, 246)(44, 181)(45, 183)(46, 190)(47, 174)(48, 191)(49, 255)(50, 257)(51, 176)(52, 261)(53, 262)(54, 177)(55, 186)(56, 178)(57, 259)(58, 179)(59, 270)(60, 272)(61, 274)(62, 253)(63, 277)(64, 269)(65, 182)(66, 248)(67, 276)(68, 185)(69, 280)(70, 282)(71, 271)(72, 242)(73, 245)(74, 283)(75, 188)(76, 285)(77, 189)(78, 254)(79, 193)(80, 241)(81, 268)(82, 288)(83, 267)(84, 205)(85, 208)(86, 226)(87, 293)(88, 198)(89, 296)(90, 297)(91, 199)(92, 201)(93, 300)(94, 302)(95, 304)(96, 291)(97, 223)(98, 204)(99, 290)(100, 306)(101, 207)(102, 308)(103, 214)(104, 301)(105, 236)(106, 210)(107, 229)(108, 299)(109, 311)(110, 219)(111, 292)(112, 238)(113, 221)(114, 227)(115, 215)(116, 295)(117, 216)(118, 298)(119, 217)(120, 218)(121, 312)(122, 307)(123, 309)(124, 294)(125, 225)(126, 228)(127, 231)(128, 303)(129, 233)(130, 305)(131, 310)(132, 237)(133, 239)(134, 240)(135, 256)(136, 289)(137, 244)(138, 281)(139, 273)(140, 263)(141, 247)(142, 275)(143, 265)(144, 260)(145, 249)(146, 284)(147, 250)(148, 286)(149, 251)(150, 252)(151, 287)(152, 279)(153, 258)(154, 278)(155, 264)(156, 266)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: chiral
Dual of E27.2172
Transitivity :: ET+ VT+
Graph:: simple
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.2174 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X1^3, X2^4, X2^4, X2^-2 * X1 * X2^-2 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 ]
Map:: non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 15, 17)(7, 18, 19)(9, 16, 22)(11, 25, 26)(12, 27, 28)(20, 33, 34)(21, 35, 36)(23, 37, 38)(24, 39, 40)(29, 45, 46)(30, 47, 48)(31, 49, 50)(32, 51, 52)(41, 61, 62)(42, 63, 64)(43, 65, 66)(44, 67, 68)(53, 77, 78)(54, 79, 80)(55, 81, 82)(56, 83, 84)(57, 85, 86)(58, 87, 88)(59, 89, 69)(60, 90, 70)(71, 97, 98)(72, 99, 100)(73, 101, 102)(74, 103, 104)(75, 105, 91)(76, 106, 92)(93, 119, 120)(94, 121, 122)(95, 123, 124)(96, 125, 126)(107, 127, 137)(108, 128, 138)(109, 139, 135)(110, 140, 136)(111, 133, 113)(112, 134, 114)(115, 141, 142)(116, 143, 144)(117, 145, 146)(118, 147, 148)(129, 149, 131)(130, 150, 132)(151, 155, 153)(152, 156, 154)(157, 159, 165, 161)(158, 162, 172, 163)(160, 167, 178, 168)(164, 176, 169, 177)(166, 179, 170, 180)(171, 185, 174, 186)(173, 187, 175, 188)(181, 197, 183, 198)(182, 199, 184, 200)(189, 209, 191, 210)(190, 211, 192, 212)(193, 213, 195, 214)(194, 215, 196, 216)(201, 225, 203, 226)(202, 227, 204, 228)(205, 229, 207, 230)(206, 231, 208, 232)(217, 247, 219, 248)(218, 249, 220, 250)(221, 251, 223, 252)(222, 233, 224, 235)(234, 263, 236, 264)(237, 265, 239, 266)(238, 267, 240, 268)(241, 269, 243, 270)(242, 271, 244, 272)(245, 273, 246, 274)(253, 283, 255, 284)(254, 285, 256, 286)(257, 287, 259, 288)(258, 289, 260, 290)(261, 291, 262, 292)(275, 301, 277, 303)(276, 298, 278, 300)(279, 297, 281, 299)(280, 305, 282, 306)(293, 307, 294, 308)(295, 309, 296, 310)(302, 311, 304, 312)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24^3 ), ( 24^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 3^52, 4^39 ]

E27.2175 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X1^4, X1^4, X1^4, X1^-1 * X2 * X1^-2 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1, X2 * X1^-2 * X2^5, X2^-1 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-2 * X1^-1 * X2^2 * X1^-1, X2^2 * X1 * X2^-2 * X1 * X2^-3 * X1 * X2^-3 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 17, 11)(5, 14, 18, 15)(7, 19, 12, 21)(8, 22, 13, 23)(10, 26, 37, 28)(16, 34, 38, 35)(20, 40, 30, 42)(24, 46, 31, 47)(25, 49, 29, 50)(27, 53, 36, 54)(32, 57, 33, 59)(39, 63, 43, 64)(41, 67, 48, 68)(44, 71, 45, 73)(51, 79, 56, 80)(52, 81, 55, 82)(58, 88, 60, 89)(61, 84, 62, 85)(65, 95, 70, 96)(66, 97, 69, 98)(72, 104, 74, 105)(75, 100, 76, 101)(77, 109, 78, 111)(83, 117, 86, 118)(87, 121, 90, 122)(91, 127, 92, 128)(93, 129, 94, 131)(99, 137, 102, 138)(103, 141, 106, 142)(107, 147, 108, 148)(110, 149, 112, 150)(113, 144, 114, 145)(115, 135, 116, 136)(119, 151, 120, 152)(123, 143, 126, 146)(124, 133, 125, 134)(130, 153, 132, 154)(139, 155, 140, 156)(157, 159, 166, 183, 194, 174, 162, 173, 193, 192, 172, 161)(158, 163, 176, 197, 187, 169, 160, 168, 186, 204, 180, 164)(165, 178, 200, 228, 212, 185, 167, 179, 201, 230, 207, 181)(170, 188, 214, 221, 195, 175, 171, 189, 216, 226, 199, 177)(182, 205, 233, 266, 242, 211, 184, 206, 234, 268, 239, 208)(190, 217, 247, 279, 243, 213, 191, 218, 248, 282, 246, 215)(196, 219, 249, 286, 258, 225, 198, 220, 250, 288, 255, 222)(202, 231, 263, 299, 259, 227, 203, 232, 264, 302, 262, 229)(209, 237, 271, 293, 276, 241, 210, 238, 272, 294, 275, 240)(223, 253, 291, 274, 296, 257, 224, 254, 292, 273, 295, 256)(235, 269, 287, 251, 289, 265, 236, 270, 285, 252, 290, 267)(244, 277, 303, 311, 305, 281, 245, 278, 304, 312, 306, 280)(260, 297, 284, 308, 309, 301, 261, 298, 283, 307, 310, 300)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 6^4 ), ( 6^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 4^39, 12^13 ]

E27.2176 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X2^3, X1^-1 * X2 * X1^-1 * X2^-1 * X1^-2 * X2^-1, X2 * X1^-5 * X2 * X1, X1^2 * X2^-1 * X1^-1 * X2^-1 * X1^3, (X2^-1 * X1^-1)^4, X1^2 * X2 * X1^-2 * X2^-1 * X1^2 * X2^-1 * X1^2 * X2^-1 ]
Map:: non-degenerate
	R = (1, 2, 6, 16, 42, 24, 48, 41, 56, 32, 12, 4)(3, 9, 23, 57, 74, 37, 35, 13, 34, 63, 27, 10)(5, 14, 36, 50, 20, 7, 19, 28, 65, 76, 40, 15)(8, 21, 52, 80, 45, 17, 39, 51, 89, 92, 55, 22)(11, 29, 66, 105, 97, 59, 25, 33, 71, 109, 68, 30)(18, 46, 82, 118, 77, 43, 54, 81, 125, 128, 84, 47)(26, 60, 98, 140, 116, 75, 38, 64, 103, 143, 100, 61)(31, 44, 78, 119, 148, 107, 67, 70, 112, 150, 111, 69)(49, 85, 129, 139, 136, 91, 53, 88, 132, 108, 130, 86)(58, 95, 138, 154, 137, 93, 72, 110, 149, 156, 126, 96)(62, 94, 122, 79, 121, 142, 99, 102, 127, 83, 124, 101)(73, 114, 120, 155, 131, 87, 104, 144, 117, 153, 152, 115)(90, 134, 106, 147, 145, 123, 133, 146, 113, 151, 141, 135)(157, 159, 161)(158, 163, 164)(160, 167, 169)(162, 173, 174)(165, 180, 181)(166, 182, 184)(168, 187, 189)(170, 193, 194)(171, 195, 197)(172, 199, 200)(175, 204, 191)(176, 205, 207)(177, 196, 209)(178, 210, 212)(179, 186, 214)(183, 218, 220)(185, 198, 223)(188, 203, 226)(190, 215, 228)(192, 217, 229)(201, 235, 237)(202, 211, 239)(206, 243, 244)(208, 242, 246)(213, 249, 250)(216, 230, 255)(219, 252, 258)(221, 231, 260)(222, 225, 262)(224, 264, 266)(227, 263, 269)(232, 271, 241)(233, 273, 268)(234, 240, 276)(236, 279, 280)(238, 278, 282)(245, 247, 289)(248, 291, 277)(251, 253, 295)(254, 257, 297)(256, 275, 300)(259, 298, 301)(261, 302, 286)(265, 290, 292)(267, 299, 307)(270, 272, 306)(274, 310, 311)(281, 283, 293)(284, 312, 309)(285, 287, 305)(288, 308, 294)(296, 303, 304)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^3 ), ( 8^12 ) }
Outer automorphisms :: chiral
Dual of E27.2178
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 3^52, 12^13 ]

E27.2177 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X1^3, X2^4, X2^4, X2^-2 * X1 * X2^-2 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1, X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 4, 160)(3, 159, 8, 164, 10, 166)(5, 161, 13, 169, 14, 170)(6, 162, 15, 171, 17, 173)(7, 163, 18, 174, 19, 175)(9, 165, 16, 172, 22, 178)(11, 167, 25, 181, 26, 182)(12, 168, 27, 183, 28, 184)(20, 176, 33, 189, 34, 190)(21, 177, 35, 191, 36, 192)(23, 179, 37, 193, 38, 194)(24, 180, 39, 195, 40, 196)(29, 185, 45, 201, 46, 202)(30, 186, 47, 203, 48, 204)(31, 187, 49, 205, 50, 206)(32, 188, 51, 207, 52, 208)(41, 197, 61, 217, 62, 218)(42, 198, 63, 219, 64, 220)(43, 199, 65, 221, 66, 222)(44, 200, 67, 223, 68, 224)(53, 209, 77, 233, 78, 234)(54, 210, 79, 235, 80, 236)(55, 211, 81, 237, 82, 238)(56, 212, 83, 239, 84, 240)(57, 213, 85, 241, 86, 242)(58, 214, 87, 243, 88, 244)(59, 215, 89, 245, 69, 225)(60, 216, 90, 246, 70, 226)(71, 227, 97, 253, 98, 254)(72, 228, 99, 255, 100, 256)(73, 229, 101, 257, 102, 258)(74, 230, 103, 259, 104, 260)(75, 231, 105, 261, 91, 247)(76, 232, 106, 262, 92, 248)(93, 249, 119, 275, 120, 276)(94, 250, 121, 277, 122, 278)(95, 251, 123, 279, 124, 280)(96, 252, 125, 281, 126, 282)(107, 263, 127, 283, 137, 293)(108, 264, 128, 284, 138, 294)(109, 265, 139, 295, 135, 291)(110, 266, 140, 296, 136, 292)(111, 267, 133, 289, 113, 269)(112, 268, 134, 290, 114, 270)(115, 271, 141, 297, 142, 298)(116, 272, 143, 299, 144, 300)(117, 273, 145, 301, 146, 302)(118, 274, 147, 303, 148, 304)(129, 285, 149, 305, 131, 287)(130, 286, 150, 306, 132, 288)(151, 307, 155, 311, 153, 309)(152, 308, 156, 312, 154, 310)
	L = (1, 159)(2, 162)(3, 165)(4, 167)(5, 157)(6, 172)(7, 158)(8, 176)(9, 161)(10, 179)(11, 178)(12, 160)(13, 177)(14, 180)(15, 185)(16, 163)(17, 187)(18, 186)(19, 188)(20, 169)(21, 164)(22, 168)(23, 170)(24, 166)(25, 197)(26, 199)(27, 198)(28, 200)(29, 174)(30, 171)(31, 175)(32, 173)(33, 209)(34, 211)(35, 210)(36, 212)(37, 213)(38, 215)(39, 214)(40, 216)(41, 183)(42, 181)(43, 184)(44, 182)(45, 225)(46, 227)(47, 226)(48, 228)(49, 229)(50, 231)(51, 230)(52, 232)(53, 191)(54, 189)(55, 192)(56, 190)(57, 195)(58, 193)(59, 196)(60, 194)(61, 247)(62, 249)(63, 248)(64, 250)(65, 251)(66, 233)(67, 252)(68, 235)(69, 203)(70, 201)(71, 204)(72, 202)(73, 207)(74, 205)(75, 208)(76, 206)(77, 224)(78, 263)(79, 222)(80, 264)(81, 265)(82, 267)(83, 266)(84, 268)(85, 269)(86, 271)(87, 270)(88, 272)(89, 273)(90, 274)(91, 219)(92, 217)(93, 220)(94, 218)(95, 223)(96, 221)(97, 283)(98, 285)(99, 284)(100, 286)(101, 287)(102, 289)(103, 288)(104, 290)(105, 291)(106, 292)(107, 236)(108, 234)(109, 239)(110, 237)(111, 240)(112, 238)(113, 243)(114, 241)(115, 244)(116, 242)(117, 246)(118, 245)(119, 301)(120, 298)(121, 303)(122, 300)(123, 297)(124, 305)(125, 299)(126, 306)(127, 255)(128, 253)(129, 256)(130, 254)(131, 259)(132, 257)(133, 260)(134, 258)(135, 262)(136, 261)(137, 307)(138, 308)(139, 309)(140, 310)(141, 281)(142, 278)(143, 279)(144, 276)(145, 277)(146, 311)(147, 275)(148, 312)(149, 282)(150, 280)(151, 294)(152, 293)(153, 296)(154, 295)(155, 304)(156, 302)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 6^52 ]

E27.2178 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X1^4, X1^4, X1^4, X1^-1 * X2 * X1^-2 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1^-1, X2 * X1^-2 * X2^5, X2^-1 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-2 * X1^-1 * X2^2 * X1^-1, X2^2 * X1 * X2^-2 * X1 * X2^-3 * X1 * X2^-3 * X1^-1 ]
Map:: non-degenerate
	R = (1, 157, 2, 158, 6, 162, 4, 160)(3, 159, 9, 165, 17, 173, 11, 167)(5, 161, 14, 170, 18, 174, 15, 171)(7, 163, 19, 175, 12, 168, 21, 177)(8, 164, 22, 178, 13, 169, 23, 179)(10, 166, 26, 182, 37, 193, 28, 184)(16, 172, 34, 190, 38, 194, 35, 191)(20, 176, 40, 196, 30, 186, 42, 198)(24, 180, 46, 202, 31, 187, 47, 203)(25, 181, 49, 205, 29, 185, 50, 206)(27, 183, 53, 209, 36, 192, 54, 210)(32, 188, 57, 213, 33, 189, 59, 215)(39, 195, 63, 219, 43, 199, 64, 220)(41, 197, 67, 223, 48, 204, 68, 224)(44, 200, 71, 227, 45, 201, 73, 229)(51, 207, 79, 235, 56, 212, 80, 236)(52, 208, 81, 237, 55, 211, 82, 238)(58, 214, 88, 244, 60, 216, 89, 245)(61, 217, 84, 240, 62, 218, 85, 241)(65, 221, 95, 251, 70, 226, 96, 252)(66, 222, 97, 253, 69, 225, 98, 254)(72, 228, 104, 260, 74, 230, 105, 261)(75, 231, 100, 256, 76, 232, 101, 257)(77, 233, 109, 265, 78, 234, 111, 267)(83, 239, 117, 273, 86, 242, 118, 274)(87, 243, 121, 277, 90, 246, 122, 278)(91, 247, 127, 283, 92, 248, 128, 284)(93, 249, 129, 285, 94, 250, 131, 287)(99, 255, 137, 293, 102, 258, 138, 294)(103, 259, 141, 297, 106, 262, 142, 298)(107, 263, 147, 303, 108, 264, 148, 304)(110, 266, 149, 305, 112, 268, 150, 306)(113, 269, 144, 300, 114, 270, 145, 301)(115, 271, 135, 291, 116, 272, 136, 292)(119, 275, 151, 307, 120, 276, 152, 308)(123, 279, 143, 299, 126, 282, 146, 302)(124, 280, 133, 289, 125, 281, 134, 290)(130, 286, 153, 309, 132, 288, 154, 310)(139, 295, 155, 311, 140, 296, 156, 312)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 176)(8, 158)(9, 178)(10, 183)(11, 179)(12, 186)(13, 160)(14, 188)(15, 189)(16, 161)(17, 193)(18, 162)(19, 171)(20, 197)(21, 170)(22, 200)(23, 201)(24, 164)(25, 165)(26, 205)(27, 194)(28, 206)(29, 167)(30, 204)(31, 169)(32, 214)(33, 216)(34, 217)(35, 218)(36, 172)(37, 192)(38, 174)(39, 175)(40, 219)(41, 187)(42, 220)(43, 177)(44, 228)(45, 230)(46, 231)(47, 232)(48, 180)(49, 233)(50, 234)(51, 181)(52, 182)(53, 237)(54, 238)(55, 184)(56, 185)(57, 191)(58, 221)(59, 190)(60, 226)(61, 247)(62, 248)(63, 249)(64, 250)(65, 195)(66, 196)(67, 253)(68, 254)(69, 198)(70, 199)(71, 203)(72, 212)(73, 202)(74, 207)(75, 263)(76, 264)(77, 266)(78, 268)(79, 269)(80, 270)(81, 271)(82, 272)(83, 208)(84, 209)(85, 210)(86, 211)(87, 213)(88, 277)(89, 278)(90, 215)(91, 279)(92, 282)(93, 286)(94, 288)(95, 289)(96, 290)(97, 291)(98, 292)(99, 222)(100, 223)(101, 224)(102, 225)(103, 227)(104, 297)(105, 298)(106, 229)(107, 299)(108, 302)(109, 236)(110, 242)(111, 235)(112, 239)(113, 287)(114, 285)(115, 293)(116, 294)(117, 295)(118, 296)(119, 240)(120, 241)(121, 303)(122, 304)(123, 243)(124, 244)(125, 245)(126, 246)(127, 307)(128, 308)(129, 252)(130, 258)(131, 251)(132, 255)(133, 265)(134, 267)(135, 274)(136, 273)(137, 276)(138, 275)(139, 256)(140, 257)(141, 284)(142, 283)(143, 259)(144, 260)(145, 261)(146, 262)(147, 311)(148, 312)(149, 281)(150, 280)(151, 310)(152, 309)(153, 301)(154, 300)(155, 305)(156, 306)
	local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2176
Transitivity :: ET+ VT+
Graph::
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.2179 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 1>)
Aut   = (C13 : C4) : C3 (small group id <156, 1>)
|r| :: 1
Presentation :: [ X2^3, X1^-1 * X2 * X1^-1 * X2^-1 * X1^-2 * X2^-1, X2 * X1^-5 * X2 * X1, X1^2 * X2^-1 * X1^-1 * X2^-1 * X1^3, (X2^-1 * X1^-1)^4, X1^2 * X2 * X1^-2 * X2^-1 * X1^2 * X2^-1 * X1^2 * X2^-1 ]
Map:: non-degenerate
	R = (1, 157, 2, 158, 6, 162, 16, 172, 42, 198, 24, 180, 48, 204, 41, 197, 56, 212, 32, 188, 12, 168, 4, 160)(3, 159, 9, 165, 23, 179, 57, 213, 74, 230, 37, 193, 35, 191, 13, 169, 34, 190, 63, 219, 27, 183, 10, 166)(5, 161, 14, 170, 36, 192, 50, 206, 20, 176, 7, 163, 19, 175, 28, 184, 65, 221, 76, 232, 40, 196, 15, 171)(8, 164, 21, 177, 52, 208, 80, 236, 45, 201, 17, 173, 39, 195, 51, 207, 89, 245, 92, 248, 55, 211, 22, 178)(11, 167, 29, 185, 66, 222, 105, 261, 97, 253, 59, 215, 25, 181, 33, 189, 71, 227, 109, 265, 68, 224, 30, 186)(18, 174, 46, 202, 82, 238, 118, 274, 77, 233, 43, 199, 54, 210, 81, 237, 125, 281, 128, 284, 84, 240, 47, 203)(26, 182, 60, 216, 98, 254, 140, 296, 116, 272, 75, 231, 38, 194, 64, 220, 103, 259, 143, 299, 100, 256, 61, 217)(31, 187, 44, 200, 78, 234, 119, 275, 148, 304, 107, 263, 67, 223, 70, 226, 112, 268, 150, 306, 111, 267, 69, 225)(49, 205, 85, 241, 129, 285, 139, 295, 136, 292, 91, 247, 53, 209, 88, 244, 132, 288, 108, 264, 130, 286, 86, 242)(58, 214, 95, 251, 138, 294, 154, 310, 137, 293, 93, 249, 72, 228, 110, 266, 149, 305, 156, 312, 126, 282, 96, 252)(62, 218, 94, 250, 122, 278, 79, 235, 121, 277, 142, 298, 99, 255, 102, 258, 127, 283, 83, 239, 124, 280, 101, 257)(73, 229, 114, 270, 120, 276, 155, 311, 131, 287, 87, 243, 104, 260, 144, 300, 117, 273, 153, 309, 152, 308, 115, 271)(90, 246, 134, 290, 106, 262, 147, 303, 145, 301, 123, 279, 133, 289, 146, 302, 113, 269, 151, 307, 141, 297, 135, 291)
	L = (1, 159)(2, 163)(3, 161)(4, 167)(5, 157)(6, 173)(7, 164)(8, 158)(9, 180)(10, 182)(11, 169)(12, 187)(13, 160)(14, 193)(15, 195)(16, 199)(17, 174)(18, 162)(19, 204)(20, 205)(21, 196)(22, 210)(23, 186)(24, 181)(25, 165)(26, 184)(27, 218)(28, 166)(29, 198)(30, 214)(31, 189)(32, 203)(33, 168)(34, 215)(35, 175)(36, 217)(37, 194)(38, 170)(39, 197)(40, 209)(41, 171)(42, 223)(43, 200)(44, 172)(45, 235)(46, 211)(47, 226)(48, 191)(49, 207)(50, 243)(51, 176)(52, 242)(53, 177)(54, 212)(55, 239)(56, 178)(57, 249)(58, 179)(59, 228)(60, 230)(61, 229)(62, 220)(63, 252)(64, 183)(65, 231)(66, 225)(67, 185)(68, 264)(69, 262)(70, 188)(71, 263)(72, 190)(73, 192)(74, 255)(75, 260)(76, 271)(77, 273)(78, 240)(79, 237)(80, 279)(81, 201)(82, 278)(83, 202)(84, 276)(85, 232)(86, 246)(87, 244)(88, 206)(89, 247)(90, 208)(91, 289)(92, 291)(93, 250)(94, 213)(95, 253)(96, 258)(97, 295)(98, 257)(99, 216)(100, 275)(101, 297)(102, 219)(103, 298)(104, 221)(105, 302)(106, 222)(107, 269)(108, 266)(109, 290)(110, 224)(111, 299)(112, 233)(113, 227)(114, 272)(115, 241)(116, 306)(117, 268)(118, 310)(119, 300)(120, 234)(121, 248)(122, 282)(123, 280)(124, 236)(125, 283)(126, 238)(127, 293)(128, 312)(129, 287)(130, 261)(131, 305)(132, 308)(133, 245)(134, 292)(135, 277)(136, 265)(137, 281)(138, 288)(139, 251)(140, 303)(141, 254)(142, 301)(143, 307)(144, 256)(145, 259)(146, 286)(147, 304)(148, 296)(149, 285)(150, 270)(151, 267)(152, 294)(153, 284)(154, 311)(155, 274)(156, 309)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2180 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^3, X2^4, (X1 * X2^-1 * X1^-1 * X2^-1)^2, X2^-2 * X1 * X2^2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1, X2^-2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2 * X1, X1 * X2^-1 * X1^-1 * X2^-2 * X1 * X2 * X1 * X2 * X1 * X2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 15, 17)(7, 18, 19)(9, 22, 23)(11, 26, 28)(12, 29, 30)(16, 37, 38)(20, 45, 44)(21, 47, 48)(24, 53, 55)(25, 56, 57)(27, 60, 61)(31, 67, 69)(32, 70, 39)(33, 71, 73)(34, 58, 74)(35, 75, 66)(36, 77, 78)(40, 84, 85)(41, 86, 88)(42, 89, 62)(43, 90, 92)(46, 95, 96)(49, 101, 100)(50, 80, 102)(51, 103, 104)(52, 105, 106)(54, 83, 108)(59, 115, 116)(63, 120, 121)(64, 122, 123)(65, 124, 126)(68, 97, 129)(72, 99, 132)(76, 131, 135)(79, 137, 133)(81, 138, 128)(82, 110, 139)(87, 136, 112)(91, 134, 127)(93, 117, 113)(94, 141, 125)(98, 114, 109)(107, 149, 140)(111, 119, 130)(118, 151, 142)(143, 147, 155)(144, 156, 148)(145, 153, 150)(146, 154, 152)(157, 159, 165, 161)(158, 162, 172, 163)(160, 167, 183, 168)(164, 176, 202, 177)(166, 180, 210, 181)(169, 187, 224, 188)(170, 189, 228, 190)(171, 191, 232, 192)(173, 195, 239, 196)(174, 197, 243, 198)(175, 199, 247, 200)(178, 205, 244, 206)(179, 207, 248, 208)(182, 214, 270, 215)(184, 218, 264, 219)(185, 220, 263, 209)(186, 221, 281, 222)(193, 235, 279, 236)(194, 237, 282, 238)(201, 249, 272, 250)(203, 253, 300, 254)(204, 255, 231, 256)(211, 265, 246, 266)(212, 267, 302, 259)(213, 268, 306, 269)(216, 273, 225, 258)(217, 274, 229, 275)(223, 283, 308, 284)(226, 251, 280, 286)(227, 261, 245, 287)(230, 289, 234, 290)(233, 292, 299, 252)(240, 262, 304, 294)(241, 296, 301, 257)(242, 297, 312, 298)(260, 278, 288, 303)(271, 305, 310, 291)(276, 295, 311, 307)(277, 285, 309, 293)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24^3 ), ( 24^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 3^52, 4^39 ]

E27.2181 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^3, X2^4, (X2 * X1 * X2 * X1^-1)^2, X2^-2 * X1 * X2^-2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 15, 17)(7, 18, 19)(9, 22, 23)(11, 26, 28)(12, 29, 30)(16, 37, 38)(20, 45, 44)(21, 47, 48)(24, 53, 55)(25, 56, 57)(27, 60, 61)(31, 67, 69)(32, 70, 39)(33, 71, 73)(34, 58, 74)(35, 75, 66)(36, 77, 78)(40, 84, 85)(41, 86, 88)(42, 89, 62)(43, 90, 92)(46, 95, 96)(49, 79, 100)(50, 101, 102)(51, 103, 104)(52, 105, 106)(54, 108, 109)(59, 116, 117)(63, 119, 120)(64, 121, 122)(65, 123, 125)(68, 94, 127)(72, 91, 124)(76, 135, 132)(80, 138, 111)(81, 133, 139)(82, 140, 97)(83, 110, 98)(87, 112, 141)(93, 130, 114)(99, 131, 129)(107, 134, 126)(113, 150, 136)(115, 151, 142)(118, 128, 137)(143, 154, 147)(144, 153, 146)(145, 148, 156)(149, 155, 152)(157, 159, 165, 161)(158, 162, 172, 163)(160, 167, 183, 168)(164, 176, 202, 177)(166, 180, 210, 181)(169, 187, 224, 188)(170, 189, 228, 190)(171, 191, 232, 192)(173, 195, 239, 196)(174, 197, 243, 198)(175, 199, 247, 200)(178, 205, 234, 206)(179, 207, 241, 208)(182, 214, 271, 215)(184, 218, 274, 219)(185, 220, 263, 209)(186, 221, 280, 222)(193, 235, 273, 236)(194, 237, 276, 238)(201, 249, 275, 250)(203, 253, 301, 254)(204, 255, 216, 256)(211, 266, 244, 267)(212, 268, 231, 259)(213, 269, 217, 270)(223, 282, 299, 251)(225, 258, 245, 264)(226, 284, 278, 285)(227, 261, 304, 286)(229, 287, 309, 288)(230, 289, 240, 290)(233, 292, 310, 293)(242, 283, 308, 291)(246, 296, 303, 260)(248, 257, 302, 298)(252, 281, 294, 300)(262, 305, 265, 272)(277, 297, 312, 307)(279, 306, 311, 295)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24^3 ), ( 24^4 ) }
Outer automorphisms :: chiral
Dual of E27.2191
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 3^52, 4^39 ]

E27.2182 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^4, (X1^-1 * X2^-1)^3, X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1^-2, (X2^-2 * X1^-1 * X2^-1)^2, X2^-3 * X1 * X2^-1 * X1^-1 * X2 * X1, X2^-1 * X1 * X2 * X1^-2 * X2^-3 * X1^2, X2^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 25, 11)(5, 14, 38, 15)(7, 19, 51, 21)(8, 22, 58, 23)(10, 28, 71, 30)(12, 33, 79, 35)(13, 36, 68, 26)(16, 42, 60, 43)(17, 45, 90, 47)(18, 48, 95, 49)(20, 53, 105, 55)(24, 62, 97, 63)(27, 69, 120, 70)(29, 72, 96, 61)(31, 76, 93, 46)(32, 78, 104, 52)(34, 56, 108, 81)(37, 75, 40, 84)(39, 67, 92, 64)(41, 80, 101, 59)(44, 82, 98, 54)(50, 99, 83, 100)(57, 109, 138, 91)(65, 115, 153, 116)(66, 117, 155, 112)(73, 110, 149, 121)(74, 125, 144, 103)(77, 94, 141, 127)(85, 123, 156, 130)(86, 111, 143, 131)(87, 129, 140, 134)(88, 113, 145, 132)(89, 102, 147, 133)(106, 142, 126, 148)(107, 151, 122, 137)(114, 136, 124, 154)(118, 150, 128, 146)(119, 152, 135, 139)(157, 159, 166, 185, 229, 280, 294, 291, 245, 200, 172, 161)(158, 163, 176, 210, 262, 306, 283, 312, 270, 220, 180, 164)(160, 168, 190, 236, 286, 303, 260, 304, 272, 228, 193, 169)(162, 173, 202, 248, 295, 271, 226, 277, 302, 257, 206, 174)(165, 182, 223, 199, 244, 290, 298, 251, 213, 177, 212, 183)(167, 187, 233, 189, 205, 254, 240, 288, 307, 266, 214, 188)(170, 195, 242, 289, 297, 255, 237, 273, 305, 261, 243, 196)(171, 197, 219, 269, 311, 275, 224, 250, 203, 184, 208, 175)(178, 215, 267, 310, 276, 231, 186, 230, 282, 232, 268, 216)(179, 217, 256, 301, 281, 241, 194, 225, 191, 209, 247, 201)(181, 221, 259, 207, 258, 293, 246, 292, 285, 235, 274, 222)(192, 238, 287, 309, 265, 218, 249, 296, 279, 227, 278, 239)(198, 211, 263, 308, 264, 300, 253, 204, 252, 299, 284, 234)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 6^4 ), ( 6^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 4^39, 12^13 ]

E27.2183 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^4, (X2^-1 * X1^-1)^3, (X2 * X1)^3, X2 * X1 * X2^-2 * X1^-1 * X2^-2 * X1, X1^-1 * X2^-1 * X1 * X2^4 * X1^-1, X2^-1 * X1^-1 * X2 * X1^-1 * X2^3 * X1, X2^-1 * X1^-2 * X2 * X1^-1 * X2^-2 * X1^2 * X2^-1 * X1^2, X1^-1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1^2 * X2^3 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 25, 11)(5, 14, 38, 15)(7, 19, 51, 21)(8, 22, 58, 23)(10, 28, 71, 30)(12, 33, 73, 35)(13, 36, 67, 26)(16, 42, 90, 43)(17, 45, 91, 47)(18, 48, 98, 49)(20, 53, 105, 55)(24, 62, 116, 63)(27, 68, 120, 69)(29, 59, 41, 74)(31, 77, 125, 78)(32, 79, 104, 52)(34, 70, 121, 83)(37, 76, 129, 85)(39, 66, 118, 82)(40, 72, 124, 88)(44, 61, 107, 54)(46, 93, 139, 95)(50, 101, 148, 102)(56, 109, 65, 110)(57, 111, 138, 92)(60, 106, 150, 114)(64, 100, 141, 94)(75, 128, 147, 112)(80, 127, 137, 133)(81, 97, 145, 130)(84, 122, 151, 113)(86, 134, 149, 115)(87, 99, 140, 126)(89, 119, 142, 123)(96, 143, 103, 144)(108, 152, 117, 146)(131, 153, 135, 155)(132, 154, 136, 156)(157, 159, 166, 185, 229, 281, 303, 255, 204, 200, 172, 161)(158, 163, 176, 210, 181, 221, 273, 240, 192, 220, 180, 164)(160, 168, 190, 238, 247, 293, 271, 216, 178, 215, 193, 169)(162, 173, 202, 250, 207, 259, 245, 196, 170, 195, 206, 174)(165, 182, 222, 199, 227, 279, 304, 288, 235, 278, 226, 183)(167, 187, 213, 177, 212, 253, 203, 252, 224, 191, 236, 188)(171, 197, 219, 261, 305, 285, 310, 267, 228, 184, 208, 175)(179, 217, 258, 295, 284, 246, 292, 301, 262, 209, 248, 201)(186, 231, 270, 223, 275, 309, 265, 297, 280, 234, 286, 232)(189, 205, 256, 241, 277, 308, 272, 312, 276, 296, 249, 237)(194, 242, 291, 299, 274, 306, 266, 225, 198, 211, 264, 243)(214, 268, 311, 283, 230, 282, 300, 260, 218, 251, 298, 269)(233, 263, 307, 289, 294, 257, 239, 290, 244, 254, 302, 287)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 6^4 ), ( 6^12 ) }
Outer automorphisms :: chiral
Dual of E27.2186
Transitivity :: ET+
Graph:: simple bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 4^39, 12^13 ]

E27.2184 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^3, (X1^2 * X2^-1)^2, (X2 * X1)^4, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-4, X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1, X1^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 16, 39, 84, 137, 122, 69, 30, 12, 4)(3, 9, 23, 55, 73, 126, 154, 120, 65, 44, 18, 10)(5, 14, 29, 67, 114, 148, 155, 145, 112, 82, 37, 15)(7, 19, 45, 78, 34, 77, 103, 58, 24, 57, 41, 20)(8, 21, 11, 28, 64, 118, 124, 135, 147, 100, 53, 22)(13, 32, 68, 56, 104, 113, 144, 107, 95, 49, 76, 33)(17, 42, 66, 97, 50, 96, 131, 91, 46, 38, 83, 43)(25, 59, 26, 61, 111, 141, 87, 54, 101, 86, 40, 60)(27, 62, 72, 31, 71, 121, 119, 132, 149, 106, 117, 63)(35, 79, 36, 81, 136, 156, 150, 110, 151, 140, 102, 80)(47, 92, 48, 94, 108, 125, 109, 90, 143, 139, 85, 93)(51, 98, 52, 70, 123, 152, 115, 146, 116, 153, 130, 99)(74, 127, 75, 129, 105, 138, 133, 88, 134, 89, 142, 128)(157, 159, 161)(158, 163, 164)(160, 167, 169)(162, 173, 174)(165, 180, 181)(166, 182, 183)(168, 185, 187)(170, 190, 191)(171, 192, 194)(172, 196, 197)(175, 202, 203)(176, 204, 205)(177, 206, 207)(178, 208, 210)(179, 212, 193)(184, 221, 222)(186, 224, 226)(188, 229, 230)(189, 231, 213)(195, 241, 239)(198, 243, 244)(199, 245, 238)(200, 228, 246)(201, 223, 209)(211, 258, 259)(214, 261, 262)(215, 263, 264)(216, 265, 266)(217, 268, 269)(218, 270, 271)(219, 272, 233)(220, 275, 232)(225, 277, 237)(227, 280, 281)(234, 286, 287)(235, 288, 289)(236, 290, 291)(240, 294, 257)(242, 296, 256)(247, 292, 300)(248, 301, 284)(249, 283, 302)(250, 303, 304)(251, 305, 252)(253, 273, 267)(254, 260, 306)(255, 307, 282)(274, 298, 310)(276, 295, 309)(278, 308, 285)(279, 311, 297)(293, 312, 299)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^3 ), ( 8^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 3^52, 12^13 ]

E27.2185 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 4, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^3, (X1^-2 * X2)^2, (X2^-1 * X1^-1)^4, X1^-1 * X2 * X1^4 * X2 * X1 * X2^-1, X1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^3, X2^-1 * X1^-1 * X2^-1 * X1^-2 * X2^-1 * X1^-2 * X2^-1 * X1, X1^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 16, 39, 84, 112, 125, 69, 30, 12, 4)(3, 9, 23, 55, 49, 100, 129, 143, 93, 44, 18, 10)(5, 14, 29, 67, 110, 104, 51, 103, 52, 82, 37, 15)(7, 19, 45, 95, 91, 142, 147, 132, 139, 87, 41, 20)(8, 21, 11, 28, 64, 63, 27, 62, 92, 105, 53, 22)(13, 32, 68, 124, 130, 80, 35, 79, 36, 81, 76, 33)(17, 42, 88, 140, 138, 150, 117, 134, 118, 137, 85, 43)(24, 57, 108, 131, 144, 155, 121, 66, 102, 50, 101, 58)(25, 59, 26, 61, 97, 46, 38, 83, 133, 151, 113, 60)(31, 71, 114, 90, 141, 96, 74, 94, 75, 128, 109, 72)(34, 77, 120, 65, 119, 153, 152, 115, 145, 111, 123, 78)(40, 73, 127, 156, 122, 135, 146, 149, 107, 116, 136, 86)(47, 98, 48, 99, 56, 89, 54, 106, 148, 154, 126, 70)(157, 159, 161)(158, 163, 164)(160, 167, 169)(162, 173, 174)(165, 180, 181)(166, 182, 183)(168, 185, 187)(170, 190, 191)(171, 192, 194)(172, 196, 197)(175, 202, 203)(176, 204, 205)(177, 206, 207)(178, 208, 210)(179, 212, 193)(184, 221, 222)(186, 224, 226)(188, 229, 230)(189, 231, 213)(195, 234, 241)(198, 245, 227)(199, 246, 247)(200, 248, 250)(201, 252, 209)(211, 263, 257)(214, 265, 266)(215, 267, 268)(216, 225, 270)(217, 251, 271)(218, 272, 273)(219, 274, 233)(220, 253, 232)(223, 278, 279)(228, 262, 275)(235, 243, 285)(236, 249, 244)(237, 287, 288)(238, 289, 290)(239, 291, 282)(240, 258, 292)(242, 280, 294)(254, 277, 281)(255, 296, 300)(256, 301, 302)(259, 293, 303)(260, 295, 283)(261, 304, 305)(264, 306, 269)(276, 310, 286)(284, 308, 299)(297, 312, 307)(298, 311, 309)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 8^3 ), ( 8^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 156 f = 39
	degree seq :: [ 3^52, 12^13 ]

E27.2186 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^3, X2^4, (X1 * X2^-1 * X1^-1 * X2^-1)^2, X2^-2 * X1 * X2^2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1, X2^-2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1^-1 * X2 * X1, X1 * X2^-1 * X1^-1 * X2^-2 * X1 * X2 * X1 * X2 * X1 * X2 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 4, 160)(3, 159, 8, 164, 10, 166)(5, 161, 13, 169, 14, 170)(6, 162, 15, 171, 17, 173)(7, 163, 18, 174, 19, 175)(9, 165, 22, 178, 23, 179)(11, 167, 26, 182, 28, 184)(12, 168, 29, 185, 30, 186)(16, 172, 37, 193, 38, 194)(20, 176, 45, 201, 44, 200)(21, 177, 47, 203, 48, 204)(24, 180, 53, 209, 55, 211)(25, 181, 56, 212, 57, 213)(27, 183, 60, 216, 61, 217)(31, 187, 67, 223, 69, 225)(32, 188, 70, 226, 39, 195)(33, 189, 71, 227, 73, 229)(34, 190, 58, 214, 74, 230)(35, 191, 75, 231, 66, 222)(36, 192, 77, 233, 78, 234)(40, 196, 84, 240, 85, 241)(41, 197, 86, 242, 88, 244)(42, 198, 89, 245, 62, 218)(43, 199, 90, 246, 92, 248)(46, 202, 95, 251, 96, 252)(49, 205, 101, 257, 100, 256)(50, 206, 80, 236, 102, 258)(51, 207, 103, 259, 104, 260)(52, 208, 105, 261, 106, 262)(54, 210, 83, 239, 108, 264)(59, 215, 115, 271, 116, 272)(63, 219, 120, 276, 121, 277)(64, 220, 122, 278, 123, 279)(65, 221, 124, 280, 126, 282)(68, 224, 97, 253, 129, 285)(72, 228, 99, 255, 132, 288)(76, 232, 131, 287, 135, 291)(79, 235, 137, 293, 133, 289)(81, 237, 138, 294, 128, 284)(82, 238, 110, 266, 139, 295)(87, 243, 136, 292, 112, 268)(91, 247, 134, 290, 127, 283)(93, 249, 117, 273, 113, 269)(94, 250, 141, 297, 125, 281)(98, 254, 114, 270, 109, 265)(107, 263, 149, 305, 140, 296)(111, 267, 119, 275, 130, 286)(118, 274, 151, 307, 142, 298)(143, 299, 147, 303, 155, 311)(144, 300, 156, 312, 148, 304)(145, 301, 153, 309, 150, 306)(146, 302, 154, 310, 152, 308)
	L = (1, 159)(2, 162)(3, 165)(4, 167)(5, 157)(6, 172)(7, 158)(8, 176)(9, 161)(10, 180)(11, 183)(12, 160)(13, 187)(14, 189)(15, 191)(16, 163)(17, 195)(18, 197)(19, 199)(20, 202)(21, 164)(22, 205)(23, 207)(24, 210)(25, 166)(26, 214)(27, 168)(28, 218)(29, 220)(30, 221)(31, 224)(32, 169)(33, 228)(34, 170)(35, 232)(36, 171)(37, 235)(38, 237)(39, 239)(40, 173)(41, 243)(42, 174)(43, 247)(44, 175)(45, 249)(46, 177)(47, 253)(48, 255)(49, 244)(50, 178)(51, 248)(52, 179)(53, 185)(54, 181)(55, 265)(56, 267)(57, 268)(58, 270)(59, 182)(60, 273)(61, 274)(62, 264)(63, 184)(64, 263)(65, 281)(66, 186)(67, 283)(68, 188)(69, 258)(70, 251)(71, 261)(72, 190)(73, 275)(74, 289)(75, 256)(76, 192)(77, 292)(78, 290)(79, 279)(80, 193)(81, 282)(82, 194)(83, 196)(84, 262)(85, 296)(86, 297)(87, 198)(88, 206)(89, 287)(90, 266)(91, 200)(92, 208)(93, 272)(94, 201)(95, 280)(96, 233)(97, 300)(98, 203)(99, 231)(100, 204)(101, 241)(102, 216)(103, 212)(104, 278)(105, 245)(106, 304)(107, 209)(108, 219)(109, 246)(110, 211)(111, 302)(112, 306)(113, 213)(114, 215)(115, 305)(116, 250)(117, 225)(118, 229)(119, 217)(120, 295)(121, 285)(122, 288)(123, 236)(124, 286)(125, 222)(126, 238)(127, 308)(128, 223)(129, 309)(130, 226)(131, 227)(132, 303)(133, 234)(134, 230)(135, 271)(136, 299)(137, 277)(138, 240)(139, 311)(140, 301)(141, 312)(142, 242)(143, 252)(144, 254)(145, 257)(146, 259)(147, 260)(148, 294)(149, 310)(150, 269)(151, 276)(152, 284)(153, 293)(154, 291)(155, 307)(156, 298)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2183
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 6^52 ]

E27.2187 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^3, X2^4, (X2 * X1 * X2 * X1^-1)^2, X2^-2 * X1 * X2^-2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 4, 160)(3, 159, 8, 164, 10, 166)(5, 161, 13, 169, 14, 170)(6, 162, 15, 171, 17, 173)(7, 163, 18, 174, 19, 175)(9, 165, 22, 178, 23, 179)(11, 167, 26, 182, 28, 184)(12, 168, 29, 185, 30, 186)(16, 172, 37, 193, 38, 194)(20, 176, 45, 201, 44, 200)(21, 177, 47, 203, 48, 204)(24, 180, 53, 209, 55, 211)(25, 181, 56, 212, 57, 213)(27, 183, 60, 216, 61, 217)(31, 187, 67, 223, 69, 225)(32, 188, 70, 226, 39, 195)(33, 189, 71, 227, 73, 229)(34, 190, 58, 214, 74, 230)(35, 191, 75, 231, 66, 222)(36, 192, 77, 233, 78, 234)(40, 196, 84, 240, 85, 241)(41, 197, 86, 242, 88, 244)(42, 198, 89, 245, 62, 218)(43, 199, 90, 246, 92, 248)(46, 202, 95, 251, 96, 252)(49, 205, 79, 235, 100, 256)(50, 206, 101, 257, 102, 258)(51, 207, 103, 259, 104, 260)(52, 208, 105, 261, 106, 262)(54, 210, 108, 264, 109, 265)(59, 215, 116, 272, 117, 273)(63, 219, 119, 275, 120, 276)(64, 220, 121, 277, 122, 278)(65, 221, 123, 279, 125, 281)(68, 224, 94, 250, 127, 283)(72, 228, 91, 247, 124, 280)(76, 232, 135, 291, 132, 288)(80, 236, 138, 294, 111, 267)(81, 237, 133, 289, 139, 295)(82, 238, 140, 296, 97, 253)(83, 239, 110, 266, 98, 254)(87, 243, 112, 268, 141, 297)(93, 249, 130, 286, 114, 270)(99, 255, 131, 287, 129, 285)(107, 263, 134, 290, 126, 282)(113, 269, 150, 306, 136, 292)(115, 271, 151, 307, 142, 298)(118, 274, 128, 284, 137, 293)(143, 299, 154, 310, 147, 303)(144, 300, 153, 309, 146, 302)(145, 301, 148, 304, 156, 312)(149, 305, 155, 311, 152, 308)
	L = (1, 159)(2, 162)(3, 165)(4, 167)(5, 157)(6, 172)(7, 158)(8, 176)(9, 161)(10, 180)(11, 183)(12, 160)(13, 187)(14, 189)(15, 191)(16, 163)(17, 195)(18, 197)(19, 199)(20, 202)(21, 164)(22, 205)(23, 207)(24, 210)(25, 166)(26, 214)(27, 168)(28, 218)(29, 220)(30, 221)(31, 224)(32, 169)(33, 228)(34, 170)(35, 232)(36, 171)(37, 235)(38, 237)(39, 239)(40, 173)(41, 243)(42, 174)(43, 247)(44, 175)(45, 249)(46, 177)(47, 253)(48, 255)(49, 234)(50, 178)(51, 241)(52, 179)(53, 185)(54, 181)(55, 266)(56, 268)(57, 269)(58, 271)(59, 182)(60, 256)(61, 270)(62, 274)(63, 184)(64, 263)(65, 280)(66, 186)(67, 282)(68, 188)(69, 258)(70, 284)(71, 261)(72, 190)(73, 287)(74, 289)(75, 259)(76, 192)(77, 292)(78, 206)(79, 273)(80, 193)(81, 276)(82, 194)(83, 196)(84, 290)(85, 208)(86, 283)(87, 198)(88, 267)(89, 264)(90, 296)(91, 200)(92, 257)(93, 275)(94, 201)(95, 223)(96, 281)(97, 301)(98, 203)(99, 216)(100, 204)(101, 302)(102, 245)(103, 212)(104, 246)(105, 304)(106, 305)(107, 209)(108, 225)(109, 272)(110, 244)(111, 211)(112, 231)(113, 217)(114, 213)(115, 215)(116, 262)(117, 236)(118, 219)(119, 250)(120, 238)(121, 297)(122, 285)(123, 306)(124, 222)(125, 294)(126, 299)(127, 308)(128, 278)(129, 226)(130, 227)(131, 309)(132, 229)(133, 240)(134, 230)(135, 242)(136, 310)(137, 233)(138, 300)(139, 279)(140, 303)(141, 312)(142, 248)(143, 251)(144, 252)(145, 254)(146, 298)(147, 260)(148, 286)(149, 265)(150, 311)(151, 277)(152, 291)(153, 288)(154, 293)(155, 295)(156, 307)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 52 e = 156 f = 52
	degree seq :: [ 6^52 ]

E27.2188 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^4, (X1^-1 * X2^-1)^3, X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1^-2, (X2^-2 * X1^-1 * X2^-1)^2, X2^-3 * X1 * X2^-1 * X1^-1 * X2 * X1, X2^-1 * X1 * X2 * X1^-2 * X2^-3 * X1^2, X2^12 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 4, 160)(3, 159, 9, 165, 25, 181, 11, 167)(5, 161, 14, 170, 38, 194, 15, 171)(7, 163, 19, 175, 51, 207, 21, 177)(8, 164, 22, 178, 58, 214, 23, 179)(10, 166, 28, 184, 71, 227, 30, 186)(12, 168, 33, 189, 79, 235, 35, 191)(13, 169, 36, 192, 68, 224, 26, 182)(16, 172, 42, 198, 60, 216, 43, 199)(17, 173, 45, 201, 90, 246, 47, 203)(18, 174, 48, 204, 95, 251, 49, 205)(20, 176, 53, 209, 105, 261, 55, 211)(24, 180, 62, 218, 97, 253, 63, 219)(27, 183, 69, 225, 120, 276, 70, 226)(29, 185, 72, 228, 96, 252, 61, 217)(31, 187, 76, 232, 93, 249, 46, 202)(32, 188, 78, 234, 104, 260, 52, 208)(34, 190, 56, 212, 108, 264, 81, 237)(37, 193, 75, 231, 40, 196, 84, 240)(39, 195, 67, 223, 92, 248, 64, 220)(41, 197, 80, 236, 101, 257, 59, 215)(44, 200, 82, 238, 98, 254, 54, 210)(50, 206, 99, 255, 83, 239, 100, 256)(57, 213, 109, 265, 138, 294, 91, 247)(65, 221, 115, 271, 153, 309, 116, 272)(66, 222, 117, 273, 155, 311, 112, 268)(73, 229, 110, 266, 149, 305, 121, 277)(74, 230, 125, 281, 144, 300, 103, 259)(77, 233, 94, 250, 141, 297, 127, 283)(85, 241, 123, 279, 156, 312, 130, 286)(86, 242, 111, 267, 143, 299, 131, 287)(87, 243, 129, 285, 140, 296, 134, 290)(88, 244, 113, 269, 145, 301, 132, 288)(89, 245, 102, 258, 147, 303, 133, 289)(106, 262, 142, 298, 126, 282, 148, 304)(107, 263, 151, 307, 122, 278, 137, 293)(114, 270, 136, 292, 124, 280, 154, 310)(118, 274, 150, 306, 128, 284, 146, 302)(119, 275, 152, 308, 135, 291, 139, 295)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 176)(8, 158)(9, 182)(10, 185)(11, 187)(12, 190)(13, 160)(14, 195)(15, 197)(16, 161)(17, 202)(18, 162)(19, 171)(20, 210)(21, 212)(22, 215)(23, 217)(24, 164)(25, 221)(26, 223)(27, 165)(28, 208)(29, 229)(30, 230)(31, 233)(32, 167)(33, 205)(34, 236)(35, 209)(36, 238)(37, 169)(38, 225)(39, 242)(40, 170)(41, 219)(42, 211)(43, 244)(44, 172)(45, 179)(46, 248)(47, 184)(48, 252)(49, 254)(50, 174)(51, 258)(52, 175)(53, 247)(54, 262)(55, 263)(56, 183)(57, 177)(58, 188)(59, 267)(60, 178)(61, 256)(62, 249)(63, 269)(64, 180)(65, 259)(66, 181)(67, 199)(68, 250)(69, 191)(70, 277)(71, 278)(72, 193)(73, 280)(74, 282)(75, 186)(76, 268)(77, 189)(78, 198)(79, 274)(80, 286)(81, 273)(82, 287)(83, 192)(84, 288)(85, 194)(86, 289)(87, 196)(88, 290)(89, 200)(90, 292)(91, 201)(92, 295)(93, 296)(94, 203)(95, 213)(96, 299)(97, 204)(98, 240)(99, 237)(100, 301)(101, 206)(102, 293)(103, 207)(104, 304)(105, 243)(106, 306)(107, 308)(108, 300)(109, 218)(110, 214)(111, 310)(112, 216)(113, 311)(114, 220)(115, 226)(116, 228)(117, 305)(118, 222)(119, 224)(120, 231)(121, 302)(122, 239)(123, 227)(124, 294)(125, 241)(126, 232)(127, 312)(128, 234)(129, 235)(130, 303)(131, 309)(132, 307)(133, 297)(134, 298)(135, 245)(136, 285)(137, 246)(138, 291)(139, 271)(140, 279)(141, 255)(142, 251)(143, 284)(144, 253)(145, 281)(146, 257)(147, 260)(148, 272)(149, 261)(150, 283)(151, 266)(152, 264)(153, 265)(154, 276)(155, 275)(156, 270)
	local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: simple
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.2189 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^4, (X2^-1 * X1^-1)^3, (X2 * X1)^3, X2 * X1 * X2^-2 * X1^-1 * X2^-2 * X1, X1^-1 * X2^-1 * X1 * X2^4 * X1^-1, X2^-1 * X1^-1 * X2 * X1^-1 * X2^3 * X1, X2^-1 * X1^-2 * X2 * X1^-1 * X2^-2 * X1^2 * X2^-1 * X1^2, X1^-1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1^2 * X2^3 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 4, 160)(3, 159, 9, 165, 25, 181, 11, 167)(5, 161, 14, 170, 38, 194, 15, 171)(7, 163, 19, 175, 51, 207, 21, 177)(8, 164, 22, 178, 58, 214, 23, 179)(10, 166, 28, 184, 71, 227, 30, 186)(12, 168, 33, 189, 73, 229, 35, 191)(13, 169, 36, 192, 67, 223, 26, 182)(16, 172, 42, 198, 90, 246, 43, 199)(17, 173, 45, 201, 91, 247, 47, 203)(18, 174, 48, 204, 98, 254, 49, 205)(20, 176, 53, 209, 105, 261, 55, 211)(24, 180, 62, 218, 116, 272, 63, 219)(27, 183, 68, 224, 120, 276, 69, 225)(29, 185, 59, 215, 41, 197, 74, 230)(31, 187, 77, 233, 125, 281, 78, 234)(32, 188, 79, 235, 104, 260, 52, 208)(34, 190, 70, 226, 121, 277, 83, 239)(37, 193, 76, 232, 129, 285, 85, 241)(39, 195, 66, 222, 118, 274, 82, 238)(40, 196, 72, 228, 124, 280, 88, 244)(44, 200, 61, 217, 107, 263, 54, 210)(46, 202, 93, 249, 139, 295, 95, 251)(50, 206, 101, 257, 148, 304, 102, 258)(56, 212, 109, 265, 65, 221, 110, 266)(57, 213, 111, 267, 138, 294, 92, 248)(60, 216, 106, 262, 150, 306, 114, 270)(64, 220, 100, 256, 141, 297, 94, 250)(75, 231, 128, 284, 147, 303, 112, 268)(80, 236, 127, 283, 137, 293, 133, 289)(81, 237, 97, 253, 145, 301, 130, 286)(84, 240, 122, 278, 151, 307, 113, 269)(86, 242, 134, 290, 149, 305, 115, 271)(87, 243, 99, 255, 140, 296, 126, 282)(89, 245, 119, 275, 142, 298, 123, 279)(96, 252, 143, 299, 103, 259, 144, 300)(108, 264, 152, 308, 117, 273, 146, 302)(131, 287, 153, 309, 135, 291, 155, 311)(132, 288, 154, 310, 136, 292, 156, 312)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 176)(8, 158)(9, 182)(10, 185)(11, 187)(12, 190)(13, 160)(14, 195)(15, 197)(16, 161)(17, 202)(18, 162)(19, 171)(20, 210)(21, 212)(22, 215)(23, 217)(24, 164)(25, 221)(26, 222)(27, 165)(28, 208)(29, 229)(30, 231)(31, 213)(32, 167)(33, 205)(34, 238)(35, 236)(36, 220)(37, 169)(38, 242)(39, 206)(40, 170)(41, 219)(42, 211)(43, 227)(44, 172)(45, 179)(46, 250)(47, 252)(48, 200)(49, 256)(50, 174)(51, 259)(52, 175)(53, 248)(54, 181)(55, 264)(56, 253)(57, 177)(58, 268)(59, 193)(60, 178)(61, 258)(62, 251)(63, 261)(64, 180)(65, 273)(66, 199)(67, 275)(68, 191)(69, 198)(70, 183)(71, 279)(72, 184)(73, 281)(74, 282)(75, 270)(76, 186)(77, 263)(78, 286)(79, 278)(80, 188)(81, 189)(82, 247)(83, 290)(84, 192)(85, 277)(86, 291)(87, 194)(88, 254)(89, 196)(90, 292)(91, 293)(92, 201)(93, 237)(94, 207)(95, 298)(96, 224)(97, 203)(98, 302)(99, 204)(100, 241)(101, 239)(102, 295)(103, 245)(104, 218)(105, 305)(106, 209)(107, 307)(108, 243)(109, 297)(110, 225)(111, 228)(112, 311)(113, 214)(114, 223)(115, 216)(116, 312)(117, 240)(118, 306)(119, 309)(120, 296)(121, 308)(122, 226)(123, 304)(124, 234)(125, 303)(126, 300)(127, 230)(128, 246)(129, 310)(130, 232)(131, 233)(132, 235)(133, 294)(134, 244)(135, 299)(136, 301)(137, 271)(138, 257)(139, 284)(140, 249)(141, 280)(142, 269)(143, 274)(144, 260)(145, 262)(146, 287)(147, 255)(148, 288)(149, 285)(150, 266)(151, 289)(152, 272)(153, 265)(154, 267)(155, 283)(156, 276)
	local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: simple
	v = 39 e = 156 f = 65
	degree seq :: [ 8^39 ]

E27.2190 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^3, (X1^2 * X2^-1)^2, (X2 * X1)^4, X2^-1 * X1^-1 * X2^-1 * X1 * X2 * X1^-4, X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1, X1^12 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 16, 172, 39, 195, 84, 240, 137, 293, 122, 278, 69, 225, 30, 186, 12, 168, 4, 160)(3, 159, 9, 165, 23, 179, 55, 211, 73, 229, 126, 282, 154, 310, 120, 276, 65, 221, 44, 200, 18, 174, 10, 166)(5, 161, 14, 170, 29, 185, 67, 223, 114, 270, 148, 304, 155, 311, 145, 301, 112, 268, 82, 238, 37, 193, 15, 171)(7, 163, 19, 175, 45, 201, 78, 234, 34, 190, 77, 233, 103, 259, 58, 214, 24, 180, 57, 213, 41, 197, 20, 176)(8, 164, 21, 177, 11, 167, 28, 184, 64, 220, 118, 274, 124, 280, 135, 291, 147, 303, 100, 256, 53, 209, 22, 178)(13, 169, 32, 188, 68, 224, 56, 212, 104, 260, 113, 269, 144, 300, 107, 263, 95, 251, 49, 205, 76, 232, 33, 189)(17, 173, 42, 198, 66, 222, 97, 253, 50, 206, 96, 252, 131, 287, 91, 247, 46, 202, 38, 194, 83, 239, 43, 199)(25, 181, 59, 215, 26, 182, 61, 217, 111, 267, 141, 297, 87, 243, 54, 210, 101, 257, 86, 242, 40, 196, 60, 216)(27, 183, 62, 218, 72, 228, 31, 187, 71, 227, 121, 277, 119, 275, 132, 288, 149, 305, 106, 262, 117, 273, 63, 219)(35, 191, 79, 235, 36, 192, 81, 237, 136, 292, 156, 312, 150, 306, 110, 266, 151, 307, 140, 296, 102, 258, 80, 236)(47, 203, 92, 248, 48, 204, 94, 250, 108, 264, 125, 281, 109, 265, 90, 246, 143, 299, 139, 295, 85, 241, 93, 249)(51, 207, 98, 254, 52, 208, 70, 226, 123, 279, 152, 308, 115, 271, 146, 302, 116, 272, 153, 309, 130, 286, 99, 255)(74, 230, 127, 283, 75, 231, 129, 285, 105, 261, 138, 294, 133, 289, 88, 244, 134, 290, 89, 245, 142, 298, 128, 284)
	L = (1, 159)(2, 163)(3, 161)(4, 167)(5, 157)(6, 173)(7, 164)(8, 158)(9, 180)(10, 182)(11, 169)(12, 185)(13, 160)(14, 190)(15, 192)(16, 196)(17, 174)(18, 162)(19, 202)(20, 204)(21, 206)(22, 208)(23, 212)(24, 181)(25, 165)(26, 183)(27, 166)(28, 221)(29, 187)(30, 224)(31, 168)(32, 229)(33, 231)(34, 191)(35, 170)(36, 194)(37, 179)(38, 171)(39, 241)(40, 197)(41, 172)(42, 243)(43, 245)(44, 228)(45, 223)(46, 203)(47, 175)(48, 205)(49, 176)(50, 207)(51, 177)(52, 210)(53, 201)(54, 178)(55, 258)(56, 193)(57, 189)(58, 261)(59, 263)(60, 265)(61, 268)(62, 270)(63, 272)(64, 275)(65, 222)(66, 184)(67, 209)(68, 226)(69, 277)(70, 186)(71, 280)(72, 246)(73, 230)(74, 188)(75, 213)(76, 220)(77, 219)(78, 286)(79, 288)(80, 290)(81, 225)(82, 199)(83, 195)(84, 294)(85, 239)(86, 296)(87, 244)(88, 198)(89, 238)(90, 200)(91, 292)(92, 301)(93, 283)(94, 303)(95, 305)(96, 251)(97, 273)(98, 260)(99, 307)(100, 242)(101, 240)(102, 259)(103, 211)(104, 306)(105, 262)(106, 214)(107, 264)(108, 215)(109, 266)(110, 216)(111, 253)(112, 269)(113, 217)(114, 271)(115, 218)(116, 233)(117, 267)(118, 298)(119, 232)(120, 295)(121, 237)(122, 308)(123, 311)(124, 281)(125, 227)(126, 255)(127, 302)(128, 248)(129, 278)(130, 287)(131, 234)(132, 289)(133, 235)(134, 291)(135, 236)(136, 300)(137, 312)(138, 257)(139, 309)(140, 256)(141, 279)(142, 310)(143, 293)(144, 247)(145, 284)(146, 249)(147, 304)(148, 250)(149, 252)(150, 254)(151, 282)(152, 285)(153, 276)(154, 274)(155, 297)(156, 299)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2191 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 4, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^3, (X1^-2 * X2)^2, (X2^-1 * X1^-1)^4, X1^-1 * X2 * X1^4 * X2 * X1 * X2^-1, X1 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^3, X2^-1 * X1^-1 * X2^-1 * X1^-2 * X2^-1 * X1^-2 * X2^-1 * X1, X1^12 ]
Map:: polytopal non-degenerate
	R = (1, 157, 2, 158, 6, 162, 16, 172, 39, 195, 84, 240, 112, 268, 125, 281, 69, 225, 30, 186, 12, 168, 4, 160)(3, 159, 9, 165, 23, 179, 55, 211, 49, 205, 100, 256, 129, 285, 143, 299, 93, 249, 44, 200, 18, 174, 10, 166)(5, 161, 14, 170, 29, 185, 67, 223, 110, 266, 104, 260, 51, 207, 103, 259, 52, 208, 82, 238, 37, 193, 15, 171)(7, 163, 19, 175, 45, 201, 95, 251, 91, 247, 142, 298, 147, 303, 132, 288, 139, 295, 87, 243, 41, 197, 20, 176)(8, 164, 21, 177, 11, 167, 28, 184, 64, 220, 63, 219, 27, 183, 62, 218, 92, 248, 105, 261, 53, 209, 22, 178)(13, 169, 32, 188, 68, 224, 124, 280, 130, 286, 80, 236, 35, 191, 79, 235, 36, 192, 81, 237, 76, 232, 33, 189)(17, 173, 42, 198, 88, 244, 140, 296, 138, 294, 150, 306, 117, 273, 134, 290, 118, 274, 137, 293, 85, 241, 43, 199)(24, 180, 57, 213, 108, 264, 131, 287, 144, 300, 155, 311, 121, 277, 66, 222, 102, 258, 50, 206, 101, 257, 58, 214)(25, 181, 59, 215, 26, 182, 61, 217, 97, 253, 46, 202, 38, 194, 83, 239, 133, 289, 151, 307, 113, 269, 60, 216)(31, 187, 71, 227, 114, 270, 90, 246, 141, 297, 96, 252, 74, 230, 94, 250, 75, 231, 128, 284, 109, 265, 72, 228)(34, 190, 77, 233, 120, 276, 65, 221, 119, 275, 153, 309, 152, 308, 115, 271, 145, 301, 111, 267, 123, 279, 78, 234)(40, 196, 73, 229, 127, 283, 156, 312, 122, 278, 135, 291, 146, 302, 149, 305, 107, 263, 116, 272, 136, 292, 86, 242)(47, 203, 98, 254, 48, 204, 99, 255, 56, 212, 89, 245, 54, 210, 106, 262, 148, 304, 154, 310, 126, 282, 70, 226)
	L = (1, 159)(2, 163)(3, 161)(4, 167)(5, 157)(6, 173)(7, 164)(8, 158)(9, 180)(10, 182)(11, 169)(12, 185)(13, 160)(14, 190)(15, 192)(16, 196)(17, 174)(18, 162)(19, 202)(20, 204)(21, 206)(22, 208)(23, 212)(24, 181)(25, 165)(26, 183)(27, 166)(28, 221)(29, 187)(30, 224)(31, 168)(32, 229)(33, 231)(34, 191)(35, 170)(36, 194)(37, 179)(38, 171)(39, 234)(40, 197)(41, 172)(42, 245)(43, 246)(44, 248)(45, 252)(46, 203)(47, 175)(48, 205)(49, 176)(50, 207)(51, 177)(52, 210)(53, 201)(54, 178)(55, 263)(56, 193)(57, 189)(58, 265)(59, 267)(60, 225)(61, 251)(62, 272)(63, 274)(64, 253)(65, 222)(66, 184)(67, 278)(68, 226)(69, 270)(70, 186)(71, 198)(72, 262)(73, 230)(74, 188)(75, 213)(76, 220)(77, 219)(78, 241)(79, 243)(80, 249)(81, 287)(82, 289)(83, 291)(84, 258)(85, 195)(86, 280)(87, 285)(88, 236)(89, 227)(90, 247)(91, 199)(92, 250)(93, 244)(94, 200)(95, 271)(96, 209)(97, 232)(98, 277)(99, 296)(100, 301)(101, 211)(102, 292)(103, 293)(104, 295)(105, 304)(106, 275)(107, 257)(108, 306)(109, 266)(110, 214)(111, 268)(112, 215)(113, 264)(114, 216)(115, 217)(116, 273)(117, 218)(118, 233)(119, 228)(120, 310)(121, 281)(122, 279)(123, 223)(124, 294)(125, 254)(126, 239)(127, 260)(128, 308)(129, 235)(130, 276)(131, 288)(132, 237)(133, 290)(134, 238)(135, 282)(136, 240)(137, 303)(138, 242)(139, 283)(140, 300)(141, 312)(142, 311)(143, 284)(144, 255)(145, 302)(146, 256)(147, 259)(148, 305)(149, 261)(150, 269)(151, 297)(152, 299)(153, 298)(154, 286)(155, 309)(156, 307)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: chiral
Dual of E27.2181
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2192 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 12, 12})
Quotient :: halfedge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^2, (X1 * X2 * X1)^3, X1^-3 * X2 * X1^-1 * X2 * X1 * X2 * X1^-3, X2 * X1 * X2 * X1^-1 * X2 * X1^-3 * X2 * X1^3, (X1^-1 * X2 * X1^-1 * X2 * X1^2 * X2)^2, (X1^-1 * X2)^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 47, 69, 88, 46, 22, 10, 4)(3, 7, 15, 31, 61, 78, 40, 77, 74, 38, 18, 8)(6, 13, 27, 54, 67, 34, 16, 33, 64, 60, 30, 14)(9, 19, 39, 75, 99, 126, 83, 125, 124, 81, 42, 20)(12, 25, 37, 72, 101, 56, 28, 55, 98, 96, 53, 26)(17, 35, 68, 113, 143, 150, 118, 149, 148, 117, 71, 36)(21, 43, 82, 100, 65, 110, 128, 142, 109, 63, 32, 44)(24, 49, 59, 105, 133, 93, 51, 92, 132, 131, 91, 50)(29, 57, 102, 123, 151, 156, 140, 114, 119, 73, 104, 58)(41, 79, 122, 130, 153, 137, 97, 129, 138, 108, 120, 80)(45, 85, 103, 66, 111, 144, 147, 155, 136, 121, 76, 86)(48, 89, 95, 135, 107, 62, 90, 112, 145, 152, 127, 84)(52, 87, 116, 70, 115, 146, 154, 139, 141, 106, 134, 94)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 48)(25, 51)(26, 52)(27, 42)(30, 59)(31, 62)(33, 65)(34, 66)(35, 69)(36, 70)(38, 73)(39, 76)(43, 83)(44, 84)(46, 87)(47, 79)(49, 90)(50, 86)(53, 95)(54, 97)(55, 99)(56, 100)(57, 88)(58, 103)(60, 106)(61, 92)(63, 108)(64, 71)(67, 112)(68, 114)(72, 118)(74, 120)(75, 93)(77, 111)(78, 115)(80, 123)(81, 117)(82, 94)(85, 128)(89, 129)(91, 130)(96, 136)(98, 104)(101, 138)(102, 139)(105, 140)(107, 119)(109, 131)(110, 143)(113, 127)(116, 147)(121, 145)(122, 149)(124, 152)(125, 146)(126, 151)(132, 134)(133, 148)(135, 154)(137, 141)(142, 156)(144, 153)(150, 155)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: chiral
Dual of E27.2193
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.2193 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 12, 12})
Quotient :: halfedge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X2^2, (X1^2 * X2)^3, X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2, X1^12, (X1^-1 * X2)^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 47, 84, 83, 46, 22, 10, 4)(3, 7, 15, 31, 61, 101, 146, 113, 72, 38, 18, 8)(6, 13, 27, 54, 93, 139, 147, 145, 100, 60, 30, 14)(9, 19, 39, 73, 71, 112, 137, 91, 52, 77, 42, 20)(12, 25, 37, 70, 111, 150, 149, 119, 138, 92, 53, 26)(16, 33, 63, 103, 98, 143, 116, 131, 86, 48, 65, 34)(17, 35, 66, 81, 45, 80, 125, 142, 97, 110, 69, 36)(21, 43, 78, 122, 121, 144, 99, 58, 29, 57, 32, 44)(24, 49, 59, 40, 74, 115, 109, 68, 108, 133, 88, 50)(28, 55, 94, 140, 136, 105, 64, 104, 130, 85, 96, 56)(41, 75, 117, 127, 82, 62, 102, 106, 67, 107, 120, 76)(51, 89, 134, 156, 151, 126, 95, 141, 148, 129, 135, 90)(79, 123, 153, 155, 128, 114, 132, 87, 118, 152, 154, 124)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 48)(25, 51)(26, 52)(27, 42)(30, 59)(31, 62)(33, 64)(34, 53)(35, 67)(36, 68)(38, 71)(39, 66)(43, 70)(44, 79)(46, 82)(47, 85)(49, 87)(50, 72)(54, 80)(55, 95)(56, 88)(57, 97)(58, 98)(60, 61)(63, 69)(65, 106)(73, 114)(74, 116)(75, 118)(76, 119)(77, 121)(78, 117)(81, 126)(83, 128)(84, 129)(86, 100)(89, 123)(90, 131)(91, 136)(92, 93)(94, 99)(96, 142)(101, 140)(102, 141)(103, 112)(104, 132)(105, 127)(107, 147)(108, 148)(109, 144)(110, 149)(111, 133)(113, 151)(115, 120)(122, 135)(124, 145)(125, 153)(130, 138)(134, 137)(139, 156)(143, 155)(146, 152)(150, 154)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: chiral
Dual of E27.2192
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.2194 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 12, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^2, (X1 * X2^2)^3, X2^4 * X1 * X2^-1 * X1 * X2 * X1 * X2^2, X2^-1 * X1 * X2^3 * X1 * X2 * X1 * X2^-1 * X1 * X2^-2, (X2 * X1 * X2^-2 * X1 * X2 * X1)^2, (X2^-1 * X1)^12 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 47)(24, 49)(26, 52)(27, 54)(28, 56)(30, 59)(32, 42)(34, 66)(35, 68)(36, 69)(38, 73)(40, 77)(43, 82)(44, 84)(46, 87)(48, 57)(50, 93)(51, 94)(53, 98)(55, 99)(58, 104)(60, 108)(61, 109)(62, 90)(63, 111)(64, 88)(65, 92)(67, 114)(70, 117)(71, 96)(72, 86)(74, 79)(75, 91)(76, 101)(78, 115)(80, 123)(81, 103)(83, 116)(85, 128)(89, 129)(95, 133)(97, 107)(100, 127)(102, 139)(105, 132)(106, 110)(112, 145)(113, 137)(118, 149)(119, 150)(120, 143)(121, 131)(122, 141)(124, 152)(125, 138)(126, 151)(130, 153)(134, 154)(135, 155)(136, 147)(140, 146)(142, 156)(144, 148)(157, 159, 164, 174, 194, 230, 210, 244, 202, 178, 166, 160)(158, 161, 168, 182, 209, 232, 195, 231, 216, 186, 170, 162)(163, 171, 188, 219, 206, 180, 167, 179, 204, 223, 190, 172)(165, 175, 196, 234, 265, 282, 238, 281, 280, 237, 198, 176)(169, 183, 211, 256, 285, 298, 260, 297, 296, 259, 213, 184)(173, 191, 185, 214, 261, 218, 187, 217, 266, 274, 226, 192)(177, 199, 239, 246, 203, 245, 284, 290, 251, 207, 181, 200)(189, 220, 268, 279, 307, 310, 293, 255, 263, 215, 262, 221)(193, 227, 222, 269, 302, 271, 224, 254, 292, 289, 275, 228)(197, 235, 278, 306, 309, 300, 267, 299, 288, 250, 264, 236)(201, 241, 248, 205, 247, 286, 295, 312, 305, 277, 233, 242)(208, 252, 249, 287, 308, 283, 240, 229, 276, 273, 291, 253)(212, 257, 294, 311, 301, 304, 270, 303, 272, 225, 243, 258)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24, 24 ), ( 24^12 ) }
Outer automorphisms :: chiral
Dual of E27.2199
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 2^78, 12^13 ]

E27.2195 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 12, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^2, (X2^-2 * X1)^3, X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1, X2^12, X2 * X1 * X2 * X1 * X2^3 * X1 * X2^-5 * X1 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 47)(24, 49)(26, 52)(27, 54)(28, 56)(30, 59)(32, 42)(34, 65)(35, 67)(36, 68)(38, 71)(40, 55)(43, 58)(44, 79)(46, 82)(48, 57)(50, 88)(51, 89)(53, 66)(60, 70)(61, 99)(62, 101)(63, 80)(64, 104)(69, 110)(72, 112)(73, 114)(74, 116)(75, 117)(76, 119)(77, 121)(78, 118)(81, 126)(83, 128)(84, 129)(85, 127)(86, 97)(87, 103)(90, 134)(91, 135)(92, 137)(93, 138)(94, 140)(95, 141)(96, 139)(98, 144)(100, 105)(102, 133)(106, 111)(107, 123)(108, 149)(109, 131)(113, 151)(115, 120)(122, 150)(124, 147)(125, 153)(130, 132)(136, 152)(142, 154)(143, 148)(145, 156)(146, 155)(157, 159, 164, 174, 194, 228, 269, 239, 202, 178, 166, 160)(158, 161, 168, 182, 209, 247, 292, 254, 216, 186, 170, 162)(163, 171, 188, 219, 259, 301, 293, 303, 262, 222, 190, 172)(165, 175, 196, 230, 215, 253, 299, 265, 224, 233, 198, 176)(167, 179, 204, 242, 260, 302, 270, 305, 267, 227, 206, 180)(169, 183, 211, 237, 201, 236, 281, 289, 245, 251, 213, 184)(173, 191, 185, 214, 252, 298, 297, 275, 288, 243, 205, 192)(177, 199, 234, 278, 277, 296, 261, 220, 189, 207, 181, 200)(187, 217, 256, 291, 287, 241, 203, 240, 286, 268, 258, 218)(193, 225, 221, 195, 229, 271, 250, 212, 249, 295, 257, 226)(197, 231, 274, 283, 238, 208, 246, 244, 210, 248, 276, 232)(223, 263, 304, 312, 300, 282, 255, 290, 294, 307, 306, 264)(235, 279, 309, 311, 284, 272, 285, 266, 273, 308, 310, 280)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24, 24 ), ( 24^12 ) }
Outer automorphisms :: chiral
Dual of E27.2198
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 2^78, 12^13 ]

E27.2196 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 12, 12})
Quotient :: edge
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ (X1^-1 * X2^-1)^2, (X1 * X2^-1)^3, X1 * X2^2 * X1 * X2 * X1^2 * X2, X2 * X1^-4 * X2^-1 * X1 * X2^-2 * X1, X1 * X2^-3 * X1 * X2 * X1^-1 * X2^-3, X1^-1 * X2^-1 * X1^2 * X2^-3 * X1 * X2^-1 * X1^-1, X1^-3 * X2 * X1^-1 * X2^-2 * X1^-3, X2^3 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1, (X1^-1 * X2^-3 * X1^-2)^2, X2^12 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 6, 16, 38, 84, 59, 100, 75, 33, 13, 4)(3, 9, 23, 53, 112, 52, 113, 67, 127, 65, 28, 11)(5, 14, 34, 76, 98, 54, 24, 56, 106, 48, 20, 7)(8, 21, 49, 107, 79, 35, 15, 36, 80, 94, 42, 17)(10, 25, 58, 118, 151, 117, 153, 108, 137, 124, 63, 27)(12, 29, 66, 109, 81, 37, 82, 130, 156, 123, 71, 31)(18, 43, 95, 144, 110, 50, 22, 51, 111, 139, 88, 39)(19, 45, 99, 69, 128, 83, 134, 145, 119, 64, 104, 47)(26, 60, 114, 155, 129, 149, 105, 142, 93, 41, 91, 62)(30, 68, 86, 136, 121, 152, 132, 77, 90, 141, 126, 70)(32, 72, 92, 78, 116, 57, 102, 150, 135, 154, 115, 55)(40, 89, 140, 125, 146, 96, 44, 97, 147, 131, 73, 85)(46, 101, 148, 122, 61, 120, 143, 133, 138, 87, 74, 103)(157, 159, 166, 182, 217, 277, 295, 291, 239, 193, 171, 161)(158, 163, 175, 202, 258, 307, 287, 312, 270, 208, 178, 164)(160, 168, 186, 225, 285, 296, 250, 299, 273, 213, 180, 165)(162, 173, 197, 248, 238, 284, 226, 283, 304, 254, 200, 174)(167, 177, 206, 265, 294, 253, 232, 288, 305, 255, 215, 181)(169, 188, 229, 274, 301, 251, 204, 261, 308, 278, 223, 185)(170, 191, 234, 249, 207, 268, 302, 275, 214, 240, 224, 187)(172, 195, 243, 222, 269, 216, 183, 212, 272, 235, 246, 196)(176, 199, 252, 209, 271, 297, 263, 309, 276, 218, 256, 201)(179, 210, 257, 203, 192, 237, 266, 293, 242, 194, 241, 211)(184, 220, 281, 311, 286, 228, 189, 230, 244, 292, 264, 205)(190, 227, 280, 300, 290, 306, 259, 231, 247, 198, 245, 233)(219, 279, 303, 289, 236, 260, 221, 282, 310, 267, 298, 262)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 4^12 ) }
Outer automorphisms :: chiral
Dual of E27.2197
Transitivity :: ET+
Graph:: simple bipartite
	v = 26 e = 156 f = 78
	degree seq :: [ 12^26 ]

E27.2197 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 12, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ X1^2, (X1 * X2^2)^3, X2^4 * X1 * X2^-1 * X1 * X2 * X1 * X2^2, X2^-1 * X1 * X2^3 * X1 * X2 * X1 * X2^-1 * X1 * X2^-2, (X2 * X1 * X2^-2 * X1 * X2 * X1)^2, (X2^-1 * X1)^12 ]
Map:: polyhedral non-degenerate
	R = (1, 157, 2, 158)(3, 159, 7, 163)(4, 160, 9, 165)(5, 161, 11, 167)(6, 162, 13, 169)(8, 164, 17, 173)(10, 166, 21, 177)(12, 168, 25, 181)(14, 170, 29, 185)(15, 171, 31, 187)(16, 172, 33, 189)(18, 174, 37, 193)(19, 175, 39, 195)(20, 176, 41, 197)(22, 178, 45, 201)(23, 179, 47, 203)(24, 180, 49, 205)(26, 182, 52, 208)(27, 183, 54, 210)(28, 184, 56, 212)(30, 186, 59, 215)(32, 188, 42, 198)(34, 190, 66, 222)(35, 191, 68, 224)(36, 192, 69, 225)(38, 194, 73, 229)(40, 196, 77, 233)(43, 199, 82, 238)(44, 200, 84, 240)(46, 202, 87, 243)(48, 204, 57, 213)(50, 206, 93, 249)(51, 207, 94, 250)(53, 209, 98, 254)(55, 211, 99, 255)(58, 214, 104, 260)(60, 216, 108, 264)(61, 217, 109, 265)(62, 218, 90, 246)(63, 219, 111, 267)(64, 220, 88, 244)(65, 221, 92, 248)(67, 223, 114, 270)(70, 226, 117, 273)(71, 227, 96, 252)(72, 228, 86, 242)(74, 230, 79, 235)(75, 231, 91, 247)(76, 232, 101, 257)(78, 234, 115, 271)(80, 236, 123, 279)(81, 237, 103, 259)(83, 239, 116, 272)(85, 241, 128, 284)(89, 245, 129, 285)(95, 251, 133, 289)(97, 253, 107, 263)(100, 256, 127, 283)(102, 258, 139, 295)(105, 261, 132, 288)(106, 262, 110, 266)(112, 268, 145, 301)(113, 269, 137, 293)(118, 274, 149, 305)(119, 275, 150, 306)(120, 276, 143, 299)(121, 277, 131, 287)(122, 278, 141, 297)(124, 280, 152, 308)(125, 281, 138, 294)(126, 282, 151, 307)(130, 286, 153, 309)(134, 290, 154, 310)(135, 291, 155, 311)(136, 292, 147, 303)(140, 296, 146, 302)(142, 298, 156, 312)(144, 300, 148, 304)
	L = (1, 159)(2, 161)(3, 164)(4, 157)(5, 168)(6, 158)(7, 171)(8, 174)(9, 175)(10, 160)(11, 179)(12, 182)(13, 183)(14, 162)(15, 188)(16, 163)(17, 191)(18, 194)(19, 196)(20, 165)(21, 199)(22, 166)(23, 204)(24, 167)(25, 200)(26, 209)(27, 211)(28, 169)(29, 214)(30, 170)(31, 217)(32, 219)(33, 220)(34, 172)(35, 185)(36, 173)(37, 227)(38, 230)(39, 231)(40, 234)(41, 235)(42, 176)(43, 239)(44, 177)(45, 241)(46, 178)(47, 245)(48, 223)(49, 247)(50, 180)(51, 181)(52, 252)(53, 232)(54, 244)(55, 256)(56, 257)(57, 184)(58, 261)(59, 262)(60, 186)(61, 266)(62, 187)(63, 206)(64, 268)(65, 189)(66, 269)(67, 190)(68, 254)(69, 243)(70, 192)(71, 222)(72, 193)(73, 276)(74, 210)(75, 216)(76, 195)(77, 242)(78, 265)(79, 278)(80, 197)(81, 198)(82, 281)(83, 246)(84, 229)(85, 248)(86, 201)(87, 258)(88, 202)(89, 284)(90, 203)(91, 286)(92, 205)(93, 287)(94, 264)(95, 207)(96, 249)(97, 208)(98, 292)(99, 263)(100, 285)(101, 294)(102, 212)(103, 213)(104, 297)(105, 218)(106, 221)(107, 215)(108, 236)(109, 282)(110, 274)(111, 299)(112, 279)(113, 302)(114, 303)(115, 224)(116, 225)(117, 291)(118, 226)(119, 228)(120, 273)(121, 233)(122, 306)(123, 307)(124, 237)(125, 280)(126, 238)(127, 240)(128, 290)(129, 298)(130, 295)(131, 308)(132, 250)(133, 275)(134, 251)(135, 253)(136, 289)(137, 255)(138, 311)(139, 312)(140, 259)(141, 296)(142, 260)(143, 288)(144, 267)(145, 304)(146, 271)(147, 272)(148, 270)(149, 277)(150, 309)(151, 310)(152, 283)(153, 300)(154, 293)(155, 301)(156, 305)
	local type(s) :: { ( 12^4 ) }
Outer automorphisms :: chiral
Dual of E27.2196
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 78 e = 156 f = 26
	degree seq :: [ 4^78 ]

E27.2198 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 12, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ (X1^-1 * X2^-1)^2, (X1 * X2^-1)^3, X1 * X2^2 * X1 * X2 * X1^2 * X2, X2 * X1^-4 * X2^-1 * X1 * X2^-2 * X1, X1 * X2^-3 * X1 * X2 * X1^-1 * X2^-3, X1^-1 * X2^-1 * X1^2 * X2^-3 * X1 * X2^-1 * X1^-1, X1^-3 * X2 * X1^-1 * X2^-2 * X1^-3, X2^3 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1, (X1^-1 * X2^-3 * X1^-2)^2, X2^12 ]
Map::
	R = (1, 157, 2, 158, 6, 162, 16, 172, 38, 194, 84, 240, 59, 215, 100, 256, 75, 231, 33, 189, 13, 169, 4, 160)(3, 159, 9, 165, 23, 179, 53, 209, 112, 268, 52, 208, 113, 269, 67, 223, 127, 283, 65, 221, 28, 184, 11, 167)(5, 161, 14, 170, 34, 190, 76, 232, 98, 254, 54, 210, 24, 180, 56, 212, 106, 262, 48, 204, 20, 176, 7, 163)(8, 164, 21, 177, 49, 205, 107, 263, 79, 235, 35, 191, 15, 171, 36, 192, 80, 236, 94, 250, 42, 198, 17, 173)(10, 166, 25, 181, 58, 214, 118, 274, 151, 307, 117, 273, 153, 309, 108, 264, 137, 293, 124, 280, 63, 219, 27, 183)(12, 168, 29, 185, 66, 222, 109, 265, 81, 237, 37, 193, 82, 238, 130, 286, 156, 312, 123, 279, 71, 227, 31, 187)(18, 174, 43, 199, 95, 251, 144, 300, 110, 266, 50, 206, 22, 178, 51, 207, 111, 267, 139, 295, 88, 244, 39, 195)(19, 175, 45, 201, 99, 255, 69, 225, 128, 284, 83, 239, 134, 290, 145, 301, 119, 275, 64, 220, 104, 260, 47, 203)(26, 182, 60, 216, 114, 270, 155, 311, 129, 285, 149, 305, 105, 261, 142, 298, 93, 249, 41, 197, 91, 247, 62, 218)(30, 186, 68, 224, 86, 242, 136, 292, 121, 277, 152, 308, 132, 288, 77, 233, 90, 246, 141, 297, 126, 282, 70, 226)(32, 188, 72, 228, 92, 248, 78, 234, 116, 272, 57, 213, 102, 258, 150, 306, 135, 291, 154, 310, 115, 271, 55, 211)(40, 196, 89, 245, 140, 296, 125, 281, 146, 302, 96, 252, 44, 200, 97, 253, 147, 303, 131, 287, 73, 229, 85, 241)(46, 202, 101, 257, 148, 304, 122, 278, 61, 217, 120, 276, 143, 299, 133, 289, 138, 294, 87, 243, 74, 230, 103, 259)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 175)(8, 158)(9, 160)(10, 182)(11, 177)(12, 186)(13, 188)(14, 191)(15, 161)(16, 195)(17, 197)(18, 162)(19, 202)(20, 199)(21, 206)(22, 164)(23, 210)(24, 165)(25, 167)(26, 217)(27, 212)(28, 220)(29, 169)(30, 225)(31, 170)(32, 229)(33, 230)(34, 227)(35, 234)(36, 237)(37, 171)(38, 241)(39, 243)(40, 172)(41, 248)(42, 245)(43, 252)(44, 174)(45, 176)(46, 258)(47, 192)(48, 261)(49, 184)(50, 265)(51, 268)(52, 178)(53, 271)(54, 257)(55, 179)(56, 272)(57, 180)(58, 240)(59, 181)(60, 183)(61, 277)(62, 256)(63, 279)(64, 281)(65, 282)(66, 269)(67, 185)(68, 187)(69, 285)(70, 283)(71, 280)(72, 189)(73, 274)(74, 244)(75, 247)(76, 288)(77, 190)(78, 249)(79, 246)(80, 260)(81, 266)(82, 284)(83, 193)(84, 224)(85, 211)(86, 194)(87, 222)(88, 292)(89, 233)(90, 196)(91, 198)(92, 238)(93, 207)(94, 299)(95, 204)(96, 209)(97, 232)(98, 200)(99, 215)(100, 201)(101, 203)(102, 307)(103, 231)(104, 221)(105, 308)(106, 219)(107, 309)(108, 205)(109, 294)(110, 293)(111, 298)(112, 302)(113, 216)(114, 208)(115, 297)(116, 235)(117, 213)(118, 301)(119, 214)(120, 218)(121, 295)(122, 223)(123, 303)(124, 300)(125, 311)(126, 310)(127, 304)(128, 226)(129, 296)(130, 228)(131, 312)(132, 305)(133, 236)(134, 306)(135, 239)(136, 264)(137, 242)(138, 253)(139, 291)(140, 250)(141, 263)(142, 262)(143, 273)(144, 290)(145, 251)(146, 275)(147, 289)(148, 254)(149, 255)(150, 259)(151, 287)(152, 278)(153, 276)(154, 267)(155, 286)(156, 270)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2195
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2199 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 12, 12})
Quotient :: loop
Aut^+ = (C13 : C4) : C3 (small group id <156, 7>)
Aut   = (C13 : C4) : C3 (small group id <156, 7>)
|r| :: 1
Presentation :: [ (X1 * X2)^2, (X1 * X2^-1)^3, X1 * X2^2 * X1 * X2 * X1^2 * X2, X1 * X2^2 * X1^-1 * X2 * X1^-1 * X2^2, X1^-1 * X2^-6 * X1 * X2^-1 * X1^-1, X1^-1 * X2^-2 * X1^-3 * X2 * X1^-3, X2^3 * X1^-1 * X2^-1 * X1^2 * X2^-2 * X1^-1, X1^12 ]
Map::
	R = (1, 157, 2, 158, 6, 162, 16, 172, 38, 194, 84, 240, 136, 292, 133, 289, 75, 231, 33, 189, 13, 169, 4, 160)(3, 159, 9, 165, 23, 179, 53, 209, 105, 261, 145, 301, 135, 291, 143, 299, 87, 243, 65, 221, 28, 184, 11, 167)(5, 161, 14, 170, 34, 190, 76, 232, 134, 290, 156, 312, 121, 277, 139, 295, 106, 262, 48, 204, 20, 176, 7, 163)(8, 164, 21, 177, 49, 205, 107, 263, 155, 311, 126, 282, 69, 225, 128, 284, 147, 303, 94, 250, 42, 198, 17, 173)(10, 166, 25, 181, 58, 214, 118, 274, 74, 230, 130, 286, 77, 233, 114, 270, 141, 297, 100, 256, 63, 219, 27, 183)(12, 168, 29, 185, 66, 222, 119, 275, 64, 220, 102, 258, 146, 302, 93, 249, 41, 197, 91, 247, 71, 227, 31, 187)(15, 171, 36, 192, 80, 236, 92, 248, 144, 300, 116, 272, 57, 213, 117, 273, 137, 293, 86, 242, 79, 235, 35, 191)(18, 174, 43, 199, 95, 251, 67, 223, 125, 281, 62, 218, 26, 182, 60, 216, 122, 278, 78, 234, 88, 244, 39, 195)(19, 175, 45, 201, 99, 255, 55, 211, 32, 188, 72, 228, 108, 264, 151, 307, 124, 280, 61, 217, 104, 260, 47, 203)(22, 178, 51, 207, 111, 267, 142, 298, 131, 287, 81, 237, 37, 193, 82, 238, 123, 279, 138, 294, 110, 266, 50, 206)(24, 180, 56, 212, 103, 259, 46, 202, 101, 257, 152, 308, 109, 265, 140, 296, 85, 241, 40, 196, 89, 245, 54, 210)(30, 186, 68, 224, 98, 254, 150, 306, 132, 288, 154, 310, 115, 271, 83, 239, 90, 246, 59, 215, 120, 276, 70, 226)(44, 200, 97, 253, 149, 305, 129, 285, 73, 229, 112, 268, 52, 208, 113, 269, 153, 309, 127, 283, 148, 304, 96, 252)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 175)(8, 158)(9, 160)(10, 182)(11, 177)(12, 186)(13, 188)(14, 191)(15, 161)(16, 195)(17, 197)(18, 162)(19, 202)(20, 199)(21, 206)(22, 164)(23, 210)(24, 165)(25, 167)(26, 217)(27, 212)(28, 220)(29, 169)(30, 225)(31, 170)(32, 229)(33, 230)(34, 227)(35, 234)(36, 237)(37, 171)(38, 241)(39, 243)(40, 172)(41, 248)(42, 245)(43, 252)(44, 174)(45, 176)(46, 258)(47, 192)(48, 261)(49, 184)(50, 265)(51, 268)(52, 178)(53, 255)(54, 250)(55, 179)(56, 272)(57, 180)(58, 246)(59, 181)(60, 183)(61, 247)(62, 276)(63, 282)(64, 283)(65, 244)(66, 251)(67, 185)(68, 187)(69, 256)(70, 281)(71, 280)(72, 189)(73, 277)(74, 287)(75, 288)(76, 286)(77, 190)(78, 263)(79, 270)(80, 260)(81, 274)(82, 271)(83, 193)(84, 293)(85, 295)(86, 194)(87, 298)(88, 235)(89, 239)(90, 196)(91, 198)(92, 301)(93, 207)(94, 232)(95, 204)(96, 213)(97, 224)(98, 200)(99, 297)(100, 201)(101, 203)(102, 221)(103, 219)(104, 218)(105, 310)(106, 296)(107, 228)(108, 205)(109, 223)(110, 307)(111, 302)(112, 211)(113, 233)(114, 208)(115, 209)(116, 306)(117, 304)(118, 222)(119, 214)(120, 312)(121, 215)(122, 238)(123, 216)(124, 294)(125, 308)(126, 305)(127, 292)(128, 226)(129, 311)(130, 231)(131, 299)(132, 300)(133, 309)(134, 303)(135, 236)(136, 279)(137, 284)(138, 240)(139, 285)(140, 266)(141, 242)(142, 290)(143, 253)(144, 249)(145, 262)(146, 259)(147, 273)(148, 275)(149, 291)(150, 264)(151, 254)(152, 269)(153, 257)(154, 289)(155, 278)(156, 267)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2194
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2200 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 12, 12})
Quotient :: halfedge
Aut^+ = C3 x (C13 : C4) (small group id <156, 9>)
Aut   = C3 x (C13 : C4) (small group id <156, 9>)
|r| :: 1
Presentation :: [ X2^2, X1^-1 * X2 * X1 * X2 * X1 * X2 * X1 * X2 * X1^-2, X1^12, X2 * X1^-3 * X2 * X1^-1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 47, 82, 81, 46, 22, 10, 4)(3, 7, 15, 31, 48, 84, 131, 116, 73, 38, 18, 8)(6, 13, 27, 55, 83, 130, 128, 80, 45, 62, 30, 14)(9, 19, 39, 50, 24, 49, 85, 133, 124, 77, 42, 20)(12, 25, 51, 87, 129, 126, 79, 44, 21, 43, 54, 26)(16, 33, 65, 105, 132, 156, 150, 115, 72, 41, 67, 34)(17, 35, 58, 28, 57, 95, 119, 152, 149, 112, 69, 36)(29, 59, 90, 52, 89, 108, 66, 107, 127, 102, 98, 60)(32, 63, 101, 144, 142, 97, 114, 71, 37, 70, 104, 64)(40, 53, 91, 111, 86, 134, 141, 96, 123, 78, 120, 75)(56, 93, 139, 145, 155, 136, 143, 100, 61, 99, 140, 94)(68, 103, 122, 76, 121, 151, 118, 74, 117, 113, 148, 110)(88, 109, 147, 154, 125, 106, 146, 138, 92, 137, 153, 135)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 48)(25, 52)(26, 53)(27, 56)(30, 61)(31, 57)(33, 50)(34, 66)(35, 68)(36, 62)(38, 72)(39, 74)(42, 76)(43, 60)(44, 78)(46, 73)(47, 83)(49, 86)(51, 88)(54, 92)(55, 89)(58, 96)(59, 97)(63, 102)(64, 103)(65, 106)(67, 109)(69, 111)(70, 108)(71, 113)(75, 119)(77, 123)(79, 125)(80, 127)(81, 124)(82, 129)(84, 132)(85, 110)(87, 134)(90, 115)(91, 136)(93, 120)(94, 114)(95, 121)(98, 105)(99, 141)(100, 101)(104, 145)(107, 126)(112, 117)(116, 149)(118, 147)(122, 153)(128, 155)(130, 152)(131, 142)(133, 156)(135, 143)(137, 150)(138, 139)(140, 154)(144, 151)(146, 148)
	local type(s) :: { ( 12^12 ) }
Outer automorphisms :: chiral positively-selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 13 e = 78 f = 13
	degree seq :: [ 12^13 ]

E27.2201 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 12, 12})
Quotient :: edge
Aut^+ = C3 x (C13 : C4) (small group id <156, 9>)
Aut   = C3 x (C13 : C4) (small group id <156, 9>)
|r| :: 1
Presentation :: [ X1^2, X2^-1 * X1 * X2 * X1 * X2 * X1 * X2 * X1 * X2^-2, X2^12, X1 * X2^-3 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2 * X1 * X2^-1 ]
Map::
	R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 47)(24, 49)(26, 53)(27, 55)(28, 57)(30, 61)(32, 63)(34, 67)(35, 68)(36, 70)(38, 54)(40, 75)(42, 76)(43, 66)(44, 78)(46, 62)(48, 82)(50, 86)(51, 87)(52, 89)(56, 94)(58, 95)(59, 85)(60, 97)(64, 103)(65, 105)(69, 110)(71, 113)(72, 114)(73, 104)(74, 117)(77, 123)(79, 125)(80, 127)(81, 124)(83, 107)(84, 126)(88, 109)(90, 133)(91, 121)(92, 130)(93, 115)(96, 119)(98, 102)(99, 106)(100, 137)(101, 118)(108, 136)(111, 145)(112, 147)(116, 146)(120, 131)(122, 153)(128, 155)(129, 135)(132, 152)(134, 142)(138, 148)(139, 149)(140, 154)(141, 151)(143, 144)(150, 156)(157, 159, 164, 174, 194, 229, 272, 237, 202, 178, 166, 160)(158, 161, 168, 182, 210, 248, 290, 256, 218, 186, 170, 162)(163, 171, 188, 220, 260, 297, 284, 236, 201, 213, 190, 172)(165, 175, 196, 203, 193, 228, 271, 306, 280, 233, 198, 176)(167, 179, 204, 239, 286, 312, 294, 255, 217, 197, 206, 180)(169, 183, 212, 187, 209, 247, 273, 307, 293, 252, 214, 184)(173, 191, 225, 267, 302, 282, 235, 200, 177, 199, 227, 192)(181, 207, 244, 288, 298, 261, 254, 216, 185, 215, 246, 208)(189, 221, 262, 224, 259, 241, 205, 240, 283, 243, 263, 222)(195, 226, 268, 251, 270, 301, 292, 250, 279, 234, 274, 230)(211, 245, 278, 232, 277, 308, 276, 231, 275, 253, 291, 249)(219, 257, 295, 289, 311, 303, 299, 265, 223, 264, 296, 258)(238, 285, 305, 269, 304, 309, 300, 266, 242, 287, 310, 281)
	L = (1, 157)(2, 158)(3, 159)(4, 160)(5, 161)(6, 162)(7, 163)(8, 164)(9, 165)(10, 166)(11, 167)(12, 168)(13, 169)(14, 170)(15, 171)(16, 172)(17, 173)(18, 174)(19, 175)(20, 176)(21, 177)(22, 178)(23, 179)(24, 180)(25, 181)(26, 182)(27, 183)(28, 184)(29, 185)(30, 186)(31, 187)(32, 188)(33, 189)(34, 190)(35, 191)(36, 192)(37, 193)(38, 194)(39, 195)(40, 196)(41, 197)(42, 198)(43, 199)(44, 200)(45, 201)(46, 202)(47, 203)(48, 204)(49, 205)(50, 206)(51, 207)(52, 208)(53, 209)(54, 210)(55, 211)(56, 212)(57, 213)(58, 214)(59, 215)(60, 216)(61, 217)(62, 218)(63, 219)(64, 220)(65, 221)(66, 222)(67, 223)(68, 224)(69, 225)(70, 226)(71, 227)(72, 228)(73, 229)(74, 230)(75, 231)(76, 232)(77, 233)(78, 234)(79, 235)(80, 236)(81, 237)(82, 238)(83, 239)(84, 240)(85, 241)(86, 242)(87, 243)(88, 244)(89, 245)(90, 246)(91, 247)(92, 248)(93, 249)(94, 250)(95, 251)(96, 252)(97, 253)(98, 254)(99, 255)(100, 256)(101, 257)(102, 258)(103, 259)(104, 260)(105, 261)(106, 262)(107, 263)(108, 264)(109, 265)(110, 266)(111, 267)(112, 268)(113, 269)(114, 270)(115, 271)(116, 272)(117, 273)(118, 274)(119, 275)(120, 276)(121, 277)(122, 278)(123, 279)(124, 280)(125, 281)(126, 282)(127, 283)(128, 284)(129, 285)(130, 286)(131, 287)(132, 288)(133, 289)(134, 290)(135, 291)(136, 292)(137, 293)(138, 294)(139, 295)(140, 296)(141, 297)(142, 298)(143, 299)(144, 300)(145, 301)(146, 302)(147, 303)(148, 304)(149, 305)(150, 306)(151, 307)(152, 308)(153, 309)(154, 310)(155, 311)(156, 312)
	local type(s) :: { ( 24, 24 ), ( 24^12 ) }
Outer automorphisms :: chiral
Dual of E27.2202
Transitivity :: ET+
Graph:: simple bipartite
	v = 91 e = 156 f = 13
	degree seq :: [ 2^78, 12^13 ]

E27.2202 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 12, 12})
Quotient :: loop
Aut^+ = C3 x (C13 : C4) (small group id <156, 9>)
Aut   = C3 x (C13 : C4) (small group id <156, 9>)
|r| :: 1
Presentation :: [ (X1 * X2)^2, X2 * X1^-1 * X2^-1 * X1^3 * X2^2, X1^-1 * X2^3 * X1^3 * X2^-1, X2 * X1^-2 * X2^2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1, X1^-1 * X2^-1 * X1 * X2^-2 * X1^2 * X2^-2 * X1^-1, X1^12, X2^12 ]
Map::
	R = (1, 157, 2, 158, 6, 162, 16, 172, 40, 196, 84, 240, 134, 290, 116, 272, 63, 219, 34, 190, 13, 169, 4, 160)(3, 159, 9, 165, 23, 179, 57, 213, 39, 195, 42, 198, 87, 243, 139, 295, 115, 271, 71, 227, 29, 185, 11, 167)(5, 161, 14, 170, 35, 191, 56, 212, 85, 241, 136, 292, 118, 274, 64, 220, 26, 182, 51, 207, 20, 176, 7, 163)(8, 164, 21, 177, 52, 208, 97, 253, 135, 291, 129, 285, 77, 233, 33, 189, 48, 204, 92, 248, 44, 200, 17, 173)(10, 166, 25, 181, 61, 217, 36, 192, 15, 171, 38, 194, 82, 238, 131, 287, 137, 293, 121, 277, 66, 222, 27, 183)(12, 168, 30, 186, 72, 228, 86, 242, 41, 197, 18, 174, 45, 201, 93, 249, 143, 299, 126, 282, 75, 231, 32, 188)(19, 175, 47, 203, 98, 254, 53, 209, 22, 178, 55, 211, 109, 265, 154, 310, 117, 273, 150, 306, 101, 257, 49, 205)(24, 180, 60, 216, 100, 256, 140, 296, 88, 244, 142, 298, 106, 262, 70, 226, 31, 187, 73, 229, 108, 264, 58, 214)(28, 184, 67, 223, 110, 266, 155, 311, 111, 267, 59, 215, 103, 259, 151, 307, 133, 289, 141, 297, 99, 255, 69, 225)(37, 193, 80, 236, 130, 286, 156, 312, 119, 275, 144, 300, 104, 260, 50, 206, 102, 258, 148, 304, 123, 279, 78, 234)(43, 199, 89, 245, 65, 221, 94, 250, 46, 202, 96, 252, 79, 235, 113, 269, 76, 232, 127, 283, 81, 237, 90, 246)(54, 210, 107, 263, 153, 309, 128, 284, 149, 305, 112, 268, 146, 302, 91, 247, 145, 301, 125, 281, 152, 308, 105, 261)(62, 218, 114, 270, 74, 230, 124, 280, 83, 239, 132, 288, 138, 294, 120, 276, 68, 224, 122, 278, 147, 303, 95, 251)
	L = (1, 159)(2, 163)(3, 166)(4, 168)(5, 157)(6, 173)(7, 175)(8, 158)(9, 160)(10, 182)(11, 184)(12, 187)(13, 189)(14, 192)(15, 161)(16, 197)(17, 199)(18, 162)(19, 204)(20, 206)(21, 209)(22, 164)(23, 214)(24, 165)(25, 167)(26, 219)(27, 221)(28, 224)(29, 226)(30, 169)(31, 227)(32, 230)(33, 232)(34, 220)(35, 234)(36, 235)(37, 170)(38, 213)(39, 171)(40, 195)(41, 180)(42, 172)(43, 186)(44, 247)(45, 250)(46, 174)(47, 176)(48, 190)(49, 256)(50, 259)(51, 183)(52, 261)(53, 262)(54, 177)(55, 191)(56, 178)(57, 267)(58, 265)(59, 179)(60, 242)(61, 251)(62, 181)(63, 271)(64, 273)(65, 275)(66, 276)(67, 185)(68, 277)(69, 279)(70, 254)(71, 272)(72, 246)(73, 188)(74, 281)(75, 269)(76, 282)(77, 284)(78, 255)(79, 258)(80, 283)(81, 193)(82, 280)(83, 194)(84, 212)(85, 196)(86, 294)(87, 296)(88, 198)(89, 200)(90, 238)(91, 236)(92, 205)(93, 303)(94, 222)(95, 201)(96, 208)(97, 202)(98, 297)(99, 203)(100, 305)(101, 215)(102, 207)(103, 306)(104, 308)(105, 300)(106, 301)(107, 229)(108, 210)(109, 223)(110, 211)(111, 218)(112, 216)(113, 217)(114, 311)(115, 293)(116, 299)(117, 291)(118, 312)(119, 292)(120, 228)(121, 295)(122, 225)(123, 309)(124, 231)(125, 298)(126, 290)(127, 233)(128, 304)(129, 310)(130, 302)(131, 237)(132, 307)(133, 239)(134, 253)(135, 240)(136, 287)(137, 241)(138, 263)(139, 289)(140, 257)(141, 243)(142, 249)(143, 244)(144, 245)(145, 248)(146, 278)(147, 268)(148, 252)(149, 285)(150, 274)(151, 260)(152, 270)(153, 288)(154, 264)(155, 286)(156, 266)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2201
Transitivity :: ET+ VT+
Graph::
	v = 13 e = 156 f = 91
	degree seq :: [ 24^13 ]

E27.2203 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 20})
Quotient :: regular
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^20 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 43, 66, 85, 101, 117, 133, 132, 116, 100, 84, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 77, 93, 109, 125, 141, 151, 135, 118, 107, 89, 68, 44, 36, 18, 8)(6, 13, 27, 51, 41, 64, 83, 99, 115, 131, 147, 149, 134, 123, 105, 87, 67, 54, 30, 14)(9, 19, 37, 62, 81, 97, 113, 129, 145, 153, 137, 119, 102, 91, 71, 46, 24, 45, 38, 20)(12, 25, 47, 40, 21, 39, 63, 82, 98, 114, 130, 146, 148, 139, 121, 103, 86, 74, 50, 26)(16, 28, 48, 69, 61, 76, 92, 108, 124, 140, 154, 160, 155, 144, 128, 111, 94, 80, 58, 33)(17, 29, 49, 70, 88, 104, 120, 136, 150, 158, 156, 142, 126, 112, 95, 78, 56, 75, 59, 34)(32, 52, 72, 60, 35, 53, 73, 90, 106, 122, 138, 152, 159, 157, 143, 127, 110, 96, 79, 57)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 142)(130, 143)(131, 144)(132, 145)(133, 148)(135, 150)(137, 152)(139, 154)(141, 155)(146, 156)(147, 157)(149, 158)(151, 159)(153, 160)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2204
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.2204 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 20})
Quotient :: regular
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, (T1^-1 * T2)^20 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 31, 28, 17, 8)(6, 13, 21, 32, 30, 18, 9, 14)(15, 25, 33, 43, 40, 27, 16, 26)(23, 34, 42, 41, 29, 36, 24, 35)(37, 47, 52, 50, 39, 49, 38, 48)(44, 53, 51, 56, 46, 55, 45, 54)(57, 65, 60, 68, 59, 67, 58, 66)(61, 69, 64, 72, 63, 71, 62, 70)(73, 83, 76, 77, 75, 80, 74, 89)(78, 117, 84, 115, 88, 113, 79, 119)(81, 127, 90, 145, 94, 133, 82, 121)(85, 135, 95, 143, 87, 125, 86, 123)(91, 147, 100, 155, 93, 131, 92, 129)(96, 157, 99, 141, 98, 139, 97, 137)(101, 159, 104, 153, 103, 151, 102, 149)(105, 150, 108, 160, 107, 154, 106, 152)(109, 138, 112, 158, 111, 142, 110, 140)(114, 148, 120, 156, 118, 132, 116, 130)(122, 144, 128, 126, 146, 124, 134, 136)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 113)(70, 115)(71, 117)(72, 119)(77, 121)(78, 123)(79, 125)(80, 127)(81, 129)(82, 131)(83, 133)(84, 135)(85, 137)(86, 139)(87, 141)(88, 143)(89, 145)(90, 147)(91, 149)(92, 151)(93, 153)(94, 155)(95, 157)(96, 152)(97, 154)(98, 160)(99, 150)(100, 159)(101, 140)(102, 142)(103, 158)(104, 138)(105, 130)(106, 132)(107, 156)(108, 148)(109, 124)(110, 126)(111, 144)(112, 136)(114, 128)(116, 122)(118, 134)(120, 146)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2203
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.2205 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, (T2^-1 * T1)^20 ]
Map:: polytopal
	R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 26, 39, 30, 18, 9, 16)(11, 20, 32, 44, 36, 23, 13, 21)(25, 37, 48, 41, 29, 40, 27, 38)(31, 42, 53, 46, 35, 45, 33, 43)(47, 57, 51, 60, 50, 59, 49, 58)(52, 61, 56, 64, 55, 63, 54, 62)(65, 73, 68, 76, 67, 75, 66, 74)(69, 110, 72, 94, 71, 92, 70, 91)(77, 134, 84, 144, 101, 147, 86, 135)(78, 137, 88, 150, 107, 153, 90, 138)(79, 139, 93, 154, 95, 141, 80, 140)(81, 130, 96, 129, 97, 132, 82, 131)(83, 143, 99, 156, 103, 146, 85, 133)(87, 149, 105, 159, 109, 152, 89, 136)(98, 155, 112, 157, 102, 145, 100, 142)(104, 158, 117, 160, 108, 151, 106, 148)(111, 127, 115, 126, 114, 125, 113, 128)(116, 123, 120, 122, 119, 121, 118, 124)(161, 162)(163, 167)(164, 169)(165, 171)(166, 173)(168, 172)(170, 174)(175, 185)(176, 187)(177, 186)(178, 189)(179, 190)(180, 191)(181, 193)(182, 192)(183, 195)(184, 196)(188, 194)(197, 207)(198, 209)(199, 208)(200, 210)(201, 211)(202, 212)(203, 214)(204, 213)(205, 215)(206, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 289)(234, 290)(235, 291)(236, 292)(237, 293)(238, 296)(239, 297)(240, 298)(241, 294)(242, 295)(243, 302)(244, 303)(245, 305)(246, 306)(247, 308)(248, 309)(249, 311)(250, 312)(251, 299)(252, 300)(253, 310)(254, 301)(255, 313)(256, 304)(257, 307)(258, 288)(259, 315)(260, 285)(261, 316)(262, 286)(263, 317)(264, 284)(265, 318)(266, 281)(267, 319)(268, 282)(269, 320)(270, 314)(271, 279)(272, 287)(273, 280)(274, 276)(275, 278)(277, 283)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 40, 40 ), ( 40^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2209
Transitivity :: ET+
Graph:: simple bipartite
	v = 100 e = 160 f = 8
	degree seq :: [ 2^80, 8^20 ]

E27.2206 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (T1^-1 * T2^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T1 * T2^-1 * T1^5 * T2^-1, T2^20 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 48, 64, 80, 96, 112, 128, 144, 132, 116, 100, 84, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 89, 105, 121, 137, 152, 140, 124, 108, 92, 76, 60, 44, 22, 8)(4, 12, 29, 49, 65, 81, 97, 113, 129, 145, 155, 141, 125, 109, 93, 77, 61, 45, 23, 9)(6, 17, 36, 53, 69, 85, 101, 117, 133, 148, 158, 149, 134, 118, 102, 86, 70, 54, 38, 18)(11, 27, 37, 32, 51, 67, 83, 99, 115, 131, 147, 156, 142, 126, 110, 94, 78, 62, 46, 24)(13, 28, 43, 59, 75, 91, 107, 123, 139, 154, 159, 150, 135, 119, 103, 87, 71, 55, 39, 20)(14, 31, 50, 66, 82, 98, 114, 130, 146, 157, 143, 127, 111, 95, 79, 63, 47, 26, 35, 16)(21, 42, 58, 74, 90, 106, 122, 138, 153, 160, 151, 136, 120, 104, 88, 72, 56, 41, 30, 34)(161, 162, 166, 176, 194, 187, 173, 164)(163, 169, 177, 168, 181, 195, 188, 171)(165, 174, 178, 197, 190, 172, 180, 167)(170, 184, 196, 183, 202, 182, 203, 186)(175, 192, 198, 189, 201, 179, 199, 191)(185, 207, 213, 206, 218, 205, 219, 204)(193, 209, 214, 200, 216, 210, 215, 211)(208, 220, 229, 223, 234, 222, 235, 221)(212, 217, 230, 226, 232, 227, 231, 225)(224, 237, 245, 236, 250, 239, 251, 238)(228, 242, 246, 243, 248, 241, 247, 233)(240, 254, 261, 253, 266, 252, 267, 255)(244, 259, 262, 257, 264, 249, 263, 258)(256, 271, 277, 270, 282, 269, 283, 268)(260, 273, 278, 265, 280, 274, 279, 275)(272, 284, 293, 287, 298, 286, 299, 285)(276, 281, 294, 290, 296, 291, 295, 289)(288, 301, 308, 300, 313, 303, 314, 302)(292, 306, 309, 307, 311, 305, 310, 297)(304, 316, 318, 315, 320, 312, 319, 317)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2210
Transitivity :: ET+
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.2207 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^20 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 138)(123, 140)(129, 142)(130, 143)(131, 144)(132, 145)(133, 148)(135, 150)(137, 152)(139, 154)(141, 155)(146, 156)(147, 157)(149, 158)(151, 159)(153, 160)(161, 162, 165, 171, 183, 203, 226, 245, 261, 277, 293, 292, 276, 260, 244, 225, 202, 182, 170, 164)(163, 167, 175, 191, 215, 237, 253, 269, 285, 301, 311, 295, 278, 267, 249, 228, 204, 196, 178, 168)(166, 173, 187, 211, 201, 224, 243, 259, 275, 291, 307, 309, 294, 283, 265, 247, 227, 214, 190, 174)(169, 179, 197, 222, 241, 257, 273, 289, 305, 313, 297, 279, 262, 251, 231, 206, 184, 205, 198, 180)(172, 185, 207, 200, 181, 199, 223, 242, 258, 274, 290, 306, 308, 299, 281, 263, 246, 234, 210, 186)(176, 188, 208, 229, 221, 236, 252, 268, 284, 300, 314, 320, 315, 304, 288, 271, 254, 240, 218, 193)(177, 189, 209, 230, 248, 264, 280, 296, 310, 318, 316, 302, 286, 272, 255, 238, 216, 235, 219, 194)(192, 212, 232, 220, 195, 213, 233, 250, 266, 282, 298, 312, 319, 317, 303, 287, 270, 256, 239, 217)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 16, 16 ), ( 16^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2208
Transitivity :: ET+
Graph:: simple bipartite
	v = 88 e = 160 f = 20
	degree seq :: [ 2^80, 20^8 ]

E27.2208 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, (T2^-1 * T1)^20 ]
Map::
	R = (1, 161, 3, 163, 8, 168, 17, 177, 28, 188, 19, 179, 10, 170, 4, 164)(2, 162, 5, 165, 12, 172, 22, 182, 34, 194, 24, 184, 14, 174, 6, 166)(7, 167, 15, 175, 26, 186, 39, 199, 30, 190, 18, 178, 9, 169, 16, 176)(11, 171, 20, 180, 32, 192, 44, 204, 36, 196, 23, 183, 13, 173, 21, 181)(25, 185, 37, 197, 48, 208, 41, 201, 29, 189, 40, 200, 27, 187, 38, 198)(31, 191, 42, 202, 53, 213, 46, 206, 35, 195, 45, 205, 33, 193, 43, 203)(47, 207, 57, 217, 51, 211, 60, 220, 50, 210, 59, 219, 49, 209, 58, 218)(52, 212, 61, 221, 56, 216, 64, 224, 55, 215, 63, 223, 54, 214, 62, 222)(65, 225, 73, 233, 68, 228, 76, 236, 67, 227, 75, 235, 66, 226, 74, 234)(69, 229, 82, 242, 72, 232, 94, 254, 71, 231, 83, 243, 70, 230, 77, 237)(78, 238, 113, 273, 86, 246, 119, 279, 88, 248, 117, 277, 79, 239, 115, 275)(80, 240, 128, 288, 91, 251, 150, 310, 93, 253, 132, 292, 81, 241, 121, 281)(84, 244, 136, 296, 97, 257, 143, 303, 87, 247, 125, 285, 85, 245, 123, 283)(89, 249, 146, 306, 102, 262, 154, 314, 92, 252, 130, 290, 90, 250, 127, 287)(95, 255, 158, 318, 99, 259, 141, 301, 98, 258, 138, 298, 96, 256, 135, 295)(100, 260, 160, 320, 104, 264, 152, 312, 103, 263, 148, 308, 101, 261, 145, 305)(105, 265, 153, 313, 108, 268, 149, 309, 107, 267, 147, 307, 106, 266, 157, 317)(109, 269, 142, 302, 112, 272, 139, 299, 111, 271, 137, 297, 110, 270, 159, 319)(114, 274, 131, 291, 120, 280, 129, 289, 118, 278, 151, 311, 116, 276, 155, 315)(122, 282, 144, 304, 133, 293, 126, 286, 156, 316, 124, 284, 134, 294, 140, 300)
	L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 172)(9, 164)(10, 174)(11, 165)(12, 168)(13, 166)(14, 170)(15, 185)(16, 187)(17, 186)(18, 189)(19, 190)(20, 191)(21, 193)(22, 192)(23, 195)(24, 196)(25, 175)(26, 177)(27, 176)(28, 194)(29, 178)(30, 179)(31, 180)(32, 182)(33, 181)(34, 188)(35, 183)(36, 184)(37, 207)(38, 209)(39, 208)(40, 210)(41, 211)(42, 212)(43, 214)(44, 213)(45, 215)(46, 216)(47, 197)(48, 199)(49, 198)(50, 200)(51, 201)(52, 202)(53, 204)(54, 203)(55, 205)(56, 206)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 217)(66, 218)(67, 219)(68, 220)(69, 221)(70, 222)(71, 223)(72, 224)(73, 273)(74, 275)(75, 277)(76, 279)(77, 281)(78, 283)(79, 285)(80, 287)(81, 290)(82, 288)(83, 292)(84, 295)(85, 298)(86, 296)(87, 301)(88, 303)(89, 305)(90, 308)(91, 306)(92, 312)(93, 314)(94, 310)(95, 317)(96, 307)(97, 318)(98, 309)(99, 313)(100, 319)(101, 297)(102, 320)(103, 299)(104, 302)(105, 315)(106, 311)(107, 289)(108, 291)(109, 304)(110, 300)(111, 284)(112, 286)(113, 233)(114, 294)(115, 234)(116, 316)(117, 235)(118, 293)(119, 236)(120, 282)(121, 237)(122, 280)(123, 238)(124, 271)(125, 239)(126, 272)(127, 240)(128, 242)(129, 267)(130, 241)(131, 268)(132, 243)(133, 278)(134, 274)(135, 244)(136, 246)(137, 261)(138, 245)(139, 263)(140, 270)(141, 247)(142, 264)(143, 248)(144, 269)(145, 249)(146, 251)(147, 256)(148, 250)(149, 258)(150, 254)(151, 266)(152, 252)(153, 259)(154, 253)(155, 265)(156, 276)(157, 255)(158, 257)(159, 260)(160, 262)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.2207
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 20 e = 160 f = 88
	degree seq :: [ 16^20 ]

E27.2209 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (T1^-1 * T2^-1)^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-3 * T2^-1 * T1, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-2, T1 * T2^-1 * T1^5 * T2^-1, T2^20 ]
Map::
	R = (1, 161, 3, 163, 10, 170, 25, 185, 48, 208, 64, 224, 80, 240, 96, 256, 112, 272, 128, 288, 144, 304, 132, 292, 116, 276, 100, 260, 84, 244, 68, 228, 52, 212, 33, 193, 15, 175, 5, 165)(2, 162, 7, 167, 19, 179, 40, 200, 57, 217, 73, 233, 89, 249, 105, 265, 121, 281, 137, 297, 152, 312, 140, 300, 124, 284, 108, 268, 92, 252, 76, 236, 60, 220, 44, 204, 22, 182, 8, 168)(4, 164, 12, 172, 29, 189, 49, 209, 65, 225, 81, 241, 97, 257, 113, 273, 129, 289, 145, 305, 155, 315, 141, 301, 125, 285, 109, 269, 93, 253, 77, 237, 61, 221, 45, 205, 23, 183, 9, 169)(6, 166, 17, 177, 36, 196, 53, 213, 69, 229, 85, 245, 101, 261, 117, 277, 133, 293, 148, 308, 158, 318, 149, 309, 134, 294, 118, 278, 102, 262, 86, 246, 70, 230, 54, 214, 38, 198, 18, 178)(11, 171, 27, 187, 37, 197, 32, 192, 51, 211, 67, 227, 83, 243, 99, 259, 115, 275, 131, 291, 147, 307, 156, 316, 142, 302, 126, 286, 110, 270, 94, 254, 78, 238, 62, 222, 46, 206, 24, 184)(13, 173, 28, 188, 43, 203, 59, 219, 75, 235, 91, 251, 107, 267, 123, 283, 139, 299, 154, 314, 159, 319, 150, 310, 135, 295, 119, 279, 103, 263, 87, 247, 71, 231, 55, 215, 39, 199, 20, 180)(14, 174, 31, 191, 50, 210, 66, 226, 82, 242, 98, 258, 114, 274, 130, 290, 146, 306, 157, 317, 143, 303, 127, 287, 111, 271, 95, 255, 79, 239, 63, 223, 47, 207, 26, 186, 35, 195, 16, 176)(21, 181, 42, 202, 58, 218, 74, 234, 90, 250, 106, 266, 122, 282, 138, 298, 153, 313, 160, 320, 151, 311, 136, 296, 120, 280, 104, 264, 88, 248, 72, 232, 56, 216, 41, 201, 30, 190, 34, 194)
	L = (1, 162)(2, 166)(3, 169)(4, 161)(5, 174)(6, 176)(7, 165)(8, 181)(9, 177)(10, 184)(11, 163)(12, 180)(13, 164)(14, 178)(15, 192)(16, 194)(17, 168)(18, 197)(19, 199)(20, 167)(21, 195)(22, 203)(23, 202)(24, 196)(25, 207)(26, 170)(27, 173)(28, 171)(29, 201)(30, 172)(31, 175)(32, 198)(33, 209)(34, 187)(35, 188)(36, 183)(37, 190)(38, 189)(39, 191)(40, 216)(41, 179)(42, 182)(43, 186)(44, 185)(45, 219)(46, 218)(47, 213)(48, 220)(49, 214)(50, 215)(51, 193)(52, 217)(53, 206)(54, 200)(55, 211)(56, 210)(57, 230)(58, 205)(59, 204)(60, 229)(61, 208)(62, 235)(63, 234)(64, 237)(65, 212)(66, 232)(67, 231)(68, 242)(69, 223)(70, 226)(71, 225)(72, 227)(73, 228)(74, 222)(75, 221)(76, 250)(77, 245)(78, 224)(79, 251)(80, 254)(81, 247)(82, 246)(83, 248)(84, 259)(85, 236)(86, 243)(87, 233)(88, 241)(89, 263)(90, 239)(91, 238)(92, 267)(93, 266)(94, 261)(95, 240)(96, 271)(97, 264)(98, 244)(99, 262)(100, 273)(101, 253)(102, 257)(103, 258)(104, 249)(105, 280)(106, 252)(107, 255)(108, 256)(109, 283)(110, 282)(111, 277)(112, 284)(113, 278)(114, 279)(115, 260)(116, 281)(117, 270)(118, 265)(119, 275)(120, 274)(121, 294)(122, 269)(123, 268)(124, 293)(125, 272)(126, 299)(127, 298)(128, 301)(129, 276)(130, 296)(131, 295)(132, 306)(133, 287)(134, 290)(135, 289)(136, 291)(137, 292)(138, 286)(139, 285)(140, 313)(141, 308)(142, 288)(143, 314)(144, 316)(145, 310)(146, 309)(147, 311)(148, 300)(149, 307)(150, 297)(151, 305)(152, 319)(153, 303)(154, 302)(155, 320)(156, 318)(157, 304)(158, 315)(159, 317)(160, 312)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2205
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 160 f = 100
	degree seq :: [ 40^8 ]

E27.2210 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T2 * T1^2)^4, T1^20 ]
Map:: polytopal non-degenerate
	R = (1, 161, 3, 163)(2, 162, 6, 166)(4, 164, 9, 169)(5, 165, 12, 172)(7, 167, 16, 176)(8, 168, 17, 177)(10, 170, 21, 181)(11, 171, 24, 184)(13, 173, 28, 188)(14, 174, 29, 189)(15, 175, 32, 192)(18, 178, 35, 195)(19, 179, 33, 193)(20, 180, 34, 194)(22, 182, 41, 201)(23, 183, 44, 204)(25, 185, 48, 208)(26, 186, 49, 209)(27, 187, 52, 212)(30, 190, 53, 213)(31, 191, 56, 216)(36, 196, 61, 221)(37, 197, 57, 217)(38, 198, 60, 220)(39, 199, 58, 218)(40, 200, 59, 219)(42, 202, 55, 215)(43, 203, 67, 227)(45, 205, 69, 229)(46, 206, 70, 230)(47, 207, 72, 232)(50, 210, 73, 233)(51, 211, 75, 235)(54, 214, 76, 236)(62, 222, 78, 238)(63, 223, 79, 239)(64, 224, 80, 240)(65, 225, 81, 241)(66, 226, 86, 246)(68, 228, 88, 248)(71, 231, 90, 250)(74, 234, 92, 252)(77, 237, 94, 254)(82, 242, 95, 255)(83, 243, 96, 256)(84, 244, 98, 258)(85, 245, 102, 262)(87, 247, 104, 264)(89, 249, 106, 266)(91, 251, 108, 268)(93, 253, 110, 270)(97, 257, 111, 271)(99, 259, 112, 272)(100, 260, 115, 275)(101, 261, 118, 278)(103, 263, 120, 280)(105, 265, 122, 282)(107, 267, 124, 284)(109, 269, 126, 286)(113, 273, 127, 287)(114, 274, 128, 288)(116, 276, 125, 285)(117, 277, 134, 294)(119, 279, 136, 296)(121, 281, 138, 298)(123, 283, 140, 300)(129, 289, 142, 302)(130, 290, 143, 303)(131, 291, 144, 304)(132, 292, 145, 305)(133, 293, 148, 308)(135, 295, 150, 310)(137, 297, 152, 312)(139, 299, 154, 314)(141, 301, 155, 315)(146, 306, 156, 316)(147, 307, 157, 317)(149, 309, 158, 318)(151, 311, 159, 319)(153, 313, 160, 320)
	L = (1, 162)(2, 165)(3, 167)(4, 161)(5, 171)(6, 173)(7, 175)(8, 163)(9, 179)(10, 164)(11, 183)(12, 185)(13, 187)(14, 166)(15, 191)(16, 188)(17, 189)(18, 168)(19, 197)(20, 169)(21, 199)(22, 170)(23, 203)(24, 205)(25, 207)(26, 172)(27, 211)(28, 208)(29, 209)(30, 174)(31, 215)(32, 212)(33, 176)(34, 177)(35, 213)(36, 178)(37, 222)(38, 180)(39, 223)(40, 181)(41, 224)(42, 182)(43, 226)(44, 196)(45, 198)(46, 184)(47, 200)(48, 229)(49, 230)(50, 186)(51, 201)(52, 232)(53, 233)(54, 190)(55, 237)(56, 235)(57, 192)(58, 193)(59, 194)(60, 195)(61, 236)(62, 241)(63, 242)(64, 243)(65, 202)(66, 245)(67, 214)(68, 204)(69, 221)(70, 248)(71, 206)(72, 220)(73, 250)(74, 210)(75, 219)(76, 252)(77, 253)(78, 216)(79, 217)(80, 218)(81, 257)(82, 258)(83, 259)(84, 225)(85, 261)(86, 234)(87, 227)(88, 264)(89, 228)(90, 266)(91, 231)(92, 268)(93, 269)(94, 240)(95, 238)(96, 239)(97, 273)(98, 274)(99, 275)(100, 244)(101, 277)(102, 251)(103, 246)(104, 280)(105, 247)(106, 282)(107, 249)(108, 284)(109, 285)(110, 256)(111, 254)(112, 255)(113, 289)(114, 290)(115, 291)(116, 260)(117, 293)(118, 267)(119, 262)(120, 296)(121, 263)(122, 298)(123, 265)(124, 300)(125, 301)(126, 272)(127, 270)(128, 271)(129, 305)(130, 306)(131, 307)(132, 276)(133, 292)(134, 283)(135, 278)(136, 310)(137, 279)(138, 312)(139, 281)(140, 314)(141, 311)(142, 286)(143, 287)(144, 288)(145, 313)(146, 308)(147, 309)(148, 299)(149, 294)(150, 318)(151, 295)(152, 319)(153, 297)(154, 320)(155, 304)(156, 302)(157, 303)(158, 316)(159, 317)(160, 315)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.2206
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.2211 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2^8, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 11, 171)(6, 166, 13, 173)(8, 168, 12, 172)(10, 170, 14, 174)(15, 175, 25, 185)(16, 176, 27, 187)(17, 177, 26, 186)(18, 178, 29, 189)(19, 179, 30, 190)(20, 180, 31, 191)(21, 181, 33, 193)(22, 182, 32, 192)(23, 183, 35, 195)(24, 184, 36, 196)(28, 188, 34, 194)(37, 197, 47, 207)(38, 198, 49, 209)(39, 199, 48, 208)(40, 200, 50, 210)(41, 201, 51, 211)(42, 202, 52, 212)(43, 203, 54, 214)(44, 204, 53, 213)(45, 205, 55, 215)(46, 206, 56, 216)(57, 217, 65, 225)(58, 218, 66, 226)(59, 219, 67, 227)(60, 220, 68, 228)(61, 221, 69, 229)(62, 222, 70, 230)(63, 223, 71, 231)(64, 224, 72, 232)(73, 233, 121, 281)(74, 234, 123, 283)(75, 235, 125, 285)(76, 236, 127, 287)(77, 237, 129, 289)(78, 238, 133, 293)(79, 239, 135, 295)(80, 240, 138, 298)(81, 241, 139, 299)(82, 242, 143, 303)(83, 243, 130, 290)(84, 244, 141, 301)(85, 245, 132, 292)(86, 246, 144, 304)(87, 247, 136, 296)(88, 248, 140, 300)(89, 249, 131, 291)(90, 250, 149, 309)(91, 251, 142, 302)(92, 252, 156, 316)(93, 253, 157, 317)(94, 254, 134, 294)(95, 255, 152, 312)(96, 256, 137, 297)(97, 257, 158, 318)(98, 258, 155, 315)(99, 259, 146, 306)(100, 260, 153, 313)(101, 261, 150, 310)(102, 262, 154, 314)(103, 263, 145, 305)(104, 264, 148, 308)(105, 265, 147, 307)(106, 266, 160, 320)(107, 267, 159, 319)(108, 268, 128, 288)(109, 269, 122, 282)(110, 270, 151, 311)(111, 271, 124, 284)(112, 272, 126, 286)(113, 273, 119, 279)(114, 274, 120, 280)(115, 275, 117, 277)(116, 276, 118, 278)(321, 481, 323, 483, 328, 488, 337, 497, 348, 508, 339, 499, 330, 490, 324, 484)(322, 482, 325, 485, 332, 492, 342, 502, 354, 514, 344, 504, 334, 494, 326, 486)(327, 487, 335, 495, 346, 506, 359, 519, 350, 510, 338, 498, 329, 489, 336, 496)(331, 491, 340, 500, 352, 512, 364, 524, 356, 516, 343, 503, 333, 493, 341, 501)(345, 505, 357, 517, 368, 528, 361, 521, 349, 509, 360, 520, 347, 507, 358, 518)(351, 511, 362, 522, 373, 533, 366, 526, 355, 515, 365, 525, 353, 513, 363, 523)(367, 527, 377, 537, 371, 531, 380, 540, 370, 530, 379, 539, 369, 529, 378, 538)(372, 532, 381, 541, 376, 536, 384, 544, 375, 535, 383, 543, 374, 534, 382, 542)(385, 545, 393, 553, 388, 548, 396, 556, 387, 547, 395, 555, 386, 546, 394, 554)(389, 549, 405, 565, 392, 552, 403, 563, 391, 551, 419, 579, 390, 550, 421, 581)(397, 557, 450, 610, 404, 564, 466, 626, 420, 580, 470, 630, 406, 566, 452, 612)(398, 558, 447, 607, 407, 567, 445, 605, 422, 582, 443, 603, 408, 568, 441, 601)(399, 559, 456, 616, 411, 571, 474, 634, 413, 573, 460, 620, 400, 560, 453, 613)(401, 561, 461, 621, 416, 576, 473, 633, 418, 578, 464, 624, 402, 562, 449, 609)(409, 569, 462, 622, 425, 585, 477, 637, 412, 572, 458, 618, 410, 570, 455, 615)(414, 574, 457, 617, 430, 590, 475, 635, 417, 577, 463, 623, 415, 575, 459, 619)(423, 583, 467, 627, 427, 587, 476, 636, 426, 586, 469, 629, 424, 584, 451, 611)(428, 588, 471, 631, 432, 592, 478, 638, 431, 591, 472, 632, 429, 589, 454, 614)(433, 593, 479, 639, 436, 596, 480, 640, 435, 595, 468, 628, 434, 594, 465, 625)(437, 597, 446, 606, 440, 600, 444, 604, 439, 599, 442, 602, 438, 598, 448, 608)
	L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 331)(6, 333)(7, 323)(8, 332)(9, 324)(10, 334)(11, 325)(12, 328)(13, 326)(14, 330)(15, 345)(16, 347)(17, 346)(18, 349)(19, 350)(20, 351)(21, 353)(22, 352)(23, 355)(24, 356)(25, 335)(26, 337)(27, 336)(28, 354)(29, 338)(30, 339)(31, 340)(32, 342)(33, 341)(34, 348)(35, 343)(36, 344)(37, 367)(38, 369)(39, 368)(40, 370)(41, 371)(42, 372)(43, 374)(44, 373)(45, 375)(46, 376)(47, 357)(48, 359)(49, 358)(50, 360)(51, 361)(52, 362)(53, 364)(54, 363)(55, 365)(56, 366)(57, 385)(58, 386)(59, 387)(60, 388)(61, 389)(62, 390)(63, 391)(64, 392)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 441)(74, 443)(75, 445)(76, 447)(77, 449)(78, 453)(79, 455)(80, 458)(81, 459)(82, 463)(83, 450)(84, 461)(85, 452)(86, 464)(87, 456)(88, 460)(89, 451)(90, 469)(91, 462)(92, 476)(93, 477)(94, 454)(95, 472)(96, 457)(97, 478)(98, 475)(99, 466)(100, 473)(101, 470)(102, 474)(103, 465)(104, 468)(105, 467)(106, 480)(107, 479)(108, 448)(109, 442)(110, 471)(111, 444)(112, 446)(113, 439)(114, 440)(115, 437)(116, 438)(117, 435)(118, 436)(119, 433)(120, 434)(121, 393)(122, 429)(123, 394)(124, 431)(125, 395)(126, 432)(127, 396)(128, 428)(129, 397)(130, 403)(131, 409)(132, 405)(133, 398)(134, 414)(135, 399)(136, 407)(137, 416)(138, 400)(139, 401)(140, 408)(141, 404)(142, 411)(143, 402)(144, 406)(145, 423)(146, 419)(147, 425)(148, 424)(149, 410)(150, 421)(151, 430)(152, 415)(153, 420)(154, 422)(155, 418)(156, 412)(157, 413)(158, 417)(159, 427)(160, 426)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2214
Graph:: bipartite
	v = 100 e = 320 f = 168
	degree seq :: [ 4^80, 16^20 ]

E27.2212 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y1^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, (Y2^-3 * Y1)^2, Y1^8, Y2^20 ]
Map::
	R = (1, 161, 2, 162, 6, 166, 16, 176, 34, 194, 27, 187, 13, 173, 4, 164)(3, 163, 9, 169, 17, 177, 8, 168, 21, 181, 35, 195, 28, 188, 11, 171)(5, 165, 14, 174, 18, 178, 37, 197, 30, 190, 12, 172, 20, 180, 7, 167)(10, 170, 24, 184, 36, 196, 23, 183, 42, 202, 22, 182, 43, 203, 26, 186)(15, 175, 32, 192, 38, 198, 29, 189, 41, 201, 19, 179, 39, 199, 31, 191)(25, 185, 47, 207, 53, 213, 46, 206, 58, 218, 45, 205, 59, 219, 44, 204)(33, 193, 49, 209, 54, 214, 40, 200, 56, 216, 50, 210, 55, 215, 51, 211)(48, 208, 60, 220, 69, 229, 63, 223, 74, 234, 62, 222, 75, 235, 61, 221)(52, 212, 57, 217, 70, 230, 66, 226, 72, 232, 67, 227, 71, 231, 65, 225)(64, 224, 77, 237, 85, 245, 76, 236, 90, 250, 79, 239, 91, 251, 78, 238)(68, 228, 82, 242, 86, 246, 83, 243, 88, 248, 81, 241, 87, 247, 73, 233)(80, 240, 94, 254, 101, 261, 93, 253, 106, 266, 92, 252, 107, 267, 95, 255)(84, 244, 99, 259, 102, 262, 97, 257, 104, 264, 89, 249, 103, 263, 98, 258)(96, 256, 111, 271, 117, 277, 110, 270, 122, 282, 109, 269, 123, 283, 108, 268)(100, 260, 113, 273, 118, 278, 105, 265, 120, 280, 114, 274, 119, 279, 115, 275)(112, 272, 124, 284, 133, 293, 127, 287, 138, 298, 126, 286, 139, 299, 125, 285)(116, 276, 121, 281, 134, 294, 130, 290, 136, 296, 131, 291, 135, 295, 129, 289)(128, 288, 141, 301, 148, 308, 140, 300, 153, 313, 143, 303, 154, 314, 142, 302)(132, 292, 146, 306, 149, 309, 147, 307, 151, 311, 145, 305, 150, 310, 137, 297)(144, 304, 156, 316, 158, 318, 155, 315, 160, 320, 152, 312, 159, 319, 157, 317)(321, 481, 323, 483, 330, 490, 345, 505, 368, 528, 384, 544, 400, 560, 416, 576, 432, 592, 448, 608, 464, 624, 452, 612, 436, 596, 420, 580, 404, 564, 388, 548, 372, 532, 353, 513, 335, 495, 325, 485)(322, 482, 327, 487, 339, 499, 360, 520, 377, 537, 393, 553, 409, 569, 425, 585, 441, 601, 457, 617, 472, 632, 460, 620, 444, 604, 428, 588, 412, 572, 396, 556, 380, 540, 364, 524, 342, 502, 328, 488)(324, 484, 332, 492, 349, 509, 369, 529, 385, 545, 401, 561, 417, 577, 433, 593, 449, 609, 465, 625, 475, 635, 461, 621, 445, 605, 429, 589, 413, 573, 397, 557, 381, 541, 365, 525, 343, 503, 329, 489)(326, 486, 337, 497, 356, 516, 373, 533, 389, 549, 405, 565, 421, 581, 437, 597, 453, 613, 468, 628, 478, 638, 469, 629, 454, 614, 438, 598, 422, 582, 406, 566, 390, 550, 374, 534, 358, 518, 338, 498)(331, 491, 347, 507, 357, 517, 352, 512, 371, 531, 387, 547, 403, 563, 419, 579, 435, 595, 451, 611, 467, 627, 476, 636, 462, 622, 446, 606, 430, 590, 414, 574, 398, 558, 382, 542, 366, 526, 344, 504)(333, 493, 348, 508, 363, 523, 379, 539, 395, 555, 411, 571, 427, 587, 443, 603, 459, 619, 474, 634, 479, 639, 470, 630, 455, 615, 439, 599, 423, 583, 407, 567, 391, 551, 375, 535, 359, 519, 340, 500)(334, 494, 351, 511, 370, 530, 386, 546, 402, 562, 418, 578, 434, 594, 450, 610, 466, 626, 477, 637, 463, 623, 447, 607, 431, 591, 415, 575, 399, 559, 383, 543, 367, 527, 346, 506, 355, 515, 336, 496)(341, 501, 362, 522, 378, 538, 394, 554, 410, 570, 426, 586, 442, 602, 458, 618, 473, 633, 480, 640, 471, 631, 456, 616, 440, 600, 424, 584, 408, 568, 392, 552, 376, 536, 361, 521, 350, 510, 354, 514)
	L = (1, 323)(2, 327)(3, 330)(4, 332)(5, 321)(6, 337)(7, 339)(8, 322)(9, 324)(10, 345)(11, 347)(12, 349)(13, 348)(14, 351)(15, 325)(16, 334)(17, 356)(18, 326)(19, 360)(20, 333)(21, 362)(22, 328)(23, 329)(24, 331)(25, 368)(26, 355)(27, 357)(28, 363)(29, 369)(30, 354)(31, 370)(32, 371)(33, 335)(34, 341)(35, 336)(36, 373)(37, 352)(38, 338)(39, 340)(40, 377)(41, 350)(42, 378)(43, 379)(44, 342)(45, 343)(46, 344)(47, 346)(48, 384)(49, 385)(50, 386)(51, 387)(52, 353)(53, 389)(54, 358)(55, 359)(56, 361)(57, 393)(58, 394)(59, 395)(60, 364)(61, 365)(62, 366)(63, 367)(64, 400)(65, 401)(66, 402)(67, 403)(68, 372)(69, 405)(70, 374)(71, 375)(72, 376)(73, 409)(74, 410)(75, 411)(76, 380)(77, 381)(78, 382)(79, 383)(80, 416)(81, 417)(82, 418)(83, 419)(84, 388)(85, 421)(86, 390)(87, 391)(88, 392)(89, 425)(90, 426)(91, 427)(92, 396)(93, 397)(94, 398)(95, 399)(96, 432)(97, 433)(98, 434)(99, 435)(100, 404)(101, 437)(102, 406)(103, 407)(104, 408)(105, 441)(106, 442)(107, 443)(108, 412)(109, 413)(110, 414)(111, 415)(112, 448)(113, 449)(114, 450)(115, 451)(116, 420)(117, 453)(118, 422)(119, 423)(120, 424)(121, 457)(122, 458)(123, 459)(124, 428)(125, 429)(126, 430)(127, 431)(128, 464)(129, 465)(130, 466)(131, 467)(132, 436)(133, 468)(134, 438)(135, 439)(136, 440)(137, 472)(138, 473)(139, 474)(140, 444)(141, 445)(142, 446)(143, 447)(144, 452)(145, 475)(146, 477)(147, 476)(148, 478)(149, 454)(150, 455)(151, 456)(152, 460)(153, 480)(154, 479)(155, 461)(156, 462)(157, 463)(158, 469)(159, 470)(160, 471)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2213
Graph:: bipartite
	v = 28 e = 320 f = 240
	degree seq :: [ 16^20, 40^8 ]

E27.2213 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^4 * Y2)^2, (Y3^-2 * Y2)^4, Y3^4 * Y2 * Y3^-6 * Y2 * Y3^7 * Y2 * Y3^-2 * Y2 * Y3, (Y3^-1 * Y1^-1)^20 ]
Map:: polytopal
	R = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)(321, 481, 322, 482)(323, 483, 327, 487)(324, 484, 329, 489)(325, 485, 331, 491)(326, 486, 333, 493)(328, 488, 337, 497)(330, 490, 341, 501)(332, 492, 345, 505)(334, 494, 349, 509)(335, 495, 343, 503)(336, 496, 347, 507)(338, 498, 355, 515)(339, 499, 344, 504)(340, 500, 348, 508)(342, 502, 361, 521)(346, 506, 367, 527)(350, 510, 373, 533)(351, 511, 365, 525)(352, 512, 371, 531)(353, 513, 363, 523)(354, 514, 369, 529)(356, 516, 374, 534)(357, 517, 366, 526)(358, 518, 372, 532)(359, 519, 364, 524)(360, 520, 370, 530)(362, 522, 368, 528)(375, 535, 390, 550)(376, 536, 395, 555)(377, 537, 388, 548)(378, 538, 394, 554)(379, 539, 386, 546)(380, 540, 393, 553)(381, 541, 397, 557)(382, 542, 391, 551)(383, 543, 389, 549)(384, 544, 387, 547)(385, 545, 401, 561)(392, 552, 405, 565)(396, 556, 409, 569)(398, 558, 411, 571)(399, 559, 410, 570)(400, 560, 414, 574)(402, 562, 407, 567)(403, 563, 406, 566)(404, 564, 418, 578)(408, 568, 422, 582)(412, 572, 426, 586)(413, 573, 425, 585)(415, 575, 427, 587)(416, 576, 431, 591)(417, 577, 421, 581)(419, 579, 423, 583)(420, 580, 435, 595)(424, 584, 439, 599)(428, 588, 443, 603)(429, 589, 442, 602)(430, 590, 441, 601)(432, 592, 444, 604)(433, 593, 438, 598)(434, 594, 437, 597)(436, 596, 440, 600)(445, 605, 459, 619)(446, 606, 458, 618)(447, 607, 457, 617)(448, 608, 461, 621)(449, 609, 455, 615)(450, 610, 454, 614)(451, 611, 453, 613)(452, 612, 465, 625)(456, 616, 468, 628)(460, 620, 472, 632)(462, 622, 474, 634)(463, 623, 473, 633)(464, 624, 476, 636)(466, 626, 470, 630)(467, 627, 469, 629)(471, 631, 479, 639)(475, 635, 480, 640)(477, 637, 478, 638)
	L = (1, 323)(2, 325)(3, 328)(4, 321)(5, 332)(6, 322)(7, 335)(8, 338)(9, 339)(10, 324)(11, 343)(12, 346)(13, 347)(14, 326)(15, 351)(16, 327)(17, 353)(18, 356)(19, 357)(20, 329)(21, 359)(22, 330)(23, 363)(24, 331)(25, 365)(26, 368)(27, 369)(28, 333)(29, 371)(30, 334)(31, 375)(32, 336)(33, 377)(34, 337)(35, 379)(36, 381)(37, 382)(38, 340)(39, 383)(40, 341)(41, 384)(42, 342)(43, 386)(44, 344)(45, 388)(46, 345)(47, 390)(48, 392)(49, 393)(50, 348)(51, 394)(52, 349)(53, 395)(54, 350)(55, 361)(56, 352)(57, 360)(58, 354)(59, 358)(60, 355)(61, 400)(62, 401)(63, 402)(64, 403)(65, 362)(66, 373)(67, 364)(68, 372)(69, 366)(70, 370)(71, 367)(72, 408)(73, 409)(74, 410)(75, 411)(76, 374)(77, 376)(78, 378)(79, 380)(80, 416)(81, 417)(82, 418)(83, 419)(84, 385)(85, 387)(86, 389)(87, 391)(88, 424)(89, 425)(90, 426)(91, 427)(92, 396)(93, 397)(94, 398)(95, 399)(96, 432)(97, 433)(98, 434)(99, 435)(100, 404)(101, 405)(102, 406)(103, 407)(104, 440)(105, 441)(106, 442)(107, 443)(108, 412)(109, 413)(110, 414)(111, 415)(112, 448)(113, 449)(114, 450)(115, 451)(116, 420)(117, 421)(118, 422)(119, 423)(120, 456)(121, 457)(122, 458)(123, 459)(124, 428)(125, 429)(126, 430)(127, 431)(128, 464)(129, 465)(130, 466)(131, 467)(132, 436)(133, 437)(134, 438)(135, 439)(136, 471)(137, 472)(138, 473)(139, 474)(140, 444)(141, 445)(142, 446)(143, 447)(144, 452)(145, 477)(146, 476)(147, 475)(148, 453)(149, 454)(150, 455)(151, 460)(152, 480)(153, 479)(154, 478)(155, 461)(156, 462)(157, 463)(158, 468)(159, 469)(160, 470)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 16, 40 ), ( 16, 40, 16, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2212
Graph:: simple bipartite
	v = 240 e = 320 f = 28
	degree seq :: [ 2^160, 4^80 ]

E27.2214 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1, Y3 * Y1^-4 * Y3^-1 * Y1^-4, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3^-1 * Y1^-2 * Y3^-1, Y1 * Y3^-4 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1^20 ]
Map:: polytopal
	R = (1, 161, 2, 162, 5, 165, 11, 171, 23, 183, 43, 203, 66, 226, 85, 245, 101, 261, 117, 277, 133, 293, 132, 292, 116, 276, 100, 260, 84, 244, 65, 225, 42, 202, 22, 182, 10, 170, 4, 164)(3, 163, 7, 167, 15, 175, 31, 191, 55, 215, 77, 237, 93, 253, 109, 269, 125, 285, 141, 301, 151, 311, 135, 295, 118, 278, 107, 267, 89, 249, 68, 228, 44, 204, 36, 196, 18, 178, 8, 168)(6, 166, 13, 173, 27, 187, 51, 211, 41, 201, 64, 224, 83, 243, 99, 259, 115, 275, 131, 291, 147, 307, 149, 309, 134, 294, 123, 283, 105, 265, 87, 247, 67, 227, 54, 214, 30, 190, 14, 174)(9, 169, 19, 179, 37, 197, 62, 222, 81, 241, 97, 257, 113, 273, 129, 289, 145, 305, 153, 313, 137, 297, 119, 279, 102, 262, 91, 251, 71, 231, 46, 206, 24, 184, 45, 205, 38, 198, 20, 180)(12, 172, 25, 185, 47, 207, 40, 200, 21, 181, 39, 199, 63, 223, 82, 242, 98, 258, 114, 274, 130, 290, 146, 306, 148, 308, 139, 299, 121, 281, 103, 263, 86, 246, 74, 234, 50, 210, 26, 186)(16, 176, 28, 188, 48, 208, 69, 229, 61, 221, 76, 236, 92, 252, 108, 268, 124, 284, 140, 300, 154, 314, 160, 320, 155, 315, 144, 304, 128, 288, 111, 271, 94, 254, 80, 240, 58, 218, 33, 193)(17, 177, 29, 189, 49, 209, 70, 230, 88, 248, 104, 264, 120, 280, 136, 296, 150, 310, 158, 318, 156, 316, 142, 302, 126, 286, 112, 272, 95, 255, 78, 238, 56, 216, 75, 235, 59, 219, 34, 194)(32, 192, 52, 212, 72, 232, 60, 220, 35, 195, 53, 213, 73, 233, 90, 250, 106, 266, 122, 282, 138, 298, 152, 312, 159, 319, 157, 317, 143, 303, 127, 287, 110, 270, 96, 256, 79, 239, 57, 217)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640)
	L = (1, 323)(2, 326)(3, 321)(4, 329)(5, 332)(6, 322)(7, 336)(8, 337)(9, 324)(10, 341)(11, 344)(12, 325)(13, 348)(14, 349)(15, 352)(16, 327)(17, 328)(18, 355)(19, 353)(20, 354)(21, 330)(22, 361)(23, 364)(24, 331)(25, 368)(26, 369)(27, 372)(28, 333)(29, 334)(30, 373)(31, 376)(32, 335)(33, 339)(34, 340)(35, 338)(36, 381)(37, 377)(38, 380)(39, 378)(40, 379)(41, 342)(42, 375)(43, 387)(44, 343)(45, 389)(46, 390)(47, 392)(48, 345)(49, 346)(50, 393)(51, 395)(52, 347)(53, 350)(54, 396)(55, 362)(56, 351)(57, 357)(58, 359)(59, 360)(60, 358)(61, 356)(62, 398)(63, 399)(64, 400)(65, 401)(66, 406)(67, 363)(68, 408)(69, 365)(70, 366)(71, 410)(72, 367)(73, 370)(74, 412)(75, 371)(76, 374)(77, 414)(78, 382)(79, 383)(80, 384)(81, 385)(82, 415)(83, 416)(84, 418)(85, 422)(86, 386)(87, 424)(88, 388)(89, 426)(90, 391)(91, 428)(92, 394)(93, 430)(94, 397)(95, 402)(96, 403)(97, 431)(98, 404)(99, 432)(100, 435)(101, 438)(102, 405)(103, 440)(104, 407)(105, 442)(106, 409)(107, 444)(108, 411)(109, 446)(110, 413)(111, 417)(112, 419)(113, 447)(114, 448)(115, 420)(116, 445)(117, 454)(118, 421)(119, 456)(120, 423)(121, 458)(122, 425)(123, 460)(124, 427)(125, 436)(126, 429)(127, 433)(128, 434)(129, 462)(130, 463)(131, 464)(132, 465)(133, 468)(134, 437)(135, 470)(136, 439)(137, 472)(138, 441)(139, 474)(140, 443)(141, 475)(142, 449)(143, 450)(144, 451)(145, 452)(146, 476)(147, 477)(148, 453)(149, 478)(150, 455)(151, 479)(152, 457)(153, 480)(154, 459)(155, 461)(156, 466)(157, 467)(158, 469)(159, 471)(160, 473)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2211
Graph:: simple bipartite
	v = 168 e = 320 f = 100
	degree seq :: [ 2^160, 40^8 ]

E27.2215 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^4 * Y1)^2, (Y2^2 * Y1)^4, (Y3 * Y2^-1)^8, Y2^20, Y2^4 * Y1 * Y2^-6 * Y1 * Y2^7 * Y1 * Y2^-2 * Y1 * Y2 ]
Map::
	R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 11, 171)(6, 166, 13, 173)(8, 168, 17, 177)(10, 170, 21, 181)(12, 172, 25, 185)(14, 174, 29, 189)(15, 175, 23, 183)(16, 176, 27, 187)(18, 178, 35, 195)(19, 179, 24, 184)(20, 180, 28, 188)(22, 182, 41, 201)(26, 186, 47, 207)(30, 190, 53, 213)(31, 191, 45, 205)(32, 192, 51, 211)(33, 193, 43, 203)(34, 194, 49, 209)(36, 196, 54, 214)(37, 197, 46, 206)(38, 198, 52, 212)(39, 199, 44, 204)(40, 200, 50, 210)(42, 202, 48, 208)(55, 215, 70, 230)(56, 216, 75, 235)(57, 217, 68, 228)(58, 218, 74, 234)(59, 219, 66, 226)(60, 220, 73, 233)(61, 221, 77, 237)(62, 222, 71, 231)(63, 223, 69, 229)(64, 224, 67, 227)(65, 225, 81, 241)(72, 232, 85, 245)(76, 236, 89, 249)(78, 238, 91, 251)(79, 239, 90, 250)(80, 240, 94, 254)(82, 242, 87, 247)(83, 243, 86, 246)(84, 244, 98, 258)(88, 248, 102, 262)(92, 252, 106, 266)(93, 253, 105, 265)(95, 255, 107, 267)(96, 256, 111, 271)(97, 257, 101, 261)(99, 259, 103, 263)(100, 260, 115, 275)(104, 264, 119, 279)(108, 268, 123, 283)(109, 269, 122, 282)(110, 270, 121, 281)(112, 272, 124, 284)(113, 273, 118, 278)(114, 274, 117, 277)(116, 276, 120, 280)(125, 285, 139, 299)(126, 286, 138, 298)(127, 287, 137, 297)(128, 288, 141, 301)(129, 289, 135, 295)(130, 290, 134, 294)(131, 291, 133, 293)(132, 292, 145, 305)(136, 296, 148, 308)(140, 300, 152, 312)(142, 302, 154, 314)(143, 303, 153, 313)(144, 304, 156, 316)(146, 306, 150, 310)(147, 307, 149, 309)(151, 311, 159, 319)(155, 315, 160, 320)(157, 317, 158, 318)(321, 481, 323, 483, 328, 488, 338, 498, 356, 516, 381, 541, 400, 560, 416, 576, 432, 592, 448, 608, 464, 624, 452, 612, 436, 596, 420, 580, 404, 564, 385, 545, 362, 522, 342, 502, 330, 490, 324, 484)(322, 482, 325, 485, 332, 492, 346, 506, 368, 528, 392, 552, 408, 568, 424, 584, 440, 600, 456, 616, 471, 631, 460, 620, 444, 604, 428, 588, 412, 572, 396, 556, 374, 534, 350, 510, 334, 494, 326, 486)(327, 487, 335, 495, 351, 511, 375, 535, 361, 521, 384, 544, 403, 563, 419, 579, 435, 595, 451, 611, 467, 627, 475, 635, 461, 621, 445, 605, 429, 589, 413, 573, 397, 557, 376, 536, 352, 512, 336, 496)(329, 489, 339, 499, 357, 517, 382, 542, 401, 561, 417, 577, 433, 593, 449, 609, 465, 625, 477, 637, 463, 623, 447, 607, 431, 591, 415, 575, 399, 559, 380, 540, 355, 515, 379, 539, 358, 518, 340, 500)(331, 491, 343, 503, 363, 523, 386, 546, 373, 533, 395, 555, 411, 571, 427, 587, 443, 603, 459, 619, 474, 634, 478, 638, 468, 628, 453, 613, 437, 597, 421, 581, 405, 565, 387, 547, 364, 524, 344, 504)(333, 493, 347, 507, 369, 529, 393, 553, 409, 569, 425, 585, 441, 601, 457, 617, 472, 632, 480, 640, 470, 630, 455, 615, 439, 599, 423, 583, 407, 567, 391, 551, 367, 527, 390, 550, 370, 530, 348, 508)(337, 497, 353, 513, 377, 537, 360, 520, 341, 501, 359, 519, 383, 543, 402, 562, 418, 578, 434, 594, 450, 610, 466, 626, 476, 636, 462, 622, 446, 606, 430, 590, 414, 574, 398, 558, 378, 538, 354, 514)(345, 505, 365, 525, 388, 548, 372, 532, 349, 509, 371, 531, 394, 554, 410, 570, 426, 586, 442, 602, 458, 618, 473, 633, 479, 639, 469, 629, 454, 614, 438, 598, 422, 582, 406, 566, 389, 549, 366, 526)
	L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 331)(6, 333)(7, 323)(8, 337)(9, 324)(10, 341)(11, 325)(12, 345)(13, 326)(14, 349)(15, 343)(16, 347)(17, 328)(18, 355)(19, 344)(20, 348)(21, 330)(22, 361)(23, 335)(24, 339)(25, 332)(26, 367)(27, 336)(28, 340)(29, 334)(30, 373)(31, 365)(32, 371)(33, 363)(34, 369)(35, 338)(36, 374)(37, 366)(38, 372)(39, 364)(40, 370)(41, 342)(42, 368)(43, 353)(44, 359)(45, 351)(46, 357)(47, 346)(48, 362)(49, 354)(50, 360)(51, 352)(52, 358)(53, 350)(54, 356)(55, 390)(56, 395)(57, 388)(58, 394)(59, 386)(60, 393)(61, 397)(62, 391)(63, 389)(64, 387)(65, 401)(66, 379)(67, 384)(68, 377)(69, 383)(70, 375)(71, 382)(72, 405)(73, 380)(74, 378)(75, 376)(76, 409)(77, 381)(78, 411)(79, 410)(80, 414)(81, 385)(82, 407)(83, 406)(84, 418)(85, 392)(86, 403)(87, 402)(88, 422)(89, 396)(90, 399)(91, 398)(92, 426)(93, 425)(94, 400)(95, 427)(96, 431)(97, 421)(98, 404)(99, 423)(100, 435)(101, 417)(102, 408)(103, 419)(104, 439)(105, 413)(106, 412)(107, 415)(108, 443)(109, 442)(110, 441)(111, 416)(112, 444)(113, 438)(114, 437)(115, 420)(116, 440)(117, 434)(118, 433)(119, 424)(120, 436)(121, 430)(122, 429)(123, 428)(124, 432)(125, 459)(126, 458)(127, 457)(128, 461)(129, 455)(130, 454)(131, 453)(132, 465)(133, 451)(134, 450)(135, 449)(136, 468)(137, 447)(138, 446)(139, 445)(140, 472)(141, 448)(142, 474)(143, 473)(144, 476)(145, 452)(146, 470)(147, 469)(148, 456)(149, 467)(150, 466)(151, 479)(152, 460)(153, 463)(154, 462)(155, 480)(156, 464)(157, 478)(158, 477)(159, 471)(160, 475)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2216
Graph:: bipartite
	v = 88 e = 320 f = 180
	degree seq :: [ 4^80, 40^8 ]

E27.2216 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C20 x C4) : C2 (small group id <160, 12>)
Aut   = $<320, 449>$ (small group id <320, 449>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-3 * Y3^2 * Y1^-1, Y1^8, (Y3 * Y2^-1)^20 ]
Map:: polytopal
	R = (1, 161, 2, 162, 6, 166, 16, 176, 34, 194, 27, 187, 13, 173, 4, 164)(3, 163, 9, 169, 17, 177, 8, 168, 21, 181, 35, 195, 28, 188, 11, 171)(5, 165, 14, 174, 18, 178, 37, 197, 30, 190, 12, 172, 20, 180, 7, 167)(10, 170, 24, 184, 36, 196, 23, 183, 42, 202, 22, 182, 43, 203, 26, 186)(15, 175, 32, 192, 38, 198, 29, 189, 41, 201, 19, 179, 39, 199, 31, 191)(25, 185, 47, 207, 53, 213, 46, 206, 58, 218, 45, 205, 59, 219, 44, 204)(33, 193, 49, 209, 54, 214, 40, 200, 56, 216, 50, 210, 55, 215, 51, 211)(48, 208, 60, 220, 69, 229, 63, 223, 74, 234, 62, 222, 75, 235, 61, 221)(52, 212, 57, 217, 70, 230, 66, 226, 72, 232, 67, 227, 71, 231, 65, 225)(64, 224, 77, 237, 85, 245, 76, 236, 90, 250, 79, 239, 91, 251, 78, 238)(68, 228, 82, 242, 86, 246, 83, 243, 88, 248, 81, 241, 87, 247, 73, 233)(80, 240, 94, 254, 101, 261, 93, 253, 106, 266, 92, 252, 107, 267, 95, 255)(84, 244, 99, 259, 102, 262, 97, 257, 104, 264, 89, 249, 103, 263, 98, 258)(96, 256, 111, 271, 117, 277, 110, 270, 122, 282, 109, 269, 123, 283, 108, 268)(100, 260, 113, 273, 118, 278, 105, 265, 120, 280, 114, 274, 119, 279, 115, 275)(112, 272, 124, 284, 133, 293, 127, 287, 138, 298, 126, 286, 139, 299, 125, 285)(116, 276, 121, 281, 134, 294, 130, 290, 136, 296, 131, 291, 135, 295, 129, 289)(128, 288, 141, 301, 148, 308, 140, 300, 153, 313, 143, 303, 154, 314, 142, 302)(132, 292, 146, 306, 149, 309, 147, 307, 151, 311, 145, 305, 150, 310, 137, 297)(144, 304, 156, 316, 158, 318, 155, 315, 160, 320, 152, 312, 159, 319, 157, 317)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640)
	L = (1, 323)(2, 327)(3, 330)(4, 332)(5, 321)(6, 337)(7, 339)(8, 322)(9, 324)(10, 345)(11, 347)(12, 349)(13, 348)(14, 351)(15, 325)(16, 334)(17, 356)(18, 326)(19, 360)(20, 333)(21, 362)(22, 328)(23, 329)(24, 331)(25, 368)(26, 355)(27, 357)(28, 363)(29, 369)(30, 354)(31, 370)(32, 371)(33, 335)(34, 341)(35, 336)(36, 373)(37, 352)(38, 338)(39, 340)(40, 377)(41, 350)(42, 378)(43, 379)(44, 342)(45, 343)(46, 344)(47, 346)(48, 384)(49, 385)(50, 386)(51, 387)(52, 353)(53, 389)(54, 358)(55, 359)(56, 361)(57, 393)(58, 394)(59, 395)(60, 364)(61, 365)(62, 366)(63, 367)(64, 400)(65, 401)(66, 402)(67, 403)(68, 372)(69, 405)(70, 374)(71, 375)(72, 376)(73, 409)(74, 410)(75, 411)(76, 380)(77, 381)(78, 382)(79, 383)(80, 416)(81, 417)(82, 418)(83, 419)(84, 388)(85, 421)(86, 390)(87, 391)(88, 392)(89, 425)(90, 426)(91, 427)(92, 396)(93, 397)(94, 398)(95, 399)(96, 432)(97, 433)(98, 434)(99, 435)(100, 404)(101, 437)(102, 406)(103, 407)(104, 408)(105, 441)(106, 442)(107, 443)(108, 412)(109, 413)(110, 414)(111, 415)(112, 448)(113, 449)(114, 450)(115, 451)(116, 420)(117, 453)(118, 422)(119, 423)(120, 424)(121, 457)(122, 458)(123, 459)(124, 428)(125, 429)(126, 430)(127, 431)(128, 464)(129, 465)(130, 466)(131, 467)(132, 436)(133, 468)(134, 438)(135, 439)(136, 440)(137, 472)(138, 473)(139, 474)(140, 444)(141, 445)(142, 446)(143, 447)(144, 452)(145, 475)(146, 477)(147, 476)(148, 478)(149, 454)(150, 455)(151, 456)(152, 460)(153, 480)(154, 479)(155, 461)(156, 462)(157, 463)(158, 469)(159, 470)(160, 471)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2215
Graph:: simple bipartite
	v = 180 e = 320 f = 88
	degree seq :: [ 2^160, 16^20 ]

E27.2217 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 20})
Quotient :: regular
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^8, T1^20 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 32, 47, 65, 86, 105, 121, 120, 104, 85, 64, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 75, 97, 113, 129, 136, 123, 106, 88, 66, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 82, 101, 117, 133, 137, 122, 107, 87, 67, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 68, 90, 108, 125, 138, 149, 143, 130, 114, 98, 76, 56, 40, 27)(23, 36, 24, 38, 50, 69, 89, 109, 124, 139, 148, 146, 134, 118, 102, 83, 62, 45, 30, 37)(41, 57, 42, 59, 77, 99, 115, 131, 144, 153, 156, 151, 140, 127, 110, 92, 70, 60, 43, 58)(52, 71, 53, 73, 63, 84, 103, 119, 135, 147, 155, 157, 150, 141, 126, 111, 91, 74, 54, 72)(78, 93, 79, 94, 81, 96, 112, 128, 142, 152, 158, 160, 159, 154, 145, 132, 116, 100, 80, 95)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 114)(98, 115)(99, 116)(104, 113)(105, 122)(107, 124)(109, 126)(111, 128)(117, 134)(118, 135)(119, 132)(120, 133)(121, 136)(123, 138)(125, 140)(127, 142)(129, 143)(130, 144)(131, 145)(137, 148)(139, 150)(141, 152)(146, 155)(147, 154)(149, 156)(151, 158)(153, 159)(157, 160)
	local type(s) :: { ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2218
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 80 f = 20
	degree seq :: [ 20^8 ]

E27.2218 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 8, 20})
Quotient :: regular
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, T1^8, T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 15, 25, 31, 22, 12, 8)(6, 13, 9, 18, 29, 32, 21, 14)(16, 26, 17, 28, 33, 43, 37, 27)(23, 34, 24, 36, 42, 41, 30, 35)(38, 47, 39, 49, 52, 50, 40, 48)(44, 53, 45, 55, 51, 56, 46, 54)(57, 65, 58, 67, 60, 68, 59, 66)(61, 69, 62, 71, 64, 72, 63, 70)(73, 80, 74, 90, 76, 85, 75, 78)(77, 118, 84, 120, 91, 119, 81, 117)(79, 126, 86, 133, 97, 136, 87, 128)(82, 129, 92, 139, 95, 132, 83, 125)(88, 135, 99, 145, 98, 134, 89, 127)(93, 131, 96, 143, 103, 140, 94, 130)(100, 138, 102, 146, 108, 147, 101, 137)(104, 142, 106, 151, 107, 144, 105, 141)(109, 149, 111, 156, 112, 150, 110, 148)(113, 153, 115, 155, 116, 154, 114, 152)(121, 158, 123, 160, 124, 159, 122, 157)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 117)(70, 118)(71, 119)(72, 120)(77, 125)(78, 126)(79, 127)(80, 128)(81, 129)(82, 130)(83, 131)(84, 132)(85, 133)(86, 134)(87, 135)(88, 137)(89, 138)(90, 136)(91, 139)(92, 140)(93, 141)(94, 142)(95, 143)(96, 144)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 121)(114, 123)(115, 122)(116, 124)
	local type(s) :: { ( 20^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2217
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 20 e = 80 f = 8
	degree seq :: [ 8^20 ]

E27.2219 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ]
Map:: polytopal
	R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 9, 18, 30, 40, 27, 16)(11, 20, 13, 23, 36, 45, 33, 21)(25, 37, 26, 39, 50, 41, 29, 38)(31, 42, 32, 44, 55, 46, 35, 43)(47, 57, 48, 59, 51, 60, 49, 58)(52, 61, 53, 63, 56, 64, 54, 62)(65, 73, 66, 75, 68, 76, 67, 74)(69, 113, 70, 115, 72, 119, 71, 117)(77, 121, 82, 134, 90, 127, 80, 123)(78, 124, 86, 143, 96, 136, 84, 126)(79, 128, 89, 150, 92, 133, 81, 130)(83, 137, 95, 157, 98, 142, 85, 139)(87, 145, 91, 153, 102, 149, 88, 147)(93, 154, 97, 146, 107, 148, 94, 156)(99, 138, 101, 141, 103, 160, 100, 158)(104, 129, 106, 132, 108, 155, 105, 151)(109, 144, 111, 125, 112, 140, 110, 159)(114, 135, 118, 122, 120, 131, 116, 152)(161, 162)(163, 167)(164, 169)(165, 171)(166, 173)(168, 174)(170, 172)(175, 185)(176, 186)(177, 187)(178, 189)(179, 190)(180, 191)(181, 192)(182, 193)(183, 195)(184, 196)(188, 194)(197, 207)(198, 208)(199, 209)(200, 210)(201, 211)(202, 212)(203, 213)(204, 214)(205, 215)(206, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 242)(234, 250)(235, 237)(236, 240)(238, 275)(239, 287)(241, 283)(243, 296)(244, 279)(245, 286)(246, 273)(247, 293)(248, 290)(249, 294)(251, 310)(252, 281)(253, 302)(254, 299)(255, 303)(256, 277)(257, 317)(258, 284)(259, 309)(260, 307)(261, 313)(262, 288)(263, 305)(264, 308)(265, 316)(266, 306)(267, 297)(268, 314)(269, 320)(270, 318)(271, 301)(272, 298)(274, 315)(276, 311)(278, 292)(280, 289)(282, 285)(291, 304)(295, 300)(312, 319)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 40, 40 ), ( 40^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2223
Transitivity :: ET+
Graph:: simple bipartite
	v = 100 e = 160 f = 8
	degree seq :: [ 2^80, 8^20 ]

E27.2220 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^20 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 21, 36, 52, 68, 84, 100, 116, 132, 120, 104, 88, 72, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 79, 95, 111, 127, 142, 128, 112, 96, 80, 64, 48, 32, 18, 8)(4, 11, 23, 39, 55, 71, 87, 103, 119, 135, 145, 131, 115, 99, 83, 67, 51, 35, 20, 9)(6, 15, 29, 45, 61, 77, 93, 109, 125, 140, 152, 141, 126, 110, 94, 78, 62, 46, 30, 16)(12, 19, 34, 50, 66, 82, 98, 114, 130, 144, 154, 147, 134, 118, 102, 86, 70, 54, 38, 22)(14, 27, 43, 59, 75, 91, 107, 123, 138, 150, 158, 151, 139, 124, 108, 92, 76, 60, 44, 28)(24, 37, 53, 69, 85, 101, 117, 133, 146, 155, 159, 153, 143, 129, 113, 97, 81, 65, 49, 33)(26, 41, 57, 73, 89, 105, 121, 136, 148, 156, 160, 157, 149, 137, 122, 106, 90, 74, 58, 42)(161, 162, 166, 174, 186, 184, 172, 164)(163, 169, 179, 193, 201, 188, 175, 168)(165, 171, 182, 197, 202, 187, 176, 167)(170, 178, 189, 204, 217, 209, 194, 180)(173, 177, 190, 203, 218, 213, 198, 183)(181, 195, 210, 225, 233, 220, 205, 192)(185, 199, 214, 229, 234, 219, 206, 191)(196, 208, 221, 236, 249, 241, 226, 211)(200, 207, 222, 235, 250, 245, 230, 215)(212, 227, 242, 257, 265, 252, 237, 224)(216, 231, 246, 261, 266, 251, 238, 223)(228, 240, 253, 268, 281, 273, 258, 243)(232, 239, 254, 267, 282, 277, 262, 247)(244, 259, 274, 289, 296, 284, 269, 256)(248, 263, 278, 293, 297, 283, 270, 255)(260, 272, 285, 299, 308, 303, 290, 275)(264, 271, 286, 298, 309, 306, 294, 279)(276, 291, 304, 313, 316, 311, 300, 288)(280, 295, 307, 315, 317, 310, 301, 287)(292, 302, 312, 318, 320, 319, 314, 305)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 4^8 ), ( 4^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2224
Transitivity :: ET+
Graph:: simple bipartite
	v = 28 e = 160 f = 80
	degree seq :: [ 8^20, 20^8 ]

E27.2221 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 8, 20})
Quotient :: edge
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^8, T1^20 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 114)(98, 115)(99, 116)(104, 113)(105, 122)(107, 124)(109, 126)(111, 128)(117, 134)(118, 135)(119, 132)(120, 133)(121, 136)(123, 138)(125, 140)(127, 142)(129, 143)(130, 144)(131, 145)(137, 148)(139, 150)(141, 152)(146, 155)(147, 154)(149, 156)(151, 158)(153, 159)(157, 160)(161, 162, 165, 171, 180, 192, 207, 225, 246, 265, 281, 280, 264, 245, 224, 206, 191, 179, 170, 164)(163, 167, 175, 185, 199, 215, 235, 257, 273, 289, 296, 283, 266, 248, 226, 209, 193, 182, 172, 168)(166, 173, 169, 178, 189, 204, 221, 242, 261, 277, 293, 297, 282, 267, 247, 227, 208, 194, 181, 174)(176, 186, 177, 188, 195, 211, 228, 250, 268, 285, 298, 309, 303, 290, 274, 258, 236, 216, 200, 187)(183, 196, 184, 198, 210, 229, 249, 269, 284, 299, 308, 306, 294, 278, 262, 243, 222, 205, 190, 197)(201, 217, 202, 219, 237, 259, 275, 291, 304, 313, 316, 311, 300, 287, 270, 252, 230, 220, 203, 218)(212, 231, 213, 233, 223, 244, 263, 279, 295, 307, 315, 317, 310, 301, 286, 271, 251, 234, 214, 232)(238, 253, 239, 254, 241, 256, 272, 288, 302, 312, 318, 320, 319, 314, 305, 292, 276, 260, 240, 255)
	L = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)
	local type(s) :: { ( 16, 16 ), ( 16^20 ) }
Outer automorphisms :: reflexible
Dual of E27.2222
Transitivity :: ET+
Graph:: simple bipartite
	v = 88 e = 160 f = 20
	degree seq :: [ 2^80, 20^8 ]

E27.2222 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 ]
Map::
	R = (1, 161, 3, 163, 8, 168, 17, 177, 28, 188, 19, 179, 10, 170, 4, 164)(2, 162, 5, 165, 12, 172, 22, 182, 34, 194, 24, 184, 14, 174, 6, 166)(7, 167, 15, 175, 9, 169, 18, 178, 30, 190, 40, 200, 27, 187, 16, 176)(11, 171, 20, 180, 13, 173, 23, 183, 36, 196, 45, 205, 33, 193, 21, 181)(25, 185, 37, 197, 26, 186, 39, 199, 50, 210, 41, 201, 29, 189, 38, 198)(31, 191, 42, 202, 32, 192, 44, 204, 55, 215, 46, 206, 35, 195, 43, 203)(47, 207, 57, 217, 48, 208, 59, 219, 51, 211, 60, 220, 49, 209, 58, 218)(52, 212, 61, 221, 53, 213, 63, 223, 56, 216, 64, 224, 54, 214, 62, 222)(65, 225, 73, 233, 66, 226, 75, 235, 68, 228, 76, 236, 67, 227, 74, 234)(69, 229, 82, 242, 70, 230, 77, 237, 72, 232, 83, 243, 71, 231, 94, 254)(78, 238, 119, 279, 79, 239, 117, 277, 88, 248, 113, 273, 86, 246, 115, 275)(80, 240, 128, 288, 81, 241, 121, 281, 93, 253, 133, 293, 91, 251, 130, 290)(84, 244, 125, 285, 85, 245, 123, 283, 98, 258, 141, 301, 87, 247, 138, 298)(89, 249, 131, 291, 90, 250, 127, 287, 103, 263, 151, 311, 92, 252, 148, 308)(95, 255, 139, 299, 96, 256, 136, 296, 99, 259, 143, 303, 97, 257, 158, 318)(100, 260, 149, 309, 101, 261, 146, 306, 104, 264, 153, 313, 102, 262, 157, 317)(105, 265, 159, 319, 106, 266, 150, 310, 108, 268, 147, 307, 107, 267, 154, 314)(109, 269, 160, 320, 110, 270, 140, 300, 112, 272, 137, 297, 111, 271, 144, 304)(114, 274, 152, 312, 116, 276, 155, 315, 120, 280, 132, 292, 118, 278, 129, 289)(122, 282, 124, 284, 134, 294, 142, 302, 156, 316, 145, 305, 135, 295, 126, 286)
	L = (1, 162)(2, 161)(3, 167)(4, 169)(5, 171)(6, 173)(7, 163)(8, 174)(9, 164)(10, 172)(11, 165)(12, 170)(13, 166)(14, 168)(15, 185)(16, 186)(17, 187)(18, 189)(19, 190)(20, 191)(21, 192)(22, 193)(23, 195)(24, 196)(25, 175)(26, 176)(27, 177)(28, 194)(29, 178)(30, 179)(31, 180)(32, 181)(33, 182)(34, 188)(35, 183)(36, 184)(37, 207)(38, 208)(39, 209)(40, 210)(41, 211)(42, 212)(43, 213)(44, 214)(45, 215)(46, 216)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 217)(66, 218)(67, 219)(68, 220)(69, 221)(70, 222)(71, 223)(72, 224)(73, 273)(74, 275)(75, 277)(76, 279)(77, 281)(78, 283)(79, 285)(80, 287)(81, 291)(82, 293)(83, 288)(84, 296)(85, 299)(86, 301)(87, 303)(88, 298)(89, 306)(90, 309)(91, 311)(92, 313)(93, 308)(94, 290)(95, 310)(96, 319)(97, 307)(98, 318)(99, 314)(100, 300)(101, 320)(102, 297)(103, 317)(104, 304)(105, 315)(106, 312)(107, 292)(108, 289)(109, 305)(110, 302)(111, 286)(112, 284)(113, 233)(114, 295)(115, 234)(116, 316)(117, 235)(118, 282)(119, 236)(120, 294)(121, 237)(122, 278)(123, 238)(124, 272)(125, 239)(126, 271)(127, 240)(128, 243)(129, 268)(130, 254)(131, 241)(132, 267)(133, 242)(134, 280)(135, 274)(136, 244)(137, 262)(138, 248)(139, 245)(140, 260)(141, 246)(142, 270)(143, 247)(144, 264)(145, 269)(146, 249)(147, 257)(148, 253)(149, 250)(150, 255)(151, 251)(152, 266)(153, 252)(154, 259)(155, 265)(156, 276)(157, 263)(158, 258)(159, 256)(160, 261)
	local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.2221
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 20 e = 160 f = 88
	degree seq :: [ 16^20 ]

E27.2223 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^20 ]
Map::
	R = (1, 161, 3, 163, 10, 170, 21, 181, 36, 196, 52, 212, 68, 228, 84, 244, 100, 260, 116, 276, 132, 292, 120, 280, 104, 264, 88, 248, 72, 232, 56, 216, 40, 200, 25, 185, 13, 173, 5, 165)(2, 162, 7, 167, 17, 177, 31, 191, 47, 207, 63, 223, 79, 239, 95, 255, 111, 271, 127, 287, 142, 302, 128, 288, 112, 272, 96, 256, 80, 240, 64, 224, 48, 208, 32, 192, 18, 178, 8, 168)(4, 164, 11, 171, 23, 183, 39, 199, 55, 215, 71, 231, 87, 247, 103, 263, 119, 279, 135, 295, 145, 305, 131, 291, 115, 275, 99, 259, 83, 243, 67, 227, 51, 211, 35, 195, 20, 180, 9, 169)(6, 166, 15, 175, 29, 189, 45, 205, 61, 221, 77, 237, 93, 253, 109, 269, 125, 285, 140, 300, 152, 312, 141, 301, 126, 286, 110, 270, 94, 254, 78, 238, 62, 222, 46, 206, 30, 190, 16, 176)(12, 172, 19, 179, 34, 194, 50, 210, 66, 226, 82, 242, 98, 258, 114, 274, 130, 290, 144, 304, 154, 314, 147, 307, 134, 294, 118, 278, 102, 262, 86, 246, 70, 230, 54, 214, 38, 198, 22, 182)(14, 174, 27, 187, 43, 203, 59, 219, 75, 235, 91, 251, 107, 267, 123, 283, 138, 298, 150, 310, 158, 318, 151, 311, 139, 299, 124, 284, 108, 268, 92, 252, 76, 236, 60, 220, 44, 204, 28, 188)(24, 184, 37, 197, 53, 213, 69, 229, 85, 245, 101, 261, 117, 277, 133, 293, 146, 306, 155, 315, 159, 319, 153, 313, 143, 303, 129, 289, 113, 273, 97, 257, 81, 241, 65, 225, 49, 209, 33, 193)(26, 186, 41, 201, 57, 217, 73, 233, 89, 249, 105, 265, 121, 281, 136, 296, 148, 308, 156, 316, 160, 320, 157, 317, 149, 309, 137, 297, 122, 282, 106, 266, 90, 250, 74, 234, 58, 218, 42, 202)
	L = (1, 162)(2, 166)(3, 169)(4, 161)(5, 171)(6, 174)(7, 165)(8, 163)(9, 179)(10, 178)(11, 182)(12, 164)(13, 177)(14, 186)(15, 168)(16, 167)(17, 190)(18, 189)(19, 193)(20, 170)(21, 195)(22, 197)(23, 173)(24, 172)(25, 199)(26, 184)(27, 176)(28, 175)(29, 204)(30, 203)(31, 185)(32, 181)(33, 201)(34, 180)(35, 210)(36, 208)(37, 202)(38, 183)(39, 214)(40, 207)(41, 188)(42, 187)(43, 218)(44, 217)(45, 192)(46, 191)(47, 222)(48, 221)(49, 194)(50, 225)(51, 196)(52, 227)(53, 198)(54, 229)(55, 200)(56, 231)(57, 209)(58, 213)(59, 206)(60, 205)(61, 236)(62, 235)(63, 216)(64, 212)(65, 233)(66, 211)(67, 242)(68, 240)(69, 234)(70, 215)(71, 246)(72, 239)(73, 220)(74, 219)(75, 250)(76, 249)(77, 224)(78, 223)(79, 254)(80, 253)(81, 226)(82, 257)(83, 228)(84, 259)(85, 230)(86, 261)(87, 232)(88, 263)(89, 241)(90, 245)(91, 238)(92, 237)(93, 268)(94, 267)(95, 248)(96, 244)(97, 265)(98, 243)(99, 274)(100, 272)(101, 266)(102, 247)(103, 278)(104, 271)(105, 252)(106, 251)(107, 282)(108, 281)(109, 256)(110, 255)(111, 286)(112, 285)(113, 258)(114, 289)(115, 260)(116, 291)(117, 262)(118, 293)(119, 264)(120, 295)(121, 273)(122, 277)(123, 270)(124, 269)(125, 299)(126, 298)(127, 280)(128, 276)(129, 296)(130, 275)(131, 304)(132, 302)(133, 297)(134, 279)(135, 307)(136, 284)(137, 283)(138, 309)(139, 308)(140, 288)(141, 287)(142, 312)(143, 290)(144, 313)(145, 292)(146, 294)(147, 315)(148, 303)(149, 306)(150, 301)(151, 300)(152, 318)(153, 316)(154, 305)(155, 317)(156, 311)(157, 310)(158, 320)(159, 314)(160, 319)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2219
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 160 f = 100
	degree seq :: [ 40^8 ]

E27.2224 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 8, 20})
Quotient :: loop
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, (T2 * T1)^8, T1^20 ]
Map:: polytopal non-degenerate
	R = (1, 161, 3, 163)(2, 162, 6, 166)(4, 164, 9, 169)(5, 165, 12, 172)(7, 167, 16, 176)(8, 168, 17, 177)(10, 170, 15, 175)(11, 171, 21, 181)(13, 173, 23, 183)(14, 174, 24, 184)(18, 178, 30, 190)(19, 179, 29, 189)(20, 180, 33, 193)(22, 182, 35, 195)(25, 185, 40, 200)(26, 186, 41, 201)(27, 187, 42, 202)(28, 188, 43, 203)(31, 191, 39, 199)(32, 192, 48, 208)(34, 194, 50, 210)(36, 196, 52, 212)(37, 197, 53, 213)(38, 198, 54, 214)(44, 204, 62, 222)(45, 205, 63, 223)(46, 206, 61, 221)(47, 207, 66, 226)(49, 209, 68, 228)(51, 211, 70, 230)(55, 215, 76, 236)(56, 216, 77, 237)(57, 217, 78, 238)(58, 218, 79, 239)(59, 219, 80, 240)(60, 220, 81, 241)(64, 224, 75, 235)(65, 225, 87, 247)(67, 227, 89, 249)(69, 229, 91, 251)(71, 231, 93, 253)(72, 232, 94, 254)(73, 233, 95, 255)(74, 234, 96, 256)(82, 242, 102, 262)(83, 243, 103, 263)(84, 244, 100, 260)(85, 245, 101, 261)(86, 246, 106, 266)(88, 248, 108, 268)(90, 250, 110, 270)(92, 252, 112, 272)(97, 257, 114, 274)(98, 258, 115, 275)(99, 259, 116, 276)(104, 264, 113, 273)(105, 265, 122, 282)(107, 267, 124, 284)(109, 269, 126, 286)(111, 271, 128, 288)(117, 277, 134, 294)(118, 278, 135, 295)(119, 279, 132, 292)(120, 280, 133, 293)(121, 281, 136, 296)(123, 283, 138, 298)(125, 285, 140, 300)(127, 287, 142, 302)(129, 289, 143, 303)(130, 290, 144, 304)(131, 291, 145, 305)(137, 297, 148, 308)(139, 299, 150, 310)(141, 301, 152, 312)(146, 306, 155, 315)(147, 307, 154, 314)(149, 309, 156, 316)(151, 311, 158, 318)(153, 313, 159, 319)(157, 317, 160, 320)
	L = (1, 162)(2, 165)(3, 167)(4, 161)(5, 171)(6, 173)(7, 175)(8, 163)(9, 178)(10, 164)(11, 180)(12, 168)(13, 169)(14, 166)(15, 185)(16, 186)(17, 188)(18, 189)(19, 170)(20, 192)(21, 174)(22, 172)(23, 196)(24, 198)(25, 199)(26, 177)(27, 176)(28, 195)(29, 204)(30, 197)(31, 179)(32, 207)(33, 182)(34, 181)(35, 211)(36, 184)(37, 183)(38, 210)(39, 215)(40, 187)(41, 217)(42, 219)(43, 218)(44, 221)(45, 190)(46, 191)(47, 225)(48, 194)(49, 193)(50, 229)(51, 228)(52, 231)(53, 233)(54, 232)(55, 235)(56, 200)(57, 202)(58, 201)(59, 237)(60, 203)(61, 242)(62, 205)(63, 244)(64, 206)(65, 246)(66, 209)(67, 208)(68, 250)(69, 249)(70, 220)(71, 213)(72, 212)(73, 223)(74, 214)(75, 257)(76, 216)(77, 259)(78, 253)(79, 254)(80, 255)(81, 256)(82, 261)(83, 222)(84, 263)(85, 224)(86, 265)(87, 227)(88, 226)(89, 269)(90, 268)(91, 234)(92, 230)(93, 239)(94, 241)(95, 238)(96, 272)(97, 273)(98, 236)(99, 275)(100, 240)(101, 277)(102, 243)(103, 279)(104, 245)(105, 281)(106, 248)(107, 247)(108, 285)(109, 284)(110, 252)(111, 251)(112, 288)(113, 289)(114, 258)(115, 291)(116, 260)(117, 293)(118, 262)(119, 295)(120, 264)(121, 280)(122, 267)(123, 266)(124, 299)(125, 298)(126, 271)(127, 270)(128, 302)(129, 296)(130, 274)(131, 304)(132, 276)(133, 297)(134, 278)(135, 307)(136, 283)(137, 282)(138, 309)(139, 308)(140, 287)(141, 286)(142, 312)(143, 290)(144, 313)(145, 292)(146, 294)(147, 315)(148, 306)(149, 303)(150, 301)(151, 300)(152, 318)(153, 316)(154, 305)(155, 317)(156, 311)(157, 310)(158, 320)(159, 314)(160, 319)
	local type(s) :: { ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E27.2220
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 80 e = 160 f = 28
	degree seq :: [ 4^80 ]

E27.2225 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y2^8, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 11, 171)(6, 166, 13, 173)(8, 168, 14, 174)(10, 170, 12, 172)(15, 175, 25, 185)(16, 176, 26, 186)(17, 177, 27, 187)(18, 178, 29, 189)(19, 179, 30, 190)(20, 180, 31, 191)(21, 181, 32, 192)(22, 182, 33, 193)(23, 183, 35, 195)(24, 184, 36, 196)(28, 188, 34, 194)(37, 197, 47, 207)(38, 198, 48, 208)(39, 199, 49, 209)(40, 200, 50, 210)(41, 201, 51, 211)(42, 202, 52, 212)(43, 203, 53, 213)(44, 204, 54, 214)(45, 205, 55, 215)(46, 206, 56, 216)(57, 217, 65, 225)(58, 218, 66, 226)(59, 219, 67, 227)(60, 220, 68, 228)(61, 221, 69, 229)(62, 222, 70, 230)(63, 223, 71, 231)(64, 224, 72, 232)(73, 233, 137, 297)(74, 234, 139, 299)(75, 235, 141, 301)(76, 236, 143, 303)(77, 237, 132, 292)(78, 238, 136, 296)(79, 239, 120, 280)(80, 240, 122, 282)(81, 241, 115, 275)(82, 242, 117, 277)(83, 243, 144, 304)(84, 244, 131, 291)(85, 245, 142, 302)(86, 246, 130, 290)(87, 247, 150, 310)(88, 248, 135, 295)(89, 249, 154, 314)(90, 250, 134, 294)(91, 251, 121, 281)(92, 252, 97, 257)(93, 253, 118, 278)(94, 254, 99, 259)(95, 255, 119, 279)(96, 256, 116, 276)(98, 258, 113, 273)(100, 260, 114, 274)(101, 261, 157, 317)(102, 262, 149, 309)(103, 263, 140, 300)(104, 264, 129, 289)(105, 265, 148, 308)(106, 266, 138, 298)(107, 267, 160, 320)(108, 268, 155, 315)(109, 269, 146, 306)(110, 270, 133, 293)(111, 271, 153, 313)(112, 272, 145, 305)(123, 283, 152, 312)(124, 284, 159, 319)(125, 285, 156, 316)(126, 286, 147, 307)(127, 287, 158, 318)(128, 288, 151, 311)(321, 481, 323, 483, 328, 488, 337, 497, 348, 508, 339, 499, 330, 490, 324, 484)(322, 482, 325, 485, 332, 492, 342, 502, 354, 514, 344, 504, 334, 494, 326, 486)(327, 487, 335, 495, 329, 489, 338, 498, 350, 510, 360, 520, 347, 507, 336, 496)(331, 491, 340, 500, 333, 493, 343, 503, 356, 516, 365, 525, 353, 513, 341, 501)(345, 505, 357, 517, 346, 506, 359, 519, 370, 530, 361, 521, 349, 509, 358, 518)(351, 511, 362, 522, 352, 512, 364, 524, 375, 535, 366, 526, 355, 515, 363, 523)(367, 527, 377, 537, 368, 528, 379, 539, 371, 531, 380, 540, 369, 529, 378, 538)(372, 532, 381, 541, 373, 533, 383, 543, 376, 536, 384, 544, 374, 534, 382, 542)(385, 545, 393, 553, 386, 546, 395, 555, 388, 548, 396, 556, 387, 547, 394, 554)(389, 549, 447, 607, 390, 550, 445, 605, 392, 552, 443, 603, 391, 551, 444, 604)(397, 557, 458, 618, 404, 564, 462, 622, 424, 584, 464, 624, 406, 566, 460, 620)(398, 558, 465, 625, 408, 568, 474, 634, 430, 590, 470, 630, 410, 570, 466, 626)(399, 559, 455, 615, 413, 573, 456, 616, 415, 575, 454, 614, 400, 560, 453, 613)(401, 561, 451, 611, 418, 578, 452, 612, 420, 580, 450, 610, 402, 562, 449, 609)(403, 563, 467, 627, 405, 565, 469, 629, 426, 586, 477, 637, 423, 583, 468, 628)(407, 567, 471, 631, 409, 569, 475, 635, 432, 592, 480, 640, 429, 589, 473, 633)(411, 571, 438, 598, 414, 574, 440, 600, 436, 596, 442, 602, 412, 572, 439, 599)(416, 576, 433, 593, 419, 579, 435, 595, 441, 601, 437, 597, 417, 577, 434, 594)(421, 581, 478, 638, 422, 582, 479, 639, 446, 606, 472, 632, 425, 585, 476, 636)(427, 587, 457, 617, 428, 588, 459, 619, 448, 608, 463, 623, 431, 591, 461, 621)
	L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 331)(6, 333)(7, 323)(8, 334)(9, 324)(10, 332)(11, 325)(12, 330)(13, 326)(14, 328)(15, 345)(16, 346)(17, 347)(18, 349)(19, 350)(20, 351)(21, 352)(22, 353)(23, 355)(24, 356)(25, 335)(26, 336)(27, 337)(28, 354)(29, 338)(30, 339)(31, 340)(32, 341)(33, 342)(34, 348)(35, 343)(36, 344)(37, 367)(38, 368)(39, 369)(40, 370)(41, 371)(42, 372)(43, 373)(44, 374)(45, 375)(46, 376)(47, 357)(48, 358)(49, 359)(50, 360)(51, 361)(52, 362)(53, 363)(54, 364)(55, 365)(56, 366)(57, 385)(58, 386)(59, 387)(60, 388)(61, 389)(62, 390)(63, 391)(64, 392)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 457)(74, 459)(75, 461)(76, 463)(77, 452)(78, 456)(79, 440)(80, 442)(81, 435)(82, 437)(83, 464)(84, 451)(85, 462)(86, 450)(87, 470)(88, 455)(89, 474)(90, 454)(91, 441)(92, 417)(93, 438)(94, 419)(95, 439)(96, 436)(97, 412)(98, 433)(99, 414)(100, 434)(101, 477)(102, 469)(103, 460)(104, 449)(105, 468)(106, 458)(107, 480)(108, 475)(109, 466)(110, 453)(111, 473)(112, 465)(113, 418)(114, 420)(115, 401)(116, 416)(117, 402)(118, 413)(119, 415)(120, 399)(121, 411)(122, 400)(123, 472)(124, 479)(125, 476)(126, 467)(127, 478)(128, 471)(129, 424)(130, 406)(131, 404)(132, 397)(133, 430)(134, 410)(135, 408)(136, 398)(137, 393)(138, 426)(139, 394)(140, 423)(141, 395)(142, 405)(143, 396)(144, 403)(145, 432)(146, 429)(147, 446)(148, 425)(149, 422)(150, 407)(151, 448)(152, 443)(153, 431)(154, 409)(155, 428)(156, 445)(157, 421)(158, 447)(159, 444)(160, 427)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2228
Graph:: bipartite
	v = 100 e = 320 f = 168
	degree seq :: [ 4^80, 16^20 ]

E27.2226 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^8, Y2^20 ]
Map::
	R = (1, 161, 2, 162, 6, 166, 14, 174, 26, 186, 24, 184, 12, 172, 4, 164)(3, 163, 9, 169, 19, 179, 33, 193, 41, 201, 28, 188, 15, 175, 8, 168)(5, 165, 11, 171, 22, 182, 37, 197, 42, 202, 27, 187, 16, 176, 7, 167)(10, 170, 18, 178, 29, 189, 44, 204, 57, 217, 49, 209, 34, 194, 20, 180)(13, 173, 17, 177, 30, 190, 43, 203, 58, 218, 53, 213, 38, 198, 23, 183)(21, 181, 35, 195, 50, 210, 65, 225, 73, 233, 60, 220, 45, 205, 32, 192)(25, 185, 39, 199, 54, 214, 69, 229, 74, 234, 59, 219, 46, 206, 31, 191)(36, 196, 48, 208, 61, 221, 76, 236, 89, 249, 81, 241, 66, 226, 51, 211)(40, 200, 47, 207, 62, 222, 75, 235, 90, 250, 85, 245, 70, 230, 55, 215)(52, 212, 67, 227, 82, 242, 97, 257, 105, 265, 92, 252, 77, 237, 64, 224)(56, 216, 71, 231, 86, 246, 101, 261, 106, 266, 91, 251, 78, 238, 63, 223)(68, 228, 80, 240, 93, 253, 108, 268, 121, 281, 113, 273, 98, 258, 83, 243)(72, 232, 79, 239, 94, 254, 107, 267, 122, 282, 117, 277, 102, 262, 87, 247)(84, 244, 99, 259, 114, 274, 129, 289, 136, 296, 124, 284, 109, 269, 96, 256)(88, 248, 103, 263, 118, 278, 133, 293, 137, 297, 123, 283, 110, 270, 95, 255)(100, 260, 112, 272, 125, 285, 139, 299, 148, 308, 143, 303, 130, 290, 115, 275)(104, 264, 111, 271, 126, 286, 138, 298, 149, 309, 146, 306, 134, 294, 119, 279)(116, 276, 131, 291, 144, 304, 153, 313, 156, 316, 151, 311, 140, 300, 128, 288)(120, 280, 135, 295, 147, 307, 155, 315, 157, 317, 150, 310, 141, 301, 127, 287)(132, 292, 142, 302, 152, 312, 158, 318, 160, 320, 159, 319, 154, 314, 145, 305)(321, 481, 323, 483, 330, 490, 341, 501, 356, 516, 372, 532, 388, 548, 404, 564, 420, 580, 436, 596, 452, 612, 440, 600, 424, 584, 408, 568, 392, 552, 376, 536, 360, 520, 345, 505, 333, 493, 325, 485)(322, 482, 327, 487, 337, 497, 351, 511, 367, 527, 383, 543, 399, 559, 415, 575, 431, 591, 447, 607, 462, 622, 448, 608, 432, 592, 416, 576, 400, 560, 384, 544, 368, 528, 352, 512, 338, 498, 328, 488)(324, 484, 331, 491, 343, 503, 359, 519, 375, 535, 391, 551, 407, 567, 423, 583, 439, 599, 455, 615, 465, 625, 451, 611, 435, 595, 419, 579, 403, 563, 387, 547, 371, 531, 355, 515, 340, 500, 329, 489)(326, 486, 335, 495, 349, 509, 365, 525, 381, 541, 397, 557, 413, 573, 429, 589, 445, 605, 460, 620, 472, 632, 461, 621, 446, 606, 430, 590, 414, 574, 398, 558, 382, 542, 366, 526, 350, 510, 336, 496)(332, 492, 339, 499, 354, 514, 370, 530, 386, 546, 402, 562, 418, 578, 434, 594, 450, 610, 464, 624, 474, 634, 467, 627, 454, 614, 438, 598, 422, 582, 406, 566, 390, 550, 374, 534, 358, 518, 342, 502)(334, 494, 347, 507, 363, 523, 379, 539, 395, 555, 411, 571, 427, 587, 443, 603, 458, 618, 470, 630, 478, 638, 471, 631, 459, 619, 444, 604, 428, 588, 412, 572, 396, 556, 380, 540, 364, 524, 348, 508)(344, 504, 357, 517, 373, 533, 389, 549, 405, 565, 421, 581, 437, 597, 453, 613, 466, 626, 475, 635, 479, 639, 473, 633, 463, 623, 449, 609, 433, 593, 417, 577, 401, 561, 385, 545, 369, 529, 353, 513)(346, 506, 361, 521, 377, 537, 393, 553, 409, 569, 425, 585, 441, 601, 456, 616, 468, 628, 476, 636, 480, 640, 477, 637, 469, 629, 457, 617, 442, 602, 426, 586, 410, 570, 394, 554, 378, 538, 362, 522)
	L = (1, 323)(2, 327)(3, 330)(4, 331)(5, 321)(6, 335)(7, 337)(8, 322)(9, 324)(10, 341)(11, 343)(12, 339)(13, 325)(14, 347)(15, 349)(16, 326)(17, 351)(18, 328)(19, 354)(20, 329)(21, 356)(22, 332)(23, 359)(24, 357)(25, 333)(26, 361)(27, 363)(28, 334)(29, 365)(30, 336)(31, 367)(32, 338)(33, 344)(34, 370)(35, 340)(36, 372)(37, 373)(38, 342)(39, 375)(40, 345)(41, 377)(42, 346)(43, 379)(44, 348)(45, 381)(46, 350)(47, 383)(48, 352)(49, 353)(50, 386)(51, 355)(52, 388)(53, 389)(54, 358)(55, 391)(56, 360)(57, 393)(58, 362)(59, 395)(60, 364)(61, 397)(62, 366)(63, 399)(64, 368)(65, 369)(66, 402)(67, 371)(68, 404)(69, 405)(70, 374)(71, 407)(72, 376)(73, 409)(74, 378)(75, 411)(76, 380)(77, 413)(78, 382)(79, 415)(80, 384)(81, 385)(82, 418)(83, 387)(84, 420)(85, 421)(86, 390)(87, 423)(88, 392)(89, 425)(90, 394)(91, 427)(92, 396)(93, 429)(94, 398)(95, 431)(96, 400)(97, 401)(98, 434)(99, 403)(100, 436)(101, 437)(102, 406)(103, 439)(104, 408)(105, 441)(106, 410)(107, 443)(108, 412)(109, 445)(110, 414)(111, 447)(112, 416)(113, 417)(114, 450)(115, 419)(116, 452)(117, 453)(118, 422)(119, 455)(120, 424)(121, 456)(122, 426)(123, 458)(124, 428)(125, 460)(126, 430)(127, 462)(128, 432)(129, 433)(130, 464)(131, 435)(132, 440)(133, 466)(134, 438)(135, 465)(136, 468)(137, 442)(138, 470)(139, 444)(140, 472)(141, 446)(142, 448)(143, 449)(144, 474)(145, 451)(146, 475)(147, 454)(148, 476)(149, 457)(150, 478)(151, 459)(152, 461)(153, 463)(154, 467)(155, 479)(156, 480)(157, 469)(158, 471)(159, 473)(160, 477)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2227
Graph:: bipartite
	v = 28 e = 320 f = 240
	degree seq :: [ 16^20, 40^8 ]

E27.2227 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, (Y3^-1 * Y2)^8, Y3^6 * Y2 * Y3^-14 * Y2, (Y3^-1 * Y1^-1)^20 ]
Map:: polytopal
	R = (1, 161)(2, 162)(3, 163)(4, 164)(5, 165)(6, 166)(7, 167)(8, 168)(9, 169)(10, 170)(11, 171)(12, 172)(13, 173)(14, 174)(15, 175)(16, 176)(17, 177)(18, 178)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 191)(32, 192)(33, 193)(34, 194)(35, 195)(36, 196)(37, 197)(38, 198)(39, 199)(40, 200)(41, 201)(42, 202)(43, 203)(44, 204)(45, 205)(46, 206)(47, 207)(48, 208)(49, 209)(50, 210)(51, 211)(52, 212)(53, 213)(54, 214)(55, 215)(56, 216)(57, 217)(58, 218)(59, 219)(60, 220)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 245)(86, 246)(87, 247)(88, 248)(89, 249)(90, 250)(91, 251)(92, 252)(93, 253)(94, 254)(95, 255)(96, 256)(97, 257)(98, 258)(99, 259)(100, 260)(101, 261)(102, 262)(103, 263)(104, 264)(105, 265)(106, 266)(107, 267)(108, 268)(109, 269)(110, 270)(111, 271)(112, 272)(113, 273)(114, 274)(115, 275)(116, 276)(117, 277)(118, 278)(119, 279)(120, 280)(121, 281)(122, 282)(123, 283)(124, 284)(125, 285)(126, 286)(127, 287)(128, 288)(129, 289)(130, 290)(131, 291)(132, 292)(133, 293)(134, 294)(135, 295)(136, 296)(137, 297)(138, 298)(139, 299)(140, 300)(141, 301)(142, 302)(143, 303)(144, 304)(145, 305)(146, 306)(147, 307)(148, 308)(149, 309)(150, 310)(151, 311)(152, 312)(153, 313)(154, 314)(155, 315)(156, 316)(157, 317)(158, 318)(159, 319)(160, 320)(321, 481, 322, 482)(323, 483, 327, 487)(324, 484, 329, 489)(325, 485, 331, 491)(326, 486, 333, 493)(328, 488, 334, 494)(330, 490, 332, 492)(335, 495, 345, 505)(336, 496, 346, 506)(337, 497, 347, 507)(338, 498, 349, 509)(339, 499, 350, 510)(340, 500, 352, 512)(341, 501, 353, 513)(342, 502, 354, 514)(343, 503, 356, 516)(344, 504, 357, 517)(348, 508, 358, 518)(351, 511, 355, 515)(359, 519, 375, 535)(360, 520, 376, 536)(361, 521, 377, 537)(362, 522, 378, 538)(363, 523, 379, 539)(364, 524, 381, 541)(365, 525, 382, 542)(366, 526, 383, 543)(367, 527, 385, 545)(368, 528, 386, 546)(369, 529, 387, 547)(370, 530, 388, 548)(371, 531, 389, 549)(372, 532, 391, 551)(373, 533, 392, 552)(374, 534, 393, 553)(380, 540, 394, 554)(384, 544, 390, 550)(395, 555, 406, 566)(396, 556, 408, 568)(397, 557, 407, 567)(398, 558, 413, 573)(399, 559, 417, 577)(400, 560, 418, 578)(401, 561, 419, 579)(402, 562, 409, 569)(403, 563, 421, 581)(404, 564, 422, 582)(405, 565, 423, 583)(410, 570, 425, 585)(411, 571, 426, 586)(412, 572, 427, 587)(414, 574, 429, 589)(415, 575, 430, 590)(416, 576, 431, 591)(420, 580, 432, 592)(424, 584, 428, 588)(433, 593, 445, 605)(434, 594, 449, 609)(435, 595, 450, 610)(436, 596, 451, 611)(437, 597, 441, 601)(438, 598, 453, 613)(439, 599, 454, 614)(440, 600, 455, 615)(442, 602, 456, 616)(443, 603, 457, 617)(444, 604, 458, 618)(446, 606, 460, 620)(447, 607, 461, 621)(448, 608, 462, 622)(452, 612, 459, 619)(463, 623, 471, 631)(464, 624, 473, 633)(465, 625, 474, 634)(466, 626, 468, 628)(467, 627, 475, 635)(469, 629, 476, 636)(470, 630, 477, 637)(472, 632, 478, 638)(479, 639, 480, 640)
	L = (1, 323)(2, 325)(3, 328)(4, 321)(5, 332)(6, 322)(7, 335)(8, 337)(9, 338)(10, 324)(11, 340)(12, 342)(13, 343)(14, 326)(15, 329)(16, 327)(17, 348)(18, 350)(19, 330)(20, 333)(21, 331)(22, 355)(23, 357)(24, 334)(25, 359)(26, 361)(27, 336)(28, 363)(29, 360)(30, 365)(31, 339)(32, 367)(33, 369)(34, 341)(35, 371)(36, 368)(37, 373)(38, 344)(39, 346)(40, 345)(41, 378)(42, 347)(43, 380)(44, 349)(45, 383)(46, 351)(47, 353)(48, 352)(49, 388)(50, 354)(51, 390)(52, 356)(53, 393)(54, 358)(55, 395)(56, 397)(57, 396)(58, 399)(59, 362)(60, 401)(61, 402)(62, 364)(63, 404)(64, 366)(65, 406)(66, 408)(67, 407)(68, 410)(69, 370)(70, 412)(71, 413)(72, 372)(73, 415)(74, 374)(75, 376)(76, 375)(77, 381)(78, 377)(79, 418)(80, 379)(81, 420)(82, 421)(83, 382)(84, 423)(85, 384)(86, 386)(87, 385)(88, 391)(89, 387)(90, 426)(91, 389)(92, 428)(93, 429)(94, 392)(95, 431)(96, 394)(97, 398)(98, 434)(99, 400)(100, 436)(101, 437)(102, 403)(103, 439)(104, 405)(105, 409)(106, 442)(107, 411)(108, 444)(109, 445)(110, 414)(111, 447)(112, 416)(113, 417)(114, 450)(115, 419)(116, 452)(117, 453)(118, 422)(119, 455)(120, 424)(121, 425)(122, 457)(123, 427)(124, 459)(125, 460)(126, 430)(127, 462)(128, 432)(129, 433)(130, 464)(131, 435)(132, 440)(133, 466)(134, 438)(135, 465)(136, 441)(137, 469)(138, 443)(139, 448)(140, 471)(141, 446)(142, 470)(143, 449)(144, 474)(145, 451)(146, 475)(147, 454)(148, 456)(149, 477)(150, 458)(151, 478)(152, 461)(153, 463)(154, 467)(155, 479)(156, 468)(157, 472)(158, 480)(159, 473)(160, 476)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 16, 40 ), ( 16, 40, 16, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2226
Graph:: simple bipartite
	v = 240 e = 320 f = 28
	degree seq :: [ 2^160, 4^80 ]

E27.2228 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-2 * Y3^-1, (Y3^-1 * Y1)^8, Y1^20 ]
Map:: polytopal
	R = (1, 161, 2, 162, 5, 165, 11, 171, 20, 180, 32, 192, 47, 207, 65, 225, 86, 246, 105, 265, 121, 281, 120, 280, 104, 264, 85, 245, 64, 224, 46, 206, 31, 191, 19, 179, 10, 170, 4, 164)(3, 163, 7, 167, 15, 175, 25, 185, 39, 199, 55, 215, 75, 235, 97, 257, 113, 273, 129, 289, 136, 296, 123, 283, 106, 266, 88, 248, 66, 226, 49, 209, 33, 193, 22, 182, 12, 172, 8, 168)(6, 166, 13, 173, 9, 169, 18, 178, 29, 189, 44, 204, 61, 221, 82, 242, 101, 261, 117, 277, 133, 293, 137, 297, 122, 282, 107, 267, 87, 247, 67, 227, 48, 208, 34, 194, 21, 181, 14, 174)(16, 176, 26, 186, 17, 177, 28, 188, 35, 195, 51, 211, 68, 228, 90, 250, 108, 268, 125, 285, 138, 298, 149, 309, 143, 303, 130, 290, 114, 274, 98, 258, 76, 236, 56, 216, 40, 200, 27, 187)(23, 183, 36, 196, 24, 184, 38, 198, 50, 210, 69, 229, 89, 249, 109, 269, 124, 284, 139, 299, 148, 308, 146, 306, 134, 294, 118, 278, 102, 262, 83, 243, 62, 222, 45, 205, 30, 190, 37, 197)(41, 201, 57, 217, 42, 202, 59, 219, 77, 237, 99, 259, 115, 275, 131, 291, 144, 304, 153, 313, 156, 316, 151, 311, 140, 300, 127, 287, 110, 270, 92, 252, 70, 230, 60, 220, 43, 203, 58, 218)(52, 212, 71, 231, 53, 213, 73, 233, 63, 223, 84, 244, 103, 263, 119, 279, 135, 295, 147, 307, 155, 315, 157, 317, 150, 310, 141, 301, 126, 286, 111, 271, 91, 251, 74, 234, 54, 214, 72, 232)(78, 238, 93, 253, 79, 239, 94, 254, 81, 241, 96, 256, 112, 272, 128, 288, 142, 302, 152, 312, 158, 318, 160, 320, 159, 319, 154, 314, 145, 305, 132, 292, 116, 276, 100, 260, 80, 240, 95, 255)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640)
	L = (1, 323)(2, 326)(3, 321)(4, 329)(5, 332)(6, 322)(7, 336)(8, 337)(9, 324)(10, 335)(11, 341)(12, 325)(13, 343)(14, 344)(15, 330)(16, 327)(17, 328)(18, 350)(19, 349)(20, 353)(21, 331)(22, 355)(23, 333)(24, 334)(25, 360)(26, 361)(27, 362)(28, 363)(29, 339)(30, 338)(31, 359)(32, 368)(33, 340)(34, 370)(35, 342)(36, 372)(37, 373)(38, 374)(39, 351)(40, 345)(41, 346)(42, 347)(43, 348)(44, 382)(45, 383)(46, 381)(47, 386)(48, 352)(49, 388)(50, 354)(51, 390)(52, 356)(53, 357)(54, 358)(55, 396)(56, 397)(57, 398)(58, 399)(59, 400)(60, 401)(61, 366)(62, 364)(63, 365)(64, 395)(65, 407)(66, 367)(67, 409)(68, 369)(69, 411)(70, 371)(71, 413)(72, 414)(73, 415)(74, 416)(75, 384)(76, 375)(77, 376)(78, 377)(79, 378)(80, 379)(81, 380)(82, 422)(83, 423)(84, 420)(85, 421)(86, 426)(87, 385)(88, 428)(89, 387)(90, 430)(91, 389)(92, 432)(93, 391)(94, 392)(95, 393)(96, 394)(97, 434)(98, 435)(99, 436)(100, 404)(101, 405)(102, 402)(103, 403)(104, 433)(105, 442)(106, 406)(107, 444)(108, 408)(109, 446)(110, 410)(111, 448)(112, 412)(113, 424)(114, 417)(115, 418)(116, 419)(117, 454)(118, 455)(119, 452)(120, 453)(121, 456)(122, 425)(123, 458)(124, 427)(125, 460)(126, 429)(127, 462)(128, 431)(129, 463)(130, 464)(131, 465)(132, 439)(133, 440)(134, 437)(135, 438)(136, 441)(137, 468)(138, 443)(139, 470)(140, 445)(141, 472)(142, 447)(143, 449)(144, 450)(145, 451)(146, 475)(147, 474)(148, 457)(149, 476)(150, 459)(151, 478)(152, 461)(153, 479)(154, 467)(155, 466)(156, 469)(157, 480)(158, 471)(159, 473)(160, 477)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2225
Graph:: simple bipartite
	v = 168 e = 320 f = 100
	degree seq :: [ 2^160, 40^8 ]

E27.2229 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^8, Y2^20 ]
Map::
	R = (1, 161, 2, 162)(3, 163, 7, 167)(4, 164, 9, 169)(5, 165, 11, 171)(6, 166, 13, 173)(8, 168, 14, 174)(10, 170, 12, 172)(15, 175, 25, 185)(16, 176, 26, 186)(17, 177, 27, 187)(18, 178, 29, 189)(19, 179, 30, 190)(20, 180, 32, 192)(21, 181, 33, 193)(22, 182, 34, 194)(23, 183, 36, 196)(24, 184, 37, 197)(28, 188, 38, 198)(31, 191, 35, 195)(39, 199, 55, 215)(40, 200, 56, 216)(41, 201, 57, 217)(42, 202, 58, 218)(43, 203, 59, 219)(44, 204, 61, 221)(45, 205, 62, 222)(46, 206, 63, 223)(47, 207, 65, 225)(48, 208, 66, 226)(49, 209, 67, 227)(50, 210, 68, 228)(51, 211, 69, 229)(52, 212, 71, 231)(53, 213, 72, 232)(54, 214, 73, 233)(60, 220, 74, 234)(64, 224, 70, 230)(75, 235, 86, 246)(76, 236, 88, 248)(77, 237, 87, 247)(78, 238, 93, 253)(79, 239, 97, 257)(80, 240, 98, 258)(81, 241, 99, 259)(82, 242, 89, 249)(83, 243, 101, 261)(84, 244, 102, 262)(85, 245, 103, 263)(90, 250, 105, 265)(91, 251, 106, 266)(92, 252, 107, 267)(94, 254, 109, 269)(95, 255, 110, 270)(96, 256, 111, 271)(100, 260, 112, 272)(104, 264, 108, 268)(113, 273, 125, 285)(114, 274, 129, 289)(115, 275, 130, 290)(116, 276, 131, 291)(117, 277, 121, 281)(118, 278, 133, 293)(119, 279, 134, 294)(120, 280, 135, 295)(122, 282, 136, 296)(123, 283, 137, 297)(124, 284, 138, 298)(126, 286, 140, 300)(127, 287, 141, 301)(128, 288, 142, 302)(132, 292, 139, 299)(143, 303, 151, 311)(144, 304, 153, 313)(145, 305, 154, 314)(146, 306, 148, 308)(147, 307, 155, 315)(149, 309, 156, 316)(150, 310, 157, 317)(152, 312, 158, 318)(159, 319, 160, 320)(321, 481, 323, 483, 328, 488, 337, 497, 348, 508, 363, 523, 380, 540, 401, 561, 420, 580, 436, 596, 452, 612, 440, 600, 424, 584, 405, 565, 384, 544, 366, 526, 351, 511, 339, 499, 330, 490, 324, 484)(322, 482, 325, 485, 332, 492, 342, 502, 355, 515, 371, 531, 390, 550, 412, 572, 428, 588, 444, 604, 459, 619, 448, 608, 432, 592, 416, 576, 394, 554, 374, 534, 358, 518, 344, 504, 334, 494, 326, 486)(327, 487, 335, 495, 329, 489, 338, 498, 350, 510, 365, 525, 383, 543, 404, 564, 423, 583, 439, 599, 455, 615, 465, 625, 451, 611, 435, 595, 419, 579, 400, 560, 379, 539, 362, 522, 347, 507, 336, 496)(331, 491, 340, 500, 333, 493, 343, 503, 357, 517, 373, 533, 393, 553, 415, 575, 431, 591, 447, 607, 462, 622, 470, 630, 458, 618, 443, 603, 427, 587, 411, 571, 389, 549, 370, 530, 354, 514, 341, 501)(345, 505, 359, 519, 346, 506, 361, 521, 378, 538, 399, 559, 418, 578, 434, 594, 450, 610, 464, 624, 474, 634, 467, 627, 454, 614, 438, 598, 422, 582, 403, 563, 382, 542, 364, 524, 349, 509, 360, 520)(352, 512, 367, 527, 353, 513, 369, 529, 388, 548, 410, 570, 426, 586, 442, 602, 457, 617, 469, 629, 477, 637, 472, 632, 461, 621, 446, 606, 430, 590, 414, 574, 392, 552, 372, 532, 356, 516, 368, 528)(375, 535, 395, 555, 376, 536, 397, 557, 381, 541, 402, 562, 421, 581, 437, 597, 453, 613, 466, 626, 475, 635, 479, 639, 473, 633, 463, 623, 449, 609, 433, 593, 417, 577, 398, 558, 377, 537, 396, 556)(385, 545, 406, 566, 386, 546, 408, 568, 391, 551, 413, 573, 429, 589, 445, 605, 460, 620, 471, 631, 478, 638, 480, 640, 476, 636, 468, 628, 456, 616, 441, 601, 425, 585, 409, 569, 387, 547, 407, 567)
	L = (1, 322)(2, 321)(3, 327)(4, 329)(5, 331)(6, 333)(7, 323)(8, 334)(9, 324)(10, 332)(11, 325)(12, 330)(13, 326)(14, 328)(15, 345)(16, 346)(17, 347)(18, 349)(19, 350)(20, 352)(21, 353)(22, 354)(23, 356)(24, 357)(25, 335)(26, 336)(27, 337)(28, 358)(29, 338)(30, 339)(31, 355)(32, 340)(33, 341)(34, 342)(35, 351)(36, 343)(37, 344)(38, 348)(39, 375)(40, 376)(41, 377)(42, 378)(43, 379)(44, 381)(45, 382)(46, 383)(47, 385)(48, 386)(49, 387)(50, 388)(51, 389)(52, 391)(53, 392)(54, 393)(55, 359)(56, 360)(57, 361)(58, 362)(59, 363)(60, 394)(61, 364)(62, 365)(63, 366)(64, 390)(65, 367)(66, 368)(67, 369)(68, 370)(69, 371)(70, 384)(71, 372)(72, 373)(73, 374)(74, 380)(75, 406)(76, 408)(77, 407)(78, 413)(79, 417)(80, 418)(81, 419)(82, 409)(83, 421)(84, 422)(85, 423)(86, 395)(87, 397)(88, 396)(89, 402)(90, 425)(91, 426)(92, 427)(93, 398)(94, 429)(95, 430)(96, 431)(97, 399)(98, 400)(99, 401)(100, 432)(101, 403)(102, 404)(103, 405)(104, 428)(105, 410)(106, 411)(107, 412)(108, 424)(109, 414)(110, 415)(111, 416)(112, 420)(113, 445)(114, 449)(115, 450)(116, 451)(117, 441)(118, 453)(119, 454)(120, 455)(121, 437)(122, 456)(123, 457)(124, 458)(125, 433)(126, 460)(127, 461)(128, 462)(129, 434)(130, 435)(131, 436)(132, 459)(133, 438)(134, 439)(135, 440)(136, 442)(137, 443)(138, 444)(139, 452)(140, 446)(141, 447)(142, 448)(143, 471)(144, 473)(145, 474)(146, 468)(147, 475)(148, 466)(149, 476)(150, 477)(151, 463)(152, 478)(153, 464)(154, 465)(155, 467)(156, 469)(157, 470)(158, 472)(159, 480)(160, 479)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E27.2230
Graph:: bipartite
	v = 88 e = 320 f = 180
	degree seq :: [ 4^80, 40^8 ]

E27.2230 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 8, 20})
Quotient :: dipole
Aut^+ = (C2 x (C5 : C8)) : C2 (small group id <160, 16>)
Aut   = $<320, 400>$ (small group id <320, 400>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3 * Y2^-1)^20 ]
Map:: polytopal
	R = (1, 161, 2, 162, 6, 166, 14, 174, 26, 186, 24, 184, 12, 172, 4, 164)(3, 163, 9, 169, 19, 179, 33, 193, 41, 201, 28, 188, 15, 175, 8, 168)(5, 165, 11, 171, 22, 182, 37, 197, 42, 202, 27, 187, 16, 176, 7, 167)(10, 170, 18, 178, 29, 189, 44, 204, 57, 217, 49, 209, 34, 194, 20, 180)(13, 173, 17, 177, 30, 190, 43, 203, 58, 218, 53, 213, 38, 198, 23, 183)(21, 181, 35, 195, 50, 210, 65, 225, 73, 233, 60, 220, 45, 205, 32, 192)(25, 185, 39, 199, 54, 214, 69, 229, 74, 234, 59, 219, 46, 206, 31, 191)(36, 196, 48, 208, 61, 221, 76, 236, 89, 249, 81, 241, 66, 226, 51, 211)(40, 200, 47, 207, 62, 222, 75, 235, 90, 250, 85, 245, 70, 230, 55, 215)(52, 212, 67, 227, 82, 242, 97, 257, 105, 265, 92, 252, 77, 237, 64, 224)(56, 216, 71, 231, 86, 246, 101, 261, 106, 266, 91, 251, 78, 238, 63, 223)(68, 228, 80, 240, 93, 253, 108, 268, 121, 281, 113, 273, 98, 258, 83, 243)(72, 232, 79, 239, 94, 254, 107, 267, 122, 282, 117, 277, 102, 262, 87, 247)(84, 244, 99, 259, 114, 274, 129, 289, 136, 296, 124, 284, 109, 269, 96, 256)(88, 248, 103, 263, 118, 278, 133, 293, 137, 297, 123, 283, 110, 270, 95, 255)(100, 260, 112, 272, 125, 285, 139, 299, 148, 308, 143, 303, 130, 290, 115, 275)(104, 264, 111, 271, 126, 286, 138, 298, 149, 309, 146, 306, 134, 294, 119, 279)(116, 276, 131, 291, 144, 304, 153, 313, 156, 316, 151, 311, 140, 300, 128, 288)(120, 280, 135, 295, 147, 307, 155, 315, 157, 317, 150, 310, 141, 301, 127, 287)(132, 292, 142, 302, 152, 312, 158, 318, 160, 320, 159, 319, 154, 314, 145, 305)(321, 481)(322, 482)(323, 483)(324, 484)(325, 485)(326, 486)(327, 487)(328, 488)(329, 489)(330, 490)(331, 491)(332, 492)(333, 493)(334, 494)(335, 495)(336, 496)(337, 497)(338, 498)(339, 499)(340, 500)(341, 501)(342, 502)(343, 503)(344, 504)(345, 505)(346, 506)(347, 507)(348, 508)(349, 509)(350, 510)(351, 511)(352, 512)(353, 513)(354, 514)(355, 515)(356, 516)(357, 517)(358, 518)(359, 519)(360, 520)(361, 521)(362, 522)(363, 523)(364, 524)(365, 525)(366, 526)(367, 527)(368, 528)(369, 529)(370, 530)(371, 531)(372, 532)(373, 533)(374, 534)(375, 535)(376, 536)(377, 537)(378, 538)(379, 539)(380, 540)(381, 541)(382, 542)(383, 543)(384, 544)(385, 545)(386, 546)(387, 547)(388, 548)(389, 549)(390, 550)(391, 551)(392, 552)(393, 553)(394, 554)(395, 555)(396, 556)(397, 557)(398, 558)(399, 559)(400, 560)(401, 561)(402, 562)(403, 563)(404, 564)(405, 565)(406, 566)(407, 567)(408, 568)(409, 569)(410, 570)(411, 571)(412, 572)(413, 573)(414, 574)(415, 575)(416, 576)(417, 577)(418, 578)(419, 579)(420, 580)(421, 581)(422, 582)(423, 583)(424, 584)(425, 585)(426, 586)(427, 587)(428, 588)(429, 589)(430, 590)(431, 591)(432, 592)(433, 593)(434, 594)(435, 595)(436, 596)(437, 597)(438, 598)(439, 599)(440, 600)(441, 601)(442, 602)(443, 603)(444, 604)(445, 605)(446, 606)(447, 607)(448, 608)(449, 609)(450, 610)(451, 611)(452, 612)(453, 613)(454, 614)(455, 615)(456, 616)(457, 617)(458, 618)(459, 619)(460, 620)(461, 621)(462, 622)(463, 623)(464, 624)(465, 625)(466, 626)(467, 627)(468, 628)(469, 629)(470, 630)(471, 631)(472, 632)(473, 633)(474, 634)(475, 635)(476, 636)(477, 637)(478, 638)(479, 639)(480, 640)
	L = (1, 323)(2, 327)(3, 330)(4, 331)(5, 321)(6, 335)(7, 337)(8, 322)(9, 324)(10, 341)(11, 343)(12, 339)(13, 325)(14, 347)(15, 349)(16, 326)(17, 351)(18, 328)(19, 354)(20, 329)(21, 356)(22, 332)(23, 359)(24, 357)(25, 333)(26, 361)(27, 363)(28, 334)(29, 365)(30, 336)(31, 367)(32, 338)(33, 344)(34, 370)(35, 340)(36, 372)(37, 373)(38, 342)(39, 375)(40, 345)(41, 377)(42, 346)(43, 379)(44, 348)(45, 381)(46, 350)(47, 383)(48, 352)(49, 353)(50, 386)(51, 355)(52, 388)(53, 389)(54, 358)(55, 391)(56, 360)(57, 393)(58, 362)(59, 395)(60, 364)(61, 397)(62, 366)(63, 399)(64, 368)(65, 369)(66, 402)(67, 371)(68, 404)(69, 405)(70, 374)(71, 407)(72, 376)(73, 409)(74, 378)(75, 411)(76, 380)(77, 413)(78, 382)(79, 415)(80, 384)(81, 385)(82, 418)(83, 387)(84, 420)(85, 421)(86, 390)(87, 423)(88, 392)(89, 425)(90, 394)(91, 427)(92, 396)(93, 429)(94, 398)(95, 431)(96, 400)(97, 401)(98, 434)(99, 403)(100, 436)(101, 437)(102, 406)(103, 439)(104, 408)(105, 441)(106, 410)(107, 443)(108, 412)(109, 445)(110, 414)(111, 447)(112, 416)(113, 417)(114, 450)(115, 419)(116, 452)(117, 453)(118, 422)(119, 455)(120, 424)(121, 456)(122, 426)(123, 458)(124, 428)(125, 460)(126, 430)(127, 462)(128, 432)(129, 433)(130, 464)(131, 435)(132, 440)(133, 466)(134, 438)(135, 465)(136, 468)(137, 442)(138, 470)(139, 444)(140, 472)(141, 446)(142, 448)(143, 449)(144, 474)(145, 451)(146, 475)(147, 454)(148, 476)(149, 457)(150, 478)(151, 459)(152, 461)(153, 463)(154, 467)(155, 479)(156, 480)(157, 469)(158, 471)(159, 473)(160, 477)(161, 481)(162, 482)(163, 483)(164, 484)(165, 485)(166, 486)(167, 487)(168, 488)(169, 489)(170, 490)(171, 491)(172, 492)(173, 493)(174, 494)(175, 495)(176, 496)(177, 497)(178, 498)(179, 499)(180, 500)(181, 501)(182, 502)(183, 503)(184, 504)(185, 505)(186, 506)(187, 507)(188, 508)(189, 509)(190, 510)(191, 511)(192, 512)(193, 513)(194, 514)(195, 515)(196, 516)(197, 517)(198, 518)(199, 519)(200, 520)(201, 521)(202, 522)(203, 523)(204, 524)(205, 525)(206, 526)(207, 527)(208, 528)(209, 529)(210, 530)(211, 531)(212, 532)(213, 533)(214, 534)(215, 535)(216, 536)(217, 537)(218, 538)(219, 539)(220, 540)(221, 541)(222, 542)(223, 543)(224, 544)(225, 545)(226, 546)(227, 547)(228, 548)(229, 549)(230, 550)(231, 551)(232, 552)(233, 553)(234, 554)(235, 555)(236, 556)(237, 557)(238, 558)(239, 559)(240, 560)(241, 561)(242, 562)(243, 563)(244, 564)(245, 565)(246, 566)(247, 567)(248, 568)(249, 569)(250, 570)(251, 571)(252, 572)(253, 573)(254, 574)(255, 575)(256, 576)(257, 577)(258, 578)(259, 579)(260, 580)(261, 581)(262, 582)(263, 583)(264, 584)(265, 585)(266, 586)(267, 587)(268, 588)(269, 589)(270, 590)(271, 591)(272, 592)(273, 593)(274, 594)(275, 595)(276, 596)(277, 597)(278, 598)(279, 599)(280, 600)(281, 601)(282, 602)(283, 603)(284, 604)(285, 605)(286, 606)(287, 607)(288, 608)(289, 609)(290, 610)(291, 611)(292, 612)(293, 613)(294, 614)(295, 615)(296, 616)(297, 617)(298, 618)(299, 619)(300, 620)(301, 621)(302, 622)(303, 623)(304, 624)(305, 625)(306, 626)(307, 627)(308, 628)(309, 629)(310, 630)(311, 631)(312, 632)(313, 633)(314, 634)(315, 635)(316, 636)(317, 637)(318, 638)(319, 639)(320, 640)
	local type(s) :: { ( 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) }
Outer automorphisms :: reflexible
Dual of E27.2229
Graph:: simple bipartite
	v = 180 e = 320 f = 88
	degree seq :: [ 2^160, 16^20 ]

E27.2231 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2 * Y3)^4, (Y3 * Y1)^26 ]
Map:: polytopal non-degenerate
	R = (1, 210, 2, 209)(3, 215, 7, 211)(4, 217, 9, 212)(5, 219, 11, 213)(6, 221, 13, 214)(8, 220, 12, 216)(10, 222, 14, 218)(15, 233, 25, 223)(16, 234, 26, 224)(17, 235, 27, 225)(18, 237, 29, 226)(19, 238, 30, 227)(20, 239, 31, 228)(21, 240, 32, 229)(22, 241, 33, 230)(23, 243, 35, 231)(24, 244, 36, 232)(28, 242, 34, 236)(37, 255, 47, 245)(38, 256, 48, 246)(39, 257, 49, 247)(40, 258, 50, 248)(41, 259, 51, 249)(42, 260, 52, 250)(43, 261, 53, 251)(44, 262, 54, 252)(45, 263, 55, 253)(46, 264, 56, 254)(57, 273, 65, 265)(58, 274, 66, 266)(59, 275, 67, 267)(60, 276, 68, 268)(61, 277, 69, 269)(62, 278, 70, 270)(63, 279, 71, 271)(64, 280, 72, 272)(73, 332, 124, 281)(74, 316, 108, 282)(75, 319, 111, 283)(76, 315, 107, 284)(77, 349, 141, 285)(78, 352, 144, 286)(79, 353, 145, 287)(80, 357, 149, 288)(81, 350, 142, 289)(82, 361, 153, 290)(83, 363, 155, 291)(84, 365, 157, 292)(85, 367, 159, 293)(86, 364, 156, 294)(87, 369, 161, 295)(88, 371, 163, 296)(89, 373, 165, 297)(90, 370, 162, 298)(91, 355, 147, 299)(92, 377, 169, 300)(93, 354, 146, 301)(94, 356, 148, 302)(95, 372, 164, 303)(96, 359, 151, 304)(97, 382, 174, 305)(98, 351, 143, 306)(99, 360, 152, 307)(100, 366, 158, 308)(101, 344, 136, 309)(102, 342, 134, 310)(103, 385, 177, 311)(104, 368, 160, 312)(105, 343, 135, 313)(106, 386, 178, 314)(109, 387, 179, 317)(110, 374, 166, 318)(112, 388, 180, 320)(113, 375, 167, 321)(114, 379, 171, 322)(115, 376, 168, 323)(116, 358, 150, 324)(117, 378, 170, 325)(118, 380, 172, 326)(119, 384, 176, 327)(120, 381, 173, 328)(121, 362, 154, 329)(122, 383, 175, 330)(123, 341, 133, 331)(125, 389, 181, 333)(126, 392, 184, 334)(127, 390, 182, 335)(128, 391, 183, 336)(129, 393, 185, 337)(130, 396, 188, 338)(131, 394, 186, 339)(132, 395, 187, 340)(137, 397, 189, 345)(138, 400, 192, 346)(139, 398, 190, 347)(140, 399, 191, 348)(193, 405, 197, 401)(194, 407, 199, 402)(195, 408, 200, 403)(196, 406, 198, 404)(201, 416, 208, 409)(202, 415, 207, 410)(203, 413, 205, 411)(204, 414, 206, 412)
	L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 50)(46, 55)(47, 57)(48, 59)(49, 58)(51, 60)(52, 61)(53, 63)(54, 62)(56, 64)(65, 73)(66, 75)(67, 74)(68, 76)(69, 133)(70, 135)(71, 134)(72, 136)(77, 142)(78, 145)(79, 147)(80, 148)(81, 151)(82, 152)(83, 141)(84, 143)(85, 156)(86, 153)(87, 144)(88, 146)(89, 162)(90, 149)(91, 167)(92, 168)(93, 169)(94, 171)(95, 150)(96, 172)(97, 173)(98, 174)(99, 176)(100, 154)(101, 155)(102, 177)(103, 157)(104, 158)(105, 159)(106, 160)(107, 161)(108, 179)(109, 163)(110, 164)(111, 165)(112, 166)(113, 181)(114, 182)(115, 184)(116, 170)(117, 183)(118, 185)(119, 186)(120, 188)(121, 175)(122, 187)(123, 178)(124, 180)(125, 189)(126, 190)(127, 192)(128, 191)(129, 193)(130, 194)(131, 196)(132, 195)(137, 201)(138, 202)(139, 204)(140, 203)(197, 208)(198, 207)(199, 206)(200, 205)(209, 212)(210, 214)(211, 216)(213, 220)(215, 224)(217, 223)(218, 227)(219, 229)(221, 228)(222, 232)(225, 236)(226, 238)(230, 242)(231, 244)(233, 246)(234, 245)(235, 248)(237, 249)(239, 251)(240, 250)(241, 253)(243, 254)(247, 258)(252, 263)(255, 266)(256, 265)(257, 268)(259, 267)(260, 270)(261, 269)(262, 272)(264, 271)(273, 282)(274, 281)(275, 284)(276, 283)(277, 342)(278, 341)(279, 344)(280, 343)(285, 351)(286, 354)(287, 356)(288, 358)(289, 360)(290, 362)(291, 364)(292, 366)(293, 368)(294, 350)(295, 370)(296, 372)(297, 374)(298, 353)(299, 376)(300, 378)(301, 355)(302, 375)(303, 377)(304, 381)(305, 383)(306, 359)(307, 380)(308, 382)(309, 385)(310, 386)(311, 349)(312, 361)(313, 363)(314, 365)(315, 387)(316, 388)(317, 352)(318, 357)(319, 369)(320, 371)(321, 390)(322, 391)(323, 389)(324, 379)(325, 392)(326, 394)(327, 395)(328, 393)(329, 384)(330, 396)(331, 367)(332, 373)(333, 398)(334, 399)(335, 397)(336, 400)(337, 402)(338, 403)(339, 401)(340, 404)(345, 410)(346, 411)(347, 409)(348, 412)(405, 415)(406, 413)(407, 416)(408, 414)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2233
Transitivity :: VT+ AT
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2232 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2 * Y3)^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 210, 2, 209)(3, 215, 7, 211)(4, 217, 9, 212)(5, 219, 11, 213)(6, 221, 13, 214)(8, 220, 12, 216)(10, 222, 14, 218)(15, 233, 25, 223)(16, 234, 26, 224)(17, 235, 27, 225)(18, 237, 29, 226)(19, 238, 30, 227)(20, 239, 31, 228)(21, 240, 32, 229)(22, 241, 33, 230)(23, 243, 35, 231)(24, 244, 36, 232)(28, 242, 34, 236)(37, 255, 47, 245)(38, 256, 48, 246)(39, 257, 49, 247)(40, 258, 50, 248)(41, 259, 51, 249)(42, 260, 52, 250)(43, 261, 53, 251)(44, 262, 54, 252)(45, 263, 55, 253)(46, 264, 56, 254)(57, 273, 65, 265)(58, 274, 66, 266)(59, 275, 67, 267)(60, 276, 68, 268)(61, 277, 69, 269)(62, 278, 70, 270)(63, 279, 71, 271)(64, 280, 72, 272)(73, 298, 90, 281)(74, 288, 80, 282)(75, 290, 82, 283)(76, 285, 77, 284)(78, 326, 118, 286)(79, 329, 121, 287)(81, 340, 132, 289)(83, 332, 124, 291)(84, 322, 114, 292)(85, 349, 141, 293)(86, 324, 116, 294)(87, 335, 127, 295)(88, 356, 148, 296)(89, 330, 122, 297)(91, 336, 128, 299)(92, 338, 130, 300)(93, 344, 136, 301)(94, 367, 159, 302)(95, 333, 125, 303)(96, 321, 113, 304)(97, 345, 137, 305)(98, 347, 139, 306)(99, 353, 145, 307)(100, 361, 153, 308)(101, 354, 146, 309)(102, 341, 133, 310)(103, 357, 149, 311)(104, 364, 156, 312)(105, 372, 164, 313)(106, 365, 157, 314)(107, 350, 142, 315)(108, 368, 160, 316)(109, 375, 167, 317)(110, 380, 172, 318)(111, 376, 168, 319)(112, 378, 170, 320)(115, 384, 176, 323)(117, 389, 181, 325)(119, 385, 177, 327)(120, 387, 179, 328)(123, 396, 188, 331)(126, 405, 197, 334)(129, 409, 201, 337)(131, 398, 190, 339)(134, 411, 203, 342)(135, 394, 186, 343)(138, 412, 204, 346)(140, 402, 194, 348)(143, 414, 206, 351)(144, 403, 195, 352)(147, 408, 200, 355)(150, 407, 199, 358)(151, 410, 202, 359)(152, 393, 185, 360)(154, 406, 198, 362)(155, 415, 207, 363)(158, 400, 192, 366)(161, 399, 191, 369)(162, 413, 205, 370)(163, 401, 193, 371)(165, 397, 189, 373)(166, 416, 208, 374)(169, 392, 184, 377)(171, 390, 182, 379)(173, 388, 180, 381)(174, 404, 196, 382)(175, 386, 178, 383)(183, 395, 187, 391)
	L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 50)(46, 55)(47, 57)(48, 59)(49, 58)(51, 60)(52, 61)(53, 63)(54, 62)(56, 64)(65, 73)(66, 75)(67, 74)(68, 76)(69, 113)(70, 116)(71, 114)(72, 118)(77, 121)(78, 124)(79, 127)(80, 122)(81, 128)(82, 132)(83, 136)(84, 125)(85, 137)(86, 141)(87, 145)(88, 146)(89, 148)(90, 130)(91, 153)(92, 133)(93, 156)(94, 157)(95, 159)(96, 139)(97, 164)(98, 142)(99, 167)(100, 168)(101, 172)(102, 149)(103, 170)(104, 176)(105, 177)(106, 181)(107, 160)(108, 179)(109, 185)(110, 186)(111, 190)(112, 188)(115, 193)(117, 195)(119, 194)(120, 197)(123, 201)(126, 204)(129, 200)(131, 202)(134, 198)(135, 203)(138, 192)(140, 205)(143, 189)(144, 206)(147, 184)(150, 180)(151, 199)(152, 207)(154, 182)(155, 196)(158, 175)(161, 171)(162, 191)(163, 208)(165, 173)(166, 187)(169, 183)(174, 178)(209, 212)(210, 214)(211, 216)(213, 220)(215, 224)(217, 223)(218, 227)(219, 229)(221, 228)(222, 232)(225, 236)(226, 238)(230, 242)(231, 244)(233, 246)(234, 245)(235, 248)(237, 249)(239, 251)(240, 250)(241, 253)(243, 254)(247, 258)(252, 263)(255, 266)(256, 265)(257, 268)(259, 267)(260, 270)(261, 269)(262, 272)(264, 271)(273, 282)(274, 281)(275, 284)(276, 283)(277, 322)(278, 321)(279, 326)(280, 324)(285, 330)(286, 333)(287, 336)(288, 338)(289, 341)(290, 329)(291, 345)(292, 347)(293, 350)(294, 332)(295, 354)(296, 357)(297, 335)(298, 340)(299, 353)(300, 356)(301, 365)(302, 368)(303, 344)(304, 349)(305, 364)(306, 367)(307, 376)(308, 378)(309, 375)(310, 361)(311, 380)(312, 385)(313, 387)(314, 384)(315, 372)(316, 389)(317, 394)(318, 396)(319, 393)(320, 398)(323, 403)(325, 405)(327, 401)(328, 402)(331, 411)(334, 414)(337, 407)(339, 409)(342, 408)(343, 415)(346, 399)(348, 412)(351, 400)(352, 416)(355, 390)(358, 392)(359, 404)(360, 410)(362, 386)(363, 406)(366, 381)(369, 383)(370, 395)(371, 413)(373, 377)(374, 397)(379, 391)(382, 388)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2234
Transitivity :: VT+ AT
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2233 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 210, 2, 214, 6, 213, 5, 209)(3, 217, 9, 225, 17, 219, 11, 211)(4, 220, 12, 226, 18, 222, 14, 212)(7, 227, 19, 223, 15, 229, 21, 215)(8, 230, 22, 224, 16, 232, 24, 216)(10, 228, 20, 221, 13, 231, 23, 218)(25, 241, 33, 235, 27, 242, 34, 233)(26, 243, 35, 236, 28, 244, 36, 234)(29, 245, 37, 239, 31, 246, 38, 237)(30, 247, 39, 240, 32, 248, 40, 238)(41, 257, 49, 251, 43, 258, 50, 249)(42, 259, 51, 252, 44, 260, 52, 250)(45, 261, 53, 255, 47, 262, 54, 253)(46, 263, 55, 256, 48, 264, 56, 254)(57, 273, 65, 267, 59, 274, 66, 265)(58, 275, 67, 268, 60, 276, 68, 266)(61, 277, 69, 271, 63, 278, 70, 269)(62, 279, 71, 272, 64, 280, 72, 270)(73, 290, 82, 283, 75, 293, 85, 281)(74, 285, 77, 284, 76, 288, 80, 282)(78, 325, 117, 287, 79, 322, 114, 286)(81, 329, 121, 291, 83, 338, 130, 289)(84, 339, 131, 294, 86, 330, 122, 292)(87, 332, 124, 297, 89, 335, 127, 295)(88, 324, 116, 299, 91, 321, 113, 296)(90, 336, 128, 300, 92, 333, 125, 298)(93, 341, 133, 302, 94, 345, 137, 301)(95, 346, 138, 304, 96, 342, 134, 303)(97, 351, 143, 306, 98, 355, 147, 305)(99, 356, 148, 308, 100, 352, 144, 307)(101, 361, 153, 310, 102, 364, 156, 309)(103, 365, 157, 312, 104, 362, 154, 311)(105, 369, 161, 314, 106, 372, 164, 313)(107, 373, 165, 316, 108, 370, 162, 315)(109, 377, 169, 318, 110, 380, 172, 317)(111, 381, 173, 320, 112, 378, 170, 319)(115, 385, 177, 326, 118, 388, 180, 323)(119, 389, 181, 328, 120, 386, 178, 327)(123, 397, 189, 340, 132, 394, 186, 331)(126, 402, 194, 337, 129, 403, 195, 334)(135, 416, 208, 347, 139, 409, 201, 343)(136, 393, 185, 349, 141, 396, 188, 344)(140, 410, 202, 350, 142, 411, 203, 348)(145, 415, 207, 357, 149, 413, 205, 353)(146, 401, 193, 359, 151, 405, 197, 354)(150, 412, 204, 360, 152, 414, 206, 358)(155, 404, 196, 366, 158, 406, 198, 363)(159, 407, 199, 368, 160, 408, 200, 367)(163, 398, 190, 374, 166, 395, 187, 371)(167, 400, 192, 376, 168, 399, 191, 375)(171, 390, 182, 382, 174, 387, 179, 379)(175, 392, 184, 384, 176, 391, 183, 383)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 113)(70, 116)(71, 117)(72, 114)(77, 121)(78, 124)(79, 127)(80, 130)(81, 133)(82, 122)(83, 137)(84, 134)(85, 131)(86, 138)(87, 143)(88, 125)(89, 147)(90, 144)(91, 128)(92, 148)(93, 153)(94, 156)(95, 154)(96, 157)(97, 161)(98, 164)(99, 162)(100, 165)(101, 169)(102, 172)(103, 170)(104, 173)(105, 177)(106, 180)(107, 178)(108, 181)(109, 185)(110, 188)(111, 186)(112, 189)(115, 193)(118, 197)(119, 195)(120, 194)(123, 201)(126, 205)(129, 207)(132, 208)(135, 198)(136, 202)(139, 196)(140, 199)(141, 203)(142, 200)(145, 187)(146, 204)(149, 190)(150, 192)(151, 206)(152, 191)(155, 179)(158, 182)(159, 184)(160, 183)(163, 174)(166, 171)(167, 175)(168, 176)(209, 212)(210, 216)(211, 218)(213, 224)(214, 226)(215, 228)(217, 234)(219, 236)(220, 233)(221, 225)(222, 235)(223, 231)(227, 238)(229, 240)(230, 237)(232, 239)(241, 250)(242, 252)(243, 249)(244, 251)(245, 254)(246, 256)(247, 253)(248, 255)(257, 266)(258, 268)(259, 265)(260, 267)(261, 270)(262, 272)(263, 269)(264, 271)(273, 282)(274, 284)(275, 281)(276, 283)(277, 322)(278, 325)(279, 321)(280, 324)(285, 330)(286, 333)(287, 336)(288, 339)(289, 342)(290, 338)(291, 346)(292, 345)(293, 329)(294, 341)(295, 352)(296, 335)(297, 356)(298, 355)(299, 332)(300, 351)(301, 362)(302, 365)(303, 364)(304, 361)(305, 370)(306, 373)(307, 372)(308, 369)(309, 378)(310, 381)(311, 380)(312, 377)(313, 386)(314, 389)(315, 388)(316, 385)(317, 394)(318, 397)(319, 396)(320, 393)(323, 403)(326, 402)(327, 405)(328, 401)(331, 411)(334, 414)(337, 412)(340, 410)(343, 408)(344, 409)(347, 407)(348, 406)(349, 416)(350, 404)(353, 399)(354, 413)(357, 400)(358, 395)(359, 415)(360, 398)(363, 391)(366, 392)(367, 387)(368, 390)(371, 384)(374, 383)(375, 382)(376, 379)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2231
Transitivity :: VT+ AT
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2234 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^4, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 210, 2, 214, 6, 213, 5, 209)(3, 217, 9, 225, 17, 219, 11, 211)(4, 220, 12, 226, 18, 222, 14, 212)(7, 227, 19, 223, 15, 229, 21, 215)(8, 230, 22, 224, 16, 232, 24, 216)(10, 228, 20, 221, 13, 231, 23, 218)(25, 241, 33, 235, 27, 242, 34, 233)(26, 243, 35, 236, 28, 244, 36, 234)(29, 245, 37, 239, 31, 246, 38, 237)(30, 247, 39, 240, 32, 248, 40, 238)(41, 257, 49, 251, 43, 258, 50, 249)(42, 259, 51, 252, 44, 260, 52, 250)(45, 261, 53, 255, 47, 262, 54, 253)(46, 263, 55, 256, 48, 264, 56, 254)(57, 273, 65, 267, 59, 274, 66, 265)(58, 275, 67, 268, 60, 276, 68, 266)(61, 277, 69, 271, 63, 278, 70, 269)(62, 279, 71, 272, 64, 280, 72, 270)(73, 337, 129, 283, 75, 341, 133, 281)(74, 339, 131, 284, 76, 343, 135, 282)(77, 345, 137, 290, 82, 349, 141, 285)(78, 350, 142, 289, 81, 354, 146, 286)(79, 355, 147, 301, 93, 358, 150, 287)(80, 359, 151, 302, 94, 361, 153, 288)(83, 368, 160, 299, 91, 371, 163, 291)(84, 372, 164, 300, 92, 374, 166, 292)(85, 365, 157, 295, 87, 346, 138, 293)(86, 378, 170, 297, 89, 369, 161, 294)(88, 347, 139, 298, 90, 366, 158, 296)(95, 362, 154, 305, 97, 351, 143, 303)(96, 356, 148, 307, 99, 388, 180, 304)(98, 352, 144, 308, 100, 363, 155, 306)(101, 397, 189, 311, 103, 399, 191, 309)(102, 400, 192, 312, 104, 402, 194, 310)(105, 405, 197, 315, 107, 407, 199, 313)(106, 408, 200, 316, 108, 410, 202, 314)(109, 380, 172, 318, 110, 375, 167, 317)(111, 376, 168, 320, 112, 381, 173, 319)(113, 411, 203, 323, 115, 406, 198, 321)(114, 409, 201, 324, 116, 412, 204, 322)(117, 398, 190, 327, 119, 403, 195, 325)(118, 404, 196, 328, 120, 401, 193, 326)(121, 370, 162, 331, 123, 386, 178, 329)(122, 387, 179, 332, 124, 373, 165, 330)(125, 389, 181, 335, 127, 357, 149, 333)(126, 360, 152, 336, 128, 390, 182, 334)(130, 367, 159, 342, 134, 348, 140, 338)(132, 379, 171, 344, 136, 384, 176, 340)(145, 413, 205, 364, 156, 414, 206, 353)(169, 391, 183, 382, 174, 393, 185, 377)(175, 394, 186, 385, 177, 396, 188, 383)(184, 415, 207, 395, 187, 416, 208, 392)
	L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 109)(70, 110)(71, 111)(72, 112)(77, 138)(78, 143)(79, 146)(80, 148)(81, 154)(82, 157)(83, 137)(84, 161)(85, 167)(86, 139)(87, 172)(88, 168)(89, 158)(90, 173)(91, 141)(92, 170)(93, 142)(94, 180)(95, 129)(96, 144)(97, 133)(98, 131)(99, 155)(100, 135)(101, 147)(102, 153)(103, 150)(104, 151)(105, 160)(106, 166)(107, 163)(108, 164)(113, 189)(114, 194)(115, 191)(116, 192)(117, 197)(118, 202)(119, 199)(120, 200)(121, 203)(122, 204)(123, 198)(124, 201)(125, 190)(126, 193)(127, 195)(128, 196)(130, 162)(132, 165)(134, 178)(136, 179)(140, 185)(145, 169)(149, 206)(152, 207)(156, 174)(159, 183)(171, 186)(175, 187)(176, 188)(177, 184)(181, 205)(182, 208)(209, 212)(210, 216)(211, 218)(213, 224)(214, 226)(215, 228)(217, 234)(219, 236)(220, 233)(221, 225)(222, 235)(223, 231)(227, 238)(229, 240)(230, 237)(232, 239)(241, 250)(242, 252)(243, 249)(244, 251)(245, 254)(246, 256)(247, 253)(248, 255)(257, 266)(258, 268)(259, 265)(260, 267)(261, 270)(262, 272)(263, 269)(264, 271)(273, 282)(274, 284)(275, 281)(276, 283)(277, 320)(278, 319)(279, 317)(280, 318)(285, 347)(286, 352)(287, 356)(288, 350)(289, 363)(290, 366)(291, 369)(292, 349)(293, 376)(294, 365)(295, 381)(296, 380)(297, 346)(298, 375)(299, 378)(300, 345)(301, 388)(302, 354)(303, 339)(304, 362)(305, 343)(306, 341)(307, 351)(308, 337)(309, 361)(310, 358)(311, 359)(312, 355)(313, 374)(314, 371)(315, 372)(316, 368)(321, 402)(322, 399)(323, 400)(324, 397)(325, 410)(326, 407)(327, 408)(328, 405)(329, 412)(330, 406)(331, 409)(332, 411)(333, 401)(334, 403)(335, 404)(336, 398)(338, 373)(340, 386)(342, 387)(344, 370)(348, 396)(353, 383)(357, 416)(360, 414)(364, 385)(367, 394)(377, 392)(379, 393)(382, 395)(384, 391)(389, 415)(390, 413)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2232
Transitivity :: VT+ AT
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2235 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^26 ]
Map:: polytopal
	R = (1, 209, 4, 212)(2, 210, 6, 214)(3, 211, 8, 216)(5, 213, 12, 220)(7, 215, 16, 224)(9, 217, 18, 226)(10, 218, 19, 227)(11, 219, 21, 229)(13, 221, 23, 231)(14, 222, 24, 232)(15, 223, 25, 233)(17, 225, 27, 235)(20, 228, 31, 239)(22, 230, 33, 241)(26, 234, 37, 245)(28, 236, 39, 247)(29, 237, 40, 248)(30, 238, 41, 249)(32, 240, 42, 250)(34, 242, 44, 252)(35, 243, 45, 253)(36, 244, 46, 254)(38, 246, 47, 255)(43, 251, 52, 260)(48, 256, 57, 265)(49, 257, 58, 266)(50, 258, 59, 267)(51, 259, 60, 268)(53, 261, 61, 269)(54, 262, 62, 270)(55, 263, 63, 271)(56, 264, 64, 272)(65, 273, 73, 281)(66, 274, 74, 282)(67, 275, 75, 283)(68, 276, 76, 284)(69, 277, 129, 337)(70, 278, 131, 339)(71, 279, 133, 341)(72, 280, 135, 343)(77, 285, 139, 347)(78, 286, 143, 351)(79, 287, 146, 354)(80, 288, 141, 349)(81, 289, 152, 360)(82, 290, 137, 345)(83, 291, 158, 366)(84, 292, 157, 365)(85, 293, 162, 370)(86, 294, 165, 373)(87, 295, 168, 376)(88, 296, 167, 375)(89, 297, 172, 380)(90, 298, 175, 383)(91, 299, 174, 382)(92, 300, 142, 350)(93, 301, 180, 388)(94, 302, 148, 356)(95, 303, 178, 386)(96, 304, 164, 372)(97, 305, 138, 346)(98, 306, 187, 395)(99, 307, 154, 362)(100, 308, 185, 393)(101, 309, 151, 359)(102, 310, 192, 400)(103, 311, 155, 363)(104, 312, 195, 403)(105, 313, 197, 405)(106, 314, 199, 407)(107, 315, 145, 353)(108, 316, 202, 410)(109, 317, 149, 357)(110, 318, 196, 404)(111, 319, 200, 408)(112, 320, 198, 406)(113, 321, 170, 378)(114, 322, 206, 414)(115, 323, 160, 368)(116, 324, 207, 415)(117, 325, 173, 381)(118, 326, 181, 389)(119, 327, 176, 384)(120, 328, 203, 411)(121, 329, 163, 371)(122, 330, 188, 396)(123, 331, 166, 374)(124, 332, 193, 401)(125, 333, 144, 352)(126, 334, 169, 377)(127, 335, 147, 355)(128, 336, 177, 385)(130, 338, 140, 348)(132, 340, 159, 367)(134, 342, 153, 361)(136, 344, 184, 392)(150, 358, 189, 397)(156, 364, 182, 390)(161, 369, 183, 391)(171, 379, 190, 398)(179, 387, 194, 402)(186, 394, 204, 412)(191, 399, 205, 413)(201, 409, 208, 416)(417, 418)(419, 423)(420, 425)(421, 427)(422, 429)(424, 433)(426, 432)(428, 438)(430, 437)(431, 436)(434, 444)(435, 446)(439, 450)(440, 452)(441, 448)(442, 447)(443, 451)(445, 449)(453, 459)(454, 458)(455, 464)(456, 466)(457, 465)(460, 469)(461, 471)(462, 470)(463, 472)(467, 468)(473, 481)(474, 483)(475, 482)(476, 484)(477, 485)(478, 487)(479, 486)(480, 488)(489, 515)(490, 516)(491, 519)(492, 531)(493, 553)(494, 557)(495, 558)(496, 564)(497, 554)(498, 570)(499, 573)(500, 571)(501, 555)(502, 574)(503, 583)(504, 565)(505, 559)(506, 584)(507, 561)(508, 594)(509, 562)(510, 545)(511, 547)(512, 567)(513, 601)(514, 568)(517, 576)(518, 580)(520, 578)(521, 603)(522, 581)(523, 586)(524, 590)(525, 549)(526, 588)(527, 596)(528, 591)(529, 551)(530, 618)(532, 608)(533, 611)(534, 615)(535, 613)(536, 623)(537, 612)(538, 614)(539, 616)(540, 622)(541, 589)(542, 592)(543, 597)(544, 619)(546, 579)(548, 582)(550, 604)(552, 609)(556, 598)(560, 605)(563, 610)(566, 572)(569, 620)(575, 599)(577, 595)(585, 606)(587, 602)(593, 624)(600, 621)(607, 617)(625, 627)(626, 629)(628, 634)(630, 638)(631, 639)(632, 637)(633, 636)(635, 644)(640, 650)(641, 649)(642, 653)(643, 652)(645, 656)(646, 655)(647, 659)(648, 658)(651, 662)(654, 661)(657, 667)(660, 666)(663, 673)(664, 672)(665, 675)(668, 678)(669, 677)(670, 680)(671, 679)(674, 676)(681, 690)(682, 689)(683, 692)(684, 691)(685, 694)(686, 693)(687, 696)(688, 695)(697, 727)(698, 723)(699, 739)(700, 724)(701, 762)(702, 766)(703, 769)(704, 773)(705, 775)(706, 779)(707, 761)(708, 784)(709, 782)(710, 788)(711, 765)(712, 794)(713, 792)(714, 798)(715, 791)(716, 772)(717, 767)(718, 755)(719, 759)(720, 781)(721, 778)(722, 763)(725, 809)(726, 776)(728, 811)(729, 816)(730, 786)(731, 802)(732, 770)(733, 753)(734, 804)(735, 826)(736, 796)(737, 757)(738, 799)(740, 789)(741, 823)(742, 831)(743, 819)(744, 821)(745, 822)(746, 830)(747, 820)(748, 824)(749, 800)(750, 827)(751, 797)(752, 805)(754, 790)(756, 817)(758, 787)(760, 812)(764, 807)(768, 814)(771, 813)(774, 785)(777, 806)(780, 795)(783, 829)(793, 832)(801, 818)(803, 815)(808, 828)(810, 825)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 16, 16 ), ( 16^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2241
Graph:: simple bipartite
	v = 312 e = 416 f = 52
	degree seq :: [ 2^208, 4^104 ]

E27.2236 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ]
Map:: polytopal
	R = (1, 209, 4, 212)(2, 210, 6, 214)(3, 211, 8, 216)(5, 213, 12, 220)(7, 215, 16, 224)(9, 217, 18, 226)(10, 218, 19, 227)(11, 219, 21, 229)(13, 221, 23, 231)(14, 222, 24, 232)(15, 223, 25, 233)(17, 225, 27, 235)(20, 228, 31, 239)(22, 230, 33, 241)(26, 234, 37, 245)(28, 236, 39, 247)(29, 237, 40, 248)(30, 238, 41, 249)(32, 240, 42, 250)(34, 242, 44, 252)(35, 243, 45, 253)(36, 244, 46, 254)(38, 246, 47, 255)(43, 251, 52, 260)(48, 256, 57, 265)(49, 257, 58, 266)(50, 258, 59, 267)(51, 259, 60, 268)(53, 261, 61, 269)(54, 262, 62, 270)(55, 263, 63, 271)(56, 264, 64, 272)(65, 273, 73, 281)(66, 274, 74, 282)(67, 275, 75, 283)(68, 276, 76, 284)(69, 277, 87, 295)(70, 278, 79, 287)(71, 279, 81, 289)(72, 280, 77, 285)(78, 286, 118, 326)(80, 288, 121, 329)(82, 290, 132, 340)(83, 291, 114, 322)(84, 292, 116, 324)(85, 293, 124, 332)(86, 294, 138, 346)(88, 296, 122, 330)(89, 297, 129, 337)(90, 298, 146, 354)(91, 299, 127, 335)(92, 300, 130, 338)(93, 301, 113, 321)(94, 302, 125, 333)(95, 303, 136, 344)(96, 304, 140, 348)(97, 305, 157, 365)(98, 306, 141, 349)(99, 307, 134, 342)(100, 308, 148, 356)(101, 309, 154, 362)(102, 310, 149, 357)(103, 311, 151, 359)(104, 312, 143, 351)(105, 313, 160, 368)(106, 314, 165, 373)(107, 315, 161, 369)(108, 316, 163, 371)(109, 317, 168, 376)(110, 318, 173, 381)(111, 319, 169, 377)(112, 320, 171, 379)(115, 323, 177, 385)(117, 325, 182, 390)(119, 327, 178, 386)(120, 328, 180, 388)(123, 331, 188, 396)(126, 334, 197, 405)(128, 336, 190, 398)(131, 339, 201, 409)(133, 341, 186, 394)(135, 343, 203, 411)(137, 345, 194, 402)(139, 347, 195, 403)(142, 350, 204, 412)(144, 352, 206, 414)(145, 353, 185, 393)(147, 355, 202, 410)(150, 358, 200, 408)(152, 360, 199, 407)(153, 361, 207, 415)(155, 363, 198, 406)(156, 364, 193, 401)(158, 366, 205, 413)(159, 367, 208, 416)(162, 370, 192, 400)(164, 372, 191, 399)(166, 374, 189, 397)(167, 375, 196, 404)(170, 378, 184, 392)(172, 380, 183, 391)(174, 382, 181, 389)(175, 383, 179, 387)(176, 384, 187, 395)(417, 418)(419, 423)(420, 425)(421, 427)(422, 429)(424, 433)(426, 432)(428, 438)(430, 437)(431, 436)(434, 444)(435, 446)(439, 450)(440, 452)(441, 448)(442, 447)(443, 451)(445, 449)(453, 459)(454, 458)(455, 464)(456, 466)(457, 465)(460, 469)(461, 471)(462, 470)(463, 472)(467, 468)(473, 481)(474, 483)(475, 482)(476, 484)(477, 485)(478, 487)(479, 486)(480, 488)(489, 529)(490, 532)(491, 530)(492, 534)(493, 537)(494, 540)(495, 538)(496, 545)(497, 548)(498, 546)(499, 541)(500, 554)(501, 556)(502, 557)(503, 543)(504, 562)(505, 564)(506, 565)(507, 550)(508, 570)(509, 552)(510, 573)(511, 559)(512, 576)(513, 577)(514, 581)(515, 567)(516, 584)(517, 585)(518, 589)(519, 587)(520, 579)(521, 593)(522, 594)(523, 598)(524, 596)(525, 601)(526, 602)(527, 606)(528, 604)(531, 609)(533, 611)(535, 610)(536, 613)(539, 617)(542, 620)(544, 618)(547, 616)(549, 619)(551, 614)(553, 621)(555, 622)(558, 608)(560, 605)(561, 623)(563, 615)(566, 600)(568, 597)(569, 612)(571, 599)(572, 624)(574, 607)(575, 603)(578, 591)(580, 588)(582, 590)(583, 595)(586, 592)(625, 627)(626, 629)(628, 634)(630, 638)(631, 639)(632, 637)(633, 636)(635, 644)(640, 650)(641, 649)(642, 653)(643, 652)(645, 656)(646, 655)(647, 659)(648, 658)(651, 662)(654, 661)(657, 667)(660, 666)(663, 673)(664, 672)(665, 675)(668, 678)(669, 677)(670, 680)(671, 679)(674, 676)(681, 690)(682, 689)(683, 692)(684, 691)(685, 694)(686, 693)(687, 696)(688, 695)(697, 738)(698, 737)(699, 742)(700, 740)(701, 746)(702, 749)(703, 751)(704, 754)(705, 745)(706, 758)(707, 760)(708, 748)(709, 765)(710, 767)(711, 756)(712, 753)(713, 773)(714, 775)(715, 770)(716, 772)(717, 762)(718, 764)(719, 781)(720, 785)(721, 787)(722, 784)(723, 778)(724, 793)(725, 795)(726, 792)(727, 797)(728, 789)(729, 802)(730, 804)(731, 801)(732, 806)(733, 810)(734, 812)(735, 809)(736, 814)(739, 819)(741, 821)(743, 817)(744, 818)(747, 827)(750, 830)(752, 825)(755, 823)(757, 831)(759, 824)(761, 828)(763, 832)(766, 815)(768, 816)(769, 826)(771, 820)(774, 807)(776, 808)(777, 822)(779, 803)(780, 829)(782, 811)(783, 813)(786, 798)(788, 799)(790, 794)(791, 805)(796, 800)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 16, 16 ), ( 16^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2242
Graph:: simple bipartite
	v = 312 e = 416 f = 52
	degree seq :: [ 2^208, 4^104 ]

E27.2237 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal
	R = (1, 209, 4, 212, 14, 222, 5, 213)(2, 210, 7, 215, 22, 230, 8, 216)(3, 211, 10, 218, 17, 225, 11, 219)(6, 214, 18, 226, 9, 217, 19, 227)(12, 220, 25, 233, 15, 223, 26, 234)(13, 221, 27, 235, 16, 224, 28, 236)(20, 228, 29, 237, 23, 231, 30, 238)(21, 229, 31, 239, 24, 232, 32, 240)(33, 241, 41, 249, 35, 243, 42, 250)(34, 242, 43, 251, 36, 244, 44, 252)(37, 245, 45, 253, 39, 247, 46, 254)(38, 246, 47, 255, 40, 248, 48, 256)(49, 257, 57, 265, 51, 259, 58, 266)(50, 258, 59, 267, 52, 260, 60, 268)(53, 261, 61, 269, 55, 263, 62, 270)(54, 262, 63, 271, 56, 264, 64, 272)(65, 273, 73, 281, 67, 275, 74, 282)(66, 274, 75, 283, 68, 276, 76, 284)(69, 277, 117, 325, 71, 279, 119, 327)(70, 278, 118, 326, 72, 280, 120, 328)(77, 285, 125, 333, 88, 296, 126, 334)(78, 286, 127, 335, 92, 300, 128, 336)(79, 287, 129, 337, 89, 297, 130, 338)(80, 288, 131, 339, 81, 289, 132, 340)(82, 290, 133, 341, 85, 293, 134, 342)(83, 291, 135, 343, 84, 292, 136, 344)(86, 294, 137, 345, 87, 295, 138, 346)(90, 298, 139, 347, 91, 299, 140, 348)(93, 301, 141, 349, 94, 302, 142, 350)(95, 303, 143, 351, 96, 304, 144, 352)(97, 305, 145, 353, 98, 306, 146, 354)(99, 307, 147, 355, 100, 308, 148, 356)(101, 309, 149, 357, 102, 310, 150, 358)(103, 311, 151, 359, 104, 312, 152, 360)(105, 313, 153, 361, 106, 314, 154, 362)(107, 315, 155, 363, 108, 316, 156, 364)(109, 317, 157, 365, 110, 318, 158, 366)(111, 319, 159, 367, 112, 320, 160, 368)(113, 321, 161, 369, 114, 322, 162, 370)(115, 323, 163, 371, 116, 324, 164, 372)(121, 329, 169, 377, 122, 330, 170, 378)(123, 331, 171, 379, 124, 332, 172, 380)(165, 373, 206, 414, 166, 374, 205, 413)(167, 375, 208, 416, 168, 376, 207, 415)(173, 381, 197, 405, 174, 382, 198, 406)(175, 383, 201, 409, 176, 384, 202, 410)(177, 385, 203, 411, 178, 386, 204, 412)(179, 387, 194, 402, 180, 388, 193, 401)(181, 389, 199, 407, 182, 390, 200, 408)(183, 391, 190, 398, 184, 392, 189, 397)(185, 393, 192, 400, 186, 394, 191, 399)(187, 395, 196, 404, 188, 396, 195, 403)(417, 418)(419, 425)(420, 428)(421, 431)(422, 433)(423, 436)(424, 439)(426, 440)(427, 437)(429, 435)(430, 438)(432, 434)(441, 449)(442, 451)(443, 452)(444, 450)(445, 453)(446, 455)(447, 456)(448, 454)(457, 465)(458, 467)(459, 468)(460, 466)(461, 469)(462, 471)(463, 472)(464, 470)(473, 481)(474, 483)(475, 484)(476, 482)(477, 485)(478, 487)(479, 488)(480, 486)(489, 494)(490, 508)(491, 505)(492, 495)(493, 533)(496, 543)(497, 544)(498, 536)(499, 541)(500, 542)(501, 534)(502, 550)(503, 549)(504, 535)(506, 546)(507, 545)(509, 547)(510, 548)(511, 556)(512, 555)(513, 551)(514, 552)(515, 554)(516, 553)(517, 557)(518, 558)(519, 560)(520, 559)(521, 561)(522, 562)(523, 564)(524, 563)(525, 565)(526, 566)(527, 568)(528, 567)(529, 569)(530, 570)(531, 572)(532, 571)(537, 573)(538, 574)(539, 576)(540, 575)(577, 581)(578, 582)(579, 584)(580, 583)(585, 591)(586, 592)(587, 594)(588, 593)(589, 622)(590, 621)(595, 617)(596, 618)(597, 623)(598, 624)(599, 613)(600, 614)(601, 616)(602, 615)(603, 620)(604, 619)(605, 610)(606, 609)(607, 611)(608, 612)(625, 627)(626, 630)(628, 637)(629, 640)(631, 645)(632, 648)(633, 646)(634, 644)(635, 647)(636, 642)(638, 641)(639, 643)(649, 658)(650, 660)(651, 657)(652, 659)(653, 662)(654, 664)(655, 661)(656, 663)(665, 674)(666, 676)(667, 673)(668, 675)(669, 678)(670, 680)(671, 677)(672, 679)(681, 690)(682, 692)(683, 689)(684, 691)(685, 694)(686, 696)(687, 693)(688, 695)(697, 703)(698, 713)(699, 702)(700, 716)(701, 742)(704, 753)(705, 754)(706, 741)(707, 757)(708, 758)(709, 743)(710, 749)(711, 750)(712, 744)(714, 751)(715, 752)(717, 763)(718, 764)(719, 755)(720, 756)(721, 761)(722, 762)(723, 759)(724, 760)(725, 767)(726, 768)(727, 765)(728, 766)(729, 771)(730, 772)(731, 769)(732, 770)(733, 775)(734, 776)(735, 773)(736, 774)(737, 779)(738, 780)(739, 777)(740, 778)(745, 783)(746, 784)(747, 781)(748, 782)(785, 791)(786, 792)(787, 789)(788, 790)(793, 801)(794, 802)(795, 799)(796, 800)(797, 832)(798, 831)(803, 827)(804, 828)(805, 830)(806, 829)(807, 823)(808, 824)(809, 821)(810, 822)(811, 825)(812, 826)(813, 820)(814, 819)(815, 818)(816, 817)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 8, 8 ), ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2239
Graph:: simple bipartite
	v = 260 e = 416 f = 104
	degree seq :: [ 2^208, 8^52 ]

E27.2238 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map:: polytopal
	R = (1, 209, 4, 212, 14, 222, 5, 213)(2, 210, 7, 215, 22, 230, 8, 216)(3, 211, 10, 218, 17, 225, 11, 219)(6, 214, 18, 226, 9, 217, 19, 227)(12, 220, 25, 233, 15, 223, 26, 234)(13, 221, 27, 235, 16, 224, 28, 236)(20, 228, 29, 237, 23, 231, 30, 238)(21, 229, 31, 239, 24, 232, 32, 240)(33, 241, 41, 249, 35, 243, 42, 250)(34, 242, 43, 251, 36, 244, 44, 252)(37, 245, 45, 253, 39, 247, 46, 254)(38, 246, 47, 255, 40, 248, 48, 256)(49, 257, 57, 265, 51, 259, 58, 266)(50, 258, 59, 267, 52, 260, 60, 268)(53, 261, 61, 269, 55, 263, 62, 270)(54, 262, 63, 271, 56, 264, 64, 272)(65, 273, 73, 281, 67, 275, 74, 282)(66, 274, 75, 283, 68, 276, 76, 284)(69, 277, 145, 353, 71, 279, 149, 357)(70, 278, 147, 355, 72, 280, 151, 359)(77, 285, 163, 371, 90, 298, 165, 373)(78, 286, 168, 376, 98, 306, 170, 378)(79, 287, 172, 380, 93, 301, 174, 382)(80, 288, 166, 374, 81, 289, 178, 386)(82, 290, 183, 391, 85, 293, 185, 393)(83, 291, 161, 369, 84, 292, 189, 397)(86, 294, 162, 370, 87, 295, 182, 390)(88, 296, 150, 358, 91, 299, 146, 354)(89, 297, 152, 360, 92, 300, 148, 356)(94, 302, 167, 375, 95, 303, 171, 379)(96, 304, 143, 351, 99, 307, 141, 349)(97, 305, 144, 352, 100, 308, 142, 350)(101, 309, 175, 383, 102, 310, 179, 387)(103, 311, 176, 384, 104, 312, 180, 388)(105, 313, 186, 394, 106, 314, 190, 398)(107, 315, 187, 395, 108, 316, 191, 399)(109, 317, 129, 337, 111, 319, 131, 339)(110, 318, 130, 338, 112, 320, 132, 340)(113, 321, 125, 333, 115, 323, 127, 335)(114, 322, 126, 334, 116, 324, 128, 336)(117, 325, 201, 409, 118, 326, 204, 412)(119, 327, 202, 410, 120, 328, 205, 413)(121, 329, 207, 415, 122, 330, 208, 416)(123, 331, 206, 414, 124, 332, 203, 411)(133, 341, 195, 403, 134, 342, 194, 402)(135, 343, 188, 396, 136, 344, 192, 400)(137, 345, 199, 407, 138, 346, 198, 406)(139, 347, 177, 385, 140, 348, 181, 389)(153, 361, 169, 377, 156, 364, 200, 408)(154, 362, 173, 381, 157, 365, 197, 405)(155, 363, 184, 392, 158, 366, 193, 401)(159, 367, 196, 404, 160, 368, 164, 372)(417, 418)(419, 425)(420, 428)(421, 431)(422, 433)(423, 436)(424, 439)(426, 440)(427, 437)(429, 435)(430, 438)(432, 434)(441, 449)(442, 451)(443, 452)(444, 450)(445, 453)(446, 455)(447, 456)(448, 454)(457, 465)(458, 467)(459, 468)(460, 466)(461, 469)(462, 471)(463, 472)(464, 470)(473, 481)(474, 483)(475, 484)(476, 482)(477, 485)(478, 487)(479, 488)(480, 486)(489, 569)(490, 572)(491, 573)(492, 570)(493, 577)(494, 582)(495, 587)(496, 591)(497, 595)(498, 598)(499, 602)(500, 606)(501, 578)(502, 607)(503, 603)(504, 581)(505, 599)(506, 605)(507, 579)(508, 601)(509, 583)(510, 596)(511, 592)(512, 586)(513, 588)(514, 594)(515, 584)(516, 590)(517, 617)(518, 620)(519, 621)(520, 618)(521, 623)(522, 624)(523, 619)(524, 622)(525, 562)(526, 568)(527, 566)(528, 564)(529, 557)(530, 560)(531, 559)(532, 558)(533, 611)(534, 610)(535, 608)(536, 604)(537, 615)(538, 614)(539, 597)(540, 593)(541, 547)(542, 546)(543, 545)(544, 548)(549, 600)(550, 609)(551, 580)(552, 612)(553, 589)(554, 613)(555, 585)(556, 616)(561, 576)(563, 574)(565, 575)(567, 571)(625, 627)(626, 630)(628, 637)(629, 640)(631, 645)(632, 648)(633, 646)(634, 644)(635, 647)(636, 642)(638, 641)(639, 643)(649, 658)(650, 660)(651, 657)(652, 659)(653, 662)(654, 664)(655, 661)(656, 663)(665, 674)(666, 676)(667, 673)(668, 675)(669, 678)(670, 680)(671, 677)(672, 679)(681, 690)(682, 692)(683, 689)(684, 691)(685, 694)(686, 696)(687, 693)(688, 695)(697, 778)(698, 781)(699, 777)(700, 780)(701, 786)(702, 791)(703, 790)(704, 800)(705, 804)(706, 785)(707, 811)(708, 815)(709, 813)(710, 810)(711, 814)(712, 809)(713, 789)(714, 806)(715, 807)(716, 787)(717, 802)(718, 799)(719, 803)(720, 798)(721, 794)(722, 795)(723, 796)(724, 792)(725, 826)(726, 829)(727, 825)(728, 828)(729, 830)(730, 827)(731, 831)(732, 832)(733, 772)(734, 770)(735, 776)(736, 774)(737, 766)(738, 765)(739, 768)(740, 767)(741, 812)(742, 816)(743, 819)(744, 818)(745, 801)(746, 805)(747, 823)(748, 822)(749, 756)(750, 755)(751, 754)(752, 753)(757, 820)(758, 788)(759, 808)(760, 817)(761, 824)(762, 793)(763, 797)(764, 821)(769, 779)(771, 784)(773, 782)(775, 783)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 8, 8 ), ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2240
Graph:: simple bipartite
	v = 260 e = 416 f = 104
	degree seq :: [ 2^208, 8^52 ]

E27.2239 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^26 ]
Map::
	R = (1, 209, 417, 625, 4, 212, 420, 628)(2, 210, 418, 626, 6, 214, 422, 630)(3, 211, 419, 627, 8, 216, 424, 632)(5, 213, 421, 629, 12, 220, 428, 636)(7, 215, 423, 631, 16, 224, 432, 640)(9, 217, 425, 633, 18, 226, 434, 642)(10, 218, 426, 634, 19, 227, 435, 643)(11, 219, 427, 635, 21, 229, 437, 645)(13, 221, 429, 637, 23, 231, 439, 647)(14, 222, 430, 638, 24, 232, 440, 648)(15, 223, 431, 639, 25, 233, 441, 649)(17, 225, 433, 641, 27, 235, 443, 651)(20, 228, 436, 644, 31, 239, 447, 655)(22, 230, 438, 646, 33, 241, 449, 657)(26, 234, 442, 650, 37, 245, 453, 661)(28, 236, 444, 652, 39, 247, 455, 663)(29, 237, 445, 653, 40, 248, 456, 664)(30, 238, 446, 654, 41, 249, 457, 665)(32, 240, 448, 656, 42, 250, 458, 666)(34, 242, 450, 658, 44, 252, 460, 668)(35, 243, 451, 659, 45, 253, 461, 669)(36, 244, 452, 660, 46, 254, 462, 670)(38, 246, 454, 662, 47, 255, 463, 671)(43, 251, 459, 667, 52, 260, 468, 676)(48, 256, 464, 672, 57, 265, 473, 681)(49, 257, 465, 673, 58, 266, 474, 682)(50, 258, 466, 674, 59, 267, 475, 683)(51, 259, 467, 675, 60, 268, 476, 684)(53, 261, 469, 677, 61, 269, 477, 685)(54, 262, 470, 678, 62, 270, 478, 686)(55, 263, 471, 679, 63, 271, 479, 687)(56, 264, 472, 680, 64, 272, 480, 688)(65, 273, 481, 689, 73, 281, 489, 697)(66, 274, 482, 690, 74, 282, 490, 698)(67, 275, 483, 691, 75, 283, 491, 699)(68, 276, 484, 692, 76, 284, 492, 700)(69, 277, 485, 693, 98, 306, 514, 722)(70, 278, 486, 694, 86, 294, 502, 710)(71, 279, 487, 695, 90, 298, 506, 714)(72, 280, 488, 696, 80, 288, 496, 704)(77, 285, 493, 701, 124, 332, 540, 748)(78, 286, 494, 702, 129, 337, 545, 753)(79, 287, 495, 703, 131, 339, 547, 755)(81, 289, 497, 705, 122, 330, 538, 746)(82, 290, 498, 706, 123, 331, 539, 747)(83, 291, 499, 707, 125, 333, 541, 749)(84, 292, 500, 708, 134, 342, 550, 758)(85, 293, 501, 709, 132, 340, 548, 756)(87, 295, 503, 711, 127, 335, 543, 751)(88, 296, 504, 712, 138, 346, 554, 762)(89, 297, 505, 713, 139, 347, 555, 763)(91, 299, 507, 715, 128, 336, 544, 752)(92, 300, 508, 716, 121, 329, 537, 745)(93, 301, 509, 717, 126, 334, 542, 750)(94, 302, 510, 718, 133, 341, 549, 757)(95, 303, 511, 719, 135, 343, 551, 759)(96, 304, 512, 720, 144, 352, 560, 768)(97, 305, 513, 721, 136, 344, 552, 760)(99, 307, 515, 723, 130, 338, 546, 754)(100, 308, 516, 724, 140, 348, 556, 764)(101, 309, 517, 725, 143, 351, 559, 767)(102, 310, 518, 726, 141, 349, 557, 765)(103, 311, 519, 727, 142, 350, 558, 766)(104, 312, 520, 728, 137, 345, 553, 761)(105, 313, 521, 729, 145, 353, 561, 769)(106, 314, 522, 730, 148, 356, 564, 772)(107, 315, 523, 731, 146, 354, 562, 770)(108, 316, 524, 732, 147, 355, 563, 771)(109, 317, 525, 733, 149, 357, 565, 773)(110, 318, 526, 734, 152, 360, 568, 776)(111, 319, 527, 735, 150, 358, 566, 774)(112, 320, 528, 736, 151, 359, 567, 775)(113, 321, 529, 737, 153, 361, 569, 777)(114, 322, 530, 738, 156, 364, 572, 780)(115, 323, 531, 739, 154, 362, 570, 778)(116, 324, 532, 740, 155, 363, 571, 779)(117, 325, 533, 741, 157, 365, 573, 781)(118, 326, 534, 742, 160, 368, 576, 784)(119, 327, 535, 743, 158, 366, 574, 782)(120, 328, 536, 744, 159, 367, 575, 783)(161, 369, 577, 785, 169, 377, 585, 793)(162, 370, 578, 786, 171, 379, 587, 795)(163, 371, 579, 787, 172, 380, 588, 796)(164, 372, 580, 788, 170, 378, 586, 794)(165, 373, 581, 789, 187, 395, 603, 811)(166, 374, 582, 790, 180, 388, 596, 804)(167, 375, 583, 791, 177, 385, 593, 801)(168, 376, 584, 792, 179, 387, 595, 803)(173, 381, 589, 797, 205, 413, 621, 829)(174, 382, 590, 798, 206, 414, 622, 830)(175, 383, 591, 799, 201, 409, 617, 825)(176, 384, 592, 800, 202, 410, 618, 826)(178, 386, 594, 802, 203, 411, 619, 827)(181, 389, 597, 805, 207, 415, 623, 831)(182, 390, 598, 806, 208, 416, 624, 832)(183, 391, 599, 807, 197, 405, 613, 821)(184, 392, 600, 808, 198, 406, 614, 822)(185, 393, 601, 809, 199, 407, 615, 823)(186, 394, 602, 810, 204, 412, 620, 828)(188, 396, 604, 812, 193, 401, 609, 817)(189, 397, 605, 813, 194, 402, 610, 818)(190, 398, 606, 814, 195, 403, 611, 819)(191, 399, 607, 815, 196, 404, 612, 820)(192, 400, 608, 816, 200, 408, 616, 824)
	L = (1, 210)(2, 209)(3, 215)(4, 217)(5, 219)(6, 221)(7, 211)(8, 225)(9, 212)(10, 224)(11, 213)(12, 230)(13, 214)(14, 229)(15, 228)(16, 218)(17, 216)(18, 236)(19, 238)(20, 223)(21, 222)(22, 220)(23, 242)(24, 244)(25, 240)(26, 239)(27, 243)(28, 226)(29, 241)(30, 227)(31, 234)(32, 233)(33, 237)(34, 231)(35, 235)(36, 232)(37, 251)(38, 250)(39, 256)(40, 258)(41, 257)(42, 246)(43, 245)(44, 261)(45, 263)(46, 262)(47, 264)(48, 247)(49, 249)(50, 248)(51, 260)(52, 259)(53, 252)(54, 254)(55, 253)(56, 255)(57, 273)(58, 275)(59, 274)(60, 276)(61, 277)(62, 279)(63, 278)(64, 280)(65, 265)(66, 267)(67, 266)(68, 268)(69, 269)(70, 271)(71, 270)(72, 272)(73, 329)(74, 331)(75, 330)(76, 332)(77, 333)(78, 335)(79, 336)(80, 337)(81, 334)(82, 342)(83, 343)(84, 344)(85, 346)(86, 340)(87, 348)(88, 349)(89, 338)(90, 339)(91, 351)(92, 341)(93, 352)(94, 345)(95, 353)(96, 354)(97, 356)(98, 347)(99, 350)(100, 357)(101, 358)(102, 360)(103, 359)(104, 355)(105, 361)(106, 362)(107, 364)(108, 363)(109, 365)(110, 366)(111, 368)(112, 367)(113, 369)(114, 370)(115, 372)(116, 371)(117, 373)(118, 374)(119, 376)(120, 375)(121, 281)(122, 283)(123, 282)(124, 284)(125, 285)(126, 289)(127, 286)(128, 287)(129, 288)(130, 297)(131, 298)(132, 294)(133, 300)(134, 290)(135, 291)(136, 292)(137, 302)(138, 293)(139, 306)(140, 295)(141, 296)(142, 307)(143, 299)(144, 301)(145, 303)(146, 304)(147, 312)(148, 305)(149, 308)(150, 309)(151, 311)(152, 310)(153, 313)(154, 314)(155, 316)(156, 315)(157, 317)(158, 318)(159, 320)(160, 319)(161, 321)(162, 322)(163, 324)(164, 323)(165, 325)(166, 326)(167, 328)(168, 327)(169, 415)(170, 414)(171, 416)(172, 413)(173, 405)(174, 408)(175, 401)(176, 404)(177, 409)(178, 403)(179, 410)(180, 412)(181, 407)(182, 406)(183, 396)(184, 399)(185, 398)(186, 402)(187, 411)(188, 391)(189, 400)(190, 393)(191, 392)(192, 397)(193, 383)(194, 394)(195, 386)(196, 384)(197, 381)(198, 390)(199, 389)(200, 382)(201, 385)(202, 387)(203, 395)(204, 388)(205, 380)(206, 378)(207, 377)(208, 379)(417, 627)(418, 629)(419, 625)(420, 634)(421, 626)(422, 638)(423, 639)(424, 637)(425, 636)(426, 628)(427, 644)(428, 633)(429, 632)(430, 630)(431, 631)(432, 650)(433, 649)(434, 653)(435, 652)(436, 635)(437, 656)(438, 655)(439, 659)(440, 658)(441, 641)(442, 640)(443, 662)(444, 643)(445, 642)(446, 661)(447, 646)(448, 645)(449, 667)(450, 648)(451, 647)(452, 666)(453, 654)(454, 651)(455, 673)(456, 672)(457, 675)(458, 660)(459, 657)(460, 678)(461, 677)(462, 680)(463, 679)(464, 664)(465, 663)(466, 676)(467, 665)(468, 674)(469, 669)(470, 668)(471, 671)(472, 670)(473, 690)(474, 689)(475, 692)(476, 691)(477, 694)(478, 693)(479, 696)(480, 695)(481, 682)(482, 681)(483, 684)(484, 683)(485, 686)(486, 685)(487, 688)(488, 687)(489, 746)(490, 745)(491, 748)(492, 747)(493, 750)(494, 752)(495, 754)(496, 756)(497, 757)(498, 749)(499, 760)(500, 761)(501, 751)(502, 763)(503, 765)(504, 766)(505, 762)(506, 753)(507, 764)(508, 758)(509, 759)(510, 768)(511, 770)(512, 771)(513, 769)(514, 755)(515, 767)(516, 774)(517, 775)(518, 773)(519, 776)(520, 772)(521, 778)(522, 779)(523, 777)(524, 780)(525, 782)(526, 783)(527, 781)(528, 784)(529, 786)(530, 787)(531, 785)(532, 788)(533, 790)(534, 791)(535, 789)(536, 792)(537, 698)(538, 697)(539, 700)(540, 699)(541, 706)(542, 701)(543, 709)(544, 702)(545, 714)(546, 703)(547, 722)(548, 704)(549, 705)(550, 716)(551, 717)(552, 707)(553, 708)(554, 713)(555, 710)(556, 715)(557, 711)(558, 712)(559, 723)(560, 718)(561, 721)(562, 719)(563, 720)(564, 728)(565, 726)(566, 724)(567, 725)(568, 727)(569, 731)(570, 729)(571, 730)(572, 732)(573, 735)(574, 733)(575, 734)(576, 736)(577, 739)(578, 737)(579, 738)(580, 740)(581, 743)(582, 741)(583, 742)(584, 744)(585, 830)(586, 829)(587, 831)(588, 832)(589, 824)(590, 823)(591, 820)(592, 819)(593, 828)(594, 818)(595, 825)(596, 827)(597, 822)(598, 821)(599, 815)(600, 814)(601, 813)(602, 817)(603, 826)(604, 816)(605, 809)(606, 808)(607, 807)(608, 812)(609, 810)(610, 802)(611, 800)(612, 799)(613, 806)(614, 805)(615, 798)(616, 797)(617, 803)(618, 811)(619, 804)(620, 801)(621, 794)(622, 793)(623, 795)(624, 796)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2237
Transitivity :: VT+
Graph:: bipartite
	v = 104 e = 416 f = 260
	degree seq :: [ 8^104 ]

E27.2240 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ]
Map::
	R = (1, 209, 417, 625, 4, 212, 420, 628)(2, 210, 418, 626, 6, 214, 422, 630)(3, 211, 419, 627, 8, 216, 424, 632)(5, 213, 421, 629, 12, 220, 428, 636)(7, 215, 423, 631, 16, 224, 432, 640)(9, 217, 425, 633, 18, 226, 434, 642)(10, 218, 426, 634, 19, 227, 435, 643)(11, 219, 427, 635, 21, 229, 437, 645)(13, 221, 429, 637, 23, 231, 439, 647)(14, 222, 430, 638, 24, 232, 440, 648)(15, 223, 431, 639, 25, 233, 441, 649)(17, 225, 433, 641, 27, 235, 443, 651)(20, 228, 436, 644, 31, 239, 447, 655)(22, 230, 438, 646, 33, 241, 449, 657)(26, 234, 442, 650, 37, 245, 453, 661)(28, 236, 444, 652, 39, 247, 455, 663)(29, 237, 445, 653, 40, 248, 456, 664)(30, 238, 446, 654, 41, 249, 457, 665)(32, 240, 448, 656, 42, 250, 458, 666)(34, 242, 450, 658, 44, 252, 460, 668)(35, 243, 451, 659, 45, 253, 461, 669)(36, 244, 452, 660, 46, 254, 462, 670)(38, 246, 454, 662, 47, 255, 463, 671)(43, 251, 459, 667, 52, 260, 468, 676)(48, 256, 464, 672, 57, 265, 473, 681)(49, 257, 465, 673, 58, 266, 474, 682)(50, 258, 466, 674, 59, 267, 475, 683)(51, 259, 467, 675, 60, 268, 476, 684)(53, 261, 469, 677, 61, 269, 477, 685)(54, 262, 470, 678, 62, 270, 478, 686)(55, 263, 471, 679, 63, 271, 479, 687)(56, 264, 472, 680, 64, 272, 480, 688)(65, 273, 481, 689, 73, 281, 489, 697)(66, 274, 482, 690, 74, 282, 490, 698)(67, 275, 483, 691, 75, 283, 491, 699)(68, 276, 484, 692, 76, 284, 492, 700)(69, 277, 485, 693, 113, 321, 529, 737)(70, 278, 486, 694, 115, 323, 531, 739)(71, 279, 487, 695, 117, 325, 533, 741)(72, 280, 488, 696, 119, 327, 535, 743)(77, 285, 493, 701, 121, 329, 537, 745)(78, 286, 494, 702, 123, 331, 539, 747)(79, 287, 495, 703, 125, 333, 541, 749)(80, 288, 496, 704, 127, 335, 543, 751)(81, 289, 497, 705, 129, 337, 545, 753)(82, 290, 498, 706, 131, 339, 547, 755)(83, 291, 499, 707, 134, 342, 550, 758)(84, 292, 500, 708, 136, 344, 552, 760)(85, 293, 501, 709, 138, 346, 554, 762)(86, 294, 502, 710, 141, 349, 557, 765)(87, 295, 503, 711, 140, 348, 556, 764)(88, 296, 504, 712, 144, 352, 560, 768)(89, 297, 505, 713, 133, 341, 549, 757)(90, 298, 506, 714, 147, 355, 563, 771)(91, 299, 507, 715, 149, 357, 565, 773)(92, 300, 508, 716, 151, 359, 567, 775)(93, 301, 509, 717, 153, 361, 569, 777)(94, 302, 510, 718, 155, 363, 571, 779)(95, 303, 511, 719, 157, 365, 573, 781)(96, 304, 512, 720, 159, 367, 575, 783)(97, 305, 513, 721, 161, 369, 577, 785)(98, 306, 514, 722, 163, 371, 579, 787)(99, 307, 515, 723, 165, 373, 581, 789)(100, 308, 516, 724, 167, 375, 583, 791)(101, 309, 517, 725, 169, 377, 585, 793)(102, 310, 518, 726, 171, 379, 587, 795)(103, 311, 519, 727, 173, 381, 589, 797)(104, 312, 520, 728, 175, 383, 591, 799)(105, 313, 521, 729, 177, 385, 593, 801)(106, 314, 522, 730, 179, 387, 595, 803)(107, 315, 523, 731, 181, 389, 597, 805)(108, 316, 524, 732, 183, 391, 599, 807)(109, 317, 525, 733, 185, 393, 601, 809)(110, 318, 526, 734, 187, 395, 603, 811)(111, 319, 527, 735, 189, 397, 605, 813)(112, 320, 528, 736, 191, 399, 607, 815)(114, 322, 530, 738, 193, 401, 609, 817)(116, 324, 532, 740, 195, 403, 611, 819)(118, 326, 534, 742, 197, 405, 613, 821)(120, 328, 536, 744, 199, 407, 615, 823)(122, 330, 538, 746, 201, 409, 617, 825)(124, 332, 540, 748, 202, 410, 618, 826)(126, 334, 542, 750, 203, 411, 619, 827)(128, 336, 544, 752, 205, 413, 621, 829)(130, 338, 546, 754, 204, 412, 620, 828)(132, 340, 548, 756, 200, 408, 616, 824)(135, 343, 551, 759, 198, 406, 614, 822)(137, 345, 553, 761, 206, 414, 622, 830)(139, 347, 555, 763, 192, 400, 608, 816)(142, 350, 558, 766, 190, 398, 606, 814)(143, 351, 559, 767, 208, 416, 624, 832)(145, 353, 561, 769, 188, 396, 604, 812)(146, 354, 562, 770, 207, 415, 623, 831)(148, 356, 564, 772, 196, 404, 612, 820)(150, 358, 566, 774, 194, 402, 610, 818)(152, 360, 568, 776, 184, 392, 600, 808)(154, 362, 570, 778, 182, 390, 598, 806)(156, 364, 572, 780, 180, 388, 596, 804)(158, 366, 574, 782, 186, 394, 602, 810)(160, 368, 576, 784, 176, 384, 592, 800)(162, 370, 578, 786, 174, 382, 590, 798)(164, 372, 580, 788, 172, 380, 588, 796)(166, 374, 582, 790, 170, 378, 586, 794)(168, 376, 584, 792, 178, 386, 594, 802)
	L = (1, 210)(2, 209)(3, 215)(4, 217)(5, 219)(6, 221)(7, 211)(8, 225)(9, 212)(10, 224)(11, 213)(12, 230)(13, 214)(14, 229)(15, 228)(16, 218)(17, 216)(18, 236)(19, 238)(20, 223)(21, 222)(22, 220)(23, 242)(24, 244)(25, 240)(26, 239)(27, 243)(28, 226)(29, 241)(30, 227)(31, 234)(32, 233)(33, 237)(34, 231)(35, 235)(36, 232)(37, 251)(38, 250)(39, 256)(40, 258)(41, 257)(42, 246)(43, 245)(44, 261)(45, 263)(46, 262)(47, 264)(48, 247)(49, 249)(50, 248)(51, 260)(52, 259)(53, 252)(54, 254)(55, 253)(56, 255)(57, 273)(58, 275)(59, 274)(60, 276)(61, 277)(62, 279)(63, 278)(64, 280)(65, 265)(66, 267)(67, 266)(68, 268)(69, 269)(70, 271)(71, 270)(72, 272)(73, 297)(74, 289)(75, 288)(76, 285)(77, 284)(78, 327)(79, 325)(80, 283)(81, 282)(82, 329)(83, 337)(84, 323)(85, 331)(86, 344)(87, 321)(88, 333)(89, 281)(90, 335)(91, 341)(92, 339)(93, 355)(94, 342)(95, 348)(96, 346)(97, 352)(98, 349)(99, 365)(100, 357)(101, 359)(102, 363)(103, 361)(104, 375)(105, 367)(106, 371)(107, 369)(108, 373)(109, 377)(110, 381)(111, 379)(112, 383)(113, 295)(114, 385)(115, 292)(116, 389)(117, 287)(118, 387)(119, 286)(120, 391)(121, 290)(122, 399)(123, 293)(124, 407)(125, 296)(126, 405)(127, 298)(128, 397)(129, 291)(130, 395)(131, 300)(132, 409)(133, 299)(134, 302)(135, 412)(136, 294)(137, 403)(138, 304)(139, 410)(140, 303)(141, 306)(142, 414)(143, 401)(144, 305)(145, 411)(146, 393)(147, 301)(148, 413)(149, 308)(150, 415)(151, 309)(152, 408)(153, 311)(154, 404)(155, 310)(156, 406)(157, 307)(158, 416)(159, 313)(160, 400)(161, 315)(162, 396)(163, 314)(164, 398)(165, 316)(166, 394)(167, 312)(168, 402)(169, 317)(170, 392)(171, 319)(172, 388)(173, 318)(174, 390)(175, 320)(176, 386)(177, 322)(178, 384)(179, 326)(180, 380)(181, 324)(182, 382)(183, 328)(184, 378)(185, 354)(186, 374)(187, 338)(188, 370)(189, 336)(190, 372)(191, 330)(192, 368)(193, 351)(194, 376)(195, 345)(196, 362)(197, 334)(198, 364)(199, 332)(200, 360)(201, 340)(202, 347)(203, 353)(204, 343)(205, 356)(206, 350)(207, 358)(208, 366)(417, 627)(418, 629)(419, 625)(420, 634)(421, 626)(422, 638)(423, 639)(424, 637)(425, 636)(426, 628)(427, 644)(428, 633)(429, 632)(430, 630)(431, 631)(432, 650)(433, 649)(434, 653)(435, 652)(436, 635)(437, 656)(438, 655)(439, 659)(440, 658)(441, 641)(442, 640)(443, 662)(444, 643)(445, 642)(446, 661)(447, 646)(448, 645)(449, 667)(450, 648)(451, 647)(452, 666)(453, 654)(454, 651)(455, 673)(456, 672)(457, 675)(458, 660)(459, 657)(460, 678)(461, 677)(462, 680)(463, 679)(464, 664)(465, 663)(466, 676)(467, 665)(468, 674)(469, 669)(470, 668)(471, 671)(472, 670)(473, 690)(474, 689)(475, 692)(476, 691)(477, 694)(478, 693)(479, 696)(480, 695)(481, 682)(482, 681)(483, 684)(484, 683)(485, 686)(486, 685)(487, 688)(488, 687)(489, 704)(490, 713)(491, 701)(492, 705)(493, 699)(494, 741)(495, 737)(496, 697)(497, 700)(498, 753)(499, 757)(500, 743)(501, 760)(502, 764)(503, 739)(504, 747)(505, 698)(506, 745)(507, 751)(508, 771)(509, 773)(510, 755)(511, 749)(512, 768)(513, 781)(514, 762)(515, 765)(516, 758)(517, 779)(518, 791)(519, 775)(520, 777)(521, 787)(522, 789)(523, 783)(524, 785)(525, 797)(526, 799)(527, 793)(528, 795)(529, 703)(530, 805)(531, 711)(532, 807)(533, 702)(534, 801)(535, 708)(536, 803)(537, 714)(538, 811)(539, 712)(540, 819)(541, 719)(542, 823)(543, 715)(544, 815)(545, 706)(546, 809)(547, 718)(548, 829)(549, 707)(550, 724)(551, 825)(552, 709)(553, 817)(554, 722)(555, 827)(556, 710)(557, 723)(558, 826)(559, 821)(560, 720)(561, 832)(562, 813)(563, 716)(564, 831)(565, 717)(566, 828)(567, 727)(568, 822)(569, 728)(570, 824)(571, 725)(572, 818)(573, 721)(574, 830)(575, 731)(576, 814)(577, 732)(578, 816)(579, 729)(580, 810)(581, 730)(582, 812)(583, 726)(584, 820)(585, 735)(586, 806)(587, 736)(588, 808)(589, 733)(590, 802)(591, 734)(592, 804)(593, 742)(594, 798)(595, 744)(596, 800)(597, 738)(598, 794)(599, 740)(600, 796)(601, 754)(602, 788)(603, 746)(604, 790)(605, 770)(606, 784)(607, 752)(608, 786)(609, 761)(610, 780)(611, 748)(612, 792)(613, 767)(614, 776)(615, 750)(616, 778)(617, 759)(618, 766)(619, 763)(620, 774)(621, 756)(622, 782)(623, 772)(624, 769)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2238
Transitivity :: VT+
Graph:: bipartite
	v = 104 e = 416 f = 260
	degree seq :: [ 8^104 ]

E27.2241 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = D16 x D26 (small group id <416, 131>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 209, 417, 625, 4, 212, 420, 628, 14, 222, 430, 638, 5, 213, 421, 629)(2, 210, 418, 626, 7, 215, 423, 631, 22, 230, 438, 646, 8, 216, 424, 632)(3, 211, 419, 627, 10, 218, 426, 634, 17, 225, 433, 641, 11, 219, 427, 635)(6, 214, 422, 630, 18, 226, 434, 642, 9, 217, 425, 633, 19, 227, 435, 643)(12, 220, 428, 636, 25, 233, 441, 649, 15, 223, 431, 639, 26, 234, 442, 650)(13, 221, 429, 637, 27, 235, 443, 651, 16, 224, 432, 640, 28, 236, 444, 652)(20, 228, 436, 644, 29, 237, 445, 653, 23, 231, 439, 647, 30, 238, 446, 654)(21, 229, 437, 645, 31, 239, 447, 655, 24, 232, 440, 648, 32, 240, 448, 656)(33, 241, 449, 657, 41, 249, 457, 665, 35, 243, 451, 659, 42, 250, 458, 666)(34, 242, 450, 658, 43, 251, 459, 667, 36, 244, 452, 660, 44, 252, 460, 668)(37, 245, 453, 661, 45, 253, 461, 669, 39, 247, 455, 663, 46, 254, 462, 670)(38, 246, 454, 662, 47, 255, 463, 671, 40, 248, 456, 664, 48, 256, 464, 672)(49, 257, 465, 673, 57, 265, 473, 681, 51, 259, 467, 675, 58, 266, 474, 682)(50, 258, 466, 674, 59, 267, 475, 683, 52, 260, 468, 676, 60, 268, 476, 684)(53, 261, 469, 677, 61, 269, 477, 685, 55, 263, 471, 679, 62, 270, 478, 686)(54, 262, 470, 678, 63, 271, 479, 687, 56, 264, 472, 680, 64, 272, 480, 688)(65, 273, 481, 689, 73, 281, 489, 697, 67, 275, 483, 691, 74, 282, 490, 698)(66, 274, 482, 690, 75, 283, 491, 699, 68, 276, 484, 692, 76, 284, 492, 700)(69, 277, 485, 693, 117, 325, 533, 741, 71, 279, 487, 695, 119, 327, 535, 743)(70, 278, 486, 694, 118, 326, 534, 742, 72, 280, 488, 696, 120, 328, 536, 744)(77, 285, 493, 701, 125, 333, 541, 749, 88, 296, 504, 712, 126, 334, 542, 750)(78, 286, 494, 702, 127, 335, 543, 751, 92, 300, 508, 716, 128, 336, 544, 752)(79, 287, 495, 703, 129, 337, 545, 753, 89, 297, 505, 713, 130, 338, 546, 754)(80, 288, 496, 704, 131, 339, 547, 755, 81, 289, 497, 705, 132, 340, 548, 756)(82, 290, 498, 706, 133, 341, 549, 757, 85, 293, 501, 709, 134, 342, 550, 758)(83, 291, 499, 707, 135, 343, 551, 759, 84, 292, 500, 708, 136, 344, 552, 760)(86, 294, 502, 710, 137, 345, 553, 761, 87, 295, 503, 711, 138, 346, 554, 762)(90, 298, 506, 714, 139, 347, 555, 763, 91, 299, 507, 715, 140, 348, 556, 764)(93, 301, 509, 717, 141, 349, 557, 765, 94, 302, 510, 718, 142, 350, 558, 766)(95, 303, 511, 719, 143, 351, 559, 767, 96, 304, 512, 720, 144, 352, 560, 768)(97, 305, 513, 721, 145, 353, 561, 769, 98, 306, 514, 722, 146, 354, 562, 770)(99, 307, 515, 723, 147, 355, 563, 771, 100, 308, 516, 724, 148, 356, 564, 772)(101, 309, 517, 725, 149, 357, 565, 773, 102, 310, 518, 726, 150, 358, 566, 774)(103, 311, 519, 727, 151, 359, 567, 775, 104, 312, 520, 728, 152, 360, 568, 776)(105, 313, 521, 729, 153, 361, 569, 777, 106, 314, 522, 730, 154, 362, 570, 778)(107, 315, 523, 731, 155, 363, 571, 779, 108, 316, 524, 732, 156, 364, 572, 780)(109, 317, 525, 733, 157, 365, 573, 781, 110, 318, 526, 734, 158, 366, 574, 782)(111, 319, 527, 735, 159, 367, 575, 783, 112, 320, 528, 736, 160, 368, 576, 784)(113, 321, 529, 737, 161, 369, 577, 785, 114, 322, 530, 738, 162, 370, 578, 786)(115, 323, 531, 739, 163, 371, 579, 787, 116, 324, 532, 740, 164, 372, 580, 788)(121, 329, 537, 745, 169, 377, 585, 793, 122, 330, 538, 746, 170, 378, 586, 794)(123, 331, 539, 747, 171, 379, 587, 795, 124, 332, 540, 748, 172, 380, 588, 796)(165, 373, 581, 789, 205, 413, 621, 829, 166, 374, 582, 790, 206, 414, 622, 830)(167, 375, 583, 791, 207, 415, 623, 831, 168, 376, 584, 792, 208, 416, 624, 832)(173, 381, 589, 797, 197, 405, 613, 821, 174, 382, 590, 798, 198, 406, 614, 822)(175, 383, 591, 799, 201, 409, 617, 825, 176, 384, 592, 800, 202, 410, 618, 826)(177, 385, 593, 801, 203, 411, 619, 827, 178, 386, 594, 802, 204, 412, 620, 828)(179, 387, 595, 803, 194, 402, 610, 818, 180, 388, 596, 804, 193, 401, 609, 817)(181, 389, 597, 805, 199, 407, 615, 823, 182, 390, 598, 806, 200, 408, 616, 824)(183, 391, 599, 807, 190, 398, 606, 814, 184, 392, 600, 808, 189, 397, 605, 813)(185, 393, 601, 809, 192, 400, 608, 816, 186, 394, 602, 810, 191, 399, 607, 815)(187, 395, 603, 811, 196, 404, 612, 820, 188, 396, 604, 812, 195, 403, 611, 819)
	L = (1, 210)(2, 209)(3, 217)(4, 220)(5, 223)(6, 225)(7, 228)(8, 231)(9, 211)(10, 232)(11, 229)(12, 212)(13, 227)(14, 230)(15, 213)(16, 226)(17, 214)(18, 224)(19, 221)(20, 215)(21, 219)(22, 222)(23, 216)(24, 218)(25, 241)(26, 243)(27, 244)(28, 242)(29, 245)(30, 247)(31, 248)(32, 246)(33, 233)(34, 236)(35, 234)(36, 235)(37, 237)(38, 240)(39, 238)(40, 239)(41, 257)(42, 259)(43, 260)(44, 258)(45, 261)(46, 263)(47, 264)(48, 262)(49, 249)(50, 252)(51, 250)(52, 251)(53, 253)(54, 256)(55, 254)(56, 255)(57, 273)(58, 275)(59, 276)(60, 274)(61, 277)(62, 279)(63, 280)(64, 278)(65, 265)(66, 268)(67, 266)(68, 267)(69, 269)(70, 272)(71, 270)(72, 271)(73, 300)(74, 286)(75, 287)(76, 297)(77, 327)(78, 282)(79, 283)(80, 335)(81, 336)(82, 326)(83, 333)(84, 334)(85, 328)(86, 342)(87, 341)(88, 325)(89, 284)(90, 338)(91, 337)(92, 281)(93, 339)(94, 340)(95, 348)(96, 347)(97, 343)(98, 344)(99, 346)(100, 345)(101, 349)(102, 350)(103, 352)(104, 351)(105, 353)(106, 354)(107, 356)(108, 355)(109, 357)(110, 358)(111, 360)(112, 359)(113, 361)(114, 362)(115, 364)(116, 363)(117, 296)(118, 290)(119, 285)(120, 293)(121, 365)(122, 366)(123, 368)(124, 367)(125, 291)(126, 292)(127, 288)(128, 289)(129, 299)(130, 298)(131, 301)(132, 302)(133, 295)(134, 294)(135, 305)(136, 306)(137, 308)(138, 307)(139, 304)(140, 303)(141, 309)(142, 310)(143, 312)(144, 311)(145, 313)(146, 314)(147, 316)(148, 315)(149, 317)(150, 318)(151, 320)(152, 319)(153, 321)(154, 322)(155, 324)(156, 323)(157, 329)(158, 330)(159, 332)(160, 331)(161, 373)(162, 374)(163, 376)(164, 375)(165, 369)(166, 370)(167, 372)(168, 371)(169, 384)(170, 383)(171, 385)(172, 386)(173, 414)(174, 413)(175, 378)(176, 377)(177, 379)(178, 380)(179, 409)(180, 410)(181, 415)(182, 416)(183, 405)(184, 406)(185, 408)(186, 407)(187, 412)(188, 411)(189, 402)(190, 401)(191, 403)(192, 404)(193, 398)(194, 397)(195, 399)(196, 400)(197, 391)(198, 392)(199, 394)(200, 393)(201, 387)(202, 388)(203, 396)(204, 395)(205, 382)(206, 381)(207, 389)(208, 390)(417, 627)(418, 630)(419, 625)(420, 637)(421, 640)(422, 626)(423, 645)(424, 648)(425, 646)(426, 644)(427, 647)(428, 642)(429, 628)(430, 641)(431, 643)(432, 629)(433, 638)(434, 636)(435, 639)(436, 634)(437, 631)(438, 633)(439, 635)(440, 632)(441, 658)(442, 660)(443, 657)(444, 659)(445, 662)(446, 664)(447, 661)(448, 663)(449, 651)(450, 649)(451, 652)(452, 650)(453, 655)(454, 653)(455, 656)(456, 654)(457, 674)(458, 676)(459, 673)(460, 675)(461, 678)(462, 680)(463, 677)(464, 679)(465, 667)(466, 665)(467, 668)(468, 666)(469, 671)(470, 669)(471, 672)(472, 670)(473, 690)(474, 692)(475, 689)(476, 691)(477, 694)(478, 696)(479, 693)(480, 695)(481, 683)(482, 681)(483, 684)(484, 682)(485, 687)(486, 685)(487, 688)(488, 686)(489, 713)(490, 703)(491, 716)(492, 702)(493, 744)(494, 700)(495, 698)(496, 753)(497, 754)(498, 743)(499, 757)(500, 758)(501, 741)(502, 749)(503, 750)(504, 742)(505, 697)(506, 751)(507, 752)(508, 699)(509, 763)(510, 764)(511, 755)(512, 756)(513, 761)(514, 762)(515, 759)(516, 760)(517, 767)(518, 768)(519, 765)(520, 766)(521, 771)(522, 772)(523, 769)(524, 770)(525, 775)(526, 776)(527, 773)(528, 774)(529, 779)(530, 780)(531, 777)(532, 778)(533, 709)(534, 712)(535, 706)(536, 701)(537, 783)(538, 784)(539, 781)(540, 782)(541, 710)(542, 711)(543, 714)(544, 715)(545, 704)(546, 705)(547, 719)(548, 720)(549, 707)(550, 708)(551, 723)(552, 724)(553, 721)(554, 722)(555, 717)(556, 718)(557, 727)(558, 728)(559, 725)(560, 726)(561, 731)(562, 732)(563, 729)(564, 730)(565, 735)(566, 736)(567, 733)(568, 734)(569, 739)(570, 740)(571, 737)(572, 738)(573, 747)(574, 748)(575, 745)(576, 746)(577, 791)(578, 792)(579, 789)(580, 790)(581, 787)(582, 788)(583, 785)(584, 786)(585, 802)(586, 801)(587, 800)(588, 799)(589, 832)(590, 831)(591, 796)(592, 795)(593, 794)(594, 793)(595, 827)(596, 828)(597, 830)(598, 829)(599, 823)(600, 824)(601, 821)(602, 822)(603, 825)(604, 826)(605, 820)(606, 819)(607, 818)(608, 817)(609, 816)(610, 815)(611, 814)(612, 813)(613, 809)(614, 810)(615, 807)(616, 808)(617, 811)(618, 812)(619, 803)(620, 804)(621, 806)(622, 805)(623, 798)(624, 797)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2235
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 416 f = 312
	degree seq :: [ 16^52 ]

E27.2242 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 135>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 209, 417, 625, 4, 212, 420, 628, 14, 222, 430, 638, 5, 213, 421, 629)(2, 210, 418, 626, 7, 215, 423, 631, 22, 230, 438, 646, 8, 216, 424, 632)(3, 211, 419, 627, 10, 218, 426, 634, 17, 225, 433, 641, 11, 219, 427, 635)(6, 214, 422, 630, 18, 226, 434, 642, 9, 217, 425, 633, 19, 227, 435, 643)(12, 220, 428, 636, 25, 233, 441, 649, 15, 223, 431, 639, 26, 234, 442, 650)(13, 221, 429, 637, 27, 235, 443, 651, 16, 224, 432, 640, 28, 236, 444, 652)(20, 228, 436, 644, 29, 237, 445, 653, 23, 231, 439, 647, 30, 238, 446, 654)(21, 229, 437, 645, 31, 239, 447, 655, 24, 232, 440, 648, 32, 240, 448, 656)(33, 241, 449, 657, 41, 249, 457, 665, 35, 243, 451, 659, 42, 250, 458, 666)(34, 242, 450, 658, 43, 251, 459, 667, 36, 244, 452, 660, 44, 252, 460, 668)(37, 245, 453, 661, 45, 253, 461, 669, 39, 247, 455, 663, 46, 254, 462, 670)(38, 246, 454, 662, 47, 255, 463, 671, 40, 248, 456, 664, 48, 256, 464, 672)(49, 257, 465, 673, 57, 265, 473, 681, 51, 259, 467, 675, 58, 266, 474, 682)(50, 258, 466, 674, 59, 267, 475, 683, 52, 260, 468, 676, 60, 268, 476, 684)(53, 261, 469, 677, 61, 269, 477, 685, 55, 263, 471, 679, 62, 270, 478, 686)(54, 262, 470, 678, 63, 271, 479, 687, 56, 264, 472, 680, 64, 272, 480, 688)(65, 273, 481, 689, 73, 281, 489, 697, 67, 275, 483, 691, 74, 282, 490, 698)(66, 274, 482, 690, 75, 283, 491, 699, 68, 276, 484, 692, 76, 284, 492, 700)(69, 277, 485, 693, 117, 325, 533, 741, 71, 279, 487, 695, 119, 327, 535, 743)(70, 278, 486, 694, 118, 326, 534, 742, 72, 280, 488, 696, 120, 328, 536, 744)(77, 285, 493, 701, 125, 333, 541, 749, 88, 296, 504, 712, 126, 334, 542, 750)(78, 286, 494, 702, 127, 335, 543, 751, 92, 300, 508, 716, 128, 336, 544, 752)(79, 287, 495, 703, 129, 337, 545, 753, 89, 297, 505, 713, 130, 338, 546, 754)(80, 288, 496, 704, 131, 339, 547, 755, 81, 289, 497, 705, 132, 340, 548, 756)(82, 290, 498, 706, 133, 341, 549, 757, 85, 293, 501, 709, 134, 342, 550, 758)(83, 291, 499, 707, 135, 343, 551, 759, 84, 292, 500, 708, 136, 344, 552, 760)(86, 294, 502, 710, 137, 345, 553, 761, 87, 295, 503, 711, 138, 346, 554, 762)(90, 298, 506, 714, 139, 347, 555, 763, 91, 299, 507, 715, 140, 348, 556, 764)(93, 301, 509, 717, 141, 349, 557, 765, 94, 302, 510, 718, 142, 350, 558, 766)(95, 303, 511, 719, 143, 351, 559, 767, 96, 304, 512, 720, 144, 352, 560, 768)(97, 305, 513, 721, 145, 353, 561, 769, 98, 306, 514, 722, 146, 354, 562, 770)(99, 307, 515, 723, 147, 355, 563, 771, 100, 308, 516, 724, 148, 356, 564, 772)(101, 309, 517, 725, 149, 357, 565, 773, 102, 310, 518, 726, 150, 358, 566, 774)(103, 311, 519, 727, 151, 359, 567, 775, 104, 312, 520, 728, 152, 360, 568, 776)(105, 313, 521, 729, 153, 361, 569, 777, 106, 314, 522, 730, 154, 362, 570, 778)(107, 315, 523, 731, 155, 363, 571, 779, 108, 316, 524, 732, 156, 364, 572, 780)(109, 317, 525, 733, 157, 365, 573, 781, 110, 318, 526, 734, 158, 366, 574, 782)(111, 319, 527, 735, 159, 367, 575, 783, 112, 320, 528, 736, 160, 368, 576, 784)(113, 321, 529, 737, 161, 369, 577, 785, 114, 322, 530, 738, 162, 370, 578, 786)(115, 323, 531, 739, 163, 371, 579, 787, 116, 324, 532, 740, 164, 372, 580, 788)(121, 329, 537, 745, 169, 377, 585, 793, 122, 330, 538, 746, 170, 378, 586, 794)(123, 331, 539, 747, 171, 379, 587, 795, 124, 332, 540, 748, 172, 380, 588, 796)(165, 373, 581, 789, 205, 413, 621, 829, 166, 374, 582, 790, 206, 414, 622, 830)(167, 375, 583, 791, 207, 415, 623, 831, 168, 376, 584, 792, 208, 416, 624, 832)(173, 381, 589, 797, 198, 406, 614, 822, 174, 382, 590, 798, 197, 405, 613, 821)(175, 383, 591, 799, 202, 410, 618, 826, 176, 384, 592, 800, 201, 409, 617, 825)(177, 385, 593, 801, 204, 412, 620, 828, 178, 386, 594, 802, 203, 411, 619, 827)(179, 387, 595, 803, 193, 401, 609, 817, 180, 388, 596, 804, 194, 402, 610, 818)(181, 389, 597, 805, 200, 408, 616, 824, 182, 390, 598, 806, 199, 407, 615, 823)(183, 391, 599, 807, 189, 397, 605, 813, 184, 392, 600, 808, 190, 398, 606, 814)(185, 393, 601, 809, 191, 399, 607, 815, 186, 394, 602, 810, 192, 400, 608, 816)(187, 395, 603, 811, 195, 403, 611, 819, 188, 396, 604, 812, 196, 404, 612, 820)
	L = (1, 210)(2, 209)(3, 217)(4, 220)(5, 223)(6, 225)(7, 228)(8, 231)(9, 211)(10, 232)(11, 229)(12, 212)(13, 227)(14, 230)(15, 213)(16, 226)(17, 214)(18, 224)(19, 221)(20, 215)(21, 219)(22, 222)(23, 216)(24, 218)(25, 241)(26, 243)(27, 244)(28, 242)(29, 245)(30, 247)(31, 248)(32, 246)(33, 233)(34, 236)(35, 234)(36, 235)(37, 237)(38, 240)(39, 238)(40, 239)(41, 257)(42, 259)(43, 260)(44, 258)(45, 261)(46, 263)(47, 264)(48, 262)(49, 249)(50, 252)(51, 250)(52, 251)(53, 253)(54, 256)(55, 254)(56, 255)(57, 273)(58, 275)(59, 276)(60, 274)(61, 277)(62, 279)(63, 280)(64, 278)(65, 265)(66, 268)(67, 266)(68, 267)(69, 269)(70, 272)(71, 270)(72, 271)(73, 286)(74, 300)(75, 297)(76, 287)(77, 325)(78, 281)(79, 284)(80, 335)(81, 336)(82, 328)(83, 333)(84, 334)(85, 326)(86, 342)(87, 341)(88, 327)(89, 283)(90, 338)(91, 337)(92, 282)(93, 339)(94, 340)(95, 348)(96, 347)(97, 343)(98, 344)(99, 346)(100, 345)(101, 349)(102, 350)(103, 352)(104, 351)(105, 353)(106, 354)(107, 356)(108, 355)(109, 357)(110, 358)(111, 360)(112, 359)(113, 361)(114, 362)(115, 364)(116, 363)(117, 285)(118, 293)(119, 296)(120, 290)(121, 365)(122, 366)(123, 368)(124, 367)(125, 291)(126, 292)(127, 288)(128, 289)(129, 299)(130, 298)(131, 301)(132, 302)(133, 295)(134, 294)(135, 305)(136, 306)(137, 308)(138, 307)(139, 304)(140, 303)(141, 309)(142, 310)(143, 312)(144, 311)(145, 313)(146, 314)(147, 316)(148, 315)(149, 317)(150, 318)(151, 320)(152, 319)(153, 321)(154, 322)(155, 324)(156, 323)(157, 329)(158, 330)(159, 332)(160, 331)(161, 373)(162, 374)(163, 376)(164, 375)(165, 369)(166, 370)(167, 372)(168, 371)(169, 383)(170, 384)(171, 386)(172, 385)(173, 413)(174, 414)(175, 377)(176, 378)(177, 380)(178, 379)(179, 410)(180, 409)(181, 416)(182, 415)(183, 406)(184, 405)(185, 407)(186, 408)(187, 411)(188, 412)(189, 401)(190, 402)(191, 404)(192, 403)(193, 397)(194, 398)(195, 400)(196, 399)(197, 392)(198, 391)(199, 393)(200, 394)(201, 388)(202, 387)(203, 395)(204, 396)(205, 381)(206, 382)(207, 390)(208, 389)(417, 627)(418, 630)(419, 625)(420, 637)(421, 640)(422, 626)(423, 645)(424, 648)(425, 646)(426, 644)(427, 647)(428, 642)(429, 628)(430, 641)(431, 643)(432, 629)(433, 638)(434, 636)(435, 639)(436, 634)(437, 631)(438, 633)(439, 635)(440, 632)(441, 658)(442, 660)(443, 657)(444, 659)(445, 662)(446, 664)(447, 661)(448, 663)(449, 651)(450, 649)(451, 652)(452, 650)(453, 655)(454, 653)(455, 656)(456, 654)(457, 674)(458, 676)(459, 673)(460, 675)(461, 678)(462, 680)(463, 677)(464, 679)(465, 667)(466, 665)(467, 668)(468, 666)(469, 671)(470, 669)(471, 672)(472, 670)(473, 690)(474, 692)(475, 689)(476, 691)(477, 694)(478, 696)(479, 693)(480, 695)(481, 683)(482, 681)(483, 684)(484, 682)(485, 687)(486, 685)(487, 688)(488, 686)(489, 703)(490, 713)(491, 702)(492, 716)(493, 742)(494, 699)(495, 697)(496, 753)(497, 754)(498, 741)(499, 757)(500, 758)(501, 743)(502, 749)(503, 750)(504, 744)(505, 698)(506, 751)(507, 752)(508, 700)(509, 763)(510, 764)(511, 755)(512, 756)(513, 761)(514, 762)(515, 759)(516, 760)(517, 767)(518, 768)(519, 765)(520, 766)(521, 771)(522, 772)(523, 769)(524, 770)(525, 775)(526, 776)(527, 773)(528, 774)(529, 779)(530, 780)(531, 777)(532, 778)(533, 706)(534, 701)(535, 709)(536, 712)(537, 783)(538, 784)(539, 781)(540, 782)(541, 710)(542, 711)(543, 714)(544, 715)(545, 704)(546, 705)(547, 719)(548, 720)(549, 707)(550, 708)(551, 723)(552, 724)(553, 721)(554, 722)(555, 717)(556, 718)(557, 727)(558, 728)(559, 725)(560, 726)(561, 731)(562, 732)(563, 729)(564, 730)(565, 735)(566, 736)(567, 733)(568, 734)(569, 739)(570, 740)(571, 737)(572, 738)(573, 747)(574, 748)(575, 745)(576, 746)(577, 791)(578, 792)(579, 789)(580, 790)(581, 787)(582, 788)(583, 785)(584, 786)(585, 801)(586, 802)(587, 799)(588, 800)(589, 831)(590, 832)(591, 795)(592, 796)(593, 793)(594, 794)(595, 828)(596, 827)(597, 829)(598, 830)(599, 824)(600, 823)(601, 822)(602, 821)(603, 826)(604, 825)(605, 819)(606, 820)(607, 817)(608, 818)(609, 815)(610, 816)(611, 813)(612, 814)(613, 810)(614, 809)(615, 808)(616, 807)(617, 812)(618, 811)(619, 804)(620, 803)(621, 805)(622, 806)(623, 797)(624, 798)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2236
Transitivity :: VT+
Graph:: bipartite
	v = 52 e = 416 f = 312
	degree seq :: [ 16^52 ]

E27.2243 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^4, (Y2 * Y1)^26 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210)(3, 211, 7, 215)(4, 212, 9, 217)(5, 213, 10, 218)(6, 214, 12, 220)(8, 216, 15, 223)(11, 219, 20, 228)(13, 221, 23, 231)(14, 222, 21, 229)(16, 224, 19, 227)(17, 225, 22, 230)(18, 226, 28, 236)(24, 232, 35, 243)(25, 233, 34, 242)(26, 234, 32, 240)(27, 235, 31, 239)(29, 237, 39, 247)(30, 238, 38, 246)(33, 241, 41, 249)(36, 244, 44, 252)(37, 245, 45, 253)(40, 248, 48, 256)(42, 250, 51, 259)(43, 251, 50, 258)(46, 254, 55, 263)(47, 255, 54, 262)(49, 257, 57, 265)(52, 260, 60, 268)(53, 261, 61, 269)(56, 264, 64, 272)(58, 266, 67, 275)(59, 267, 66, 274)(62, 270, 75, 283)(63, 271, 90, 298)(65, 273, 77, 285)(68, 276, 85, 293)(69, 277, 117, 325)(70, 278, 113, 321)(71, 279, 120, 328)(72, 280, 122, 330)(73, 281, 124, 332)(74, 282, 126, 334)(76, 284, 127, 335)(78, 286, 123, 331)(79, 287, 109, 317)(80, 288, 133, 341)(81, 289, 111, 319)(82, 290, 132, 340)(83, 291, 115, 323)(84, 292, 136, 344)(86, 294, 130, 338)(87, 295, 128, 336)(88, 296, 129, 337)(89, 297, 138, 346)(91, 299, 118, 326)(92, 300, 131, 339)(93, 301, 135, 343)(94, 302, 119, 327)(95, 303, 143, 351)(96, 304, 121, 329)(97, 305, 145, 353)(98, 306, 125, 333)(99, 307, 139, 347)(100, 308, 140, 348)(101, 309, 141, 349)(102, 310, 142, 350)(103, 311, 151, 359)(104, 312, 134, 342)(105, 313, 153, 361)(106, 314, 137, 345)(107, 315, 147, 355)(108, 316, 148, 356)(110, 318, 149, 357)(112, 320, 150, 358)(114, 322, 162, 370)(116, 324, 144, 352)(146, 354, 159, 367)(152, 360, 174, 382)(154, 362, 170, 378)(155, 363, 161, 369)(156, 364, 164, 372)(157, 365, 205, 413)(158, 366, 165, 373)(160, 368, 176, 384)(163, 371, 175, 383)(166, 374, 200, 408)(167, 375, 202, 410)(168, 376, 207, 415)(169, 377, 194, 402)(171, 379, 204, 412)(172, 380, 208, 416)(173, 381, 192, 400)(177, 385, 198, 406)(178, 386, 206, 414)(179, 387, 196, 404)(180, 388, 203, 411)(181, 389, 201, 409)(182, 390, 185, 393)(183, 391, 195, 403)(184, 392, 199, 407)(186, 394, 197, 405)(187, 395, 190, 398)(188, 396, 189, 397)(191, 399, 193, 401)(417, 625, 419, 627)(418, 626, 421, 629)(420, 628, 424, 632)(422, 630, 427, 635)(423, 631, 429, 637)(425, 633, 432, 640)(426, 634, 434, 642)(428, 636, 437, 645)(430, 638, 440, 648)(431, 639, 441, 649)(433, 641, 443, 651)(435, 643, 445, 653)(436, 644, 446, 654)(438, 646, 448, 656)(439, 647, 449, 657)(442, 650, 452, 660)(444, 652, 453, 661)(447, 655, 456, 664)(450, 658, 458, 666)(451, 659, 459, 667)(454, 662, 462, 670)(455, 663, 463, 671)(457, 665, 465, 673)(460, 668, 468, 676)(461, 669, 469, 677)(464, 672, 472, 680)(466, 674, 474, 682)(467, 675, 475, 683)(470, 678, 478, 686)(471, 679, 479, 687)(473, 681, 481, 689)(476, 684, 484, 692)(477, 685, 525, 733)(480, 688, 527, 735)(482, 690, 529, 737)(483, 691, 531, 739)(485, 693, 534, 742)(486, 694, 535, 743)(487, 695, 537, 745)(488, 696, 539, 747)(489, 697, 541, 749)(490, 698, 543, 751)(491, 699, 544, 752)(492, 700, 545, 753)(493, 701, 546, 754)(494, 702, 547, 755)(495, 703, 548, 756)(496, 704, 550, 758)(497, 705, 538, 746)(498, 706, 551, 759)(499, 707, 536, 744)(500, 708, 553, 761)(501, 709, 542, 750)(502, 710, 554, 762)(503, 711, 540, 748)(504, 712, 555, 763)(505, 713, 556, 764)(506, 714, 533, 741)(507, 715, 552, 760)(508, 716, 557, 765)(509, 717, 558, 766)(510, 718, 549, 757)(511, 719, 560, 768)(512, 720, 559, 767)(513, 721, 562, 770)(514, 722, 561, 769)(515, 723, 563, 771)(516, 724, 564, 772)(517, 725, 565, 773)(518, 726, 566, 774)(519, 727, 568, 776)(520, 728, 567, 775)(521, 729, 570, 778)(522, 730, 569, 777)(523, 731, 571, 779)(524, 732, 572, 780)(526, 734, 574, 782)(528, 736, 576, 784)(530, 738, 579, 787)(532, 740, 578, 786)(573, 781, 620, 828)(575, 783, 621, 829)(577, 785, 623, 831)(580, 788, 618, 826)(581, 789, 624, 832)(582, 790, 608, 816)(583, 791, 610, 818)(584, 792, 617, 825)(585, 793, 601, 809)(586, 794, 619, 827)(587, 795, 611, 819)(588, 796, 615, 823)(589, 797, 598, 806)(590, 798, 622, 830)(591, 799, 613, 821)(592, 800, 616, 824)(593, 801, 605, 813)(594, 802, 614, 822)(595, 803, 603, 811)(596, 804, 612, 820)(597, 805, 609, 817)(599, 807, 604, 812)(600, 808, 607, 815)(602, 810, 606, 814)
	L = (1, 420)(2, 422)(3, 424)(4, 417)(5, 427)(6, 418)(7, 430)(8, 419)(9, 433)(10, 435)(11, 421)(12, 438)(13, 440)(14, 423)(15, 442)(16, 443)(17, 425)(18, 445)(19, 426)(20, 447)(21, 448)(22, 428)(23, 450)(24, 429)(25, 452)(26, 431)(27, 432)(28, 454)(29, 434)(30, 456)(31, 436)(32, 437)(33, 458)(34, 439)(35, 460)(36, 441)(37, 462)(38, 444)(39, 464)(40, 446)(41, 466)(42, 449)(43, 468)(44, 451)(45, 470)(46, 453)(47, 472)(48, 455)(49, 474)(50, 457)(51, 476)(52, 459)(53, 478)(54, 461)(55, 480)(56, 463)(57, 482)(58, 465)(59, 484)(60, 467)(61, 506)(62, 469)(63, 527)(64, 471)(65, 529)(66, 473)(67, 501)(68, 475)(69, 488)(70, 490)(71, 492)(72, 485)(73, 494)(74, 486)(75, 497)(76, 487)(77, 499)(78, 489)(79, 503)(80, 504)(81, 491)(82, 507)(83, 493)(84, 508)(85, 483)(86, 510)(87, 495)(88, 496)(89, 512)(90, 477)(91, 498)(92, 500)(93, 514)(94, 502)(95, 515)(96, 505)(97, 517)(98, 509)(99, 511)(100, 520)(101, 513)(102, 522)(103, 523)(104, 516)(105, 526)(106, 518)(107, 519)(108, 532)(109, 533)(110, 521)(111, 479)(112, 575)(113, 481)(114, 577)(115, 542)(116, 524)(117, 525)(118, 539)(119, 543)(120, 546)(121, 545)(122, 544)(123, 534)(124, 548)(125, 547)(126, 531)(127, 535)(128, 538)(129, 537)(130, 536)(131, 541)(132, 540)(133, 554)(134, 555)(135, 552)(136, 551)(137, 557)(138, 549)(139, 550)(140, 559)(141, 553)(142, 561)(143, 556)(144, 563)(145, 558)(146, 565)(147, 560)(148, 567)(149, 562)(150, 569)(151, 564)(152, 571)(153, 566)(154, 574)(155, 568)(156, 578)(157, 581)(158, 570)(159, 528)(160, 621)(161, 530)(162, 572)(163, 623)(164, 590)(165, 573)(166, 587)(167, 591)(168, 594)(169, 593)(170, 592)(171, 582)(172, 596)(173, 595)(174, 580)(175, 583)(176, 586)(177, 585)(178, 584)(179, 589)(180, 588)(181, 602)(182, 603)(183, 600)(184, 599)(185, 605)(186, 597)(187, 598)(188, 607)(189, 601)(190, 609)(191, 604)(192, 611)(193, 606)(194, 613)(195, 608)(196, 615)(197, 610)(198, 617)(199, 612)(200, 619)(201, 614)(202, 622)(203, 616)(204, 624)(205, 576)(206, 618)(207, 579)(208, 620)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2248
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2244 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2, (Y3^2 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^26, Y3^-12 * Y2 * Y3^2 * Y1 * Y3^-10 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210)(3, 211, 9, 217)(4, 212, 12, 220)(5, 213, 14, 222)(6, 214, 16, 224)(7, 215, 19, 227)(8, 216, 21, 229)(10, 218, 24, 232)(11, 219, 26, 234)(13, 221, 22, 230)(15, 223, 20, 228)(17, 225, 34, 242)(18, 226, 36, 244)(23, 231, 37, 245)(25, 233, 43, 251)(27, 235, 33, 241)(28, 236, 38, 246)(29, 237, 41, 249)(30, 238, 50, 258)(31, 239, 39, 247)(32, 240, 44, 252)(35, 243, 53, 261)(40, 248, 60, 268)(42, 250, 54, 262)(45, 253, 58, 266)(46, 254, 59, 267)(47, 255, 65, 273)(48, 256, 55, 263)(49, 257, 56, 264)(51, 259, 62, 270)(52, 260, 61, 269)(57, 265, 73, 281)(63, 271, 75, 283)(64, 272, 76, 284)(66, 274, 79, 287)(67, 275, 71, 279)(68, 276, 72, 280)(69, 277, 84, 292)(70, 278, 80, 288)(74, 282, 87, 295)(77, 285, 92, 300)(78, 286, 88, 296)(81, 289, 91, 299)(82, 290, 97, 305)(83, 291, 89, 297)(85, 293, 94, 302)(86, 294, 93, 301)(90, 298, 105, 313)(95, 303, 107, 315)(96, 304, 108, 316)(98, 306, 111, 319)(99, 307, 103, 311)(100, 308, 104, 312)(101, 309, 116, 324)(102, 310, 112, 320)(106, 314, 119, 327)(109, 317, 124, 332)(110, 318, 120, 328)(113, 321, 123, 331)(114, 322, 129, 337)(115, 323, 121, 329)(117, 325, 126, 334)(118, 326, 125, 333)(122, 330, 137, 345)(127, 335, 139, 347)(128, 336, 140, 348)(130, 338, 143, 351)(131, 339, 135, 343)(132, 340, 136, 344)(133, 341, 148, 356)(134, 342, 144, 352)(138, 346, 151, 359)(141, 349, 156, 364)(142, 350, 152, 360)(145, 353, 155, 363)(146, 354, 161, 369)(147, 355, 153, 361)(149, 357, 158, 366)(150, 358, 157, 365)(154, 362, 169, 377)(159, 367, 171, 379)(160, 368, 172, 380)(162, 370, 175, 383)(163, 371, 167, 375)(164, 372, 168, 376)(165, 373, 180, 388)(166, 374, 176, 384)(170, 378, 183, 391)(173, 381, 188, 396)(174, 382, 184, 392)(177, 385, 187, 395)(178, 386, 193, 401)(179, 387, 185, 393)(181, 389, 190, 398)(182, 390, 189, 397)(186, 394, 200, 408)(191, 399, 202, 410)(192, 400, 203, 411)(194, 402, 201, 409)(195, 403, 198, 406)(196, 404, 199, 407)(197, 405, 205, 413)(204, 412, 207, 415)(206, 414, 208, 416)(417, 625, 419, 627)(418, 626, 422, 630)(420, 628, 427, 635)(421, 629, 426, 634)(423, 631, 434, 642)(424, 632, 433, 641)(425, 633, 436, 644)(428, 636, 443, 651)(429, 637, 432, 640)(430, 638, 442, 650)(431, 639, 441, 649)(435, 643, 453, 661)(437, 645, 452, 660)(438, 646, 451, 659)(439, 647, 456, 664)(440, 648, 460, 668)(444, 652, 464, 672)(445, 653, 465, 673)(446, 654, 449, 657)(447, 655, 461, 669)(448, 656, 463, 671)(450, 658, 470, 678)(454, 662, 474, 682)(455, 663, 475, 683)(457, 665, 471, 679)(458, 666, 473, 681)(459, 667, 477, 685)(462, 670, 480, 688)(466, 674, 483, 691)(467, 675, 469, 677)(468, 676, 482, 690)(472, 680, 488, 696)(476, 684, 491, 699)(478, 686, 490, 698)(479, 687, 493, 701)(481, 689, 496, 704)(484, 692, 499, 707)(485, 693, 487, 695)(486, 694, 498, 706)(489, 697, 504, 712)(492, 700, 507, 715)(494, 702, 506, 714)(495, 703, 509, 717)(497, 705, 512, 720)(500, 708, 515, 723)(501, 709, 503, 711)(502, 710, 514, 722)(505, 713, 520, 728)(508, 716, 523, 731)(510, 718, 522, 730)(511, 719, 525, 733)(513, 721, 528, 736)(516, 724, 531, 739)(517, 725, 519, 727)(518, 726, 530, 738)(521, 729, 536, 744)(524, 732, 539, 747)(526, 734, 538, 746)(527, 735, 541, 749)(529, 737, 544, 752)(532, 740, 547, 755)(533, 741, 535, 743)(534, 742, 546, 754)(537, 745, 552, 760)(540, 748, 555, 763)(542, 750, 554, 762)(543, 751, 557, 765)(545, 753, 560, 768)(548, 756, 563, 771)(549, 757, 551, 759)(550, 758, 562, 770)(553, 761, 568, 776)(556, 764, 571, 779)(558, 766, 570, 778)(559, 767, 573, 781)(561, 769, 576, 784)(564, 772, 579, 787)(565, 773, 567, 775)(566, 774, 578, 786)(569, 777, 584, 792)(572, 780, 587, 795)(574, 782, 586, 794)(575, 783, 589, 797)(577, 785, 592, 800)(580, 788, 595, 803)(581, 789, 583, 791)(582, 790, 594, 802)(585, 793, 600, 808)(588, 796, 603, 811)(590, 798, 602, 810)(591, 799, 605, 813)(593, 801, 608, 816)(596, 804, 611, 819)(597, 805, 599, 807)(598, 806, 610, 818)(601, 809, 615, 823)(604, 812, 618, 826)(606, 814, 617, 825)(607, 815, 620, 828)(609, 817, 621, 829)(612, 820, 622, 830)(613, 821, 614, 822)(616, 824, 623, 831)(619, 827, 624, 832)
	L = (1, 420)(2, 423)(3, 426)(4, 429)(5, 417)(6, 433)(7, 436)(8, 418)(9, 434)(10, 441)(11, 419)(12, 444)(13, 446)(14, 447)(15, 421)(16, 427)(17, 451)(18, 422)(19, 454)(20, 456)(21, 457)(22, 424)(23, 425)(24, 461)(25, 463)(26, 464)(27, 465)(28, 430)(29, 428)(30, 467)(31, 460)(32, 431)(33, 432)(34, 471)(35, 473)(36, 474)(37, 475)(38, 437)(39, 435)(40, 477)(41, 470)(42, 438)(43, 439)(44, 480)(45, 442)(46, 440)(47, 482)(48, 443)(49, 483)(50, 445)(51, 485)(52, 448)(53, 449)(54, 488)(55, 452)(56, 450)(57, 490)(58, 453)(59, 491)(60, 455)(61, 493)(62, 458)(63, 459)(64, 496)(65, 462)(66, 498)(67, 499)(68, 466)(69, 501)(70, 468)(71, 469)(72, 504)(73, 472)(74, 506)(75, 507)(76, 476)(77, 509)(78, 478)(79, 479)(80, 512)(81, 481)(82, 514)(83, 515)(84, 484)(85, 517)(86, 486)(87, 487)(88, 520)(89, 489)(90, 522)(91, 523)(92, 492)(93, 525)(94, 494)(95, 495)(96, 528)(97, 497)(98, 530)(99, 531)(100, 500)(101, 533)(102, 502)(103, 503)(104, 536)(105, 505)(106, 538)(107, 539)(108, 508)(109, 541)(110, 510)(111, 511)(112, 544)(113, 513)(114, 546)(115, 547)(116, 516)(117, 549)(118, 518)(119, 519)(120, 552)(121, 521)(122, 554)(123, 555)(124, 524)(125, 557)(126, 526)(127, 527)(128, 560)(129, 529)(130, 562)(131, 563)(132, 532)(133, 565)(134, 534)(135, 535)(136, 568)(137, 537)(138, 570)(139, 571)(140, 540)(141, 573)(142, 542)(143, 543)(144, 576)(145, 545)(146, 578)(147, 579)(148, 548)(149, 581)(150, 550)(151, 551)(152, 584)(153, 553)(154, 586)(155, 587)(156, 556)(157, 589)(158, 558)(159, 559)(160, 592)(161, 561)(162, 594)(163, 595)(164, 564)(165, 597)(166, 566)(167, 567)(168, 600)(169, 569)(170, 602)(171, 603)(172, 572)(173, 605)(174, 574)(175, 575)(176, 608)(177, 577)(178, 610)(179, 611)(180, 580)(181, 613)(182, 582)(183, 583)(184, 615)(185, 585)(186, 617)(187, 618)(188, 588)(189, 620)(190, 590)(191, 591)(192, 621)(193, 593)(194, 614)(195, 622)(196, 596)(197, 598)(198, 599)(199, 623)(200, 601)(201, 607)(202, 624)(203, 604)(204, 606)(205, 612)(206, 609)(207, 619)(208, 616)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2249
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2245 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^4, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210)(3, 211, 7, 215)(4, 212, 9, 217)(5, 213, 10, 218)(6, 214, 12, 220)(8, 216, 15, 223)(11, 219, 20, 228)(13, 221, 23, 231)(14, 222, 21, 229)(16, 224, 19, 227)(17, 225, 22, 230)(18, 226, 28, 236)(24, 232, 35, 243)(25, 233, 34, 242)(26, 234, 32, 240)(27, 235, 31, 239)(29, 237, 39, 247)(30, 238, 38, 246)(33, 241, 41, 249)(36, 244, 44, 252)(37, 245, 45, 253)(40, 248, 48, 256)(42, 250, 51, 259)(43, 251, 50, 258)(46, 254, 55, 263)(47, 255, 54, 262)(49, 257, 57, 265)(52, 260, 60, 268)(53, 261, 61, 269)(56, 264, 64, 272)(58, 266, 67, 275)(59, 267, 66, 274)(62, 270, 114, 322)(63, 271, 113, 321)(65, 273, 117, 325)(68, 276, 119, 327)(69, 277, 121, 329)(70, 278, 124, 332)(71, 279, 127, 335)(72, 280, 130, 338)(73, 281, 133, 341)(74, 282, 136, 344)(75, 283, 138, 346)(76, 284, 140, 348)(77, 285, 142, 350)(78, 286, 145, 353)(79, 287, 147, 355)(80, 288, 149, 357)(81, 289, 152, 360)(82, 290, 131, 339)(83, 291, 150, 358)(84, 292, 158, 366)(85, 293, 128, 336)(86, 294, 161, 369)(87, 295, 143, 351)(88, 296, 165, 373)(89, 297, 134, 342)(90, 298, 168, 376)(91, 299, 170, 378)(92, 300, 122, 330)(93, 301, 162, 370)(94, 302, 174, 382)(95, 303, 176, 384)(96, 304, 125, 333)(97, 305, 153, 361)(98, 306, 180, 388)(99, 307, 156, 364)(100, 308, 181, 389)(101, 309, 185, 393)(102, 310, 186, 394)(103, 311, 189, 397)(104, 312, 191, 399)(105, 313, 193, 401)(106, 314, 195, 403)(107, 315, 197, 405)(108, 316, 198, 406)(109, 317, 201, 409)(110, 318, 202, 410)(111, 319, 205, 413)(112, 320, 203, 411)(115, 323, 207, 415)(116, 324, 199, 407)(118, 326, 194, 402)(120, 328, 208, 416)(123, 331, 184, 392)(126, 334, 188, 396)(129, 337, 173, 381)(132, 340, 169, 377)(135, 343, 179, 387)(137, 345, 175, 383)(139, 347, 200, 408)(141, 349, 148, 356)(144, 352, 177, 385)(146, 354, 204, 412)(151, 359, 171, 379)(154, 362, 167, 375)(155, 363, 190, 398)(157, 365, 192, 400)(159, 367, 166, 374)(160, 368, 163, 371)(164, 372, 196, 404)(172, 380, 182, 390)(178, 386, 187, 395)(183, 391, 206, 414)(417, 625, 419, 627)(418, 626, 421, 629)(420, 628, 424, 632)(422, 630, 427, 635)(423, 631, 429, 637)(425, 633, 432, 640)(426, 634, 434, 642)(428, 636, 437, 645)(430, 638, 440, 648)(431, 639, 441, 649)(433, 641, 443, 651)(435, 643, 445, 653)(436, 644, 446, 654)(438, 646, 448, 656)(439, 647, 449, 657)(442, 650, 452, 660)(444, 652, 453, 661)(447, 655, 456, 664)(450, 658, 458, 666)(451, 659, 459, 667)(454, 662, 462, 670)(455, 663, 463, 671)(457, 665, 465, 673)(460, 668, 468, 676)(461, 669, 469, 677)(464, 672, 472, 680)(466, 674, 474, 682)(467, 675, 475, 683)(470, 678, 478, 686)(471, 679, 479, 687)(473, 681, 481, 689)(476, 684, 484, 692)(477, 685, 498, 706)(480, 688, 515, 723)(482, 690, 494, 702)(483, 691, 512, 720)(485, 693, 538, 746)(486, 694, 541, 749)(487, 695, 544, 752)(488, 696, 547, 755)(489, 697, 550, 758)(490, 698, 533, 741)(491, 699, 529, 737)(492, 700, 552, 760)(493, 701, 559, 767)(495, 703, 546, 754)(496, 704, 566, 774)(497, 705, 569, 777)(499, 707, 572, 780)(500, 708, 565, 773)(501, 709, 561, 769)(502, 710, 578, 786)(503, 711, 535, 743)(504, 712, 558, 766)(505, 713, 554, 762)(506, 714, 556, 764)(507, 715, 581, 789)(508, 716, 530, 738)(509, 717, 537, 745)(510, 718, 563, 771)(511, 719, 574, 782)(513, 721, 540, 748)(514, 722, 597, 805)(516, 724, 543, 751)(517, 725, 602, 810)(518, 726, 549, 757)(519, 727, 584, 792)(520, 728, 586, 794)(521, 729, 590, 798)(522, 730, 592, 800)(523, 731, 614, 822)(524, 732, 568, 776)(525, 733, 618, 826)(526, 734, 577, 785)(527, 735, 605, 813)(528, 736, 607, 815)(531, 739, 609, 817)(532, 740, 611, 819)(534, 742, 624, 832)(536, 744, 596, 804)(539, 747, 616, 824)(542, 750, 620, 828)(545, 753, 604, 812)(548, 756, 608, 816)(551, 759, 600, 808)(553, 761, 612, 820)(555, 763, 623, 831)(557, 765, 593, 801)(560, 768, 610, 818)(562, 770, 621, 829)(564, 772, 587, 795)(567, 775, 606, 814)(570, 778, 589, 797)(571, 779, 622, 830)(573, 781, 617, 825)(575, 783, 585, 793)(576, 784, 603, 811)(579, 787, 595, 803)(580, 788, 613, 821)(582, 790, 591, 799)(583, 791, 598, 806)(588, 796, 615, 823)(594, 802, 619, 827)(599, 807, 601, 809)
	L = (1, 420)(2, 422)(3, 424)(4, 417)(5, 427)(6, 418)(7, 430)(8, 419)(9, 433)(10, 435)(11, 421)(12, 438)(13, 440)(14, 423)(15, 442)(16, 443)(17, 425)(18, 445)(19, 426)(20, 447)(21, 448)(22, 428)(23, 450)(24, 429)(25, 452)(26, 431)(27, 432)(28, 454)(29, 434)(30, 456)(31, 436)(32, 437)(33, 458)(34, 439)(35, 460)(36, 441)(37, 462)(38, 444)(39, 464)(40, 446)(41, 466)(42, 449)(43, 468)(44, 451)(45, 470)(46, 453)(47, 472)(48, 455)(49, 474)(50, 457)(51, 476)(52, 459)(53, 478)(54, 461)(55, 480)(56, 463)(57, 482)(58, 465)(59, 484)(60, 467)(61, 529)(62, 469)(63, 515)(64, 471)(65, 494)(66, 473)(67, 535)(68, 475)(69, 488)(70, 490)(71, 492)(72, 485)(73, 495)(74, 486)(75, 498)(76, 487)(77, 501)(78, 481)(79, 489)(80, 505)(81, 506)(82, 491)(83, 508)(84, 509)(85, 493)(86, 510)(87, 512)(88, 513)(89, 496)(90, 497)(91, 516)(92, 499)(93, 500)(94, 502)(95, 518)(96, 503)(97, 504)(98, 519)(99, 479)(100, 507)(101, 521)(102, 511)(103, 514)(104, 524)(105, 517)(106, 526)(107, 527)(108, 520)(109, 531)(110, 522)(111, 523)(112, 536)(113, 477)(114, 572)(115, 525)(116, 599)(117, 541)(118, 562)(119, 483)(120, 528)(121, 565)(122, 547)(123, 548)(124, 558)(125, 533)(126, 553)(127, 581)(128, 552)(129, 557)(130, 550)(131, 538)(132, 539)(133, 574)(134, 546)(135, 564)(136, 544)(137, 542)(138, 566)(139, 571)(140, 569)(141, 545)(142, 540)(143, 561)(144, 576)(145, 559)(146, 534)(147, 578)(148, 551)(149, 537)(150, 554)(151, 583)(152, 586)(153, 556)(154, 585)(155, 555)(156, 530)(157, 588)(158, 549)(159, 589)(160, 560)(161, 592)(162, 563)(163, 591)(164, 594)(165, 543)(166, 595)(167, 567)(168, 597)(169, 570)(170, 568)(171, 600)(172, 573)(173, 575)(174, 602)(175, 579)(176, 577)(177, 604)(178, 580)(179, 582)(180, 607)(181, 584)(182, 606)(183, 532)(184, 587)(185, 611)(186, 590)(187, 610)(188, 593)(189, 614)(190, 598)(191, 596)(192, 616)(193, 618)(194, 603)(195, 601)(196, 620)(197, 619)(198, 605)(199, 617)(200, 608)(201, 615)(202, 609)(203, 613)(204, 612)(205, 624)(206, 623)(207, 622)(208, 621)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2247
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2246 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 223>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210)(3, 211, 9, 217)(4, 212, 7, 215)(5, 213, 8, 216)(6, 214, 13, 221)(10, 218, 18, 226)(11, 219, 19, 227)(12, 220, 16, 224)(14, 222, 22, 230)(15, 223, 23, 231)(17, 225, 25, 233)(20, 228, 28, 236)(21, 229, 29, 237)(24, 232, 32, 240)(26, 234, 34, 242)(27, 235, 35, 243)(30, 238, 38, 246)(31, 239, 39, 247)(33, 241, 41, 249)(36, 244, 44, 252)(37, 245, 45, 253)(40, 248, 48, 256)(42, 250, 50, 258)(43, 251, 51, 259)(46, 254, 54, 262)(47, 255, 55, 263)(49, 257, 57, 265)(52, 260, 60, 268)(53, 261, 61, 269)(56, 264, 64, 272)(58, 266, 66, 274)(59, 267, 67, 275)(62, 270, 109, 317)(63, 271, 111, 319)(65, 273, 113, 321)(68, 276, 114, 322)(69, 277, 117, 325)(70, 278, 119, 327)(71, 279, 121, 329)(72, 280, 122, 330)(73, 281, 124, 332)(74, 282, 125, 333)(75, 283, 126, 334)(76, 284, 128, 336)(77, 285, 130, 338)(78, 286, 127, 335)(79, 287, 129, 337)(80, 288, 131, 339)(81, 289, 133, 341)(82, 290, 123, 331)(83, 291, 134, 342)(84, 292, 135, 343)(85, 293, 136, 344)(86, 294, 120, 328)(87, 295, 137, 345)(88, 296, 138, 346)(89, 297, 118, 326)(90, 298, 139, 347)(91, 299, 132, 340)(92, 300, 140, 348)(93, 301, 141, 349)(94, 302, 142, 350)(95, 303, 143, 351)(96, 304, 144, 352)(97, 305, 145, 353)(98, 306, 146, 354)(99, 307, 147, 355)(100, 308, 148, 356)(101, 309, 149, 357)(102, 310, 150, 358)(103, 311, 151, 359)(104, 312, 152, 360)(105, 313, 153, 361)(106, 314, 154, 362)(107, 315, 155, 363)(108, 316, 156, 364)(110, 318, 159, 367)(112, 320, 160, 368)(115, 323, 164, 372)(116, 324, 165, 373)(157, 365, 206, 414)(158, 366, 205, 413)(161, 369, 203, 411)(162, 370, 204, 412)(163, 371, 207, 415)(166, 374, 192, 400)(167, 375, 191, 399)(168, 376, 199, 407)(169, 377, 200, 408)(170, 378, 190, 398)(171, 379, 189, 397)(172, 380, 197, 405)(173, 381, 198, 406)(174, 382, 196, 404)(175, 383, 195, 403)(176, 384, 194, 402)(177, 385, 193, 401)(178, 386, 202, 410)(179, 387, 201, 409)(180, 388, 184, 392)(181, 389, 183, 391)(182, 390, 208, 416)(185, 393, 188, 396)(186, 394, 187, 395)(417, 625, 419, 627)(418, 626, 422, 630)(420, 628, 427, 635)(421, 629, 426, 634)(423, 631, 431, 639)(424, 632, 430, 638)(425, 633, 433, 641)(428, 636, 436, 644)(429, 637, 437, 645)(432, 640, 440, 648)(434, 642, 443, 651)(435, 643, 442, 650)(438, 646, 447, 655)(439, 647, 446, 654)(441, 649, 449, 657)(444, 652, 452, 660)(445, 653, 453, 661)(448, 656, 456, 664)(450, 658, 459, 667)(451, 659, 458, 666)(454, 662, 463, 671)(455, 663, 462, 670)(457, 665, 465, 673)(460, 668, 468, 676)(461, 669, 469, 677)(464, 672, 472, 680)(466, 674, 475, 683)(467, 675, 474, 682)(470, 678, 479, 687)(471, 679, 478, 686)(473, 681, 481, 689)(476, 684, 484, 692)(477, 685, 495, 703)(480, 688, 507, 715)(482, 690, 505, 713)(483, 691, 490, 698)(485, 693, 534, 742)(486, 694, 536, 744)(487, 695, 527, 735)(488, 696, 539, 747)(489, 697, 529, 737)(491, 699, 543, 751)(492, 700, 545, 753)(493, 701, 547, 755)(494, 702, 548, 756)(496, 704, 541, 749)(497, 705, 550, 758)(498, 706, 530, 738)(499, 707, 537, 745)(500, 708, 538, 746)(501, 709, 540, 748)(502, 710, 525, 733)(503, 711, 542, 750)(504, 712, 544, 752)(506, 714, 556, 764)(508, 716, 533, 741)(509, 717, 558, 766)(510, 718, 535, 743)(511, 719, 551, 759)(512, 720, 552, 760)(513, 721, 553, 761)(514, 722, 554, 762)(515, 723, 564, 772)(516, 724, 546, 754)(517, 725, 566, 774)(518, 726, 549, 757)(519, 727, 559, 767)(520, 728, 560, 768)(521, 729, 561, 769)(522, 730, 562, 770)(523, 731, 572, 780)(524, 732, 555, 763)(526, 734, 576, 784)(528, 736, 557, 765)(531, 739, 567, 775)(532, 740, 568, 776)(563, 771, 579, 787)(565, 773, 598, 806)(569, 777, 573, 781)(570, 778, 574, 782)(571, 779, 578, 786)(575, 783, 594, 802)(577, 785, 623, 831)(580, 788, 585, 793)(581, 789, 584, 792)(582, 790, 616, 824)(583, 791, 615, 823)(586, 794, 614, 822)(587, 795, 613, 821)(588, 796, 621, 829)(589, 797, 622, 830)(590, 798, 619, 827)(591, 799, 620, 828)(592, 800, 617, 825)(593, 801, 618, 826)(595, 803, 624, 832)(596, 804, 608, 816)(597, 805, 607, 815)(599, 807, 606, 814)(600, 808, 605, 813)(601, 809, 611, 819)(602, 810, 612, 820)(603, 811, 609, 817)(604, 812, 610, 818)
	L = (1, 420)(2, 423)(3, 426)(4, 428)(5, 417)(6, 430)(7, 432)(8, 418)(9, 434)(10, 436)(11, 419)(12, 421)(13, 438)(14, 440)(15, 422)(16, 424)(17, 442)(18, 444)(19, 425)(20, 427)(21, 446)(22, 448)(23, 429)(24, 431)(25, 450)(26, 452)(27, 433)(28, 435)(29, 454)(30, 456)(31, 437)(32, 439)(33, 458)(34, 460)(35, 441)(36, 443)(37, 462)(38, 464)(39, 445)(40, 447)(41, 466)(42, 468)(43, 449)(44, 451)(45, 470)(46, 472)(47, 453)(48, 455)(49, 474)(50, 476)(51, 457)(52, 459)(53, 478)(54, 480)(55, 461)(56, 463)(57, 482)(58, 484)(59, 465)(60, 467)(61, 525)(62, 507)(63, 469)(64, 471)(65, 490)(66, 530)(67, 473)(68, 475)(69, 488)(70, 491)(71, 494)(72, 496)(73, 485)(74, 498)(75, 499)(76, 486)(77, 500)(78, 502)(79, 487)(80, 489)(81, 503)(82, 505)(83, 492)(84, 508)(85, 493)(86, 495)(87, 510)(88, 497)(89, 481)(90, 511)(91, 479)(92, 501)(93, 513)(94, 504)(95, 516)(96, 506)(97, 518)(98, 509)(99, 519)(100, 512)(101, 521)(102, 514)(103, 524)(104, 515)(105, 528)(106, 517)(107, 531)(108, 520)(109, 548)(110, 573)(111, 477)(112, 522)(113, 541)(114, 483)(115, 579)(116, 523)(117, 538)(118, 529)(119, 542)(120, 545)(121, 543)(122, 547)(123, 534)(124, 533)(125, 539)(126, 550)(127, 536)(128, 535)(129, 537)(130, 551)(131, 540)(132, 527)(133, 553)(134, 544)(135, 556)(136, 546)(137, 558)(138, 549)(139, 559)(140, 552)(141, 561)(142, 554)(143, 564)(144, 555)(145, 566)(146, 557)(147, 567)(148, 560)(149, 569)(150, 562)(151, 572)(152, 563)(153, 576)(154, 565)(155, 580)(156, 568)(157, 598)(158, 526)(159, 622)(160, 570)(161, 585)(162, 584)(163, 532)(164, 623)(165, 571)(166, 590)(167, 591)(168, 577)(169, 578)(170, 592)(171, 593)(172, 595)(173, 594)(174, 583)(175, 582)(176, 587)(177, 586)(178, 588)(179, 589)(180, 601)(181, 602)(182, 574)(183, 603)(184, 604)(185, 597)(186, 596)(187, 600)(188, 599)(189, 609)(190, 610)(191, 611)(192, 612)(193, 606)(194, 605)(195, 608)(196, 607)(197, 617)(198, 618)(199, 619)(200, 620)(201, 614)(202, 613)(203, 616)(204, 615)(205, 575)(206, 624)(207, 581)(208, 621)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2250
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2247 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 6, 214, 5, 213)(3, 211, 9, 217, 14, 222, 11, 219)(4, 212, 12, 220, 15, 223, 8, 216)(7, 215, 16, 224, 13, 221, 18, 226)(10, 218, 21, 229, 24, 232, 20, 228)(17, 225, 27, 235, 23, 231, 26, 234)(19, 227, 29, 237, 22, 230, 31, 239)(25, 233, 33, 241, 28, 236, 35, 243)(30, 238, 39, 247, 32, 240, 38, 246)(34, 242, 43, 251, 36, 244, 42, 250)(37, 245, 45, 253, 40, 248, 47, 255)(41, 249, 49, 257, 44, 252, 51, 259)(46, 254, 55, 263, 48, 256, 54, 262)(50, 258, 59, 267, 52, 260, 58, 266)(53, 261, 61, 269, 56, 264, 63, 271)(57, 265, 65, 273, 60, 268, 67, 275)(62, 270, 71, 279, 64, 272, 70, 278)(66, 274, 115, 323, 68, 276, 113, 321)(69, 277, 117, 325, 72, 280, 120, 328)(73, 281, 121, 329, 78, 286, 123, 331)(74, 282, 124, 332, 77, 285, 126, 334)(75, 283, 127, 335, 86, 294, 125, 333)(76, 284, 128, 336, 87, 295, 129, 337)(79, 287, 122, 330, 85, 293, 130, 338)(80, 288, 131, 339, 84, 292, 133, 341)(81, 289, 134, 342, 83, 291, 135, 343)(82, 290, 132, 340, 92, 300, 136, 344)(88, 296, 137, 345, 89, 297, 138, 346)(90, 298, 139, 347, 91, 299, 140, 348)(93, 301, 141, 349, 94, 302, 142, 350)(95, 303, 143, 351, 96, 304, 144, 352)(97, 305, 145, 353, 98, 306, 146, 354)(99, 307, 147, 355, 100, 308, 148, 356)(101, 309, 149, 357, 102, 310, 150, 358)(103, 311, 151, 359, 104, 312, 152, 360)(105, 313, 153, 361, 106, 314, 154, 362)(107, 315, 155, 363, 108, 316, 156, 364)(109, 317, 157, 365, 110, 318, 158, 366)(111, 319, 159, 367, 112, 320, 160, 368)(114, 322, 162, 370, 116, 324, 164, 372)(118, 326, 166, 374, 119, 327, 167, 375)(161, 369, 208, 416, 163, 371, 207, 415)(165, 373, 205, 413, 168, 376, 206, 414)(169, 377, 194, 402, 171, 379, 193, 401)(170, 378, 202, 410, 178, 386, 201, 409)(172, 380, 191, 399, 174, 382, 192, 400)(173, 381, 199, 407, 175, 383, 200, 408)(176, 384, 197, 405, 177, 385, 198, 406)(179, 387, 196, 404, 181, 389, 195, 403)(180, 388, 203, 411, 184, 392, 204, 412)(182, 390, 185, 393, 183, 391, 186, 394)(187, 395, 190, 398, 188, 396, 189, 397)(417, 625, 419, 627)(418, 626, 423, 631)(420, 628, 426, 634)(421, 629, 429, 637)(422, 630, 430, 638)(424, 632, 433, 641)(425, 633, 435, 643)(427, 635, 438, 646)(428, 636, 439, 647)(431, 639, 440, 648)(432, 640, 441, 649)(434, 642, 444, 652)(436, 644, 446, 654)(437, 645, 448, 656)(442, 650, 450, 658)(443, 651, 452, 660)(445, 653, 453, 661)(447, 655, 456, 664)(449, 657, 457, 665)(451, 659, 460, 668)(454, 662, 462, 670)(455, 663, 464, 672)(458, 666, 466, 674)(459, 667, 468, 676)(461, 669, 469, 677)(463, 671, 472, 680)(465, 673, 473, 681)(467, 675, 476, 684)(470, 678, 478, 686)(471, 679, 480, 688)(474, 682, 482, 690)(475, 683, 484, 692)(477, 685, 485, 693)(479, 687, 488, 696)(481, 689, 508, 716)(483, 691, 498, 706)(486, 694, 501, 709)(487, 695, 495, 703)(489, 697, 538, 746)(490, 698, 541, 749)(491, 699, 529, 737)(492, 700, 536, 744)(493, 701, 543, 751)(494, 702, 546, 754)(496, 704, 548, 756)(497, 705, 539, 747)(499, 707, 537, 745)(500, 708, 552, 760)(502, 710, 531, 739)(503, 711, 533, 741)(504, 712, 542, 750)(505, 713, 540, 748)(506, 714, 544, 752)(507, 715, 545, 753)(509, 717, 547, 755)(510, 718, 549, 757)(511, 719, 551, 759)(512, 720, 550, 758)(513, 721, 554, 762)(514, 722, 553, 761)(515, 723, 555, 763)(516, 724, 556, 764)(517, 725, 557, 765)(518, 726, 558, 766)(519, 727, 560, 768)(520, 728, 559, 767)(521, 729, 562, 770)(522, 730, 561, 769)(523, 731, 563, 771)(524, 732, 564, 772)(525, 733, 565, 773)(526, 734, 566, 774)(527, 735, 568, 776)(528, 736, 567, 775)(530, 738, 570, 778)(532, 740, 569, 777)(534, 742, 571, 779)(535, 743, 572, 780)(573, 781, 577, 785)(574, 782, 579, 787)(575, 783, 584, 792)(576, 784, 581, 789)(578, 786, 596, 804)(580, 788, 600, 808)(582, 790, 586, 794)(583, 791, 594, 802)(585, 793, 617, 825)(587, 795, 618, 826)(588, 796, 616, 824)(589, 797, 624, 832)(590, 798, 615, 823)(591, 799, 623, 831)(592, 800, 621, 829)(593, 801, 622, 830)(595, 803, 620, 828)(597, 805, 619, 827)(598, 806, 610, 818)(599, 807, 609, 817)(601, 809, 607, 815)(602, 810, 608, 816)(603, 811, 614, 822)(604, 812, 613, 821)(605, 813, 611, 819)(606, 814, 612, 820)
	L = (1, 420)(2, 424)(3, 426)(4, 417)(5, 428)(6, 431)(7, 433)(8, 418)(9, 436)(10, 419)(11, 437)(12, 421)(13, 439)(14, 440)(15, 422)(16, 442)(17, 423)(18, 443)(19, 446)(20, 425)(21, 427)(22, 448)(23, 429)(24, 430)(25, 450)(26, 432)(27, 434)(28, 452)(29, 454)(30, 435)(31, 455)(32, 438)(33, 458)(34, 441)(35, 459)(36, 444)(37, 462)(38, 445)(39, 447)(40, 464)(41, 466)(42, 449)(43, 451)(44, 468)(45, 470)(46, 453)(47, 471)(48, 456)(49, 474)(50, 457)(51, 475)(52, 460)(53, 478)(54, 461)(55, 463)(56, 480)(57, 482)(58, 465)(59, 467)(60, 484)(61, 486)(62, 469)(63, 487)(64, 472)(65, 529)(66, 473)(67, 531)(68, 476)(69, 501)(70, 477)(71, 479)(72, 495)(73, 503)(74, 500)(75, 508)(76, 494)(77, 496)(78, 492)(79, 488)(80, 493)(81, 507)(82, 502)(83, 506)(84, 490)(85, 485)(86, 498)(87, 489)(88, 510)(89, 509)(90, 499)(91, 497)(92, 491)(93, 505)(94, 504)(95, 516)(96, 515)(97, 518)(98, 517)(99, 512)(100, 511)(101, 514)(102, 513)(103, 524)(104, 523)(105, 526)(106, 525)(107, 520)(108, 519)(109, 522)(110, 521)(111, 535)(112, 534)(113, 481)(114, 579)(115, 483)(116, 577)(117, 538)(118, 528)(119, 527)(120, 546)(121, 544)(122, 533)(123, 545)(124, 547)(125, 552)(126, 549)(127, 548)(128, 537)(129, 539)(130, 536)(131, 540)(132, 543)(133, 542)(134, 555)(135, 556)(136, 541)(137, 557)(138, 558)(139, 550)(140, 551)(141, 553)(142, 554)(143, 563)(144, 564)(145, 565)(146, 566)(147, 559)(148, 560)(149, 561)(150, 562)(151, 571)(152, 572)(153, 573)(154, 574)(155, 567)(156, 568)(157, 569)(158, 570)(159, 582)(160, 583)(161, 532)(162, 624)(163, 530)(164, 623)(165, 594)(166, 575)(167, 576)(168, 586)(169, 593)(170, 584)(171, 592)(172, 597)(173, 596)(174, 595)(175, 600)(176, 587)(177, 585)(178, 581)(179, 590)(180, 589)(181, 588)(182, 604)(183, 603)(184, 591)(185, 606)(186, 605)(187, 599)(188, 598)(189, 602)(190, 601)(191, 612)(192, 611)(193, 614)(194, 613)(195, 608)(196, 607)(197, 610)(198, 609)(199, 620)(200, 619)(201, 622)(202, 621)(203, 616)(204, 615)(205, 618)(206, 617)(207, 580)(208, 578)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2245
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2248 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 6, 214, 5, 213)(3, 211, 9, 217, 14, 222, 11, 219)(4, 212, 12, 220, 15, 223, 8, 216)(7, 215, 16, 224, 13, 221, 18, 226)(10, 218, 21, 229, 24, 232, 20, 228)(17, 225, 27, 235, 23, 231, 26, 234)(19, 227, 29, 237, 22, 230, 31, 239)(25, 233, 33, 241, 28, 236, 35, 243)(30, 238, 39, 247, 32, 240, 38, 246)(34, 242, 43, 251, 36, 244, 42, 250)(37, 245, 45, 253, 40, 248, 47, 255)(41, 249, 49, 257, 44, 252, 51, 259)(46, 254, 55, 263, 48, 256, 54, 262)(50, 258, 59, 267, 52, 260, 58, 266)(53, 261, 61, 269, 56, 264, 63, 271)(57, 265, 65, 273, 60, 268, 67, 275)(62, 270, 71, 279, 64, 272, 70, 278)(66, 274, 123, 331, 68, 276, 121, 329)(69, 277, 125, 333, 72, 280, 128, 336)(73, 281, 129, 337, 78, 286, 131, 339)(74, 282, 132, 340, 77, 285, 134, 342)(75, 283, 133, 341, 86, 294, 136, 344)(76, 284, 137, 345, 87, 295, 139, 347)(79, 287, 140, 348, 85, 293, 130, 338)(80, 288, 141, 349, 84, 292, 143, 351)(81, 289, 144, 352, 83, 291, 145, 353)(82, 290, 146, 354, 96, 304, 142, 350)(88, 296, 150, 358, 90, 298, 151, 359)(89, 297, 138, 346, 95, 303, 149, 357)(91, 299, 148, 356, 94, 302, 135, 343)(92, 300, 153, 361, 93, 301, 154, 362)(97, 305, 157, 365, 98, 306, 158, 366)(99, 307, 159, 367, 101, 309, 160, 368)(100, 308, 147, 355, 102, 310, 156, 364)(103, 311, 161, 369, 105, 313, 162, 370)(104, 312, 152, 360, 106, 314, 155, 363)(107, 315, 163, 371, 108, 316, 164, 372)(109, 317, 165, 373, 110, 318, 166, 374)(111, 319, 167, 375, 112, 320, 168, 376)(113, 321, 169, 377, 114, 322, 170, 378)(115, 323, 171, 379, 116, 324, 172, 380)(117, 325, 173, 381, 118, 326, 174, 382)(119, 327, 175, 383, 120, 328, 176, 384)(122, 330, 178, 386, 124, 332, 179, 387)(126, 334, 182, 390, 127, 335, 183, 391)(177, 385, 206, 414, 180, 388, 205, 413)(181, 389, 190, 398, 184, 392, 188, 396)(185, 393, 191, 399, 187, 395, 202, 410)(186, 394, 192, 400, 196, 404, 189, 397)(193, 401, 201, 409, 195, 403, 208, 416)(194, 402, 198, 406, 203, 411, 200, 408)(197, 405, 204, 412, 199, 407, 207, 415)(417, 625, 419, 627)(418, 626, 423, 631)(420, 628, 426, 634)(421, 629, 429, 637)(422, 630, 430, 638)(424, 632, 433, 641)(425, 633, 435, 643)(427, 635, 438, 646)(428, 636, 439, 647)(431, 639, 440, 648)(432, 640, 441, 649)(434, 642, 444, 652)(436, 644, 446, 654)(437, 645, 448, 656)(442, 650, 450, 658)(443, 651, 452, 660)(445, 653, 453, 661)(447, 655, 456, 664)(449, 657, 457, 665)(451, 659, 460, 668)(454, 662, 462, 670)(455, 663, 464, 672)(458, 666, 466, 674)(459, 667, 468, 676)(461, 669, 469, 677)(463, 671, 472, 680)(465, 673, 473, 681)(467, 675, 476, 684)(470, 678, 478, 686)(471, 679, 480, 688)(474, 682, 482, 690)(475, 683, 484, 692)(477, 685, 485, 693)(479, 687, 488, 696)(481, 689, 507, 715)(483, 691, 510, 718)(486, 694, 522, 730)(487, 695, 520, 728)(489, 697, 546, 754)(490, 698, 549, 757)(491, 699, 551, 759)(492, 700, 554, 762)(493, 701, 552, 760)(494, 702, 556, 764)(495, 703, 541, 749)(496, 704, 558, 766)(497, 705, 545, 753)(498, 706, 563, 771)(499, 707, 547, 755)(500, 708, 562, 770)(501, 709, 544, 752)(502, 710, 564, 772)(503, 711, 565, 773)(504, 712, 548, 756)(505, 713, 568, 776)(506, 714, 550, 758)(508, 716, 555, 763)(509, 717, 553, 761)(511, 719, 571, 779)(512, 720, 572, 780)(513, 721, 559, 767)(514, 722, 557, 765)(515, 723, 560, 768)(516, 724, 537, 745)(517, 725, 561, 769)(518, 726, 539, 747)(519, 727, 566, 774)(521, 729, 567, 775)(523, 731, 570, 778)(524, 732, 569, 777)(525, 733, 574, 782)(526, 734, 573, 781)(527, 735, 575, 783)(528, 736, 576, 784)(529, 737, 577, 785)(530, 738, 578, 786)(531, 739, 580, 788)(532, 740, 579, 787)(533, 741, 582, 790)(534, 742, 581, 789)(535, 743, 583, 791)(536, 744, 584, 792)(538, 746, 585, 793)(540, 748, 586, 794)(542, 750, 588, 796)(543, 751, 587, 795)(589, 797, 596, 804)(590, 798, 593, 801)(591, 799, 597, 805)(592, 800, 600, 808)(594, 802, 618, 826)(595, 803, 607, 815)(598, 806, 623, 831)(599, 807, 620, 828)(601, 809, 608, 816)(602, 810, 604, 812)(603, 811, 605, 813)(606, 814, 612, 820)(609, 817, 614, 822)(610, 818, 615, 823)(611, 819, 616, 824)(613, 821, 619, 827)(617, 825, 622, 830)(621, 829, 624, 832)
	L = (1, 420)(2, 424)(3, 426)(4, 417)(5, 428)(6, 431)(7, 433)(8, 418)(9, 436)(10, 419)(11, 437)(12, 421)(13, 439)(14, 440)(15, 422)(16, 442)(17, 423)(18, 443)(19, 446)(20, 425)(21, 427)(22, 448)(23, 429)(24, 430)(25, 450)(26, 432)(27, 434)(28, 452)(29, 454)(30, 435)(31, 455)(32, 438)(33, 458)(34, 441)(35, 459)(36, 444)(37, 462)(38, 445)(39, 447)(40, 464)(41, 466)(42, 449)(43, 451)(44, 468)(45, 470)(46, 453)(47, 471)(48, 456)(49, 474)(50, 457)(51, 475)(52, 460)(53, 478)(54, 461)(55, 463)(56, 480)(57, 482)(58, 465)(59, 467)(60, 484)(61, 486)(62, 469)(63, 487)(64, 472)(65, 537)(66, 473)(67, 539)(68, 476)(69, 522)(70, 477)(71, 479)(72, 520)(73, 492)(74, 496)(75, 498)(76, 489)(77, 500)(78, 503)(79, 505)(80, 490)(81, 508)(82, 491)(83, 509)(84, 493)(85, 511)(86, 512)(87, 494)(88, 513)(89, 495)(90, 514)(91, 516)(92, 497)(93, 499)(94, 518)(95, 501)(96, 502)(97, 504)(98, 506)(99, 523)(100, 507)(101, 524)(102, 510)(103, 525)(104, 488)(105, 526)(106, 485)(107, 515)(108, 517)(109, 519)(110, 521)(111, 531)(112, 532)(113, 533)(114, 534)(115, 527)(116, 528)(117, 529)(118, 530)(119, 542)(120, 543)(121, 481)(122, 593)(123, 483)(124, 596)(125, 568)(126, 535)(127, 536)(128, 571)(129, 555)(130, 554)(131, 553)(132, 559)(133, 558)(134, 557)(135, 563)(136, 562)(137, 547)(138, 546)(139, 545)(140, 565)(141, 550)(142, 549)(143, 548)(144, 570)(145, 569)(146, 552)(147, 551)(148, 572)(149, 556)(150, 574)(151, 573)(152, 541)(153, 561)(154, 560)(155, 544)(156, 564)(157, 567)(158, 566)(159, 580)(160, 579)(161, 582)(162, 581)(163, 576)(164, 575)(165, 578)(166, 577)(167, 588)(168, 587)(169, 590)(170, 589)(171, 584)(172, 583)(173, 586)(174, 585)(175, 599)(176, 598)(177, 538)(178, 621)(179, 622)(180, 540)(181, 620)(182, 592)(183, 591)(184, 623)(185, 611)(186, 610)(187, 609)(188, 615)(189, 614)(190, 613)(191, 617)(192, 616)(193, 603)(194, 602)(195, 601)(196, 619)(197, 606)(198, 605)(199, 604)(200, 608)(201, 607)(202, 624)(203, 612)(204, 597)(205, 594)(206, 595)(207, 600)(208, 618)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2243
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2249 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = D8 x D26 (small group id <208, 39>)
Aut   = C2 x D8 x D26 (small group id <416, 216>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, Y1^4, (Y3^-1, Y1^-1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 7, 215, 5, 213)(3, 211, 11, 219, 16, 224, 13, 221)(4, 212, 9, 217, 6, 214, 10, 218)(8, 216, 17, 225, 15, 223, 19, 227)(12, 220, 22, 230, 14, 222, 23, 231)(18, 226, 26, 234, 20, 228, 27, 235)(21, 229, 29, 237, 24, 232, 31, 239)(25, 233, 33, 241, 28, 236, 35, 243)(30, 238, 38, 246, 32, 240, 39, 247)(34, 242, 42, 250, 36, 244, 43, 251)(37, 245, 45, 253, 40, 248, 47, 255)(41, 249, 49, 257, 44, 252, 51, 259)(46, 254, 54, 262, 48, 256, 55, 263)(50, 258, 58, 266, 52, 260, 59, 267)(53, 261, 61, 269, 56, 264, 63, 271)(57, 265, 65, 273, 60, 268, 67, 275)(62, 270, 70, 278, 64, 272, 71, 279)(66, 274, 75, 283, 68, 276, 73, 281)(69, 277, 77, 285, 72, 280, 78, 286)(74, 282, 109, 317, 80, 288, 111, 319)(76, 284, 113, 321, 79, 287, 115, 323)(81, 289, 107, 315, 82, 290, 105, 313)(83, 291, 114, 322, 84, 292, 120, 328)(85, 293, 116, 324, 86, 294, 119, 327)(87, 295, 118, 326, 88, 296, 117, 325)(89, 297, 122, 330, 90, 298, 121, 329)(91, 299, 123, 331, 92, 300, 124, 332)(93, 301, 125, 333, 94, 302, 126, 334)(95, 303, 128, 336, 96, 304, 127, 335)(97, 305, 130, 338, 98, 306, 129, 337)(99, 307, 131, 339, 100, 308, 132, 340)(101, 309, 133, 341, 102, 310, 134, 342)(103, 311, 136, 344, 104, 312, 135, 343)(106, 314, 138, 346, 108, 316, 137, 345)(110, 318, 139, 347, 112, 320, 140, 348)(141, 349, 147, 355, 142, 350, 145, 353)(143, 351, 149, 357, 144, 352, 151, 359)(146, 354, 153, 361, 148, 356, 155, 363)(150, 358, 158, 366, 152, 360, 157, 365)(154, 362, 190, 398, 160, 368, 189, 397)(156, 364, 195, 403, 159, 367, 193, 401)(161, 369, 185, 393, 162, 370, 187, 395)(163, 371, 200, 408, 164, 372, 194, 402)(165, 373, 199, 407, 166, 374, 196, 404)(167, 375, 197, 405, 168, 376, 198, 406)(169, 377, 201, 409, 170, 378, 202, 410)(171, 379, 204, 412, 172, 380, 203, 411)(173, 381, 192, 400, 174, 382, 191, 399)(175, 383, 205, 413, 176, 384, 206, 414)(177, 385, 207, 415, 178, 386, 208, 416)(179, 387, 182, 390, 180, 388, 181, 389)(183, 391, 188, 396, 184, 392, 186, 394)(417, 625, 419, 627)(418, 626, 424, 632)(420, 628, 430, 638)(421, 629, 431, 639)(422, 630, 428, 636)(423, 631, 432, 640)(425, 633, 436, 644)(426, 634, 434, 642)(427, 635, 437, 645)(429, 637, 440, 648)(433, 641, 441, 649)(435, 643, 444, 652)(438, 646, 448, 656)(439, 647, 446, 654)(442, 650, 452, 660)(443, 651, 450, 658)(445, 653, 453, 661)(447, 655, 456, 664)(449, 657, 457, 665)(451, 659, 460, 668)(454, 662, 464, 672)(455, 663, 462, 670)(458, 666, 468, 676)(459, 667, 466, 674)(461, 669, 469, 677)(463, 671, 472, 680)(465, 673, 473, 681)(467, 675, 476, 684)(470, 678, 480, 688)(471, 679, 478, 686)(474, 682, 484, 692)(475, 683, 482, 690)(477, 685, 485, 693)(479, 687, 488, 696)(481, 689, 521, 729)(483, 691, 523, 731)(486, 694, 527, 735)(487, 695, 525, 733)(489, 697, 529, 737)(490, 698, 530, 738)(491, 699, 531, 739)(492, 700, 532, 740)(493, 701, 533, 741)(494, 702, 534, 742)(495, 703, 535, 743)(496, 704, 536, 744)(497, 705, 537, 745)(498, 706, 538, 746)(499, 707, 539, 747)(500, 708, 540, 748)(501, 709, 541, 749)(502, 710, 542, 750)(503, 711, 543, 751)(504, 712, 544, 752)(505, 713, 545, 753)(506, 714, 546, 754)(507, 715, 547, 755)(508, 716, 548, 756)(509, 717, 549, 757)(510, 718, 550, 758)(511, 719, 551, 759)(512, 720, 552, 760)(513, 721, 553, 761)(514, 722, 554, 762)(515, 723, 555, 763)(516, 724, 556, 764)(517, 725, 557, 765)(518, 726, 558, 766)(519, 727, 559, 767)(520, 728, 560, 768)(522, 730, 562, 770)(524, 732, 564, 772)(526, 734, 566, 774)(528, 736, 568, 776)(561, 769, 601, 809)(563, 771, 603, 811)(565, 773, 605, 813)(567, 775, 606, 814)(569, 777, 609, 817)(570, 778, 610, 818)(571, 779, 611, 819)(572, 780, 612, 820)(573, 781, 613, 821)(574, 782, 614, 822)(575, 783, 615, 823)(576, 784, 616, 824)(577, 785, 617, 825)(578, 786, 618, 826)(579, 787, 619, 827)(580, 788, 620, 828)(581, 789, 607, 815)(582, 790, 608, 816)(583, 791, 621, 829)(584, 792, 622, 830)(585, 793, 623, 831)(586, 794, 624, 832)(587, 795, 597, 805)(588, 796, 598, 806)(589, 797, 596, 804)(590, 798, 595, 803)(591, 799, 604, 812)(592, 800, 602, 810)(593, 801, 599, 807)(594, 802, 600, 808)
	L = (1, 420)(2, 425)(3, 428)(4, 423)(5, 426)(6, 417)(7, 422)(8, 434)(9, 421)(10, 418)(11, 438)(12, 432)(13, 439)(14, 419)(15, 436)(16, 430)(17, 442)(18, 431)(19, 443)(20, 424)(21, 446)(22, 429)(23, 427)(24, 448)(25, 450)(26, 435)(27, 433)(28, 452)(29, 454)(30, 440)(31, 455)(32, 437)(33, 458)(34, 444)(35, 459)(36, 441)(37, 462)(38, 447)(39, 445)(40, 464)(41, 466)(42, 451)(43, 449)(44, 468)(45, 470)(46, 456)(47, 471)(48, 453)(49, 474)(50, 460)(51, 475)(52, 457)(53, 478)(54, 463)(55, 461)(56, 480)(57, 482)(58, 467)(59, 465)(60, 484)(61, 486)(62, 472)(63, 487)(64, 469)(65, 491)(66, 476)(67, 489)(68, 473)(69, 525)(70, 479)(71, 477)(72, 527)(73, 481)(74, 493)(75, 483)(76, 497)(77, 496)(78, 490)(79, 498)(80, 494)(81, 495)(82, 492)(83, 503)(84, 504)(85, 505)(86, 506)(87, 500)(88, 499)(89, 502)(90, 501)(91, 511)(92, 512)(93, 513)(94, 514)(95, 508)(96, 507)(97, 510)(98, 509)(99, 519)(100, 520)(101, 522)(102, 524)(103, 516)(104, 515)(105, 529)(106, 518)(107, 531)(108, 517)(109, 488)(110, 565)(111, 485)(112, 567)(113, 523)(114, 534)(115, 521)(116, 538)(117, 530)(118, 536)(119, 537)(120, 533)(121, 532)(122, 535)(123, 544)(124, 543)(125, 546)(126, 545)(127, 539)(128, 540)(129, 541)(130, 542)(131, 552)(132, 551)(133, 554)(134, 553)(135, 547)(136, 548)(137, 549)(138, 550)(139, 560)(140, 559)(141, 564)(142, 562)(143, 555)(144, 556)(145, 569)(146, 557)(147, 571)(148, 558)(149, 528)(150, 606)(151, 526)(152, 605)(153, 563)(154, 574)(155, 561)(156, 578)(157, 570)(158, 576)(159, 577)(160, 573)(161, 572)(162, 575)(163, 584)(164, 583)(165, 586)(166, 585)(167, 579)(168, 580)(169, 581)(170, 582)(171, 592)(172, 591)(173, 594)(174, 593)(175, 587)(176, 588)(177, 589)(178, 590)(179, 600)(180, 599)(181, 604)(182, 602)(183, 595)(184, 596)(185, 611)(186, 597)(187, 609)(188, 598)(189, 566)(190, 568)(191, 623)(192, 624)(193, 601)(194, 613)(195, 603)(196, 617)(197, 616)(198, 610)(199, 618)(200, 614)(201, 615)(202, 612)(203, 621)(204, 622)(205, 620)(206, 619)(207, 608)(208, 607)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2244
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2250 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 4})
Quotient :: dipole
Aut^+ = (C4 x D26) : C2 (small group id <208, 42>)
Aut   = (D8 x D26) : C2 (small group id <416, 223>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), Y1^4, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 7, 215, 5, 213)(3, 211, 11, 219, 16, 224, 13, 221)(4, 212, 9, 217, 6, 214, 10, 218)(8, 216, 17, 225, 15, 223, 19, 227)(12, 220, 22, 230, 14, 222, 23, 231)(18, 226, 26, 234, 20, 228, 27, 235)(21, 229, 29, 237, 24, 232, 31, 239)(25, 233, 33, 241, 28, 236, 35, 243)(30, 238, 38, 246, 32, 240, 39, 247)(34, 242, 42, 250, 36, 244, 43, 251)(37, 245, 45, 253, 40, 248, 47, 255)(41, 249, 49, 257, 44, 252, 51, 259)(46, 254, 54, 262, 48, 256, 55, 263)(50, 258, 58, 266, 52, 260, 59, 267)(53, 261, 61, 269, 56, 264, 63, 271)(57, 265, 65, 273, 60, 268, 67, 275)(62, 270, 70, 278, 64, 272, 71, 279)(66, 274, 75, 283, 68, 276, 84, 292)(69, 277, 76, 284, 72, 280, 78, 286)(73, 281, 114, 322, 79, 287, 113, 321)(74, 282, 119, 327, 77, 285, 122, 330)(80, 288, 111, 319, 81, 289, 109, 317)(82, 290, 117, 325, 83, 291, 130, 338)(85, 293, 120, 328, 86, 294, 126, 334)(87, 295, 128, 336, 88, 296, 124, 332)(89, 297, 134, 342, 90, 298, 132, 340)(91, 299, 136, 344, 92, 300, 138, 346)(93, 301, 141, 349, 94, 302, 143, 351)(95, 303, 147, 355, 96, 304, 145, 353)(97, 305, 151, 359, 98, 306, 149, 357)(99, 307, 153, 361, 100, 308, 155, 363)(101, 309, 157, 365, 102, 310, 159, 367)(103, 311, 163, 371, 104, 312, 161, 369)(105, 313, 167, 375, 106, 314, 165, 373)(107, 315, 169, 377, 108, 316, 171, 379)(110, 318, 173, 381, 112, 320, 175, 383)(115, 323, 179, 387, 116, 324, 177, 385)(118, 326, 193, 401, 131, 339, 194, 402)(121, 329, 201, 409, 127, 335, 199, 407)(123, 331, 183, 391, 140, 348, 181, 389)(125, 333, 185, 393, 129, 337, 187, 395)(133, 341, 189, 397, 135, 343, 191, 399)(137, 345, 206, 414, 139, 347, 197, 405)(142, 350, 204, 412, 144, 352, 200, 408)(146, 354, 202, 410, 148, 356, 205, 413)(150, 358, 207, 415, 152, 360, 198, 406)(154, 362, 192, 400, 156, 364, 190, 398)(158, 366, 186, 394, 160, 368, 188, 396)(162, 370, 208, 416, 164, 372, 203, 411)(166, 374, 195, 403, 168, 376, 196, 404)(170, 378, 174, 382, 172, 380, 176, 384)(178, 386, 182, 390, 180, 388, 184, 392)(417, 625, 419, 627)(418, 626, 424, 632)(420, 628, 430, 638)(421, 629, 431, 639)(422, 630, 428, 636)(423, 631, 432, 640)(425, 633, 436, 644)(426, 634, 434, 642)(427, 635, 437, 645)(429, 637, 440, 648)(433, 641, 441, 649)(435, 643, 444, 652)(438, 646, 448, 656)(439, 647, 446, 654)(442, 650, 452, 660)(443, 651, 450, 658)(445, 653, 453, 661)(447, 655, 456, 664)(449, 657, 457, 665)(451, 659, 460, 668)(454, 662, 464, 672)(455, 663, 462, 670)(458, 666, 468, 676)(459, 667, 466, 674)(461, 669, 469, 677)(463, 671, 472, 680)(465, 673, 473, 681)(467, 675, 476, 684)(470, 678, 480, 688)(471, 679, 478, 686)(474, 682, 484, 692)(475, 683, 482, 690)(477, 685, 485, 693)(479, 687, 488, 696)(481, 689, 525, 733)(483, 691, 527, 735)(486, 694, 530, 738)(487, 695, 529, 737)(489, 697, 533, 741)(490, 698, 536, 744)(491, 699, 535, 743)(492, 700, 540, 748)(493, 701, 542, 750)(494, 702, 544, 752)(495, 703, 546, 754)(496, 704, 548, 756)(497, 705, 550, 758)(498, 706, 552, 760)(499, 707, 554, 762)(500, 708, 538, 746)(501, 709, 557, 765)(502, 710, 559, 767)(503, 711, 561, 769)(504, 712, 563, 771)(505, 713, 565, 773)(506, 714, 567, 775)(507, 715, 569, 777)(508, 716, 571, 779)(509, 717, 573, 781)(510, 718, 575, 783)(511, 719, 577, 785)(512, 720, 579, 787)(513, 721, 581, 789)(514, 722, 583, 791)(515, 723, 585, 793)(516, 724, 587, 795)(517, 725, 589, 797)(518, 726, 591, 799)(519, 727, 593, 801)(520, 728, 595, 803)(521, 729, 597, 805)(522, 730, 599, 807)(523, 731, 601, 809)(524, 732, 603, 811)(526, 734, 605, 813)(528, 736, 607, 815)(531, 739, 610, 818)(532, 740, 609, 817)(534, 742, 613, 821)(537, 745, 616, 824)(539, 747, 615, 823)(541, 749, 618, 826)(543, 751, 620, 828)(545, 753, 621, 829)(547, 755, 622, 830)(549, 757, 623, 831)(551, 759, 614, 822)(553, 761, 606, 814)(555, 763, 608, 816)(556, 764, 617, 825)(558, 766, 604, 812)(560, 768, 602, 810)(562, 770, 624, 832)(564, 772, 619, 827)(566, 774, 611, 819)(568, 776, 612, 820)(570, 778, 592, 800)(572, 780, 590, 798)(574, 782, 586, 794)(576, 784, 588, 796)(578, 786, 598, 806)(580, 788, 600, 808)(582, 790, 596, 804)(584, 792, 594, 802)
	L = (1, 420)(2, 425)(3, 428)(4, 423)(5, 426)(6, 417)(7, 422)(8, 434)(9, 421)(10, 418)(11, 438)(12, 432)(13, 439)(14, 419)(15, 436)(16, 430)(17, 442)(18, 431)(19, 443)(20, 424)(21, 446)(22, 429)(23, 427)(24, 448)(25, 450)(26, 435)(27, 433)(28, 452)(29, 454)(30, 440)(31, 455)(32, 437)(33, 458)(34, 444)(35, 459)(36, 441)(37, 462)(38, 447)(39, 445)(40, 464)(41, 466)(42, 451)(43, 449)(44, 468)(45, 470)(46, 456)(47, 471)(48, 453)(49, 474)(50, 460)(51, 475)(52, 457)(53, 478)(54, 463)(55, 461)(56, 480)(57, 482)(58, 467)(59, 465)(60, 484)(61, 486)(62, 472)(63, 487)(64, 469)(65, 491)(66, 476)(67, 500)(68, 473)(69, 529)(70, 479)(71, 477)(72, 530)(73, 494)(74, 497)(75, 483)(76, 489)(77, 496)(78, 495)(79, 492)(80, 490)(81, 493)(82, 504)(83, 503)(84, 481)(85, 506)(86, 505)(87, 498)(88, 499)(89, 501)(90, 502)(91, 512)(92, 511)(93, 514)(94, 513)(95, 507)(96, 508)(97, 509)(98, 510)(99, 520)(100, 519)(101, 522)(102, 521)(103, 515)(104, 516)(105, 517)(106, 518)(107, 532)(108, 531)(109, 538)(110, 556)(111, 535)(112, 539)(113, 488)(114, 485)(115, 523)(116, 524)(117, 540)(118, 541)(119, 525)(120, 548)(121, 549)(122, 527)(123, 526)(124, 546)(125, 547)(126, 550)(127, 551)(128, 533)(129, 534)(130, 544)(131, 545)(132, 542)(133, 543)(134, 536)(135, 537)(136, 561)(137, 562)(138, 563)(139, 564)(140, 528)(141, 565)(142, 566)(143, 567)(144, 568)(145, 554)(146, 555)(147, 552)(148, 553)(149, 559)(150, 560)(151, 557)(152, 558)(153, 577)(154, 578)(155, 579)(156, 580)(157, 581)(158, 582)(159, 583)(160, 584)(161, 571)(162, 572)(163, 569)(164, 570)(165, 575)(166, 576)(167, 573)(168, 574)(169, 593)(170, 594)(171, 595)(172, 596)(173, 597)(174, 598)(175, 599)(176, 600)(177, 587)(178, 588)(179, 585)(180, 586)(181, 591)(182, 592)(183, 589)(184, 590)(185, 610)(186, 611)(187, 609)(188, 612)(189, 615)(190, 619)(191, 617)(192, 624)(193, 601)(194, 603)(195, 604)(196, 602)(197, 621)(198, 620)(199, 607)(200, 614)(201, 605)(202, 613)(203, 608)(204, 623)(205, 622)(206, 618)(207, 616)(208, 606)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E27.2246
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2251 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 4, 4})
Quotient :: edge
Aut^+ = C4 x (C13 : C4) (small group id <208, 30>)
Aut   = C4 x (C13 : C4) (small group id <208, 30>)
|r| :: 1
Presentation :: [ X2^4, X1^4, X2 * X1^-1 * X2^-2 * X1 * X2, (X2^-1 * X1^-1 * X2 * X1^-1)^2, (X2^-1 * X1^-1)^4, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^2 * X2 * X1^2 * X2^-1 * X1^2, X1^-1 * X2 * X1^-2 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2^-1 * X1^-2 * X2^-1 * X1^-1, X2 * X1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2^-1 * X1^-2 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 23, 11)(5, 14, 33, 15)(7, 18, 39, 20)(8, 21, 44, 22)(10, 19, 35, 26)(12, 29, 53, 30)(13, 31, 56, 32)(16, 34, 57, 36)(17, 37, 62, 38)(24, 47, 73, 48)(25, 49, 76, 50)(27, 51, 65, 40)(28, 52, 66, 41)(42, 67, 85, 58)(43, 68, 86, 59)(45, 69, 97, 70)(46, 71, 102, 72)(54, 60, 87, 81)(55, 61, 88, 82)(63, 89, 123, 90)(64, 91, 128, 92)(74, 105, 135, 98)(75, 106, 136, 99)(77, 100, 137, 107)(78, 101, 138, 108)(79, 109, 147, 110)(80, 111, 150, 112)(83, 115, 153, 116)(84, 117, 158, 118)(93, 129, 165, 124)(94, 130, 166, 125)(95, 126, 167, 131)(96, 127, 168, 132)(103, 139, 175, 140)(104, 141, 178, 142)(113, 151, 163, 148)(114, 152, 164, 149)(119, 159, 133, 154)(120, 160, 134, 155)(121, 156, 185, 161)(122, 157, 186, 162)(143, 176, 197, 179)(144, 177, 198, 180)(145, 181, 193, 169)(146, 182, 194, 170)(171, 195, 173, 187)(172, 196, 174, 188)(183, 189, 201, 191)(184, 190, 202, 192)(199, 203, 207, 205)(200, 204, 208, 206)(209, 211, 218, 213)(210, 215, 227, 216)(212, 220, 234, 221)(214, 224, 243, 225)(217, 232, 222, 233)(219, 235, 223, 236)(226, 248, 229, 249)(228, 250, 230, 251)(231, 253, 241, 254)(237, 262, 239, 263)(238, 255, 240, 257)(242, 266, 245, 267)(244, 268, 246, 269)(247, 271, 252, 272)(256, 282, 258, 283)(259, 285, 260, 286)(261, 287, 264, 288)(265, 291, 270, 292)(273, 301, 274, 302)(275, 303, 276, 304)(277, 306, 279, 307)(278, 308, 280, 309)(281, 311, 284, 312)(289, 321, 290, 322)(293, 327, 294, 328)(295, 329, 296, 330)(297, 332, 299, 333)(298, 334, 300, 335)(305, 341, 310, 342)(313, 351, 314, 352)(315, 353, 316, 354)(317, 356, 319, 357)(318, 347, 320, 349)(323, 362, 325, 363)(324, 364, 326, 365)(331, 371, 336, 372)(337, 377, 338, 378)(339, 379, 340, 380)(343, 366, 344, 361)(345, 381, 346, 382)(348, 384, 350, 385)(355, 373, 358, 374)(359, 391, 360, 392)(367, 395, 368, 396)(369, 397, 370, 398)(375, 399, 376, 400)(383, 401, 386, 402)(387, 394, 388, 393)(389, 407, 390, 408)(403, 411, 404, 412)(405, 413, 406, 414)(409, 415, 410, 416)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: chiral
Dual of E27.2252
Transitivity :: ET+
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2252 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 4, 4})
Quotient :: loop
Aut^+ = C4 x (C13 : C4) (small group id <208, 30>)
Aut   = C4 x (C13 : C4) (small group id <208, 30>)
|r| :: 1
Presentation :: [ X2^4, X1^4, X2 * X1^-1 * X2^-2 * X1 * X2, (X2^-1 * X1^-1 * X2 * X1^-1)^2, (X2^-1 * X1^-1)^4, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^2 * X2 * X1^2 * X2^-1 * X1^2, X1^-1 * X2 * X1^-2 * X2 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2^-1 * X1^-2 * X2^-1 * X1^-1, X2 * X1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2^-1 * X1^-2 * X2^-1 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 6, 214, 4, 212)(3, 211, 9, 217, 23, 231, 11, 219)(5, 213, 14, 222, 33, 241, 15, 223)(7, 215, 18, 226, 39, 247, 20, 228)(8, 216, 21, 229, 44, 252, 22, 230)(10, 218, 19, 227, 35, 243, 26, 234)(12, 220, 29, 237, 53, 261, 30, 238)(13, 221, 31, 239, 56, 264, 32, 240)(16, 224, 34, 242, 57, 265, 36, 244)(17, 225, 37, 245, 62, 270, 38, 246)(24, 232, 47, 255, 73, 281, 48, 256)(25, 233, 49, 257, 76, 284, 50, 258)(27, 235, 51, 259, 65, 273, 40, 248)(28, 236, 52, 260, 66, 274, 41, 249)(42, 250, 67, 275, 85, 293, 58, 266)(43, 251, 68, 276, 86, 294, 59, 267)(45, 253, 69, 277, 97, 305, 70, 278)(46, 254, 71, 279, 102, 310, 72, 280)(54, 262, 60, 268, 87, 295, 81, 289)(55, 263, 61, 269, 88, 296, 82, 290)(63, 271, 89, 297, 123, 331, 90, 298)(64, 272, 91, 299, 128, 336, 92, 300)(74, 282, 105, 313, 135, 343, 98, 306)(75, 283, 106, 314, 136, 344, 99, 307)(77, 285, 100, 308, 137, 345, 107, 315)(78, 286, 101, 309, 138, 346, 108, 316)(79, 287, 109, 317, 147, 355, 110, 318)(80, 288, 111, 319, 150, 358, 112, 320)(83, 291, 115, 323, 153, 361, 116, 324)(84, 292, 117, 325, 158, 366, 118, 326)(93, 301, 129, 337, 165, 373, 124, 332)(94, 302, 130, 338, 166, 374, 125, 333)(95, 303, 126, 334, 167, 375, 131, 339)(96, 304, 127, 335, 168, 376, 132, 340)(103, 311, 139, 347, 175, 383, 140, 348)(104, 312, 141, 349, 178, 386, 142, 350)(113, 321, 151, 359, 163, 371, 148, 356)(114, 322, 152, 360, 164, 372, 149, 357)(119, 327, 159, 367, 133, 341, 154, 362)(120, 328, 160, 368, 134, 342, 155, 363)(121, 329, 156, 364, 185, 393, 161, 369)(122, 330, 157, 365, 186, 394, 162, 370)(143, 351, 176, 384, 197, 405, 179, 387)(144, 352, 177, 385, 198, 406, 180, 388)(145, 353, 181, 389, 193, 401, 169, 377)(146, 354, 182, 390, 194, 402, 170, 378)(171, 379, 195, 403, 173, 381, 187, 395)(172, 380, 196, 404, 174, 382, 188, 396)(183, 391, 189, 397, 201, 409, 191, 399)(184, 392, 190, 398, 202, 410, 192, 400)(199, 407, 203, 411, 207, 415, 205, 413)(200, 408, 204, 412, 208, 416, 206, 414)
	L = (1, 211)(2, 215)(3, 218)(4, 220)(5, 209)(6, 224)(7, 227)(8, 210)(9, 232)(10, 213)(11, 235)(12, 234)(13, 212)(14, 233)(15, 236)(16, 243)(17, 214)(18, 248)(19, 216)(20, 250)(21, 249)(22, 251)(23, 253)(24, 222)(25, 217)(26, 221)(27, 223)(28, 219)(29, 262)(30, 255)(31, 263)(32, 257)(33, 254)(34, 266)(35, 225)(36, 268)(37, 267)(38, 269)(39, 271)(40, 229)(41, 226)(42, 230)(43, 228)(44, 272)(45, 241)(46, 231)(47, 240)(48, 282)(49, 238)(50, 283)(51, 285)(52, 286)(53, 287)(54, 239)(55, 237)(56, 288)(57, 291)(58, 245)(59, 242)(60, 246)(61, 244)(62, 292)(63, 252)(64, 247)(65, 301)(66, 302)(67, 303)(68, 304)(69, 306)(70, 308)(71, 307)(72, 309)(73, 311)(74, 258)(75, 256)(76, 312)(77, 260)(78, 259)(79, 264)(80, 261)(81, 321)(82, 322)(83, 270)(84, 265)(85, 327)(86, 328)(87, 329)(88, 330)(89, 332)(90, 334)(91, 333)(92, 335)(93, 274)(94, 273)(95, 276)(96, 275)(97, 341)(98, 279)(99, 277)(100, 280)(101, 278)(102, 342)(103, 284)(104, 281)(105, 351)(106, 352)(107, 353)(108, 354)(109, 356)(110, 347)(111, 357)(112, 349)(113, 290)(114, 289)(115, 362)(116, 364)(117, 363)(118, 365)(119, 294)(120, 293)(121, 296)(122, 295)(123, 371)(124, 299)(125, 297)(126, 300)(127, 298)(128, 372)(129, 377)(130, 378)(131, 379)(132, 380)(133, 310)(134, 305)(135, 366)(136, 361)(137, 381)(138, 382)(139, 320)(140, 384)(141, 318)(142, 385)(143, 314)(144, 313)(145, 316)(146, 315)(147, 373)(148, 319)(149, 317)(150, 374)(151, 391)(152, 392)(153, 343)(154, 325)(155, 323)(156, 326)(157, 324)(158, 344)(159, 395)(160, 396)(161, 397)(162, 398)(163, 336)(164, 331)(165, 358)(166, 355)(167, 399)(168, 400)(169, 338)(170, 337)(171, 340)(172, 339)(173, 346)(174, 345)(175, 401)(176, 350)(177, 348)(178, 402)(179, 394)(180, 393)(181, 407)(182, 408)(183, 360)(184, 359)(185, 387)(186, 388)(187, 368)(188, 367)(189, 370)(190, 369)(191, 376)(192, 375)(193, 386)(194, 383)(195, 411)(196, 412)(197, 413)(198, 414)(199, 390)(200, 389)(201, 415)(202, 416)(203, 404)(204, 403)(205, 406)(206, 405)(207, 410)(208, 409)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: chiral
Dual of E27.2251
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2253 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 4, 4})
Quotient :: edge
Aut^+ = C52 : C4 (small group id <208, 31>)
Aut   = C52 : C4 (small group id <208, 31>)
|r| :: 1
Presentation :: [ X1^4, X2^4, X2^2 * X1 * X2^2 * X1^-1, (X2^-1 * X1^-1)^4, X2 * X1^-1 * X2 * X1^2 * X2^2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2 * X1^2 * X2^-1 * X1^-2 * X2^-1 * X1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 23, 11)(5, 14, 33, 15)(7, 18, 39, 20)(8, 21, 44, 22)(10, 19, 35, 26)(12, 29, 53, 30)(13, 31, 56, 32)(16, 34, 57, 36)(17, 37, 62, 38)(24, 47, 73, 48)(25, 49, 76, 50)(27, 51, 65, 40)(28, 52, 66, 41)(42, 67, 85, 58)(43, 68, 86, 59)(45, 69, 97, 70)(46, 71, 102, 72)(54, 60, 87, 81)(55, 61, 88, 82)(63, 89, 123, 90)(64, 91, 128, 92)(74, 105, 135, 98)(75, 106, 136, 99)(77, 100, 137, 107)(78, 101, 138, 108)(79, 109, 147, 110)(80, 111, 150, 112)(83, 115, 153, 116)(84, 117, 158, 118)(93, 129, 165, 124)(94, 130, 166, 125)(95, 126, 167, 131)(96, 127, 168, 132)(103, 139, 175, 140)(104, 141, 178, 142)(113, 151, 164, 148)(114, 152, 163, 149)(119, 159, 134, 154)(120, 160, 133, 155)(121, 156, 185, 161)(122, 157, 186, 162)(143, 176, 197, 179)(144, 177, 198, 180)(145, 181, 193, 169)(146, 182, 194, 170)(171, 195, 174, 187)(172, 196, 173, 188)(183, 189, 201, 192)(184, 190, 202, 191)(199, 204, 207, 206)(200, 203, 208, 205)(209, 211, 218, 213)(210, 215, 227, 216)(212, 220, 234, 221)(214, 224, 243, 225)(217, 232, 222, 233)(219, 235, 223, 236)(226, 248, 229, 249)(228, 250, 230, 251)(231, 253, 241, 254)(237, 262, 239, 263)(238, 255, 240, 257)(242, 266, 245, 267)(244, 268, 246, 269)(247, 271, 252, 272)(256, 282, 258, 283)(259, 285, 260, 286)(261, 287, 264, 288)(265, 291, 270, 292)(273, 301, 274, 302)(275, 303, 276, 304)(277, 306, 279, 307)(278, 308, 280, 309)(281, 311, 284, 312)(289, 321, 290, 322)(293, 327, 294, 328)(295, 329, 296, 330)(297, 332, 299, 333)(298, 334, 300, 335)(305, 341, 310, 342)(313, 351, 314, 352)(315, 353, 316, 354)(317, 356, 319, 357)(318, 347, 320, 349)(323, 362, 325, 363)(324, 364, 326, 365)(331, 371, 336, 372)(337, 377, 338, 378)(339, 379, 340, 380)(343, 361, 344, 366)(345, 381, 346, 382)(348, 384, 350, 385)(355, 374, 358, 373)(359, 391, 360, 392)(367, 395, 368, 396)(369, 397, 370, 398)(375, 399, 376, 400)(383, 402, 386, 401)(387, 393, 388, 394)(389, 407, 390, 408)(403, 411, 404, 412)(405, 413, 406, 414)(409, 415, 410, 416)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: chiral
Dual of E27.2254
Transitivity :: ET+
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2254 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 4, 4})
Quotient :: loop
Aut^+ = C52 : C4 (small group id <208, 31>)
Aut   = C52 : C4 (small group id <208, 31>)
|r| :: 1
Presentation :: [ X1^4, X2^4, X2^2 * X1 * X2^2 * X1^-1, (X2^-1 * X1^-1)^4, X2 * X1^-1 * X2 * X1^2 * X2^2 * X1 * X2 * X1^-1 * X2^-1 * X1^-1, X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2 * X1^2 * X2^-1 * X1^-2 * X2^-1 * X1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 209, 2, 210, 6, 214, 4, 212)(3, 211, 9, 217, 23, 231, 11, 219)(5, 213, 14, 222, 33, 241, 15, 223)(7, 215, 18, 226, 39, 247, 20, 228)(8, 216, 21, 229, 44, 252, 22, 230)(10, 218, 19, 227, 35, 243, 26, 234)(12, 220, 29, 237, 53, 261, 30, 238)(13, 221, 31, 239, 56, 264, 32, 240)(16, 224, 34, 242, 57, 265, 36, 244)(17, 225, 37, 245, 62, 270, 38, 246)(24, 232, 47, 255, 73, 281, 48, 256)(25, 233, 49, 257, 76, 284, 50, 258)(27, 235, 51, 259, 65, 273, 40, 248)(28, 236, 52, 260, 66, 274, 41, 249)(42, 250, 67, 275, 85, 293, 58, 266)(43, 251, 68, 276, 86, 294, 59, 267)(45, 253, 69, 277, 97, 305, 70, 278)(46, 254, 71, 279, 102, 310, 72, 280)(54, 262, 60, 268, 87, 295, 81, 289)(55, 263, 61, 269, 88, 296, 82, 290)(63, 271, 89, 297, 123, 331, 90, 298)(64, 272, 91, 299, 128, 336, 92, 300)(74, 282, 105, 313, 135, 343, 98, 306)(75, 283, 106, 314, 136, 344, 99, 307)(77, 285, 100, 308, 137, 345, 107, 315)(78, 286, 101, 309, 138, 346, 108, 316)(79, 287, 109, 317, 147, 355, 110, 318)(80, 288, 111, 319, 150, 358, 112, 320)(83, 291, 115, 323, 153, 361, 116, 324)(84, 292, 117, 325, 158, 366, 118, 326)(93, 301, 129, 337, 165, 373, 124, 332)(94, 302, 130, 338, 166, 374, 125, 333)(95, 303, 126, 334, 167, 375, 131, 339)(96, 304, 127, 335, 168, 376, 132, 340)(103, 311, 139, 347, 175, 383, 140, 348)(104, 312, 141, 349, 178, 386, 142, 350)(113, 321, 151, 359, 164, 372, 148, 356)(114, 322, 152, 360, 163, 371, 149, 357)(119, 327, 159, 367, 134, 342, 154, 362)(120, 328, 160, 368, 133, 341, 155, 363)(121, 329, 156, 364, 185, 393, 161, 369)(122, 330, 157, 365, 186, 394, 162, 370)(143, 351, 176, 384, 197, 405, 179, 387)(144, 352, 177, 385, 198, 406, 180, 388)(145, 353, 181, 389, 193, 401, 169, 377)(146, 354, 182, 390, 194, 402, 170, 378)(171, 379, 195, 403, 174, 382, 187, 395)(172, 380, 196, 404, 173, 381, 188, 396)(183, 391, 189, 397, 201, 409, 192, 400)(184, 392, 190, 398, 202, 410, 191, 399)(199, 407, 204, 412, 207, 415, 206, 414)(200, 408, 203, 411, 208, 416, 205, 413)
	L = (1, 211)(2, 215)(3, 218)(4, 220)(5, 209)(6, 224)(7, 227)(8, 210)(9, 232)(10, 213)(11, 235)(12, 234)(13, 212)(14, 233)(15, 236)(16, 243)(17, 214)(18, 248)(19, 216)(20, 250)(21, 249)(22, 251)(23, 253)(24, 222)(25, 217)(26, 221)(27, 223)(28, 219)(29, 262)(30, 255)(31, 263)(32, 257)(33, 254)(34, 266)(35, 225)(36, 268)(37, 267)(38, 269)(39, 271)(40, 229)(41, 226)(42, 230)(43, 228)(44, 272)(45, 241)(46, 231)(47, 240)(48, 282)(49, 238)(50, 283)(51, 285)(52, 286)(53, 287)(54, 239)(55, 237)(56, 288)(57, 291)(58, 245)(59, 242)(60, 246)(61, 244)(62, 292)(63, 252)(64, 247)(65, 301)(66, 302)(67, 303)(68, 304)(69, 306)(70, 308)(71, 307)(72, 309)(73, 311)(74, 258)(75, 256)(76, 312)(77, 260)(78, 259)(79, 264)(80, 261)(81, 321)(82, 322)(83, 270)(84, 265)(85, 327)(86, 328)(87, 329)(88, 330)(89, 332)(90, 334)(91, 333)(92, 335)(93, 274)(94, 273)(95, 276)(96, 275)(97, 341)(98, 279)(99, 277)(100, 280)(101, 278)(102, 342)(103, 284)(104, 281)(105, 351)(106, 352)(107, 353)(108, 354)(109, 356)(110, 347)(111, 357)(112, 349)(113, 290)(114, 289)(115, 362)(116, 364)(117, 363)(118, 365)(119, 294)(120, 293)(121, 296)(122, 295)(123, 371)(124, 299)(125, 297)(126, 300)(127, 298)(128, 372)(129, 377)(130, 378)(131, 379)(132, 380)(133, 310)(134, 305)(135, 361)(136, 366)(137, 381)(138, 382)(139, 320)(140, 384)(141, 318)(142, 385)(143, 314)(144, 313)(145, 316)(146, 315)(147, 374)(148, 319)(149, 317)(150, 373)(151, 391)(152, 392)(153, 344)(154, 325)(155, 323)(156, 326)(157, 324)(158, 343)(159, 395)(160, 396)(161, 397)(162, 398)(163, 336)(164, 331)(165, 355)(166, 358)(167, 399)(168, 400)(169, 338)(170, 337)(171, 340)(172, 339)(173, 346)(174, 345)(175, 402)(176, 350)(177, 348)(178, 401)(179, 393)(180, 394)(181, 407)(182, 408)(183, 360)(184, 359)(185, 388)(186, 387)(187, 368)(188, 367)(189, 370)(190, 369)(191, 376)(192, 375)(193, 383)(194, 386)(195, 411)(196, 412)(197, 413)(198, 414)(199, 390)(200, 389)(201, 415)(202, 416)(203, 404)(204, 403)(205, 406)(206, 405)(207, 410)(208, 409)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: chiral
Dual of E27.2253
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2255 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 8, 8})
Quotient :: halfedge
Aut^+ = (C13 : C8) : C2 (small group id <208, 28>)
Aut   = (C13 : C8) : C2 (small group id <208, 28>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X1^-2 * X2 * X1^-2)^2, X1 * X2 * X1 * X2 * X1^-3 * X2 * X1 * X2, X1 * X2 * X1^2 * X2 * X1 * X2 * X1^-1 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 46, 38, 18, 8)(6, 13, 27, 53, 45, 60, 30, 14)(9, 19, 39, 48, 24, 47, 42, 20)(12, 25, 49, 44, 21, 43, 52, 26)(16, 33, 63, 93, 70, 41, 65, 34)(17, 35, 56, 28, 55, 83, 67, 36)(29, 57, 78, 50, 77, 110, 86, 58)(32, 61, 89, 69, 37, 68, 92, 62)(40, 51, 79, 107, 75, 74, 104, 72)(54, 81, 115, 88, 59, 87, 118, 82)(64, 95, 127, 90, 126, 165, 133, 96)(66, 91, 128, 159, 119, 100, 137, 98)(71, 101, 139, 106, 73, 105, 141, 102)(76, 108, 146, 114, 80, 113, 149, 109)(84, 120, 156, 116, 99, 138, 161, 121)(85, 117, 157, 179, 150, 124, 163, 122)(94, 130, 167, 135, 97, 134, 169, 131)(103, 142, 158, 140, 145, 177, 155, 143)(111, 151, 125, 147, 123, 164, 129, 152)(112, 148, 178, 176, 144, 154, 182, 153)(132, 168, 191, 197, 189, 171, 192, 170)(136, 172, 185, 160, 184, 200, 190, 173)(162, 186, 166, 180, 198, 194, 174, 187)(175, 181, 199, 183, 196, 195, 202, 188)(193, 201, 206, 203, 207, 205, 208, 204)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 55)(33, 48)(34, 64)(35, 66)(36, 60)(38, 70)(39, 71)(42, 73)(43, 58)(44, 74)(47, 75)(49, 76)(52, 80)(53, 77)(56, 84)(57, 85)(61, 90)(62, 91)(63, 94)(65, 97)(67, 99)(68, 96)(69, 100)(72, 103)(78, 111)(79, 112)(81, 116)(82, 117)(83, 119)(86, 123)(87, 121)(88, 124)(89, 125)(92, 129)(93, 126)(95, 132)(98, 136)(101, 140)(102, 134)(104, 144)(105, 143)(106, 130)(107, 145)(108, 147)(109, 148)(110, 150)(113, 152)(114, 154)(115, 155)(118, 158)(120, 160)(122, 162)(127, 149)(128, 166)(131, 168)(133, 146)(135, 171)(137, 174)(138, 173)(139, 156)(141, 161)(142, 175)(151, 180)(153, 181)(157, 183)(159, 184)(163, 188)(164, 187)(165, 189)(167, 190)(169, 185)(170, 182)(172, 193)(176, 195)(177, 196)(178, 197)(179, 198)(186, 201)(191, 203)(192, 204)(194, 205)(199, 206)(200, 207)(202, 208)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: chiral positively-selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.2256 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 8, 8})
Quotient :: edge
Aut^+ = (C13 : C8) : C2 (small group id <208, 28>)
Aut   = (C13 : C8) : C2 (small group id <208, 28>)
|r| :: 1
Presentation :: [ X1^2, X2^8, X2^-2 * X1 * X2^4 * X1 * X2^-2, X2 * X1 * X2^-3 * X1 * X2 * X1 * X2 * X1, X2^-2 * X1 * X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^2 * X1 * X2^-2 * X1, X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^-1 * X1 ]
Map::
	R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 46)(24, 48)(26, 52)(27, 54)(28, 56)(30, 60)(32, 61)(34, 65)(35, 66)(36, 68)(38, 53)(40, 72)(42, 73)(43, 64)(44, 74)(47, 75)(49, 79)(50, 80)(51, 82)(55, 86)(57, 87)(58, 78)(59, 88)(62, 91)(63, 92)(67, 97)(69, 99)(70, 100)(71, 101)(76, 109)(77, 110)(81, 115)(83, 117)(84, 118)(85, 119)(89, 124)(90, 126)(93, 130)(94, 131)(95, 122)(96, 132)(98, 135)(102, 141)(103, 142)(104, 113)(105, 140)(106, 107)(108, 146)(111, 150)(112, 151)(114, 152)(116, 155)(120, 161)(121, 162)(123, 160)(125, 165)(127, 167)(128, 168)(129, 169)(133, 153)(134, 171)(136, 173)(137, 157)(138, 174)(139, 175)(143, 163)(144, 164)(145, 177)(147, 179)(148, 180)(149, 181)(154, 183)(156, 185)(158, 186)(159, 187)(166, 190)(170, 192)(172, 194)(176, 195)(178, 197)(182, 199)(184, 201)(188, 202)(189, 203)(191, 200)(193, 198)(196, 206)(204, 207)(205, 208)(209, 211, 216, 226, 246, 230, 218, 212)(210, 213, 220, 234, 261, 238, 222, 214)(215, 223, 240, 270, 253, 264, 242, 224)(217, 227, 248, 254, 245, 278, 250, 228)(219, 231, 255, 284, 268, 249, 257, 232)(221, 235, 263, 239, 260, 292, 265, 236)(225, 243, 275, 252, 229, 251, 277, 244)(233, 258, 289, 267, 237, 266, 291, 259)(241, 271, 301, 274, 299, 336, 302, 272)(247, 276, 306, 344, 308, 282, 310, 279)(256, 285, 319, 288, 317, 356, 320, 286)(262, 290, 324, 364, 326, 296, 328, 293)(269, 297, 333, 304, 273, 303, 335, 298)(280, 311, 351, 314, 281, 313, 352, 312)(283, 315, 353, 322, 287, 321, 355, 316)(294, 329, 371, 332, 295, 331, 372, 330)(300, 334, 374, 399, 376, 340, 378, 337)(305, 341, 359, 346, 307, 345, 358, 342)(309, 347, 375, 350, 381, 397, 373, 348)(318, 354, 386, 406, 388, 360, 390, 357)(323, 361, 339, 366, 325, 365, 338, 362)(327, 367, 387, 370, 393, 404, 385, 368)(343, 379, 401, 384, 349, 382, 389, 380)(363, 391, 408, 396, 369, 394, 377, 392)(383, 402, 412, 398, 411, 403, 413, 400)(395, 409, 415, 405, 414, 410, 416, 407)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: chiral
Dual of E27.2257
Transitivity :: ET+
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.2257 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 8, 8})
Quotient :: loop
Aut^+ = (C13 : C8) : C2 (small group id <208, 28>)
Aut   = (C13 : C8) : C2 (small group id <208, 28>)
|r| :: 1
Presentation :: [ (X1^-1 * X2^-1)^2, (X2^-1 * X1^-1)^2, (X2 * X1)^2, X2^4 * X1^4, X1^8, X2^4 * X1^-4, X1^2 * X2^-1 * X1 * X2^4 * X1^-2 * X2^-1 * X1, X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^2 * X1^2, X2^2 * X1^2 * X2^-2 * X1^2 * X2^-1 * X1^-2 * X2 * X1^-1 * X2^2 * X1 ]
Map::
	R = (1, 209, 2, 210, 6, 214, 16, 224, 40, 248, 34, 242, 13, 221, 4, 212)(3, 211, 9, 217, 23, 231, 57, 265, 39, 247, 42, 250, 29, 237, 11, 219)(5, 213, 14, 222, 35, 243, 56, 264, 26, 234, 51, 259, 20, 228, 7, 215)(8, 216, 21, 229, 52, 260, 33, 241, 48, 256, 79, 287, 44, 252, 17, 225)(10, 218, 25, 233, 61, 269, 36, 244, 15, 223, 38, 246, 64, 272, 27, 235)(12, 220, 30, 238, 69, 277, 75, 283, 41, 249, 18, 226, 45, 253, 32, 240)(19, 227, 47, 255, 83, 291, 53, 261, 22, 230, 55, 263, 86, 294, 49, 257)(24, 232, 60, 268, 98, 306, 68, 276, 31, 239, 70, 278, 95, 303, 58, 266)(28, 236, 65, 273, 106, 314, 137, 345, 93, 301, 59, 267, 96, 304, 67, 275)(37, 245, 74, 282, 89, 297, 50, 258, 87, 295, 131, 339, 112, 320, 72, 280)(43, 251, 76, 284, 116, 324, 80, 288, 46, 254, 82, 290, 119, 327, 77, 285)(54, 262, 92, 300, 122, 330, 78, 286, 120, 328, 161, 369, 134, 342, 90, 298)(62, 270, 102, 310, 148, 356, 105, 313, 66, 274, 107, 315, 145, 353, 100, 308)(63, 271, 103, 311, 150, 358, 113, 321, 73, 281, 101, 309, 146, 354, 104, 312)(71, 279, 81, 289, 124, 332, 155, 363, 115, 323, 109, 317, 151, 359, 111, 319)(84, 292, 127, 335, 168, 376, 130, 338, 88, 296, 132, 340, 166, 374, 125, 333)(85, 293, 128, 336, 170, 378, 135, 343, 91, 299, 126, 334, 108, 316, 129, 337)(94, 302, 138, 346, 172, 380, 140, 348, 97, 305, 141, 349, 163, 371, 136, 344)(99, 307, 143, 351, 175, 383, 139, 347, 110, 318, 153, 361, 176, 384, 142, 350)(114, 322, 118, 326, 159, 367, 154, 362, 164, 372, 123, 331, 157, 365, 133, 341)(117, 325, 158, 366, 186, 394, 160, 368, 121, 329, 162, 370, 184, 392, 156, 364)(144, 352, 178, 386, 196, 404, 180, 388, 147, 355, 181, 389, 195, 403, 177, 385)(149, 357, 167, 375, 191, 399, 179, 387, 152, 360, 165, 373, 189, 397, 182, 390)(169, 377, 185, 393, 201, 409, 190, 398, 171, 379, 183, 391, 199, 407, 192, 400)(173, 381, 193, 401, 202, 410, 187, 395, 174, 382, 194, 402, 200, 408, 188, 396)(197, 405, 203, 411, 207, 415, 205, 413, 198, 406, 204, 412, 208, 416, 206, 414)
	L = (1, 211)(2, 215)(3, 218)(4, 220)(5, 209)(6, 225)(7, 227)(8, 210)(9, 212)(10, 234)(11, 236)(12, 239)(13, 241)(14, 244)(15, 213)(16, 249)(17, 251)(18, 214)(19, 256)(20, 258)(21, 261)(22, 216)(23, 266)(24, 217)(25, 219)(26, 248)(27, 271)(28, 274)(29, 276)(30, 221)(31, 250)(32, 279)(33, 254)(34, 264)(35, 280)(36, 281)(37, 222)(38, 265)(39, 223)(40, 247)(41, 232)(42, 224)(43, 238)(44, 286)(45, 288)(46, 226)(47, 228)(48, 242)(49, 293)(50, 296)(51, 235)(52, 298)(53, 299)(54, 229)(55, 243)(56, 230)(57, 301)(58, 302)(59, 231)(60, 283)(61, 308)(62, 233)(63, 245)(64, 313)(65, 237)(66, 246)(67, 316)(68, 305)(69, 285)(70, 240)(71, 307)(72, 292)(73, 295)(74, 312)(75, 323)(76, 252)(77, 326)(78, 329)(79, 257)(80, 331)(81, 253)(82, 260)(83, 333)(84, 255)(85, 262)(86, 338)(87, 259)(88, 263)(89, 341)(90, 325)(91, 328)(92, 337)(93, 270)(94, 273)(95, 347)(96, 348)(97, 267)(98, 350)(99, 268)(100, 352)(101, 269)(102, 345)(103, 272)(104, 359)(105, 355)(106, 344)(107, 275)(108, 357)(109, 277)(110, 278)(111, 354)(112, 362)(113, 332)(114, 282)(115, 318)(116, 364)(117, 284)(118, 289)(119, 368)(120, 287)(121, 290)(122, 371)(123, 317)(124, 322)(125, 373)(126, 291)(127, 320)(128, 294)(129, 304)(130, 375)(131, 321)(132, 297)(133, 377)(134, 380)(135, 314)(136, 300)(137, 378)(138, 303)(139, 382)(140, 369)(141, 306)(142, 381)(143, 319)(144, 311)(145, 387)(146, 388)(147, 309)(148, 390)(149, 310)(150, 385)(151, 372)(152, 315)(153, 363)(154, 379)(155, 358)(156, 391)(157, 324)(158, 342)(159, 327)(160, 393)(161, 343)(162, 330)(163, 395)(164, 339)(165, 336)(166, 398)(167, 334)(168, 400)(169, 335)(170, 360)(171, 340)(172, 396)(173, 346)(174, 349)(175, 403)(176, 404)(177, 351)(178, 353)(179, 406)(180, 361)(181, 356)(182, 405)(183, 367)(184, 408)(185, 365)(186, 410)(187, 366)(188, 370)(189, 374)(190, 412)(191, 376)(192, 411)(193, 384)(194, 383)(195, 413)(196, 414)(197, 386)(198, 389)(199, 392)(200, 416)(201, 394)(202, 415)(203, 397)(204, 399)(205, 401)(206, 402)(207, 407)(208, 409)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: chiral
Dual of E27.2256
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.2258 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 8, 8})
Quotient :: halfedge
Aut^+ = (C13 : C8) : C2 (small group id <208, 29>)
Aut   = (C13 : C8) : C2 (small group id <208, 29>)
|r| :: 1
Presentation :: [ X2^2, X1^8, X1^2 * X2 * X1^-4 * X2 * X1^2, X1 * X2 * X1 * X2 * X1^-3 * X2 * X1 * X2, X1^-1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^-1, X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-1 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 46, 38, 18, 8)(6, 13, 27, 53, 45, 60, 30, 14)(9, 19, 39, 48, 24, 47, 42, 20)(12, 25, 49, 44, 21, 43, 52, 26)(16, 33, 63, 93, 70, 41, 65, 34)(17, 35, 56, 28, 55, 83, 67, 36)(29, 57, 78, 50, 77, 110, 86, 58)(32, 61, 89, 69, 37, 68, 92, 62)(40, 51, 79, 107, 75, 74, 104, 72)(54, 81, 115, 88, 59, 87, 118, 82)(64, 95, 127, 90, 126, 165, 133, 96)(66, 91, 128, 159, 119, 100, 137, 98)(71, 101, 139, 106, 73, 105, 141, 102)(76, 108, 146, 114, 80, 113, 149, 109)(84, 120, 156, 116, 99, 138, 161, 121)(85, 117, 157, 179, 150, 124, 163, 122)(94, 130, 167, 135, 97, 134, 169, 131)(103, 142, 155, 140, 145, 177, 158, 143)(111, 151, 129, 147, 123, 164, 125, 152)(112, 148, 178, 176, 144, 154, 182, 153)(132, 168, 191, 199, 189, 171, 193, 170)(136, 172, 185, 160, 184, 201, 192, 173)(162, 186, 174, 180, 197, 190, 166, 187)(175, 181, 198, 188, 196, 195, 200, 183)(194, 203, 206, 205, 208, 202, 207, 204)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 37)(19, 40)(20, 41)(22, 45)(23, 46)(25, 50)(26, 51)(27, 54)(30, 59)(31, 55)(33, 48)(34, 64)(35, 66)(36, 60)(38, 70)(39, 71)(42, 73)(43, 58)(44, 74)(47, 75)(49, 76)(52, 80)(53, 77)(56, 84)(57, 85)(61, 90)(62, 91)(63, 94)(65, 97)(67, 99)(68, 96)(69, 100)(72, 103)(78, 111)(79, 112)(81, 116)(82, 117)(83, 119)(86, 123)(87, 121)(88, 124)(89, 125)(92, 129)(93, 126)(95, 132)(98, 136)(101, 140)(102, 134)(104, 144)(105, 143)(106, 130)(107, 145)(108, 147)(109, 148)(110, 150)(113, 152)(114, 154)(115, 155)(118, 158)(120, 160)(122, 162)(127, 146)(128, 166)(131, 168)(133, 149)(135, 171)(137, 174)(138, 173)(139, 161)(141, 156)(142, 175)(151, 180)(153, 181)(157, 183)(159, 184)(163, 188)(164, 187)(165, 189)(167, 185)(169, 192)(170, 178)(172, 194)(176, 195)(177, 196)(179, 197)(182, 199)(186, 202)(190, 203)(191, 204)(193, 205)(198, 206)(200, 207)(201, 208)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: chiral positively-selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 26 e = 104 f = 26
	degree seq :: [ 8^26 ]

E27.2259 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 8, 8})
Quotient :: edge
Aut^+ = (C13 : C8) : C2 (small group id <208, 29>)
Aut   = (C13 : C8) : C2 (small group id <208, 29>)
|r| :: 1
Presentation :: [ X1^2, X2^8, (X2^-3 * X1 * X2^-1)^2, X2^-1 * X1 * X2 * X1 * X2 * X1 * X2 * X1 * X2^-2, X2^-1 * X1 * X2^-2 * X1 * X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1 * X2^-1, X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^-1 * X1 ]
Map::
	R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 21)(12, 25)(14, 29)(15, 31)(16, 33)(18, 37)(19, 39)(20, 41)(22, 45)(23, 46)(24, 48)(26, 52)(27, 54)(28, 56)(30, 60)(32, 61)(34, 65)(35, 66)(36, 68)(38, 53)(40, 72)(42, 73)(43, 64)(44, 74)(47, 75)(49, 79)(50, 80)(51, 82)(55, 86)(57, 87)(58, 78)(59, 88)(62, 91)(63, 92)(67, 97)(69, 99)(70, 100)(71, 101)(76, 109)(77, 110)(81, 115)(83, 117)(84, 118)(85, 119)(89, 124)(90, 126)(93, 130)(94, 131)(95, 122)(96, 132)(98, 135)(102, 141)(103, 142)(104, 113)(105, 140)(106, 107)(108, 146)(111, 150)(112, 151)(114, 152)(116, 155)(120, 161)(121, 162)(123, 160)(125, 165)(127, 167)(128, 168)(129, 169)(133, 157)(134, 171)(136, 173)(137, 153)(138, 174)(139, 175)(143, 164)(144, 163)(145, 177)(147, 179)(148, 180)(149, 181)(154, 183)(156, 185)(158, 186)(159, 187)(166, 189)(170, 192)(172, 193)(176, 195)(178, 196)(182, 199)(184, 200)(188, 202)(190, 201)(191, 204)(194, 197)(198, 207)(203, 206)(205, 208)(209, 211, 216, 226, 246, 230, 218, 212)(210, 213, 220, 234, 261, 238, 222, 214)(215, 223, 240, 270, 253, 264, 242, 224)(217, 227, 248, 254, 245, 278, 250, 228)(219, 231, 255, 284, 268, 249, 257, 232)(221, 235, 263, 239, 260, 292, 265, 236)(225, 243, 275, 252, 229, 251, 277, 244)(233, 258, 289, 267, 237, 266, 291, 259)(241, 271, 301, 274, 299, 336, 302, 272)(247, 276, 306, 344, 308, 282, 310, 279)(256, 285, 319, 288, 317, 356, 320, 286)(262, 290, 324, 364, 326, 296, 328, 293)(269, 297, 333, 304, 273, 303, 335, 298)(280, 311, 351, 314, 281, 313, 352, 312)(283, 315, 353, 322, 287, 321, 355, 316)(294, 329, 371, 332, 295, 331, 372, 330)(300, 334, 374, 398, 376, 340, 378, 337)(305, 341, 358, 346, 307, 345, 359, 342)(309, 347, 373, 350, 381, 399, 375, 348)(318, 354, 386, 405, 388, 360, 390, 357)(323, 361, 338, 366, 325, 365, 339, 362)(327, 367, 385, 370, 393, 406, 387, 368)(343, 379, 389, 384, 349, 382, 402, 380)(363, 391, 377, 396, 369, 394, 409, 392)(383, 401, 413, 400, 412, 403, 411, 397)(395, 408, 416, 407, 415, 410, 414, 404)
	L = (1, 209)(2, 210)(3, 211)(4, 212)(5, 213)(6, 214)(7, 215)(8, 216)(9, 217)(10, 218)(11, 219)(12, 220)(13, 221)(14, 222)(15, 223)(16, 224)(17, 225)(18, 226)(19, 227)(20, 228)(21, 229)(22, 230)(23, 231)(24, 232)(25, 233)(26, 234)(27, 235)(28, 236)(29, 237)(30, 238)(31, 239)(32, 240)(33, 241)(34, 242)(35, 243)(36, 244)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 269)(62, 270)(63, 271)(64, 272)(65, 273)(66, 274)(67, 275)(68, 276)(69, 277)(70, 278)(71, 279)(72, 280)(73, 281)(74, 282)(75, 283)(76, 284)(77, 285)(78, 286)(79, 287)(80, 288)(81, 289)(82, 290)(83, 291)(84, 292)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 317)(110, 318)(111, 319)(112, 320)(113, 321)(114, 322)(115, 323)(116, 324)(117, 325)(118, 326)(119, 327)(120, 328)(121, 329)(122, 330)(123, 331)(124, 332)(125, 333)(126, 334)(127, 335)(128, 336)(129, 337)(130, 338)(131, 339)(132, 340)(133, 341)(134, 342)(135, 343)(136, 344)(137, 345)(138, 346)(139, 347)(140, 348)(141, 349)(142, 350)(143, 351)(144, 352)(145, 353)(146, 354)(147, 355)(148, 356)(149, 357)(150, 358)(151, 359)(152, 360)(153, 361)(154, 362)(155, 363)(156, 364)(157, 365)(158, 366)(159, 367)(160, 368)(161, 369)(162, 370)(163, 371)(164, 372)(165, 373)(166, 374)(167, 375)(168, 376)(169, 377)(170, 378)(171, 379)(172, 380)(173, 381)(174, 382)(175, 383)(176, 384)(177, 385)(178, 386)(179, 387)(180, 388)(181, 389)(182, 390)(183, 391)(184, 392)(185, 393)(186, 394)(187, 395)(188, 396)(189, 397)(190, 398)(191, 399)(192, 400)(193, 401)(194, 402)(195, 403)(196, 404)(197, 405)(198, 406)(199, 407)(200, 408)(201, 409)(202, 410)(203, 411)(204, 412)(205, 413)(206, 414)(207, 415)(208, 416)
	local type(s) :: { ( 16, 16 ), ( 16^8 ) }
Outer automorphisms :: chiral
Dual of E27.2260
Transitivity :: ET+
Graph:: simple bipartite
	v = 130 e = 208 f = 26
	degree seq :: [ 2^104, 8^26 ]

E27.2260 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 8, 8})
Quotient :: loop
Aut^+ = (C13 : C8) : C2 (small group id <208, 29>)
Aut   = (C13 : C8) : C2 (small group id <208, 29>)
|r| :: 1
Presentation :: [ (X2 * X1)^2, X2 * X1^-1 * X2^-1 * X1^2 * X2^-1 * X1^-1 * X2, X1^-1 * X2^4 * X1^-3, X2^4 * X1^4, (X1^-1 * X2 * X1^-2)^2, (X2 * X1^-1 * X2^2)^2, X2^8, X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1^2 ]
Map::
	R = (1, 209, 2, 210, 6, 214, 16, 224, 40, 248, 34, 242, 13, 221, 4, 212)(3, 211, 9, 217, 23, 231, 57, 265, 39, 247, 42, 250, 29, 237, 11, 219)(5, 213, 14, 222, 35, 243, 56, 264, 26, 234, 51, 259, 20, 228, 7, 215)(8, 216, 21, 229, 52, 260, 33, 241, 48, 256, 79, 287, 44, 252, 17, 225)(10, 218, 25, 233, 61, 269, 36, 244, 15, 223, 38, 246, 64, 272, 27, 235)(12, 220, 30, 238, 69, 277, 75, 283, 41, 249, 18, 226, 45, 253, 32, 240)(19, 227, 47, 255, 83, 291, 53, 261, 22, 230, 55, 263, 86, 294, 49, 257)(24, 232, 60, 268, 98, 306, 68, 276, 31, 239, 70, 278, 95, 303, 58, 266)(28, 236, 65, 273, 106, 314, 137, 345, 93, 301, 59, 267, 96, 304, 67, 275)(37, 245, 74, 282, 89, 297, 50, 258, 87, 295, 131, 339, 112, 320, 72, 280)(43, 251, 76, 284, 116, 324, 80, 288, 46, 254, 82, 290, 119, 327, 77, 285)(54, 262, 92, 300, 122, 330, 78, 286, 120, 328, 162, 370, 134, 342, 90, 298)(62, 270, 102, 310, 148, 356, 105, 313, 66, 274, 107, 315, 145, 353, 100, 308)(63, 271, 103, 311, 150, 358, 113, 321, 73, 281, 101, 309, 146, 354, 104, 312)(71, 279, 81, 289, 124, 332, 155, 363, 115, 323, 109, 317, 152, 360, 111, 319)(84, 292, 127, 335, 169, 377, 130, 338, 88, 296, 132, 340, 166, 374, 125, 333)(85, 293, 128, 336, 108, 316, 135, 343, 91, 299, 126, 334, 167, 375, 129, 337)(94, 302, 138, 346, 164, 372, 136, 344, 97, 305, 141, 349, 172, 380, 139, 347)(99, 307, 143, 351, 175, 383, 140, 348, 110, 318, 153, 361, 176, 384, 142, 350)(114, 322, 123, 331, 157, 365, 154, 362, 160, 368, 118, 326, 159, 367, 133, 341)(117, 325, 158, 366, 186, 394, 161, 369, 121, 329, 163, 371, 184, 392, 156, 364)(144, 352, 178, 386, 195, 403, 177, 385, 147, 355, 181, 389, 196, 404, 179, 387)(149, 357, 165, 373, 189, 397, 180, 388, 151, 359, 168, 376, 191, 399, 182, 390)(170, 378, 183, 391, 199, 407, 190, 398, 171, 379, 185, 393, 201, 409, 192, 400)(173, 381, 193, 401, 200, 408, 188, 396, 174, 382, 194, 402, 202, 410, 187, 395)(197, 405, 204, 412, 207, 415, 206, 414, 198, 406, 203, 411, 208, 416, 205, 413)
	L = (1, 211)(2, 215)(3, 218)(4, 220)(5, 209)(6, 225)(7, 227)(8, 210)(9, 212)(10, 234)(11, 236)(12, 239)(13, 241)(14, 244)(15, 213)(16, 249)(17, 251)(18, 214)(19, 256)(20, 258)(21, 261)(22, 216)(23, 266)(24, 217)(25, 219)(26, 248)(27, 271)(28, 274)(29, 276)(30, 221)(31, 250)(32, 279)(33, 254)(34, 264)(35, 280)(36, 281)(37, 222)(38, 265)(39, 223)(40, 247)(41, 232)(42, 224)(43, 238)(44, 286)(45, 288)(46, 226)(47, 228)(48, 242)(49, 293)(50, 296)(51, 235)(52, 298)(53, 299)(54, 229)(55, 243)(56, 230)(57, 301)(58, 302)(59, 231)(60, 283)(61, 308)(62, 233)(63, 245)(64, 313)(65, 237)(66, 246)(67, 316)(68, 305)(69, 285)(70, 240)(71, 307)(72, 292)(73, 295)(74, 312)(75, 323)(76, 252)(77, 326)(78, 329)(79, 257)(80, 331)(81, 253)(82, 260)(83, 333)(84, 255)(85, 262)(86, 338)(87, 259)(88, 263)(89, 341)(90, 325)(91, 328)(92, 337)(93, 270)(94, 273)(95, 348)(96, 344)(97, 267)(98, 350)(99, 268)(100, 352)(101, 269)(102, 345)(103, 272)(104, 332)(105, 355)(106, 347)(107, 275)(108, 357)(109, 277)(110, 278)(111, 358)(112, 362)(113, 360)(114, 282)(115, 318)(116, 364)(117, 284)(118, 289)(119, 369)(120, 287)(121, 290)(122, 372)(123, 317)(124, 368)(125, 373)(126, 291)(127, 320)(128, 294)(129, 314)(130, 376)(131, 321)(132, 297)(133, 378)(134, 380)(135, 304)(136, 300)(137, 375)(138, 303)(139, 370)(140, 382)(141, 306)(142, 381)(143, 319)(144, 311)(145, 388)(146, 385)(147, 309)(148, 390)(149, 310)(150, 387)(151, 315)(152, 322)(153, 363)(154, 379)(155, 354)(156, 391)(157, 324)(158, 342)(159, 327)(160, 339)(161, 393)(162, 343)(163, 330)(164, 395)(165, 336)(166, 398)(167, 359)(168, 334)(169, 400)(170, 335)(171, 340)(172, 396)(173, 346)(174, 349)(175, 403)(176, 404)(177, 351)(178, 353)(179, 361)(180, 406)(181, 356)(182, 405)(183, 367)(184, 408)(185, 365)(186, 410)(187, 366)(188, 371)(189, 374)(190, 412)(191, 377)(192, 411)(193, 384)(194, 383)(195, 413)(196, 414)(197, 386)(198, 389)(199, 392)(200, 416)(201, 394)(202, 415)(203, 397)(204, 399)(205, 401)(206, 402)(207, 407)(208, 409)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: chiral
Dual of E27.2259
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 26 e = 208 f = 130
	degree seq :: [ 16^26 ]

E27.2261 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 108})
Quotient :: regular
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, T1^-2 * T2 * T1^25 * T2 * T1^-27 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 109, 133, 130, 134, 138, 142, 147, 152, 158, 193, 198, 202, 209, 211, 208, 199, 195, 189, 186, 181, 178, 173, 168, 172, 159, 116, 107, 104, 99, 96, 90, 85, 75, 80, 76, 81, 87, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 111, 126, 120, 117, 118, 121, 127, 132, 137, 141, 145, 150, 157, 201, 210, 212, 207, 200, 194, 190, 185, 182, 177, 174, 167, 171, 160, 114, 108, 103, 100, 95, 92, 82, 77, 71, 74, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 113, 122, 128, 125, 131, 136, 140, 144, 149, 154, 162, 206, 216, 213, 203, 197, 191, 188, 183, 180, 175, 170, 165, 164, 156, 110, 146, 101, 106, 93, 98, 79, 89, 70, 88, 72, 91, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 115, 124, 119, 123, 129, 135, 139, 143, 148, 153, 161, 205, 215, 214, 204, 196, 192, 187, 184, 179, 176, 169, 166, 163, 155, 151, 105, 112, 97, 102, 86, 94, 73, 84, 69, 83, 78, 62, 55, 46, 39, 30, 22, 12, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 91)(63, 111)(67, 87)(68, 115)(69, 117)(70, 118)(71, 119)(72, 120)(73, 121)(74, 122)(75, 123)(76, 124)(77, 125)(78, 126)(79, 127)(80, 128)(81, 113)(82, 129)(83, 109)(84, 130)(85, 131)(86, 132)(88, 133)(89, 134)(90, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 147)(103, 148)(104, 149)(105, 150)(106, 152)(107, 153)(108, 154)(110, 157)(112, 158)(114, 161)(116, 162)(146, 193)(151, 198)(155, 201)(156, 202)(159, 205)(160, 206)(163, 209)(164, 210)(165, 211)(166, 212)(167, 213)(168, 214)(169, 208)(170, 207)(171, 215)(172, 216)(173, 203)(174, 204)(175, 199)(176, 200)(177, 197)(178, 196)(179, 195)(180, 194)(181, 191)(182, 192)(183, 189)(184, 190)(185, 188)(186, 187)
	local type(s) :: { ( 4^108 ) }
Outer automorphisms :: reflexible
Dual of E27.2262
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 108 f = 54
	degree seq :: [ 108^2 ]

E27.2262 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 108})
Quotient :: regular
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 65, 38, 67)(39, 69, 43, 72)(40, 73, 42, 76)(41, 77, 48, 79)(44, 84, 47, 86)(45, 82, 46, 70)(49, 80, 50, 74)(51, 95, 52, 97)(53, 99, 54, 101)(55, 89, 56, 87)(57, 105, 58, 107)(59, 109, 60, 111)(61, 113, 62, 115)(63, 117, 64, 119)(66, 122, 68, 121)(71, 127, 83, 125)(75, 132, 81, 130)(78, 136, 92, 135)(85, 141, 91, 140)(88, 126, 90, 128)(93, 131, 94, 133)(96, 152, 98, 151)(100, 156, 102, 155)(103, 143, 104, 144)(106, 162, 108, 161)(110, 166, 112, 165)(114, 170, 116, 169)(118, 174, 120, 173)(123, 177, 124, 178)(129, 181, 139, 183)(134, 186, 138, 188)(137, 191, 148, 192)(142, 196, 147, 197)(145, 184, 146, 182)(149, 189, 150, 187)(153, 207, 154, 208)(157, 211, 158, 212)(159, 200, 160, 199)(163, 213, 164, 214)(167, 210, 168, 209)(171, 203, 172, 198)(175, 193, 176, 204)(179, 185, 180, 195)(190, 215, 194, 216)(201, 205, 202, 206)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 56)(36, 55)(39, 70)(40, 74)(41, 76)(42, 80)(43, 82)(44, 69)(45, 87)(46, 89)(47, 72)(48, 73)(49, 67)(50, 65)(51, 77)(52, 79)(53, 84)(54, 86)(57, 95)(58, 97)(59, 99)(60, 101)(61, 105)(62, 107)(63, 109)(64, 111)(66, 113)(68, 115)(71, 128)(75, 133)(78, 130)(81, 131)(83, 126)(85, 127)(88, 144)(90, 143)(91, 125)(92, 132)(93, 121)(94, 122)(96, 136)(98, 135)(100, 141)(102, 140)(103, 119)(104, 117)(106, 152)(108, 151)(110, 156)(112, 155)(114, 162)(116, 161)(118, 166)(120, 165)(123, 170)(124, 169)(129, 182)(134, 187)(137, 188)(138, 189)(139, 184)(142, 181)(145, 199)(146, 200)(147, 183)(148, 186)(149, 178)(150, 177)(153, 191)(154, 192)(157, 196)(158, 197)(159, 173)(160, 174)(163, 207)(164, 208)(167, 211)(168, 212)(171, 213)(172, 214)(175, 210)(176, 209)(179, 203)(180, 198)(185, 206)(190, 201)(193, 216)(194, 202)(195, 205)(204, 215)
	local type(s) :: { ( 108^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2261
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 54 e = 108 f = 2
	degree seq :: [ 4^54 ]

E27.2263 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 108})
Quotient :: edge
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 3, 12, 5)(2, 7, 21, 9)(4, 16, 6, 17)(8, 25, 10, 26)(11, 29, 18, 31)(13, 33, 14, 34)(15, 30, 19, 32)(20, 39, 27, 41)(22, 43, 23, 44)(24, 40, 28, 42)(35, 58, 36, 59)(37, 61, 38, 62)(45, 72, 46, 73)(47, 75, 48, 76)(49, 77, 53, 79)(50, 81, 51, 82)(52, 78, 54, 80)(55, 85, 56, 86)(57, 83, 60, 84)(63, 93, 67, 95)(64, 97, 65, 98)(66, 94, 68, 96)(69, 101, 70, 102)(71, 99, 74, 100)(87, 118, 88, 119)(89, 121, 90, 122)(91, 123, 92, 124)(103, 134, 104, 135)(105, 137, 106, 138)(107, 139, 108, 140)(109, 129, 110, 130)(111, 141, 112, 142)(113, 126, 114, 125)(115, 145, 116, 146)(117, 143, 120, 144)(127, 155, 128, 156)(131, 159, 132, 160)(133, 157, 136, 158)(147, 174, 148, 175)(149, 177, 150, 178)(151, 179, 152, 180)(153, 181, 154, 182)(161, 188, 162, 189)(163, 191, 164, 192)(165, 193, 166, 194)(167, 195, 168, 196)(169, 190, 170, 187)(171, 197, 172, 198)(173, 183, 176, 184)(185, 207, 186, 208)(199, 216, 200, 215)(201, 213, 202, 214)(203, 212, 204, 211)(205, 209, 206, 210)(217, 218)(219, 227)(220, 231)(221, 234)(222, 235)(223, 236)(224, 240)(225, 243)(226, 244)(228, 237)(229, 241)(230, 242)(232, 238)(233, 239)(245, 265)(246, 268)(247, 269)(248, 270)(249, 266)(250, 267)(251, 273)(252, 276)(253, 274)(254, 275)(255, 279)(256, 282)(257, 283)(258, 284)(259, 280)(260, 281)(261, 287)(262, 290)(263, 288)(264, 289)(271, 291)(272, 292)(277, 285)(278, 286)(293, 312)(294, 311)(295, 310)(296, 309)(297, 325)(298, 326)(299, 329)(300, 330)(301, 327)(302, 328)(303, 333)(304, 336)(305, 334)(306, 335)(307, 337)(308, 338)(313, 341)(314, 342)(315, 345)(316, 346)(317, 343)(318, 344)(319, 349)(320, 352)(321, 350)(322, 351)(323, 353)(324, 354)(331, 355)(332, 356)(339, 347)(340, 348)(357, 373)(358, 374)(359, 371)(360, 372)(361, 385)(362, 386)(363, 389)(364, 392)(365, 390)(366, 391)(367, 393)(368, 394)(369, 395)(370, 396)(375, 399)(376, 400)(377, 403)(378, 406)(379, 404)(380, 405)(381, 407)(382, 408)(383, 409)(384, 410)(387, 411)(388, 412)(397, 401)(398, 402)(413, 426)(414, 425)(415, 424)(416, 423)(417, 432)(418, 431)(419, 429)(420, 430)(421, 428)(422, 427)
	L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 289)(74, 290)(75, 291)(76, 292)(77, 293)(78, 294)(79, 295)(80, 296)(81, 297)(82, 298)(83, 299)(84, 300)(85, 301)(86, 302)(87, 303)(88, 304)(89, 305)(90, 306)(91, 307)(92, 308)(93, 309)(94, 310)(95, 311)(96, 312)(97, 313)(98, 314)(99, 315)(100, 316)(101, 317)(102, 318)(103, 319)(104, 320)(105, 321)(106, 322)(107, 323)(108, 324)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 216, 216 ), ( 216^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2267
Transitivity :: ET+
Graph:: simple bipartite
	v = 162 e = 216 f = 2
	degree seq :: [ 2^108, 4^54 ]

E27.2264 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 108})
Quotient :: edge
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-54 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 110, 125, 137, 144, 154, 160, 170, 176, 187, 202, 189, 205, 215, 214, 201, 213, 216, 184, 175, 167, 159, 151, 143, 134, 122, 133, 142, 106, 101, 97, 93, 89, 85, 80, 73, 79, 84, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 105, 124, 116, 127, 135, 146, 152, 162, 168, 178, 183, 204, 195, 207, 211, 199, 193, 191, 181, 173, 165, 157, 149, 140, 131, 120, 114, 112, 104, 100, 96, 92, 88, 83, 78, 72, 69, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 107, 113, 121, 130, 141, 148, 158, 164, 174, 180, 185, 192, 200, 210, 208, 197, 209, 188, 179, 171, 163, 155, 147, 138, 128, 118, 129, 109, 103, 99, 95, 91, 87, 82, 76, 71, 77, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 111, 115, 119, 132, 139, 150, 156, 166, 172, 182, 190, 194, 198, 212, 206, 196, 203, 186, 177, 169, 161, 153, 145, 136, 126, 117, 123, 108, 102, 98, 94, 90, 86, 81, 75, 70, 74, 64, 56, 48, 40, 32, 24, 16, 8)(217, 218, 222, 220)(219, 225, 229, 224)(221, 227, 230, 223)(226, 232, 237, 233)(228, 231, 238, 235)(234, 241, 245, 240)(236, 243, 246, 239)(242, 248, 253, 249)(244, 247, 254, 251)(250, 257, 261, 256)(252, 259, 262, 255)(258, 264, 269, 265)(260, 263, 270, 267)(266, 273, 277, 272)(268, 275, 278, 271)(274, 280, 321, 281)(276, 279, 300, 283)(282, 293, 340, 290)(284, 327, 295, 323)(285, 329, 289, 331)(286, 332, 287, 326)(288, 335, 296, 337)(291, 341, 292, 343)(294, 346, 301, 348)(297, 351, 298, 353)(299, 355, 305, 357)(302, 360, 303, 362)(304, 364, 309, 366)(306, 368, 307, 370)(308, 372, 313, 374)(310, 376, 311, 378)(312, 380, 317, 382)(314, 384, 315, 386)(316, 388, 322, 390)(318, 392, 319, 394)(320, 396, 358, 398)(324, 399, 325, 403)(328, 406, 349, 401)(330, 408, 338, 410)(333, 411, 334, 405)(336, 414, 350, 416)(339, 418, 345, 420)(342, 421, 344, 423)(347, 426, 359, 428)(352, 427, 354, 431)(356, 422, 367, 424)(361, 430, 363, 415)(365, 413, 375, 412)(369, 409, 371, 417)(373, 419, 383, 425)(377, 429, 379, 407)(381, 404, 391, 402)(385, 397, 387, 432)(389, 393, 400, 395)
	L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 289)(74, 290)(75, 291)(76, 292)(77, 293)(78, 294)(79, 295)(80, 296)(81, 297)(82, 298)(83, 299)(84, 300)(85, 301)(86, 302)(87, 303)(88, 304)(89, 305)(90, 306)(91, 307)(92, 308)(93, 309)(94, 310)(95, 311)(96, 312)(97, 313)(98, 314)(99, 315)(100, 316)(101, 317)(102, 318)(103, 319)(104, 320)(105, 321)(106, 322)(107, 323)(108, 324)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 4^4 ), ( 4^108 ) }
Outer automorphisms :: reflexible
Dual of E27.2268
Transitivity :: ET+
Graph:: bipartite
	v = 56 e = 216 f = 108
	degree seq :: [ 4^54, 108^2 ]

E27.2265 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 108})
Quotient :: edge
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^25 * T2 * T1^-27 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 115)(63, 123)(67, 112)(68, 127)(69, 129)(70, 130)(71, 131)(72, 132)(73, 133)(74, 134)(75, 135)(76, 136)(77, 137)(78, 138)(79, 139)(80, 140)(81, 141)(82, 142)(83, 143)(84, 144)(85, 145)(86, 146)(87, 147)(88, 148)(89, 149)(90, 150)(91, 151)(92, 152)(93, 153)(94, 154)(95, 155)(96, 156)(97, 157)(98, 158)(99, 159)(100, 160)(101, 161)(102, 162)(103, 163)(104, 164)(105, 165)(106, 125)(107, 166)(108, 167)(109, 121)(110, 168)(111, 169)(113, 171)(114, 172)(116, 173)(117, 174)(118, 176)(119, 177)(120, 178)(122, 180)(124, 182)(126, 184)(128, 186)(170, 216)(175, 210)(179, 201)(181, 204)(183, 214)(185, 197)(187, 200)(188, 207)(189, 211)(190, 194)(191, 213)(192, 202)(193, 205)(195, 215)(196, 199)(198, 208)(203, 206)(209, 212)(217, 218, 221, 227, 236, 245, 253, 261, 269, 277, 337, 378, 370, 360, 367, 361, 368, 376, 382, 387, 392, 398, 432, 426, 420, 409, 415, 410, 416, 423, 429, 401, 342, 336, 330, 326, 317, 311, 299, 293, 287, 290, 296, 305, 314, 322, 328, 282, 274, 266, 258, 250, 242, 232, 239, 233, 240, 248, 256, 264, 272, 280, 339, 380, 372, 363, 354, 348, 345, 346, 349, 355, 364, 373, 381, 385, 390, 396, 417, 411, 405, 408, 414, 422, 428, 399, 344, 335, 332, 324, 319, 309, 302, 291, 297, 292, 298, 306, 315, 284, 276, 268, 260, 252, 244, 235, 226, 220)(219, 223, 231, 241, 249, 257, 265, 273, 281, 341, 375, 365, 358, 350, 357, 353, 362, 371, 379, 384, 389, 394, 402, 413, 425, 404, 424, 406, 427, 421, 395, 391, 333, 340, 321, 329, 304, 316, 289, 301, 285, 300, 294, 318, 312, 331, 279, 270, 263, 254, 247, 237, 230, 222, 229, 225, 234, 243, 251, 259, 267, 275, 283, 343, 374, 366, 356, 352, 347, 351, 359, 369, 377, 383, 388, 393, 400, 430, 407, 419, 403, 418, 412, 431, 397, 338, 386, 327, 334, 313, 323, 295, 308, 286, 307, 288, 310, 303, 325, 320, 278, 271, 262, 255, 246, 238, 228, 224)
	L = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 289)(74, 290)(75, 291)(76, 292)(77, 293)(78, 294)(79, 295)(80, 296)(81, 297)(82, 298)(83, 299)(84, 300)(85, 301)(86, 302)(87, 303)(88, 304)(89, 305)(90, 306)(91, 307)(92, 308)(93, 309)(94, 310)(95, 311)(96, 312)(97, 313)(98, 314)(99, 315)(100, 316)(101, 317)(102, 318)(103, 319)(104, 320)(105, 321)(106, 322)(107, 323)(108, 324)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)
	local type(s) :: { ( 8, 8 ), ( 8^108 ) }
Outer automorphisms :: reflexible
Dual of E27.2266
Transitivity :: ET+
Graph:: simple bipartite
	v = 110 e = 216 f = 54
	degree seq :: [ 2^108, 108^2 ]

E27.2266 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 108})
Quotient :: loop
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 217, 3, 219, 8, 224, 4, 220)(2, 218, 5, 221, 11, 227, 6, 222)(7, 223, 13, 229, 9, 225, 14, 230)(10, 226, 15, 231, 12, 228, 16, 232)(17, 233, 21, 237, 18, 234, 22, 238)(19, 235, 23, 239, 20, 236, 24, 240)(25, 241, 29, 245, 26, 242, 30, 246)(27, 243, 31, 247, 28, 244, 32, 248)(33, 249, 37, 253, 34, 250, 38, 254)(35, 251, 44, 260, 36, 252, 39, 255)(40, 256, 57, 273, 41, 257, 59, 275)(42, 258, 68, 284, 43, 259, 61, 277)(45, 261, 65, 281, 46, 262, 63, 279)(47, 263, 70, 286, 48, 264, 67, 283)(49, 265, 75, 291, 50, 266, 73, 289)(51, 267, 79, 295, 52, 268, 77, 293)(53, 269, 83, 299, 54, 270, 81, 297)(55, 271, 87, 303, 56, 272, 85, 301)(58, 274, 91, 307, 60, 276, 89, 305)(62, 278, 93, 309, 72, 288, 95, 311)(64, 280, 98, 314, 66, 282, 97, 313)(69, 285, 101, 317, 71, 287, 102, 318)(74, 290, 104, 320, 76, 292, 105, 321)(78, 294, 108, 324, 80, 296, 109, 325)(82, 298, 113, 329, 84, 300, 114, 330)(86, 302, 117, 333, 88, 304, 118, 334)(90, 306, 121, 337, 92, 308, 122, 338)(94, 310, 125, 341, 96, 312, 126, 342)(99, 315, 129, 345, 100, 316, 130, 346)(103, 319, 134, 350, 112, 328, 133, 349)(106, 322, 137, 353, 107, 323, 138, 354)(110, 326, 142, 358, 111, 327, 141, 357)(115, 331, 145, 361, 116, 332, 144, 360)(119, 335, 149, 365, 120, 336, 148, 364)(123, 339, 154, 370, 124, 340, 153, 369)(127, 343, 158, 374, 128, 344, 157, 373)(131, 347, 162, 378, 132, 348, 161, 377)(135, 351, 166, 382, 136, 352, 165, 381)(139, 355, 170, 386, 140, 356, 169, 385)(143, 359, 173, 389, 152, 368, 174, 390)(146, 362, 178, 394, 147, 363, 177, 393)(150, 366, 181, 397, 151, 367, 182, 398)(155, 371, 184, 400, 156, 372, 185, 401)(159, 375, 188, 404, 160, 376, 189, 405)(163, 379, 193, 409, 164, 380, 194, 410)(167, 383, 197, 413, 168, 384, 198, 414)(171, 387, 201, 417, 172, 388, 202, 418)(175, 391, 205, 421, 176, 392, 206, 422)(179, 395, 209, 425, 180, 396, 210, 426)(183, 399, 214, 430, 192, 408, 213, 429)(186, 402, 216, 432, 187, 403, 215, 431)(190, 406, 212, 428, 191, 407, 211, 427)(195, 411, 207, 423, 196, 412, 208, 424)(199, 415, 203, 419, 200, 416, 204, 420)
	L = (1, 218)(2, 217)(3, 223)(4, 225)(5, 226)(6, 228)(7, 219)(8, 227)(9, 220)(10, 221)(11, 224)(12, 222)(13, 233)(14, 234)(15, 235)(16, 236)(17, 229)(18, 230)(19, 231)(20, 232)(21, 241)(22, 242)(23, 243)(24, 244)(25, 237)(26, 238)(27, 239)(28, 240)(29, 249)(30, 250)(31, 251)(32, 252)(33, 245)(34, 246)(35, 247)(36, 248)(37, 273)(38, 275)(39, 277)(40, 279)(41, 281)(42, 283)(43, 286)(44, 284)(45, 289)(46, 291)(47, 293)(48, 295)(49, 297)(50, 299)(51, 301)(52, 303)(53, 305)(54, 307)(55, 309)(56, 311)(57, 253)(58, 314)(59, 254)(60, 313)(61, 255)(62, 318)(63, 256)(64, 321)(65, 257)(66, 320)(67, 258)(68, 260)(69, 325)(70, 259)(71, 324)(72, 317)(73, 261)(74, 330)(75, 262)(76, 329)(77, 263)(78, 334)(79, 264)(80, 333)(81, 265)(82, 338)(83, 266)(84, 337)(85, 267)(86, 342)(87, 268)(88, 341)(89, 269)(90, 346)(91, 270)(92, 345)(93, 271)(94, 350)(95, 272)(96, 349)(97, 276)(98, 274)(99, 353)(100, 354)(101, 288)(102, 278)(103, 357)(104, 282)(105, 280)(106, 360)(107, 361)(108, 287)(109, 285)(110, 364)(111, 365)(112, 358)(113, 292)(114, 290)(115, 369)(116, 370)(117, 296)(118, 294)(119, 373)(120, 374)(121, 300)(122, 298)(123, 377)(124, 378)(125, 304)(126, 302)(127, 381)(128, 382)(129, 308)(130, 306)(131, 385)(132, 386)(133, 312)(134, 310)(135, 389)(136, 390)(137, 315)(138, 316)(139, 394)(140, 393)(141, 319)(142, 328)(143, 398)(144, 322)(145, 323)(146, 401)(147, 400)(148, 326)(149, 327)(150, 405)(151, 404)(152, 397)(153, 331)(154, 332)(155, 410)(156, 409)(157, 335)(158, 336)(159, 414)(160, 413)(161, 339)(162, 340)(163, 418)(164, 417)(165, 343)(166, 344)(167, 422)(168, 421)(169, 347)(170, 348)(171, 426)(172, 425)(173, 351)(174, 352)(175, 430)(176, 429)(177, 356)(178, 355)(179, 432)(180, 431)(181, 368)(182, 359)(183, 427)(184, 363)(185, 362)(186, 424)(187, 423)(188, 367)(189, 366)(190, 420)(191, 419)(192, 428)(193, 372)(194, 371)(195, 415)(196, 416)(197, 376)(198, 375)(199, 411)(200, 412)(201, 380)(202, 379)(203, 407)(204, 406)(205, 384)(206, 383)(207, 403)(208, 402)(209, 388)(210, 387)(211, 399)(212, 408)(213, 392)(214, 391)(215, 396)(216, 395)
	local type(s) :: { ( 2, 108, 2, 108, 2, 108, 2, 108 ) }
Outer automorphisms :: reflexible
Dual of E27.2265
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 54 e = 216 f = 110
	degree seq :: [ 8^54 ]

E27.2267 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 108})
Quotient :: loop
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-54 * T1^-1 ]
Map::
	R = (1, 217, 3, 219, 10, 226, 18, 234, 26, 242, 34, 250, 42, 258, 50, 266, 58, 274, 66, 282, 103, 319, 91, 307, 87, 303, 75, 291, 72, 288, 76, 292, 85, 301, 92, 308, 101, 317, 107, 323, 115, 331, 118, 334, 124, 340, 184, 400, 215, 431, 213, 429, 204, 420, 197, 413, 190, 406, 199, 415, 206, 422, 185, 401, 178, 394, 173, 389, 169, 385, 164, 380, 157, 373, 149, 365, 141, 357, 133, 349, 127, 343, 131, 347, 139, 355, 147, 363, 155, 371, 163, 379, 122, 338, 62, 278, 54, 270, 46, 262, 38, 254, 30, 246, 22, 238, 14, 230, 6, 222, 13, 229, 21, 237, 29, 245, 37, 253, 45, 261, 53, 269, 61, 277, 113, 329, 109, 325, 99, 315, 95, 311, 83, 299, 79, 295, 70, 286, 77, 293, 84, 300, 93, 309, 100, 316, 108, 324, 114, 330, 119, 335, 123, 339, 182, 398, 216, 432, 212, 428, 205, 421, 196, 412, 191, 407, 198, 414, 207, 423, 187, 403, 180, 396, 175, 391, 170, 386, 165, 381, 158, 374, 150, 366, 142, 358, 134, 350, 128, 344, 132, 348, 140, 356, 148, 364, 156, 372, 68, 284, 60, 276, 52, 268, 44, 260, 36, 252, 28, 244, 20, 236, 12, 228, 5, 221)(2, 218, 7, 223, 15, 231, 23, 239, 31, 247, 39, 255, 47, 263, 55, 271, 63, 279, 111, 327, 94, 310, 97, 313, 78, 294, 81, 297, 69, 285, 82, 298, 80, 296, 98, 314, 96, 312, 112, 328, 110, 326, 121, 337, 120, 336, 179, 395, 214, 430, 208, 424, 201, 417, 192, 408, 189, 405, 194, 410, 203, 419, 210, 426, 181, 397, 176, 392, 171, 387, 166, 382, 161, 377, 153, 369, 145, 361, 137, 353, 129, 345, 135, 351, 143, 359, 151, 367, 159, 375, 125, 341, 65, 281, 57, 273, 49, 265, 41, 257, 33, 249, 25, 241, 17, 233, 9, 225, 4, 220, 11, 227, 19, 235, 27, 243, 35, 251, 43, 259, 51, 267, 59, 275, 67, 283, 102, 318, 105, 321, 86, 302, 89, 305, 71, 287, 74, 290, 73, 289, 90, 306, 88, 304, 106, 322, 104, 320, 117, 333, 116, 332, 174, 390, 126, 342, 186, 402, 209, 425, 200, 416, 193, 409, 188, 404, 195, 411, 202, 418, 211, 427, 183, 399, 177, 393, 172, 388, 167, 383, 162, 378, 154, 370, 146, 362, 138, 354, 130, 346, 136, 352, 144, 360, 152, 368, 160, 376, 168, 384, 64, 280, 56, 272, 48, 264, 40, 256, 32, 248, 24, 240, 16, 232, 8, 224)
	L = (1, 218)(2, 222)(3, 225)(4, 217)(5, 227)(6, 220)(7, 221)(8, 219)(9, 229)(10, 232)(11, 230)(12, 231)(13, 224)(14, 223)(15, 238)(16, 237)(17, 226)(18, 241)(19, 228)(20, 243)(21, 233)(22, 235)(23, 236)(24, 234)(25, 245)(26, 248)(27, 246)(28, 247)(29, 240)(30, 239)(31, 254)(32, 253)(33, 242)(34, 257)(35, 244)(36, 259)(37, 249)(38, 251)(39, 252)(40, 250)(41, 261)(42, 264)(43, 262)(44, 263)(45, 256)(46, 255)(47, 270)(48, 269)(49, 258)(50, 273)(51, 260)(52, 275)(53, 265)(54, 267)(55, 268)(56, 266)(57, 277)(58, 280)(59, 278)(60, 279)(61, 272)(62, 271)(63, 338)(64, 329)(65, 274)(66, 341)(67, 276)(68, 318)(69, 343)(70, 345)(71, 347)(72, 346)(73, 349)(74, 344)(75, 351)(76, 353)(77, 354)(78, 355)(79, 352)(80, 357)(81, 348)(82, 350)(83, 359)(84, 361)(85, 362)(86, 363)(87, 360)(88, 365)(89, 356)(90, 358)(91, 367)(92, 369)(93, 370)(94, 371)(95, 368)(96, 373)(97, 364)(98, 366)(99, 375)(100, 377)(101, 378)(102, 379)(103, 376)(104, 380)(105, 372)(106, 374)(107, 382)(108, 383)(109, 384)(110, 385)(111, 284)(112, 381)(113, 281)(114, 387)(115, 388)(116, 389)(117, 386)(118, 392)(119, 393)(120, 394)(121, 391)(122, 283)(123, 397)(124, 399)(125, 325)(126, 401)(127, 290)(128, 285)(129, 288)(130, 286)(131, 297)(132, 287)(133, 298)(134, 289)(135, 295)(136, 291)(137, 293)(138, 292)(139, 305)(140, 294)(141, 306)(142, 296)(143, 303)(144, 299)(145, 301)(146, 300)(147, 313)(148, 302)(149, 314)(150, 304)(151, 311)(152, 307)(153, 309)(154, 308)(155, 321)(156, 310)(157, 322)(158, 312)(159, 319)(160, 315)(161, 317)(162, 316)(163, 327)(164, 328)(165, 320)(166, 324)(167, 323)(168, 282)(169, 333)(170, 326)(171, 331)(172, 330)(173, 337)(174, 396)(175, 332)(176, 335)(177, 334)(178, 390)(179, 403)(180, 336)(181, 340)(182, 427)(183, 339)(184, 426)(185, 395)(186, 423)(187, 342)(188, 421)(189, 420)(190, 416)(191, 417)(192, 412)(193, 413)(194, 428)(195, 429)(196, 409)(197, 408)(198, 425)(199, 424)(200, 407)(201, 406)(202, 432)(203, 431)(204, 404)(205, 405)(206, 402)(207, 430)(208, 414)(209, 415)(210, 398)(211, 400)(212, 411)(213, 410)(214, 422)(215, 418)(216, 419)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2263
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 216 f = 162
	degree seq :: [ 216^2 ]

E27.2268 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 108})
Quotient :: loop
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^-2 * T2 * T1^25 * T2 * T1^-27 ]
Map:: polytopal non-degenerate
	R = (1, 217, 3, 219)(2, 218, 6, 222)(4, 220, 9, 225)(5, 221, 12, 228)(7, 223, 16, 232)(8, 224, 17, 233)(10, 226, 15, 231)(11, 227, 21, 237)(13, 229, 23, 239)(14, 230, 24, 240)(18, 234, 26, 242)(19, 235, 27, 243)(20, 236, 30, 246)(22, 238, 32, 248)(25, 241, 34, 250)(28, 244, 33, 249)(29, 245, 38, 254)(31, 247, 40, 256)(35, 251, 42, 258)(36, 252, 43, 259)(37, 253, 46, 262)(39, 255, 48, 264)(41, 257, 50, 266)(44, 260, 49, 265)(45, 261, 54, 270)(47, 263, 56, 272)(51, 267, 58, 274)(52, 268, 59, 275)(53, 269, 62, 278)(55, 271, 64, 280)(57, 273, 66, 282)(60, 276, 65, 281)(61, 277, 69, 285)(63, 279, 103, 319)(67, 283, 73, 289)(68, 284, 107, 323)(70, 286, 101, 317)(71, 287, 105, 321)(72, 288, 109, 325)(74, 290, 110, 326)(75, 291, 111, 327)(76, 292, 112, 328)(77, 293, 113, 329)(78, 294, 114, 330)(79, 295, 115, 331)(80, 296, 116, 332)(81, 297, 117, 333)(82, 298, 118, 334)(83, 299, 119, 335)(84, 300, 120, 336)(85, 301, 121, 337)(86, 302, 122, 338)(87, 303, 123, 339)(88, 304, 124, 340)(89, 305, 125, 341)(90, 306, 126, 342)(91, 307, 127, 343)(92, 308, 128, 344)(93, 309, 129, 345)(94, 310, 131, 347)(95, 311, 132, 348)(96, 312, 133, 349)(97, 313, 134, 350)(98, 314, 136, 352)(99, 315, 137, 353)(100, 316, 138, 354)(102, 318, 141, 357)(104, 320, 142, 358)(106, 322, 145, 361)(108, 324, 146, 362)(130, 346, 169, 385)(135, 351, 174, 390)(139, 355, 177, 393)(140, 356, 178, 394)(143, 359, 181, 397)(144, 360, 182, 398)(147, 363, 185, 401)(148, 364, 186, 402)(149, 365, 187, 403)(150, 366, 188, 404)(151, 367, 189, 405)(152, 368, 190, 406)(153, 369, 191, 407)(154, 370, 192, 408)(155, 371, 193, 409)(156, 372, 194, 410)(157, 373, 195, 411)(158, 374, 196, 412)(159, 375, 197, 413)(160, 376, 198, 414)(161, 377, 199, 415)(162, 378, 200, 416)(163, 379, 201, 417)(164, 380, 202, 418)(165, 381, 203, 419)(166, 382, 204, 420)(167, 383, 205, 421)(168, 384, 206, 422)(170, 386, 207, 423)(171, 387, 208, 424)(172, 388, 209, 425)(173, 389, 210, 426)(175, 391, 211, 427)(176, 392, 212, 428)(179, 395, 215, 431)(180, 396, 216, 432)(183, 399, 214, 430)(184, 400, 213, 429)
	L = (1, 218)(2, 221)(3, 223)(4, 217)(5, 227)(6, 229)(7, 231)(8, 219)(9, 234)(10, 220)(11, 236)(12, 224)(13, 225)(14, 222)(15, 241)(16, 239)(17, 240)(18, 243)(19, 226)(20, 245)(21, 230)(22, 228)(23, 233)(24, 248)(25, 249)(26, 232)(27, 251)(28, 235)(29, 253)(30, 238)(31, 237)(32, 256)(33, 257)(34, 242)(35, 259)(36, 244)(37, 261)(38, 247)(39, 246)(40, 264)(41, 265)(42, 250)(43, 267)(44, 252)(45, 269)(46, 255)(47, 254)(48, 272)(49, 273)(50, 258)(51, 275)(52, 260)(53, 277)(54, 263)(55, 262)(56, 280)(57, 281)(58, 266)(59, 283)(60, 268)(61, 317)(62, 271)(63, 270)(64, 319)(65, 321)(66, 274)(67, 323)(68, 276)(69, 279)(70, 297)(71, 289)(72, 294)(73, 282)(74, 284)(75, 287)(76, 298)(77, 291)(78, 285)(79, 290)(80, 302)(81, 278)(82, 286)(83, 295)(84, 293)(85, 306)(86, 288)(87, 300)(88, 299)(89, 310)(90, 292)(91, 304)(92, 303)(93, 314)(94, 296)(95, 308)(96, 307)(97, 320)(98, 301)(99, 312)(100, 311)(101, 325)(102, 346)(103, 333)(104, 305)(105, 326)(106, 316)(107, 327)(108, 315)(109, 328)(110, 329)(111, 331)(112, 332)(113, 335)(114, 334)(115, 336)(116, 337)(117, 330)(118, 338)(119, 339)(120, 340)(121, 341)(122, 342)(123, 343)(124, 344)(125, 345)(126, 347)(127, 348)(128, 349)(129, 350)(130, 309)(131, 352)(132, 353)(133, 354)(134, 357)(135, 313)(136, 358)(137, 361)(138, 362)(139, 351)(140, 318)(141, 393)(142, 385)(143, 324)(144, 322)(145, 397)(146, 398)(147, 356)(148, 355)(149, 360)(150, 359)(151, 364)(152, 363)(153, 366)(154, 365)(155, 368)(156, 367)(157, 370)(158, 369)(159, 372)(160, 371)(161, 374)(162, 373)(163, 376)(164, 375)(165, 378)(166, 377)(167, 380)(168, 379)(169, 390)(170, 382)(171, 381)(172, 384)(173, 383)(174, 394)(175, 387)(176, 386)(177, 401)(178, 402)(179, 389)(180, 388)(181, 403)(182, 404)(183, 392)(184, 391)(185, 405)(186, 406)(187, 407)(188, 408)(189, 409)(190, 410)(191, 411)(192, 412)(193, 413)(194, 414)(195, 415)(196, 416)(197, 417)(198, 418)(199, 419)(200, 420)(201, 421)(202, 422)(203, 423)(204, 424)(205, 425)(206, 426)(207, 427)(208, 428)(209, 431)(210, 432)(211, 430)(212, 429)(213, 396)(214, 395)(215, 400)(216, 399)
	local type(s) :: { ( 4, 108, 4, 108 ) }
Outer automorphisms :: reflexible
Dual of E27.2264
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 108 e = 216 f = 56
	degree seq :: [ 4^108 ]

E27.2269 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^108 ]
Map::
	R = (1, 217, 2, 218)(3, 219, 7, 223)(4, 220, 9, 225)(5, 221, 10, 226)(6, 222, 12, 228)(8, 224, 11, 227)(13, 229, 17, 233)(14, 230, 18, 234)(15, 231, 19, 235)(16, 232, 20, 236)(21, 237, 25, 241)(22, 238, 26, 242)(23, 239, 27, 243)(24, 240, 28, 244)(29, 245, 33, 249)(30, 246, 34, 250)(31, 247, 35, 251)(32, 248, 36, 252)(37, 253, 61, 277)(38, 254, 63, 279)(39, 255, 65, 281)(40, 256, 69, 285)(41, 257, 71, 287)(42, 258, 74, 290)(43, 259, 76, 292)(44, 260, 79, 295)(45, 261, 66, 282)(46, 262, 77, 293)(47, 263, 68, 284)(48, 264, 72, 288)(49, 265, 85, 301)(50, 266, 87, 303)(51, 267, 89, 305)(52, 268, 91, 307)(53, 269, 93, 309)(54, 270, 95, 311)(55, 271, 97, 313)(56, 272, 99, 315)(57, 273, 101, 317)(58, 274, 103, 319)(59, 275, 105, 321)(60, 276, 107, 323)(62, 278, 109, 325)(64, 280, 111, 327)(67, 283, 113, 329)(70, 286, 117, 333)(73, 289, 119, 335)(75, 291, 122, 338)(78, 294, 124, 340)(80, 296, 127, 343)(81, 297, 114, 330)(82, 298, 125, 341)(83, 299, 116, 332)(84, 300, 120, 336)(86, 302, 133, 349)(88, 304, 135, 351)(90, 306, 137, 353)(92, 308, 139, 355)(94, 310, 141, 357)(96, 312, 143, 359)(98, 314, 145, 361)(100, 316, 147, 363)(102, 318, 149, 365)(104, 320, 151, 367)(106, 322, 153, 369)(108, 324, 155, 371)(110, 326, 157, 373)(112, 328, 159, 375)(115, 331, 161, 377)(118, 334, 165, 381)(121, 337, 167, 383)(123, 339, 170, 386)(126, 342, 172, 388)(128, 344, 175, 391)(129, 345, 162, 378)(130, 346, 173, 389)(131, 347, 164, 380)(132, 348, 168, 384)(134, 350, 181, 397)(136, 352, 183, 399)(138, 354, 185, 401)(140, 356, 187, 403)(142, 358, 189, 405)(144, 360, 191, 407)(146, 362, 193, 409)(148, 364, 195, 411)(150, 366, 197, 413)(152, 368, 199, 415)(154, 370, 201, 417)(156, 372, 203, 419)(158, 374, 205, 421)(160, 376, 207, 423)(163, 379, 209, 425)(166, 382, 211, 427)(169, 385, 213, 429)(171, 387, 215, 431)(174, 390, 206, 422)(176, 392, 208, 424)(177, 393, 210, 426)(178, 394, 216, 432)(179, 395, 212, 428)(180, 396, 214, 430)(182, 398, 204, 420)(184, 400, 202, 418)(186, 402, 200, 416)(188, 404, 198, 414)(190, 406, 194, 410)(192, 408, 196, 412)(433, 649, 435, 651, 440, 656, 436, 652)(434, 650, 437, 653, 443, 659, 438, 654)(439, 655, 445, 661, 441, 657, 446, 662)(442, 658, 447, 663, 444, 660, 448, 664)(449, 665, 453, 669, 450, 666, 454, 670)(451, 667, 455, 671, 452, 668, 456, 672)(457, 673, 461, 677, 458, 674, 462, 678)(459, 675, 463, 679, 460, 676, 464, 680)(465, 681, 469, 685, 466, 682, 470, 686)(467, 683, 477, 693, 468, 684, 479, 695)(471, 687, 498, 714, 478, 694, 500, 716)(472, 688, 493, 709, 480, 696, 495, 711)(473, 689, 504, 720, 474, 690, 501, 717)(475, 691, 509, 725, 476, 692, 497, 713)(481, 697, 506, 722, 482, 698, 503, 719)(483, 699, 511, 727, 484, 700, 508, 724)(485, 701, 519, 735, 486, 702, 517, 733)(487, 703, 523, 739, 488, 704, 521, 737)(489, 705, 527, 743, 490, 706, 525, 741)(491, 707, 531, 747, 492, 708, 529, 745)(494, 710, 535, 751, 496, 712, 533, 749)(499, 715, 546, 762, 514, 730, 548, 764)(502, 718, 541, 757, 516, 732, 543, 759)(505, 721, 552, 768, 507, 723, 549, 765)(510, 726, 557, 773, 512, 728, 545, 761)(513, 729, 539, 755, 515, 731, 537, 753)(518, 734, 554, 770, 520, 736, 551, 767)(522, 738, 559, 775, 524, 740, 556, 772)(526, 742, 567, 783, 528, 744, 565, 781)(530, 746, 571, 787, 532, 748, 569, 785)(534, 750, 575, 791, 536, 752, 573, 789)(538, 754, 579, 795, 540, 756, 577, 793)(542, 758, 583, 799, 544, 760, 581, 797)(547, 763, 594, 810, 562, 778, 596, 812)(550, 766, 589, 805, 564, 780, 591, 807)(553, 769, 600, 816, 555, 771, 597, 813)(558, 774, 605, 821, 560, 776, 593, 809)(561, 777, 587, 803, 563, 779, 585, 801)(566, 782, 602, 818, 568, 784, 599, 815)(570, 786, 607, 823, 572, 788, 604, 820)(574, 790, 615, 831, 576, 792, 613, 829)(578, 794, 619, 835, 580, 796, 617, 833)(582, 798, 623, 839, 584, 800, 621, 837)(586, 802, 627, 843, 588, 804, 625, 841)(590, 806, 631, 847, 592, 808, 629, 845)(595, 811, 642, 858, 610, 826, 644, 860)(598, 814, 637, 853, 612, 828, 639, 855)(601, 817, 646, 862, 603, 819, 643, 859)(606, 822, 648, 864, 608, 824, 641, 857)(609, 825, 635, 851, 611, 827, 633, 849)(614, 830, 647, 863, 616, 832, 645, 861)(618, 834, 640, 856, 620, 836, 638, 854)(622, 838, 634, 850, 624, 840, 636, 852)(626, 842, 630, 846, 628, 844, 632, 848)
	L = (1, 434)(2, 433)(3, 439)(4, 441)(5, 442)(6, 444)(7, 435)(8, 443)(9, 436)(10, 437)(11, 440)(12, 438)(13, 449)(14, 450)(15, 451)(16, 452)(17, 445)(18, 446)(19, 447)(20, 448)(21, 457)(22, 458)(23, 459)(24, 460)(25, 453)(26, 454)(27, 455)(28, 456)(29, 465)(30, 466)(31, 467)(32, 468)(33, 461)(34, 462)(35, 463)(36, 464)(37, 493)(38, 495)(39, 497)(40, 501)(41, 503)(42, 506)(43, 508)(44, 511)(45, 498)(46, 509)(47, 500)(48, 504)(49, 517)(50, 519)(51, 521)(52, 523)(53, 525)(54, 527)(55, 529)(56, 531)(57, 533)(58, 535)(59, 537)(60, 539)(61, 469)(62, 541)(63, 470)(64, 543)(65, 471)(66, 477)(67, 545)(68, 479)(69, 472)(70, 549)(71, 473)(72, 480)(73, 551)(74, 474)(75, 554)(76, 475)(77, 478)(78, 556)(79, 476)(80, 559)(81, 546)(82, 557)(83, 548)(84, 552)(85, 481)(86, 565)(87, 482)(88, 567)(89, 483)(90, 569)(91, 484)(92, 571)(93, 485)(94, 573)(95, 486)(96, 575)(97, 487)(98, 577)(99, 488)(100, 579)(101, 489)(102, 581)(103, 490)(104, 583)(105, 491)(106, 585)(107, 492)(108, 587)(109, 494)(110, 589)(111, 496)(112, 591)(113, 499)(114, 513)(115, 593)(116, 515)(117, 502)(118, 597)(119, 505)(120, 516)(121, 599)(122, 507)(123, 602)(124, 510)(125, 514)(126, 604)(127, 512)(128, 607)(129, 594)(130, 605)(131, 596)(132, 600)(133, 518)(134, 613)(135, 520)(136, 615)(137, 522)(138, 617)(139, 524)(140, 619)(141, 526)(142, 621)(143, 528)(144, 623)(145, 530)(146, 625)(147, 532)(148, 627)(149, 534)(150, 629)(151, 536)(152, 631)(153, 538)(154, 633)(155, 540)(156, 635)(157, 542)(158, 637)(159, 544)(160, 639)(161, 547)(162, 561)(163, 641)(164, 563)(165, 550)(166, 643)(167, 553)(168, 564)(169, 645)(170, 555)(171, 647)(172, 558)(173, 562)(174, 638)(175, 560)(176, 640)(177, 642)(178, 648)(179, 644)(180, 646)(181, 566)(182, 636)(183, 568)(184, 634)(185, 570)(186, 632)(187, 572)(188, 630)(189, 574)(190, 626)(191, 576)(192, 628)(193, 578)(194, 622)(195, 580)(196, 624)(197, 582)(198, 620)(199, 584)(200, 618)(201, 586)(202, 616)(203, 588)(204, 614)(205, 590)(206, 606)(207, 592)(208, 608)(209, 595)(210, 609)(211, 598)(212, 611)(213, 601)(214, 612)(215, 603)(216, 610)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 2, 216, 2, 216 ), ( 2, 216, 2, 216, 2, 216, 2, 216 ) }
Outer automorphisms :: reflexible
Dual of E27.2272
Graph:: bipartite
	v = 162 e = 432 f = 218
	degree seq :: [ 4^108, 8^54 ]

E27.2270 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^53 * Y1 * Y2^-1 * Y1^-1 ]
Map::
	R = (1, 217, 2, 218, 6, 222, 4, 220)(3, 219, 9, 225, 13, 229, 8, 224)(5, 221, 11, 227, 14, 230, 7, 223)(10, 226, 16, 232, 21, 237, 17, 233)(12, 228, 15, 231, 22, 238, 19, 235)(18, 234, 25, 241, 29, 245, 24, 240)(20, 236, 27, 243, 30, 246, 23, 239)(26, 242, 32, 248, 37, 253, 33, 249)(28, 244, 31, 247, 38, 254, 35, 251)(34, 250, 41, 257, 45, 261, 40, 256)(36, 252, 43, 259, 46, 262, 39, 255)(42, 258, 48, 264, 53, 269, 49, 265)(44, 260, 47, 263, 54, 270, 51, 267)(50, 266, 57, 273, 61, 277, 56, 272)(52, 268, 59, 275, 62, 278, 55, 271)(58, 274, 64, 280, 73, 289, 65, 281)(60, 276, 63, 279, 102, 318, 67, 283)(66, 282, 104, 320, 69, 285, 107, 323)(68, 284, 70, 286, 109, 325, 72, 288)(71, 287, 111, 327, 77, 293, 113, 329)(74, 290, 116, 332, 76, 292, 118, 334)(75, 291, 119, 335, 81, 297, 121, 337)(78, 294, 124, 340, 80, 296, 126, 342)(79, 295, 127, 343, 85, 301, 129, 345)(82, 298, 132, 348, 84, 300, 134, 350)(83, 299, 135, 351, 89, 305, 137, 353)(86, 302, 140, 356, 88, 304, 142, 358)(87, 303, 143, 359, 93, 309, 145, 361)(90, 306, 148, 364, 92, 308, 150, 366)(91, 307, 151, 367, 97, 313, 153, 369)(94, 310, 156, 372, 96, 312, 158, 374)(95, 311, 159, 375, 101, 317, 161, 377)(98, 314, 164, 380, 100, 316, 166, 382)(99, 315, 167, 383, 115, 331, 169, 385)(103, 319, 173, 389, 106, 322, 172, 388)(105, 321, 176, 392, 108, 324, 175, 391)(110, 326, 181, 397, 114, 330, 180, 396)(112, 328, 184, 400, 123, 339, 183, 399)(117, 333, 189, 405, 122, 338, 188, 404)(120, 336, 192, 408, 131, 347, 191, 407)(125, 341, 197, 413, 130, 346, 196, 412)(128, 344, 200, 416, 139, 355, 199, 415)(133, 349, 205, 421, 138, 354, 204, 420)(136, 352, 208, 424, 147, 363, 207, 423)(141, 357, 213, 429, 146, 362, 212, 428)(144, 360, 215, 431, 155, 371, 214, 430)(149, 365, 209, 425, 154, 370, 216, 432)(152, 368, 206, 422, 163, 379, 210, 426)(157, 373, 211, 427, 162, 378, 201, 417)(160, 376, 202, 418, 171, 387, 198, 414)(165, 381, 193, 409, 170, 386, 203, 419)(168, 384, 190, 406, 187, 403, 194, 410)(174, 390, 195, 411, 178, 394, 185, 401)(177, 393, 186, 402, 179, 395, 182, 398)(433, 649, 435, 651, 442, 658, 450, 666, 458, 674, 466, 682, 474, 690, 482, 698, 490, 706, 498, 714, 509, 725, 513, 729, 517, 733, 521, 737, 525, 741, 529, 745, 533, 749, 547, 763, 540, 756, 544, 760, 552, 768, 560, 776, 568, 784, 576, 792, 584, 800, 592, 808, 600, 816, 609, 825, 627, 843, 635, 851, 643, 859, 648, 864, 645, 861, 636, 852, 629, 845, 620, 836, 613, 829, 605, 821, 598, 814, 588, 804, 582, 798, 572, 788, 566, 782, 556, 772, 550, 766, 541, 757, 534, 750, 494, 710, 486, 702, 478, 694, 470, 686, 462, 678, 454, 670, 446, 662, 438, 654, 445, 661, 453, 669, 461, 677, 469, 685, 477, 693, 485, 701, 493, 709, 505, 721, 501, 717, 503, 719, 507, 723, 511, 727, 515, 731, 519, 735, 523, 739, 527, 743, 531, 747, 537, 753, 555, 771, 563, 779, 571, 787, 579, 795, 587, 803, 595, 811, 603, 819, 619, 835, 611, 827, 617, 833, 625, 841, 633, 849, 641, 857, 644, 860, 637, 853, 628, 844, 621, 837, 612, 828, 604, 820, 596, 812, 590, 806, 580, 796, 574, 790, 564, 780, 558, 774, 548, 764, 500, 716, 492, 708, 484, 700, 476, 692, 468, 684, 460, 676, 452, 668, 444, 660, 437, 653)(434, 650, 439, 655, 447, 663, 455, 671, 463, 679, 471, 687, 479, 695, 487, 703, 495, 711, 504, 720, 508, 724, 512, 728, 516, 732, 520, 736, 524, 740, 528, 744, 532, 748, 538, 754, 542, 758, 549, 765, 557, 773, 565, 781, 573, 789, 581, 797, 589, 805, 597, 813, 606, 822, 618, 834, 626, 842, 634, 850, 642, 858, 647, 863, 639, 855, 632, 848, 623, 839, 616, 832, 608, 824, 601, 817, 591, 807, 585, 801, 575, 791, 569, 785, 559, 775, 553, 769, 543, 759, 536, 752, 497, 713, 489, 705, 481, 697, 473, 689, 465, 681, 457, 673, 449, 665, 441, 657, 436, 652, 443, 659, 451, 667, 459, 675, 467, 683, 475, 691, 483, 699, 491, 707, 499, 715, 502, 718, 506, 722, 510, 726, 514, 730, 518, 734, 522, 738, 526, 742, 530, 746, 535, 751, 546, 762, 554, 770, 562, 778, 570, 786, 578, 794, 586, 802, 594, 810, 602, 818, 610, 826, 614, 830, 622, 838, 630, 846, 638, 854, 646, 862, 640, 856, 631, 847, 624, 840, 615, 831, 607, 823, 599, 815, 593, 809, 583, 799, 577, 793, 567, 783, 561, 777, 551, 767, 545, 761, 539, 755, 496, 712, 488, 704, 480, 696, 472, 688, 464, 680, 456, 672, 448, 664, 440, 656)
	L = (1, 435)(2, 439)(3, 442)(4, 443)(5, 433)(6, 445)(7, 447)(8, 434)(9, 436)(10, 450)(11, 451)(12, 437)(13, 453)(14, 438)(15, 455)(16, 440)(17, 441)(18, 458)(19, 459)(20, 444)(21, 461)(22, 446)(23, 463)(24, 448)(25, 449)(26, 466)(27, 467)(28, 452)(29, 469)(30, 454)(31, 471)(32, 456)(33, 457)(34, 474)(35, 475)(36, 460)(37, 477)(38, 462)(39, 479)(40, 464)(41, 465)(42, 482)(43, 483)(44, 468)(45, 485)(46, 470)(47, 487)(48, 472)(49, 473)(50, 490)(51, 491)(52, 476)(53, 493)(54, 478)(55, 495)(56, 480)(57, 481)(58, 498)(59, 499)(60, 484)(61, 505)(62, 486)(63, 504)(64, 488)(65, 489)(66, 509)(67, 502)(68, 492)(69, 503)(70, 506)(71, 507)(72, 508)(73, 501)(74, 510)(75, 511)(76, 512)(77, 513)(78, 514)(79, 515)(80, 516)(81, 517)(82, 518)(83, 519)(84, 520)(85, 521)(86, 522)(87, 523)(88, 524)(89, 525)(90, 526)(91, 527)(92, 528)(93, 529)(94, 530)(95, 531)(96, 532)(97, 533)(98, 535)(99, 537)(100, 538)(101, 547)(102, 494)(103, 546)(104, 497)(105, 555)(106, 542)(107, 496)(108, 544)(109, 534)(110, 549)(111, 536)(112, 552)(113, 539)(114, 554)(115, 540)(116, 500)(117, 557)(118, 541)(119, 545)(120, 560)(121, 543)(122, 562)(123, 563)(124, 550)(125, 565)(126, 548)(127, 553)(128, 568)(129, 551)(130, 570)(131, 571)(132, 558)(133, 573)(134, 556)(135, 561)(136, 576)(137, 559)(138, 578)(139, 579)(140, 566)(141, 581)(142, 564)(143, 569)(144, 584)(145, 567)(146, 586)(147, 587)(148, 574)(149, 589)(150, 572)(151, 577)(152, 592)(153, 575)(154, 594)(155, 595)(156, 582)(157, 597)(158, 580)(159, 585)(160, 600)(161, 583)(162, 602)(163, 603)(164, 590)(165, 606)(166, 588)(167, 593)(168, 609)(169, 591)(170, 610)(171, 619)(172, 596)(173, 598)(174, 618)(175, 599)(176, 601)(177, 627)(178, 614)(179, 617)(180, 604)(181, 605)(182, 622)(183, 607)(184, 608)(185, 625)(186, 626)(187, 611)(188, 613)(189, 612)(190, 630)(191, 616)(192, 615)(193, 633)(194, 634)(195, 635)(196, 621)(197, 620)(198, 638)(199, 624)(200, 623)(201, 641)(202, 642)(203, 643)(204, 629)(205, 628)(206, 646)(207, 632)(208, 631)(209, 644)(210, 647)(211, 648)(212, 637)(213, 636)(214, 640)(215, 639)(216, 645)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2271
Graph:: bipartite
	v = 56 e = 432 f = 324
	degree seq :: [ 8^54, 216^2 ]

E27.2271 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, Y3^51 * Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^108 ]
Map:: polytopal
	R = (1, 217)(2, 218)(3, 219)(4, 220)(5, 221)(6, 222)(7, 223)(8, 224)(9, 225)(10, 226)(11, 227)(12, 228)(13, 229)(14, 230)(15, 231)(16, 232)(17, 233)(18, 234)(19, 235)(20, 236)(21, 237)(22, 238)(23, 239)(24, 240)(25, 241)(26, 242)(27, 243)(28, 244)(29, 245)(30, 246)(31, 247)(32, 248)(33, 249)(34, 250)(35, 251)(36, 252)(37, 253)(38, 254)(39, 255)(40, 256)(41, 257)(42, 258)(43, 259)(44, 260)(45, 261)(46, 262)(47, 263)(48, 264)(49, 265)(50, 266)(51, 267)(52, 268)(53, 269)(54, 270)(55, 271)(56, 272)(57, 273)(58, 274)(59, 275)(60, 276)(61, 277)(62, 278)(63, 279)(64, 280)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 289)(74, 290)(75, 291)(76, 292)(77, 293)(78, 294)(79, 295)(80, 296)(81, 297)(82, 298)(83, 299)(84, 300)(85, 301)(86, 302)(87, 303)(88, 304)(89, 305)(90, 306)(91, 307)(92, 308)(93, 309)(94, 310)(95, 311)(96, 312)(97, 313)(98, 314)(99, 315)(100, 316)(101, 317)(102, 318)(103, 319)(104, 320)(105, 321)(106, 322)(107, 323)(108, 324)(109, 325)(110, 326)(111, 327)(112, 328)(113, 329)(114, 330)(115, 331)(116, 332)(117, 333)(118, 334)(119, 335)(120, 336)(121, 337)(122, 338)(123, 339)(124, 340)(125, 341)(126, 342)(127, 343)(128, 344)(129, 345)(130, 346)(131, 347)(132, 348)(133, 349)(134, 350)(135, 351)(136, 352)(137, 353)(138, 354)(139, 355)(140, 356)(141, 357)(142, 358)(143, 359)(144, 360)(145, 361)(146, 362)(147, 363)(148, 364)(149, 365)(150, 366)(151, 367)(152, 368)(153, 369)(154, 370)(155, 371)(156, 372)(157, 373)(158, 374)(159, 375)(160, 376)(161, 377)(162, 378)(163, 379)(164, 380)(165, 381)(166, 382)(167, 383)(168, 384)(169, 385)(170, 386)(171, 387)(172, 388)(173, 389)(174, 390)(175, 391)(176, 392)(177, 393)(178, 394)(179, 395)(180, 396)(181, 397)(182, 398)(183, 399)(184, 400)(185, 401)(186, 402)(187, 403)(188, 404)(189, 405)(190, 406)(191, 407)(192, 408)(193, 409)(194, 410)(195, 411)(196, 412)(197, 413)(198, 414)(199, 415)(200, 416)(201, 417)(202, 418)(203, 419)(204, 420)(205, 421)(206, 422)(207, 423)(208, 424)(209, 425)(210, 426)(211, 427)(212, 428)(213, 429)(214, 430)(215, 431)(216, 432)(433, 649, 434, 650)(435, 651, 439, 655)(436, 652, 441, 657)(437, 653, 443, 659)(438, 654, 445, 661)(440, 656, 446, 662)(442, 658, 444, 660)(447, 663, 452, 668)(448, 664, 455, 671)(449, 665, 457, 673)(450, 666, 453, 669)(451, 667, 459, 675)(454, 670, 461, 677)(456, 672, 463, 679)(458, 674, 464, 680)(460, 676, 462, 678)(465, 681, 471, 687)(466, 682, 473, 689)(467, 683, 469, 685)(468, 684, 475, 691)(470, 686, 477, 693)(472, 688, 479, 695)(474, 690, 480, 696)(476, 692, 478, 694)(481, 697, 487, 703)(482, 698, 489, 705)(483, 699, 485, 701)(484, 700, 491, 707)(486, 702, 493, 709)(488, 704, 495, 711)(490, 706, 496, 712)(492, 708, 494, 710)(497, 713, 510, 726)(498, 714, 539, 755)(499, 715, 541, 757)(500, 716, 506, 722)(501, 717, 543, 759)(502, 718, 545, 761)(503, 719, 547, 763)(504, 720, 549, 765)(505, 721, 551, 767)(507, 723, 554, 770)(508, 724, 556, 772)(509, 725, 558, 774)(511, 727, 561, 777)(512, 728, 563, 779)(513, 729, 565, 781)(514, 730, 567, 783)(515, 731, 569, 785)(516, 732, 571, 787)(517, 733, 573, 789)(518, 734, 575, 791)(519, 735, 577, 793)(520, 736, 579, 795)(521, 737, 581, 797)(522, 738, 583, 799)(523, 739, 585, 801)(524, 740, 587, 803)(525, 741, 589, 805)(526, 742, 591, 807)(527, 743, 593, 809)(528, 744, 595, 811)(529, 745, 597, 813)(530, 746, 599, 815)(531, 747, 601, 817)(532, 748, 603, 819)(533, 749, 605, 821)(534, 750, 607, 823)(535, 751, 609, 825)(536, 752, 611, 827)(537, 753, 613, 829)(538, 754, 615, 831)(540, 756, 617, 833)(542, 758, 619, 835)(544, 760, 621, 837)(546, 762, 623, 839)(548, 764, 625, 841)(550, 766, 627, 843)(552, 768, 629, 845)(553, 769, 631, 847)(555, 771, 633, 849)(557, 773, 635, 851)(559, 775, 637, 853)(560, 776, 639, 855)(562, 778, 636, 852)(564, 780, 641, 857)(566, 782, 643, 859)(568, 784, 638, 854)(570, 786, 645, 861)(572, 788, 647, 863)(574, 790, 642, 858)(576, 792, 646, 862)(578, 794, 624, 840)(580, 796, 626, 842)(582, 798, 622, 838)(584, 800, 630, 846)(586, 802, 634, 850)(588, 804, 648, 864)(590, 806, 618, 834)(592, 808, 644, 860)(594, 810, 620, 836)(596, 812, 628, 844)(598, 814, 640, 856)(600, 816, 632, 848)(602, 818, 606, 822)(604, 820, 610, 826)(608, 824, 614, 830)(612, 828, 616, 832)
	L = (1, 435)(2, 437)(3, 440)(4, 433)(5, 444)(6, 434)(7, 447)(8, 449)(9, 450)(10, 436)(11, 452)(12, 454)(13, 455)(14, 438)(15, 441)(16, 439)(17, 458)(18, 459)(19, 442)(20, 445)(21, 443)(22, 462)(23, 463)(24, 446)(25, 448)(26, 466)(27, 467)(28, 451)(29, 453)(30, 470)(31, 471)(32, 456)(33, 457)(34, 474)(35, 475)(36, 460)(37, 461)(38, 478)(39, 479)(40, 464)(41, 465)(42, 482)(43, 483)(44, 468)(45, 469)(46, 486)(47, 487)(48, 472)(49, 473)(50, 490)(51, 491)(52, 476)(53, 477)(54, 494)(55, 495)(56, 480)(57, 481)(58, 498)(59, 499)(60, 484)(61, 485)(62, 507)(63, 510)(64, 488)(65, 489)(66, 516)(67, 506)(68, 492)(69, 503)(70, 505)(71, 508)(72, 501)(73, 511)(74, 502)(75, 513)(76, 514)(77, 515)(78, 504)(79, 517)(80, 518)(81, 509)(82, 519)(83, 520)(84, 512)(85, 521)(86, 522)(87, 523)(88, 524)(89, 525)(90, 526)(91, 527)(92, 528)(93, 529)(94, 530)(95, 531)(96, 532)(97, 533)(98, 534)(99, 535)(100, 536)(101, 537)(102, 538)(103, 540)(104, 542)(105, 555)(106, 560)(107, 497)(108, 572)(109, 493)(110, 553)(111, 539)(112, 548)(113, 554)(114, 552)(115, 571)(116, 557)(117, 496)(118, 544)(119, 565)(120, 562)(121, 546)(122, 541)(123, 566)(124, 563)(125, 568)(126, 545)(127, 570)(128, 550)(129, 558)(130, 574)(131, 543)(132, 576)(133, 500)(134, 559)(135, 575)(136, 578)(137, 551)(138, 580)(139, 549)(140, 564)(141, 569)(142, 582)(143, 547)(144, 584)(145, 583)(146, 586)(147, 561)(148, 588)(149, 579)(150, 590)(151, 556)(152, 592)(153, 591)(154, 594)(155, 573)(156, 596)(157, 587)(158, 598)(159, 567)(160, 600)(161, 599)(162, 602)(163, 581)(164, 604)(165, 595)(166, 606)(167, 577)(168, 608)(169, 607)(170, 610)(171, 589)(172, 612)(173, 603)(174, 614)(175, 585)(176, 616)(177, 615)(178, 618)(179, 597)(180, 620)(181, 611)(182, 634)(183, 593)(184, 640)(185, 639)(186, 648)(187, 605)(188, 632)(189, 617)(190, 626)(191, 633)(192, 630)(193, 647)(194, 636)(195, 609)(196, 622)(197, 643)(198, 635)(199, 613)(200, 624)(201, 619)(202, 644)(203, 641)(204, 637)(205, 623)(206, 646)(207, 601)(208, 628)(209, 621)(210, 645)(211, 631)(212, 638)(213, 629)(214, 625)(215, 627)(216, 642)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 8, 216 ), ( 8, 216, 8, 216 ) }
Outer automorphisms :: reflexible
Dual of E27.2270
Graph:: simple bipartite
	v = 324 e = 432 f = 56
	degree seq :: [ 2^216, 4^108 ]

E27.2272 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1^25 * Y3 * Y1^-27 ]
Map::
	R = (1, 217, 2, 218, 5, 221, 11, 227, 20, 236, 29, 245, 37, 253, 45, 261, 53, 269, 61, 277, 71, 287, 75, 291, 80, 296, 85, 301, 89, 305, 93, 309, 97, 313, 102, 318, 139, 355, 147, 363, 151, 367, 155, 371, 159, 375, 163, 379, 167, 383, 172, 388, 179, 395, 213, 429, 212, 428, 208, 424, 204, 420, 200, 416, 196, 412, 192, 408, 188, 404, 183, 399, 145, 361, 138, 354, 133, 349, 128, 344, 124, 340, 120, 336, 116, 332, 111, 327, 108, 324, 107, 323, 105, 321, 66, 282, 58, 274, 50, 266, 42, 258, 34, 250, 26, 242, 16, 232, 23, 239, 17, 233, 24, 240, 32, 248, 40, 256, 48, 264, 56, 272, 64, 280, 72, 288, 76, 292, 73, 289, 77, 293, 81, 297, 86, 302, 90, 306, 94, 310, 98, 314, 103, 319, 140, 356, 148, 364, 152, 368, 156, 372, 160, 376, 164, 380, 168, 384, 173, 389, 180, 396, 214, 430, 211, 427, 207, 423, 203, 419, 199, 415, 195, 411, 191, 407, 187, 403, 181, 397, 174, 390, 169, 385, 143, 359, 136, 352, 131, 347, 127, 343, 123, 339, 119, 335, 115, 331, 68, 284, 60, 276, 52, 268, 44, 260, 36, 252, 28, 244, 19, 235, 10, 226, 4, 220)(3, 219, 7, 223, 15, 231, 25, 241, 33, 249, 41, 257, 49, 265, 57, 273, 65, 281, 69, 285, 78, 294, 74, 290, 87, 303, 84, 300, 95, 311, 92, 308, 104, 320, 100, 316, 137, 353, 146, 362, 149, 365, 154, 370, 157, 373, 162, 378, 165, 381, 171, 387, 175, 391, 184, 400, 216, 432, 209, 425, 206, 422, 201, 417, 198, 414, 193, 409, 190, 406, 185, 401, 178, 394, 141, 357, 135, 351, 129, 345, 126, 342, 121, 337, 118, 334, 112, 328, 110, 326, 101, 317, 63, 279, 54, 270, 47, 263, 38, 254, 31, 247, 21, 237, 14, 230, 6, 222, 13, 229, 9, 225, 18, 234, 27, 243, 35, 251, 43, 259, 51, 267, 59, 275, 67, 283, 82, 298, 70, 286, 83, 299, 79, 295, 91, 307, 88, 304, 99, 315, 96, 312, 132, 348, 106, 322, 144, 360, 150, 366, 153, 369, 158, 374, 161, 377, 166, 382, 170, 386, 176, 392, 182, 398, 215, 431, 210, 426, 205, 421, 202, 418, 197, 413, 194, 410, 189, 405, 186, 402, 177, 393, 142, 358, 134, 350, 130, 346, 125, 341, 122, 338, 117, 333, 114, 330, 109, 325, 113, 329, 62, 278, 55, 271, 46, 262, 39, 255, 30, 246, 22, 238, 12, 228, 8, 224)(433, 649)(434, 650)(435, 651)(436, 652)(437, 653)(438, 654)(439, 655)(440, 656)(441, 657)(442, 658)(443, 659)(444, 660)(445, 661)(446, 662)(447, 663)(448, 664)(449, 665)(450, 666)(451, 667)(452, 668)(453, 669)(454, 670)(455, 671)(456, 672)(457, 673)(458, 674)(459, 675)(460, 676)(461, 677)(462, 678)(463, 679)(464, 680)(465, 681)(466, 682)(467, 683)(468, 684)(469, 685)(470, 686)(471, 687)(472, 688)(473, 689)(474, 690)(475, 691)(476, 692)(477, 693)(478, 694)(479, 695)(480, 696)(481, 697)(482, 698)(483, 699)(484, 700)(485, 701)(486, 702)(487, 703)(488, 704)(489, 705)(490, 706)(491, 707)(492, 708)(493, 709)(494, 710)(495, 711)(496, 712)(497, 713)(498, 714)(499, 715)(500, 716)(501, 717)(502, 718)(503, 719)(504, 720)(505, 721)(506, 722)(507, 723)(508, 724)(509, 725)(510, 726)(511, 727)(512, 728)(513, 729)(514, 730)(515, 731)(516, 732)(517, 733)(518, 734)(519, 735)(520, 736)(521, 737)(522, 738)(523, 739)(524, 740)(525, 741)(526, 742)(527, 743)(528, 744)(529, 745)(530, 746)(531, 747)(532, 748)(533, 749)(534, 750)(535, 751)(536, 752)(537, 753)(538, 754)(539, 755)(540, 756)(541, 757)(542, 758)(543, 759)(544, 760)(545, 761)(546, 762)(547, 763)(548, 764)(549, 765)(550, 766)(551, 767)(552, 768)(553, 769)(554, 770)(555, 771)(556, 772)(557, 773)(558, 774)(559, 775)(560, 776)(561, 777)(562, 778)(563, 779)(564, 780)(565, 781)(566, 782)(567, 783)(568, 784)(569, 785)(570, 786)(571, 787)(572, 788)(573, 789)(574, 790)(575, 791)(576, 792)(577, 793)(578, 794)(579, 795)(580, 796)(581, 797)(582, 798)(583, 799)(584, 800)(585, 801)(586, 802)(587, 803)(588, 804)(589, 805)(590, 806)(591, 807)(592, 808)(593, 809)(594, 810)(595, 811)(596, 812)(597, 813)(598, 814)(599, 815)(600, 816)(601, 817)(602, 818)(603, 819)(604, 820)(605, 821)(606, 822)(607, 823)(608, 824)(609, 825)(610, 826)(611, 827)(612, 828)(613, 829)(614, 830)(615, 831)(616, 832)(617, 833)(618, 834)(619, 835)(620, 836)(621, 837)(622, 838)(623, 839)(624, 840)(625, 841)(626, 842)(627, 843)(628, 844)(629, 845)(630, 846)(631, 847)(632, 848)(633, 849)(634, 850)(635, 851)(636, 852)(637, 853)(638, 854)(639, 855)(640, 856)(641, 857)(642, 858)(643, 859)(644, 860)(645, 861)(646, 862)(647, 863)(648, 864)
	L = (1, 435)(2, 438)(3, 433)(4, 441)(5, 444)(6, 434)(7, 448)(8, 449)(9, 436)(10, 447)(11, 453)(12, 437)(13, 455)(14, 456)(15, 442)(16, 439)(17, 440)(18, 458)(19, 459)(20, 462)(21, 443)(22, 464)(23, 445)(24, 446)(25, 466)(26, 450)(27, 451)(28, 465)(29, 470)(30, 452)(31, 472)(32, 454)(33, 460)(34, 457)(35, 474)(36, 475)(37, 478)(38, 461)(39, 480)(40, 463)(41, 482)(42, 467)(43, 468)(44, 481)(45, 486)(46, 469)(47, 488)(48, 471)(49, 476)(50, 473)(51, 490)(52, 491)(53, 494)(54, 477)(55, 496)(56, 479)(57, 498)(58, 483)(59, 484)(60, 497)(61, 533)(62, 485)(63, 504)(64, 487)(65, 492)(66, 489)(67, 537)(68, 514)(69, 539)(70, 540)(71, 541)(72, 495)(73, 542)(74, 543)(75, 544)(76, 545)(77, 546)(78, 547)(79, 548)(80, 549)(81, 550)(82, 500)(83, 551)(84, 552)(85, 553)(86, 554)(87, 555)(88, 556)(89, 557)(90, 558)(91, 559)(92, 560)(93, 561)(94, 562)(95, 563)(96, 565)(97, 566)(98, 567)(99, 568)(100, 570)(101, 493)(102, 573)(103, 574)(104, 575)(105, 499)(106, 577)(107, 501)(108, 502)(109, 503)(110, 505)(111, 506)(112, 507)(113, 508)(114, 509)(115, 510)(116, 511)(117, 512)(118, 513)(119, 515)(120, 516)(121, 517)(122, 518)(123, 519)(124, 520)(125, 521)(126, 522)(127, 523)(128, 524)(129, 525)(130, 526)(131, 527)(132, 601)(133, 528)(134, 529)(135, 530)(136, 531)(137, 606)(138, 532)(139, 609)(140, 610)(141, 534)(142, 535)(143, 536)(144, 613)(145, 538)(146, 615)(147, 617)(148, 618)(149, 619)(150, 620)(151, 621)(152, 622)(153, 623)(154, 624)(155, 625)(156, 626)(157, 627)(158, 628)(159, 629)(160, 630)(161, 631)(162, 632)(163, 633)(164, 634)(165, 635)(166, 636)(167, 637)(168, 638)(169, 564)(170, 639)(171, 640)(172, 641)(173, 642)(174, 569)(175, 643)(176, 644)(177, 571)(178, 572)(179, 647)(180, 648)(181, 576)(182, 646)(183, 578)(184, 645)(185, 579)(186, 580)(187, 581)(188, 582)(189, 583)(190, 584)(191, 585)(192, 586)(193, 587)(194, 588)(195, 589)(196, 590)(197, 591)(198, 592)(199, 593)(200, 594)(201, 595)(202, 596)(203, 597)(204, 598)(205, 599)(206, 600)(207, 602)(208, 603)(209, 604)(210, 605)(211, 607)(212, 608)(213, 616)(214, 614)(215, 611)(216, 612)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2269
Graph:: simple bipartite
	v = 218 e = 432 f = 162
	degree seq :: [ 2^216, 216^2 ]

E27.2273 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^49 * Y1 * Y2^-5 * Y1 ]
Map::
	R = (1, 217, 2, 218)(3, 219, 7, 223)(4, 220, 9, 225)(5, 221, 11, 227)(6, 222, 13, 229)(8, 224, 14, 230)(10, 226, 12, 228)(15, 231, 20, 236)(16, 232, 23, 239)(17, 233, 25, 241)(18, 234, 21, 237)(19, 235, 27, 243)(22, 238, 29, 245)(24, 240, 31, 247)(26, 242, 32, 248)(28, 244, 30, 246)(33, 249, 39, 255)(34, 250, 41, 257)(35, 251, 37, 253)(36, 252, 43, 259)(38, 254, 45, 261)(40, 256, 47, 263)(42, 258, 48, 264)(44, 260, 46, 262)(49, 265, 55, 271)(50, 266, 57, 273)(51, 267, 53, 269)(52, 268, 59, 275)(54, 270, 61, 277)(56, 272, 63, 279)(58, 274, 64, 280)(60, 276, 62, 278)(65, 281, 88, 304)(66, 282, 112, 328)(67, 283, 113, 329)(68, 284, 89, 305)(69, 285, 115, 331)(70, 286, 116, 332)(71, 287, 117, 333)(72, 288, 118, 334)(73, 289, 119, 335)(74, 290, 120, 336)(75, 291, 121, 337)(76, 292, 122, 338)(77, 293, 123, 339)(78, 294, 124, 340)(79, 295, 125, 341)(80, 296, 126, 342)(81, 297, 127, 343)(82, 298, 128, 344)(83, 299, 129, 345)(84, 300, 130, 346)(85, 301, 131, 347)(86, 302, 132, 348)(87, 303, 133, 349)(90, 306, 134, 350)(91, 307, 135, 351)(92, 308, 136, 352)(93, 309, 137, 353)(94, 310, 138, 354)(95, 311, 139, 355)(96, 312, 140, 356)(97, 313, 141, 357)(98, 314, 142, 358)(99, 315, 143, 359)(100, 316, 144, 360)(101, 317, 145, 361)(102, 318, 146, 362)(103, 319, 147, 363)(104, 320, 148, 364)(105, 321, 150, 366)(106, 322, 151, 367)(107, 323, 152, 368)(108, 324, 153, 369)(109, 325, 155, 371)(110, 326, 156, 372)(111, 327, 158, 374)(114, 330, 160, 376)(149, 365, 195, 411)(154, 370, 200, 416)(157, 373, 204, 420)(159, 375, 202, 418)(161, 377, 208, 424)(162, 378, 209, 425)(163, 379, 210, 426)(164, 380, 211, 427)(165, 381, 212, 428)(166, 382, 206, 422)(167, 383, 213, 429)(168, 384, 214, 430)(169, 385, 215, 431)(170, 386, 216, 432)(171, 387, 205, 421)(172, 388, 207, 423)(173, 389, 203, 419)(174, 390, 201, 417)(175, 391, 199, 415)(176, 392, 198, 414)(177, 393, 196, 412)(178, 394, 197, 413)(179, 395, 193, 409)(180, 396, 194, 410)(181, 397, 192, 408)(182, 398, 191, 407)(183, 399, 190, 406)(184, 400, 189, 405)(185, 401, 187, 403)(186, 402, 188, 404)(433, 649, 435, 651, 440, 656, 449, 665, 458, 674, 466, 682, 474, 690, 482, 698, 490, 706, 498, 714, 509, 725, 502, 718, 507, 723, 513, 729, 523, 739, 526, 742, 531, 747, 534, 750, 539, 755, 542, 758, 589, 805, 602, 818, 596, 812, 604, 820, 607, 823, 612, 828, 615, 831, 620, 836, 623, 839, 629, 845, 633, 849, 646, 862, 642, 858, 638, 854, 592, 808, 585, 801, 580, 796, 576, 792, 572, 788, 568, 784, 563, 779, 556, 772, 550, 766, 547, 763, 549, 765, 554, 770, 545, 761, 493, 709, 485, 701, 477, 693, 469, 685, 461, 677, 453, 669, 443, 659, 452, 668, 445, 661, 455, 671, 463, 679, 471, 687, 479, 695, 487, 703, 495, 711, 520, 736, 516, 732, 505, 721, 514, 730, 506, 722, 515, 731, 522, 738, 527, 743, 530, 746, 535, 751, 538, 754, 543, 759, 591, 807, 601, 817, 597, 813, 603, 819, 608, 824, 611, 827, 616, 832, 619, 835, 624, 840, 628, 844, 635, 851, 645, 861, 641, 857, 640, 856, 632, 848, 627, 843, 587, 803, 582, 798, 577, 793, 573, 789, 569, 785, 565, 781, 557, 773, 564, 780, 558, 774, 500, 716, 492, 708, 484, 700, 476, 692, 468, 684, 460, 676, 451, 667, 442, 658, 436, 652)(434, 650, 437, 653, 444, 660, 454, 670, 462, 678, 470, 686, 478, 694, 486, 702, 494, 710, 508, 724, 512, 728, 501, 717, 511, 727, 510, 726, 525, 741, 524, 740, 533, 749, 532, 748, 541, 757, 540, 756, 586, 802, 598, 814, 594, 810, 600, 816, 605, 821, 610, 826, 613, 829, 618, 834, 621, 837, 626, 842, 630, 846, 639, 855, 644, 860, 648, 864, 634, 850, 588, 804, 583, 799, 578, 794, 574, 790, 570, 786, 566, 782, 559, 775, 552, 768, 548, 764, 551, 767, 544, 760, 497, 713, 489, 705, 481, 697, 473, 689, 465, 681, 457, 673, 448, 664, 439, 655, 447, 663, 441, 657, 450, 666, 459, 675, 467, 683, 475, 691, 483, 699, 491, 707, 499, 715, 521, 737, 503, 719, 518, 734, 504, 720, 519, 735, 517, 733, 529, 745, 528, 744, 537, 753, 536, 752, 581, 797, 546, 762, 593, 809, 595, 811, 599, 815, 606, 822, 609, 825, 614, 830, 617, 833, 622, 838, 625, 841, 631, 847, 637, 853, 643, 859, 647, 863, 636, 852, 590, 806, 584, 800, 579, 795, 575, 791, 571, 787, 567, 783, 561, 777, 553, 769, 560, 776, 555, 771, 562, 778, 496, 712, 488, 704, 480, 696, 472, 688, 464, 680, 456, 672, 446, 662, 438, 654)
	L = (1, 434)(2, 433)(3, 439)(4, 441)(5, 443)(6, 445)(7, 435)(8, 446)(9, 436)(10, 444)(11, 437)(12, 442)(13, 438)(14, 440)(15, 452)(16, 455)(17, 457)(18, 453)(19, 459)(20, 447)(21, 450)(22, 461)(23, 448)(24, 463)(25, 449)(26, 464)(27, 451)(28, 462)(29, 454)(30, 460)(31, 456)(32, 458)(33, 471)(34, 473)(35, 469)(36, 475)(37, 467)(38, 477)(39, 465)(40, 479)(41, 466)(42, 480)(43, 468)(44, 478)(45, 470)(46, 476)(47, 472)(48, 474)(49, 487)(50, 489)(51, 485)(52, 491)(53, 483)(54, 493)(55, 481)(56, 495)(57, 482)(58, 496)(59, 484)(60, 494)(61, 486)(62, 492)(63, 488)(64, 490)(65, 520)(66, 544)(67, 545)(68, 521)(69, 547)(70, 548)(71, 549)(72, 550)(73, 551)(74, 552)(75, 553)(76, 554)(77, 555)(78, 556)(79, 557)(80, 558)(81, 559)(82, 560)(83, 561)(84, 562)(85, 563)(86, 564)(87, 565)(88, 497)(89, 500)(90, 566)(91, 567)(92, 568)(93, 569)(94, 570)(95, 571)(96, 572)(97, 573)(98, 574)(99, 575)(100, 576)(101, 577)(102, 578)(103, 579)(104, 580)(105, 582)(106, 583)(107, 584)(108, 585)(109, 587)(110, 588)(111, 590)(112, 498)(113, 499)(114, 592)(115, 501)(116, 502)(117, 503)(118, 504)(119, 505)(120, 506)(121, 507)(122, 508)(123, 509)(124, 510)(125, 511)(126, 512)(127, 513)(128, 514)(129, 515)(130, 516)(131, 517)(132, 518)(133, 519)(134, 522)(135, 523)(136, 524)(137, 525)(138, 526)(139, 527)(140, 528)(141, 529)(142, 530)(143, 531)(144, 532)(145, 533)(146, 534)(147, 535)(148, 536)(149, 627)(150, 537)(151, 538)(152, 539)(153, 540)(154, 632)(155, 541)(156, 542)(157, 636)(158, 543)(159, 634)(160, 546)(161, 640)(162, 641)(163, 642)(164, 643)(165, 644)(166, 638)(167, 645)(168, 646)(169, 647)(170, 648)(171, 637)(172, 639)(173, 635)(174, 633)(175, 631)(176, 630)(177, 628)(178, 629)(179, 625)(180, 626)(181, 624)(182, 623)(183, 622)(184, 621)(185, 619)(186, 620)(187, 617)(188, 618)(189, 616)(190, 615)(191, 614)(192, 613)(193, 611)(194, 612)(195, 581)(196, 609)(197, 610)(198, 608)(199, 607)(200, 586)(201, 606)(202, 591)(203, 605)(204, 589)(205, 603)(206, 598)(207, 604)(208, 593)(209, 594)(210, 595)(211, 596)(212, 597)(213, 599)(214, 600)(215, 601)(216, 602)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2274
Graph:: bipartite
	v = 110 e = 432 f = 270
	degree seq :: [ 4^108, 216^2 ]

E27.2274 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 108})
Quotient :: dipole
Aut^+ = C4 x D54 (small group id <216, 5>)
Aut   = $<432, 47>$ (small group id <432, 47>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-54 * Y1^-1, (Y3 * Y2^-1)^108 ]
Map::
	R = (1, 217, 2, 218, 6, 222, 4, 220)(3, 219, 9, 225, 13, 229, 8, 224)(5, 221, 11, 227, 14, 230, 7, 223)(10, 226, 16, 232, 21, 237, 17, 233)(12, 228, 15, 231, 22, 238, 19, 235)(18, 234, 25, 241, 29, 245, 24, 240)(20, 236, 27, 243, 30, 246, 23, 239)(26, 242, 32, 248, 37, 253, 33, 249)(28, 244, 31, 247, 38, 254, 35, 251)(34, 250, 41, 257, 45, 261, 40, 256)(36, 252, 43, 259, 46, 262, 39, 255)(42, 258, 48, 264, 53, 269, 49, 265)(44, 260, 47, 263, 54, 270, 51, 267)(50, 266, 57, 273, 61, 277, 56, 272)(52, 268, 59, 275, 62, 278, 55, 271)(58, 274, 64, 280, 101, 317, 65, 281)(60, 276, 63, 279, 74, 290, 67, 283)(66, 282, 69, 285, 109, 325, 72, 288)(68, 284, 107, 323, 71, 287, 103, 319)(70, 286, 110, 326, 77, 293, 105, 321)(73, 289, 111, 327, 76, 292, 112, 328)(75, 291, 113, 329, 81, 297, 114, 330)(78, 294, 115, 331, 80, 296, 116, 332)(79, 295, 117, 333, 85, 301, 118, 334)(82, 298, 119, 335, 84, 300, 120, 336)(83, 299, 121, 337, 89, 305, 122, 338)(86, 302, 123, 339, 88, 304, 124, 340)(87, 303, 125, 341, 93, 309, 126, 342)(90, 306, 127, 343, 92, 308, 128, 344)(91, 307, 129, 345, 97, 313, 130, 346)(94, 310, 131, 347, 96, 312, 132, 348)(95, 311, 133, 349, 102, 318, 134, 350)(98, 314, 136, 352, 100, 316, 137, 353)(99, 315, 138, 354, 135, 351, 139, 355)(104, 320, 142, 358, 108, 324, 143, 359)(106, 322, 146, 362, 140, 356, 147, 363)(141, 357, 177, 393, 144, 360, 178, 394)(145, 361, 181, 397, 148, 364, 182, 398)(149, 365, 185, 401, 150, 366, 186, 402)(151, 367, 187, 403, 152, 368, 188, 404)(153, 369, 189, 405, 154, 370, 190, 406)(155, 371, 191, 407, 156, 372, 192, 408)(157, 373, 193, 409, 158, 374, 194, 410)(159, 375, 195, 411, 160, 376, 196, 412)(161, 377, 197, 413, 162, 378, 198, 414)(163, 379, 199, 415, 164, 380, 200, 416)(165, 381, 201, 417, 166, 382, 202, 418)(167, 383, 203, 419, 168, 384, 204, 420)(169, 385, 205, 421, 170, 386, 206, 422)(171, 387, 207, 423, 172, 388, 208, 424)(173, 389, 209, 425, 174, 390, 210, 426)(175, 391, 211, 427, 176, 392, 212, 428)(179, 395, 215, 431, 180, 396, 216, 432)(183, 399, 213, 429, 184, 400, 214, 430)(433, 649)(434, 650)(435, 651)(436, 652)(437, 653)(438, 654)(439, 655)(440, 656)(441, 657)(442, 658)(443, 659)(444, 660)(445, 661)(446, 662)(447, 663)(448, 664)(449, 665)(450, 666)(451, 667)(452, 668)(453, 669)(454, 670)(455, 671)(456, 672)(457, 673)(458, 674)(459, 675)(460, 676)(461, 677)(462, 678)(463, 679)(464, 680)(465, 681)(466, 682)(467, 683)(468, 684)(469, 685)(470, 686)(471, 687)(472, 688)(473, 689)(474, 690)(475, 691)(476, 692)(477, 693)(478, 694)(479, 695)(480, 696)(481, 697)(482, 698)(483, 699)(484, 700)(485, 701)(486, 702)(487, 703)(488, 704)(489, 705)(490, 706)(491, 707)(492, 708)(493, 709)(494, 710)(495, 711)(496, 712)(497, 713)(498, 714)(499, 715)(500, 716)(501, 717)(502, 718)(503, 719)(504, 720)(505, 721)(506, 722)(507, 723)(508, 724)(509, 725)(510, 726)(511, 727)(512, 728)(513, 729)(514, 730)(515, 731)(516, 732)(517, 733)(518, 734)(519, 735)(520, 736)(521, 737)(522, 738)(523, 739)(524, 740)(525, 741)(526, 742)(527, 743)(528, 744)(529, 745)(530, 746)(531, 747)(532, 748)(533, 749)(534, 750)(535, 751)(536, 752)(537, 753)(538, 754)(539, 755)(540, 756)(541, 757)(542, 758)(543, 759)(544, 760)(545, 761)(546, 762)(547, 763)(548, 764)(549, 765)(550, 766)(551, 767)(552, 768)(553, 769)(554, 770)(555, 771)(556, 772)(557, 773)(558, 774)(559, 775)(560, 776)(561, 777)(562, 778)(563, 779)(564, 780)(565, 781)(566, 782)(567, 783)(568, 784)(569, 785)(570, 786)(571, 787)(572, 788)(573, 789)(574, 790)(575, 791)(576, 792)(577, 793)(578, 794)(579, 795)(580, 796)(581, 797)(582, 798)(583, 799)(584, 800)(585, 801)(586, 802)(587, 803)(588, 804)(589, 805)(590, 806)(591, 807)(592, 808)(593, 809)(594, 810)(595, 811)(596, 812)(597, 813)(598, 814)(599, 815)(600, 816)(601, 817)(602, 818)(603, 819)(604, 820)(605, 821)(606, 822)(607, 823)(608, 824)(609, 825)(610, 826)(611, 827)(612, 828)(613, 829)(614, 830)(615, 831)(616, 832)(617, 833)(618, 834)(619, 835)(620, 836)(621, 837)(622, 838)(623, 839)(624, 840)(625, 841)(626, 842)(627, 843)(628, 844)(629, 845)(630, 846)(631, 847)(632, 848)(633, 849)(634, 850)(635, 851)(636, 852)(637, 853)(638, 854)(639, 855)(640, 856)(641, 857)(642, 858)(643, 859)(644, 860)(645, 861)(646, 862)(647, 863)(648, 864)
	L = (1, 435)(2, 439)(3, 442)(4, 443)(5, 433)(6, 445)(7, 447)(8, 434)(9, 436)(10, 450)(11, 451)(12, 437)(13, 453)(14, 438)(15, 455)(16, 440)(17, 441)(18, 458)(19, 459)(20, 444)(21, 461)(22, 446)(23, 463)(24, 448)(25, 449)(26, 466)(27, 467)(28, 452)(29, 469)(30, 454)(31, 471)(32, 456)(33, 457)(34, 474)(35, 475)(36, 460)(37, 477)(38, 462)(39, 479)(40, 464)(41, 465)(42, 482)(43, 483)(44, 468)(45, 485)(46, 470)(47, 487)(48, 472)(49, 473)(50, 490)(51, 491)(52, 476)(53, 493)(54, 478)(55, 495)(56, 480)(57, 481)(58, 498)(59, 499)(60, 484)(61, 533)(62, 486)(63, 535)(64, 488)(65, 489)(66, 537)(67, 539)(68, 492)(69, 497)(70, 504)(71, 506)(72, 496)(73, 503)(74, 494)(75, 509)(76, 500)(77, 501)(78, 508)(79, 513)(80, 505)(81, 502)(82, 512)(83, 517)(84, 510)(85, 507)(86, 516)(87, 521)(88, 514)(89, 511)(90, 520)(91, 525)(92, 518)(93, 515)(94, 524)(95, 529)(96, 522)(97, 519)(98, 528)(99, 534)(100, 526)(101, 541)(102, 523)(103, 544)(104, 532)(105, 546)(106, 567)(107, 543)(108, 530)(109, 542)(110, 545)(111, 547)(112, 548)(113, 549)(114, 550)(115, 551)(116, 552)(117, 553)(118, 554)(119, 555)(120, 556)(121, 557)(122, 558)(123, 559)(124, 560)(125, 561)(126, 562)(127, 563)(128, 564)(129, 565)(130, 566)(131, 568)(132, 569)(133, 570)(134, 571)(135, 527)(136, 574)(137, 575)(138, 578)(139, 579)(140, 531)(141, 540)(142, 609)(143, 610)(144, 536)(145, 572)(146, 613)(147, 614)(148, 538)(149, 573)(150, 576)(151, 577)(152, 580)(153, 582)(154, 581)(155, 584)(156, 583)(157, 586)(158, 585)(159, 588)(160, 587)(161, 590)(162, 589)(163, 592)(164, 591)(165, 594)(166, 593)(167, 596)(168, 595)(169, 598)(170, 597)(171, 600)(172, 599)(173, 602)(174, 601)(175, 604)(176, 603)(177, 618)(178, 617)(179, 606)(180, 605)(181, 620)(182, 619)(183, 608)(184, 607)(185, 621)(186, 622)(187, 623)(188, 624)(189, 625)(190, 626)(191, 627)(192, 628)(193, 629)(194, 630)(195, 631)(196, 632)(197, 633)(198, 634)(199, 635)(200, 636)(201, 637)(202, 638)(203, 639)(204, 640)(205, 641)(206, 642)(207, 643)(208, 644)(209, 647)(210, 648)(211, 645)(212, 646)(213, 612)(214, 611)(215, 616)(216, 615)(217, 649)(218, 650)(219, 651)(220, 652)(221, 653)(222, 654)(223, 655)(224, 656)(225, 657)(226, 658)(227, 659)(228, 660)(229, 661)(230, 662)(231, 663)(232, 664)(233, 665)(234, 666)(235, 667)(236, 668)(237, 669)(238, 670)(239, 671)(240, 672)(241, 673)(242, 674)(243, 675)(244, 676)(245, 677)(246, 678)(247, 679)(248, 680)(249, 681)(250, 682)(251, 683)(252, 684)(253, 685)(254, 686)(255, 687)(256, 688)(257, 689)(258, 690)(259, 691)(260, 692)(261, 693)(262, 694)(263, 695)(264, 696)(265, 697)(266, 698)(267, 699)(268, 700)(269, 701)(270, 702)(271, 703)(272, 704)(273, 705)(274, 706)(275, 707)(276, 708)(277, 709)(278, 710)(279, 711)(280, 712)(281, 713)(282, 714)(283, 715)(284, 716)(285, 717)(286, 718)(287, 719)(288, 720)(289, 721)(290, 722)(291, 723)(292, 724)(293, 725)(294, 726)(295, 727)(296, 728)(297, 729)(298, 730)(299, 731)(300, 732)(301, 733)(302, 734)(303, 735)(304, 736)(305, 737)(306, 738)(307, 739)(308, 740)(309, 741)(310, 742)(311, 743)(312, 744)(313, 745)(314, 746)(315, 747)(316, 748)(317, 749)(318, 750)(319, 751)(320, 752)(321, 753)(322, 754)(323, 755)(324, 756)(325, 757)(326, 758)(327, 759)(328, 760)(329, 761)(330, 762)(331, 763)(332, 764)(333, 765)(334, 766)(335, 767)(336, 768)(337, 769)(338, 770)(339, 771)(340, 772)(341, 773)(342, 774)(343, 775)(344, 776)(345, 777)(346, 778)(347, 779)(348, 780)(349, 781)(350, 782)(351, 783)(352, 784)(353, 785)(354, 786)(355, 787)(356, 788)(357, 789)(358, 790)(359, 791)(360, 792)(361, 793)(362, 794)(363, 795)(364, 796)(365, 797)(366, 798)(367, 799)(368, 800)(369, 801)(370, 802)(371, 803)(372, 804)(373, 805)(374, 806)(375, 807)(376, 808)(377, 809)(378, 810)(379, 811)(380, 812)(381, 813)(382, 814)(383, 815)(384, 816)(385, 817)(386, 818)(387, 819)(388, 820)(389, 821)(390, 822)(391, 823)(392, 824)(393, 825)(394, 826)(395, 827)(396, 828)(397, 829)(398, 830)(399, 831)(400, 832)(401, 833)(402, 834)(403, 835)(404, 836)(405, 837)(406, 838)(407, 839)(408, 840)(409, 841)(410, 842)(411, 843)(412, 844)(413, 845)(414, 846)(415, 847)(416, 848)(417, 849)(418, 850)(419, 851)(420, 852)(421, 853)(422, 854)(423, 855)(424, 856)(425, 857)(426, 858)(427, 859)(428, 860)(429, 861)(430, 862)(431, 863)(432, 864)
	local type(s) :: { ( 4, 216 ), ( 4, 216, 4, 216, 4, 216, 4, 216 ) }
Outer automorphisms :: reflexible
Dual of E27.2273
Graph:: simple bipartite
	v = 270 e = 432 f = 110
	degree seq :: [ 2^216, 8^54 ]

E27.2275 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 56})
Quotient :: regular
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^56 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 75, 80, 76, 81, 87, 94, 98, 102, 106, 111, 156, 172, 165, 169, 175, 179, 183, 187, 191, 196, 203, 223, 219, 213, 209, 207, 161, 154, 149, 144, 140, 136, 130, 123, 118, 115, 116, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 89, 70, 88, 72, 90, 85, 99, 96, 107, 104, 148, 114, 160, 162, 168, 173, 178, 181, 186, 189, 195, 199, 208, 221, 216, 211, 217, 202, 157, 151, 145, 142, 137, 132, 124, 121, 117, 120, 127, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 73, 84, 69, 83, 78, 95, 92, 103, 100, 112, 108, 153, 164, 163, 167, 174, 177, 182, 185, 190, 194, 200, 206, 222, 215, 212, 218, 201, 158, 150, 146, 141, 138, 131, 126, 119, 125, 122, 109, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 91, 82, 77, 71, 74, 79, 86, 93, 97, 101, 105, 110, 155, 171, 166, 170, 176, 180, 184, 188, 192, 197, 204, 224, 220, 214, 210, 205, 198, 193, 159, 152, 147, 143, 139, 135, 128, 133, 129, 134, 113, 66, 58, 50, 42, 34, 26)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 109)(63, 91)(67, 113)(68, 73)(69, 115)(70, 116)(71, 117)(72, 118)(74, 119)(75, 120)(76, 121)(77, 122)(78, 123)(79, 124)(80, 125)(81, 126)(82, 127)(83, 128)(84, 129)(85, 130)(86, 131)(87, 132)(88, 133)(89, 134)(90, 135)(92, 136)(93, 137)(94, 138)(95, 139)(96, 140)(97, 141)(98, 142)(99, 143)(100, 144)(101, 145)(102, 146)(103, 147)(104, 149)(105, 150)(106, 151)(107, 152)(108, 154)(110, 157)(111, 158)(112, 159)(114, 161)(148, 193)(153, 198)(155, 201)(156, 202)(160, 205)(162, 209)(163, 210)(164, 207)(165, 211)(166, 212)(167, 213)(168, 214)(169, 215)(170, 216)(171, 217)(172, 218)(173, 219)(174, 220)(175, 221)(176, 222)(177, 223)(178, 224)(179, 206)(180, 208)(181, 203)(182, 204)(183, 199)(184, 200)(185, 196)(186, 197)(187, 194)(188, 195)(189, 191)(190, 192)
	local type(s) :: { ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2276
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 4 e = 112 f = 56
	degree seq :: [ 56^4 ]

E27.2276 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 56})
Quotient :: regular
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^56 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 57, 38, 59)(39, 61, 41, 63)(40, 64, 44, 66)(42, 68, 43, 70)(45, 73, 46, 75)(47, 77, 48, 79)(49, 81, 50, 83)(51, 85, 52, 87)(53, 89, 54, 91)(55, 93, 56, 95)(58, 98, 60, 97)(62, 102, 67, 101)(65, 105, 72, 104)(69, 109, 71, 108)(74, 114, 76, 113)(78, 118, 80, 117)(82, 122, 84, 121)(86, 126, 88, 125)(90, 130, 92, 129)(94, 134, 96, 133)(99, 137, 100, 138)(103, 141, 107, 142)(106, 144, 112, 145)(110, 148, 111, 149)(115, 153, 116, 154)(119, 157, 120, 158)(123, 161, 124, 162)(127, 165, 128, 166)(131, 169, 132, 170)(135, 173, 136, 174)(139, 178, 140, 177)(143, 182, 147, 181)(146, 185, 152, 184)(150, 189, 151, 188)(155, 194, 156, 193)(159, 198, 160, 197)(163, 202, 164, 201)(167, 206, 168, 205)(171, 210, 172, 209)(175, 214, 176, 213)(179, 217, 180, 218)(183, 221, 187, 222)(186, 223, 192, 224)(190, 220, 191, 219)(195, 216, 196, 215)(199, 211, 200, 212)(203, 207, 204, 208)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 41)(40, 57)(42, 61)(43, 63)(44, 59)(45, 64)(46, 66)(47, 68)(48, 70)(49, 73)(50, 75)(51, 77)(52, 79)(53, 81)(54, 83)(55, 85)(56, 87)(58, 89)(60, 91)(62, 93)(65, 98)(67, 95)(69, 102)(71, 101)(72, 97)(74, 105)(76, 104)(78, 109)(80, 108)(82, 114)(84, 113)(86, 118)(88, 117)(90, 122)(92, 121)(94, 126)(96, 125)(99, 130)(100, 129)(103, 134)(106, 137)(107, 133)(110, 141)(111, 142)(112, 138)(115, 144)(116, 145)(119, 148)(120, 149)(123, 153)(124, 154)(127, 157)(128, 158)(131, 161)(132, 162)(135, 165)(136, 166)(139, 169)(140, 170)(143, 173)(146, 178)(147, 174)(150, 182)(151, 181)(152, 177)(155, 185)(156, 184)(159, 189)(160, 188)(163, 194)(164, 193)(167, 198)(168, 197)(171, 202)(172, 201)(175, 206)(176, 205)(179, 210)(180, 209)(183, 214)(186, 217)(187, 213)(190, 221)(191, 222)(192, 218)(195, 223)(196, 224)(199, 220)(200, 219)(203, 216)(204, 215)(207, 211)(208, 212)
	local type(s) :: { ( 56^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2275
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 56 e = 112 f = 4
	degree seq :: [ 4^56 ]

E27.2277 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^56 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 57, 36, 59)(39, 61, 42, 63)(40, 64, 45, 66)(41, 67, 43, 69)(44, 72, 46, 74)(47, 77, 48, 79)(49, 81, 50, 83)(51, 85, 52, 87)(53, 89, 54, 91)(55, 93, 56, 95)(58, 98, 60, 97)(62, 102, 70, 101)(65, 105, 75, 104)(68, 108, 71, 107)(73, 113, 76, 112)(78, 118, 80, 117)(82, 122, 84, 121)(86, 126, 88, 125)(90, 130, 92, 129)(94, 134, 96, 133)(99, 137, 100, 138)(103, 141, 110, 142)(106, 144, 115, 145)(109, 147, 111, 148)(114, 152, 116, 153)(119, 157, 120, 158)(123, 161, 124, 162)(127, 165, 128, 166)(131, 169, 132, 170)(135, 173, 136, 174)(139, 178, 140, 177)(143, 182, 150, 181)(146, 185, 155, 184)(149, 188, 151, 187)(154, 193, 156, 192)(159, 198, 160, 197)(163, 202, 164, 201)(167, 206, 168, 205)(171, 210, 172, 209)(175, 214, 176, 213)(179, 217, 180, 218)(183, 221, 190, 222)(186, 223, 195, 224)(189, 220, 191, 219)(194, 216, 196, 215)(199, 211, 200, 212)(203, 207, 204, 208)(225, 226)(227, 231)(228, 233)(229, 234)(230, 236)(232, 235)(237, 241)(238, 242)(239, 243)(240, 244)(245, 249)(246, 250)(247, 251)(248, 252)(253, 257)(254, 258)(255, 259)(256, 260)(261, 263)(262, 266)(264, 281)(265, 285)(267, 287)(268, 288)(269, 283)(270, 290)(271, 291)(272, 293)(273, 296)(274, 298)(275, 301)(276, 303)(277, 305)(278, 307)(279, 309)(280, 311)(282, 313)(284, 315)(286, 317)(289, 322)(292, 326)(294, 319)(295, 325)(297, 329)(299, 321)(300, 328)(302, 332)(304, 331)(306, 337)(308, 336)(310, 342)(312, 341)(314, 346)(316, 345)(318, 350)(320, 349)(323, 354)(324, 353)(327, 358)(330, 361)(333, 365)(334, 357)(335, 366)(338, 368)(339, 362)(340, 369)(343, 371)(344, 372)(347, 376)(348, 377)(351, 381)(352, 382)(355, 385)(356, 386)(359, 389)(360, 390)(363, 393)(364, 394)(367, 397)(370, 402)(373, 406)(374, 398)(375, 405)(378, 409)(379, 401)(380, 408)(383, 412)(384, 411)(387, 417)(388, 416)(391, 422)(392, 421)(395, 426)(396, 425)(399, 430)(400, 429)(403, 434)(404, 433)(407, 438)(410, 441)(413, 445)(414, 437)(415, 446)(418, 447)(419, 442)(420, 448)(423, 444)(424, 443)(427, 440)(428, 439)(431, 435)(432, 436)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 112, 112 ), ( 112^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2281
Transitivity :: ET+
Graph:: simple bipartite
	v = 168 e = 224 f = 4
	degree seq :: [ 2^112, 4^56 ]

E27.2278 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^56 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 73, 69, 71, 78, 85, 90, 95, 99, 103, 107, 113, 126, 116, 122, 137, 149, 159, 168, 176, 184, 192, 201, 212, 205, 206, 215, 221, 197, 190, 180, 174, 164, 157, 142, 131, 118, 134, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 83, 76, 70, 75, 82, 89, 94, 98, 102, 106, 111, 145, 133, 119, 130, 143, 156, 165, 173, 181, 189, 198, 220, 216, 208, 204, 210, 200, 193, 183, 177, 167, 160, 148, 138, 121, 117, 125, 153, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 84, 77, 72, 79, 86, 91, 96, 100, 104, 108, 114, 147, 135, 124, 139, 151, 161, 170, 178, 186, 194, 202, 222, 217, 209, 203, 211, 199, 191, 185, 175, 169, 158, 150, 136, 123, 115, 127, 112, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 93, 88, 81, 74, 80, 87, 92, 97, 101, 105, 109, 163, 154, 141, 128, 140, 152, 162, 171, 179, 187, 195, 224, 223, 218, 213, 207, 214, 219, 196, 188, 182, 172, 166, 155, 144, 129, 120, 132, 146, 110, 62, 54, 46, 38, 30, 22, 14)(225, 226, 230, 228)(227, 233, 237, 232)(229, 235, 238, 231)(234, 240, 245, 241)(236, 239, 246, 243)(242, 249, 253, 248)(244, 251, 254, 247)(250, 256, 261, 257)(252, 255, 262, 259)(258, 265, 269, 264)(260, 267, 270, 263)(266, 272, 277, 273)(268, 271, 278, 275)(274, 281, 285, 280)(276, 283, 286, 279)(282, 288, 317, 289)(284, 287, 334, 291)(290, 336, 312, 377)(292, 308, 370, 307)(293, 339, 298, 341)(294, 342, 296, 344)(295, 345, 304, 347)(297, 349, 305, 351)(299, 353, 303, 355)(300, 356, 301, 358)(302, 360, 311, 362)(306, 366, 310, 368)(309, 372, 316, 374)(313, 379, 315, 381)(314, 382, 321, 384)(318, 388, 320, 390)(319, 391, 325, 393)(322, 396, 324, 398)(323, 399, 329, 401)(326, 404, 328, 406)(327, 407, 333, 409)(330, 412, 332, 414)(331, 415, 387, 417)(335, 421, 338, 420)(337, 424, 378, 423)(340, 428, 352, 427)(343, 431, 348, 430)(346, 433, 364, 432)(350, 435, 365, 434)(354, 429, 363, 437)(357, 439, 359, 438)(361, 440, 376, 441)(367, 442, 375, 436)(369, 443, 371, 445)(373, 446, 386, 444)(380, 425, 385, 447)(383, 422, 395, 426)(389, 448, 394, 416)(392, 418, 403, 413)(397, 408, 402, 419)(400, 405, 411, 410)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2282
Transitivity :: ET+
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2279 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^56 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 54)(47, 56)(51, 58)(52, 59)(53, 62)(55, 64)(57, 66)(60, 65)(61, 101)(63, 72)(67, 105)(68, 71)(69, 107)(70, 109)(73, 113)(74, 115)(75, 117)(76, 119)(77, 121)(78, 123)(79, 125)(80, 127)(81, 129)(82, 131)(83, 133)(84, 135)(85, 137)(86, 139)(87, 141)(88, 143)(89, 145)(90, 147)(91, 149)(92, 151)(93, 153)(94, 155)(95, 157)(96, 159)(97, 161)(98, 163)(99, 165)(100, 167)(102, 170)(103, 172)(104, 174)(106, 176)(108, 169)(110, 180)(111, 182)(112, 184)(114, 187)(116, 190)(118, 189)(120, 194)(122, 196)(124, 199)(126, 179)(128, 198)(130, 204)(132, 186)(134, 208)(136, 207)(138, 212)(140, 193)(142, 216)(144, 215)(146, 220)(148, 203)(150, 221)(152, 223)(154, 217)(156, 211)(158, 224)(160, 213)(162, 210)(164, 219)(166, 205)(168, 222)(171, 200)(173, 218)(175, 214)(177, 195)(178, 202)(181, 191)(183, 206)(185, 209)(188, 197)(192, 201)(225, 226, 229, 235, 244, 253, 261, 269, 277, 285, 303, 306, 310, 314, 318, 322, 327, 336, 332, 334, 338, 344, 354, 362, 370, 378, 386, 395, 425, 430, 438, 446, 448, 447, 440, 431, 423, 413, 406, 398, 391, 381, 375, 365, 359, 347, 341, 292, 284, 276, 268, 260, 252, 243, 234, 228)(227, 231, 239, 249, 257, 265, 273, 281, 289, 301, 299, 304, 308, 312, 316, 320, 324, 330, 335, 340, 348, 358, 366, 374, 382, 390, 399, 421, 416, 426, 434, 442, 444, 435, 428, 417, 411, 403, 393, 385, 396, 369, 379, 353, 363, 337, 349, 331, 286, 279, 270, 263, 254, 246, 236, 232)(230, 237, 233, 242, 251, 259, 267, 275, 283, 291, 295, 298, 302, 307, 311, 315, 319, 323, 328, 346, 342, 352, 360, 368, 376, 384, 392, 401, 407, 415, 424, 433, 441, 443, 436, 427, 418, 410, 404, 394, 408, 377, 387, 361, 371, 343, 355, 333, 325, 287, 278, 271, 262, 255, 245, 238)(240, 247, 241, 248, 256, 264, 272, 280, 288, 296, 293, 294, 297, 300, 305, 309, 313, 317, 321, 326, 350, 356, 364, 372, 380, 388, 397, 409, 402, 405, 412, 419, 429, 437, 445, 439, 432, 422, 414, 420, 400, 389, 383, 373, 367, 357, 351, 339, 345, 329, 290, 282, 274, 266, 258, 250)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 8 ), ( 8^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2280
Transitivity :: ET+
Graph:: simple bipartite
	v = 116 e = 224 f = 56
	degree seq :: [ 2^112, 56^4 ]

E27.2280 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^56 ]
Map::
	R = (1, 225, 3, 227, 8, 232, 4, 228)(2, 226, 5, 229, 11, 235, 6, 230)(7, 231, 13, 237, 9, 233, 14, 238)(10, 234, 15, 239, 12, 236, 16, 240)(17, 241, 21, 245, 18, 242, 22, 246)(19, 243, 23, 247, 20, 244, 24, 248)(25, 249, 29, 253, 26, 250, 30, 254)(27, 251, 31, 255, 28, 252, 32, 256)(33, 257, 37, 261, 34, 258, 38, 262)(35, 259, 73, 297, 36, 260, 75, 299)(39, 263, 82, 306, 46, 270, 83, 307)(40, 264, 85, 309, 49, 273, 86, 310)(41, 265, 87, 311, 42, 266, 88, 312)(43, 267, 89, 313, 44, 268, 90, 314)(45, 269, 92, 316, 47, 271, 81, 305)(48, 272, 95, 319, 50, 274, 84, 308)(51, 275, 97, 321, 52, 276, 98, 322)(53, 277, 99, 323, 54, 278, 100, 324)(55, 279, 93, 317, 56, 280, 91, 315)(57, 281, 96, 320, 58, 282, 94, 318)(59, 283, 105, 329, 60, 284, 106, 330)(61, 285, 107, 331, 62, 286, 108, 332)(63, 287, 102, 326, 64, 288, 101, 325)(65, 289, 104, 328, 66, 290, 103, 327)(67, 291, 113, 337, 68, 292, 114, 338)(69, 293, 115, 339, 70, 294, 116, 340)(71, 295, 110, 334, 72, 296, 109, 333)(74, 298, 112, 336, 76, 300, 111, 335)(77, 301, 125, 349, 79, 303, 127, 351)(78, 302, 129, 353, 80, 304, 130, 354)(117, 341, 126, 350, 118, 342, 128, 352)(119, 343, 169, 393, 123, 347, 171, 395)(120, 344, 173, 397, 121, 345, 174, 398)(122, 346, 170, 394, 124, 348, 172, 396)(131, 355, 182, 406, 132, 356, 183, 407)(133, 357, 185, 409, 134, 358, 186, 410)(135, 359, 188, 412, 136, 360, 189, 413)(137, 361, 191, 415, 138, 362, 192, 416)(139, 363, 193, 417, 140, 364, 194, 418)(141, 365, 195, 419, 142, 366, 196, 420)(143, 367, 184, 408, 144, 368, 181, 405)(145, 369, 190, 414, 146, 370, 187, 411)(147, 371, 201, 425, 148, 372, 202, 426)(149, 373, 203, 427, 150, 374, 204, 428)(151, 375, 198, 422, 152, 376, 197, 421)(153, 377, 200, 424, 154, 378, 199, 423)(155, 379, 209, 433, 156, 380, 210, 434)(157, 381, 211, 435, 158, 382, 212, 436)(159, 383, 206, 430, 160, 384, 205, 429)(161, 385, 208, 432, 162, 386, 207, 431)(163, 387, 217, 441, 164, 388, 218, 442)(165, 389, 179, 403, 166, 390, 180, 404)(167, 391, 214, 438, 168, 392, 213, 437)(175, 399, 216, 440, 176, 400, 215, 439)(177, 401, 223, 447, 178, 402, 224, 448)(219, 443, 222, 446, 220, 444, 221, 445)
	L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 234)(6, 236)(7, 227)(8, 235)(9, 228)(10, 229)(11, 232)(12, 230)(13, 241)(14, 242)(15, 243)(16, 244)(17, 237)(18, 238)(19, 239)(20, 240)(21, 249)(22, 250)(23, 251)(24, 252)(25, 245)(26, 246)(27, 247)(28, 248)(29, 257)(30, 258)(31, 259)(32, 260)(33, 253)(34, 254)(35, 255)(36, 256)(37, 301)(38, 303)(39, 305)(40, 308)(41, 309)(42, 310)(43, 306)(44, 307)(45, 315)(46, 316)(47, 317)(48, 318)(49, 319)(50, 320)(51, 311)(52, 312)(53, 313)(54, 314)(55, 325)(56, 326)(57, 327)(58, 328)(59, 321)(60, 322)(61, 323)(62, 324)(63, 333)(64, 334)(65, 335)(66, 336)(67, 329)(68, 330)(69, 331)(70, 332)(71, 341)(72, 342)(73, 343)(74, 346)(75, 347)(76, 348)(77, 261)(78, 337)(79, 262)(80, 338)(81, 263)(82, 267)(83, 268)(84, 264)(85, 265)(86, 266)(87, 275)(88, 276)(89, 277)(90, 278)(91, 269)(92, 270)(93, 271)(94, 272)(95, 273)(96, 274)(97, 283)(98, 284)(99, 285)(100, 286)(101, 279)(102, 280)(103, 281)(104, 282)(105, 291)(106, 292)(107, 293)(108, 294)(109, 287)(110, 288)(111, 289)(112, 290)(113, 302)(114, 304)(115, 344)(116, 345)(117, 295)(118, 296)(119, 297)(120, 339)(121, 340)(122, 298)(123, 299)(124, 300)(125, 396)(126, 395)(127, 394)(128, 393)(129, 401)(130, 402)(131, 405)(132, 408)(133, 406)(134, 407)(135, 411)(136, 414)(137, 412)(138, 413)(139, 415)(140, 416)(141, 409)(142, 410)(143, 421)(144, 422)(145, 423)(146, 424)(147, 417)(148, 418)(149, 419)(150, 420)(151, 429)(152, 430)(153, 431)(154, 432)(155, 425)(156, 426)(157, 427)(158, 428)(159, 437)(160, 438)(161, 439)(162, 440)(163, 433)(164, 434)(165, 435)(166, 436)(167, 443)(168, 444)(169, 352)(170, 351)(171, 350)(172, 349)(173, 445)(174, 446)(175, 447)(176, 448)(177, 353)(178, 354)(179, 441)(180, 442)(181, 355)(182, 357)(183, 358)(184, 356)(185, 365)(186, 366)(187, 359)(188, 361)(189, 362)(190, 360)(191, 363)(192, 364)(193, 371)(194, 372)(195, 373)(196, 374)(197, 367)(198, 368)(199, 369)(200, 370)(201, 379)(202, 380)(203, 381)(204, 382)(205, 375)(206, 376)(207, 377)(208, 378)(209, 387)(210, 388)(211, 389)(212, 390)(213, 383)(214, 384)(215, 385)(216, 386)(217, 403)(218, 404)(219, 391)(220, 392)(221, 397)(222, 398)(223, 399)(224, 400)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2279
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 56 e = 224 f = 116
	degree seq :: [ 8^56 ]

E27.2281 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^56 ]
Map::
	R = (1, 225, 3, 227, 10, 234, 18, 242, 26, 250, 34, 258, 42, 266, 50, 274, 58, 282, 66, 290, 109, 333, 117, 341, 122, 346, 126, 350, 130, 354, 134, 358, 138, 362, 142, 366, 147, 371, 156, 380, 194, 418, 199, 423, 203, 427, 207, 431, 211, 435, 215, 439, 219, 443, 223, 447, 191, 415, 186, 410, 181, 405, 178, 402, 173, 397, 170, 394, 165, 389, 162, 386, 157, 381, 149, 373, 112, 336, 102, 326, 100, 324, 94, 318, 92, 316, 86, 310, 84, 308, 75, 299, 72, 296, 68, 292, 60, 284, 52, 276, 44, 268, 36, 260, 28, 252, 20, 244, 12, 236, 5, 229)(2, 226, 7, 231, 15, 239, 23, 247, 31, 255, 39, 263, 47, 271, 55, 279, 63, 287, 107, 331, 115, 339, 120, 344, 124, 348, 128, 352, 132, 356, 136, 360, 140, 364, 145, 369, 152, 376, 190, 414, 197, 421, 201, 425, 205, 429, 209, 433, 213, 437, 217, 441, 221, 445, 195, 419, 188, 412, 183, 407, 180, 404, 175, 399, 172, 396, 167, 391, 164, 388, 159, 383, 153, 377, 148, 372, 103, 327, 106, 330, 95, 319, 97, 321, 87, 311, 89, 313, 77, 301, 79, 303, 69, 293, 80, 304, 64, 288, 56, 280, 48, 272, 40, 264, 32, 256, 24, 248, 16, 240, 8, 232)(4, 228, 11, 235, 19, 243, 27, 251, 35, 259, 43, 267, 51, 275, 59, 283, 67, 291, 111, 335, 114, 338, 119, 343, 123, 347, 127, 351, 131, 355, 135, 359, 139, 363, 144, 368, 151, 375, 189, 413, 198, 422, 202, 426, 206, 430, 210, 434, 214, 438, 218, 442, 222, 446, 196, 420, 187, 411, 184, 408, 179, 403, 176, 400, 171, 395, 168, 392, 163, 387, 160, 384, 154, 378, 110, 334, 143, 367, 99, 323, 101, 325, 91, 315, 93, 317, 83, 307, 85, 309, 71, 295, 74, 298, 73, 297, 65, 289, 57, 281, 49, 273, 41, 265, 33, 257, 25, 249, 17, 241, 9, 233)(6, 230, 13, 237, 21, 245, 29, 253, 37, 261, 45, 269, 53, 277, 61, 285, 105, 329, 118, 342, 113, 337, 116, 340, 121, 345, 125, 349, 129, 353, 133, 357, 137, 361, 141, 365, 146, 370, 155, 379, 193, 417, 200, 424, 204, 428, 208, 432, 212, 436, 216, 440, 220, 444, 224, 448, 192, 416, 185, 409, 182, 406, 177, 401, 174, 398, 169, 393, 166, 390, 161, 385, 158, 382, 150, 374, 108, 332, 104, 328, 98, 322, 96, 320, 90, 314, 88, 312, 81, 305, 78, 302, 70, 294, 76, 300, 82, 306, 62, 286, 54, 278, 46, 270, 38, 262, 30, 254, 22, 246, 14, 238)
	L = (1, 226)(2, 230)(3, 233)(4, 225)(5, 235)(6, 228)(7, 229)(8, 227)(9, 237)(10, 240)(11, 238)(12, 239)(13, 232)(14, 231)(15, 246)(16, 245)(17, 234)(18, 249)(19, 236)(20, 251)(21, 241)(22, 243)(23, 244)(24, 242)(25, 253)(26, 256)(27, 254)(28, 255)(29, 248)(30, 247)(31, 262)(32, 261)(33, 250)(34, 265)(35, 252)(36, 267)(37, 257)(38, 259)(39, 260)(40, 258)(41, 269)(42, 272)(43, 270)(44, 271)(45, 264)(46, 263)(47, 278)(48, 277)(49, 266)(50, 281)(51, 268)(52, 283)(53, 273)(54, 275)(55, 276)(56, 274)(57, 285)(58, 288)(59, 286)(60, 287)(61, 280)(62, 279)(63, 306)(64, 329)(65, 282)(66, 297)(67, 284)(68, 335)(69, 337)(70, 338)(71, 340)(72, 339)(73, 342)(74, 333)(75, 343)(76, 331)(77, 345)(78, 344)(79, 341)(80, 290)(81, 347)(82, 291)(83, 349)(84, 348)(85, 346)(86, 351)(87, 353)(88, 352)(89, 350)(90, 355)(91, 357)(92, 356)(93, 354)(94, 359)(95, 361)(96, 360)(97, 358)(98, 363)(99, 365)(100, 364)(101, 362)(102, 368)(103, 370)(104, 369)(105, 289)(106, 366)(107, 292)(108, 375)(109, 293)(110, 379)(111, 300)(112, 376)(113, 298)(114, 296)(115, 294)(116, 303)(117, 295)(118, 304)(119, 302)(120, 299)(121, 309)(122, 301)(123, 308)(124, 305)(125, 313)(126, 307)(127, 312)(128, 310)(129, 317)(130, 311)(131, 316)(132, 314)(133, 321)(134, 315)(135, 320)(136, 318)(137, 325)(138, 319)(139, 324)(140, 322)(141, 330)(142, 323)(143, 371)(144, 328)(145, 326)(146, 367)(147, 327)(148, 380)(149, 413)(150, 414)(151, 336)(152, 332)(153, 417)(154, 418)(155, 372)(156, 334)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 419)(186, 420)(187, 415)(188, 416)(189, 374)(190, 373)(191, 412)(192, 411)(193, 378)(194, 377)(195, 410)(196, 409)(197, 382)(198, 381)(199, 384)(200, 383)(201, 386)(202, 385)(203, 388)(204, 387)(205, 390)(206, 389)(207, 392)(208, 391)(209, 394)(210, 393)(211, 396)(212, 395)(213, 398)(214, 397)(215, 400)(216, 399)(217, 402)(218, 401)(219, 404)(220, 403)(221, 406)(222, 405)(223, 408)(224, 407)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2277
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 224 f = 168
	degree seq :: [ 112^4 ]

E27.2282 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^56 ]
Map:: polytopal non-degenerate
	R = (1, 225, 3, 227)(2, 226, 6, 230)(4, 228, 9, 233)(5, 229, 12, 236)(7, 231, 16, 240)(8, 232, 17, 241)(10, 234, 15, 239)(11, 235, 21, 245)(13, 237, 23, 247)(14, 238, 24, 248)(18, 242, 26, 250)(19, 243, 27, 251)(20, 244, 30, 254)(22, 246, 32, 256)(25, 249, 34, 258)(28, 252, 33, 257)(29, 253, 38, 262)(31, 255, 40, 264)(35, 259, 42, 266)(36, 260, 43, 267)(37, 261, 46, 270)(39, 263, 48, 272)(41, 265, 50, 274)(44, 268, 49, 273)(45, 269, 54, 278)(47, 271, 56, 280)(51, 275, 58, 282)(52, 276, 59, 283)(53, 277, 62, 286)(55, 279, 64, 288)(57, 281, 66, 290)(60, 284, 65, 289)(61, 285, 75, 299)(63, 287, 107, 331)(67, 291, 86, 310)(68, 292, 111, 335)(69, 293, 113, 337)(70, 294, 105, 329)(71, 295, 116, 340)(72, 296, 118, 342)(73, 297, 120, 344)(74, 298, 122, 346)(76, 300, 125, 349)(77, 301, 127, 351)(78, 302, 129, 353)(79, 303, 131, 355)(80, 304, 133, 357)(81, 305, 109, 333)(82, 306, 136, 360)(83, 307, 138, 362)(84, 308, 140, 364)(85, 309, 142, 366)(87, 311, 145, 369)(88, 312, 147, 371)(89, 313, 149, 373)(90, 314, 151, 375)(91, 315, 153, 377)(92, 316, 155, 379)(93, 317, 157, 381)(94, 318, 159, 383)(95, 319, 161, 385)(96, 320, 163, 387)(97, 321, 165, 389)(98, 322, 167, 391)(99, 323, 169, 393)(100, 324, 171, 395)(101, 325, 173, 397)(102, 326, 175, 399)(103, 327, 177, 401)(104, 328, 179, 403)(106, 330, 182, 406)(108, 332, 184, 408)(110, 334, 187, 411)(112, 336, 189, 413)(114, 338, 191, 415)(115, 339, 181, 405)(117, 341, 194, 418)(119, 343, 196, 420)(121, 345, 198, 422)(123, 347, 200, 424)(124, 348, 202, 426)(126, 350, 204, 428)(128, 352, 206, 430)(130, 354, 208, 432)(132, 356, 210, 434)(134, 358, 212, 436)(135, 359, 186, 410)(137, 361, 215, 439)(139, 363, 216, 440)(141, 365, 217, 441)(143, 367, 219, 443)(144, 368, 221, 445)(146, 370, 223, 447)(148, 372, 207, 431)(150, 374, 205, 429)(152, 376, 224, 448)(154, 378, 218, 442)(156, 380, 197, 421)(158, 382, 195, 419)(160, 384, 213, 437)(162, 386, 211, 435)(164, 388, 193, 417)(166, 390, 192, 416)(168, 392, 220, 444)(170, 394, 201, 425)(172, 396, 203, 427)(174, 398, 190, 414)(176, 400, 214, 438)(178, 402, 209, 433)(180, 404, 183, 407)(185, 409, 222, 446)(188, 412, 199, 423)
	L = (1, 226)(2, 229)(3, 231)(4, 225)(5, 235)(6, 237)(7, 239)(8, 227)(9, 242)(10, 228)(11, 244)(12, 232)(13, 233)(14, 230)(15, 249)(16, 247)(17, 248)(18, 251)(19, 234)(20, 253)(21, 238)(22, 236)(23, 241)(24, 256)(25, 257)(26, 240)(27, 259)(28, 243)(29, 261)(30, 246)(31, 245)(32, 264)(33, 265)(34, 250)(35, 267)(36, 252)(37, 269)(38, 255)(39, 254)(40, 272)(41, 273)(42, 258)(43, 275)(44, 260)(45, 277)(46, 263)(47, 262)(48, 280)(49, 281)(50, 266)(51, 283)(52, 268)(53, 285)(54, 271)(55, 270)(56, 288)(57, 289)(58, 274)(59, 291)(60, 276)(61, 329)(62, 279)(63, 278)(64, 331)(65, 333)(66, 282)(67, 335)(68, 284)(69, 292)(70, 297)(71, 293)(72, 302)(73, 286)(74, 294)(75, 287)(76, 295)(77, 298)(78, 299)(79, 296)(80, 309)(81, 310)(82, 300)(83, 303)(84, 301)(85, 305)(86, 290)(87, 304)(88, 306)(89, 308)(90, 307)(91, 311)(92, 312)(93, 314)(94, 313)(95, 315)(96, 316)(97, 318)(98, 317)(99, 319)(100, 320)(101, 322)(102, 321)(103, 323)(104, 324)(105, 342)(106, 326)(107, 344)(108, 325)(109, 337)(110, 327)(111, 366)(112, 328)(113, 357)(114, 336)(115, 345)(116, 369)(117, 338)(118, 351)(119, 354)(120, 353)(121, 330)(122, 355)(123, 339)(124, 332)(125, 377)(126, 341)(127, 362)(128, 347)(129, 346)(130, 348)(131, 364)(132, 343)(133, 349)(134, 367)(135, 368)(136, 385)(137, 350)(138, 373)(139, 356)(140, 375)(141, 352)(142, 340)(143, 359)(144, 334)(145, 360)(146, 358)(147, 393)(148, 361)(149, 381)(150, 365)(151, 383)(152, 363)(153, 371)(154, 370)(155, 401)(156, 372)(157, 389)(158, 376)(159, 391)(160, 374)(161, 379)(162, 378)(163, 411)(164, 380)(165, 397)(166, 384)(167, 399)(168, 382)(169, 387)(170, 386)(171, 445)(172, 388)(173, 406)(174, 392)(175, 408)(176, 390)(177, 395)(178, 394)(179, 410)(180, 396)(181, 420)(182, 426)(183, 400)(184, 422)(185, 398)(186, 415)(187, 403)(188, 402)(189, 443)(190, 404)(191, 436)(192, 414)(193, 423)(194, 447)(195, 416)(196, 430)(197, 433)(198, 432)(199, 407)(200, 434)(201, 417)(202, 405)(203, 409)(204, 442)(205, 419)(206, 440)(207, 425)(208, 424)(209, 427)(210, 441)(211, 421)(212, 428)(213, 444)(214, 446)(215, 435)(216, 429)(217, 448)(218, 431)(219, 418)(220, 438)(221, 413)(222, 412)(223, 439)(224, 437)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2278
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2283 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 225, 2, 226)(3, 227, 7, 231)(4, 228, 9, 233)(5, 229, 10, 234)(6, 230, 12, 236)(8, 232, 11, 235)(13, 237, 17, 241)(14, 238, 18, 242)(15, 239, 19, 243)(16, 240, 20, 244)(21, 245, 25, 249)(22, 246, 26, 250)(23, 247, 27, 251)(24, 248, 28, 252)(29, 253, 33, 257)(30, 254, 34, 258)(31, 255, 35, 259)(32, 256, 36, 260)(37, 261, 42, 266)(38, 262, 39, 263)(40, 264, 59, 283)(41, 265, 61, 285)(43, 267, 63, 287)(44, 268, 64, 288)(45, 269, 57, 281)(46, 270, 66, 290)(47, 271, 67, 291)(48, 272, 69, 293)(49, 273, 72, 296)(50, 274, 74, 298)(51, 275, 77, 301)(52, 276, 79, 303)(53, 277, 81, 305)(54, 278, 83, 307)(55, 279, 85, 309)(56, 280, 87, 311)(58, 282, 89, 313)(60, 284, 91, 315)(62, 286, 95, 319)(65, 289, 97, 321)(68, 292, 102, 326)(70, 294, 93, 317)(71, 295, 101, 325)(73, 297, 105, 329)(75, 299, 98, 322)(76, 300, 104, 328)(78, 302, 108, 332)(80, 304, 107, 331)(82, 306, 113, 337)(84, 308, 112, 336)(86, 310, 118, 342)(88, 312, 117, 341)(90, 314, 122, 346)(92, 316, 121, 345)(94, 318, 126, 350)(96, 320, 125, 349)(99, 323, 130, 354)(100, 324, 129, 353)(103, 327, 133, 357)(106, 330, 138, 362)(109, 333, 141, 365)(110, 334, 134, 358)(111, 335, 142, 366)(114, 338, 144, 368)(115, 339, 137, 361)(116, 340, 145, 369)(119, 343, 147, 371)(120, 344, 148, 372)(123, 347, 152, 376)(124, 348, 153, 377)(127, 351, 157, 381)(128, 352, 158, 382)(131, 355, 161, 385)(132, 356, 162, 386)(135, 359, 165, 389)(136, 360, 166, 390)(139, 363, 169, 393)(140, 364, 170, 394)(143, 367, 174, 398)(146, 370, 177, 401)(149, 373, 182, 406)(150, 374, 173, 397)(151, 375, 181, 405)(154, 378, 185, 409)(155, 379, 178, 402)(156, 380, 184, 408)(159, 383, 188, 412)(160, 384, 187, 411)(163, 387, 193, 417)(164, 388, 192, 416)(167, 391, 198, 422)(168, 392, 197, 421)(171, 395, 202, 426)(172, 396, 201, 425)(175, 399, 206, 430)(176, 400, 205, 429)(179, 403, 210, 434)(180, 404, 209, 433)(183, 407, 213, 437)(186, 410, 218, 442)(189, 413, 221, 445)(190, 414, 214, 438)(191, 415, 222, 446)(194, 418, 224, 448)(195, 419, 217, 441)(196, 420, 223, 447)(199, 423, 220, 444)(200, 424, 219, 443)(203, 427, 216, 440)(204, 428, 215, 439)(207, 431, 211, 435)(208, 432, 212, 436)(449, 673, 451, 675, 456, 680, 452, 676)(450, 674, 453, 677, 459, 683, 454, 678)(455, 679, 461, 685, 457, 681, 462, 686)(458, 682, 463, 687, 460, 684, 464, 688)(465, 689, 469, 693, 466, 690, 470, 694)(467, 691, 471, 695, 468, 692, 472, 696)(473, 697, 477, 701, 474, 698, 478, 702)(475, 699, 479, 703, 476, 700, 480, 704)(481, 705, 485, 709, 482, 706, 486, 710)(483, 707, 505, 729, 484, 708, 507, 731)(487, 711, 509, 733, 490, 714, 511, 735)(488, 712, 512, 736, 493, 717, 514, 738)(489, 713, 515, 739, 491, 715, 517, 741)(492, 716, 520, 744, 494, 718, 522, 746)(495, 719, 525, 749, 496, 720, 527, 751)(497, 721, 529, 753, 498, 722, 531, 755)(499, 723, 533, 757, 500, 724, 535, 759)(501, 725, 537, 761, 502, 726, 539, 763)(503, 727, 541, 765, 504, 728, 543, 767)(506, 730, 546, 770, 508, 732, 545, 769)(510, 734, 550, 774, 518, 742, 549, 773)(513, 737, 553, 777, 523, 747, 552, 776)(516, 740, 556, 780, 519, 743, 555, 779)(521, 745, 561, 785, 524, 748, 560, 784)(526, 750, 566, 790, 528, 752, 565, 789)(530, 754, 570, 794, 532, 756, 569, 793)(534, 758, 574, 798, 536, 760, 573, 797)(538, 762, 578, 802, 540, 764, 577, 801)(542, 766, 582, 806, 544, 768, 581, 805)(547, 771, 585, 809, 548, 772, 586, 810)(551, 775, 589, 813, 558, 782, 590, 814)(554, 778, 592, 816, 563, 787, 593, 817)(557, 781, 595, 819, 559, 783, 596, 820)(562, 786, 600, 824, 564, 788, 601, 825)(567, 791, 605, 829, 568, 792, 606, 830)(571, 795, 609, 833, 572, 796, 610, 834)(575, 799, 613, 837, 576, 800, 614, 838)(579, 803, 617, 841, 580, 804, 618, 842)(583, 807, 621, 845, 584, 808, 622, 846)(587, 811, 626, 850, 588, 812, 625, 849)(591, 815, 630, 854, 598, 822, 629, 853)(594, 818, 633, 857, 603, 827, 632, 856)(597, 821, 636, 860, 599, 823, 635, 859)(602, 826, 641, 865, 604, 828, 640, 864)(607, 831, 646, 870, 608, 832, 645, 869)(611, 835, 650, 874, 612, 836, 649, 873)(615, 839, 654, 878, 616, 840, 653, 877)(619, 843, 658, 882, 620, 844, 657, 881)(623, 847, 662, 886, 624, 848, 661, 885)(627, 851, 665, 889, 628, 852, 666, 890)(631, 855, 669, 893, 638, 862, 670, 894)(634, 858, 672, 896, 643, 867, 671, 895)(637, 861, 668, 892, 639, 863, 667, 891)(642, 866, 664, 888, 644, 868, 663, 887)(647, 871, 659, 883, 648, 872, 660, 884)(651, 875, 655, 879, 652, 876, 656, 880)
	L = (1, 450)(2, 449)(3, 455)(4, 457)(5, 458)(6, 460)(7, 451)(8, 459)(9, 452)(10, 453)(11, 456)(12, 454)(13, 465)(14, 466)(15, 467)(16, 468)(17, 461)(18, 462)(19, 463)(20, 464)(21, 473)(22, 474)(23, 475)(24, 476)(25, 469)(26, 470)(27, 471)(28, 472)(29, 481)(30, 482)(31, 483)(32, 484)(33, 477)(34, 478)(35, 479)(36, 480)(37, 490)(38, 487)(39, 486)(40, 507)(41, 509)(42, 485)(43, 511)(44, 512)(45, 505)(46, 514)(47, 515)(48, 517)(49, 520)(50, 522)(51, 525)(52, 527)(53, 529)(54, 531)(55, 533)(56, 535)(57, 493)(58, 537)(59, 488)(60, 539)(61, 489)(62, 543)(63, 491)(64, 492)(65, 545)(66, 494)(67, 495)(68, 550)(69, 496)(70, 541)(71, 549)(72, 497)(73, 553)(74, 498)(75, 546)(76, 552)(77, 499)(78, 556)(79, 500)(80, 555)(81, 501)(82, 561)(83, 502)(84, 560)(85, 503)(86, 566)(87, 504)(88, 565)(89, 506)(90, 570)(91, 508)(92, 569)(93, 518)(94, 574)(95, 510)(96, 573)(97, 513)(98, 523)(99, 578)(100, 577)(101, 519)(102, 516)(103, 581)(104, 524)(105, 521)(106, 586)(107, 528)(108, 526)(109, 589)(110, 582)(111, 590)(112, 532)(113, 530)(114, 592)(115, 585)(116, 593)(117, 536)(118, 534)(119, 595)(120, 596)(121, 540)(122, 538)(123, 600)(124, 601)(125, 544)(126, 542)(127, 605)(128, 606)(129, 548)(130, 547)(131, 609)(132, 610)(133, 551)(134, 558)(135, 613)(136, 614)(137, 563)(138, 554)(139, 617)(140, 618)(141, 557)(142, 559)(143, 622)(144, 562)(145, 564)(146, 625)(147, 567)(148, 568)(149, 630)(150, 621)(151, 629)(152, 571)(153, 572)(154, 633)(155, 626)(156, 632)(157, 575)(158, 576)(159, 636)(160, 635)(161, 579)(162, 580)(163, 641)(164, 640)(165, 583)(166, 584)(167, 646)(168, 645)(169, 587)(170, 588)(171, 650)(172, 649)(173, 598)(174, 591)(175, 654)(176, 653)(177, 594)(178, 603)(179, 658)(180, 657)(181, 599)(182, 597)(183, 661)(184, 604)(185, 602)(186, 666)(187, 608)(188, 607)(189, 669)(190, 662)(191, 670)(192, 612)(193, 611)(194, 672)(195, 665)(196, 671)(197, 616)(198, 615)(199, 668)(200, 667)(201, 620)(202, 619)(203, 664)(204, 663)(205, 624)(206, 623)(207, 659)(208, 660)(209, 628)(210, 627)(211, 655)(212, 656)(213, 631)(214, 638)(215, 652)(216, 651)(217, 643)(218, 634)(219, 648)(220, 647)(221, 637)(222, 639)(223, 644)(224, 642)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2286
Graph:: bipartite
	v = 168 e = 448 f = 228
	degree seq :: [ 4^112, 8^56 ]

E27.2284 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^4, Y2^56 ]
Map::
	R = (1, 225, 2, 226, 6, 230, 4, 228)(3, 227, 9, 233, 13, 237, 8, 232)(5, 229, 11, 235, 14, 238, 7, 231)(10, 234, 16, 240, 21, 245, 17, 241)(12, 236, 15, 239, 22, 246, 19, 243)(18, 242, 25, 249, 29, 253, 24, 248)(20, 244, 27, 251, 30, 254, 23, 247)(26, 250, 32, 256, 37, 261, 33, 257)(28, 252, 31, 255, 38, 262, 35, 259)(34, 258, 41, 265, 45, 269, 40, 264)(36, 260, 43, 267, 46, 270, 39, 263)(42, 266, 48, 272, 53, 277, 49, 273)(44, 268, 47, 271, 54, 278, 51, 275)(50, 274, 57, 281, 61, 285, 56, 280)(52, 276, 59, 283, 62, 286, 55, 279)(58, 282, 64, 288, 113, 337, 65, 289)(60, 284, 63, 287, 98, 322, 67, 291)(66, 290, 96, 320, 142, 366, 88, 312)(68, 292, 119, 343, 92, 316, 115, 339)(69, 293, 121, 345, 74, 298, 122, 346)(70, 294, 123, 347, 72, 296, 124, 348)(71, 295, 125, 349, 81, 305, 126, 350)(73, 297, 127, 351, 82, 306, 128, 352)(75, 299, 129, 353, 79, 303, 130, 354)(76, 300, 131, 355, 77, 301, 132, 356)(78, 302, 133, 357, 89, 313, 134, 358)(80, 304, 117, 341, 90, 314, 135, 359)(83, 307, 136, 360, 87, 311, 137, 361)(84, 308, 138, 362, 85, 309, 139, 363)(86, 310, 140, 364, 95, 319, 141, 365)(91, 315, 143, 367, 94, 318, 144, 368)(93, 317, 145, 369, 101, 325, 146, 370)(97, 321, 147, 371, 100, 324, 148, 372)(99, 323, 149, 373, 105, 329, 150, 374)(102, 326, 151, 375, 104, 328, 152, 376)(103, 327, 153, 377, 109, 333, 154, 378)(106, 330, 155, 379, 108, 332, 156, 380)(107, 331, 157, 381, 114, 338, 158, 382)(110, 334, 160, 384, 112, 336, 161, 385)(111, 335, 162, 386, 159, 383, 163, 387)(116, 340, 167, 391, 120, 344, 168, 392)(118, 342, 171, 395, 164, 388, 172, 396)(165, 389, 213, 437, 166, 390, 214, 438)(169, 393, 217, 441, 170, 394, 218, 442)(173, 397, 215, 439, 174, 398, 216, 440)(175, 399, 212, 436, 176, 400, 211, 435)(177, 401, 210, 434, 178, 402, 209, 433)(179, 403, 221, 445, 180, 404, 222, 446)(181, 405, 207, 431, 182, 406, 208, 432)(183, 407, 219, 443, 184, 408, 220, 444)(185, 409, 205, 429, 186, 410, 206, 430)(187, 411, 204, 428, 188, 412, 203, 427)(189, 413, 223, 447, 190, 414, 224, 448)(191, 415, 202, 426, 192, 416, 201, 425)(193, 417, 199, 423, 194, 418, 200, 424)(195, 419, 197, 421, 196, 420, 198, 422)(449, 673, 451, 675, 458, 682, 466, 690, 474, 698, 482, 706, 490, 714, 498, 722, 506, 730, 514, 738, 565, 789, 575, 799, 569, 793, 573, 797, 581, 805, 588, 812, 593, 817, 597, 821, 601, 825, 605, 829, 610, 834, 619, 843, 665, 889, 669, 893, 663, 887, 658, 882, 653, 877, 650, 874, 645, 869, 642, 866, 635, 859, 630, 854, 623, 847, 632, 856, 637, 861, 614, 838, 564, 788, 560, 784, 554, 778, 552, 776, 545, 769, 542, 766, 531, 755, 527, 751, 518, 742, 525, 749, 532, 756, 516, 740, 508, 732, 500, 724, 492, 716, 484, 708, 476, 700, 468, 692, 460, 684, 453, 677)(450, 674, 455, 679, 463, 687, 471, 695, 479, 703, 487, 711, 495, 719, 503, 727, 511, 735, 563, 787, 586, 810, 579, 803, 571, 795, 577, 801, 584, 808, 591, 815, 595, 819, 599, 823, 603, 827, 608, 832, 615, 839, 661, 885, 671, 895, 667, 891, 660, 884, 655, 879, 652, 876, 647, 871, 644, 868, 639, 863, 634, 858, 625, 849, 622, 846, 627, 851, 618, 842, 566, 790, 607, 831, 555, 779, 557, 781, 547, 771, 549, 773, 534, 758, 537, 761, 519, 743, 522, 746, 521, 745, 538, 762, 536, 760, 512, 736, 504, 728, 496, 720, 488, 712, 480, 704, 472, 696, 464, 688, 456, 680)(452, 676, 459, 683, 467, 691, 475, 699, 483, 707, 491, 715, 499, 723, 507, 731, 515, 739, 567, 791, 587, 811, 580, 804, 572, 796, 578, 802, 585, 809, 592, 816, 596, 820, 600, 824, 604, 828, 609, 833, 616, 840, 662, 886, 672, 896, 668, 892, 659, 883, 656, 880, 651, 875, 648, 872, 643, 867, 640, 864, 633, 857, 626, 850, 621, 845, 628, 852, 617, 841, 612, 836, 559, 783, 562, 786, 551, 775, 553, 777, 541, 765, 543, 767, 526, 750, 529, 753, 517, 741, 530, 754, 528, 752, 544, 768, 513, 737, 505, 729, 497, 721, 489, 713, 481, 705, 473, 697, 465, 689, 457, 681)(454, 678, 461, 685, 469, 693, 477, 701, 485, 709, 493, 717, 501, 725, 509, 733, 561, 785, 590, 814, 583, 807, 576, 800, 570, 794, 574, 798, 582, 806, 589, 813, 594, 818, 598, 822, 602, 826, 606, 830, 611, 835, 620, 844, 666, 890, 670, 894, 664, 888, 657, 881, 654, 878, 649, 873, 646, 870, 641, 865, 636, 860, 629, 853, 624, 848, 631, 855, 638, 862, 613, 837, 568, 792, 558, 782, 556, 780, 550, 774, 548, 772, 539, 763, 535, 759, 523, 747, 520, 744, 524, 748, 533, 757, 540, 764, 546, 770, 510, 734, 502, 726, 494, 718, 486, 710, 478, 702, 470, 694, 462, 686)
	L = (1, 451)(2, 455)(3, 458)(4, 459)(5, 449)(6, 461)(7, 463)(8, 450)(9, 452)(10, 466)(11, 467)(12, 453)(13, 469)(14, 454)(15, 471)(16, 456)(17, 457)(18, 474)(19, 475)(20, 460)(21, 477)(22, 462)(23, 479)(24, 464)(25, 465)(26, 482)(27, 483)(28, 468)(29, 485)(30, 470)(31, 487)(32, 472)(33, 473)(34, 490)(35, 491)(36, 476)(37, 493)(38, 478)(39, 495)(40, 480)(41, 481)(42, 498)(43, 499)(44, 484)(45, 501)(46, 486)(47, 503)(48, 488)(49, 489)(50, 506)(51, 507)(52, 492)(53, 509)(54, 494)(55, 511)(56, 496)(57, 497)(58, 514)(59, 515)(60, 500)(61, 561)(62, 502)(63, 563)(64, 504)(65, 505)(66, 565)(67, 567)(68, 508)(69, 530)(70, 525)(71, 522)(72, 524)(73, 538)(74, 521)(75, 520)(76, 533)(77, 532)(78, 529)(79, 518)(80, 544)(81, 517)(82, 528)(83, 527)(84, 516)(85, 540)(86, 537)(87, 523)(88, 512)(89, 519)(90, 536)(91, 535)(92, 546)(93, 543)(94, 531)(95, 526)(96, 513)(97, 542)(98, 510)(99, 549)(100, 539)(101, 534)(102, 548)(103, 553)(104, 545)(105, 541)(106, 552)(107, 557)(108, 550)(109, 547)(110, 556)(111, 562)(112, 554)(113, 590)(114, 551)(115, 586)(116, 560)(117, 575)(118, 607)(119, 587)(120, 558)(121, 573)(122, 574)(123, 577)(124, 578)(125, 581)(126, 582)(127, 569)(128, 570)(129, 584)(130, 585)(131, 571)(132, 572)(133, 588)(134, 589)(135, 576)(136, 591)(137, 592)(138, 579)(139, 580)(140, 593)(141, 594)(142, 583)(143, 595)(144, 596)(145, 597)(146, 598)(147, 599)(148, 600)(149, 601)(150, 602)(151, 603)(152, 604)(153, 605)(154, 606)(155, 608)(156, 609)(157, 610)(158, 611)(159, 555)(160, 615)(161, 616)(162, 619)(163, 620)(164, 559)(165, 568)(166, 564)(167, 661)(168, 662)(169, 612)(170, 566)(171, 665)(172, 666)(173, 628)(174, 627)(175, 632)(176, 631)(177, 622)(178, 621)(179, 618)(180, 617)(181, 624)(182, 623)(183, 638)(184, 637)(185, 626)(186, 625)(187, 630)(188, 629)(189, 614)(190, 613)(191, 634)(192, 633)(193, 636)(194, 635)(195, 640)(196, 639)(197, 642)(198, 641)(199, 644)(200, 643)(201, 646)(202, 645)(203, 648)(204, 647)(205, 650)(206, 649)(207, 652)(208, 651)(209, 654)(210, 653)(211, 656)(212, 655)(213, 671)(214, 672)(215, 658)(216, 657)(217, 669)(218, 670)(219, 660)(220, 659)(221, 663)(222, 664)(223, 667)(224, 668)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2285
Graph:: bipartite
	v = 60 e = 448 f = 336
	degree seq :: [ 8^56, 112^4 ]

E27.2285 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, Y3^26 * Y2 * Y3^-30 * Y2, (Y3^-1 * Y1^-1)^56 ]
Map:: polytopal
	R = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)(449, 673, 450, 674)(451, 675, 455, 679)(452, 676, 457, 681)(453, 677, 459, 683)(454, 678, 461, 685)(456, 680, 462, 686)(458, 682, 460, 684)(463, 687, 468, 692)(464, 688, 471, 695)(465, 689, 473, 697)(466, 690, 469, 693)(467, 691, 475, 699)(470, 694, 477, 701)(472, 696, 479, 703)(474, 698, 480, 704)(476, 700, 478, 702)(481, 705, 487, 711)(482, 706, 489, 713)(483, 707, 485, 709)(484, 708, 491, 715)(486, 710, 493, 717)(488, 712, 495, 719)(490, 714, 496, 720)(492, 716, 494, 718)(497, 721, 503, 727)(498, 722, 505, 729)(499, 723, 501, 725)(500, 724, 507, 731)(502, 726, 509, 733)(504, 728, 511, 735)(506, 730, 512, 736)(508, 732, 510, 734)(513, 737, 551, 775)(514, 738, 517, 741)(515, 739, 521, 745)(516, 740, 555, 779)(518, 742, 549, 773)(519, 743, 553, 777)(520, 744, 557, 781)(522, 746, 558, 782)(523, 747, 559, 783)(524, 748, 560, 784)(525, 749, 561, 785)(526, 750, 562, 786)(527, 751, 563, 787)(528, 752, 564, 788)(529, 753, 565, 789)(530, 754, 566, 790)(531, 755, 567, 791)(532, 756, 568, 792)(533, 757, 569, 793)(534, 758, 570, 794)(535, 759, 571, 795)(536, 760, 572, 796)(537, 761, 573, 797)(538, 762, 574, 798)(539, 763, 575, 799)(540, 764, 576, 800)(541, 765, 577, 801)(542, 766, 578, 802)(543, 767, 579, 803)(544, 768, 581, 805)(545, 769, 582, 806)(546, 770, 583, 807)(547, 771, 584, 808)(548, 772, 586, 810)(550, 774, 589, 813)(552, 776, 590, 814)(554, 778, 593, 817)(556, 780, 594, 818)(580, 804, 619, 843)(585, 809, 624, 848)(587, 811, 625, 849)(588, 812, 626, 850)(591, 815, 629, 853)(592, 816, 630, 854)(595, 819, 633, 857)(596, 820, 634, 858)(597, 821, 635, 859)(598, 822, 636, 860)(599, 823, 637, 861)(600, 824, 638, 862)(601, 825, 639, 863)(602, 826, 640, 864)(603, 827, 641, 865)(604, 828, 642, 866)(605, 829, 643, 867)(606, 830, 644, 868)(607, 831, 645, 869)(608, 832, 646, 870)(609, 833, 647, 871)(610, 834, 648, 872)(611, 835, 649, 873)(612, 836, 650, 874)(613, 837, 651, 875)(614, 838, 652, 876)(615, 839, 653, 877)(616, 840, 654, 878)(617, 841, 655, 879)(618, 842, 656, 880)(620, 844, 657, 881)(621, 845, 658, 882)(622, 846, 659, 883)(623, 847, 660, 884)(627, 851, 663, 887)(628, 852, 664, 888)(631, 855, 667, 891)(632, 856, 668, 892)(661, 885, 672, 896)(662, 886, 671, 895)(665, 889, 669, 893)(666, 890, 670, 894)
	L = (1, 451)(2, 453)(3, 456)(4, 449)(5, 460)(6, 450)(7, 463)(8, 465)(9, 466)(10, 452)(11, 468)(12, 470)(13, 471)(14, 454)(15, 457)(16, 455)(17, 474)(18, 475)(19, 458)(20, 461)(21, 459)(22, 478)(23, 479)(24, 462)(25, 464)(26, 482)(27, 483)(28, 467)(29, 469)(30, 486)(31, 487)(32, 472)(33, 473)(34, 490)(35, 491)(36, 476)(37, 477)(38, 494)(39, 495)(40, 480)(41, 481)(42, 498)(43, 499)(44, 484)(45, 485)(46, 502)(47, 503)(48, 488)(49, 489)(50, 506)(51, 507)(52, 492)(53, 493)(54, 510)(55, 511)(56, 496)(57, 497)(58, 514)(59, 515)(60, 500)(61, 501)(62, 549)(63, 551)(64, 504)(65, 505)(66, 553)(67, 555)(68, 508)(69, 513)(70, 521)(71, 528)(72, 516)(73, 509)(74, 525)(75, 518)(76, 523)(77, 517)(78, 530)(79, 520)(80, 512)(81, 527)(82, 519)(83, 534)(84, 524)(85, 532)(86, 522)(87, 538)(88, 529)(89, 536)(90, 526)(91, 542)(92, 533)(93, 540)(94, 531)(95, 546)(96, 537)(97, 544)(98, 535)(99, 552)(100, 541)(101, 557)(102, 548)(103, 564)(104, 539)(105, 558)(106, 580)(107, 559)(108, 545)(109, 560)(110, 562)(111, 563)(112, 565)(113, 566)(114, 567)(115, 568)(116, 561)(117, 569)(118, 570)(119, 571)(120, 572)(121, 573)(122, 574)(123, 575)(124, 576)(125, 577)(126, 578)(127, 579)(128, 581)(129, 582)(130, 583)(131, 584)(132, 543)(133, 586)(134, 589)(135, 590)(136, 593)(137, 547)(138, 594)(139, 556)(140, 550)(141, 625)(142, 619)(143, 585)(144, 554)(145, 629)(146, 626)(147, 588)(148, 587)(149, 592)(150, 591)(151, 596)(152, 595)(153, 598)(154, 597)(155, 600)(156, 599)(157, 602)(158, 601)(159, 604)(160, 603)(161, 606)(162, 605)(163, 608)(164, 607)(165, 610)(166, 609)(167, 612)(168, 611)(169, 614)(170, 613)(171, 624)(172, 616)(173, 615)(174, 618)(175, 617)(176, 630)(177, 633)(178, 634)(179, 621)(180, 620)(181, 635)(182, 636)(183, 623)(184, 622)(185, 637)(186, 638)(187, 639)(188, 640)(189, 641)(190, 642)(191, 643)(192, 644)(193, 645)(194, 646)(195, 647)(196, 648)(197, 649)(198, 650)(199, 651)(200, 652)(201, 653)(202, 654)(203, 655)(204, 656)(205, 657)(206, 658)(207, 659)(208, 660)(209, 663)(210, 664)(211, 667)(212, 668)(213, 628)(214, 627)(215, 672)(216, 671)(217, 632)(218, 631)(219, 669)(220, 670)(221, 662)(222, 661)(223, 666)(224, 665)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 8, 112 ), ( 8, 112, 8, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2284
Graph:: simple bipartite
	v = 336 e = 448 f = 60
	degree seq :: [ 2^224, 4^112 ]

E27.2286 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^56 ]
Map:: polytopal
	R = (1, 225, 2, 226, 5, 229, 11, 235, 20, 244, 29, 253, 37, 261, 45, 269, 53, 277, 61, 285, 85, 309, 82, 306, 86, 310, 90, 314, 94, 318, 98, 322, 102, 326, 107, 331, 128, 352, 118, 342, 112, 336, 114, 338, 120, 344, 130, 354, 140, 364, 150, 374, 158, 382, 166, 390, 174, 398, 182, 406, 220, 444, 216, 440, 222, 446, 223, 447, 213, 437, 205, 429, 193, 417, 199, 423, 187, 411, 177, 401, 171, 395, 161, 385, 155, 379, 145, 369, 137, 361, 123, 347, 131, 355, 68, 292, 60, 284, 52, 276, 44, 268, 36, 260, 28, 252, 19, 243, 10, 234, 4, 228)(3, 227, 7, 231, 15, 239, 25, 249, 33, 257, 41, 265, 49, 273, 57, 281, 65, 289, 74, 298, 80, 304, 77, 301, 83, 307, 88, 312, 92, 316, 96, 320, 100, 324, 104, 328, 110, 334, 125, 349, 116, 340, 124, 348, 134, 358, 146, 370, 154, 378, 162, 386, 170, 394, 178, 402, 186, 410, 200, 424, 212, 436, 206, 430, 218, 442, 224, 448, 197, 421, 215, 439, 189, 413, 181, 405, 207, 431, 165, 389, 175, 399, 149, 373, 159, 383, 129, 353, 143, 367, 113, 337, 141, 365, 117, 341, 62, 286, 55, 279, 46, 270, 39, 263, 30, 254, 22, 246, 12, 236, 8, 232)(6, 230, 13, 237, 9, 233, 18, 242, 27, 251, 35, 259, 43, 267, 51, 275, 59, 283, 67, 291, 76, 300, 71, 295, 75, 299, 81, 305, 87, 311, 91, 315, 95, 319, 99, 323, 103, 327, 108, 332, 122, 346, 132, 356, 127, 351, 138, 362, 148, 372, 156, 380, 164, 388, 172, 396, 180, 404, 188, 412, 204, 428, 194, 418, 202, 426, 214, 438, 209, 433, 221, 445, 191, 415, 219, 443, 195, 419, 173, 397, 183, 407, 157, 381, 167, 391, 139, 363, 151, 375, 119, 343, 135, 359, 111, 335, 105, 329, 63, 287, 54, 278, 47, 271, 38, 262, 31, 255, 21, 245, 14, 238)(16, 240, 23, 247, 17, 241, 24, 248, 32, 256, 40, 264, 48, 272, 56, 280, 64, 288, 78, 302, 72, 296, 69, 293, 70, 294, 73, 297, 79, 303, 84, 308, 89, 313, 93, 317, 97, 321, 101, 325, 106, 330, 142, 366, 136, 360, 144, 368, 152, 376, 160, 384, 168, 392, 176, 400, 184, 408, 208, 432, 196, 420, 190, 414, 192, 416, 198, 422, 210, 434, 217, 441, 201, 425, 211, 435, 203, 427, 185, 409, 179, 403, 169, 393, 163, 387, 153, 377, 147, 371, 133, 357, 126, 350, 115, 339, 121, 345, 109, 333, 66, 290, 58, 282, 50, 274, 42, 266, 34, 258, 26, 250)(449, 673)(450, 674)(451, 675)(452, 676)(453, 677)(454, 678)(455, 679)(456, 680)(457, 681)(458, 682)(459, 683)(460, 684)(461, 685)(462, 686)(463, 687)(464, 688)(465, 689)(466, 690)(467, 691)(468, 692)(469, 693)(470, 694)(471, 695)(472, 696)(473, 697)(474, 698)(475, 699)(476, 700)(477, 701)(478, 702)(479, 703)(480, 704)(481, 705)(482, 706)(483, 707)(484, 708)(485, 709)(486, 710)(487, 711)(488, 712)(489, 713)(490, 714)(491, 715)(492, 716)(493, 717)(494, 718)(495, 719)(496, 720)(497, 721)(498, 722)(499, 723)(500, 724)(501, 725)(502, 726)(503, 727)(504, 728)(505, 729)(506, 730)(507, 731)(508, 732)(509, 733)(510, 734)(511, 735)(512, 736)(513, 737)(514, 738)(515, 739)(516, 740)(517, 741)(518, 742)(519, 743)(520, 744)(521, 745)(522, 746)(523, 747)(524, 748)(525, 749)(526, 750)(527, 751)(528, 752)(529, 753)(530, 754)(531, 755)(532, 756)(533, 757)(534, 758)(535, 759)(536, 760)(537, 761)(538, 762)(539, 763)(540, 764)(541, 765)(542, 766)(543, 767)(544, 768)(545, 769)(546, 770)(547, 771)(548, 772)(549, 773)(550, 774)(551, 775)(552, 776)(553, 777)(554, 778)(555, 779)(556, 780)(557, 781)(558, 782)(559, 783)(560, 784)(561, 785)(562, 786)(563, 787)(564, 788)(565, 789)(566, 790)(567, 791)(568, 792)(569, 793)(570, 794)(571, 795)(572, 796)(573, 797)(574, 798)(575, 799)(576, 800)(577, 801)(578, 802)(579, 803)(580, 804)(581, 805)(582, 806)(583, 807)(584, 808)(585, 809)(586, 810)(587, 811)(588, 812)(589, 813)(590, 814)(591, 815)(592, 816)(593, 817)(594, 818)(595, 819)(596, 820)(597, 821)(598, 822)(599, 823)(600, 824)(601, 825)(602, 826)(603, 827)(604, 828)(605, 829)(606, 830)(607, 831)(608, 832)(609, 833)(610, 834)(611, 835)(612, 836)(613, 837)(614, 838)(615, 839)(616, 840)(617, 841)(618, 842)(619, 843)(620, 844)(621, 845)(622, 846)(623, 847)(624, 848)(625, 849)(626, 850)(627, 851)(628, 852)(629, 853)(630, 854)(631, 855)(632, 856)(633, 857)(634, 858)(635, 859)(636, 860)(637, 861)(638, 862)(639, 863)(640, 864)(641, 865)(642, 866)(643, 867)(644, 868)(645, 869)(646, 870)(647, 871)(648, 872)(649, 873)(650, 874)(651, 875)(652, 876)(653, 877)(654, 878)(655, 879)(656, 880)(657, 881)(658, 882)(659, 883)(660, 884)(661, 885)(662, 886)(663, 887)(664, 888)(665, 889)(666, 890)(667, 891)(668, 892)(669, 893)(670, 894)(671, 895)(672, 896)
	L = (1, 451)(2, 454)(3, 449)(4, 457)(5, 460)(6, 450)(7, 464)(8, 465)(9, 452)(10, 463)(11, 469)(12, 453)(13, 471)(14, 472)(15, 458)(16, 455)(17, 456)(18, 474)(19, 475)(20, 478)(21, 459)(22, 480)(23, 461)(24, 462)(25, 482)(26, 466)(27, 467)(28, 481)(29, 486)(30, 468)(31, 488)(32, 470)(33, 476)(34, 473)(35, 490)(36, 491)(37, 494)(38, 477)(39, 496)(40, 479)(41, 498)(42, 483)(43, 484)(44, 497)(45, 502)(46, 485)(47, 504)(48, 487)(49, 492)(50, 489)(51, 506)(52, 507)(53, 510)(54, 493)(55, 512)(56, 495)(57, 514)(58, 499)(59, 500)(60, 513)(61, 553)(62, 501)(63, 526)(64, 503)(65, 508)(66, 505)(67, 557)(68, 524)(69, 559)(70, 561)(71, 563)(72, 565)(73, 567)(74, 569)(75, 571)(76, 516)(77, 574)(78, 511)(79, 577)(80, 579)(81, 581)(82, 583)(83, 585)(84, 587)(85, 589)(86, 591)(87, 593)(88, 595)(89, 597)(90, 599)(91, 601)(92, 603)(93, 605)(94, 607)(95, 609)(96, 611)(97, 613)(98, 615)(99, 617)(100, 619)(101, 621)(102, 623)(103, 625)(104, 627)(105, 509)(106, 629)(107, 631)(108, 633)(109, 515)(110, 635)(111, 517)(112, 637)(113, 518)(114, 639)(115, 519)(116, 641)(117, 520)(118, 643)(119, 521)(120, 645)(121, 522)(122, 647)(123, 523)(124, 649)(125, 651)(126, 525)(127, 653)(128, 655)(129, 527)(130, 657)(131, 528)(132, 659)(133, 529)(134, 661)(135, 530)(136, 663)(137, 531)(138, 665)(139, 532)(140, 666)(141, 533)(142, 667)(143, 534)(144, 669)(145, 535)(146, 658)(147, 536)(148, 671)(149, 537)(150, 650)(151, 538)(152, 672)(153, 539)(154, 670)(155, 540)(156, 646)(157, 541)(158, 660)(159, 542)(160, 662)(161, 543)(162, 640)(163, 544)(164, 664)(165, 545)(166, 652)(167, 546)(168, 654)(169, 547)(170, 668)(171, 548)(172, 638)(173, 549)(174, 634)(175, 550)(176, 642)(177, 551)(178, 644)(179, 552)(180, 630)(181, 554)(182, 628)(183, 555)(184, 648)(185, 556)(186, 622)(187, 558)(188, 656)(189, 560)(190, 620)(191, 562)(192, 610)(193, 564)(194, 624)(195, 566)(196, 626)(197, 568)(198, 604)(199, 570)(200, 632)(201, 572)(202, 598)(203, 573)(204, 614)(205, 575)(206, 616)(207, 576)(208, 636)(209, 578)(210, 594)(211, 580)(212, 606)(213, 582)(214, 608)(215, 584)(216, 612)(217, 586)(218, 588)(219, 590)(220, 618)(221, 592)(222, 602)(223, 596)(224, 600)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2283
Graph:: simple bipartite
	v = 228 e = 448 f = 168
	degree seq :: [ 2^224, 112^4 ]

E27.2287 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^56 ]
Map::
	R = (1, 225, 2, 226)(3, 227, 7, 231)(4, 228, 9, 233)(5, 229, 11, 235)(6, 230, 13, 237)(8, 232, 14, 238)(10, 234, 12, 236)(15, 239, 20, 244)(16, 240, 23, 247)(17, 241, 25, 249)(18, 242, 21, 245)(19, 243, 27, 251)(22, 246, 29, 253)(24, 248, 31, 255)(26, 250, 32, 256)(28, 252, 30, 254)(33, 257, 39, 263)(34, 258, 41, 265)(35, 259, 37, 261)(36, 260, 43, 267)(38, 262, 45, 269)(40, 264, 47, 271)(42, 266, 48, 272)(44, 268, 46, 270)(49, 273, 55, 279)(50, 274, 57, 281)(51, 275, 53, 277)(52, 276, 59, 283)(54, 278, 61, 285)(56, 280, 63, 287)(58, 282, 64, 288)(60, 284, 62, 286)(65, 289, 69, 293)(66, 290, 99, 323)(67, 291, 101, 325)(68, 292, 71, 295)(70, 294, 104, 328)(72, 296, 107, 331)(73, 297, 109, 333)(74, 298, 111, 335)(75, 299, 113, 337)(76, 300, 115, 339)(77, 301, 117, 341)(78, 302, 119, 343)(79, 303, 121, 345)(80, 304, 123, 347)(81, 305, 125, 349)(82, 306, 127, 351)(83, 307, 129, 353)(84, 308, 131, 355)(85, 309, 133, 357)(86, 310, 135, 359)(87, 311, 137, 361)(88, 312, 139, 363)(89, 313, 141, 365)(90, 314, 143, 367)(91, 315, 145, 369)(92, 316, 147, 371)(93, 317, 149, 373)(94, 318, 151, 375)(95, 319, 153, 377)(96, 320, 155, 379)(97, 321, 157, 381)(98, 322, 159, 383)(100, 324, 161, 385)(102, 326, 163, 387)(103, 327, 165, 389)(105, 329, 167, 391)(106, 330, 169, 393)(108, 332, 171, 395)(110, 334, 173, 397)(112, 336, 175, 399)(114, 338, 177, 401)(116, 340, 179, 403)(118, 342, 181, 405)(120, 344, 183, 407)(122, 346, 185, 409)(124, 348, 187, 411)(126, 350, 189, 413)(128, 352, 191, 415)(130, 354, 193, 417)(132, 356, 195, 419)(134, 358, 197, 421)(136, 360, 199, 423)(138, 362, 201, 425)(140, 364, 203, 427)(142, 366, 205, 429)(144, 368, 207, 431)(146, 370, 209, 433)(148, 372, 211, 435)(150, 374, 213, 437)(152, 376, 215, 439)(154, 378, 217, 441)(156, 380, 219, 443)(158, 382, 221, 445)(160, 384, 223, 447)(162, 386, 214, 438)(164, 388, 218, 442)(166, 390, 222, 446)(168, 392, 220, 444)(170, 394, 224, 448)(172, 396, 206, 430)(174, 398, 210, 434)(176, 400, 202, 426)(178, 402, 204, 428)(180, 404, 216, 440)(182, 406, 208, 432)(184, 408, 212, 436)(186, 410, 190, 414)(188, 412, 194, 418)(192, 416, 198, 422)(196, 420, 200, 424)(449, 673, 451, 675, 456, 680, 465, 689, 474, 698, 482, 706, 490, 714, 498, 722, 506, 730, 514, 738, 526, 750, 530, 754, 534, 758, 538, 762, 542, 766, 546, 770, 551, 775, 553, 777, 556, 780, 562, 786, 570, 794, 578, 802, 586, 810, 594, 818, 602, 826, 610, 834, 632, 856, 640, 864, 648, 872, 656, 880, 664, 888, 672, 896, 669, 893, 667, 891, 653, 877, 651, 875, 637, 861, 635, 859, 623, 847, 621, 845, 611, 835, 597, 821, 595, 819, 581, 805, 579, 803, 565, 789, 563, 787, 516, 740, 508, 732, 500, 724, 492, 716, 484, 708, 476, 700, 467, 691, 458, 682, 452, 676)(450, 674, 453, 677, 460, 684, 470, 694, 478, 702, 486, 710, 494, 718, 502, 726, 510, 734, 521, 745, 524, 748, 528, 752, 532, 756, 536, 760, 540, 764, 544, 768, 550, 774, 554, 778, 560, 784, 566, 790, 574, 798, 582, 806, 590, 814, 598, 822, 606, 830, 622, 846, 628, 852, 636, 860, 644, 868, 652, 876, 660, 884, 668, 892, 665, 889, 671, 895, 649, 873, 655, 879, 633, 857, 639, 863, 619, 843, 609, 833, 613, 837, 593, 817, 599, 823, 577, 801, 583, 807, 561, 785, 567, 791, 552, 776, 512, 736, 504, 728, 496, 720, 488, 712, 480, 704, 472, 696, 462, 686, 454, 678)(455, 679, 463, 687, 457, 681, 466, 690, 475, 699, 483, 707, 491, 715, 499, 723, 507, 731, 515, 739, 519, 743, 522, 746, 525, 749, 529, 753, 533, 757, 537, 761, 541, 765, 545, 769, 558, 782, 564, 788, 572, 796, 580, 804, 588, 812, 596, 820, 604, 828, 612, 836, 618, 842, 624, 848, 630, 854, 638, 862, 646, 870, 654, 878, 662, 886, 670, 894, 657, 881, 663, 887, 641, 865, 647, 871, 625, 849, 631, 855, 615, 839, 601, 825, 607, 831, 585, 809, 591, 815, 569, 793, 575, 799, 555, 779, 547, 771, 513, 737, 505, 729, 497, 721, 489, 713, 481, 705, 473, 697, 464, 688)(459, 683, 468, 692, 461, 685, 471, 695, 479, 703, 487, 711, 495, 719, 503, 727, 511, 735, 517, 741, 518, 742, 520, 744, 523, 747, 527, 751, 531, 755, 535, 759, 539, 763, 543, 767, 548, 772, 568, 792, 576, 800, 584, 808, 592, 816, 600, 824, 608, 832, 614, 838, 616, 840, 620, 844, 626, 850, 634, 858, 642, 866, 650, 874, 658, 882, 666, 890, 661, 885, 659, 883, 645, 869, 643, 867, 629, 853, 627, 851, 617, 841, 605, 829, 603, 827, 589, 813, 587, 811, 573, 797, 571, 795, 559, 783, 557, 781, 549, 773, 509, 733, 501, 725, 493, 717, 485, 709, 477, 701, 469, 693)
	L = (1, 450)(2, 449)(3, 455)(4, 457)(5, 459)(6, 461)(7, 451)(8, 462)(9, 452)(10, 460)(11, 453)(12, 458)(13, 454)(14, 456)(15, 468)(16, 471)(17, 473)(18, 469)(19, 475)(20, 463)(21, 466)(22, 477)(23, 464)(24, 479)(25, 465)(26, 480)(27, 467)(28, 478)(29, 470)(30, 476)(31, 472)(32, 474)(33, 487)(34, 489)(35, 485)(36, 491)(37, 483)(38, 493)(39, 481)(40, 495)(41, 482)(42, 496)(43, 484)(44, 494)(45, 486)(46, 492)(47, 488)(48, 490)(49, 503)(50, 505)(51, 501)(52, 507)(53, 499)(54, 509)(55, 497)(56, 511)(57, 498)(58, 512)(59, 500)(60, 510)(61, 502)(62, 508)(63, 504)(64, 506)(65, 517)(66, 547)(67, 549)(68, 519)(69, 513)(70, 552)(71, 516)(72, 555)(73, 557)(74, 559)(75, 561)(76, 563)(77, 565)(78, 567)(79, 569)(80, 571)(81, 573)(82, 575)(83, 577)(84, 579)(85, 581)(86, 583)(87, 585)(88, 587)(89, 589)(90, 591)(91, 593)(92, 595)(93, 597)(94, 599)(95, 601)(96, 603)(97, 605)(98, 607)(99, 514)(100, 609)(101, 515)(102, 611)(103, 613)(104, 518)(105, 615)(106, 617)(107, 520)(108, 619)(109, 521)(110, 621)(111, 522)(112, 623)(113, 523)(114, 625)(115, 524)(116, 627)(117, 525)(118, 629)(119, 526)(120, 631)(121, 527)(122, 633)(123, 528)(124, 635)(125, 529)(126, 637)(127, 530)(128, 639)(129, 531)(130, 641)(131, 532)(132, 643)(133, 533)(134, 645)(135, 534)(136, 647)(137, 535)(138, 649)(139, 536)(140, 651)(141, 537)(142, 653)(143, 538)(144, 655)(145, 539)(146, 657)(147, 540)(148, 659)(149, 541)(150, 661)(151, 542)(152, 663)(153, 543)(154, 665)(155, 544)(156, 667)(157, 545)(158, 669)(159, 546)(160, 671)(161, 548)(162, 662)(163, 550)(164, 666)(165, 551)(166, 670)(167, 553)(168, 668)(169, 554)(170, 672)(171, 556)(172, 654)(173, 558)(174, 658)(175, 560)(176, 650)(177, 562)(178, 652)(179, 564)(180, 664)(181, 566)(182, 656)(183, 568)(184, 660)(185, 570)(186, 638)(187, 572)(188, 642)(189, 574)(190, 634)(191, 576)(192, 646)(193, 578)(194, 636)(195, 580)(196, 648)(197, 582)(198, 640)(199, 584)(200, 644)(201, 586)(202, 624)(203, 588)(204, 626)(205, 590)(206, 620)(207, 592)(208, 630)(209, 594)(210, 622)(211, 596)(212, 632)(213, 598)(214, 610)(215, 600)(216, 628)(217, 602)(218, 612)(219, 604)(220, 616)(221, 606)(222, 614)(223, 608)(224, 618)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2288
Graph:: bipartite
	v = 116 e = 448 f = 280
	degree seq :: [ 4^112, 112^4 ]

E27.2288 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C56 x C2) : C2 (small group id <224, 27>)
Aut   = $<448, 266>$ (small group id <448, 266>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^56 ]
Map:: polytopal
	R = (1, 225, 2, 226, 6, 230, 4, 228)(3, 227, 9, 233, 13, 237, 8, 232)(5, 229, 11, 235, 14, 238, 7, 231)(10, 234, 16, 240, 21, 245, 17, 241)(12, 236, 15, 239, 22, 246, 19, 243)(18, 242, 25, 249, 29, 253, 24, 248)(20, 244, 27, 251, 30, 254, 23, 247)(26, 250, 32, 256, 37, 261, 33, 257)(28, 252, 31, 255, 38, 262, 35, 259)(34, 258, 41, 265, 45, 269, 40, 264)(36, 260, 43, 267, 46, 270, 39, 263)(42, 266, 48, 272, 53, 277, 49, 273)(44, 268, 47, 271, 54, 278, 51, 275)(50, 274, 57, 281, 61, 285, 56, 280)(52, 276, 59, 283, 62, 286, 55, 279)(58, 282, 64, 288, 105, 329, 65, 289)(60, 284, 63, 287, 78, 302, 67, 291)(66, 290, 75, 299, 124, 348, 79, 303)(68, 292, 111, 335, 71, 295, 107, 331)(69, 293, 113, 337, 74, 298, 115, 339)(70, 294, 110, 334, 72, 296, 117, 341)(73, 297, 120, 344, 81, 305, 122, 346)(76, 300, 126, 350, 77, 301, 128, 352)(80, 304, 132, 356, 85, 309, 134, 358)(82, 306, 136, 360, 83, 307, 138, 362)(84, 308, 140, 364, 89, 313, 142, 366)(86, 310, 144, 368, 87, 311, 146, 370)(88, 312, 148, 372, 93, 317, 150, 374)(90, 314, 152, 376, 91, 315, 154, 378)(92, 316, 156, 380, 97, 321, 158, 382)(94, 318, 160, 384, 95, 319, 162, 386)(96, 320, 164, 388, 101, 325, 166, 390)(98, 322, 168, 392, 99, 323, 170, 394)(100, 324, 172, 396, 106, 330, 174, 398)(102, 326, 176, 400, 103, 327, 178, 402)(104, 328, 180, 404, 130, 354, 182, 406)(108, 332, 183, 407, 109, 333, 187, 411)(112, 336, 190, 414, 118, 342, 185, 409)(114, 338, 192, 416, 123, 347, 194, 418)(116, 340, 189, 413, 119, 343, 196, 420)(121, 345, 199, 423, 135, 359, 201, 425)(125, 349, 203, 427, 131, 355, 205, 429)(127, 351, 206, 430, 129, 353, 208, 432)(133, 357, 212, 436, 143, 367, 214, 438)(137, 361, 216, 440, 139, 363, 218, 442)(141, 365, 220, 444, 151, 375, 222, 446)(145, 369, 224, 448, 147, 371, 221, 445)(149, 373, 219, 443, 159, 383, 217, 441)(153, 377, 213, 437, 155, 379, 223, 447)(157, 381, 207, 431, 167, 391, 209, 433)(161, 385, 215, 439, 163, 387, 200, 424)(165, 389, 198, 422, 175, 399, 195, 419)(169, 393, 193, 417, 171, 395, 202, 426)(173, 397, 204, 428, 184, 408, 211, 435)(177, 401, 191, 415, 179, 403, 197, 421)(181, 405, 186, 410, 210, 434, 188, 412)(449, 673)(450, 674)(451, 675)(452, 676)(453, 677)(454, 678)(455, 679)(456, 680)(457, 681)(458, 682)(459, 683)(460, 684)(461, 685)(462, 686)(463, 687)(464, 688)(465, 689)(466, 690)(467, 691)(468, 692)(469, 693)(470, 694)(471, 695)(472, 696)(473, 697)(474, 698)(475, 699)(476, 700)(477, 701)(478, 702)(479, 703)(480, 704)(481, 705)(482, 706)(483, 707)(484, 708)(485, 709)(486, 710)(487, 711)(488, 712)(489, 713)(490, 714)(491, 715)(492, 716)(493, 717)(494, 718)(495, 719)(496, 720)(497, 721)(498, 722)(499, 723)(500, 724)(501, 725)(502, 726)(503, 727)(504, 728)(505, 729)(506, 730)(507, 731)(508, 732)(509, 733)(510, 734)(511, 735)(512, 736)(513, 737)(514, 738)(515, 739)(516, 740)(517, 741)(518, 742)(519, 743)(520, 744)(521, 745)(522, 746)(523, 747)(524, 748)(525, 749)(526, 750)(527, 751)(528, 752)(529, 753)(530, 754)(531, 755)(532, 756)(533, 757)(534, 758)(535, 759)(536, 760)(537, 761)(538, 762)(539, 763)(540, 764)(541, 765)(542, 766)(543, 767)(544, 768)(545, 769)(546, 770)(547, 771)(548, 772)(549, 773)(550, 774)(551, 775)(552, 776)(553, 777)(554, 778)(555, 779)(556, 780)(557, 781)(558, 782)(559, 783)(560, 784)(561, 785)(562, 786)(563, 787)(564, 788)(565, 789)(566, 790)(567, 791)(568, 792)(569, 793)(570, 794)(571, 795)(572, 796)(573, 797)(574, 798)(575, 799)(576, 800)(577, 801)(578, 802)(579, 803)(580, 804)(581, 805)(582, 806)(583, 807)(584, 808)(585, 809)(586, 810)(587, 811)(588, 812)(589, 813)(590, 814)(591, 815)(592, 816)(593, 817)(594, 818)(595, 819)(596, 820)(597, 821)(598, 822)(599, 823)(600, 824)(601, 825)(602, 826)(603, 827)(604, 828)(605, 829)(606, 830)(607, 831)(608, 832)(609, 833)(610, 834)(611, 835)(612, 836)(613, 837)(614, 838)(615, 839)(616, 840)(617, 841)(618, 842)(619, 843)(620, 844)(621, 845)(622, 846)(623, 847)(624, 848)(625, 849)(626, 850)(627, 851)(628, 852)(629, 853)(630, 854)(631, 855)(632, 856)(633, 857)(634, 858)(635, 859)(636, 860)(637, 861)(638, 862)(639, 863)(640, 864)(641, 865)(642, 866)(643, 867)(644, 868)(645, 869)(646, 870)(647, 871)(648, 872)(649, 873)(650, 874)(651, 875)(652, 876)(653, 877)(654, 878)(655, 879)(656, 880)(657, 881)(658, 882)(659, 883)(660, 884)(661, 885)(662, 886)(663, 887)(664, 888)(665, 889)(666, 890)(667, 891)(668, 892)(669, 893)(670, 894)(671, 895)(672, 896)
	L = (1, 451)(2, 455)(3, 458)(4, 459)(5, 449)(6, 461)(7, 463)(8, 450)(9, 452)(10, 466)(11, 467)(12, 453)(13, 469)(14, 454)(15, 471)(16, 456)(17, 457)(18, 474)(19, 475)(20, 460)(21, 477)(22, 462)(23, 479)(24, 464)(25, 465)(26, 482)(27, 483)(28, 468)(29, 485)(30, 470)(31, 487)(32, 472)(33, 473)(34, 490)(35, 491)(36, 476)(37, 493)(38, 478)(39, 495)(40, 480)(41, 481)(42, 498)(43, 499)(44, 484)(45, 501)(46, 486)(47, 503)(48, 488)(49, 489)(50, 506)(51, 507)(52, 492)(53, 509)(54, 494)(55, 511)(56, 496)(57, 497)(58, 514)(59, 515)(60, 500)(61, 553)(62, 502)(63, 555)(64, 504)(65, 505)(66, 558)(67, 559)(68, 508)(69, 519)(70, 523)(71, 526)(72, 527)(73, 517)(74, 516)(75, 513)(76, 518)(77, 520)(78, 510)(79, 512)(80, 521)(81, 522)(82, 524)(83, 525)(84, 528)(85, 529)(86, 530)(87, 531)(88, 532)(89, 533)(90, 534)(91, 535)(92, 536)(93, 537)(94, 538)(95, 539)(96, 540)(97, 541)(98, 542)(99, 543)(100, 544)(101, 545)(102, 546)(103, 547)(104, 548)(105, 572)(106, 549)(107, 563)(108, 550)(109, 551)(110, 576)(111, 561)(112, 552)(113, 570)(114, 566)(115, 568)(116, 573)(117, 574)(118, 578)(119, 579)(120, 582)(121, 562)(122, 580)(123, 560)(124, 565)(125, 557)(126, 586)(127, 564)(128, 584)(129, 567)(130, 554)(131, 556)(132, 590)(133, 569)(134, 588)(135, 571)(136, 594)(137, 575)(138, 592)(139, 577)(140, 598)(141, 581)(142, 596)(143, 583)(144, 602)(145, 585)(146, 600)(147, 587)(148, 606)(149, 589)(150, 604)(151, 591)(152, 610)(153, 593)(154, 608)(155, 595)(156, 614)(157, 597)(158, 612)(159, 599)(160, 618)(161, 601)(162, 616)(163, 603)(164, 622)(165, 605)(166, 620)(167, 607)(168, 626)(169, 609)(170, 624)(171, 611)(172, 630)(173, 613)(174, 628)(175, 615)(176, 635)(177, 617)(178, 631)(179, 619)(180, 633)(181, 621)(182, 638)(183, 651)(184, 623)(185, 642)(186, 625)(187, 653)(188, 627)(189, 656)(190, 640)(191, 629)(192, 649)(193, 645)(194, 647)(195, 652)(196, 654)(197, 658)(198, 659)(199, 662)(200, 641)(201, 660)(202, 639)(203, 644)(204, 636)(205, 637)(206, 666)(207, 643)(208, 664)(209, 646)(210, 632)(211, 634)(212, 670)(213, 648)(214, 668)(215, 650)(216, 669)(217, 655)(218, 672)(219, 657)(220, 665)(221, 661)(222, 667)(223, 663)(224, 671)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 4, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2287
Graph:: simple bipartite
	v = 280 e = 448 f = 116
	degree seq :: [ 2^224, 8^56 ]

E27.2289 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 56})
Quotient :: regular
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^4, (T2 * T1^4)^2, T2 * T1 * T2 * T1^-1 * T2 * T1^-3 * T2 * T1^-1, T1^26 * T2 * T1^-2 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 45, 68, 85, 101, 117, 133, 149, 165, 181, 197, 213, 207, 191, 174, 160, 143, 127, 110, 96, 79, 61, 32, 54, 73, 63, 36, 57, 75, 91, 107, 123, 139, 155, 171, 187, 203, 219, 212, 196, 180, 164, 148, 132, 116, 100, 84, 67, 44, 22, 10, 4)(3, 7, 15, 31, 59, 77, 93, 109, 125, 141, 157, 173, 189, 205, 214, 204, 185, 167, 150, 140, 121, 103, 86, 76, 52, 26, 12, 25, 49, 42, 21, 41, 65, 82, 98, 114, 130, 146, 162, 178, 194, 210, 217, 199, 182, 172, 153, 135, 118, 108, 89, 70, 46, 37, 18, 8)(6, 13, 27, 53, 43, 66, 83, 99, 115, 131, 147, 163, 179, 195, 211, 220, 201, 183, 166, 156, 137, 119, 102, 92, 72, 48, 24, 47, 40, 20, 9, 19, 38, 64, 81, 97, 113, 129, 145, 161, 177, 193, 209, 215, 198, 188, 169, 151, 134, 124, 105, 87, 69, 58, 30, 14)(16, 33, 50, 29, 56, 71, 90, 104, 122, 136, 154, 168, 186, 200, 218, 223, 222, 206, 190, 176, 159, 142, 126, 112, 95, 78, 60, 39, 55, 28, 17, 35, 51, 74, 88, 106, 120, 138, 152, 170, 184, 202, 216, 224, 221, 208, 192, 175, 158, 144, 128, 111, 94, 80, 62, 34)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 60)(34, 53)(35, 47)(37, 56)(38, 61)(40, 63)(41, 62)(42, 55)(44, 59)(45, 69)(48, 71)(49, 73)(52, 75)(58, 74)(64, 80)(65, 79)(66, 78)(67, 81)(68, 86)(70, 88)(72, 91)(76, 90)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 107)(92, 106)(93, 110)(97, 112)(99, 111)(100, 115)(101, 118)(103, 120)(105, 123)(108, 122)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 139)(124, 138)(129, 144)(130, 143)(131, 142)(132, 145)(133, 150)(135, 152)(137, 155)(140, 154)(141, 158)(146, 159)(147, 160)(148, 162)(149, 166)(151, 168)(153, 171)(156, 170)(157, 174)(161, 176)(163, 175)(164, 179)(165, 182)(167, 184)(169, 187)(172, 186)(173, 190)(177, 191)(178, 192)(180, 189)(181, 198)(183, 200)(185, 203)(188, 202)(193, 208)(194, 207)(195, 206)(196, 209)(197, 214)(199, 216)(201, 219)(204, 218)(205, 221)(210, 222)(211, 213)(212, 217)(215, 223)(220, 224)
	local type(s) :: { ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2290
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 4 e = 112 f = 56
	degree seq :: [ 56^4 ]

E27.2290 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 56})
Quotient :: regular
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 32, 25)(15, 26, 33, 27)(21, 35, 29, 36)(22, 37, 30, 38)(23, 34, 44, 39)(40, 49, 42, 50)(41, 51, 43, 52)(45, 53, 47, 54)(46, 55, 48, 56)(57, 65, 59, 66)(58, 67, 60, 68)(61, 69, 63, 70)(62, 71, 64, 72)(73, 113, 75, 117)(74, 115, 76, 119)(77, 121, 89, 123)(78, 124, 82, 126)(79, 127, 100, 129)(80, 130, 81, 132)(83, 135, 93, 137)(84, 138, 85, 140)(86, 142, 90, 144)(87, 145, 88, 147)(91, 151, 92, 153)(94, 156, 95, 158)(96, 160, 97, 162)(98, 164, 99, 166)(101, 169, 102, 171)(103, 173, 104, 175)(105, 177, 106, 179)(107, 181, 108, 183)(109, 185, 110, 187)(111, 189, 112, 191)(114, 194, 116, 193)(118, 198, 120, 197)(122, 202, 128, 201)(125, 206, 136, 205)(131, 212, 143, 211)(133, 215, 150, 214)(134, 217, 155, 208)(139, 213, 157, 216)(141, 221, 159, 220)(146, 218, 152, 207)(148, 222, 154, 219)(149, 210, 168, 204)(161, 223, 165, 203)(163, 224, 167, 209)(170, 195, 174, 199)(172, 196, 176, 200)(178, 186, 182, 190)(180, 188, 184, 192)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 100)(70, 89)(71, 79)(72, 77)(78, 119)(80, 121)(81, 127)(82, 117)(83, 115)(84, 124)(85, 135)(86, 123)(87, 130)(88, 142)(90, 129)(91, 132)(92, 144)(93, 113)(94, 126)(95, 137)(96, 138)(97, 156)(98, 140)(99, 158)(101, 145)(102, 151)(103, 147)(104, 153)(105, 160)(106, 164)(107, 162)(108, 166)(109, 169)(110, 173)(111, 171)(112, 175)(114, 177)(116, 181)(118, 179)(120, 183)(122, 191)(125, 197)(128, 187)(131, 202)(133, 201)(134, 198)(136, 193)(139, 206)(141, 205)(143, 210)(146, 212)(148, 211)(149, 189)(150, 204)(152, 215)(154, 214)(155, 194)(157, 217)(159, 208)(161, 213)(163, 216)(165, 221)(167, 220)(168, 185)(170, 218)(172, 207)(174, 222)(176, 219)(178, 223)(180, 203)(182, 224)(184, 209)(186, 195)(188, 199)(190, 196)(192, 200)
	local type(s) :: { ( 56^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2289
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 56 e = 112 f = 4
	degree seq :: [ 4^56 ]

E27.2291 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 28, 40)(25, 41, 30, 42)(31, 44, 36, 45)(33, 46, 38, 47)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 73, 67, 74)(66, 75, 68, 76)(69, 89, 71, 77)(70, 104, 72, 82)(78, 113, 94, 117)(79, 115, 95, 119)(80, 128, 92, 130)(81, 121, 93, 133)(83, 136, 85, 138)(84, 123, 86, 125)(87, 146, 90, 148)(88, 127, 91, 131)(96, 141, 98, 143)(97, 135, 99, 139)(100, 152, 102, 154)(101, 145, 103, 149)(105, 164, 107, 166)(106, 160, 108, 162)(109, 172, 111, 174)(110, 168, 112, 170)(114, 181, 118, 183)(116, 177, 120, 179)(122, 185, 134, 187)(124, 194, 126, 197)(129, 211, 132, 202)(137, 216, 140, 205)(142, 215, 144, 204)(147, 218, 150, 210)(151, 189, 176, 191)(153, 217, 155, 208)(156, 209, 157, 201)(158, 193, 159, 196)(161, 220, 163, 213)(165, 219, 167, 212)(169, 223, 171, 207)(173, 222, 175, 206)(178, 221, 180, 203)(182, 224, 184, 214)(186, 195, 188, 198)(190, 199, 192, 200)(225, 226)(227, 231)(228, 233)(229, 234)(230, 236)(232, 239)(235, 244)(237, 247)(238, 249)(240, 252)(241, 254)(242, 255)(243, 257)(245, 260)(246, 262)(248, 258)(250, 256)(251, 261)(253, 259)(263, 273)(264, 274)(265, 275)(266, 276)(267, 272)(268, 277)(269, 278)(270, 279)(271, 280)(281, 289)(282, 290)(283, 291)(284, 292)(285, 293)(286, 294)(287, 295)(288, 296)(297, 337)(298, 339)(299, 341)(300, 343)(301, 345)(302, 347)(303, 349)(304, 351)(305, 355)(306, 357)(307, 359)(308, 363)(309, 365)(310, 367)(311, 369)(312, 373)(313, 352)(314, 376)(315, 378)(316, 370)(317, 372)(318, 360)(319, 362)(320, 384)(321, 386)(322, 388)(323, 390)(324, 392)(325, 394)(326, 396)(327, 398)(328, 354)(329, 401)(330, 403)(331, 405)(332, 407)(333, 409)(334, 411)(335, 413)(336, 415)(338, 418)(340, 421)(342, 417)(344, 420)(346, 426)(348, 429)(350, 428)(353, 434)(356, 432)(358, 425)(361, 437)(364, 436)(366, 444)(368, 443)(371, 431)(374, 430)(375, 435)(377, 447)(379, 446)(380, 442)(381, 441)(382, 440)(383, 439)(385, 427)(387, 438)(389, 445)(391, 448)(393, 422)(395, 424)(397, 419)(399, 423)(400, 433)(402, 410)(404, 414)(406, 412)(408, 416)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 112, 112 ), ( 112^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2295
Transitivity :: ET+
Graph:: simple bipartite
	v = 168 e = 224 f = 4
	degree seq :: [ 2^112, 4^56 ]

E27.2292 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ F^2, T1^4, (T2 * T1)^2, T1^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-2, (T2^-1 * T1)^4, (T2^-3 * T1)^2, T2^-2 * T1 * T2^23 * T1 * T2^-3 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 24, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 216, 200, 184, 168, 152, 136, 120, 104, 88, 72, 56, 39, 28, 42, 19, 41, 58, 74, 90, 106, 122, 138, 154, 170, 186, 202, 218, 212, 196, 180, 164, 148, 132, 116, 100, 84, 68, 52, 32, 14, 5)(2, 7, 17, 38, 57, 73, 89, 105, 121, 137, 153, 169, 185, 201, 217, 206, 190, 174, 158, 142, 126, 110, 94, 78, 62, 46, 23, 11, 26, 35, 31, 51, 67, 83, 99, 115, 131, 147, 163, 179, 195, 211, 220, 204, 188, 172, 156, 140, 124, 108, 92, 76, 60, 44, 20, 8)(4, 12, 27, 49, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 222, 207, 191, 175, 159, 143, 127, 111, 95, 79, 63, 47, 25, 34, 30, 13, 29, 50, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 221, 205, 189, 173, 157, 141, 125, 109, 93, 77, 61, 45, 22, 9)(6, 15, 33, 53, 69, 85, 101, 117, 133, 149, 165, 181, 197, 213, 223, 215, 199, 183, 167, 151, 135, 119, 103, 87, 71, 55, 37, 18, 40, 21, 43, 59, 75, 91, 107, 123, 139, 155, 171, 187, 203, 219, 224, 214, 198, 182, 166, 150, 134, 118, 102, 86, 70, 54, 36, 16)(225, 226, 230, 228)(227, 233, 245, 235)(229, 237, 242, 231)(232, 243, 258, 239)(234, 247, 257, 249)(236, 240, 259, 252)(238, 255, 260, 253)(241, 261, 251, 263)(244, 267, 246, 265)(248, 271, 283, 268)(250, 264, 254, 266)(256, 273, 279, 275)(262, 280, 274, 278)(269, 277, 270, 282)(272, 284, 293, 285)(276, 281, 294, 289)(286, 299, 287, 298)(288, 301, 315, 302)(290, 296, 291, 295)(292, 306, 311, 297)(300, 314, 303, 309)(304, 318, 325, 319)(305, 310, 307, 312)(308, 323, 326, 322)(313, 327, 321, 328)(316, 331, 317, 330)(320, 335, 347, 332)(324, 337, 343, 339)(329, 344, 338, 342)(333, 341, 334, 346)(336, 348, 357, 349)(340, 345, 358, 353)(350, 363, 351, 362)(352, 365, 379, 366)(354, 360, 355, 359)(356, 370, 375, 361)(364, 378, 367, 373)(368, 382, 389, 383)(369, 374, 371, 376)(372, 387, 390, 386)(377, 391, 385, 392)(380, 395, 381, 394)(384, 399, 411, 396)(388, 401, 407, 403)(393, 408, 402, 406)(397, 405, 398, 410)(400, 412, 421, 413)(404, 409, 422, 417)(414, 427, 415, 426)(416, 429, 443, 430)(418, 424, 419, 423)(420, 434, 439, 425)(428, 442, 431, 437)(432, 441, 447, 446)(433, 438, 435, 440)(436, 444, 448, 445)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 4^4 ), ( 4^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2296
Transitivity :: ET+
Graph:: simple bipartite
	v = 60 e = 224 f = 112
	degree seq :: [ 4^56, 56^4 ]

E27.2293 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 56})
Quotient :: edge
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^4, T2 * T1^2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1, (T2 * T1^-4)^2, T1^22 * T2 * T1^-6 * T2 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 60)(34, 53)(35, 47)(37, 56)(38, 61)(40, 63)(41, 62)(42, 55)(44, 59)(45, 69)(48, 71)(49, 73)(52, 75)(58, 74)(64, 80)(65, 79)(66, 78)(67, 81)(68, 86)(70, 88)(72, 91)(76, 90)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 107)(92, 106)(93, 110)(97, 112)(99, 111)(100, 115)(101, 118)(103, 120)(105, 123)(108, 122)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 139)(124, 138)(129, 144)(130, 143)(131, 142)(132, 145)(133, 150)(135, 152)(137, 155)(140, 154)(141, 158)(146, 159)(147, 160)(148, 162)(149, 166)(151, 168)(153, 171)(156, 170)(157, 174)(161, 176)(163, 175)(164, 179)(165, 182)(167, 184)(169, 187)(172, 186)(173, 190)(177, 191)(178, 192)(180, 189)(181, 198)(183, 200)(185, 203)(188, 202)(193, 208)(194, 207)(195, 206)(196, 209)(197, 214)(199, 216)(201, 219)(204, 218)(205, 221)(210, 222)(211, 213)(212, 217)(215, 223)(220, 224)(225, 226, 229, 235, 247, 269, 292, 309, 325, 341, 357, 373, 389, 405, 421, 437, 431, 415, 398, 384, 367, 351, 334, 320, 303, 285, 256, 278, 297, 287, 260, 281, 299, 315, 331, 347, 363, 379, 395, 411, 427, 443, 436, 420, 404, 388, 372, 356, 340, 324, 308, 291, 268, 246, 234, 228)(227, 231, 239, 255, 283, 301, 317, 333, 349, 365, 381, 397, 413, 429, 438, 428, 409, 391, 374, 364, 345, 327, 310, 300, 276, 250, 236, 249, 273, 266, 245, 265, 289, 306, 322, 338, 354, 370, 386, 402, 418, 434, 441, 423, 406, 396, 377, 359, 342, 332, 313, 294, 270, 261, 242, 232)(230, 237, 251, 277, 267, 290, 307, 323, 339, 355, 371, 387, 403, 419, 435, 444, 425, 407, 390, 380, 361, 343, 326, 316, 296, 272, 248, 271, 264, 244, 233, 243, 262, 288, 305, 321, 337, 353, 369, 385, 401, 417, 433, 439, 422, 412, 393, 375, 358, 348, 329, 311, 293, 282, 254, 238)(240, 257, 274, 253, 280, 295, 314, 328, 346, 360, 378, 392, 410, 424, 442, 447, 446, 430, 414, 400, 383, 366, 350, 336, 319, 302, 284, 263, 279, 252, 241, 259, 275, 298, 312, 330, 344, 362, 376, 394, 408, 426, 440, 448, 445, 432, 416, 399, 382, 368, 352, 335, 318, 304, 286, 258)
	L = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)
	local type(s) :: { ( 8, 8 ), ( 8^56 ) }
Outer automorphisms :: reflexible
Dual of E27.2294
Transitivity :: ET+
Graph:: simple bipartite
	v = 116 e = 224 f = 56
	degree seq :: [ 2^112, 56^4 ]

E27.2294 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-2 * T1 * T2^-1 * T1 * T2 ]
Map::
	R = (1, 225, 3, 227, 8, 232, 4, 228)(2, 226, 5, 229, 11, 235, 6, 230)(7, 231, 13, 237, 24, 248, 14, 238)(9, 233, 16, 240, 29, 253, 17, 241)(10, 234, 18, 242, 32, 256, 19, 243)(12, 236, 21, 245, 37, 261, 22, 246)(15, 239, 26, 250, 43, 267, 27, 251)(20, 244, 34, 258, 48, 272, 35, 259)(23, 247, 39, 263, 28, 252, 40, 264)(25, 249, 41, 265, 30, 254, 42, 266)(31, 255, 44, 268, 36, 260, 45, 269)(33, 257, 46, 270, 38, 262, 47, 271)(49, 273, 57, 281, 51, 275, 58, 282)(50, 274, 59, 283, 52, 276, 60, 284)(53, 277, 61, 285, 55, 279, 62, 286)(54, 278, 63, 287, 56, 280, 64, 288)(65, 289, 73, 297, 67, 291, 74, 298)(66, 290, 75, 299, 68, 292, 76, 300)(69, 293, 100, 324, 71, 295, 85, 309)(70, 294, 97, 321, 72, 296, 83, 307)(77, 301, 130, 354, 84, 308, 132, 356)(78, 302, 121, 345, 86, 310, 125, 349)(79, 303, 136, 360, 80, 304, 138, 362)(81, 305, 142, 366, 82, 306, 144, 368)(87, 311, 139, 363, 88, 312, 155, 379)(89, 313, 123, 347, 107, 331, 127, 351)(90, 314, 135, 359, 91, 315, 162, 386)(92, 316, 145, 369, 93, 317, 167, 391)(94, 318, 150, 374, 112, 336, 147, 371)(95, 319, 141, 365, 96, 320, 174, 398)(98, 322, 129, 353, 99, 323, 170, 394)(101, 325, 133, 357, 102, 326, 158, 382)(103, 327, 156, 380, 104, 328, 163, 387)(105, 329, 153, 377, 106, 330, 160, 384)(108, 332, 168, 392, 109, 333, 175, 399)(110, 334, 165, 389, 111, 335, 172, 396)(113, 337, 185, 409, 114, 338, 189, 413)(115, 339, 183, 407, 116, 340, 187, 411)(117, 341, 194, 418, 118, 342, 198, 422)(119, 343, 192, 416, 120, 344, 196, 420)(122, 346, 203, 427, 124, 348, 207, 431)(126, 350, 201, 425, 128, 352, 205, 429)(131, 355, 224, 448, 149, 373, 222, 446)(134, 358, 223, 447, 152, 376, 219, 443)(137, 361, 214, 438, 140, 364, 216, 440)(143, 367, 206, 430, 146, 370, 208, 432)(148, 372, 213, 437, 177, 401, 209, 433)(151, 375, 215, 439, 180, 404, 211, 435)(154, 378, 193, 417, 157, 381, 195, 419)(159, 383, 221, 445, 191, 415, 217, 441)(161, 385, 197, 421, 164, 388, 199, 423)(166, 390, 184, 408, 169, 393, 186, 410)(171, 395, 220, 444, 200, 424, 218, 442)(173, 397, 188, 412, 176, 400, 190, 414)(178, 402, 202, 426, 179, 403, 204, 428)(181, 405, 210, 434, 182, 406, 212, 436)
	L = (1, 226)(2, 225)(3, 231)(4, 233)(5, 234)(6, 236)(7, 227)(8, 239)(9, 228)(10, 229)(11, 244)(12, 230)(13, 247)(14, 249)(15, 232)(16, 252)(17, 254)(18, 255)(19, 257)(20, 235)(21, 260)(22, 262)(23, 237)(24, 258)(25, 238)(26, 256)(27, 261)(28, 240)(29, 259)(30, 241)(31, 242)(32, 250)(33, 243)(34, 248)(35, 253)(36, 245)(37, 251)(38, 246)(39, 273)(40, 274)(41, 275)(42, 276)(43, 272)(44, 277)(45, 278)(46, 279)(47, 280)(48, 267)(49, 263)(50, 264)(51, 265)(52, 266)(53, 268)(54, 269)(55, 270)(56, 271)(57, 289)(58, 290)(59, 291)(60, 292)(61, 293)(62, 294)(63, 295)(64, 296)(65, 281)(66, 282)(67, 283)(68, 284)(69, 285)(70, 286)(71, 287)(72, 288)(73, 345)(74, 347)(75, 349)(76, 351)(77, 353)(78, 357)(79, 359)(80, 363)(81, 365)(82, 369)(83, 371)(84, 366)(85, 374)(86, 360)(87, 377)(88, 380)(89, 382)(90, 384)(91, 387)(92, 389)(93, 392)(94, 394)(95, 396)(96, 399)(97, 356)(98, 398)(99, 391)(100, 354)(101, 386)(102, 379)(103, 407)(104, 409)(105, 411)(106, 413)(107, 362)(108, 416)(109, 418)(110, 420)(111, 422)(112, 368)(113, 425)(114, 427)(115, 429)(116, 431)(117, 433)(118, 435)(119, 437)(120, 439)(121, 297)(122, 441)(123, 298)(124, 443)(125, 299)(126, 445)(127, 300)(128, 447)(129, 301)(130, 324)(131, 432)(132, 321)(133, 302)(134, 440)(135, 303)(136, 310)(137, 419)(138, 331)(139, 304)(140, 423)(141, 305)(142, 308)(143, 410)(144, 336)(145, 306)(146, 414)(147, 307)(148, 448)(149, 428)(150, 309)(151, 446)(152, 436)(153, 311)(154, 390)(155, 326)(156, 312)(157, 397)(158, 313)(159, 438)(160, 314)(161, 393)(162, 325)(163, 315)(164, 400)(165, 316)(166, 378)(167, 323)(168, 317)(169, 385)(170, 318)(171, 430)(172, 319)(173, 381)(174, 322)(175, 320)(176, 388)(177, 444)(178, 408)(179, 412)(180, 442)(181, 417)(182, 421)(183, 327)(184, 402)(185, 328)(186, 367)(187, 329)(188, 403)(189, 330)(190, 370)(191, 434)(192, 332)(193, 405)(194, 333)(195, 361)(196, 334)(197, 406)(198, 335)(199, 364)(200, 426)(201, 337)(202, 424)(203, 338)(204, 373)(205, 339)(206, 395)(207, 340)(208, 355)(209, 341)(210, 415)(211, 342)(212, 376)(213, 343)(214, 383)(215, 344)(216, 358)(217, 346)(218, 404)(219, 348)(220, 401)(221, 350)(222, 375)(223, 352)(224, 372)
	local type(s) :: { ( 2, 56, 2, 56, 2, 56, 2, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2293
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 56 e = 224 f = 116
	degree seq :: [ 8^56 ]

E27.2295 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ F^2, T1^4, (T2 * T1)^2, T1^4, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-2, (T2^-1 * T1)^4, (T2^-3 * T1)^2, T2^-2 * T1 * T2^23 * T1 * T2^-3 ]
Map::
	R = (1, 225, 3, 227, 10, 234, 24, 248, 48, 272, 64, 288, 80, 304, 96, 320, 112, 336, 128, 352, 144, 368, 160, 384, 176, 400, 192, 416, 208, 432, 216, 440, 200, 424, 184, 408, 168, 392, 152, 376, 136, 360, 120, 344, 104, 328, 88, 312, 72, 296, 56, 280, 39, 263, 28, 252, 42, 266, 19, 243, 41, 265, 58, 282, 74, 298, 90, 314, 106, 330, 122, 346, 138, 362, 154, 378, 170, 394, 186, 410, 202, 426, 218, 442, 212, 436, 196, 420, 180, 404, 164, 388, 148, 372, 132, 356, 116, 340, 100, 324, 84, 308, 68, 292, 52, 276, 32, 256, 14, 238, 5, 229)(2, 226, 7, 231, 17, 241, 38, 262, 57, 281, 73, 297, 89, 313, 105, 329, 121, 345, 137, 361, 153, 377, 169, 393, 185, 409, 201, 425, 217, 441, 206, 430, 190, 414, 174, 398, 158, 382, 142, 366, 126, 350, 110, 334, 94, 318, 78, 302, 62, 286, 46, 270, 23, 247, 11, 235, 26, 250, 35, 259, 31, 255, 51, 275, 67, 291, 83, 307, 99, 323, 115, 339, 131, 355, 147, 371, 163, 387, 179, 403, 195, 419, 211, 435, 220, 444, 204, 428, 188, 412, 172, 396, 156, 380, 140, 364, 124, 348, 108, 332, 92, 316, 76, 300, 60, 284, 44, 268, 20, 244, 8, 232)(4, 228, 12, 236, 27, 251, 49, 273, 65, 289, 81, 305, 97, 321, 113, 337, 129, 353, 145, 369, 161, 385, 177, 401, 193, 417, 209, 433, 222, 446, 207, 431, 191, 415, 175, 399, 159, 383, 143, 367, 127, 351, 111, 335, 95, 319, 79, 303, 63, 287, 47, 271, 25, 249, 34, 258, 30, 254, 13, 237, 29, 253, 50, 274, 66, 290, 82, 306, 98, 322, 114, 338, 130, 354, 146, 370, 162, 386, 178, 402, 194, 418, 210, 434, 221, 445, 205, 429, 189, 413, 173, 397, 157, 381, 141, 365, 125, 349, 109, 333, 93, 317, 77, 301, 61, 285, 45, 269, 22, 246, 9, 233)(6, 230, 15, 239, 33, 257, 53, 277, 69, 293, 85, 309, 101, 325, 117, 341, 133, 357, 149, 373, 165, 389, 181, 405, 197, 421, 213, 437, 223, 447, 215, 439, 199, 423, 183, 407, 167, 391, 151, 375, 135, 359, 119, 343, 103, 327, 87, 311, 71, 295, 55, 279, 37, 261, 18, 242, 40, 264, 21, 245, 43, 267, 59, 283, 75, 299, 91, 315, 107, 331, 123, 347, 139, 363, 155, 379, 171, 395, 187, 411, 203, 427, 219, 443, 224, 448, 214, 438, 198, 422, 182, 406, 166, 390, 150, 374, 134, 358, 118, 342, 102, 326, 86, 310, 70, 294, 54, 278, 36, 260, 16, 240)
	L = (1, 226)(2, 230)(3, 233)(4, 225)(5, 237)(6, 228)(7, 229)(8, 243)(9, 245)(10, 247)(11, 227)(12, 240)(13, 242)(14, 255)(15, 232)(16, 259)(17, 261)(18, 231)(19, 258)(20, 267)(21, 235)(22, 265)(23, 257)(24, 271)(25, 234)(26, 264)(27, 263)(28, 236)(29, 238)(30, 266)(31, 260)(32, 273)(33, 249)(34, 239)(35, 252)(36, 253)(37, 251)(38, 280)(39, 241)(40, 254)(41, 244)(42, 250)(43, 246)(44, 248)(45, 277)(46, 282)(47, 283)(48, 284)(49, 279)(50, 278)(51, 256)(52, 281)(53, 270)(54, 262)(55, 275)(56, 274)(57, 294)(58, 269)(59, 268)(60, 293)(61, 272)(62, 299)(63, 298)(64, 301)(65, 276)(66, 296)(67, 295)(68, 306)(69, 285)(70, 289)(71, 290)(72, 291)(73, 292)(74, 286)(75, 287)(76, 314)(77, 315)(78, 288)(79, 309)(80, 318)(81, 310)(82, 311)(83, 312)(84, 323)(85, 300)(86, 307)(87, 297)(88, 305)(89, 327)(90, 303)(91, 302)(92, 331)(93, 330)(94, 325)(95, 304)(96, 335)(97, 328)(98, 308)(99, 326)(100, 337)(101, 319)(102, 322)(103, 321)(104, 313)(105, 344)(106, 316)(107, 317)(108, 320)(109, 341)(110, 346)(111, 347)(112, 348)(113, 343)(114, 342)(115, 324)(116, 345)(117, 334)(118, 329)(119, 339)(120, 338)(121, 358)(122, 333)(123, 332)(124, 357)(125, 336)(126, 363)(127, 362)(128, 365)(129, 340)(130, 360)(131, 359)(132, 370)(133, 349)(134, 353)(135, 354)(136, 355)(137, 356)(138, 350)(139, 351)(140, 378)(141, 379)(142, 352)(143, 373)(144, 382)(145, 374)(146, 375)(147, 376)(148, 387)(149, 364)(150, 371)(151, 361)(152, 369)(153, 391)(154, 367)(155, 366)(156, 395)(157, 394)(158, 389)(159, 368)(160, 399)(161, 392)(162, 372)(163, 390)(164, 401)(165, 383)(166, 386)(167, 385)(168, 377)(169, 408)(170, 380)(171, 381)(172, 384)(173, 405)(174, 410)(175, 411)(176, 412)(177, 407)(178, 406)(179, 388)(180, 409)(181, 398)(182, 393)(183, 403)(184, 402)(185, 422)(186, 397)(187, 396)(188, 421)(189, 400)(190, 427)(191, 426)(192, 429)(193, 404)(194, 424)(195, 423)(196, 434)(197, 413)(198, 417)(199, 418)(200, 419)(201, 420)(202, 414)(203, 415)(204, 442)(205, 443)(206, 416)(207, 437)(208, 441)(209, 438)(210, 439)(211, 440)(212, 444)(213, 428)(214, 435)(215, 425)(216, 433)(217, 447)(218, 431)(219, 430)(220, 448)(221, 436)(222, 432)(223, 446)(224, 445)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2291
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 224 f = 168
	degree seq :: [ 112^4 ]

E27.2296 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 56})
Quotient :: loop
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^4, T2 * T1^2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1, (T2 * T1^-4)^2, T1^22 * T2 * T1^-6 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 225, 3, 227)(2, 226, 6, 230)(4, 228, 9, 233)(5, 229, 12, 236)(7, 231, 16, 240)(8, 232, 17, 241)(10, 234, 21, 245)(11, 235, 24, 248)(13, 237, 28, 252)(14, 238, 29, 253)(15, 239, 32, 256)(18, 242, 36, 260)(19, 243, 39, 263)(20, 244, 33, 257)(22, 246, 43, 267)(23, 247, 46, 270)(25, 249, 50, 274)(26, 250, 51, 275)(27, 251, 54, 278)(30, 254, 57, 281)(31, 255, 60, 284)(34, 258, 53, 277)(35, 259, 47, 271)(37, 261, 56, 280)(38, 262, 61, 285)(40, 264, 63, 287)(41, 265, 62, 286)(42, 266, 55, 279)(44, 268, 59, 283)(45, 269, 69, 293)(48, 272, 71, 295)(49, 273, 73, 297)(52, 276, 75, 299)(58, 282, 74, 298)(64, 288, 80, 304)(65, 289, 79, 303)(66, 290, 78, 302)(67, 291, 81, 305)(68, 292, 86, 310)(70, 294, 88, 312)(72, 296, 91, 315)(76, 300, 90, 314)(77, 301, 94, 318)(82, 306, 95, 319)(83, 307, 96, 320)(84, 308, 98, 322)(85, 309, 102, 326)(87, 311, 104, 328)(89, 313, 107, 331)(92, 316, 106, 330)(93, 317, 110, 334)(97, 321, 112, 336)(99, 323, 111, 335)(100, 324, 115, 339)(101, 325, 118, 342)(103, 327, 120, 344)(105, 329, 123, 347)(108, 332, 122, 346)(109, 333, 126, 350)(113, 337, 127, 351)(114, 338, 128, 352)(116, 340, 125, 349)(117, 341, 134, 358)(119, 343, 136, 360)(121, 345, 139, 363)(124, 348, 138, 362)(129, 353, 144, 368)(130, 354, 143, 367)(131, 355, 142, 366)(132, 356, 145, 369)(133, 357, 150, 374)(135, 359, 152, 376)(137, 361, 155, 379)(140, 364, 154, 378)(141, 365, 158, 382)(146, 370, 159, 383)(147, 371, 160, 384)(148, 372, 162, 386)(149, 373, 166, 390)(151, 375, 168, 392)(153, 377, 171, 395)(156, 380, 170, 394)(157, 381, 174, 398)(161, 385, 176, 400)(163, 387, 175, 399)(164, 388, 179, 403)(165, 389, 182, 406)(167, 391, 184, 408)(169, 393, 187, 411)(172, 396, 186, 410)(173, 397, 190, 414)(177, 401, 191, 415)(178, 402, 192, 416)(180, 404, 189, 413)(181, 405, 198, 422)(183, 407, 200, 424)(185, 409, 203, 427)(188, 412, 202, 426)(193, 417, 208, 432)(194, 418, 207, 431)(195, 419, 206, 430)(196, 420, 209, 433)(197, 421, 214, 438)(199, 423, 216, 440)(201, 425, 219, 443)(204, 428, 218, 442)(205, 429, 221, 445)(210, 434, 222, 446)(211, 435, 213, 437)(212, 436, 217, 441)(215, 439, 223, 447)(220, 444, 224, 448)
	L = (1, 226)(2, 229)(3, 231)(4, 225)(5, 235)(6, 237)(7, 239)(8, 227)(9, 243)(10, 228)(11, 247)(12, 249)(13, 251)(14, 230)(15, 255)(16, 257)(17, 259)(18, 232)(19, 262)(20, 233)(21, 265)(22, 234)(23, 269)(24, 271)(25, 273)(26, 236)(27, 277)(28, 241)(29, 280)(30, 238)(31, 283)(32, 278)(33, 274)(34, 240)(35, 275)(36, 281)(37, 242)(38, 288)(39, 279)(40, 244)(41, 289)(42, 245)(43, 290)(44, 246)(45, 292)(46, 261)(47, 264)(48, 248)(49, 266)(50, 253)(51, 298)(52, 250)(53, 267)(54, 297)(55, 252)(56, 295)(57, 299)(58, 254)(59, 301)(60, 263)(61, 256)(62, 258)(63, 260)(64, 305)(65, 306)(66, 307)(67, 268)(68, 309)(69, 282)(70, 270)(71, 314)(72, 272)(73, 287)(74, 312)(75, 315)(76, 276)(77, 317)(78, 284)(79, 285)(80, 286)(81, 321)(82, 322)(83, 323)(84, 291)(85, 325)(86, 300)(87, 293)(88, 330)(89, 294)(90, 328)(91, 331)(92, 296)(93, 333)(94, 304)(95, 302)(96, 303)(97, 337)(98, 338)(99, 339)(100, 308)(101, 341)(102, 316)(103, 310)(104, 346)(105, 311)(106, 344)(107, 347)(108, 313)(109, 349)(110, 320)(111, 318)(112, 319)(113, 353)(114, 354)(115, 355)(116, 324)(117, 357)(118, 332)(119, 326)(120, 362)(121, 327)(122, 360)(123, 363)(124, 329)(125, 365)(126, 336)(127, 334)(128, 335)(129, 369)(130, 370)(131, 371)(132, 340)(133, 373)(134, 348)(135, 342)(136, 378)(137, 343)(138, 376)(139, 379)(140, 345)(141, 381)(142, 350)(143, 351)(144, 352)(145, 385)(146, 386)(147, 387)(148, 356)(149, 389)(150, 364)(151, 358)(152, 394)(153, 359)(154, 392)(155, 395)(156, 361)(157, 397)(158, 368)(159, 366)(160, 367)(161, 401)(162, 402)(163, 403)(164, 372)(165, 405)(166, 380)(167, 374)(168, 410)(169, 375)(170, 408)(171, 411)(172, 377)(173, 413)(174, 384)(175, 382)(176, 383)(177, 417)(178, 418)(179, 419)(180, 388)(181, 421)(182, 396)(183, 390)(184, 426)(185, 391)(186, 424)(187, 427)(188, 393)(189, 429)(190, 400)(191, 398)(192, 399)(193, 433)(194, 434)(195, 435)(196, 404)(197, 437)(198, 412)(199, 406)(200, 442)(201, 407)(202, 440)(203, 443)(204, 409)(205, 438)(206, 414)(207, 415)(208, 416)(209, 439)(210, 441)(211, 444)(212, 420)(213, 431)(214, 428)(215, 422)(216, 448)(217, 423)(218, 447)(219, 436)(220, 425)(221, 432)(222, 430)(223, 446)(224, 445)
	local type(s) :: { ( 4, 56, 4, 56 ) }
Outer automorphisms :: reflexible
Dual of E27.2292
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 112 e = 224 f = 60
	degree seq :: [ 4^112 ]

E27.2297 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, R * Y2^-2 * R * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2 * R * Y2^2 * R * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^56 ]
Map::
	R = (1, 225, 2, 226)(3, 227, 7, 231)(4, 228, 9, 233)(5, 229, 10, 234)(6, 230, 12, 236)(8, 232, 15, 239)(11, 235, 20, 244)(13, 237, 23, 247)(14, 238, 25, 249)(16, 240, 28, 252)(17, 241, 30, 254)(18, 242, 31, 255)(19, 243, 33, 257)(21, 245, 36, 260)(22, 246, 38, 262)(24, 248, 34, 258)(26, 250, 32, 256)(27, 251, 37, 261)(29, 253, 35, 259)(39, 263, 49, 273)(40, 264, 50, 274)(41, 265, 51, 275)(42, 266, 52, 276)(43, 267, 48, 272)(44, 268, 53, 277)(45, 269, 54, 278)(46, 270, 55, 279)(47, 271, 56, 280)(57, 281, 65, 289)(58, 282, 66, 290)(59, 283, 67, 291)(60, 284, 68, 292)(61, 285, 69, 293)(62, 286, 70, 294)(63, 287, 71, 295)(64, 288, 72, 296)(73, 297, 87, 311)(74, 298, 78, 302)(75, 299, 103, 327)(76, 300, 84, 308)(77, 301, 119, 343)(79, 303, 129, 353)(80, 304, 128, 352)(81, 305, 132, 356)(82, 306, 126, 350)(83, 307, 120, 344)(85, 309, 135, 359)(86, 310, 131, 355)(88, 312, 139, 363)(89, 313, 130, 354)(90, 314, 142, 366)(91, 315, 134, 358)(92, 316, 117, 341)(93, 317, 146, 370)(94, 318, 133, 357)(95, 319, 145, 369)(96, 320, 125, 349)(97, 321, 138, 362)(98, 322, 127, 351)(99, 323, 141, 365)(100, 324, 137, 361)(101, 325, 140, 364)(102, 326, 136, 360)(104, 328, 148, 372)(105, 329, 144, 368)(106, 330, 147, 371)(107, 331, 143, 367)(108, 332, 118, 342)(109, 333, 152, 376)(110, 334, 150, 374)(111, 335, 151, 375)(112, 336, 149, 373)(113, 337, 156, 380)(114, 338, 154, 378)(115, 339, 155, 379)(116, 340, 153, 377)(121, 345, 160, 384)(122, 346, 158, 382)(123, 347, 159, 383)(124, 348, 157, 381)(161, 385, 168, 392)(162, 386, 167, 391)(163, 387, 166, 390)(164, 388, 165, 389)(169, 393, 179, 403)(170, 394, 180, 404)(171, 395, 177, 401)(172, 396, 178, 402)(173, 397, 215, 439)(174, 398, 216, 440)(175, 399, 213, 437)(176, 400, 214, 438)(181, 405, 221, 445)(182, 406, 222, 446)(183, 407, 223, 447)(184, 408, 224, 448)(185, 409, 220, 444)(186, 410, 218, 442)(187, 411, 219, 443)(188, 412, 217, 441)(189, 413, 210, 434)(190, 414, 212, 436)(191, 415, 209, 433)(192, 416, 211, 435)(193, 417, 206, 430)(194, 418, 208, 432)(195, 419, 205, 429)(196, 420, 207, 431)(197, 421, 201, 425)(198, 422, 203, 427)(199, 423, 202, 426)(200, 424, 204, 428)(449, 673, 451, 675, 456, 680, 452, 676)(450, 674, 453, 677, 459, 683, 454, 678)(455, 679, 461, 685, 472, 696, 462, 686)(457, 681, 464, 688, 477, 701, 465, 689)(458, 682, 466, 690, 480, 704, 467, 691)(460, 684, 469, 693, 485, 709, 470, 694)(463, 687, 474, 698, 491, 715, 475, 699)(468, 692, 482, 706, 496, 720, 483, 707)(471, 695, 487, 711, 476, 700, 488, 712)(473, 697, 489, 713, 478, 702, 490, 714)(479, 703, 492, 716, 484, 708, 493, 717)(481, 705, 494, 718, 486, 710, 495, 719)(497, 721, 505, 729, 499, 723, 506, 730)(498, 722, 507, 731, 500, 724, 508, 732)(501, 725, 509, 733, 503, 727, 510, 734)(502, 726, 511, 735, 504, 728, 512, 736)(513, 737, 521, 745, 515, 739, 522, 746)(514, 738, 523, 747, 516, 740, 524, 748)(517, 741, 565, 789, 519, 743, 567, 791)(518, 742, 566, 790, 520, 744, 568, 792)(525, 749, 573, 797, 531, 755, 574, 798)(526, 750, 575, 799, 532, 756, 576, 800)(527, 751, 578, 802, 528, 752, 579, 803)(529, 753, 581, 805, 530, 754, 582, 806)(533, 757, 584, 808, 534, 758, 585, 809)(535, 759, 586, 810, 551, 775, 577, 801)(536, 760, 588, 812, 537, 761, 589, 813)(538, 762, 591, 815, 539, 763, 592, 816)(540, 764, 593, 817, 556, 780, 580, 804)(541, 765, 595, 819, 542, 766, 596, 820)(543, 767, 594, 818, 544, 768, 590, 814)(545, 769, 587, 811, 546, 770, 583, 807)(547, 771, 597, 821, 548, 772, 598, 822)(549, 773, 599, 823, 550, 774, 600, 824)(552, 776, 601, 825, 553, 777, 602, 826)(554, 778, 603, 827, 555, 779, 604, 828)(557, 781, 605, 829, 558, 782, 606, 830)(559, 783, 607, 831, 560, 784, 608, 832)(561, 785, 609, 833, 562, 786, 610, 834)(563, 787, 611, 835, 564, 788, 612, 836)(569, 793, 617, 841, 570, 794, 618, 842)(571, 795, 619, 843, 572, 796, 620, 844)(613, 837, 661, 885, 615, 839, 662, 886)(614, 838, 663, 887, 616, 840, 664, 888)(621, 845, 668, 892, 623, 847, 666, 890)(622, 846, 667, 891, 624, 848, 665, 889)(625, 849, 669, 893, 627, 851, 670, 894)(626, 850, 671, 895, 628, 852, 672, 896)(629, 853, 658, 882, 631, 855, 660, 884)(630, 854, 657, 881, 632, 856, 659, 883)(633, 857, 654, 878, 635, 859, 656, 880)(634, 858, 653, 877, 636, 860, 655, 879)(637, 861, 649, 873, 639, 863, 651, 875)(638, 862, 650, 874, 640, 864, 652, 876)(641, 865, 645, 869, 643, 867, 647, 871)(642, 866, 646, 870, 644, 868, 648, 872)
	L = (1, 450)(2, 449)(3, 455)(4, 457)(5, 458)(6, 460)(7, 451)(8, 463)(9, 452)(10, 453)(11, 468)(12, 454)(13, 471)(14, 473)(15, 456)(16, 476)(17, 478)(18, 479)(19, 481)(20, 459)(21, 484)(22, 486)(23, 461)(24, 482)(25, 462)(26, 480)(27, 485)(28, 464)(29, 483)(30, 465)(31, 466)(32, 474)(33, 467)(34, 472)(35, 477)(36, 469)(37, 475)(38, 470)(39, 497)(40, 498)(41, 499)(42, 500)(43, 496)(44, 501)(45, 502)(46, 503)(47, 504)(48, 491)(49, 487)(50, 488)(51, 489)(52, 490)(53, 492)(54, 493)(55, 494)(56, 495)(57, 513)(58, 514)(59, 515)(60, 516)(61, 517)(62, 518)(63, 519)(64, 520)(65, 505)(66, 506)(67, 507)(68, 508)(69, 509)(70, 510)(71, 511)(72, 512)(73, 535)(74, 526)(75, 551)(76, 532)(77, 567)(78, 522)(79, 577)(80, 576)(81, 580)(82, 574)(83, 568)(84, 524)(85, 583)(86, 579)(87, 521)(88, 587)(89, 578)(90, 590)(91, 582)(92, 565)(93, 594)(94, 581)(95, 593)(96, 573)(97, 586)(98, 575)(99, 589)(100, 585)(101, 588)(102, 584)(103, 523)(104, 596)(105, 592)(106, 595)(107, 591)(108, 566)(109, 600)(110, 598)(111, 599)(112, 597)(113, 604)(114, 602)(115, 603)(116, 601)(117, 540)(118, 556)(119, 525)(120, 531)(121, 608)(122, 606)(123, 607)(124, 605)(125, 544)(126, 530)(127, 546)(128, 528)(129, 527)(130, 537)(131, 534)(132, 529)(133, 542)(134, 539)(135, 533)(136, 550)(137, 548)(138, 545)(139, 536)(140, 549)(141, 547)(142, 538)(143, 555)(144, 553)(145, 543)(146, 541)(147, 554)(148, 552)(149, 560)(150, 558)(151, 559)(152, 557)(153, 564)(154, 562)(155, 563)(156, 561)(157, 572)(158, 570)(159, 571)(160, 569)(161, 616)(162, 615)(163, 614)(164, 613)(165, 612)(166, 611)(167, 610)(168, 609)(169, 627)(170, 628)(171, 625)(172, 626)(173, 663)(174, 664)(175, 661)(176, 662)(177, 619)(178, 620)(179, 617)(180, 618)(181, 669)(182, 670)(183, 671)(184, 672)(185, 668)(186, 666)(187, 667)(188, 665)(189, 658)(190, 660)(191, 657)(192, 659)(193, 654)(194, 656)(195, 653)(196, 655)(197, 649)(198, 651)(199, 650)(200, 652)(201, 645)(202, 647)(203, 646)(204, 648)(205, 643)(206, 641)(207, 644)(208, 642)(209, 639)(210, 637)(211, 640)(212, 638)(213, 623)(214, 624)(215, 621)(216, 622)(217, 636)(218, 634)(219, 635)(220, 633)(221, 629)(222, 630)(223, 631)(224, 632)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2300
Graph:: bipartite
	v = 168 e = 448 f = 228
	degree seq :: [ 4^112, 8^56 ]

E27.2298 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-2 * Y1^-1, Y2^-2 * Y1 * Y2^-1 * Y1^2 * Y2^-1 * Y1, (Y2 * Y1^-1)^4, Y1 * Y2^27 * Y1 * Y2^-1 ]
Map::
	R = (1, 225, 2, 226, 6, 230, 4, 228)(3, 227, 9, 233, 21, 245, 11, 235)(5, 229, 13, 237, 18, 242, 7, 231)(8, 232, 19, 243, 34, 258, 15, 239)(10, 234, 23, 247, 33, 257, 25, 249)(12, 236, 16, 240, 35, 259, 28, 252)(14, 238, 31, 255, 36, 260, 29, 253)(17, 241, 37, 261, 27, 251, 39, 263)(20, 244, 43, 267, 22, 246, 41, 265)(24, 248, 47, 271, 59, 283, 44, 268)(26, 250, 40, 264, 30, 254, 42, 266)(32, 256, 49, 273, 55, 279, 51, 275)(38, 262, 56, 280, 50, 274, 54, 278)(45, 269, 53, 277, 46, 270, 58, 282)(48, 272, 60, 284, 69, 293, 61, 285)(52, 276, 57, 281, 70, 294, 65, 289)(62, 286, 75, 299, 63, 287, 74, 298)(64, 288, 77, 301, 91, 315, 78, 302)(66, 290, 72, 296, 67, 291, 71, 295)(68, 292, 82, 306, 87, 311, 73, 297)(76, 300, 90, 314, 79, 303, 85, 309)(80, 304, 94, 318, 101, 325, 95, 319)(81, 305, 86, 310, 83, 307, 88, 312)(84, 308, 99, 323, 102, 326, 98, 322)(89, 313, 103, 327, 97, 321, 104, 328)(92, 316, 107, 331, 93, 317, 106, 330)(96, 320, 111, 335, 123, 347, 108, 332)(100, 324, 113, 337, 119, 343, 115, 339)(105, 329, 120, 344, 114, 338, 118, 342)(109, 333, 117, 341, 110, 334, 122, 346)(112, 336, 124, 348, 133, 357, 125, 349)(116, 340, 121, 345, 134, 358, 129, 353)(126, 350, 139, 363, 127, 351, 138, 362)(128, 352, 141, 365, 155, 379, 142, 366)(130, 354, 136, 360, 131, 355, 135, 359)(132, 356, 146, 370, 151, 375, 137, 361)(140, 364, 154, 378, 143, 367, 149, 373)(144, 368, 158, 382, 165, 389, 159, 383)(145, 369, 150, 374, 147, 371, 152, 376)(148, 372, 163, 387, 166, 390, 162, 386)(153, 377, 167, 391, 161, 385, 168, 392)(156, 380, 171, 395, 157, 381, 170, 394)(160, 384, 175, 399, 187, 411, 172, 396)(164, 388, 177, 401, 183, 407, 179, 403)(169, 393, 184, 408, 178, 402, 182, 406)(173, 397, 181, 405, 174, 398, 186, 410)(176, 400, 188, 412, 197, 421, 189, 413)(180, 404, 185, 409, 198, 422, 193, 417)(190, 414, 203, 427, 191, 415, 202, 426)(192, 416, 205, 429, 219, 443, 206, 430)(194, 418, 200, 424, 195, 419, 199, 423)(196, 420, 210, 434, 215, 439, 201, 425)(204, 428, 218, 442, 207, 431, 213, 437)(208, 432, 217, 441, 223, 447, 222, 446)(209, 433, 214, 438, 211, 435, 216, 440)(212, 436, 220, 444, 224, 448, 221, 445)(449, 673, 451, 675, 458, 682, 472, 696, 496, 720, 512, 736, 528, 752, 544, 768, 560, 784, 576, 800, 592, 816, 608, 832, 624, 848, 640, 864, 656, 880, 664, 888, 648, 872, 632, 856, 616, 840, 600, 824, 584, 808, 568, 792, 552, 776, 536, 760, 520, 744, 504, 728, 487, 711, 476, 700, 490, 714, 467, 691, 489, 713, 506, 730, 522, 746, 538, 762, 554, 778, 570, 794, 586, 810, 602, 826, 618, 842, 634, 858, 650, 874, 666, 890, 660, 884, 644, 868, 628, 852, 612, 836, 596, 820, 580, 804, 564, 788, 548, 772, 532, 756, 516, 740, 500, 724, 480, 704, 462, 686, 453, 677)(450, 674, 455, 679, 465, 689, 486, 710, 505, 729, 521, 745, 537, 761, 553, 777, 569, 793, 585, 809, 601, 825, 617, 841, 633, 857, 649, 873, 665, 889, 654, 878, 638, 862, 622, 846, 606, 830, 590, 814, 574, 798, 558, 782, 542, 766, 526, 750, 510, 734, 494, 718, 471, 695, 459, 683, 474, 698, 483, 707, 479, 703, 499, 723, 515, 739, 531, 755, 547, 771, 563, 787, 579, 803, 595, 819, 611, 835, 627, 851, 643, 867, 659, 883, 668, 892, 652, 876, 636, 860, 620, 844, 604, 828, 588, 812, 572, 796, 556, 780, 540, 764, 524, 748, 508, 732, 492, 716, 468, 692, 456, 680)(452, 676, 460, 684, 475, 699, 497, 721, 513, 737, 529, 753, 545, 769, 561, 785, 577, 801, 593, 817, 609, 833, 625, 849, 641, 865, 657, 881, 670, 894, 655, 879, 639, 863, 623, 847, 607, 831, 591, 815, 575, 799, 559, 783, 543, 767, 527, 751, 511, 735, 495, 719, 473, 697, 482, 706, 478, 702, 461, 685, 477, 701, 498, 722, 514, 738, 530, 754, 546, 770, 562, 786, 578, 802, 594, 818, 610, 834, 626, 850, 642, 866, 658, 882, 669, 893, 653, 877, 637, 861, 621, 845, 605, 829, 589, 813, 573, 797, 557, 781, 541, 765, 525, 749, 509, 733, 493, 717, 470, 694, 457, 681)(454, 678, 463, 687, 481, 705, 501, 725, 517, 741, 533, 757, 549, 773, 565, 789, 581, 805, 597, 821, 613, 837, 629, 853, 645, 869, 661, 885, 671, 895, 663, 887, 647, 871, 631, 855, 615, 839, 599, 823, 583, 807, 567, 791, 551, 775, 535, 759, 519, 743, 503, 727, 485, 709, 466, 690, 488, 712, 469, 693, 491, 715, 507, 731, 523, 747, 539, 763, 555, 779, 571, 795, 587, 811, 603, 827, 619, 843, 635, 859, 651, 875, 667, 891, 672, 896, 662, 886, 646, 870, 630, 854, 614, 838, 598, 822, 582, 806, 566, 790, 550, 774, 534, 758, 518, 742, 502, 726, 484, 708, 464, 688)
	L = (1, 451)(2, 455)(3, 458)(4, 460)(5, 449)(6, 463)(7, 465)(8, 450)(9, 452)(10, 472)(11, 474)(12, 475)(13, 477)(14, 453)(15, 481)(16, 454)(17, 486)(18, 488)(19, 489)(20, 456)(21, 491)(22, 457)(23, 459)(24, 496)(25, 482)(26, 483)(27, 497)(28, 490)(29, 498)(30, 461)(31, 499)(32, 462)(33, 501)(34, 478)(35, 479)(36, 464)(37, 466)(38, 505)(39, 476)(40, 469)(41, 506)(42, 467)(43, 507)(44, 468)(45, 470)(46, 471)(47, 473)(48, 512)(49, 513)(50, 514)(51, 515)(52, 480)(53, 517)(54, 484)(55, 485)(56, 487)(57, 521)(58, 522)(59, 523)(60, 492)(61, 493)(62, 494)(63, 495)(64, 528)(65, 529)(66, 530)(67, 531)(68, 500)(69, 533)(70, 502)(71, 503)(72, 504)(73, 537)(74, 538)(75, 539)(76, 508)(77, 509)(78, 510)(79, 511)(80, 544)(81, 545)(82, 546)(83, 547)(84, 516)(85, 549)(86, 518)(87, 519)(88, 520)(89, 553)(90, 554)(91, 555)(92, 524)(93, 525)(94, 526)(95, 527)(96, 560)(97, 561)(98, 562)(99, 563)(100, 532)(101, 565)(102, 534)(103, 535)(104, 536)(105, 569)(106, 570)(107, 571)(108, 540)(109, 541)(110, 542)(111, 543)(112, 576)(113, 577)(114, 578)(115, 579)(116, 548)(117, 581)(118, 550)(119, 551)(120, 552)(121, 585)(122, 586)(123, 587)(124, 556)(125, 557)(126, 558)(127, 559)(128, 592)(129, 593)(130, 594)(131, 595)(132, 564)(133, 597)(134, 566)(135, 567)(136, 568)(137, 601)(138, 602)(139, 603)(140, 572)(141, 573)(142, 574)(143, 575)(144, 608)(145, 609)(146, 610)(147, 611)(148, 580)(149, 613)(150, 582)(151, 583)(152, 584)(153, 617)(154, 618)(155, 619)(156, 588)(157, 589)(158, 590)(159, 591)(160, 624)(161, 625)(162, 626)(163, 627)(164, 596)(165, 629)(166, 598)(167, 599)(168, 600)(169, 633)(170, 634)(171, 635)(172, 604)(173, 605)(174, 606)(175, 607)(176, 640)(177, 641)(178, 642)(179, 643)(180, 612)(181, 645)(182, 614)(183, 615)(184, 616)(185, 649)(186, 650)(187, 651)(188, 620)(189, 621)(190, 622)(191, 623)(192, 656)(193, 657)(194, 658)(195, 659)(196, 628)(197, 661)(198, 630)(199, 631)(200, 632)(201, 665)(202, 666)(203, 667)(204, 636)(205, 637)(206, 638)(207, 639)(208, 664)(209, 670)(210, 669)(211, 668)(212, 644)(213, 671)(214, 646)(215, 647)(216, 648)(217, 654)(218, 660)(219, 672)(220, 652)(221, 653)(222, 655)(223, 663)(224, 662)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2299
Graph:: bipartite
	v = 60 e = 448 f = 336
	degree seq :: [ 8^56, 112^4 ]

E27.2299 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, Y3^-3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y3^26 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^56 ]
Map:: polytopal
	R = (1, 225)(2, 226)(3, 227)(4, 228)(5, 229)(6, 230)(7, 231)(8, 232)(9, 233)(10, 234)(11, 235)(12, 236)(13, 237)(14, 238)(15, 239)(16, 240)(17, 241)(18, 242)(19, 243)(20, 244)(21, 245)(22, 246)(23, 247)(24, 248)(25, 249)(26, 250)(27, 251)(28, 252)(29, 253)(30, 254)(31, 255)(32, 256)(33, 257)(34, 258)(35, 259)(36, 260)(37, 261)(38, 262)(39, 263)(40, 264)(41, 265)(42, 266)(43, 267)(44, 268)(45, 269)(46, 270)(47, 271)(48, 272)(49, 273)(50, 274)(51, 275)(52, 276)(53, 277)(54, 278)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 284)(61, 285)(62, 286)(63, 287)(64, 288)(65, 289)(66, 290)(67, 291)(68, 292)(69, 293)(70, 294)(71, 295)(72, 296)(73, 297)(74, 298)(75, 299)(76, 300)(77, 301)(78, 302)(79, 303)(80, 304)(81, 305)(82, 306)(83, 307)(84, 308)(85, 309)(86, 310)(87, 311)(88, 312)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 329)(106, 330)(107, 331)(108, 332)(109, 333)(110, 334)(111, 335)(112, 336)(113, 337)(114, 338)(115, 339)(116, 340)(117, 341)(118, 342)(119, 343)(120, 344)(121, 345)(122, 346)(123, 347)(124, 348)(125, 349)(126, 350)(127, 351)(128, 352)(129, 353)(130, 354)(131, 355)(132, 356)(133, 357)(134, 358)(135, 359)(136, 360)(137, 361)(138, 362)(139, 363)(140, 364)(141, 365)(142, 366)(143, 367)(144, 368)(145, 369)(146, 370)(147, 371)(148, 372)(149, 373)(150, 374)(151, 375)(152, 376)(153, 377)(154, 378)(155, 379)(156, 380)(157, 381)(158, 382)(159, 383)(160, 384)(161, 385)(162, 386)(163, 387)(164, 388)(165, 389)(166, 390)(167, 391)(168, 392)(169, 393)(170, 394)(171, 395)(172, 396)(173, 397)(174, 398)(175, 399)(176, 400)(177, 401)(178, 402)(179, 403)(180, 404)(181, 405)(182, 406)(183, 407)(184, 408)(185, 409)(186, 410)(187, 411)(188, 412)(189, 413)(190, 414)(191, 415)(192, 416)(193, 417)(194, 418)(195, 419)(196, 420)(197, 421)(198, 422)(199, 423)(200, 424)(201, 425)(202, 426)(203, 427)(204, 428)(205, 429)(206, 430)(207, 431)(208, 432)(209, 433)(210, 434)(211, 435)(212, 436)(213, 437)(214, 438)(215, 439)(216, 440)(217, 441)(218, 442)(219, 443)(220, 444)(221, 445)(222, 446)(223, 447)(224, 448)(449, 673, 450, 674)(451, 675, 455, 679)(452, 676, 457, 681)(453, 677, 459, 683)(454, 678, 461, 685)(456, 680, 465, 689)(458, 682, 469, 693)(460, 684, 473, 697)(462, 686, 477, 701)(463, 687, 476, 700)(464, 688, 480, 704)(466, 690, 484, 708)(467, 691, 486, 710)(468, 692, 471, 695)(470, 694, 491, 715)(472, 696, 494, 718)(474, 698, 498, 722)(475, 699, 500, 724)(478, 702, 505, 729)(479, 703, 496, 720)(481, 705, 503, 727)(482, 706, 493, 717)(483, 707, 501, 725)(485, 709, 506, 730)(487, 711, 497, 721)(488, 712, 504, 728)(489, 713, 495, 719)(490, 714, 502, 726)(492, 716, 499, 723)(507, 731, 521, 745)(508, 732, 517, 741)(509, 733, 522, 746)(510, 734, 523, 747)(511, 735, 525, 749)(512, 736, 516, 740)(513, 737, 518, 742)(514, 738, 519, 743)(515, 739, 529, 753)(520, 744, 533, 757)(524, 748, 537, 761)(526, 750, 539, 763)(527, 751, 538, 762)(528, 752, 542, 766)(530, 754, 535, 759)(531, 755, 534, 758)(532, 756, 546, 770)(536, 760, 550, 774)(540, 764, 554, 778)(541, 765, 555, 779)(543, 767, 553, 777)(544, 768, 559, 783)(545, 769, 551, 775)(547, 771, 549, 773)(548, 772, 563, 787)(552, 776, 567, 791)(556, 780, 571, 795)(557, 781, 570, 794)(558, 782, 569, 793)(560, 784, 572, 796)(561, 785, 566, 790)(562, 786, 565, 789)(564, 788, 568, 792)(573, 797, 585, 809)(574, 798, 586, 810)(575, 799, 587, 811)(576, 800, 589, 813)(577, 801, 581, 805)(578, 802, 582, 806)(579, 803, 583, 807)(580, 804, 593, 817)(584, 808, 597, 821)(588, 812, 601, 825)(590, 814, 603, 827)(591, 815, 602, 826)(592, 816, 606, 830)(594, 818, 599, 823)(595, 819, 598, 822)(596, 820, 610, 834)(600, 824, 614, 838)(604, 828, 618, 842)(605, 829, 619, 843)(607, 831, 617, 841)(608, 832, 623, 847)(609, 833, 615, 839)(611, 835, 613, 837)(612, 836, 627, 851)(616, 840, 631, 855)(620, 844, 635, 859)(621, 845, 634, 858)(622, 846, 633, 857)(624, 848, 636, 860)(625, 849, 630, 854)(626, 850, 629, 853)(628, 852, 632, 856)(637, 861, 649, 873)(638, 862, 650, 874)(639, 863, 651, 875)(640, 864, 653, 877)(641, 865, 645, 869)(642, 866, 646, 870)(643, 867, 647, 871)(644, 868, 657, 881)(648, 872, 661, 885)(652, 876, 665, 889)(654, 878, 667, 891)(655, 879, 666, 890)(656, 880, 664, 888)(658, 882, 663, 887)(659, 883, 662, 886)(660, 884, 668, 892)(669, 893, 672, 896)(670, 894, 671, 895)
	L = (1, 451)(2, 453)(3, 456)(4, 449)(5, 460)(6, 450)(7, 463)(8, 466)(9, 467)(10, 452)(11, 471)(12, 474)(13, 475)(14, 454)(15, 479)(16, 455)(17, 482)(18, 485)(19, 487)(20, 457)(21, 489)(22, 458)(23, 493)(24, 459)(25, 496)(26, 499)(27, 501)(28, 461)(29, 503)(30, 462)(31, 494)(32, 505)(33, 464)(34, 508)(35, 465)(36, 500)(37, 511)(38, 502)(39, 512)(40, 468)(41, 513)(42, 469)(43, 514)(44, 470)(45, 480)(46, 491)(47, 472)(48, 517)(49, 473)(50, 486)(51, 520)(52, 488)(53, 521)(54, 476)(55, 522)(56, 477)(57, 523)(58, 478)(59, 481)(60, 490)(61, 483)(62, 484)(63, 528)(64, 529)(65, 530)(66, 531)(67, 492)(68, 495)(69, 504)(70, 497)(71, 498)(72, 536)(73, 537)(74, 538)(75, 539)(76, 506)(77, 507)(78, 509)(79, 510)(80, 544)(81, 545)(82, 546)(83, 547)(84, 515)(85, 516)(86, 518)(87, 519)(88, 552)(89, 553)(90, 554)(91, 555)(92, 524)(93, 525)(94, 526)(95, 527)(96, 560)(97, 561)(98, 562)(99, 563)(100, 532)(101, 533)(102, 534)(103, 535)(104, 568)(105, 569)(106, 570)(107, 571)(108, 540)(109, 541)(110, 542)(111, 543)(112, 576)(113, 577)(114, 578)(115, 579)(116, 548)(117, 549)(118, 550)(119, 551)(120, 584)(121, 585)(122, 586)(123, 587)(124, 556)(125, 557)(126, 558)(127, 559)(128, 592)(129, 593)(130, 594)(131, 595)(132, 564)(133, 565)(134, 566)(135, 567)(136, 600)(137, 601)(138, 602)(139, 603)(140, 572)(141, 573)(142, 574)(143, 575)(144, 608)(145, 609)(146, 610)(147, 611)(148, 580)(149, 581)(150, 582)(151, 583)(152, 616)(153, 617)(154, 618)(155, 619)(156, 588)(157, 589)(158, 590)(159, 591)(160, 624)(161, 625)(162, 626)(163, 627)(164, 596)(165, 597)(166, 598)(167, 599)(168, 632)(169, 633)(170, 634)(171, 635)(172, 604)(173, 605)(174, 606)(175, 607)(176, 640)(177, 641)(178, 642)(179, 643)(180, 612)(181, 613)(182, 614)(183, 615)(184, 648)(185, 649)(186, 650)(187, 651)(188, 620)(189, 621)(190, 622)(191, 623)(192, 656)(193, 657)(194, 658)(195, 659)(196, 628)(197, 629)(198, 630)(199, 631)(200, 664)(201, 665)(202, 666)(203, 667)(204, 636)(205, 637)(206, 638)(207, 639)(208, 662)(209, 669)(210, 668)(211, 670)(212, 644)(213, 645)(214, 646)(215, 647)(216, 654)(217, 671)(218, 660)(219, 672)(220, 652)(221, 653)(222, 655)(223, 661)(224, 663)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 8, 112 ), ( 8, 112, 8, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2298
Graph:: simple bipartite
	v = 336 e = 448 f = 60
	degree seq :: [ 2^224, 4^112 ]

E27.2300 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y1^-1 * Y3)^4, (Y3 * Y1^-4)^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1^14 * Y3 * Y1^-14, Y1^56 ]
Map:: polytopal
	R = (1, 225, 2, 226, 5, 229, 11, 235, 23, 247, 45, 269, 68, 292, 85, 309, 101, 325, 117, 341, 133, 357, 149, 373, 165, 389, 181, 405, 197, 421, 213, 437, 207, 431, 191, 415, 174, 398, 160, 384, 143, 367, 127, 351, 110, 334, 96, 320, 79, 303, 61, 285, 32, 256, 54, 278, 73, 297, 63, 287, 36, 260, 57, 281, 75, 299, 91, 315, 107, 331, 123, 347, 139, 363, 155, 379, 171, 395, 187, 411, 203, 427, 219, 443, 212, 436, 196, 420, 180, 404, 164, 388, 148, 372, 132, 356, 116, 340, 100, 324, 84, 308, 67, 291, 44, 268, 22, 246, 10, 234, 4, 228)(3, 227, 7, 231, 15, 239, 31, 255, 59, 283, 77, 301, 93, 317, 109, 333, 125, 349, 141, 365, 157, 381, 173, 397, 189, 413, 205, 429, 214, 438, 204, 428, 185, 409, 167, 391, 150, 374, 140, 364, 121, 345, 103, 327, 86, 310, 76, 300, 52, 276, 26, 250, 12, 236, 25, 249, 49, 273, 42, 266, 21, 245, 41, 265, 65, 289, 82, 306, 98, 322, 114, 338, 130, 354, 146, 370, 162, 386, 178, 402, 194, 418, 210, 434, 217, 441, 199, 423, 182, 406, 172, 396, 153, 377, 135, 359, 118, 342, 108, 332, 89, 313, 70, 294, 46, 270, 37, 261, 18, 242, 8, 232)(6, 230, 13, 237, 27, 251, 53, 277, 43, 267, 66, 290, 83, 307, 99, 323, 115, 339, 131, 355, 147, 371, 163, 387, 179, 403, 195, 419, 211, 435, 220, 444, 201, 425, 183, 407, 166, 390, 156, 380, 137, 361, 119, 343, 102, 326, 92, 316, 72, 296, 48, 272, 24, 248, 47, 271, 40, 264, 20, 244, 9, 233, 19, 243, 38, 262, 64, 288, 81, 305, 97, 321, 113, 337, 129, 353, 145, 369, 161, 385, 177, 401, 193, 417, 209, 433, 215, 439, 198, 422, 188, 412, 169, 393, 151, 375, 134, 358, 124, 348, 105, 329, 87, 311, 69, 293, 58, 282, 30, 254, 14, 238)(16, 240, 33, 257, 50, 274, 29, 253, 56, 280, 71, 295, 90, 314, 104, 328, 122, 346, 136, 360, 154, 378, 168, 392, 186, 410, 200, 424, 218, 442, 223, 447, 222, 446, 206, 430, 190, 414, 176, 400, 159, 383, 142, 366, 126, 350, 112, 336, 95, 319, 78, 302, 60, 284, 39, 263, 55, 279, 28, 252, 17, 241, 35, 259, 51, 275, 74, 298, 88, 312, 106, 330, 120, 344, 138, 362, 152, 376, 170, 394, 184, 408, 202, 426, 216, 440, 224, 448, 221, 445, 208, 432, 192, 416, 175, 399, 158, 382, 144, 368, 128, 352, 111, 335, 94, 318, 80, 304, 62, 286, 34, 258)(449, 673)(450, 674)(451, 675)(452, 676)(453, 677)(454, 678)(455, 679)(456, 680)(457, 681)(458, 682)(459, 683)(460, 684)(461, 685)(462, 686)(463, 687)(464, 688)(465, 689)(466, 690)(467, 691)(468, 692)(469, 693)(470, 694)(471, 695)(472, 696)(473, 697)(474, 698)(475, 699)(476, 700)(477, 701)(478, 702)(479, 703)(480, 704)(481, 705)(482, 706)(483, 707)(484, 708)(485, 709)(486, 710)(487, 711)(488, 712)(489, 713)(490, 714)(491, 715)(492, 716)(493, 717)(494, 718)(495, 719)(496, 720)(497, 721)(498, 722)(499, 723)(500, 724)(501, 725)(502, 726)(503, 727)(504, 728)(505, 729)(506, 730)(507, 731)(508, 732)(509, 733)(510, 734)(511, 735)(512, 736)(513, 737)(514, 738)(515, 739)(516, 740)(517, 741)(518, 742)(519, 743)(520, 744)(521, 745)(522, 746)(523, 747)(524, 748)(525, 749)(526, 750)(527, 751)(528, 752)(529, 753)(530, 754)(531, 755)(532, 756)(533, 757)(534, 758)(535, 759)(536, 760)(537, 761)(538, 762)(539, 763)(540, 764)(541, 765)(542, 766)(543, 767)(544, 768)(545, 769)(546, 770)(547, 771)(548, 772)(549, 773)(550, 774)(551, 775)(552, 776)(553, 777)(554, 778)(555, 779)(556, 780)(557, 781)(558, 782)(559, 783)(560, 784)(561, 785)(562, 786)(563, 787)(564, 788)(565, 789)(566, 790)(567, 791)(568, 792)(569, 793)(570, 794)(571, 795)(572, 796)(573, 797)(574, 798)(575, 799)(576, 800)(577, 801)(578, 802)(579, 803)(580, 804)(581, 805)(582, 806)(583, 807)(584, 808)(585, 809)(586, 810)(587, 811)(588, 812)(589, 813)(590, 814)(591, 815)(592, 816)(593, 817)(594, 818)(595, 819)(596, 820)(597, 821)(598, 822)(599, 823)(600, 824)(601, 825)(602, 826)(603, 827)(604, 828)(605, 829)(606, 830)(607, 831)(608, 832)(609, 833)(610, 834)(611, 835)(612, 836)(613, 837)(614, 838)(615, 839)(616, 840)(617, 841)(618, 842)(619, 843)(620, 844)(621, 845)(622, 846)(623, 847)(624, 848)(625, 849)(626, 850)(627, 851)(628, 852)(629, 853)(630, 854)(631, 855)(632, 856)(633, 857)(634, 858)(635, 859)(636, 860)(637, 861)(638, 862)(639, 863)(640, 864)(641, 865)(642, 866)(643, 867)(644, 868)(645, 869)(646, 870)(647, 871)(648, 872)(649, 873)(650, 874)(651, 875)(652, 876)(653, 877)(654, 878)(655, 879)(656, 880)(657, 881)(658, 882)(659, 883)(660, 884)(661, 885)(662, 886)(663, 887)(664, 888)(665, 889)(666, 890)(667, 891)(668, 892)(669, 893)(670, 894)(671, 895)(672, 896)
	L = (1, 451)(2, 454)(3, 449)(4, 457)(5, 460)(6, 450)(7, 464)(8, 465)(9, 452)(10, 469)(11, 472)(12, 453)(13, 476)(14, 477)(15, 480)(16, 455)(17, 456)(18, 484)(19, 487)(20, 481)(21, 458)(22, 491)(23, 494)(24, 459)(25, 498)(26, 499)(27, 502)(28, 461)(29, 462)(30, 505)(31, 508)(32, 463)(33, 468)(34, 501)(35, 495)(36, 466)(37, 504)(38, 509)(39, 467)(40, 511)(41, 510)(42, 503)(43, 470)(44, 507)(45, 517)(46, 471)(47, 483)(48, 519)(49, 521)(50, 473)(51, 474)(52, 523)(53, 482)(54, 475)(55, 490)(56, 485)(57, 478)(58, 522)(59, 492)(60, 479)(61, 486)(62, 489)(63, 488)(64, 528)(65, 527)(66, 526)(67, 529)(68, 534)(69, 493)(70, 536)(71, 496)(72, 539)(73, 497)(74, 506)(75, 500)(76, 538)(77, 542)(78, 514)(79, 513)(80, 512)(81, 515)(82, 543)(83, 544)(84, 546)(85, 550)(86, 516)(87, 552)(88, 518)(89, 555)(90, 524)(91, 520)(92, 554)(93, 558)(94, 525)(95, 530)(96, 531)(97, 560)(98, 532)(99, 559)(100, 563)(101, 566)(102, 533)(103, 568)(104, 535)(105, 571)(106, 540)(107, 537)(108, 570)(109, 574)(110, 541)(111, 547)(112, 545)(113, 575)(114, 576)(115, 548)(116, 573)(117, 582)(118, 549)(119, 584)(120, 551)(121, 587)(122, 556)(123, 553)(124, 586)(125, 564)(126, 557)(127, 561)(128, 562)(129, 592)(130, 591)(131, 590)(132, 593)(133, 598)(134, 565)(135, 600)(136, 567)(137, 603)(138, 572)(139, 569)(140, 602)(141, 606)(142, 579)(143, 578)(144, 577)(145, 580)(146, 607)(147, 608)(148, 610)(149, 614)(150, 581)(151, 616)(152, 583)(153, 619)(154, 588)(155, 585)(156, 618)(157, 622)(158, 589)(159, 594)(160, 595)(161, 624)(162, 596)(163, 623)(164, 627)(165, 630)(166, 597)(167, 632)(168, 599)(169, 635)(170, 604)(171, 601)(172, 634)(173, 638)(174, 605)(175, 611)(176, 609)(177, 639)(178, 640)(179, 612)(180, 637)(181, 646)(182, 613)(183, 648)(184, 615)(185, 651)(186, 620)(187, 617)(188, 650)(189, 628)(190, 621)(191, 625)(192, 626)(193, 656)(194, 655)(195, 654)(196, 657)(197, 662)(198, 629)(199, 664)(200, 631)(201, 667)(202, 636)(203, 633)(204, 666)(205, 669)(206, 643)(207, 642)(208, 641)(209, 644)(210, 670)(211, 661)(212, 665)(213, 659)(214, 645)(215, 671)(216, 647)(217, 660)(218, 652)(219, 649)(220, 672)(221, 653)(222, 658)(223, 663)(224, 668)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2297
Graph:: simple bipartite
	v = 228 e = 448 f = 168
	degree seq :: [ 2^224, 112^4 ]

E27.2301 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^4, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2^-2 * Y1, (Y2^-4 * Y1)^2, Y2^10 * Y1 * Y2^-18 * Y1, (Y2^-1 * R * Y2^-13)^2 ]
Map::
	R = (1, 225, 2, 226)(3, 227, 7, 231)(4, 228, 9, 233)(5, 229, 11, 235)(6, 230, 13, 237)(8, 232, 17, 241)(10, 234, 21, 245)(12, 236, 25, 249)(14, 238, 29, 253)(15, 239, 28, 252)(16, 240, 32, 256)(18, 242, 36, 260)(19, 243, 38, 262)(20, 244, 23, 247)(22, 246, 43, 267)(24, 248, 46, 270)(26, 250, 50, 274)(27, 251, 52, 276)(30, 254, 57, 281)(31, 255, 48, 272)(33, 257, 55, 279)(34, 258, 45, 269)(35, 259, 53, 277)(37, 261, 58, 282)(39, 263, 49, 273)(40, 264, 56, 280)(41, 265, 47, 271)(42, 266, 54, 278)(44, 268, 51, 275)(59, 283, 73, 297)(60, 284, 69, 293)(61, 285, 74, 298)(62, 286, 75, 299)(63, 287, 77, 301)(64, 288, 68, 292)(65, 289, 70, 294)(66, 290, 71, 295)(67, 291, 81, 305)(72, 296, 85, 309)(76, 300, 89, 313)(78, 302, 91, 315)(79, 303, 90, 314)(80, 304, 94, 318)(82, 306, 87, 311)(83, 307, 86, 310)(84, 308, 98, 322)(88, 312, 102, 326)(92, 316, 106, 330)(93, 317, 107, 331)(95, 319, 105, 329)(96, 320, 111, 335)(97, 321, 103, 327)(99, 323, 101, 325)(100, 324, 115, 339)(104, 328, 119, 343)(108, 332, 123, 347)(109, 333, 122, 346)(110, 334, 121, 345)(112, 336, 124, 348)(113, 337, 118, 342)(114, 338, 117, 341)(116, 340, 120, 344)(125, 349, 137, 361)(126, 350, 138, 362)(127, 351, 139, 363)(128, 352, 141, 365)(129, 353, 133, 357)(130, 354, 134, 358)(131, 355, 135, 359)(132, 356, 145, 369)(136, 360, 149, 373)(140, 364, 153, 377)(142, 366, 155, 379)(143, 367, 154, 378)(144, 368, 158, 382)(146, 370, 151, 375)(147, 371, 150, 374)(148, 372, 162, 386)(152, 376, 166, 390)(156, 380, 170, 394)(157, 381, 171, 395)(159, 383, 169, 393)(160, 384, 175, 399)(161, 385, 167, 391)(163, 387, 165, 389)(164, 388, 179, 403)(168, 392, 183, 407)(172, 396, 187, 411)(173, 397, 186, 410)(174, 398, 185, 409)(176, 400, 188, 412)(177, 401, 182, 406)(178, 402, 181, 405)(180, 404, 184, 408)(189, 413, 201, 425)(190, 414, 202, 426)(191, 415, 203, 427)(192, 416, 205, 429)(193, 417, 197, 421)(194, 418, 198, 422)(195, 419, 199, 423)(196, 420, 209, 433)(200, 424, 213, 437)(204, 428, 217, 441)(206, 430, 219, 443)(207, 431, 218, 442)(208, 432, 216, 440)(210, 434, 215, 439)(211, 435, 214, 438)(212, 436, 220, 444)(221, 445, 224, 448)(222, 446, 223, 447)(449, 673, 451, 675, 456, 680, 466, 690, 485, 709, 511, 735, 528, 752, 544, 768, 560, 784, 576, 800, 592, 816, 608, 832, 624, 848, 640, 864, 656, 880, 662, 886, 646, 870, 630, 854, 614, 838, 598, 822, 582, 806, 566, 790, 550, 774, 534, 758, 518, 742, 497, 721, 473, 697, 496, 720, 517, 741, 504, 728, 477, 701, 503, 727, 522, 746, 538, 762, 554, 778, 570, 794, 586, 810, 602, 826, 618, 842, 634, 858, 650, 874, 666, 890, 660, 884, 644, 868, 628, 852, 612, 836, 596, 820, 580, 804, 564, 788, 548, 772, 532, 756, 515, 739, 492, 716, 470, 694, 458, 682, 452, 676)(450, 674, 453, 677, 460, 684, 474, 698, 499, 723, 520, 744, 536, 760, 552, 776, 568, 792, 584, 808, 600, 824, 616, 840, 632, 856, 648, 872, 664, 888, 654, 878, 638, 862, 622, 846, 606, 830, 590, 814, 574, 798, 558, 782, 542, 766, 526, 750, 509, 733, 483, 707, 465, 689, 482, 706, 508, 732, 490, 714, 469, 693, 489, 713, 513, 737, 530, 754, 546, 770, 562, 786, 578, 802, 594, 818, 610, 834, 626, 850, 642, 866, 658, 882, 668, 892, 652, 876, 636, 860, 620, 844, 604, 828, 588, 812, 572, 796, 556, 780, 540, 764, 524, 748, 506, 730, 478, 702, 462, 686, 454, 678)(455, 679, 463, 687, 479, 703, 494, 718, 491, 715, 514, 738, 531, 755, 547, 771, 563, 787, 579, 803, 595, 819, 611, 835, 627, 851, 643, 867, 659, 883, 670, 894, 655, 879, 639, 863, 623, 847, 607, 831, 591, 815, 575, 799, 559, 783, 543, 767, 527, 751, 510, 734, 484, 708, 500, 724, 488, 712, 468, 692, 457, 681, 467, 691, 487, 711, 512, 736, 529, 753, 545, 769, 561, 785, 577, 801, 593, 817, 609, 833, 625, 849, 641, 865, 657, 881, 669, 893, 653, 877, 637, 861, 621, 845, 605, 829, 589, 813, 573, 797, 557, 781, 541, 765, 525, 749, 507, 731, 481, 705, 464, 688)(459, 683, 471, 695, 493, 717, 480, 704, 505, 729, 523, 747, 539, 763, 555, 779, 571, 795, 587, 811, 603, 827, 619, 843, 635, 859, 651, 875, 667, 891, 672, 896, 663, 887, 647, 871, 631, 855, 615, 839, 599, 823, 583, 807, 567, 791, 551, 775, 535, 759, 519, 743, 498, 722, 486, 710, 502, 726, 476, 700, 461, 685, 475, 699, 501, 725, 521, 745, 537, 761, 553, 777, 569, 793, 585, 809, 601, 825, 617, 841, 633, 857, 649, 873, 665, 889, 671, 895, 661, 885, 645, 869, 629, 853, 613, 837, 597, 821, 581, 805, 565, 789, 549, 773, 533, 757, 516, 740, 495, 719, 472, 696)
	L = (1, 450)(2, 449)(3, 455)(4, 457)(5, 459)(6, 461)(7, 451)(8, 465)(9, 452)(10, 469)(11, 453)(12, 473)(13, 454)(14, 477)(15, 476)(16, 480)(17, 456)(18, 484)(19, 486)(20, 471)(21, 458)(22, 491)(23, 468)(24, 494)(25, 460)(26, 498)(27, 500)(28, 463)(29, 462)(30, 505)(31, 496)(32, 464)(33, 503)(34, 493)(35, 501)(36, 466)(37, 506)(38, 467)(39, 497)(40, 504)(41, 495)(42, 502)(43, 470)(44, 499)(45, 482)(46, 472)(47, 489)(48, 479)(49, 487)(50, 474)(51, 492)(52, 475)(53, 483)(54, 490)(55, 481)(56, 488)(57, 478)(58, 485)(59, 521)(60, 517)(61, 522)(62, 523)(63, 525)(64, 516)(65, 518)(66, 519)(67, 529)(68, 512)(69, 508)(70, 513)(71, 514)(72, 533)(73, 507)(74, 509)(75, 510)(76, 537)(77, 511)(78, 539)(79, 538)(80, 542)(81, 515)(82, 535)(83, 534)(84, 546)(85, 520)(86, 531)(87, 530)(88, 550)(89, 524)(90, 527)(91, 526)(92, 554)(93, 555)(94, 528)(95, 553)(96, 559)(97, 551)(98, 532)(99, 549)(100, 563)(101, 547)(102, 536)(103, 545)(104, 567)(105, 543)(106, 540)(107, 541)(108, 571)(109, 570)(110, 569)(111, 544)(112, 572)(113, 566)(114, 565)(115, 548)(116, 568)(117, 562)(118, 561)(119, 552)(120, 564)(121, 558)(122, 557)(123, 556)(124, 560)(125, 585)(126, 586)(127, 587)(128, 589)(129, 581)(130, 582)(131, 583)(132, 593)(133, 577)(134, 578)(135, 579)(136, 597)(137, 573)(138, 574)(139, 575)(140, 601)(141, 576)(142, 603)(143, 602)(144, 606)(145, 580)(146, 599)(147, 598)(148, 610)(149, 584)(150, 595)(151, 594)(152, 614)(153, 588)(154, 591)(155, 590)(156, 618)(157, 619)(158, 592)(159, 617)(160, 623)(161, 615)(162, 596)(163, 613)(164, 627)(165, 611)(166, 600)(167, 609)(168, 631)(169, 607)(170, 604)(171, 605)(172, 635)(173, 634)(174, 633)(175, 608)(176, 636)(177, 630)(178, 629)(179, 612)(180, 632)(181, 626)(182, 625)(183, 616)(184, 628)(185, 622)(186, 621)(187, 620)(188, 624)(189, 649)(190, 650)(191, 651)(192, 653)(193, 645)(194, 646)(195, 647)(196, 657)(197, 641)(198, 642)(199, 643)(200, 661)(201, 637)(202, 638)(203, 639)(204, 665)(205, 640)(206, 667)(207, 666)(208, 664)(209, 644)(210, 663)(211, 662)(212, 668)(213, 648)(214, 659)(215, 658)(216, 656)(217, 652)(218, 655)(219, 654)(220, 660)(221, 672)(222, 671)(223, 670)(224, 669)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2302
Graph:: bipartite
	v = 116 e = 448 f = 280
	degree seq :: [ 4^112, 112^4 ]

E27.2302 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 56})
Quotient :: dipole
Aut^+ = (C7 x (C8 : C2)) : C2 (small group id <224, 31>)
Aut   = $<448, 281>$ (small group id <448, 281>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y1^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1^-1)^4, (Y3^-3 * Y1)^2, Y3 * Y1^-1 * Y3^-27 * Y1^-1, (Y3 * Y2^-1)^56 ]
Map:: polytopal
	R = (1, 225, 2, 226, 6, 230, 4, 228)(3, 227, 9, 233, 21, 245, 11, 235)(5, 229, 13, 237, 18, 242, 7, 231)(8, 232, 19, 243, 34, 258, 15, 239)(10, 234, 23, 247, 33, 257, 25, 249)(12, 236, 16, 240, 35, 259, 28, 252)(14, 238, 31, 255, 36, 260, 29, 253)(17, 241, 37, 261, 27, 251, 39, 263)(20, 244, 43, 267, 22, 246, 41, 265)(24, 248, 47, 271, 59, 283, 44, 268)(26, 250, 40, 264, 30, 254, 42, 266)(32, 256, 49, 273, 55, 279, 51, 275)(38, 262, 56, 280, 50, 274, 54, 278)(45, 269, 53, 277, 46, 270, 58, 282)(48, 272, 60, 284, 69, 293, 61, 285)(52, 276, 57, 281, 70, 294, 65, 289)(62, 286, 75, 299, 63, 287, 74, 298)(64, 288, 77, 301, 91, 315, 78, 302)(66, 290, 72, 296, 67, 291, 71, 295)(68, 292, 82, 306, 87, 311, 73, 297)(76, 300, 90, 314, 79, 303, 85, 309)(80, 304, 94, 318, 101, 325, 95, 319)(81, 305, 86, 310, 83, 307, 88, 312)(84, 308, 99, 323, 102, 326, 98, 322)(89, 313, 103, 327, 97, 321, 104, 328)(92, 316, 107, 331, 93, 317, 106, 330)(96, 320, 111, 335, 123, 347, 108, 332)(100, 324, 113, 337, 119, 343, 115, 339)(105, 329, 120, 344, 114, 338, 118, 342)(109, 333, 117, 341, 110, 334, 122, 346)(112, 336, 124, 348, 133, 357, 125, 349)(116, 340, 121, 345, 134, 358, 129, 353)(126, 350, 139, 363, 127, 351, 138, 362)(128, 352, 141, 365, 155, 379, 142, 366)(130, 354, 136, 360, 131, 355, 135, 359)(132, 356, 146, 370, 151, 375, 137, 361)(140, 364, 154, 378, 143, 367, 149, 373)(144, 368, 158, 382, 165, 389, 159, 383)(145, 369, 150, 374, 147, 371, 152, 376)(148, 372, 163, 387, 166, 390, 162, 386)(153, 377, 167, 391, 161, 385, 168, 392)(156, 380, 171, 395, 157, 381, 170, 394)(160, 384, 175, 399, 187, 411, 172, 396)(164, 388, 177, 401, 183, 407, 179, 403)(169, 393, 184, 408, 178, 402, 182, 406)(173, 397, 181, 405, 174, 398, 186, 410)(176, 400, 188, 412, 197, 421, 189, 413)(180, 404, 185, 409, 198, 422, 193, 417)(190, 414, 203, 427, 191, 415, 202, 426)(192, 416, 205, 429, 219, 443, 206, 430)(194, 418, 200, 424, 195, 419, 199, 423)(196, 420, 210, 434, 215, 439, 201, 425)(204, 428, 218, 442, 207, 431, 213, 437)(208, 432, 217, 441, 223, 447, 222, 446)(209, 433, 214, 438, 211, 435, 216, 440)(212, 436, 220, 444, 224, 448, 221, 445)(449, 673)(450, 674)(451, 675)(452, 676)(453, 677)(454, 678)(455, 679)(456, 680)(457, 681)(458, 682)(459, 683)(460, 684)(461, 685)(462, 686)(463, 687)(464, 688)(465, 689)(466, 690)(467, 691)(468, 692)(469, 693)(470, 694)(471, 695)(472, 696)(473, 697)(474, 698)(475, 699)(476, 700)(477, 701)(478, 702)(479, 703)(480, 704)(481, 705)(482, 706)(483, 707)(484, 708)(485, 709)(486, 710)(487, 711)(488, 712)(489, 713)(490, 714)(491, 715)(492, 716)(493, 717)(494, 718)(495, 719)(496, 720)(497, 721)(498, 722)(499, 723)(500, 724)(501, 725)(502, 726)(503, 727)(504, 728)(505, 729)(506, 730)(507, 731)(508, 732)(509, 733)(510, 734)(511, 735)(512, 736)(513, 737)(514, 738)(515, 739)(516, 740)(517, 741)(518, 742)(519, 743)(520, 744)(521, 745)(522, 746)(523, 747)(524, 748)(525, 749)(526, 750)(527, 751)(528, 752)(529, 753)(530, 754)(531, 755)(532, 756)(533, 757)(534, 758)(535, 759)(536, 760)(537, 761)(538, 762)(539, 763)(540, 764)(541, 765)(542, 766)(543, 767)(544, 768)(545, 769)(546, 770)(547, 771)(548, 772)(549, 773)(550, 774)(551, 775)(552, 776)(553, 777)(554, 778)(555, 779)(556, 780)(557, 781)(558, 782)(559, 783)(560, 784)(561, 785)(562, 786)(563, 787)(564, 788)(565, 789)(566, 790)(567, 791)(568, 792)(569, 793)(570, 794)(571, 795)(572, 796)(573, 797)(574, 798)(575, 799)(576, 800)(577, 801)(578, 802)(579, 803)(580, 804)(581, 805)(582, 806)(583, 807)(584, 808)(585, 809)(586, 810)(587, 811)(588, 812)(589, 813)(590, 814)(591, 815)(592, 816)(593, 817)(594, 818)(595, 819)(596, 820)(597, 821)(598, 822)(599, 823)(600, 824)(601, 825)(602, 826)(603, 827)(604, 828)(605, 829)(606, 830)(607, 831)(608, 832)(609, 833)(610, 834)(611, 835)(612, 836)(613, 837)(614, 838)(615, 839)(616, 840)(617, 841)(618, 842)(619, 843)(620, 844)(621, 845)(622, 846)(623, 847)(624, 848)(625, 849)(626, 850)(627, 851)(628, 852)(629, 853)(630, 854)(631, 855)(632, 856)(633, 857)(634, 858)(635, 859)(636, 860)(637, 861)(638, 862)(639, 863)(640, 864)(641, 865)(642, 866)(643, 867)(644, 868)(645, 869)(646, 870)(647, 871)(648, 872)(649, 873)(650, 874)(651, 875)(652, 876)(653, 877)(654, 878)(655, 879)(656, 880)(657, 881)(658, 882)(659, 883)(660, 884)(661, 885)(662, 886)(663, 887)(664, 888)(665, 889)(666, 890)(667, 891)(668, 892)(669, 893)(670, 894)(671, 895)(672, 896)
	L = (1, 451)(2, 455)(3, 458)(4, 460)(5, 449)(6, 463)(7, 465)(8, 450)(9, 452)(10, 472)(11, 474)(12, 475)(13, 477)(14, 453)(15, 481)(16, 454)(17, 486)(18, 488)(19, 489)(20, 456)(21, 491)(22, 457)(23, 459)(24, 496)(25, 482)(26, 483)(27, 497)(28, 490)(29, 498)(30, 461)(31, 499)(32, 462)(33, 501)(34, 478)(35, 479)(36, 464)(37, 466)(38, 505)(39, 476)(40, 469)(41, 506)(42, 467)(43, 507)(44, 468)(45, 470)(46, 471)(47, 473)(48, 512)(49, 513)(50, 514)(51, 515)(52, 480)(53, 517)(54, 484)(55, 485)(56, 487)(57, 521)(58, 522)(59, 523)(60, 492)(61, 493)(62, 494)(63, 495)(64, 528)(65, 529)(66, 530)(67, 531)(68, 500)(69, 533)(70, 502)(71, 503)(72, 504)(73, 537)(74, 538)(75, 539)(76, 508)(77, 509)(78, 510)(79, 511)(80, 544)(81, 545)(82, 546)(83, 547)(84, 516)(85, 549)(86, 518)(87, 519)(88, 520)(89, 553)(90, 554)(91, 555)(92, 524)(93, 525)(94, 526)(95, 527)(96, 560)(97, 561)(98, 562)(99, 563)(100, 532)(101, 565)(102, 534)(103, 535)(104, 536)(105, 569)(106, 570)(107, 571)(108, 540)(109, 541)(110, 542)(111, 543)(112, 576)(113, 577)(114, 578)(115, 579)(116, 548)(117, 581)(118, 550)(119, 551)(120, 552)(121, 585)(122, 586)(123, 587)(124, 556)(125, 557)(126, 558)(127, 559)(128, 592)(129, 593)(130, 594)(131, 595)(132, 564)(133, 597)(134, 566)(135, 567)(136, 568)(137, 601)(138, 602)(139, 603)(140, 572)(141, 573)(142, 574)(143, 575)(144, 608)(145, 609)(146, 610)(147, 611)(148, 580)(149, 613)(150, 582)(151, 583)(152, 584)(153, 617)(154, 618)(155, 619)(156, 588)(157, 589)(158, 590)(159, 591)(160, 624)(161, 625)(162, 626)(163, 627)(164, 596)(165, 629)(166, 598)(167, 599)(168, 600)(169, 633)(170, 634)(171, 635)(172, 604)(173, 605)(174, 606)(175, 607)(176, 640)(177, 641)(178, 642)(179, 643)(180, 612)(181, 645)(182, 614)(183, 615)(184, 616)(185, 649)(186, 650)(187, 651)(188, 620)(189, 621)(190, 622)(191, 623)(192, 656)(193, 657)(194, 658)(195, 659)(196, 628)(197, 661)(198, 630)(199, 631)(200, 632)(201, 665)(202, 666)(203, 667)(204, 636)(205, 637)(206, 638)(207, 639)(208, 664)(209, 670)(210, 669)(211, 668)(212, 644)(213, 671)(214, 646)(215, 647)(216, 648)(217, 654)(218, 660)(219, 672)(220, 652)(221, 653)(222, 655)(223, 663)(224, 662)(225, 673)(226, 674)(227, 675)(228, 676)(229, 677)(230, 678)(231, 679)(232, 680)(233, 681)(234, 682)(235, 683)(236, 684)(237, 685)(238, 686)(239, 687)(240, 688)(241, 689)(242, 690)(243, 691)(244, 692)(245, 693)(246, 694)(247, 695)(248, 696)(249, 697)(250, 698)(251, 699)(252, 700)(253, 701)(254, 702)(255, 703)(256, 704)(257, 705)(258, 706)(259, 707)(260, 708)(261, 709)(262, 710)(263, 711)(264, 712)(265, 713)(266, 714)(267, 715)(268, 716)(269, 717)(270, 718)(271, 719)(272, 720)(273, 721)(274, 722)(275, 723)(276, 724)(277, 725)(278, 726)(279, 727)(280, 728)(281, 729)(282, 730)(283, 731)(284, 732)(285, 733)(286, 734)(287, 735)(288, 736)(289, 737)(290, 738)(291, 739)(292, 740)(293, 741)(294, 742)(295, 743)(296, 744)(297, 745)(298, 746)(299, 747)(300, 748)(301, 749)(302, 750)(303, 751)(304, 752)(305, 753)(306, 754)(307, 755)(308, 756)(309, 757)(310, 758)(311, 759)(312, 760)(313, 761)(314, 762)(315, 763)(316, 764)(317, 765)(318, 766)(319, 767)(320, 768)(321, 769)(322, 770)(323, 771)(324, 772)(325, 773)(326, 774)(327, 775)(328, 776)(329, 777)(330, 778)(331, 779)(332, 780)(333, 781)(334, 782)(335, 783)(336, 784)(337, 785)(338, 786)(339, 787)(340, 788)(341, 789)(342, 790)(343, 791)(344, 792)(345, 793)(346, 794)(347, 795)(348, 796)(349, 797)(350, 798)(351, 799)(352, 800)(353, 801)(354, 802)(355, 803)(356, 804)(357, 805)(358, 806)(359, 807)(360, 808)(361, 809)(362, 810)(363, 811)(364, 812)(365, 813)(366, 814)(367, 815)(368, 816)(369, 817)(370, 818)(371, 819)(372, 820)(373, 821)(374, 822)(375, 823)(376, 824)(377, 825)(378, 826)(379, 827)(380, 828)(381, 829)(382, 830)(383, 831)(384, 832)(385, 833)(386, 834)(387, 835)(388, 836)(389, 837)(390, 838)(391, 839)(392, 840)(393, 841)(394, 842)(395, 843)(396, 844)(397, 845)(398, 846)(399, 847)(400, 848)(401, 849)(402, 850)(403, 851)(404, 852)(405, 853)(406, 854)(407, 855)(408, 856)(409, 857)(410, 858)(411, 859)(412, 860)(413, 861)(414, 862)(415, 863)(416, 864)(417, 865)(418, 866)(419, 867)(420, 868)(421, 869)(422, 870)(423, 871)(424, 872)(425, 873)(426, 874)(427, 875)(428, 876)(429, 877)(430, 878)(431, 879)(432, 880)(433, 881)(434, 882)(435, 883)(436, 884)(437, 885)(438, 886)(439, 887)(440, 888)(441, 889)(442, 890)(443, 891)(444, 892)(445, 893)(446, 894)(447, 895)(448, 896)
	local type(s) :: { ( 4, 112 ), ( 4, 112, 4, 112, 4, 112, 4, 112 ) }
Outer automorphisms :: reflexible
Dual of E27.2301
Graph:: simple bipartite
	v = 280 e = 448 f = 116
	degree seq :: [ 2^224, 8^56 ]

E27.2303 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 5, 12})
Quotient :: regular
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-3 * T2 * T1^2, (T1^-1 * T2)^5, T1^12, T1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-1 * T2 * T1, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 43, 73, 72, 42, 22, 10, 4)(3, 7, 15, 24, 45, 76, 114, 105, 64, 37, 18, 8)(6, 13, 27, 44, 75, 116, 113, 71, 41, 21, 30, 14)(9, 19, 26, 12, 25, 46, 74, 115, 111, 69, 40, 20)(16, 32, 57, 77, 119, 160, 150, 104, 63, 36, 60, 33)(17, 34, 56, 31, 55, 91, 118, 159, 131, 102, 62, 35)(28, 50, 85, 117, 93, 139, 112, 136, 90, 54, 87, 51)(29, 52, 84, 49, 83, 125, 158, 151, 106, 70, 89, 53)(38, 65, 80, 47, 79, 122, 157, 127, 110, 68, 108, 66)(39, 67, 82, 48, 81, 121, 78, 120, 98, 143, 95, 58)(59, 96, 141, 94, 140, 180, 198, 188, 146, 103, 145, 97)(61, 99, 138, 92, 137, 177, 197, 182, 149, 101, 148, 100)(86, 129, 170, 128, 169, 207, 179, 213, 173, 135, 172, 130)(88, 132, 168, 126, 167, 205, 192, 209, 176, 134, 175, 133)(107, 152, 164, 123, 163, 202, 162, 201, 195, 156, 194, 153)(109, 154, 166, 124, 165, 200, 161, 199, 184, 142, 183, 155)(144, 185, 218, 181, 217, 231, 221, 196, 220, 187, 204, 186)(147, 189, 212, 178, 211, 171, 210, 227, 208, 191, 223, 190)(174, 214, 193, 206, 226, 203, 225, 236, 224, 216, 230, 215)(219, 233, 222, 232, 240, 228, 239, 229, 238, 235, 237, 234)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 58)(33, 59)(34, 61)(35, 50)(40, 68)(41, 70)(42, 69)(43, 74)(45, 77)(46, 78)(51, 86)(52, 88)(53, 79)(55, 92)(56, 93)(57, 94)(60, 98)(62, 101)(63, 103)(64, 102)(65, 106)(66, 107)(67, 109)(71, 112)(72, 113)(73, 114)(75, 117)(76, 118)(80, 123)(81, 124)(82, 119)(83, 126)(84, 127)(85, 128)(87, 131)(89, 134)(90, 135)(91, 136)(95, 142)(96, 144)(97, 137)(99, 146)(100, 147)(104, 121)(105, 150)(108, 125)(110, 156)(111, 143)(115, 157)(116, 158)(120, 161)(122, 162)(129, 171)(130, 167)(132, 173)(133, 174)(138, 178)(139, 179)(140, 181)(141, 182)(145, 187)(148, 180)(149, 191)(151, 192)(152, 193)(153, 165)(154, 195)(155, 196)(159, 197)(160, 198)(163, 203)(164, 199)(166, 204)(168, 206)(169, 208)(170, 209)(172, 212)(175, 207)(176, 216)(177, 210)(183, 202)(184, 217)(185, 200)(186, 219)(188, 221)(189, 222)(190, 213)(194, 215)(201, 224)(205, 225)(211, 228)(214, 229)(218, 232)(220, 235)(223, 234)(226, 237)(227, 238)(230, 240)(231, 239)(233, 236)
	local type(s) :: { ( 5^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2304
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 20 e = 120 f = 48
	degree seq :: [ 12^20 ]

E27.2304 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 5, 12})
Quotient :: regular
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^2 * T2 * T1^2 * T2 * T1^2, (T2 * T1^-1 * T2 * T1^2)^3, (T2 * T1^-2 * T2 * T1^2 * T2 * T1^-1)^2, (T2 * T1^2 * T2 * T1^-2 * T2 * T1^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 33, 36, 19)(11, 21, 39, 42, 22)(15, 28, 51, 54, 29)(16, 30, 55, 58, 31)(20, 37, 67, 70, 38)(24, 44, 79, 82, 45)(25, 46, 83, 86, 47)(27, 49, 89, 92, 50)(32, 59, 102, 105, 60)(34, 62, 108, 110, 63)(35, 64, 111, 112, 65)(40, 72, 123, 126, 73)(41, 74, 127, 130, 75)(43, 77, 133, 136, 78)(48, 87, 143, 146, 88)(52, 80, 124, 154, 94)(53, 95, 155, 157, 96)(56, 81, 138, 162, 99)(57, 85, 129, 163, 100)(61, 106, 170, 172, 107)(66, 113, 177, 179, 114)(68, 116, 182, 184, 117)(69, 118, 185, 186, 119)(71, 121, 161, 190, 122)(76, 131, 195, 198, 132)(84, 125, 169, 204, 141)(90, 137, 201, 194, 148)(91, 149, 144, 192, 150)(93, 152, 142, 197, 153)(97, 158, 214, 215, 159)(98, 135, 199, 196, 160)(101, 145, 206, 173, 164)(103, 139, 202, 171, 166)(104, 167, 220, 221, 168)(109, 174, 208, 147, 175)(115, 180, 203, 224, 181)(120, 187, 213, 156, 188)(128, 183, 207, 228, 193)(134, 191, 227, 223, 178)(140, 189, 225, 222, 176)(151, 210, 234, 226, 200)(165, 218, 235, 229, 205)(209, 219, 236, 238, 230)(211, 231, 239, 237, 217)(212, 233, 240, 232, 216)
	L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 32)(18, 34)(19, 35)(21, 40)(22, 41)(23, 43)(26, 48)(28, 52)(29, 53)(30, 56)(31, 57)(33, 61)(36, 66)(37, 68)(38, 69)(39, 71)(42, 76)(44, 80)(45, 81)(46, 84)(47, 85)(49, 90)(50, 91)(51, 93)(54, 97)(55, 98)(58, 101)(59, 103)(60, 104)(62, 94)(63, 109)(64, 96)(65, 100)(67, 115)(70, 120)(72, 124)(73, 125)(74, 128)(75, 129)(77, 134)(78, 135)(79, 137)(82, 139)(83, 140)(86, 142)(87, 144)(88, 145)(89, 147)(92, 151)(95, 156)(99, 161)(102, 165)(105, 169)(106, 153)(107, 171)(108, 173)(110, 176)(111, 150)(112, 168)(113, 159)(114, 178)(116, 154)(117, 183)(118, 175)(119, 163)(121, 167)(122, 189)(123, 191)(126, 192)(127, 158)(130, 194)(131, 196)(132, 197)(133, 157)(136, 200)(138, 179)(141, 203)(143, 205)(146, 207)(148, 188)(149, 209)(152, 211)(155, 212)(160, 184)(162, 216)(164, 217)(166, 219)(170, 193)(172, 210)(174, 198)(177, 218)(180, 206)(181, 214)(182, 220)(185, 202)(186, 223)(187, 222)(190, 226)(195, 229)(199, 230)(201, 231)(204, 232)(208, 233)(213, 235)(215, 236)(221, 237)(224, 234)(225, 238)(227, 239)(228, 240)
	local type(s) :: { ( 12^5 ) }
Outer automorphisms :: reflexible
Dual of E27.2303
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 48 e = 120 f = 20
	degree seq :: [ 5^48 ]

E27.2305 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 12})
Quotient :: edge
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2, (T1 * T2^-1 * T1 * T2^2)^3, (T2 * T1 * T2^-2 * T1 * T2^2 * T1)^2, (T2 * T1 * T2^2 * T1 * T2^-2 * T1)^2 ]
Map:: polytopal
	R = (1, 3, 8, 10, 4)(2, 5, 12, 14, 6)(7, 15, 28, 30, 16)(9, 18, 34, 36, 19)(11, 21, 40, 42, 22)(13, 24, 46, 48, 25)(17, 31, 58, 60, 32)(20, 37, 68, 70, 38)(23, 43, 78, 80, 44)(26, 49, 88, 90, 50)(27, 51, 91, 92, 52)(29, 54, 96, 97, 55)(33, 61, 106, 108, 62)(35, 64, 111, 112, 65)(39, 71, 121, 122, 72)(41, 74, 126, 127, 75)(45, 81, 136, 138, 82)(47, 84, 141, 142, 85)(53, 93, 152, 153, 94)(56, 98, 159, 160, 99)(57, 100, 161, 162, 101)(59, 103, 166, 167, 104)(63, 109, 174, 176, 110)(66, 113, 177, 179, 114)(67, 115, 180, 182, 116)(69, 118, 185, 186, 119)(73, 123, 157, 190, 124)(76, 128, 193, 194, 129)(77, 130, 195, 196, 131)(79, 133, 158, 199, 134)(83, 139, 204, 205, 140)(86, 143, 206, 170, 144)(87, 145, 208, 175, 146)(89, 148, 212, 213, 149)(95, 154, 150, 214, 155)(102, 163, 137, 202, 164)(105, 168, 220, 221, 169)(107, 171, 197, 132, 172)(117, 183, 216, 224, 184)(120, 187, 191, 125, 188)(135, 200, 230, 231, 201)(147, 210, 226, 234, 211)(151, 215, 235, 223, 178)(156, 217, 236, 222, 173)(165, 181, 218, 237, 219)(189, 225, 238, 233, 207)(192, 227, 239, 232, 203)(198, 209, 228, 240, 229)(241, 242)(243, 247)(244, 249)(245, 251)(246, 253)(248, 257)(250, 260)(252, 263)(254, 266)(255, 267)(256, 269)(258, 273)(259, 275)(261, 279)(262, 281)(264, 285)(265, 287)(268, 293)(270, 296)(271, 297)(272, 299)(274, 303)(276, 306)(277, 307)(278, 309)(280, 313)(282, 316)(283, 317)(284, 319)(286, 323)(288, 326)(289, 327)(290, 329)(291, 311)(292, 321)(294, 335)(295, 324)(298, 342)(300, 345)(301, 312)(302, 347)(304, 315)(305, 325)(308, 357)(310, 360)(314, 365)(318, 372)(320, 375)(322, 377)(328, 387)(330, 390)(331, 370)(332, 385)(333, 391)(334, 379)(336, 396)(337, 397)(338, 398)(339, 383)(340, 361)(341, 394)(343, 405)(344, 381)(346, 410)(348, 413)(349, 364)(350, 415)(351, 374)(352, 389)(353, 369)(354, 418)(355, 362)(356, 421)(358, 412)(359, 382)(363, 429)(366, 432)(367, 392)(368, 406)(371, 428)(373, 438)(376, 419)(378, 443)(380, 422)(384, 447)(386, 449)(388, 403)(393, 441)(395, 456)(399, 451)(400, 458)(401, 455)(402, 439)(404, 457)(407, 436)(408, 445)(409, 430)(411, 461)(414, 459)(416, 440)(417, 450)(420, 452)(423, 446)(424, 433)(425, 448)(426, 463)(427, 462)(431, 466)(434, 468)(435, 465)(437, 467)(442, 471)(444, 469)(453, 473)(454, 472)(460, 474)(464, 470)(475, 478)(476, 480)(477, 479)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 24, 24 ), ( 24^5 ) }
Outer automorphisms :: reflexible
Dual of E27.2309
Transitivity :: ET+
Graph:: simple bipartite
	v = 168 e = 240 f = 20
	degree seq :: [ 2^120, 5^48 ]

E27.2306 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 12})
Quotient :: edge
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^5, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2^3 * T1^-2 * T2^-3 * T1^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, T2 * T1^-2 * T2^3 * T1^-1 * T2 * T1 * T2^-1 * T1, T2^12 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 25, 57, 111, 169, 100, 49, 37, 15, 5)(2, 7, 18, 43, 26, 59, 115, 155, 86, 50, 21, 8)(4, 12, 30, 58, 113, 168, 143, 78, 36, 54, 23, 9)(6, 16, 38, 80, 44, 90, 158, 116, 127, 87, 41, 17)(11, 27, 62, 112, 167, 99, 76, 35, 14, 34, 56, 24)(13, 32, 70, 114, 81, 142, 177, 107, 53, 106, 66, 29)(19, 45, 92, 60, 117, 154, 98, 48, 20, 47, 89, 42)(22, 51, 101, 67, 31, 68, 130, 181, 141, 77, 104, 52)(28, 64, 123, 128, 140, 75, 139, 131, 110, 74, 119, 61)(33, 72, 109, 55, 108, 97, 120, 63, 121, 96, 137, 73)(39, 82, 147, 91, 159, 191, 153, 85, 40, 84, 145, 79)(46, 94, 157, 88, 156, 152, 160, 93, 161, 151, 165, 95)(65, 125, 188, 133, 71, 134, 197, 146, 176, 105, 175, 126)(69, 132, 194, 196, 174, 103, 173, 198, 170, 102, 171, 129)(83, 149, 203, 144, 202, 190, 204, 148, 205, 189, 209, 150)(118, 182, 224, 186, 124, 187, 138, 201, 223, 180, 193, 183)(122, 185, 136, 200, 222, 179, 135, 199, 166, 178, 221, 184)(162, 214, 164, 216, 236, 212, 163, 215, 210, 211, 235, 213)(172, 219, 237, 217, 228, 226, 192, 218, 238, 225, 195, 220)(206, 232, 208, 234, 240, 230, 207, 233, 227, 229, 239, 231)(241, 242, 246, 253, 244)(243, 249, 262, 268, 251)(245, 254, 273, 259, 247)(248, 260, 286, 279, 256)(250, 264, 295, 300, 266)(252, 269, 305, 309, 271)(255, 276, 317, 314, 274)(257, 280, 323, 311, 272)(258, 282, 328, 331, 284)(261, 289, 339, 336, 287)(263, 293, 345, 342, 291)(265, 283, 320, 354, 298)(267, 301, 358, 362, 303)(270, 307, 368, 352, 297)(275, 315, 378, 375, 312)(277, 290, 327, 346, 294)(278, 319, 384, 386, 321)(281, 326, 394, 391, 324)(285, 313, 376, 402, 333)(288, 337, 406, 403, 334)(292, 343, 412, 364, 304)(296, 350, 420, 418, 348)(299, 332, 400, 393, 356)(302, 360, 338, 395, 351)(306, 367, 431, 429, 365)(308, 369, 432, 433, 371)(310, 373, 436, 421, 353)(316, 340, 408, 370, 379)(318, 382, 437, 413, 344)(322, 335, 404, 446, 388)(325, 392, 450, 447, 389)(329, 361, 424, 451, 396)(330, 387, 444, 415, 347)(341, 410, 457, 441, 380)(349, 419, 456, 405, 357)(355, 398, 417, 383, 409)(359, 381, 434, 465, 422)(363, 426, 440, 377, 407)(366, 430, 467, 435, 372)(374, 390, 448, 468, 438)(385, 401, 453, 469, 442)(397, 452, 474, 449, 399)(411, 416, 443, 470, 458)(414, 428, 445, 471, 459)(423, 466, 472, 454, 425)(427, 460, 473, 455, 439)(461, 463, 477, 479, 475)(462, 464, 478, 480, 476)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4^5 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2310
Transitivity :: ET+
Graph:: simple bipartite
	v = 68 e = 240 f = 120
	degree seq :: [ 5^48, 12^20 ]

E27.2307 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 12})
Quotient :: edge
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, (T2 * T1^-1)^5, T1^12, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-1, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^3 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 36)(19, 38)(20, 39)(22, 37)(23, 44)(25, 47)(26, 48)(27, 49)(30, 54)(32, 58)(33, 59)(34, 61)(35, 50)(40, 68)(41, 70)(42, 69)(43, 74)(45, 77)(46, 78)(51, 86)(52, 88)(53, 79)(55, 92)(56, 93)(57, 94)(60, 98)(62, 101)(63, 103)(64, 102)(65, 106)(66, 107)(67, 109)(71, 112)(72, 113)(73, 114)(75, 117)(76, 118)(80, 123)(81, 124)(82, 119)(83, 126)(84, 127)(85, 128)(87, 131)(89, 134)(90, 135)(91, 136)(95, 142)(96, 144)(97, 137)(99, 146)(100, 147)(104, 121)(105, 150)(108, 125)(110, 156)(111, 143)(115, 157)(116, 158)(120, 161)(122, 162)(129, 171)(130, 167)(132, 173)(133, 174)(138, 178)(139, 179)(140, 181)(141, 182)(145, 187)(148, 180)(149, 191)(151, 192)(152, 193)(153, 165)(154, 195)(155, 196)(159, 197)(160, 198)(163, 203)(164, 199)(166, 204)(168, 206)(169, 208)(170, 209)(172, 212)(175, 207)(176, 216)(177, 210)(183, 202)(184, 217)(185, 200)(186, 219)(188, 221)(189, 222)(190, 213)(194, 215)(201, 224)(205, 225)(211, 228)(214, 229)(218, 232)(220, 235)(223, 234)(226, 237)(227, 238)(230, 240)(231, 239)(233, 236)(241, 242, 245, 251, 263, 283, 313, 312, 282, 262, 250, 244)(243, 247, 255, 264, 285, 316, 354, 345, 304, 277, 258, 248)(246, 253, 267, 284, 315, 356, 353, 311, 281, 261, 270, 254)(249, 259, 266, 252, 265, 286, 314, 355, 351, 309, 280, 260)(256, 272, 297, 317, 359, 400, 390, 344, 303, 276, 300, 273)(257, 274, 296, 271, 295, 331, 358, 399, 371, 342, 302, 275)(268, 290, 325, 357, 333, 379, 352, 376, 330, 294, 327, 291)(269, 292, 324, 289, 323, 365, 398, 391, 346, 310, 329, 293)(278, 305, 320, 287, 319, 362, 397, 367, 350, 308, 348, 306)(279, 307, 322, 288, 321, 361, 318, 360, 338, 383, 335, 298)(299, 336, 381, 334, 380, 420, 438, 428, 386, 343, 385, 337)(301, 339, 378, 332, 377, 417, 437, 422, 389, 341, 388, 340)(326, 369, 410, 368, 409, 447, 419, 453, 413, 375, 412, 370)(328, 372, 408, 366, 407, 445, 432, 449, 416, 374, 415, 373)(347, 392, 404, 363, 403, 442, 402, 441, 435, 396, 434, 393)(349, 394, 406, 364, 405, 440, 401, 439, 424, 382, 423, 395)(384, 425, 458, 421, 457, 471, 461, 436, 460, 427, 444, 426)(387, 429, 452, 418, 451, 411, 450, 467, 448, 431, 463, 430)(414, 454, 433, 446, 466, 443, 465, 476, 464, 456, 470, 455)(459, 473, 462, 472, 480, 468, 479, 469, 478, 475, 477, 474)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 10, 10 ), ( 10^12 ) }
Outer automorphisms :: reflexible
Dual of E27.2308
Transitivity :: ET+
Graph:: simple bipartite
	v = 140 e = 240 f = 48
	degree seq :: [ 2^120, 12^20 ]

E27.2308 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 12})
Quotient :: loop
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1, T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2 * T1 * T2^-1 * T1 * T2, (T1 * T2^-1 * T1 * T2^2)^3, (T2 * T1 * T2^-2 * T1 * T2^2 * T1)^2, (T2 * T1 * T2^2 * T1 * T2^-2 * T1)^2 ]
Map::
	R = (1, 241, 3, 243, 8, 248, 10, 250, 4, 244)(2, 242, 5, 245, 12, 252, 14, 254, 6, 246)(7, 247, 15, 255, 28, 268, 30, 270, 16, 256)(9, 249, 18, 258, 34, 274, 36, 276, 19, 259)(11, 251, 21, 261, 40, 280, 42, 282, 22, 262)(13, 253, 24, 264, 46, 286, 48, 288, 25, 265)(17, 257, 31, 271, 58, 298, 60, 300, 32, 272)(20, 260, 37, 277, 68, 308, 70, 310, 38, 278)(23, 263, 43, 283, 78, 318, 80, 320, 44, 284)(26, 266, 49, 289, 88, 328, 90, 330, 50, 290)(27, 267, 51, 291, 91, 331, 92, 332, 52, 292)(29, 269, 54, 294, 96, 336, 97, 337, 55, 295)(33, 273, 61, 301, 106, 346, 108, 348, 62, 302)(35, 275, 64, 304, 111, 351, 112, 352, 65, 305)(39, 279, 71, 311, 121, 361, 122, 362, 72, 312)(41, 281, 74, 314, 126, 366, 127, 367, 75, 315)(45, 285, 81, 321, 136, 376, 138, 378, 82, 322)(47, 287, 84, 324, 141, 381, 142, 382, 85, 325)(53, 293, 93, 333, 152, 392, 153, 393, 94, 334)(56, 296, 98, 338, 159, 399, 160, 400, 99, 339)(57, 297, 100, 340, 161, 401, 162, 402, 101, 341)(59, 299, 103, 343, 166, 406, 167, 407, 104, 344)(63, 303, 109, 349, 174, 414, 176, 416, 110, 350)(66, 306, 113, 353, 177, 417, 179, 419, 114, 354)(67, 307, 115, 355, 180, 420, 182, 422, 116, 356)(69, 309, 118, 358, 185, 425, 186, 426, 119, 359)(73, 313, 123, 363, 157, 397, 190, 430, 124, 364)(76, 316, 128, 368, 193, 433, 194, 434, 129, 369)(77, 317, 130, 370, 195, 435, 196, 436, 131, 371)(79, 319, 133, 373, 158, 398, 199, 439, 134, 374)(83, 323, 139, 379, 204, 444, 205, 445, 140, 380)(86, 326, 143, 383, 206, 446, 170, 410, 144, 384)(87, 327, 145, 385, 208, 448, 175, 415, 146, 386)(89, 329, 148, 388, 212, 452, 213, 453, 149, 389)(95, 335, 154, 394, 150, 390, 214, 454, 155, 395)(102, 342, 163, 403, 137, 377, 202, 442, 164, 404)(105, 345, 168, 408, 220, 460, 221, 461, 169, 409)(107, 347, 171, 411, 197, 437, 132, 372, 172, 412)(117, 357, 183, 423, 216, 456, 224, 464, 184, 424)(120, 360, 187, 427, 191, 431, 125, 365, 188, 428)(135, 375, 200, 440, 230, 470, 231, 471, 201, 441)(147, 387, 210, 450, 226, 466, 234, 474, 211, 451)(151, 391, 215, 455, 235, 475, 223, 463, 178, 418)(156, 396, 217, 457, 236, 476, 222, 462, 173, 413)(165, 405, 181, 421, 218, 458, 237, 477, 219, 459)(189, 429, 225, 465, 238, 478, 233, 473, 207, 447)(192, 432, 227, 467, 239, 479, 232, 472, 203, 443)(198, 438, 209, 449, 228, 468, 240, 480, 229, 469)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 260)(11, 245)(12, 263)(13, 246)(14, 266)(15, 267)(16, 269)(17, 248)(18, 273)(19, 275)(20, 250)(21, 279)(22, 281)(23, 252)(24, 285)(25, 287)(26, 254)(27, 255)(28, 293)(29, 256)(30, 296)(31, 297)(32, 299)(33, 258)(34, 303)(35, 259)(36, 306)(37, 307)(38, 309)(39, 261)(40, 313)(41, 262)(42, 316)(43, 317)(44, 319)(45, 264)(46, 323)(47, 265)(48, 326)(49, 327)(50, 329)(51, 311)(52, 321)(53, 268)(54, 335)(55, 324)(56, 270)(57, 271)(58, 342)(59, 272)(60, 345)(61, 312)(62, 347)(63, 274)(64, 315)(65, 325)(66, 276)(67, 277)(68, 357)(69, 278)(70, 360)(71, 291)(72, 301)(73, 280)(74, 365)(75, 304)(76, 282)(77, 283)(78, 372)(79, 284)(80, 375)(81, 292)(82, 377)(83, 286)(84, 295)(85, 305)(86, 288)(87, 289)(88, 387)(89, 290)(90, 390)(91, 370)(92, 385)(93, 391)(94, 379)(95, 294)(96, 396)(97, 397)(98, 398)(99, 383)(100, 361)(101, 394)(102, 298)(103, 405)(104, 381)(105, 300)(106, 410)(107, 302)(108, 413)(109, 364)(110, 415)(111, 374)(112, 389)(113, 369)(114, 418)(115, 362)(116, 421)(117, 308)(118, 412)(119, 382)(120, 310)(121, 340)(122, 355)(123, 429)(124, 349)(125, 314)(126, 432)(127, 392)(128, 406)(129, 353)(130, 331)(131, 428)(132, 318)(133, 438)(134, 351)(135, 320)(136, 419)(137, 322)(138, 443)(139, 334)(140, 422)(141, 344)(142, 359)(143, 339)(144, 447)(145, 332)(146, 449)(147, 328)(148, 403)(149, 352)(150, 330)(151, 333)(152, 367)(153, 441)(154, 341)(155, 456)(156, 336)(157, 337)(158, 338)(159, 451)(160, 458)(161, 455)(162, 439)(163, 388)(164, 457)(165, 343)(166, 368)(167, 436)(168, 445)(169, 430)(170, 346)(171, 461)(172, 358)(173, 348)(174, 459)(175, 350)(176, 440)(177, 450)(178, 354)(179, 376)(180, 452)(181, 356)(182, 380)(183, 446)(184, 433)(185, 448)(186, 463)(187, 462)(188, 371)(189, 363)(190, 409)(191, 466)(192, 366)(193, 424)(194, 468)(195, 465)(196, 407)(197, 467)(198, 373)(199, 402)(200, 416)(201, 393)(202, 471)(203, 378)(204, 469)(205, 408)(206, 423)(207, 384)(208, 425)(209, 386)(210, 417)(211, 399)(212, 420)(213, 473)(214, 472)(215, 401)(216, 395)(217, 404)(218, 400)(219, 414)(220, 474)(221, 411)(222, 427)(223, 426)(224, 470)(225, 435)(226, 431)(227, 437)(228, 434)(229, 444)(230, 464)(231, 442)(232, 454)(233, 453)(234, 460)(235, 478)(236, 480)(237, 479)(238, 475)(239, 477)(240, 476)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2307
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 48 e = 240 f = 140
	degree seq :: [ 10^48 ]

E27.2309 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 12})
Quotient :: loop
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ F^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^5, T2 * T1^-1 * T2^-4 * T1^-1 * T2, T2^3 * T1^-2 * T2^-3 * T1^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2, T2 * T1^-2 * T2^3 * T1^-1 * T2 * T1 * T2^-1 * T1, T2^12 ]
Map::
	R = (1, 241, 3, 243, 10, 250, 25, 265, 57, 297, 111, 351, 169, 409, 100, 340, 49, 289, 37, 277, 15, 255, 5, 245)(2, 242, 7, 247, 18, 258, 43, 283, 26, 266, 59, 299, 115, 355, 155, 395, 86, 326, 50, 290, 21, 261, 8, 248)(4, 244, 12, 252, 30, 270, 58, 298, 113, 353, 168, 408, 143, 383, 78, 318, 36, 276, 54, 294, 23, 263, 9, 249)(6, 246, 16, 256, 38, 278, 80, 320, 44, 284, 90, 330, 158, 398, 116, 356, 127, 367, 87, 327, 41, 281, 17, 257)(11, 251, 27, 267, 62, 302, 112, 352, 167, 407, 99, 339, 76, 316, 35, 275, 14, 254, 34, 274, 56, 296, 24, 264)(13, 253, 32, 272, 70, 310, 114, 354, 81, 321, 142, 382, 177, 417, 107, 347, 53, 293, 106, 346, 66, 306, 29, 269)(19, 259, 45, 285, 92, 332, 60, 300, 117, 357, 154, 394, 98, 338, 48, 288, 20, 260, 47, 287, 89, 329, 42, 282)(22, 262, 51, 291, 101, 341, 67, 307, 31, 271, 68, 308, 130, 370, 181, 421, 141, 381, 77, 317, 104, 344, 52, 292)(28, 268, 64, 304, 123, 363, 128, 368, 140, 380, 75, 315, 139, 379, 131, 371, 110, 350, 74, 314, 119, 359, 61, 301)(33, 273, 72, 312, 109, 349, 55, 295, 108, 348, 97, 337, 120, 360, 63, 303, 121, 361, 96, 336, 137, 377, 73, 313)(39, 279, 82, 322, 147, 387, 91, 331, 159, 399, 191, 431, 153, 393, 85, 325, 40, 280, 84, 324, 145, 385, 79, 319)(46, 286, 94, 334, 157, 397, 88, 328, 156, 396, 152, 392, 160, 400, 93, 333, 161, 401, 151, 391, 165, 405, 95, 335)(65, 305, 125, 365, 188, 428, 133, 373, 71, 311, 134, 374, 197, 437, 146, 386, 176, 416, 105, 345, 175, 415, 126, 366)(69, 309, 132, 372, 194, 434, 196, 436, 174, 414, 103, 343, 173, 413, 198, 438, 170, 410, 102, 342, 171, 411, 129, 369)(83, 323, 149, 389, 203, 443, 144, 384, 202, 442, 190, 430, 204, 444, 148, 388, 205, 445, 189, 429, 209, 449, 150, 390)(118, 358, 182, 422, 224, 464, 186, 426, 124, 364, 187, 427, 138, 378, 201, 441, 223, 463, 180, 420, 193, 433, 183, 423)(122, 362, 185, 425, 136, 376, 200, 440, 222, 462, 179, 419, 135, 375, 199, 439, 166, 406, 178, 418, 221, 461, 184, 424)(162, 402, 214, 454, 164, 404, 216, 456, 236, 476, 212, 452, 163, 403, 215, 455, 210, 450, 211, 451, 235, 475, 213, 453)(172, 412, 219, 459, 237, 477, 217, 457, 228, 468, 226, 466, 192, 432, 218, 458, 238, 478, 225, 465, 195, 435, 220, 460)(206, 446, 232, 472, 208, 448, 234, 474, 240, 480, 230, 470, 207, 447, 233, 473, 227, 467, 229, 469, 239, 479, 231, 471)
	L = (1, 242)(2, 246)(3, 249)(4, 241)(5, 254)(6, 253)(7, 245)(8, 260)(9, 262)(10, 264)(11, 243)(12, 269)(13, 244)(14, 273)(15, 276)(16, 248)(17, 280)(18, 282)(19, 247)(20, 286)(21, 289)(22, 268)(23, 293)(24, 295)(25, 283)(26, 250)(27, 301)(28, 251)(29, 305)(30, 307)(31, 252)(32, 257)(33, 259)(34, 255)(35, 315)(36, 317)(37, 290)(38, 319)(39, 256)(40, 323)(41, 326)(42, 328)(43, 320)(44, 258)(45, 313)(46, 279)(47, 261)(48, 337)(49, 339)(50, 327)(51, 263)(52, 343)(53, 345)(54, 277)(55, 300)(56, 350)(57, 270)(58, 265)(59, 332)(60, 266)(61, 358)(62, 360)(63, 267)(64, 292)(65, 309)(66, 367)(67, 368)(68, 369)(69, 271)(70, 373)(71, 272)(72, 275)(73, 376)(74, 274)(75, 378)(76, 340)(77, 314)(78, 382)(79, 384)(80, 354)(81, 278)(82, 335)(83, 311)(84, 281)(85, 392)(86, 394)(87, 346)(88, 331)(89, 361)(90, 387)(91, 284)(92, 400)(93, 285)(94, 288)(95, 404)(96, 287)(97, 406)(98, 395)(99, 336)(100, 408)(101, 410)(102, 291)(103, 412)(104, 318)(105, 342)(106, 294)(107, 330)(108, 296)(109, 419)(110, 420)(111, 302)(112, 297)(113, 310)(114, 298)(115, 398)(116, 299)(117, 349)(118, 362)(119, 381)(120, 338)(121, 424)(122, 303)(123, 426)(124, 304)(125, 306)(126, 430)(127, 431)(128, 352)(129, 432)(130, 379)(131, 308)(132, 366)(133, 436)(134, 390)(135, 312)(136, 402)(137, 407)(138, 375)(139, 316)(140, 341)(141, 434)(142, 437)(143, 409)(144, 386)(145, 401)(146, 321)(147, 444)(148, 322)(149, 325)(150, 448)(151, 324)(152, 450)(153, 356)(154, 391)(155, 351)(156, 329)(157, 452)(158, 417)(159, 397)(160, 393)(161, 453)(162, 333)(163, 334)(164, 446)(165, 357)(166, 403)(167, 363)(168, 370)(169, 355)(170, 457)(171, 416)(172, 364)(173, 344)(174, 428)(175, 347)(176, 443)(177, 383)(178, 348)(179, 456)(180, 418)(181, 353)(182, 359)(183, 466)(184, 451)(185, 423)(186, 440)(187, 460)(188, 445)(189, 365)(190, 467)(191, 429)(192, 433)(193, 371)(194, 465)(195, 372)(196, 421)(197, 413)(198, 374)(199, 427)(200, 377)(201, 380)(202, 385)(203, 470)(204, 415)(205, 471)(206, 388)(207, 389)(208, 468)(209, 399)(210, 447)(211, 396)(212, 474)(213, 469)(214, 425)(215, 439)(216, 405)(217, 441)(218, 411)(219, 414)(220, 473)(221, 463)(222, 464)(223, 477)(224, 478)(225, 422)(226, 472)(227, 435)(228, 438)(229, 442)(230, 458)(231, 459)(232, 454)(233, 455)(234, 449)(235, 461)(236, 462)(237, 479)(238, 480)(239, 475)(240, 476)
	local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) }
Outer automorphisms :: reflexible
Dual of E27.2305
Transitivity :: ET+ VT+ AT
Graph::
	v = 20 e = 240 f = 168
	degree seq :: [ 24^20 ]

E27.2310 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 12})
Quotient :: loop
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^3 * T2 * T1^-2, (T2 * T1^-1)^5, T1^12, T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-1, (T2 * T1 * T2 * T1^-1 * T2 * T1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 241, 3, 243)(2, 242, 6, 246)(4, 244, 9, 249)(5, 245, 12, 252)(7, 247, 16, 256)(8, 248, 17, 257)(10, 250, 21, 261)(11, 251, 24, 264)(13, 253, 28, 268)(14, 254, 29, 269)(15, 255, 31, 271)(18, 258, 36, 276)(19, 259, 38, 278)(20, 260, 39, 279)(22, 262, 37, 277)(23, 263, 44, 284)(25, 265, 47, 287)(26, 266, 48, 288)(27, 267, 49, 289)(30, 270, 54, 294)(32, 272, 58, 298)(33, 273, 59, 299)(34, 274, 61, 301)(35, 275, 50, 290)(40, 280, 68, 308)(41, 281, 70, 310)(42, 282, 69, 309)(43, 283, 74, 314)(45, 285, 77, 317)(46, 286, 78, 318)(51, 291, 86, 326)(52, 292, 88, 328)(53, 293, 79, 319)(55, 295, 92, 332)(56, 296, 93, 333)(57, 297, 94, 334)(60, 300, 98, 338)(62, 302, 101, 341)(63, 303, 103, 343)(64, 304, 102, 342)(65, 305, 106, 346)(66, 306, 107, 347)(67, 307, 109, 349)(71, 311, 112, 352)(72, 312, 113, 353)(73, 313, 114, 354)(75, 315, 117, 357)(76, 316, 118, 358)(80, 320, 123, 363)(81, 321, 124, 364)(82, 322, 119, 359)(83, 323, 126, 366)(84, 324, 127, 367)(85, 325, 128, 368)(87, 327, 131, 371)(89, 329, 134, 374)(90, 330, 135, 375)(91, 331, 136, 376)(95, 335, 142, 382)(96, 336, 144, 384)(97, 337, 137, 377)(99, 339, 146, 386)(100, 340, 147, 387)(104, 344, 121, 361)(105, 345, 150, 390)(108, 348, 125, 365)(110, 350, 156, 396)(111, 351, 143, 383)(115, 355, 157, 397)(116, 356, 158, 398)(120, 360, 161, 401)(122, 362, 162, 402)(129, 369, 171, 411)(130, 370, 167, 407)(132, 372, 173, 413)(133, 373, 174, 414)(138, 378, 178, 418)(139, 379, 179, 419)(140, 380, 181, 421)(141, 381, 182, 422)(145, 385, 187, 427)(148, 388, 180, 420)(149, 389, 191, 431)(151, 391, 192, 432)(152, 392, 193, 433)(153, 393, 165, 405)(154, 394, 195, 435)(155, 395, 196, 436)(159, 399, 197, 437)(160, 400, 198, 438)(163, 403, 203, 443)(164, 404, 199, 439)(166, 406, 204, 444)(168, 408, 206, 446)(169, 409, 208, 448)(170, 410, 209, 449)(172, 412, 212, 452)(175, 415, 207, 447)(176, 416, 216, 456)(177, 417, 210, 450)(183, 423, 202, 442)(184, 424, 217, 457)(185, 425, 200, 440)(186, 426, 219, 459)(188, 428, 221, 461)(189, 429, 222, 462)(190, 430, 213, 453)(194, 434, 215, 455)(201, 441, 224, 464)(205, 445, 225, 465)(211, 451, 228, 468)(214, 454, 229, 469)(218, 458, 232, 472)(220, 460, 235, 475)(223, 463, 234, 474)(226, 466, 237, 477)(227, 467, 238, 478)(230, 470, 240, 480)(231, 471, 239, 479)(233, 473, 236, 476)
	L = (1, 242)(2, 245)(3, 247)(4, 241)(5, 251)(6, 253)(7, 255)(8, 243)(9, 259)(10, 244)(11, 263)(12, 265)(13, 267)(14, 246)(15, 264)(16, 272)(17, 274)(18, 248)(19, 266)(20, 249)(21, 270)(22, 250)(23, 283)(24, 285)(25, 286)(26, 252)(27, 284)(28, 290)(29, 292)(30, 254)(31, 295)(32, 297)(33, 256)(34, 296)(35, 257)(36, 300)(37, 258)(38, 305)(39, 307)(40, 260)(41, 261)(42, 262)(43, 313)(44, 315)(45, 316)(46, 314)(47, 319)(48, 321)(49, 323)(50, 325)(51, 268)(52, 324)(53, 269)(54, 327)(55, 331)(56, 271)(57, 317)(58, 279)(59, 336)(60, 273)(61, 339)(62, 275)(63, 276)(64, 277)(65, 320)(66, 278)(67, 322)(68, 348)(69, 280)(70, 329)(71, 281)(72, 282)(73, 312)(74, 355)(75, 356)(76, 354)(77, 359)(78, 360)(79, 362)(80, 287)(81, 361)(82, 288)(83, 365)(84, 289)(85, 357)(86, 369)(87, 291)(88, 372)(89, 293)(90, 294)(91, 358)(92, 377)(93, 379)(94, 380)(95, 298)(96, 381)(97, 299)(98, 383)(99, 378)(100, 301)(101, 388)(102, 302)(103, 385)(104, 303)(105, 304)(106, 310)(107, 392)(108, 306)(109, 394)(110, 308)(111, 309)(112, 376)(113, 311)(114, 345)(115, 351)(116, 353)(117, 333)(118, 399)(119, 400)(120, 338)(121, 318)(122, 397)(123, 403)(124, 405)(125, 398)(126, 407)(127, 350)(128, 409)(129, 410)(130, 326)(131, 342)(132, 408)(133, 328)(134, 415)(135, 412)(136, 330)(137, 417)(138, 332)(139, 352)(140, 420)(141, 334)(142, 423)(143, 335)(144, 425)(145, 337)(146, 343)(147, 429)(148, 340)(149, 341)(150, 344)(151, 346)(152, 404)(153, 347)(154, 406)(155, 349)(156, 434)(157, 367)(158, 391)(159, 371)(160, 390)(161, 439)(162, 441)(163, 442)(164, 363)(165, 440)(166, 364)(167, 445)(168, 366)(169, 447)(170, 368)(171, 450)(172, 370)(173, 375)(174, 454)(175, 373)(176, 374)(177, 437)(178, 451)(179, 453)(180, 438)(181, 457)(182, 389)(183, 395)(184, 382)(185, 458)(186, 384)(187, 444)(188, 386)(189, 452)(190, 387)(191, 463)(192, 449)(193, 446)(194, 393)(195, 396)(196, 460)(197, 422)(198, 428)(199, 424)(200, 401)(201, 435)(202, 402)(203, 465)(204, 426)(205, 432)(206, 466)(207, 419)(208, 431)(209, 416)(210, 467)(211, 411)(212, 418)(213, 413)(214, 433)(215, 414)(216, 470)(217, 471)(218, 421)(219, 473)(220, 427)(221, 436)(222, 472)(223, 430)(224, 456)(225, 476)(226, 443)(227, 448)(228, 479)(229, 478)(230, 455)(231, 461)(232, 480)(233, 462)(234, 459)(235, 477)(236, 464)(237, 474)(238, 475)(239, 469)(240, 468)
	local type(s) :: { ( 5, 12, 5, 12 ) }
Outer automorphisms :: reflexible
Dual of E27.2306
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 120 e = 240 f = 68
	degree seq :: [ 4^120 ]

E27.2311 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^5, (R * Y2 * Y3^-1)^2, (R * Y2^2 * Y1)^2, Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2, (Y2 * Y1 * Y2^-1 * Y1 * Y2)^3, (Y2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1)^2, (Y2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1)^2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 9, 249)(5, 245, 11, 251)(6, 246, 13, 253)(8, 248, 17, 257)(10, 250, 20, 260)(12, 252, 23, 263)(14, 254, 26, 266)(15, 255, 27, 267)(16, 256, 29, 269)(18, 258, 33, 273)(19, 259, 35, 275)(21, 261, 39, 279)(22, 262, 41, 281)(24, 264, 45, 285)(25, 265, 47, 287)(28, 268, 53, 293)(30, 270, 56, 296)(31, 271, 57, 297)(32, 272, 59, 299)(34, 274, 63, 303)(36, 276, 66, 306)(37, 277, 67, 307)(38, 278, 69, 309)(40, 280, 73, 313)(42, 282, 76, 316)(43, 283, 77, 317)(44, 284, 79, 319)(46, 286, 83, 323)(48, 288, 86, 326)(49, 289, 87, 327)(50, 290, 89, 329)(51, 291, 71, 311)(52, 292, 81, 321)(54, 294, 95, 335)(55, 295, 84, 324)(58, 298, 102, 342)(60, 300, 105, 345)(61, 301, 72, 312)(62, 302, 107, 347)(64, 304, 75, 315)(65, 305, 85, 325)(68, 308, 117, 357)(70, 310, 120, 360)(74, 314, 125, 365)(78, 318, 132, 372)(80, 320, 135, 375)(82, 322, 137, 377)(88, 328, 147, 387)(90, 330, 150, 390)(91, 331, 130, 370)(92, 332, 145, 385)(93, 333, 151, 391)(94, 334, 139, 379)(96, 336, 156, 396)(97, 337, 157, 397)(98, 338, 158, 398)(99, 339, 143, 383)(100, 340, 121, 361)(101, 341, 154, 394)(103, 343, 165, 405)(104, 344, 141, 381)(106, 346, 170, 410)(108, 348, 173, 413)(109, 349, 124, 364)(110, 350, 175, 415)(111, 351, 134, 374)(112, 352, 149, 389)(113, 353, 129, 369)(114, 354, 178, 418)(115, 355, 122, 362)(116, 356, 181, 421)(118, 358, 172, 412)(119, 359, 142, 382)(123, 363, 189, 429)(126, 366, 192, 432)(127, 367, 152, 392)(128, 368, 166, 406)(131, 371, 188, 428)(133, 373, 198, 438)(136, 376, 179, 419)(138, 378, 203, 443)(140, 380, 182, 422)(144, 384, 207, 447)(146, 386, 209, 449)(148, 388, 163, 403)(153, 393, 201, 441)(155, 395, 216, 456)(159, 399, 211, 451)(160, 400, 218, 458)(161, 401, 215, 455)(162, 402, 199, 439)(164, 404, 217, 457)(167, 407, 196, 436)(168, 408, 205, 445)(169, 409, 190, 430)(171, 411, 221, 461)(174, 414, 219, 459)(176, 416, 200, 440)(177, 417, 210, 450)(180, 420, 212, 452)(183, 423, 206, 446)(184, 424, 193, 433)(185, 425, 208, 448)(186, 426, 223, 463)(187, 427, 222, 462)(191, 431, 226, 466)(194, 434, 228, 468)(195, 435, 225, 465)(197, 437, 227, 467)(202, 442, 231, 471)(204, 444, 229, 469)(213, 453, 233, 473)(214, 454, 232, 472)(220, 460, 234, 474)(224, 464, 230, 470)(235, 475, 238, 478)(236, 476, 240, 480)(237, 477, 239, 479)(481, 721, 483, 723, 488, 728, 490, 730, 484, 724)(482, 722, 485, 725, 492, 732, 494, 734, 486, 726)(487, 727, 495, 735, 508, 748, 510, 750, 496, 736)(489, 729, 498, 738, 514, 754, 516, 756, 499, 739)(491, 731, 501, 741, 520, 760, 522, 762, 502, 742)(493, 733, 504, 744, 526, 766, 528, 768, 505, 745)(497, 737, 511, 751, 538, 778, 540, 780, 512, 752)(500, 740, 517, 757, 548, 788, 550, 790, 518, 758)(503, 743, 523, 763, 558, 798, 560, 800, 524, 764)(506, 746, 529, 769, 568, 808, 570, 810, 530, 770)(507, 747, 531, 771, 571, 811, 572, 812, 532, 772)(509, 749, 534, 774, 576, 816, 577, 817, 535, 775)(513, 753, 541, 781, 586, 826, 588, 828, 542, 782)(515, 755, 544, 784, 591, 831, 592, 832, 545, 785)(519, 759, 551, 791, 601, 841, 602, 842, 552, 792)(521, 761, 554, 794, 606, 846, 607, 847, 555, 795)(525, 765, 561, 801, 616, 856, 618, 858, 562, 802)(527, 767, 564, 804, 621, 861, 622, 862, 565, 805)(533, 773, 573, 813, 632, 872, 633, 873, 574, 814)(536, 776, 578, 818, 639, 879, 640, 880, 579, 819)(537, 777, 580, 820, 641, 881, 642, 882, 581, 821)(539, 779, 583, 823, 646, 886, 647, 887, 584, 824)(543, 783, 589, 829, 654, 894, 656, 896, 590, 830)(546, 786, 593, 833, 657, 897, 659, 899, 594, 834)(547, 787, 595, 835, 660, 900, 662, 902, 596, 836)(549, 789, 598, 838, 665, 905, 666, 906, 599, 839)(553, 793, 603, 843, 637, 877, 670, 910, 604, 844)(556, 796, 608, 848, 673, 913, 674, 914, 609, 849)(557, 797, 610, 850, 675, 915, 676, 916, 611, 851)(559, 799, 613, 853, 638, 878, 679, 919, 614, 854)(563, 803, 619, 859, 684, 924, 685, 925, 620, 860)(566, 806, 623, 863, 686, 926, 650, 890, 624, 864)(567, 807, 625, 865, 688, 928, 655, 895, 626, 866)(569, 809, 628, 868, 692, 932, 693, 933, 629, 869)(575, 815, 634, 874, 630, 870, 694, 934, 635, 875)(582, 822, 643, 883, 617, 857, 682, 922, 644, 884)(585, 825, 648, 888, 700, 940, 701, 941, 649, 889)(587, 827, 651, 891, 677, 917, 612, 852, 652, 892)(597, 837, 663, 903, 696, 936, 704, 944, 664, 904)(600, 840, 667, 907, 671, 911, 605, 845, 668, 908)(615, 855, 680, 920, 710, 950, 711, 951, 681, 921)(627, 867, 690, 930, 706, 946, 714, 954, 691, 931)(631, 871, 695, 935, 715, 955, 703, 943, 658, 898)(636, 876, 697, 937, 716, 956, 702, 942, 653, 893)(645, 885, 661, 901, 698, 938, 717, 957, 699, 939)(669, 909, 705, 945, 718, 958, 713, 953, 687, 927)(672, 912, 707, 947, 719, 959, 712, 952, 683, 923)(678, 918, 689, 929, 708, 948, 720, 960, 709, 949)
	L = (1, 482)(2, 481)(3, 487)(4, 489)(5, 491)(6, 493)(7, 483)(8, 497)(9, 484)(10, 500)(11, 485)(12, 503)(13, 486)(14, 506)(15, 507)(16, 509)(17, 488)(18, 513)(19, 515)(20, 490)(21, 519)(22, 521)(23, 492)(24, 525)(25, 527)(26, 494)(27, 495)(28, 533)(29, 496)(30, 536)(31, 537)(32, 539)(33, 498)(34, 543)(35, 499)(36, 546)(37, 547)(38, 549)(39, 501)(40, 553)(41, 502)(42, 556)(43, 557)(44, 559)(45, 504)(46, 563)(47, 505)(48, 566)(49, 567)(50, 569)(51, 551)(52, 561)(53, 508)(54, 575)(55, 564)(56, 510)(57, 511)(58, 582)(59, 512)(60, 585)(61, 552)(62, 587)(63, 514)(64, 555)(65, 565)(66, 516)(67, 517)(68, 597)(69, 518)(70, 600)(71, 531)(72, 541)(73, 520)(74, 605)(75, 544)(76, 522)(77, 523)(78, 612)(79, 524)(80, 615)(81, 532)(82, 617)(83, 526)(84, 535)(85, 545)(86, 528)(87, 529)(88, 627)(89, 530)(90, 630)(91, 610)(92, 625)(93, 631)(94, 619)(95, 534)(96, 636)(97, 637)(98, 638)(99, 623)(100, 601)(101, 634)(102, 538)(103, 645)(104, 621)(105, 540)(106, 650)(107, 542)(108, 653)(109, 604)(110, 655)(111, 614)(112, 629)(113, 609)(114, 658)(115, 602)(116, 661)(117, 548)(118, 652)(119, 622)(120, 550)(121, 580)(122, 595)(123, 669)(124, 589)(125, 554)(126, 672)(127, 632)(128, 646)(129, 593)(130, 571)(131, 668)(132, 558)(133, 678)(134, 591)(135, 560)(136, 659)(137, 562)(138, 683)(139, 574)(140, 662)(141, 584)(142, 599)(143, 579)(144, 687)(145, 572)(146, 689)(147, 568)(148, 643)(149, 592)(150, 570)(151, 573)(152, 607)(153, 681)(154, 581)(155, 696)(156, 576)(157, 577)(158, 578)(159, 691)(160, 698)(161, 695)(162, 679)(163, 628)(164, 697)(165, 583)(166, 608)(167, 676)(168, 685)(169, 670)(170, 586)(171, 701)(172, 598)(173, 588)(174, 699)(175, 590)(176, 680)(177, 690)(178, 594)(179, 616)(180, 692)(181, 596)(182, 620)(183, 686)(184, 673)(185, 688)(186, 703)(187, 702)(188, 611)(189, 603)(190, 649)(191, 706)(192, 606)(193, 664)(194, 708)(195, 705)(196, 647)(197, 707)(198, 613)(199, 642)(200, 656)(201, 633)(202, 711)(203, 618)(204, 709)(205, 648)(206, 663)(207, 624)(208, 665)(209, 626)(210, 657)(211, 639)(212, 660)(213, 713)(214, 712)(215, 641)(216, 635)(217, 644)(218, 640)(219, 654)(220, 714)(221, 651)(222, 667)(223, 666)(224, 710)(225, 675)(226, 671)(227, 677)(228, 674)(229, 684)(230, 704)(231, 682)(232, 694)(233, 693)(234, 700)(235, 718)(236, 720)(237, 719)(238, 715)(239, 717)(240, 716)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.2314
Graph:: bipartite
	v = 168 e = 480 f = 260
	degree seq :: [ 4^120, 10^48 ]

E27.2312 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^5, Y2^3 * Y1^-1 * Y2^-3 * Y1, Y2 * Y1^-1 * Y2^3 * Y1^-2 * Y2 * Y1 * Y2^-1 * Y1, Y1^-1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, Y2^12, (Y2^2 * Y1^-1 * Y2 * Y1^-2)^2, (Y2^2 * Y1^-2 * Y2 * Y1^-1)^2 ]
Map::
	R = (1, 241, 2, 242, 6, 246, 13, 253, 4, 244)(3, 243, 9, 249, 22, 262, 28, 268, 11, 251)(5, 245, 14, 254, 33, 273, 19, 259, 7, 247)(8, 248, 20, 260, 46, 286, 39, 279, 16, 256)(10, 250, 24, 264, 55, 295, 60, 300, 26, 266)(12, 252, 29, 269, 65, 305, 69, 309, 31, 271)(15, 255, 36, 276, 77, 317, 74, 314, 34, 274)(17, 257, 40, 280, 83, 323, 71, 311, 32, 272)(18, 258, 42, 282, 88, 328, 91, 331, 44, 284)(21, 261, 49, 289, 99, 339, 96, 336, 47, 287)(23, 263, 53, 293, 105, 345, 102, 342, 51, 291)(25, 265, 43, 283, 80, 320, 114, 354, 58, 298)(27, 267, 61, 301, 118, 358, 122, 362, 63, 303)(30, 270, 67, 307, 128, 368, 112, 352, 57, 297)(35, 275, 75, 315, 138, 378, 135, 375, 72, 312)(37, 277, 50, 290, 87, 327, 106, 346, 54, 294)(38, 278, 79, 319, 144, 384, 146, 386, 81, 321)(41, 281, 86, 326, 154, 394, 151, 391, 84, 324)(45, 285, 73, 313, 136, 376, 162, 402, 93, 333)(48, 288, 97, 337, 166, 406, 163, 403, 94, 334)(52, 292, 103, 343, 172, 412, 124, 364, 64, 304)(56, 296, 110, 350, 180, 420, 178, 418, 108, 348)(59, 299, 92, 332, 160, 400, 153, 393, 116, 356)(62, 302, 120, 360, 98, 338, 155, 395, 111, 351)(66, 306, 127, 367, 191, 431, 189, 429, 125, 365)(68, 308, 129, 369, 192, 432, 193, 433, 131, 371)(70, 310, 133, 373, 196, 436, 181, 421, 113, 353)(76, 316, 100, 340, 168, 408, 130, 370, 139, 379)(78, 318, 142, 382, 197, 437, 173, 413, 104, 344)(82, 322, 95, 335, 164, 404, 206, 446, 148, 388)(85, 325, 152, 392, 210, 450, 207, 447, 149, 389)(89, 329, 121, 361, 184, 424, 211, 451, 156, 396)(90, 330, 147, 387, 204, 444, 175, 415, 107, 347)(101, 341, 170, 410, 217, 457, 201, 441, 140, 380)(109, 349, 179, 419, 216, 456, 165, 405, 117, 357)(115, 355, 158, 398, 177, 417, 143, 383, 169, 409)(119, 359, 141, 381, 194, 434, 225, 465, 182, 422)(123, 363, 186, 426, 200, 440, 137, 377, 167, 407)(126, 366, 190, 430, 227, 467, 195, 435, 132, 372)(134, 374, 150, 390, 208, 448, 228, 468, 198, 438)(145, 385, 161, 401, 213, 453, 229, 469, 202, 442)(157, 397, 212, 452, 234, 474, 209, 449, 159, 399)(171, 411, 176, 416, 203, 443, 230, 470, 218, 458)(174, 414, 188, 428, 205, 445, 231, 471, 219, 459)(183, 423, 226, 466, 232, 472, 214, 454, 185, 425)(187, 427, 220, 460, 233, 473, 215, 455, 199, 439)(221, 461, 223, 463, 237, 477, 239, 479, 235, 475)(222, 462, 224, 464, 238, 478, 240, 480, 236, 476)(481, 721, 483, 723, 490, 730, 505, 745, 537, 777, 591, 831, 649, 889, 580, 820, 529, 769, 517, 757, 495, 735, 485, 725)(482, 722, 487, 727, 498, 738, 523, 763, 506, 746, 539, 779, 595, 835, 635, 875, 566, 806, 530, 770, 501, 741, 488, 728)(484, 724, 492, 732, 510, 750, 538, 778, 593, 833, 648, 888, 623, 863, 558, 798, 516, 756, 534, 774, 503, 743, 489, 729)(486, 726, 496, 736, 518, 758, 560, 800, 524, 764, 570, 810, 638, 878, 596, 836, 607, 847, 567, 807, 521, 761, 497, 737)(491, 731, 507, 747, 542, 782, 592, 832, 647, 887, 579, 819, 556, 796, 515, 755, 494, 734, 514, 754, 536, 776, 504, 744)(493, 733, 512, 752, 550, 790, 594, 834, 561, 801, 622, 862, 657, 897, 587, 827, 533, 773, 586, 826, 546, 786, 509, 749)(499, 739, 525, 765, 572, 812, 540, 780, 597, 837, 634, 874, 578, 818, 528, 768, 500, 740, 527, 767, 569, 809, 522, 762)(502, 742, 531, 771, 581, 821, 547, 787, 511, 751, 548, 788, 610, 850, 661, 901, 621, 861, 557, 797, 584, 824, 532, 772)(508, 748, 544, 784, 603, 843, 608, 848, 620, 860, 555, 795, 619, 859, 611, 851, 590, 830, 554, 794, 599, 839, 541, 781)(513, 753, 552, 792, 589, 829, 535, 775, 588, 828, 577, 817, 600, 840, 543, 783, 601, 841, 576, 816, 617, 857, 553, 793)(519, 759, 562, 802, 627, 867, 571, 811, 639, 879, 671, 911, 633, 873, 565, 805, 520, 760, 564, 804, 625, 865, 559, 799)(526, 766, 574, 814, 637, 877, 568, 808, 636, 876, 632, 872, 640, 880, 573, 813, 641, 881, 631, 871, 645, 885, 575, 815)(545, 785, 605, 845, 668, 908, 613, 853, 551, 791, 614, 854, 677, 917, 626, 866, 656, 896, 585, 825, 655, 895, 606, 846)(549, 789, 612, 852, 674, 914, 676, 916, 654, 894, 583, 823, 653, 893, 678, 918, 650, 890, 582, 822, 651, 891, 609, 849)(563, 803, 629, 869, 683, 923, 624, 864, 682, 922, 670, 910, 684, 924, 628, 868, 685, 925, 669, 909, 689, 929, 630, 870)(598, 838, 662, 902, 704, 944, 666, 906, 604, 844, 667, 907, 618, 858, 681, 921, 703, 943, 660, 900, 673, 913, 663, 903)(602, 842, 665, 905, 616, 856, 680, 920, 702, 942, 659, 899, 615, 855, 679, 919, 646, 886, 658, 898, 701, 941, 664, 904)(642, 882, 694, 934, 644, 884, 696, 936, 716, 956, 692, 932, 643, 883, 695, 935, 690, 930, 691, 931, 715, 955, 693, 933)(652, 892, 699, 939, 717, 957, 697, 937, 708, 948, 706, 946, 672, 912, 698, 938, 718, 958, 705, 945, 675, 915, 700, 940)(686, 926, 712, 952, 688, 928, 714, 954, 720, 960, 710, 950, 687, 927, 713, 953, 707, 947, 709, 949, 719, 959, 711, 951)
	L = (1, 483)(2, 487)(3, 490)(4, 492)(5, 481)(6, 496)(7, 498)(8, 482)(9, 484)(10, 505)(11, 507)(12, 510)(13, 512)(14, 514)(15, 485)(16, 518)(17, 486)(18, 523)(19, 525)(20, 527)(21, 488)(22, 531)(23, 489)(24, 491)(25, 537)(26, 539)(27, 542)(28, 544)(29, 493)(30, 538)(31, 548)(32, 550)(33, 552)(34, 536)(35, 494)(36, 534)(37, 495)(38, 560)(39, 562)(40, 564)(41, 497)(42, 499)(43, 506)(44, 570)(45, 572)(46, 574)(47, 569)(48, 500)(49, 517)(50, 501)(51, 581)(52, 502)(53, 586)(54, 503)(55, 588)(56, 504)(57, 591)(58, 593)(59, 595)(60, 597)(61, 508)(62, 592)(63, 601)(64, 603)(65, 605)(66, 509)(67, 511)(68, 610)(69, 612)(70, 594)(71, 614)(72, 589)(73, 513)(74, 599)(75, 619)(76, 515)(77, 584)(78, 516)(79, 519)(80, 524)(81, 622)(82, 627)(83, 629)(84, 625)(85, 520)(86, 530)(87, 521)(88, 636)(89, 522)(90, 638)(91, 639)(92, 540)(93, 641)(94, 637)(95, 526)(96, 617)(97, 600)(98, 528)(99, 556)(100, 529)(101, 547)(102, 651)(103, 653)(104, 532)(105, 655)(106, 546)(107, 533)(108, 577)(109, 535)(110, 554)(111, 649)(112, 647)(113, 648)(114, 561)(115, 635)(116, 607)(117, 634)(118, 662)(119, 541)(120, 543)(121, 576)(122, 665)(123, 608)(124, 667)(125, 668)(126, 545)(127, 567)(128, 620)(129, 549)(130, 661)(131, 590)(132, 674)(133, 551)(134, 677)(135, 679)(136, 680)(137, 553)(138, 681)(139, 611)(140, 555)(141, 557)(142, 657)(143, 558)(144, 682)(145, 559)(146, 656)(147, 571)(148, 685)(149, 683)(150, 563)(151, 645)(152, 640)(153, 565)(154, 578)(155, 566)(156, 632)(157, 568)(158, 596)(159, 671)(160, 573)(161, 631)(162, 694)(163, 695)(164, 696)(165, 575)(166, 658)(167, 579)(168, 623)(169, 580)(170, 582)(171, 609)(172, 699)(173, 678)(174, 583)(175, 606)(176, 585)(177, 587)(178, 701)(179, 615)(180, 673)(181, 621)(182, 704)(183, 598)(184, 602)(185, 616)(186, 604)(187, 618)(188, 613)(189, 689)(190, 684)(191, 633)(192, 698)(193, 663)(194, 676)(195, 700)(196, 654)(197, 626)(198, 650)(199, 646)(200, 702)(201, 703)(202, 670)(203, 624)(204, 628)(205, 669)(206, 712)(207, 713)(208, 714)(209, 630)(210, 691)(211, 715)(212, 643)(213, 642)(214, 644)(215, 690)(216, 716)(217, 708)(218, 718)(219, 717)(220, 652)(221, 664)(222, 659)(223, 660)(224, 666)(225, 675)(226, 672)(227, 709)(228, 706)(229, 719)(230, 687)(231, 686)(232, 688)(233, 707)(234, 720)(235, 693)(236, 692)(237, 697)(238, 705)(239, 711)(240, 710)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2313
Graph:: bipartite
	v = 68 e = 480 f = 360
	degree seq :: [ 10^48, 24^20 ]

E27.2313 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-3 * Y2, (Y3 * Y2)^5, Y3 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	R = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)(481, 721, 482, 722)(483, 723, 487, 727)(484, 724, 489, 729)(485, 725, 491, 731)(486, 726, 493, 733)(488, 728, 497, 737)(490, 730, 501, 741)(492, 732, 505, 745)(494, 734, 509, 749)(495, 735, 511, 751)(496, 736, 513, 753)(498, 738, 506, 746)(499, 739, 518, 758)(500, 740, 519, 759)(502, 742, 510, 750)(503, 743, 523, 763)(504, 744, 525, 765)(507, 747, 530, 770)(508, 748, 531, 771)(512, 752, 536, 776)(514, 754, 540, 780)(515, 755, 541, 781)(516, 756, 543, 783)(517, 757, 537, 777)(520, 760, 548, 788)(521, 761, 550, 790)(522, 762, 549, 789)(524, 764, 554, 794)(526, 766, 558, 798)(527, 767, 559, 799)(528, 768, 561, 801)(529, 769, 555, 795)(532, 772, 566, 806)(533, 773, 568, 808)(534, 774, 567, 807)(535, 775, 571, 811)(538, 778, 576, 816)(539, 779, 577, 817)(542, 782, 581, 821)(544, 784, 582, 822)(545, 785, 586, 826)(546, 786, 587, 827)(547, 787, 589, 829)(551, 791, 592, 832)(552, 792, 593, 833)(553, 793, 594, 834)(556, 796, 599, 839)(557, 797, 600, 840)(560, 800, 604, 844)(562, 802, 605, 845)(563, 803, 609, 849)(564, 804, 610, 850)(565, 805, 612, 852)(569, 809, 615, 855)(570, 810, 616, 856)(572, 812, 614, 854)(573, 813, 619, 859)(574, 814, 621, 861)(575, 815, 607, 847)(578, 818, 626, 866)(579, 819, 627, 867)(580, 820, 628, 868)(583, 823, 630, 870)(584, 824, 598, 838)(585, 825, 608, 848)(588, 828, 620, 860)(590, 830, 636, 876)(591, 831, 595, 835)(596, 836, 639, 879)(597, 837, 641, 881)(601, 841, 646, 886)(602, 842, 647, 887)(603, 843, 648, 888)(606, 846, 650, 890)(611, 851, 640, 880)(613, 853, 656, 896)(617, 857, 657, 897)(618, 858, 658, 898)(622, 862, 661, 901)(623, 863, 663, 903)(624, 864, 664, 904)(625, 865, 666, 906)(629, 869, 662, 902)(631, 871, 672, 912)(632, 872, 673, 913)(633, 873, 670, 910)(634, 874, 675, 915)(635, 875, 676, 916)(637, 877, 677, 917)(638, 878, 678, 918)(642, 882, 681, 921)(643, 883, 683, 923)(644, 884, 684, 924)(645, 885, 686, 926)(649, 889, 682, 922)(651, 891, 692, 932)(652, 892, 693, 933)(653, 893, 690, 930)(654, 894, 695, 935)(655, 895, 696, 936)(659, 899, 689, 929)(660, 900, 698, 938)(665, 905, 691, 931)(667, 907, 702, 942)(668, 908, 703, 943)(669, 909, 679, 919)(671, 911, 685, 925)(674, 914, 700, 940)(680, 920, 705, 945)(687, 927, 709, 949)(688, 928, 710, 950)(694, 934, 707, 947)(697, 937, 711, 951)(699, 939, 713, 953)(701, 941, 715, 955)(704, 944, 716, 956)(706, 946, 718, 958)(708, 948, 720, 960)(712, 952, 719, 959)(714, 954, 717, 957)
	L = (1, 483)(2, 485)(3, 488)(4, 481)(5, 492)(6, 482)(7, 495)(8, 498)(9, 499)(10, 484)(11, 503)(12, 506)(13, 507)(14, 486)(15, 512)(16, 487)(17, 515)(18, 517)(19, 516)(20, 489)(21, 514)(22, 490)(23, 524)(24, 491)(25, 527)(26, 529)(27, 528)(28, 493)(29, 526)(30, 494)(31, 531)(32, 537)(33, 538)(34, 496)(35, 542)(36, 497)(37, 544)(38, 545)(39, 547)(40, 500)(41, 501)(42, 502)(43, 519)(44, 555)(45, 556)(46, 504)(47, 560)(48, 505)(49, 562)(50, 563)(51, 565)(52, 508)(53, 509)(54, 510)(55, 511)(56, 573)(57, 575)(58, 574)(59, 513)(60, 572)(61, 577)(62, 582)(63, 583)(64, 585)(65, 580)(66, 518)(67, 584)(68, 588)(69, 520)(70, 578)(71, 521)(72, 522)(73, 523)(74, 596)(75, 598)(76, 597)(77, 525)(78, 595)(79, 600)(80, 605)(81, 606)(82, 608)(83, 603)(84, 530)(85, 607)(86, 611)(87, 532)(88, 601)(89, 533)(90, 534)(91, 617)(92, 535)(93, 620)(94, 536)(95, 622)(96, 623)(97, 625)(98, 539)(99, 540)(100, 541)(101, 602)(102, 629)(103, 615)(104, 543)(105, 552)(106, 550)(107, 632)(108, 546)(109, 634)(110, 548)(111, 549)(112, 604)(113, 551)(114, 637)(115, 553)(116, 640)(117, 554)(118, 642)(119, 643)(120, 645)(121, 557)(122, 558)(123, 559)(124, 579)(125, 649)(126, 592)(127, 561)(128, 570)(129, 568)(130, 652)(131, 564)(132, 654)(133, 566)(134, 567)(135, 581)(136, 569)(137, 655)(138, 571)(139, 658)(140, 661)(141, 590)(142, 593)(143, 660)(144, 576)(145, 662)(146, 665)(147, 659)(148, 668)(149, 591)(150, 670)(151, 586)(152, 669)(153, 587)(154, 671)(155, 589)(156, 674)(157, 635)(158, 594)(159, 678)(160, 681)(161, 613)(162, 616)(163, 680)(164, 599)(165, 682)(166, 685)(167, 679)(168, 688)(169, 614)(170, 690)(171, 609)(172, 689)(173, 610)(174, 691)(175, 612)(176, 694)(177, 686)(178, 697)(179, 618)(180, 619)(181, 631)(182, 621)(183, 627)(184, 699)(185, 624)(186, 701)(187, 626)(188, 677)(189, 628)(190, 683)(191, 630)(192, 696)(193, 698)(194, 633)(195, 636)(196, 687)(197, 666)(198, 704)(199, 638)(200, 639)(201, 651)(202, 641)(203, 647)(204, 706)(205, 644)(206, 708)(207, 646)(208, 657)(209, 648)(210, 663)(211, 650)(212, 676)(213, 705)(214, 653)(215, 656)(216, 667)(217, 672)(218, 712)(219, 673)(220, 664)(221, 675)(222, 714)(223, 711)(224, 692)(225, 717)(226, 693)(227, 684)(228, 695)(229, 719)(230, 716)(231, 718)(232, 703)(233, 720)(234, 700)(235, 702)(236, 713)(237, 710)(238, 715)(239, 707)(240, 709)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 10, 24 ), ( 10, 24, 10, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.2312
Graph:: simple bipartite
	v = 360 e = 480 f = 68
	degree seq :: [ 2^240, 4^120 ]

E27.2314 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-2, (Y1^-1 * Y3)^5, Y1^12, Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^-1 ]
Map:: polytopal
	R = (1, 241, 2, 242, 5, 245, 11, 251, 23, 263, 43, 283, 73, 313, 72, 312, 42, 282, 22, 262, 10, 250, 4, 244)(3, 243, 7, 247, 15, 255, 24, 264, 45, 285, 76, 316, 114, 354, 105, 345, 64, 304, 37, 277, 18, 258, 8, 248)(6, 246, 13, 253, 27, 267, 44, 284, 75, 315, 116, 356, 113, 353, 71, 311, 41, 281, 21, 261, 30, 270, 14, 254)(9, 249, 19, 259, 26, 266, 12, 252, 25, 265, 46, 286, 74, 314, 115, 355, 111, 351, 69, 309, 40, 280, 20, 260)(16, 256, 32, 272, 57, 297, 77, 317, 119, 359, 160, 400, 150, 390, 104, 344, 63, 303, 36, 276, 60, 300, 33, 273)(17, 257, 34, 274, 56, 296, 31, 271, 55, 295, 91, 331, 118, 358, 159, 399, 131, 371, 102, 342, 62, 302, 35, 275)(28, 268, 50, 290, 85, 325, 117, 357, 93, 333, 139, 379, 112, 352, 136, 376, 90, 330, 54, 294, 87, 327, 51, 291)(29, 269, 52, 292, 84, 324, 49, 289, 83, 323, 125, 365, 158, 398, 151, 391, 106, 346, 70, 310, 89, 329, 53, 293)(38, 278, 65, 305, 80, 320, 47, 287, 79, 319, 122, 362, 157, 397, 127, 367, 110, 350, 68, 308, 108, 348, 66, 306)(39, 279, 67, 307, 82, 322, 48, 288, 81, 321, 121, 361, 78, 318, 120, 360, 98, 338, 143, 383, 95, 335, 58, 298)(59, 299, 96, 336, 141, 381, 94, 334, 140, 380, 180, 420, 198, 438, 188, 428, 146, 386, 103, 343, 145, 385, 97, 337)(61, 301, 99, 339, 138, 378, 92, 332, 137, 377, 177, 417, 197, 437, 182, 422, 149, 389, 101, 341, 148, 388, 100, 340)(86, 326, 129, 369, 170, 410, 128, 368, 169, 409, 207, 447, 179, 419, 213, 453, 173, 413, 135, 375, 172, 412, 130, 370)(88, 328, 132, 372, 168, 408, 126, 366, 167, 407, 205, 445, 192, 432, 209, 449, 176, 416, 134, 374, 175, 415, 133, 373)(107, 347, 152, 392, 164, 404, 123, 363, 163, 403, 202, 442, 162, 402, 201, 441, 195, 435, 156, 396, 194, 434, 153, 393)(109, 349, 154, 394, 166, 406, 124, 364, 165, 405, 200, 440, 161, 401, 199, 439, 184, 424, 142, 382, 183, 423, 155, 395)(144, 384, 185, 425, 218, 458, 181, 421, 217, 457, 231, 471, 221, 461, 196, 436, 220, 460, 187, 427, 204, 444, 186, 426)(147, 387, 189, 429, 212, 452, 178, 418, 211, 451, 171, 411, 210, 450, 227, 467, 208, 448, 191, 431, 223, 463, 190, 430)(174, 414, 214, 454, 193, 433, 206, 446, 226, 466, 203, 443, 225, 465, 236, 476, 224, 464, 216, 456, 230, 470, 215, 455)(219, 459, 233, 473, 222, 462, 232, 472, 240, 480, 228, 468, 239, 479, 229, 469, 238, 478, 235, 475, 237, 477, 234, 474)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960)
	L = (1, 483)(2, 486)(3, 481)(4, 489)(5, 492)(6, 482)(7, 496)(8, 497)(9, 484)(10, 501)(11, 504)(12, 485)(13, 508)(14, 509)(15, 511)(16, 487)(17, 488)(18, 516)(19, 518)(20, 519)(21, 490)(22, 517)(23, 524)(24, 491)(25, 527)(26, 528)(27, 529)(28, 493)(29, 494)(30, 534)(31, 495)(32, 538)(33, 539)(34, 541)(35, 530)(36, 498)(37, 502)(38, 499)(39, 500)(40, 548)(41, 550)(42, 549)(43, 554)(44, 503)(45, 557)(46, 558)(47, 505)(48, 506)(49, 507)(50, 515)(51, 566)(52, 568)(53, 559)(54, 510)(55, 572)(56, 573)(57, 574)(58, 512)(59, 513)(60, 578)(61, 514)(62, 581)(63, 583)(64, 582)(65, 586)(66, 587)(67, 589)(68, 520)(69, 522)(70, 521)(71, 592)(72, 593)(73, 594)(74, 523)(75, 597)(76, 598)(77, 525)(78, 526)(79, 533)(80, 603)(81, 604)(82, 599)(83, 606)(84, 607)(85, 608)(86, 531)(87, 611)(88, 532)(89, 614)(90, 615)(91, 616)(92, 535)(93, 536)(94, 537)(95, 622)(96, 624)(97, 617)(98, 540)(99, 626)(100, 627)(101, 542)(102, 544)(103, 543)(104, 601)(105, 630)(106, 545)(107, 546)(108, 605)(109, 547)(110, 636)(111, 623)(112, 551)(113, 552)(114, 553)(115, 637)(116, 638)(117, 555)(118, 556)(119, 562)(120, 641)(121, 584)(122, 642)(123, 560)(124, 561)(125, 588)(126, 563)(127, 564)(128, 565)(129, 651)(130, 647)(131, 567)(132, 653)(133, 654)(134, 569)(135, 570)(136, 571)(137, 577)(138, 658)(139, 659)(140, 661)(141, 662)(142, 575)(143, 591)(144, 576)(145, 667)(146, 579)(147, 580)(148, 660)(149, 671)(150, 585)(151, 672)(152, 673)(153, 645)(154, 675)(155, 676)(156, 590)(157, 595)(158, 596)(159, 677)(160, 678)(161, 600)(162, 602)(163, 683)(164, 679)(165, 633)(166, 684)(167, 610)(168, 686)(169, 688)(170, 689)(171, 609)(172, 692)(173, 612)(174, 613)(175, 687)(176, 696)(177, 690)(178, 618)(179, 619)(180, 628)(181, 620)(182, 621)(183, 682)(184, 697)(185, 680)(186, 699)(187, 625)(188, 701)(189, 702)(190, 693)(191, 629)(192, 631)(193, 632)(194, 695)(195, 634)(196, 635)(197, 639)(198, 640)(199, 644)(200, 665)(201, 704)(202, 663)(203, 643)(204, 646)(205, 705)(206, 648)(207, 655)(208, 649)(209, 650)(210, 657)(211, 708)(212, 652)(213, 670)(214, 709)(215, 674)(216, 656)(217, 664)(218, 712)(219, 666)(220, 715)(221, 668)(222, 669)(223, 714)(224, 681)(225, 685)(226, 717)(227, 718)(228, 691)(229, 694)(230, 720)(231, 719)(232, 698)(233, 716)(234, 703)(235, 700)(236, 713)(237, 706)(238, 707)(239, 711)(240, 710)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.2311
Graph:: simple bipartite
	v = 260 e = 480 f = 168
	degree seq :: [ 2^240, 24^20 ]

E27.2315 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^3 * Y1 * Y2^-3 * Y1, (Y2^-2 * R * Y2^-1)^2, (Y3 * Y2^-1)^5, (Y2 * Y1)^5, Y2^12, Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-1 ]
Map::
	R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 9, 249)(5, 245, 11, 251)(6, 246, 13, 253)(8, 248, 17, 257)(10, 250, 21, 261)(12, 252, 25, 265)(14, 254, 29, 269)(15, 255, 31, 271)(16, 256, 33, 273)(18, 258, 26, 266)(19, 259, 38, 278)(20, 260, 39, 279)(22, 262, 30, 270)(23, 263, 43, 283)(24, 264, 45, 285)(27, 267, 50, 290)(28, 268, 51, 291)(32, 272, 56, 296)(34, 274, 60, 300)(35, 275, 61, 301)(36, 276, 63, 303)(37, 277, 57, 297)(40, 280, 68, 308)(41, 281, 70, 310)(42, 282, 69, 309)(44, 284, 74, 314)(46, 286, 78, 318)(47, 287, 79, 319)(48, 288, 81, 321)(49, 289, 75, 315)(52, 292, 86, 326)(53, 293, 88, 328)(54, 294, 87, 327)(55, 295, 91, 331)(58, 298, 96, 336)(59, 299, 97, 337)(62, 302, 101, 341)(64, 304, 102, 342)(65, 305, 106, 346)(66, 306, 107, 347)(67, 307, 109, 349)(71, 311, 112, 352)(72, 312, 113, 353)(73, 313, 114, 354)(76, 316, 119, 359)(77, 317, 120, 360)(80, 320, 124, 364)(82, 322, 125, 365)(83, 323, 129, 369)(84, 324, 130, 370)(85, 325, 132, 372)(89, 329, 135, 375)(90, 330, 136, 376)(92, 332, 134, 374)(93, 333, 139, 379)(94, 334, 141, 381)(95, 335, 127, 367)(98, 338, 146, 386)(99, 339, 147, 387)(100, 340, 148, 388)(103, 343, 150, 390)(104, 344, 118, 358)(105, 345, 128, 368)(108, 348, 140, 380)(110, 350, 156, 396)(111, 351, 115, 355)(116, 356, 159, 399)(117, 357, 161, 401)(121, 361, 166, 406)(122, 362, 167, 407)(123, 363, 168, 408)(126, 366, 170, 410)(131, 371, 160, 400)(133, 373, 176, 416)(137, 377, 177, 417)(138, 378, 178, 418)(142, 382, 181, 421)(143, 383, 183, 423)(144, 384, 184, 424)(145, 385, 186, 426)(149, 389, 182, 422)(151, 391, 192, 432)(152, 392, 193, 433)(153, 393, 190, 430)(154, 394, 195, 435)(155, 395, 196, 436)(157, 397, 197, 437)(158, 398, 198, 438)(162, 402, 201, 441)(163, 403, 203, 443)(164, 404, 204, 444)(165, 405, 206, 446)(169, 409, 202, 442)(171, 411, 212, 452)(172, 412, 213, 453)(173, 413, 210, 450)(174, 414, 215, 455)(175, 415, 216, 456)(179, 419, 209, 449)(180, 420, 218, 458)(185, 425, 211, 451)(187, 427, 222, 462)(188, 428, 223, 463)(189, 429, 199, 439)(191, 431, 205, 445)(194, 434, 220, 460)(200, 440, 225, 465)(207, 447, 229, 469)(208, 448, 230, 470)(214, 454, 227, 467)(217, 457, 231, 471)(219, 459, 233, 473)(221, 461, 235, 475)(224, 464, 236, 476)(226, 466, 238, 478)(228, 468, 240, 480)(232, 472, 239, 479)(234, 474, 237, 477)(481, 721, 483, 723, 488, 728, 498, 738, 517, 757, 544, 784, 585, 825, 552, 792, 522, 762, 502, 742, 490, 730, 484, 724)(482, 722, 485, 725, 492, 732, 506, 746, 529, 769, 562, 802, 608, 848, 570, 810, 534, 774, 510, 750, 494, 734, 486, 726)(487, 727, 495, 735, 512, 752, 537, 777, 575, 815, 622, 862, 593, 833, 551, 791, 521, 761, 501, 741, 514, 754, 496, 736)(489, 729, 499, 739, 516, 756, 497, 737, 515, 755, 542, 782, 582, 822, 629, 869, 591, 831, 549, 789, 520, 760, 500, 740)(491, 731, 503, 743, 524, 764, 555, 795, 598, 838, 642, 882, 616, 856, 569, 809, 533, 773, 509, 749, 526, 766, 504, 744)(493, 733, 507, 747, 528, 768, 505, 745, 527, 767, 560, 800, 605, 845, 649, 889, 614, 854, 567, 807, 532, 772, 508, 748)(511, 751, 531, 771, 565, 805, 607, 847, 561, 801, 606, 846, 592, 832, 604, 844, 579, 819, 540, 780, 572, 812, 535, 775)(513, 753, 538, 778, 574, 814, 536, 776, 573, 813, 620, 860, 661, 901, 631, 871, 586, 826, 550, 790, 578, 818, 539, 779)(518, 758, 545, 785, 580, 820, 541, 781, 577, 817, 625, 865, 662, 902, 621, 861, 590, 830, 548, 788, 588, 828, 546, 786)(519, 759, 547, 787, 584, 824, 543, 783, 583, 823, 615, 855, 581, 821, 602, 842, 558, 798, 595, 835, 553, 793, 523, 763)(525, 765, 556, 796, 597, 837, 554, 794, 596, 836, 640, 880, 681, 921, 651, 891, 609, 849, 568, 808, 601, 841, 557, 797)(530, 770, 563, 803, 603, 843, 559, 799, 600, 840, 645, 885, 682, 922, 641, 881, 613, 853, 566, 806, 611, 851, 564, 804)(571, 811, 617, 857, 655, 895, 612, 852, 654, 894, 691, 931, 650, 890, 690, 930, 663, 903, 627, 867, 659, 899, 618, 858)(576, 816, 623, 863, 660, 900, 619, 859, 658, 898, 697, 937, 672, 912, 696, 936, 667, 907, 626, 866, 665, 905, 624, 864)(587, 827, 632, 872, 669, 909, 628, 868, 668, 908, 677, 917, 666, 906, 701, 941, 675, 915, 636, 876, 674, 914, 633, 873)(589, 829, 634, 874, 671, 911, 630, 870, 670, 910, 683, 923, 647, 887, 679, 919, 638, 878, 594, 834, 637, 877, 635, 875)(599, 839, 643, 883, 680, 920, 639, 879, 678, 918, 704, 944, 692, 932, 676, 916, 687, 927, 646, 886, 685, 925, 644, 884)(610, 850, 652, 892, 689, 929, 648, 888, 688, 928, 657, 897, 686, 926, 708, 948, 695, 935, 656, 896, 694, 934, 653, 893)(664, 904, 699, 939, 673, 913, 698, 938, 712, 952, 703, 943, 711, 951, 718, 958, 715, 955, 702, 942, 714, 954, 700, 940)(684, 924, 706, 946, 693, 933, 705, 945, 717, 957, 710, 950, 716, 956, 713, 953, 720, 960, 709, 949, 719, 959, 707, 947)
	L = (1, 482)(2, 481)(3, 487)(4, 489)(5, 491)(6, 493)(7, 483)(8, 497)(9, 484)(10, 501)(11, 485)(12, 505)(13, 486)(14, 509)(15, 511)(16, 513)(17, 488)(18, 506)(19, 518)(20, 519)(21, 490)(22, 510)(23, 523)(24, 525)(25, 492)(26, 498)(27, 530)(28, 531)(29, 494)(30, 502)(31, 495)(32, 536)(33, 496)(34, 540)(35, 541)(36, 543)(37, 537)(38, 499)(39, 500)(40, 548)(41, 550)(42, 549)(43, 503)(44, 554)(45, 504)(46, 558)(47, 559)(48, 561)(49, 555)(50, 507)(51, 508)(52, 566)(53, 568)(54, 567)(55, 571)(56, 512)(57, 517)(58, 576)(59, 577)(60, 514)(61, 515)(62, 581)(63, 516)(64, 582)(65, 586)(66, 587)(67, 589)(68, 520)(69, 522)(70, 521)(71, 592)(72, 593)(73, 594)(74, 524)(75, 529)(76, 599)(77, 600)(78, 526)(79, 527)(80, 604)(81, 528)(82, 605)(83, 609)(84, 610)(85, 612)(86, 532)(87, 534)(88, 533)(89, 615)(90, 616)(91, 535)(92, 614)(93, 619)(94, 621)(95, 607)(96, 538)(97, 539)(98, 626)(99, 627)(100, 628)(101, 542)(102, 544)(103, 630)(104, 598)(105, 608)(106, 545)(107, 546)(108, 620)(109, 547)(110, 636)(111, 595)(112, 551)(113, 552)(114, 553)(115, 591)(116, 639)(117, 641)(118, 584)(119, 556)(120, 557)(121, 646)(122, 647)(123, 648)(124, 560)(125, 562)(126, 650)(127, 575)(128, 585)(129, 563)(130, 564)(131, 640)(132, 565)(133, 656)(134, 572)(135, 569)(136, 570)(137, 657)(138, 658)(139, 573)(140, 588)(141, 574)(142, 661)(143, 663)(144, 664)(145, 666)(146, 578)(147, 579)(148, 580)(149, 662)(150, 583)(151, 672)(152, 673)(153, 670)(154, 675)(155, 676)(156, 590)(157, 677)(158, 678)(159, 596)(160, 611)(161, 597)(162, 681)(163, 683)(164, 684)(165, 686)(166, 601)(167, 602)(168, 603)(169, 682)(170, 606)(171, 692)(172, 693)(173, 690)(174, 695)(175, 696)(176, 613)(177, 617)(178, 618)(179, 689)(180, 698)(181, 622)(182, 629)(183, 623)(184, 624)(185, 691)(186, 625)(187, 702)(188, 703)(189, 679)(190, 633)(191, 685)(192, 631)(193, 632)(194, 700)(195, 634)(196, 635)(197, 637)(198, 638)(199, 669)(200, 705)(201, 642)(202, 649)(203, 643)(204, 644)(205, 671)(206, 645)(207, 709)(208, 710)(209, 659)(210, 653)(211, 665)(212, 651)(213, 652)(214, 707)(215, 654)(216, 655)(217, 711)(218, 660)(219, 713)(220, 674)(221, 715)(222, 667)(223, 668)(224, 716)(225, 680)(226, 718)(227, 694)(228, 720)(229, 687)(230, 688)(231, 697)(232, 719)(233, 699)(234, 717)(235, 701)(236, 704)(237, 714)(238, 706)(239, 712)(240, 708)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E27.2316
Graph:: bipartite
	v = 140 e = 480 f = 288
	degree seq :: [ 4^120, 24^20 ]

E27.2316 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 12})
Quotient :: dipole
Aut^+ = SL(2,5) : C2 (small group id <240, 93>)
Aut   = $<480, 959>$ (small group id <480, 959>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^5, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^-4 * Y1^-1 * Y3, Y1^-1 * Y3^-4 * Y1^-1 * Y3^2, Y3 * Y1^-2 * Y3^3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3, Y3^12, Y3^2 * Y1^-1 * Y3 * Y1^-1 * Y3^5 * Y1^-2, (Y3 * Y2^-1)^12 ]
Map:: polytopal
	R = (1, 241, 2, 242, 6, 246, 13, 253, 4, 244)(3, 243, 9, 249, 22, 262, 28, 268, 11, 251)(5, 245, 14, 254, 33, 273, 19, 259, 7, 247)(8, 248, 20, 260, 46, 286, 39, 279, 16, 256)(10, 250, 24, 264, 55, 295, 60, 300, 26, 266)(12, 252, 29, 269, 65, 305, 69, 309, 31, 271)(15, 255, 36, 276, 77, 317, 74, 314, 34, 274)(17, 257, 40, 280, 83, 323, 71, 311, 32, 272)(18, 258, 42, 282, 88, 328, 91, 331, 44, 284)(21, 261, 49, 289, 99, 339, 96, 336, 47, 287)(23, 263, 53, 293, 105, 345, 102, 342, 51, 291)(25, 265, 43, 283, 80, 320, 114, 354, 58, 298)(27, 267, 61, 301, 118, 358, 122, 362, 63, 303)(30, 270, 67, 307, 128, 368, 112, 352, 57, 297)(35, 275, 75, 315, 138, 378, 135, 375, 72, 312)(37, 277, 50, 290, 87, 327, 106, 346, 54, 294)(38, 278, 79, 319, 144, 384, 146, 386, 81, 321)(41, 281, 86, 326, 154, 394, 151, 391, 84, 324)(45, 285, 73, 313, 136, 376, 162, 402, 93, 333)(48, 288, 97, 337, 166, 406, 163, 403, 94, 334)(52, 292, 103, 343, 172, 412, 124, 364, 64, 304)(56, 296, 110, 350, 180, 420, 178, 418, 108, 348)(59, 299, 92, 332, 160, 400, 153, 393, 116, 356)(62, 302, 120, 360, 98, 338, 155, 395, 111, 351)(66, 306, 127, 367, 191, 431, 189, 429, 125, 365)(68, 308, 129, 369, 192, 432, 193, 433, 131, 371)(70, 310, 133, 373, 196, 436, 181, 421, 113, 353)(76, 316, 100, 340, 168, 408, 130, 370, 139, 379)(78, 318, 142, 382, 197, 437, 173, 413, 104, 344)(82, 322, 95, 335, 164, 404, 206, 446, 148, 388)(85, 325, 152, 392, 210, 450, 207, 447, 149, 389)(89, 329, 121, 361, 184, 424, 211, 451, 156, 396)(90, 330, 147, 387, 204, 444, 175, 415, 107, 347)(101, 341, 170, 410, 217, 457, 201, 441, 140, 380)(109, 349, 179, 419, 216, 456, 165, 405, 117, 357)(115, 355, 158, 398, 177, 417, 143, 383, 169, 409)(119, 359, 141, 381, 194, 434, 225, 465, 182, 422)(123, 363, 186, 426, 200, 440, 137, 377, 167, 407)(126, 366, 190, 430, 227, 467, 195, 435, 132, 372)(134, 374, 150, 390, 208, 448, 228, 468, 198, 438)(145, 385, 161, 401, 213, 453, 229, 469, 202, 442)(157, 397, 212, 452, 234, 474, 209, 449, 159, 399)(171, 411, 176, 416, 203, 443, 230, 470, 218, 458)(174, 414, 188, 428, 205, 445, 231, 471, 219, 459)(183, 423, 226, 466, 232, 472, 214, 454, 185, 425)(187, 427, 220, 460, 233, 473, 215, 455, 199, 439)(221, 461, 223, 463, 237, 477, 239, 479, 235, 475)(222, 462, 224, 464, 238, 478, 240, 480, 236, 476)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960)
	L = (1, 483)(2, 487)(3, 490)(4, 492)(5, 481)(6, 496)(7, 498)(8, 482)(9, 484)(10, 505)(11, 507)(12, 510)(13, 512)(14, 514)(15, 485)(16, 518)(17, 486)(18, 523)(19, 525)(20, 527)(21, 488)(22, 531)(23, 489)(24, 491)(25, 537)(26, 539)(27, 542)(28, 544)(29, 493)(30, 538)(31, 548)(32, 550)(33, 552)(34, 536)(35, 494)(36, 534)(37, 495)(38, 560)(39, 562)(40, 564)(41, 497)(42, 499)(43, 506)(44, 570)(45, 572)(46, 574)(47, 569)(48, 500)(49, 517)(50, 501)(51, 581)(52, 502)(53, 586)(54, 503)(55, 588)(56, 504)(57, 591)(58, 593)(59, 595)(60, 597)(61, 508)(62, 592)(63, 601)(64, 603)(65, 605)(66, 509)(67, 511)(68, 610)(69, 612)(70, 594)(71, 614)(72, 589)(73, 513)(74, 599)(75, 619)(76, 515)(77, 584)(78, 516)(79, 519)(80, 524)(81, 622)(82, 627)(83, 629)(84, 625)(85, 520)(86, 530)(87, 521)(88, 636)(89, 522)(90, 638)(91, 639)(92, 540)(93, 641)(94, 637)(95, 526)(96, 617)(97, 600)(98, 528)(99, 556)(100, 529)(101, 547)(102, 651)(103, 653)(104, 532)(105, 655)(106, 546)(107, 533)(108, 577)(109, 535)(110, 554)(111, 649)(112, 647)(113, 648)(114, 561)(115, 635)(116, 607)(117, 634)(118, 662)(119, 541)(120, 543)(121, 576)(122, 665)(123, 608)(124, 667)(125, 668)(126, 545)(127, 567)(128, 620)(129, 549)(130, 661)(131, 590)(132, 674)(133, 551)(134, 677)(135, 679)(136, 680)(137, 553)(138, 681)(139, 611)(140, 555)(141, 557)(142, 657)(143, 558)(144, 682)(145, 559)(146, 656)(147, 571)(148, 685)(149, 683)(150, 563)(151, 645)(152, 640)(153, 565)(154, 578)(155, 566)(156, 632)(157, 568)(158, 596)(159, 671)(160, 573)(161, 631)(162, 694)(163, 695)(164, 696)(165, 575)(166, 658)(167, 579)(168, 623)(169, 580)(170, 582)(171, 609)(172, 699)(173, 678)(174, 583)(175, 606)(176, 585)(177, 587)(178, 701)(179, 615)(180, 673)(181, 621)(182, 704)(183, 598)(184, 602)(185, 616)(186, 604)(187, 618)(188, 613)(189, 689)(190, 684)(191, 633)(192, 698)(193, 663)(194, 676)(195, 700)(196, 654)(197, 626)(198, 650)(199, 646)(200, 702)(201, 703)(202, 670)(203, 624)(204, 628)(205, 669)(206, 712)(207, 713)(208, 714)(209, 630)(210, 691)(211, 715)(212, 643)(213, 642)(214, 644)(215, 690)(216, 716)(217, 708)(218, 718)(219, 717)(220, 652)(221, 664)(222, 659)(223, 660)(224, 666)(225, 675)(226, 672)(227, 709)(228, 706)(229, 719)(230, 687)(231, 686)(232, 688)(233, 707)(234, 720)(235, 693)(236, 692)(237, 697)(238, 705)(239, 711)(240, 710)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E27.2315
Graph:: simple bipartite
	v = 288 e = 480 f = 140
	degree seq :: [ 2^240, 10^48 ]

E27.2317 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 30})
Quotient :: regular
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-3 * T2)^2, (T1^-1 * T2)^4, T1^30 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 41, 61, 80, 97, 113, 129, 145, 161, 177, 193, 209, 208, 192, 176, 160, 144, 128, 112, 96, 79, 60, 40, 22, 10, 4)(3, 7, 15, 31, 51, 71, 89, 105, 121, 137, 153, 169, 185, 201, 217, 224, 213, 195, 178, 165, 147, 130, 117, 99, 81, 65, 43, 24, 18, 8)(6, 13, 27, 21, 39, 59, 78, 95, 111, 127, 143, 159, 175, 191, 207, 223, 227, 211, 194, 181, 163, 146, 133, 115, 98, 84, 63, 42, 30, 14)(9, 19, 37, 57, 76, 93, 109, 125, 141, 157, 173, 189, 205, 221, 225, 210, 197, 179, 162, 149, 131, 114, 101, 82, 62, 46, 26, 12, 25, 20)(16, 33, 53, 36, 45, 67, 86, 100, 118, 135, 148, 166, 183, 196, 214, 229, 235, 232, 218, 204, 187, 170, 156, 139, 122, 108, 91, 72, 55, 34)(17, 35, 50, 64, 85, 103, 116, 134, 151, 164, 182, 199, 212, 228, 237, 231, 219, 202, 186, 171, 154, 138, 123, 106, 90, 73, 52, 32, 48, 28)(29, 49, 68, 83, 102, 119, 132, 150, 167, 180, 198, 215, 226, 236, 234, 222, 206, 190, 174, 158, 142, 126, 110, 94, 77, 58, 38, 47, 66, 44)(54, 75, 92, 107, 124, 140, 155, 172, 188, 203, 220, 233, 239, 240, 238, 230, 216, 200, 184, 168, 152, 136, 120, 104, 88, 70, 56, 74, 87, 69)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 42)(25, 44)(26, 45)(27, 47)(30, 50)(34, 54)(35, 56)(37, 55)(39, 52)(40, 57)(41, 62)(43, 64)(46, 68)(48, 69)(49, 70)(51, 72)(53, 74)(58, 75)(59, 77)(60, 78)(61, 81)(63, 83)(65, 86)(66, 87)(67, 88)(71, 90)(73, 92)(76, 94)(79, 89)(80, 98)(82, 100)(84, 103)(85, 104)(91, 107)(93, 108)(95, 106)(96, 109)(97, 114)(99, 116)(101, 119)(102, 120)(105, 122)(110, 124)(111, 126)(112, 127)(113, 130)(115, 132)(117, 135)(118, 136)(121, 138)(123, 140)(125, 142)(128, 137)(129, 146)(131, 148)(133, 151)(134, 152)(139, 155)(141, 156)(143, 154)(144, 157)(145, 162)(147, 164)(149, 167)(150, 168)(153, 170)(158, 172)(159, 174)(160, 175)(161, 178)(163, 180)(165, 183)(166, 184)(169, 186)(171, 188)(173, 190)(176, 185)(177, 194)(179, 196)(181, 199)(182, 200)(187, 203)(189, 204)(191, 202)(192, 205)(193, 210)(195, 212)(197, 215)(198, 216)(201, 218)(206, 220)(207, 222)(208, 223)(209, 224)(211, 226)(213, 229)(214, 230)(217, 231)(219, 233)(221, 234)(225, 235)(227, 237)(228, 238)(232, 239)(236, 240)
	local type(s) :: { ( 4^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2318
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 120 f = 60
	degree seq :: [ 30^8 ]

E27.2318 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 30})
Quotient :: regular
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1 * T2 * T1^-1)^2, (T1 * T2)^30 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 33, 25)(15, 26, 32, 27)(21, 35, 30, 36)(22, 37, 29, 38)(23, 39, 44, 34)(40, 49, 43, 50)(41, 51, 42, 52)(45, 53, 48, 54)(46, 55, 47, 56)(57, 65, 60, 66)(58, 67, 59, 68)(61, 69, 64, 70)(62, 71, 63, 72)(73, 113, 76, 119)(74, 115, 75, 117)(77, 121, 89, 123)(78, 124, 82, 126)(79, 127, 100, 129)(80, 130, 81, 132)(83, 135, 93, 137)(84, 138, 85, 140)(86, 142, 90, 144)(87, 145, 88, 147)(91, 151, 92, 153)(94, 156, 95, 158)(96, 160, 97, 162)(98, 164, 99, 166)(101, 169, 102, 171)(103, 173, 104, 175)(105, 177, 106, 179)(107, 181, 108, 183)(109, 185, 110, 187)(111, 189, 112, 191)(114, 194, 116, 193)(118, 198, 120, 197)(122, 202, 168, 201)(125, 206, 155, 205)(128, 204, 149, 209)(131, 212, 150, 211)(133, 215, 143, 214)(134, 217, 136, 208)(139, 221, 157, 220)(141, 224, 159, 223)(146, 228, 152, 227)(148, 231, 154, 230)(161, 232, 165, 235)(163, 229, 167, 236)(170, 239, 174, 222)(172, 238, 176, 225)(178, 226, 182, 213)(180, 234, 184, 216)(186, 237, 190, 218)(188, 219, 192, 207)(195, 240, 199, 233)(196, 210, 200, 203)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 89)(70, 79)(71, 100)(72, 77)(78, 117)(80, 129)(81, 123)(82, 113)(83, 119)(84, 137)(85, 126)(86, 121)(87, 144)(88, 132)(90, 127)(91, 142)(92, 130)(93, 115)(94, 135)(95, 124)(96, 156)(97, 140)(98, 158)(99, 138)(101, 151)(102, 147)(103, 153)(104, 145)(105, 164)(106, 162)(107, 166)(108, 160)(109, 173)(110, 171)(111, 175)(112, 169)(114, 181)(116, 179)(118, 183)(120, 177)(122, 185)(125, 194)(128, 187)(131, 209)(133, 201)(134, 198)(136, 193)(139, 217)(141, 205)(143, 204)(146, 215)(148, 211)(149, 189)(150, 202)(152, 212)(154, 214)(155, 197)(157, 206)(159, 208)(161, 224)(163, 220)(165, 221)(167, 223)(168, 191)(170, 231)(172, 227)(174, 228)(176, 230)(178, 229)(180, 235)(182, 232)(184, 236)(186, 238)(188, 222)(190, 239)(192, 225)(195, 234)(196, 213)(199, 226)(200, 216)(203, 207)(210, 218)(219, 233)(237, 240)
	local type(s) :: { ( 30^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2317
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 60 e = 120 f = 8
	degree seq :: [ 4^60 ]

E27.2319 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 30})
Quotient :: edge
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^30 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 30, 40)(25, 41, 28, 42)(31, 44, 38, 45)(33, 46, 36, 47)(49, 57, 52, 58)(50, 59, 51, 60)(53, 61, 56, 62)(54, 63, 55, 64)(65, 73, 68, 74)(66, 75, 67, 76)(69, 113, 72, 119)(70, 115, 71, 117)(77, 121, 86, 123)(78, 124, 85, 126)(79, 127, 81, 129)(80, 130, 100, 132)(82, 134, 84, 136)(83, 137, 99, 139)(87, 143, 89, 145)(88, 146, 91, 148)(90, 150, 92, 152)(93, 155, 95, 157)(94, 158, 97, 160)(96, 162, 98, 164)(101, 169, 102, 171)(103, 173, 104, 175)(105, 177, 106, 179)(107, 181, 108, 183)(109, 185, 110, 187)(111, 189, 112, 191)(114, 194, 116, 193)(118, 198, 120, 197)(122, 202, 168, 201)(125, 206, 167, 205)(128, 210, 153, 209)(131, 204, 142, 213)(133, 215, 147, 212)(135, 218, 165, 217)(138, 208, 141, 221)(140, 223, 159, 220)(144, 228, 151, 227)(149, 232, 154, 230)(156, 229, 163, 236)(161, 233, 166, 234)(170, 238, 174, 224)(172, 237, 176, 219)(178, 235, 182, 216)(180, 231, 184, 211)(186, 222, 190, 207)(188, 239, 192, 225)(195, 214, 199, 203)(196, 240, 200, 226)(241, 242)(243, 247)(244, 249)(245, 250)(246, 252)(248, 255)(251, 260)(253, 263)(254, 265)(256, 268)(257, 270)(258, 271)(259, 273)(261, 276)(262, 278)(264, 275)(266, 277)(267, 272)(269, 274)(279, 289)(280, 290)(281, 291)(282, 292)(283, 288)(284, 293)(285, 294)(286, 295)(287, 296)(297, 305)(298, 306)(299, 307)(300, 308)(301, 309)(302, 310)(303, 311)(304, 312)(313, 320)(314, 326)(315, 317)(316, 340)(318, 355)(319, 363)(321, 372)(322, 366)(323, 353)(324, 379)(325, 359)(327, 369)(328, 370)(329, 388)(330, 367)(331, 361)(332, 386)(333, 376)(334, 377)(335, 400)(336, 374)(337, 364)(338, 398)(339, 357)(341, 385)(342, 390)(343, 383)(344, 392)(345, 397)(346, 402)(347, 395)(348, 404)(349, 411)(350, 413)(351, 409)(352, 415)(354, 419)(356, 421)(358, 417)(360, 423)(362, 425)(365, 434)(368, 444)(371, 427)(373, 442)(375, 448)(378, 433)(380, 446)(381, 438)(382, 429)(384, 452)(387, 453)(389, 450)(391, 449)(393, 441)(394, 455)(396, 460)(399, 461)(401, 458)(403, 457)(405, 445)(406, 463)(407, 437)(408, 431)(410, 470)(412, 468)(414, 467)(416, 472)(418, 474)(420, 469)(422, 476)(424, 473)(426, 459)(428, 478)(430, 464)(432, 477)(435, 451)(436, 475)(439, 456)(440, 471)(443, 447)(454, 465)(462, 466)(479, 480)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 60, 60 ), ( 60^4 ) }
Outer automorphisms :: reflexible
Dual of E27.2323
Transitivity :: ET+
Graph:: simple bipartite
	v = 180 e = 240 f = 8
	degree seq :: [ 2^120, 4^60 ]

E27.2320 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 30})
Quotient :: edge
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-2 * T1)^2, T2^30 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 24, 43, 60, 76, 92, 108, 124, 140, 156, 172, 188, 204, 220, 208, 192, 176, 160, 144, 128, 112, 96, 80, 64, 47, 29, 14, 5)(2, 7, 17, 35, 54, 70, 86, 102, 118, 134, 150, 166, 182, 198, 214, 229, 216, 200, 184, 168, 152, 136, 120, 104, 88, 72, 56, 38, 20, 8)(4, 12, 26, 45, 62, 78, 94, 110, 126, 142, 158, 174, 190, 206, 222, 232, 218, 202, 186, 170, 154, 138, 122, 106, 90, 74, 58, 41, 22, 9)(6, 15, 30, 49, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 225, 236, 227, 212, 196, 180, 164, 148, 132, 116, 100, 84, 68, 52, 33, 16)(11, 25, 13, 28, 46, 63, 79, 95, 111, 127, 143, 159, 175, 191, 207, 223, 233, 219, 203, 187, 171, 155, 139, 123, 107, 91, 75, 59, 42, 23)(18, 36, 19, 37, 55, 71, 87, 103, 119, 135, 151, 167, 183, 199, 215, 230, 238, 228, 213, 197, 181, 165, 149, 133, 117, 101, 85, 69, 53, 34)(21, 39, 57, 73, 89, 105, 121, 137, 153, 169, 185, 201, 217, 231, 239, 234, 221, 205, 189, 173, 157, 141, 125, 109, 93, 77, 61, 44, 27, 40)(31, 50, 32, 51, 67, 83, 99, 115, 131, 147, 163, 179, 195, 211, 226, 237, 240, 235, 224, 209, 193, 177, 161, 145, 129, 113, 97, 81, 65, 48)(241, 242, 246, 244)(243, 249, 261, 251)(245, 253, 258, 247)(248, 259, 271, 255)(250, 263, 277, 260)(252, 256, 272, 267)(254, 266, 284, 268)(257, 274, 291, 273)(262, 270, 288, 279)(264, 278, 289, 281)(265, 280, 290, 276)(269, 275, 292, 285)(282, 297, 305, 295)(283, 298, 313, 299)(286, 301, 307, 293)(287, 303, 309, 294)(296, 311, 321, 306)(300, 315, 327, 312)(302, 308, 323, 317)(304, 318, 333, 319)(310, 325, 339, 324)(314, 322, 337, 329)(316, 328, 338, 330)(320, 326, 340, 334)(331, 345, 353, 343)(332, 346, 361, 347)(335, 349, 355, 341)(336, 351, 357, 342)(344, 359, 369, 354)(348, 363, 375, 360)(350, 356, 371, 365)(352, 366, 381, 367)(358, 373, 387, 372)(362, 370, 385, 377)(364, 376, 386, 378)(368, 374, 388, 382)(379, 393, 401, 391)(380, 394, 409, 395)(383, 397, 403, 389)(384, 399, 405, 390)(392, 407, 417, 402)(396, 411, 423, 408)(398, 404, 419, 413)(400, 414, 429, 415)(406, 421, 435, 420)(410, 418, 433, 425)(412, 424, 434, 426)(416, 422, 436, 430)(427, 441, 449, 439)(428, 442, 457, 443)(431, 445, 451, 437)(432, 447, 453, 438)(440, 455, 464, 450)(444, 459, 470, 456)(446, 452, 466, 461)(448, 462, 474, 463)(454, 468, 477, 467)(458, 465, 475, 471)(460, 469, 476, 472)(473, 479, 480, 478)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4^4 ), ( 4^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2324
Transitivity :: ET+
Graph:: simple bipartite
	v = 68 e = 240 f = 120
	degree seq :: [ 4^60, 30^8 ]

E27.2321 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 30})
Quotient :: edge
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T1^-3 * T2)^2, T1^30 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 42)(25, 44)(26, 45)(27, 47)(30, 50)(34, 54)(35, 56)(37, 55)(39, 52)(40, 57)(41, 62)(43, 64)(46, 68)(48, 69)(49, 70)(51, 72)(53, 74)(58, 75)(59, 77)(60, 78)(61, 81)(63, 83)(65, 86)(66, 87)(67, 88)(71, 90)(73, 92)(76, 94)(79, 89)(80, 98)(82, 100)(84, 103)(85, 104)(91, 107)(93, 108)(95, 106)(96, 109)(97, 114)(99, 116)(101, 119)(102, 120)(105, 122)(110, 124)(111, 126)(112, 127)(113, 130)(115, 132)(117, 135)(118, 136)(121, 138)(123, 140)(125, 142)(128, 137)(129, 146)(131, 148)(133, 151)(134, 152)(139, 155)(141, 156)(143, 154)(144, 157)(145, 162)(147, 164)(149, 167)(150, 168)(153, 170)(158, 172)(159, 174)(160, 175)(161, 178)(163, 180)(165, 183)(166, 184)(169, 186)(171, 188)(173, 190)(176, 185)(177, 194)(179, 196)(181, 199)(182, 200)(187, 203)(189, 204)(191, 202)(192, 205)(193, 210)(195, 212)(197, 215)(198, 216)(201, 218)(206, 220)(207, 222)(208, 223)(209, 224)(211, 226)(213, 229)(214, 230)(217, 231)(219, 233)(221, 234)(225, 235)(227, 237)(228, 238)(232, 239)(236, 240)(241, 242, 245, 251, 263, 281, 301, 320, 337, 353, 369, 385, 401, 417, 433, 449, 448, 432, 416, 400, 384, 368, 352, 336, 319, 300, 280, 262, 250, 244)(243, 247, 255, 271, 291, 311, 329, 345, 361, 377, 393, 409, 425, 441, 457, 464, 453, 435, 418, 405, 387, 370, 357, 339, 321, 305, 283, 264, 258, 248)(246, 253, 267, 261, 279, 299, 318, 335, 351, 367, 383, 399, 415, 431, 447, 463, 467, 451, 434, 421, 403, 386, 373, 355, 338, 324, 303, 282, 270, 254)(249, 259, 277, 297, 316, 333, 349, 365, 381, 397, 413, 429, 445, 461, 465, 450, 437, 419, 402, 389, 371, 354, 341, 322, 302, 286, 266, 252, 265, 260)(256, 273, 293, 276, 285, 307, 326, 340, 358, 375, 388, 406, 423, 436, 454, 469, 475, 472, 458, 444, 427, 410, 396, 379, 362, 348, 331, 312, 295, 274)(257, 275, 290, 304, 325, 343, 356, 374, 391, 404, 422, 439, 452, 468, 477, 471, 459, 442, 426, 411, 394, 378, 363, 346, 330, 313, 292, 272, 288, 268)(269, 289, 308, 323, 342, 359, 372, 390, 407, 420, 438, 455, 466, 476, 474, 462, 446, 430, 414, 398, 382, 366, 350, 334, 317, 298, 278, 287, 306, 284)(294, 315, 332, 347, 364, 380, 395, 412, 428, 443, 460, 473, 479, 480, 478, 470, 456, 440, 424, 408, 392, 376, 360, 344, 328, 310, 296, 314, 327, 309)
	L = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 8, 8 ), ( 8^30 ) }
Outer automorphisms :: reflexible
Dual of E27.2322
Transitivity :: ET+
Graph:: simple bipartite
	v = 128 e = 240 f = 60
	degree seq :: [ 2^120, 30^8 ]

E27.2322 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 30})
Quotient :: loop
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^30 ]
Map::
	R = (1, 241, 3, 243, 8, 248, 4, 244)(2, 242, 5, 245, 11, 251, 6, 246)(7, 247, 13, 253, 24, 264, 14, 254)(9, 249, 16, 256, 29, 269, 17, 257)(10, 250, 18, 258, 32, 272, 19, 259)(12, 252, 21, 261, 37, 277, 22, 262)(15, 255, 26, 266, 43, 283, 27, 267)(20, 260, 34, 274, 48, 288, 35, 275)(23, 263, 39, 279, 30, 270, 40, 280)(25, 265, 41, 281, 28, 268, 42, 282)(31, 271, 44, 284, 38, 278, 45, 285)(33, 273, 46, 286, 36, 276, 47, 287)(49, 289, 57, 297, 52, 292, 58, 298)(50, 290, 59, 299, 51, 291, 60, 300)(53, 293, 61, 301, 56, 296, 62, 302)(54, 294, 63, 303, 55, 295, 64, 304)(65, 305, 73, 313, 68, 308, 74, 314)(66, 306, 75, 315, 67, 307, 76, 316)(69, 309, 113, 353, 72, 312, 119, 359)(70, 310, 115, 355, 71, 311, 117, 357)(77, 317, 121, 361, 86, 326, 123, 363)(78, 318, 124, 364, 85, 325, 126, 366)(79, 319, 127, 367, 81, 321, 129, 369)(80, 320, 130, 370, 100, 340, 132, 372)(82, 322, 134, 374, 84, 324, 136, 376)(83, 323, 137, 377, 99, 339, 139, 379)(87, 327, 143, 383, 89, 329, 145, 385)(88, 328, 146, 386, 91, 331, 148, 388)(90, 330, 150, 390, 92, 332, 152, 392)(93, 333, 155, 395, 95, 335, 157, 397)(94, 334, 158, 398, 97, 337, 160, 400)(96, 336, 162, 402, 98, 338, 164, 404)(101, 341, 169, 409, 102, 342, 171, 411)(103, 343, 173, 413, 104, 344, 175, 415)(105, 345, 177, 417, 106, 346, 179, 419)(107, 347, 181, 421, 108, 348, 183, 423)(109, 349, 185, 425, 110, 350, 187, 427)(111, 351, 189, 429, 112, 352, 191, 431)(114, 354, 194, 434, 116, 356, 196, 436)(118, 358, 197, 437, 120, 360, 193, 433)(122, 362, 202, 442, 168, 408, 204, 444)(125, 365, 206, 446, 167, 407, 208, 448)(128, 368, 210, 450, 153, 393, 212, 452)(131, 371, 213, 453, 142, 382, 201, 441)(133, 373, 209, 449, 147, 387, 216, 456)(135, 375, 218, 458, 165, 405, 220, 460)(138, 378, 221, 461, 141, 381, 205, 445)(140, 380, 217, 457, 159, 399, 224, 464)(144, 384, 228, 468, 151, 391, 230, 470)(149, 389, 227, 467, 154, 394, 233, 473)(156, 396, 236, 476, 163, 403, 229, 469)(161, 401, 234, 474, 166, 406, 232, 472)(170, 410, 223, 463, 174, 414, 238, 478)(172, 412, 219, 459, 176, 416, 237, 477)(178, 418, 215, 455, 182, 422, 235, 475)(180, 420, 211, 451, 184, 424, 231, 471)(186, 426, 207, 447, 190, 430, 222, 462)(188, 428, 225, 465, 192, 432, 239, 479)(195, 435, 203, 443, 199, 439, 214, 454)(198, 438, 226, 466, 200, 440, 240, 480)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 250)(6, 252)(7, 243)(8, 255)(9, 244)(10, 245)(11, 260)(12, 246)(13, 263)(14, 265)(15, 248)(16, 268)(17, 270)(18, 271)(19, 273)(20, 251)(21, 276)(22, 278)(23, 253)(24, 275)(25, 254)(26, 277)(27, 272)(28, 256)(29, 274)(30, 257)(31, 258)(32, 267)(33, 259)(34, 269)(35, 264)(36, 261)(37, 266)(38, 262)(39, 289)(40, 290)(41, 291)(42, 292)(43, 288)(44, 293)(45, 294)(46, 295)(47, 296)(48, 283)(49, 279)(50, 280)(51, 281)(52, 282)(53, 284)(54, 285)(55, 286)(56, 287)(57, 305)(58, 306)(59, 307)(60, 308)(61, 309)(62, 310)(63, 311)(64, 312)(65, 297)(66, 298)(67, 299)(68, 300)(69, 301)(70, 302)(71, 303)(72, 304)(73, 317)(74, 340)(75, 320)(76, 326)(77, 313)(78, 353)(79, 361)(80, 315)(81, 370)(82, 364)(83, 355)(84, 377)(85, 357)(86, 316)(87, 367)(88, 372)(89, 386)(90, 369)(91, 363)(92, 388)(93, 374)(94, 379)(95, 398)(96, 376)(97, 366)(98, 400)(99, 359)(100, 314)(101, 383)(102, 392)(103, 385)(104, 390)(105, 395)(106, 404)(107, 397)(108, 402)(109, 409)(110, 415)(111, 411)(112, 413)(113, 318)(114, 417)(115, 323)(116, 423)(117, 325)(118, 419)(119, 339)(120, 421)(121, 319)(122, 425)(123, 331)(124, 322)(125, 434)(126, 337)(127, 327)(128, 442)(129, 330)(130, 321)(131, 427)(132, 328)(133, 453)(134, 333)(135, 446)(136, 336)(137, 324)(138, 436)(139, 334)(140, 461)(141, 437)(142, 429)(143, 341)(144, 450)(145, 343)(146, 329)(147, 444)(148, 332)(149, 456)(150, 344)(151, 449)(152, 342)(153, 441)(154, 452)(155, 345)(156, 458)(157, 347)(158, 335)(159, 448)(160, 338)(161, 464)(162, 348)(163, 457)(164, 346)(165, 445)(166, 460)(167, 433)(168, 431)(169, 349)(170, 468)(171, 351)(172, 473)(173, 352)(174, 467)(175, 350)(176, 470)(177, 354)(178, 476)(179, 358)(180, 472)(181, 360)(182, 474)(183, 356)(184, 469)(185, 362)(186, 463)(187, 371)(188, 477)(189, 382)(190, 459)(191, 408)(192, 478)(193, 407)(194, 365)(195, 455)(196, 378)(197, 381)(198, 471)(199, 451)(200, 475)(201, 393)(202, 368)(203, 447)(204, 387)(205, 405)(206, 375)(207, 443)(208, 399)(209, 391)(210, 384)(211, 439)(212, 394)(213, 373)(214, 465)(215, 435)(216, 389)(217, 403)(218, 396)(219, 430)(220, 406)(221, 380)(222, 466)(223, 426)(224, 401)(225, 454)(226, 462)(227, 414)(228, 410)(229, 424)(230, 416)(231, 438)(232, 420)(233, 412)(234, 422)(235, 440)(236, 418)(237, 428)(238, 432)(239, 480)(240, 479)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2321
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 60 e = 240 f = 128
	degree seq :: [ 8^60 ]

E27.2323 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 30})
Quotient :: loop
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-2 * T1)^2, T2^30 ]
Map::
	R = (1, 241, 3, 243, 10, 250, 24, 264, 43, 283, 60, 300, 76, 316, 92, 332, 108, 348, 124, 364, 140, 380, 156, 396, 172, 412, 188, 428, 204, 444, 220, 460, 208, 448, 192, 432, 176, 416, 160, 400, 144, 384, 128, 368, 112, 352, 96, 336, 80, 320, 64, 304, 47, 287, 29, 269, 14, 254, 5, 245)(2, 242, 7, 247, 17, 257, 35, 275, 54, 294, 70, 310, 86, 326, 102, 342, 118, 358, 134, 374, 150, 390, 166, 406, 182, 422, 198, 438, 214, 454, 229, 469, 216, 456, 200, 440, 184, 424, 168, 408, 152, 392, 136, 376, 120, 360, 104, 344, 88, 328, 72, 312, 56, 296, 38, 278, 20, 260, 8, 248)(4, 244, 12, 252, 26, 266, 45, 285, 62, 302, 78, 318, 94, 334, 110, 350, 126, 366, 142, 382, 158, 398, 174, 414, 190, 430, 206, 446, 222, 462, 232, 472, 218, 458, 202, 442, 186, 426, 170, 410, 154, 394, 138, 378, 122, 362, 106, 346, 90, 330, 74, 314, 58, 298, 41, 281, 22, 262, 9, 249)(6, 246, 15, 255, 30, 270, 49, 289, 66, 306, 82, 322, 98, 338, 114, 354, 130, 370, 146, 386, 162, 402, 178, 418, 194, 434, 210, 450, 225, 465, 236, 476, 227, 467, 212, 452, 196, 436, 180, 420, 164, 404, 148, 388, 132, 372, 116, 356, 100, 340, 84, 324, 68, 308, 52, 292, 33, 273, 16, 256)(11, 251, 25, 265, 13, 253, 28, 268, 46, 286, 63, 303, 79, 319, 95, 335, 111, 351, 127, 367, 143, 383, 159, 399, 175, 415, 191, 431, 207, 447, 223, 463, 233, 473, 219, 459, 203, 443, 187, 427, 171, 411, 155, 395, 139, 379, 123, 363, 107, 347, 91, 331, 75, 315, 59, 299, 42, 282, 23, 263)(18, 258, 36, 276, 19, 259, 37, 277, 55, 295, 71, 311, 87, 327, 103, 343, 119, 359, 135, 375, 151, 391, 167, 407, 183, 423, 199, 439, 215, 455, 230, 470, 238, 478, 228, 468, 213, 453, 197, 437, 181, 421, 165, 405, 149, 389, 133, 373, 117, 357, 101, 341, 85, 325, 69, 309, 53, 293, 34, 274)(21, 261, 39, 279, 57, 297, 73, 313, 89, 329, 105, 345, 121, 361, 137, 377, 153, 393, 169, 409, 185, 425, 201, 441, 217, 457, 231, 471, 239, 479, 234, 474, 221, 461, 205, 445, 189, 429, 173, 413, 157, 397, 141, 381, 125, 365, 109, 349, 93, 333, 77, 317, 61, 301, 44, 284, 27, 267, 40, 280)(31, 271, 50, 290, 32, 272, 51, 291, 67, 307, 83, 323, 99, 339, 115, 355, 131, 371, 147, 387, 163, 403, 179, 419, 195, 435, 211, 451, 226, 466, 237, 477, 240, 480, 235, 475, 224, 464, 209, 449, 193, 433, 177, 417, 161, 401, 145, 385, 129, 369, 113, 353, 97, 337, 81, 321, 65, 305, 48, 288)
	L = (1, 242)(2, 246)(3, 249)(4, 241)(5, 253)(6, 244)(7, 245)(8, 259)(9, 261)(10, 263)(11, 243)(12, 256)(13, 258)(14, 266)(15, 248)(16, 272)(17, 274)(18, 247)(19, 271)(20, 250)(21, 251)(22, 270)(23, 277)(24, 278)(25, 280)(26, 284)(27, 252)(28, 254)(29, 275)(30, 288)(31, 255)(32, 267)(33, 257)(34, 291)(35, 292)(36, 265)(37, 260)(38, 289)(39, 262)(40, 290)(41, 264)(42, 297)(43, 298)(44, 268)(45, 269)(46, 301)(47, 303)(48, 279)(49, 281)(50, 276)(51, 273)(52, 285)(53, 286)(54, 287)(55, 282)(56, 311)(57, 305)(58, 313)(59, 283)(60, 315)(61, 307)(62, 308)(63, 309)(64, 318)(65, 295)(66, 296)(67, 293)(68, 323)(69, 294)(70, 325)(71, 321)(72, 300)(73, 299)(74, 322)(75, 327)(76, 328)(77, 302)(78, 333)(79, 304)(80, 326)(81, 306)(82, 337)(83, 317)(84, 310)(85, 339)(86, 340)(87, 312)(88, 338)(89, 314)(90, 316)(91, 345)(92, 346)(93, 319)(94, 320)(95, 349)(96, 351)(97, 329)(98, 330)(99, 324)(100, 334)(101, 335)(102, 336)(103, 331)(104, 359)(105, 353)(106, 361)(107, 332)(108, 363)(109, 355)(110, 356)(111, 357)(112, 366)(113, 343)(114, 344)(115, 341)(116, 371)(117, 342)(118, 373)(119, 369)(120, 348)(121, 347)(122, 370)(123, 375)(124, 376)(125, 350)(126, 381)(127, 352)(128, 374)(129, 354)(130, 385)(131, 365)(132, 358)(133, 387)(134, 388)(135, 360)(136, 386)(137, 362)(138, 364)(139, 393)(140, 394)(141, 367)(142, 368)(143, 397)(144, 399)(145, 377)(146, 378)(147, 372)(148, 382)(149, 383)(150, 384)(151, 379)(152, 407)(153, 401)(154, 409)(155, 380)(156, 411)(157, 403)(158, 404)(159, 405)(160, 414)(161, 391)(162, 392)(163, 389)(164, 419)(165, 390)(166, 421)(167, 417)(168, 396)(169, 395)(170, 418)(171, 423)(172, 424)(173, 398)(174, 429)(175, 400)(176, 422)(177, 402)(178, 433)(179, 413)(180, 406)(181, 435)(182, 436)(183, 408)(184, 434)(185, 410)(186, 412)(187, 441)(188, 442)(189, 415)(190, 416)(191, 445)(192, 447)(193, 425)(194, 426)(195, 420)(196, 430)(197, 431)(198, 432)(199, 427)(200, 455)(201, 449)(202, 457)(203, 428)(204, 459)(205, 451)(206, 452)(207, 453)(208, 462)(209, 439)(210, 440)(211, 437)(212, 466)(213, 438)(214, 468)(215, 464)(216, 444)(217, 443)(218, 465)(219, 470)(220, 469)(221, 446)(222, 474)(223, 448)(224, 450)(225, 475)(226, 461)(227, 454)(228, 477)(229, 476)(230, 456)(231, 458)(232, 460)(233, 479)(234, 463)(235, 471)(236, 472)(237, 467)(238, 473)(239, 480)(240, 478)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2319
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 240 f = 180
	degree seq :: [ 60^8 ]

E27.2324 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 30})
Quotient :: loop
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T1^-3 * T2)^2, T1^30 ]
Map:: polytopal non-degenerate
	R = (1, 241, 3, 243)(2, 242, 6, 246)(4, 244, 9, 249)(5, 245, 12, 252)(7, 247, 16, 256)(8, 248, 17, 257)(10, 250, 21, 261)(11, 251, 24, 264)(13, 253, 28, 268)(14, 254, 29, 269)(15, 255, 32, 272)(18, 258, 36, 276)(19, 259, 38, 278)(20, 260, 33, 273)(22, 262, 31, 271)(23, 263, 42, 282)(25, 265, 44, 284)(26, 266, 45, 285)(27, 267, 47, 287)(30, 270, 50, 290)(34, 274, 54, 294)(35, 275, 56, 296)(37, 277, 55, 295)(39, 279, 52, 292)(40, 280, 57, 297)(41, 281, 62, 302)(43, 283, 64, 304)(46, 286, 68, 308)(48, 288, 69, 309)(49, 289, 70, 310)(51, 291, 72, 312)(53, 293, 74, 314)(58, 298, 75, 315)(59, 299, 77, 317)(60, 300, 78, 318)(61, 301, 81, 321)(63, 303, 83, 323)(65, 305, 86, 326)(66, 306, 87, 327)(67, 307, 88, 328)(71, 311, 90, 330)(73, 313, 92, 332)(76, 316, 94, 334)(79, 319, 89, 329)(80, 320, 98, 338)(82, 322, 100, 340)(84, 324, 103, 343)(85, 325, 104, 344)(91, 331, 107, 347)(93, 333, 108, 348)(95, 335, 106, 346)(96, 336, 109, 349)(97, 337, 114, 354)(99, 339, 116, 356)(101, 341, 119, 359)(102, 342, 120, 360)(105, 345, 122, 362)(110, 350, 124, 364)(111, 351, 126, 366)(112, 352, 127, 367)(113, 353, 130, 370)(115, 355, 132, 372)(117, 357, 135, 375)(118, 358, 136, 376)(121, 361, 138, 378)(123, 363, 140, 380)(125, 365, 142, 382)(128, 368, 137, 377)(129, 369, 146, 386)(131, 371, 148, 388)(133, 373, 151, 391)(134, 374, 152, 392)(139, 379, 155, 395)(141, 381, 156, 396)(143, 383, 154, 394)(144, 384, 157, 397)(145, 385, 162, 402)(147, 387, 164, 404)(149, 389, 167, 407)(150, 390, 168, 408)(153, 393, 170, 410)(158, 398, 172, 412)(159, 399, 174, 414)(160, 400, 175, 415)(161, 401, 178, 418)(163, 403, 180, 420)(165, 405, 183, 423)(166, 406, 184, 424)(169, 409, 186, 426)(171, 411, 188, 428)(173, 413, 190, 430)(176, 416, 185, 425)(177, 417, 194, 434)(179, 419, 196, 436)(181, 421, 199, 439)(182, 422, 200, 440)(187, 427, 203, 443)(189, 429, 204, 444)(191, 431, 202, 442)(192, 432, 205, 445)(193, 433, 210, 450)(195, 435, 212, 452)(197, 437, 215, 455)(198, 438, 216, 456)(201, 441, 218, 458)(206, 446, 220, 460)(207, 447, 222, 462)(208, 448, 223, 463)(209, 449, 224, 464)(211, 451, 226, 466)(213, 453, 229, 469)(214, 454, 230, 470)(217, 457, 231, 471)(219, 459, 233, 473)(221, 461, 234, 474)(225, 465, 235, 475)(227, 467, 237, 477)(228, 468, 238, 478)(232, 472, 239, 479)(236, 476, 240, 480)
	L = (1, 242)(2, 245)(3, 247)(4, 241)(5, 251)(6, 253)(7, 255)(8, 243)(9, 259)(10, 244)(11, 263)(12, 265)(13, 267)(14, 246)(15, 271)(16, 273)(17, 275)(18, 248)(19, 277)(20, 249)(21, 279)(22, 250)(23, 281)(24, 258)(25, 260)(26, 252)(27, 261)(28, 257)(29, 289)(30, 254)(31, 291)(32, 288)(33, 293)(34, 256)(35, 290)(36, 285)(37, 297)(38, 287)(39, 299)(40, 262)(41, 301)(42, 270)(43, 264)(44, 269)(45, 307)(46, 266)(47, 306)(48, 268)(49, 308)(50, 304)(51, 311)(52, 272)(53, 276)(54, 315)(55, 274)(56, 314)(57, 316)(58, 278)(59, 318)(60, 280)(61, 320)(62, 286)(63, 282)(64, 325)(65, 283)(66, 284)(67, 326)(68, 323)(69, 294)(70, 296)(71, 329)(72, 295)(73, 292)(74, 327)(75, 332)(76, 333)(77, 298)(78, 335)(79, 300)(80, 337)(81, 305)(82, 302)(83, 342)(84, 303)(85, 343)(86, 340)(87, 309)(88, 310)(89, 345)(90, 313)(91, 312)(92, 347)(93, 349)(94, 317)(95, 351)(96, 319)(97, 353)(98, 324)(99, 321)(100, 358)(101, 322)(102, 359)(103, 356)(104, 328)(105, 361)(106, 330)(107, 364)(108, 331)(109, 365)(110, 334)(111, 367)(112, 336)(113, 369)(114, 341)(115, 338)(116, 374)(117, 339)(118, 375)(119, 372)(120, 344)(121, 377)(122, 348)(123, 346)(124, 380)(125, 381)(126, 350)(127, 383)(128, 352)(129, 385)(130, 357)(131, 354)(132, 390)(133, 355)(134, 391)(135, 388)(136, 360)(137, 393)(138, 363)(139, 362)(140, 395)(141, 397)(142, 366)(143, 399)(144, 368)(145, 401)(146, 373)(147, 370)(148, 406)(149, 371)(150, 407)(151, 404)(152, 376)(153, 409)(154, 378)(155, 412)(156, 379)(157, 413)(158, 382)(159, 415)(160, 384)(161, 417)(162, 389)(163, 386)(164, 422)(165, 387)(166, 423)(167, 420)(168, 392)(169, 425)(170, 396)(171, 394)(172, 428)(173, 429)(174, 398)(175, 431)(176, 400)(177, 433)(178, 405)(179, 402)(180, 438)(181, 403)(182, 439)(183, 436)(184, 408)(185, 441)(186, 411)(187, 410)(188, 443)(189, 445)(190, 414)(191, 447)(192, 416)(193, 449)(194, 421)(195, 418)(196, 454)(197, 419)(198, 455)(199, 452)(200, 424)(201, 457)(202, 426)(203, 460)(204, 427)(205, 461)(206, 430)(207, 463)(208, 432)(209, 448)(210, 437)(211, 434)(212, 468)(213, 435)(214, 469)(215, 466)(216, 440)(217, 464)(218, 444)(219, 442)(220, 473)(221, 465)(222, 446)(223, 467)(224, 453)(225, 450)(226, 476)(227, 451)(228, 477)(229, 475)(230, 456)(231, 459)(232, 458)(233, 479)(234, 462)(235, 472)(236, 474)(237, 471)(238, 470)(239, 480)(240, 478)
	local type(s) :: { ( 4, 30, 4, 30 ) }
Outer automorphisms :: reflexible
Dual of E27.2320
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 120 e = 240 f = 68
	degree seq :: [ 4^120 ]

E27.2325 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2, (Y2^-2 * Y1)^4, (Y3 * Y2^-1)^30 ]
Map::
	R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 9, 249)(5, 245, 10, 250)(6, 246, 12, 252)(8, 248, 15, 255)(11, 251, 20, 260)(13, 253, 23, 263)(14, 254, 25, 265)(16, 256, 28, 268)(17, 257, 30, 270)(18, 258, 31, 271)(19, 259, 33, 273)(21, 261, 36, 276)(22, 262, 38, 278)(24, 264, 35, 275)(26, 266, 37, 277)(27, 267, 32, 272)(29, 269, 34, 274)(39, 279, 49, 289)(40, 280, 50, 290)(41, 281, 51, 291)(42, 282, 52, 292)(43, 283, 48, 288)(44, 284, 53, 293)(45, 285, 54, 294)(46, 286, 55, 295)(47, 287, 56, 296)(57, 297, 65, 305)(58, 298, 66, 306)(59, 299, 67, 307)(60, 300, 68, 308)(61, 301, 69, 309)(62, 302, 70, 310)(63, 303, 71, 311)(64, 304, 72, 312)(73, 313, 103, 343)(74, 314, 86, 326)(75, 315, 88, 328)(76, 316, 106, 346)(77, 317, 133, 373)(78, 318, 136, 376)(79, 319, 138, 378)(80, 320, 137, 377)(81, 321, 135, 375)(82, 322, 134, 374)(83, 323, 128, 368)(84, 324, 147, 387)(85, 325, 126, 366)(87, 327, 150, 390)(89, 329, 140, 380)(90, 330, 139, 379)(91, 331, 157, 397)(92, 332, 142, 382)(93, 333, 141, 381)(94, 334, 144, 384)(95, 335, 143, 383)(96, 336, 162, 402)(97, 337, 146, 386)(98, 338, 145, 385)(99, 339, 125, 365)(100, 340, 149, 389)(101, 341, 148, 388)(102, 342, 127, 367)(104, 344, 152, 392)(105, 345, 151, 391)(107, 347, 154, 394)(108, 348, 153, 393)(109, 349, 156, 396)(110, 350, 155, 395)(111, 351, 164, 404)(112, 352, 159, 399)(113, 353, 158, 398)(114, 354, 161, 401)(115, 355, 160, 400)(116, 356, 163, 403)(117, 357, 166, 406)(118, 358, 165, 405)(119, 359, 168, 408)(120, 360, 167, 407)(121, 361, 170, 410)(122, 362, 169, 409)(123, 363, 172, 412)(124, 364, 171, 411)(129, 369, 174, 414)(130, 370, 173, 413)(131, 371, 176, 416)(132, 372, 175, 415)(177, 417, 184, 424)(178, 418, 181, 421)(179, 419, 183, 423)(180, 420, 182, 422)(185, 425, 213, 453)(186, 426, 220, 460)(187, 427, 206, 446)(188, 428, 192, 432)(189, 429, 239, 479)(190, 430, 230, 470)(191, 431, 231, 471)(193, 433, 234, 474)(194, 434, 235, 475)(195, 435, 228, 468)(196, 436, 225, 465)(197, 437, 226, 466)(198, 438, 227, 467)(199, 439, 224, 464)(200, 440, 221, 461)(201, 441, 222, 462)(202, 442, 223, 463)(203, 443, 240, 480)(204, 444, 232, 472)(205, 445, 229, 469)(207, 447, 236, 476)(208, 448, 233, 473)(209, 449, 216, 456)(210, 450, 215, 455)(211, 451, 214, 454)(212, 452, 217, 457)(218, 458, 237, 477)(219, 459, 238, 478)(481, 721, 483, 723, 488, 728, 484, 724)(482, 722, 485, 725, 491, 731, 486, 726)(487, 727, 493, 733, 504, 744, 494, 734)(489, 729, 496, 736, 509, 749, 497, 737)(490, 730, 498, 738, 512, 752, 499, 739)(492, 732, 501, 741, 517, 757, 502, 742)(495, 735, 506, 746, 523, 763, 507, 747)(500, 740, 514, 754, 528, 768, 515, 755)(503, 743, 519, 759, 510, 750, 520, 760)(505, 745, 521, 761, 508, 748, 522, 762)(511, 751, 524, 764, 518, 758, 525, 765)(513, 753, 526, 766, 516, 756, 527, 767)(529, 769, 537, 777, 532, 772, 538, 778)(530, 770, 539, 779, 531, 771, 540, 780)(533, 773, 541, 781, 536, 776, 542, 782)(534, 774, 543, 783, 535, 775, 544, 784)(545, 785, 553, 793, 548, 788, 554, 794)(546, 786, 555, 795, 547, 787, 556, 796)(549, 789, 605, 845, 552, 792, 608, 848)(550, 790, 606, 846, 551, 791, 607, 847)(557, 797, 614, 854, 576, 816, 615, 855)(558, 798, 617, 857, 571, 811, 618, 858)(559, 799, 619, 859, 585, 825, 620, 860)(560, 800, 621, 861, 584, 824, 622, 862)(561, 801, 623, 863, 581, 821, 624, 864)(562, 802, 625, 865, 580, 820, 626, 866)(563, 803, 613, 853, 565, 805, 627, 867)(564, 804, 628, 868, 596, 836, 629, 869)(566, 806, 616, 856, 568, 808, 630, 870)(567, 807, 631, 871, 591, 831, 632, 872)(569, 809, 633, 873, 573, 813, 634, 874)(570, 810, 635, 875, 572, 812, 636, 876)(574, 814, 638, 878, 578, 818, 639, 879)(575, 815, 640, 880, 577, 817, 641, 881)(579, 819, 643, 883, 582, 822, 642, 882)(583, 823, 644, 884, 586, 826, 637, 877)(587, 827, 645, 885, 590, 830, 646, 886)(588, 828, 647, 887, 589, 829, 648, 888)(592, 832, 649, 889, 595, 835, 650, 890)(593, 833, 651, 891, 594, 834, 652, 892)(597, 837, 653, 893, 600, 840, 654, 894)(598, 838, 655, 895, 599, 839, 656, 896)(601, 841, 657, 897, 604, 844, 658, 898)(602, 842, 659, 899, 603, 843, 660, 900)(609, 849, 665, 905, 612, 852, 666, 906)(610, 850, 667, 907, 611, 851, 668, 908)(661, 901, 717, 957, 663, 903, 718, 958)(662, 902, 719, 959, 664, 904, 720, 960)(669, 909, 711, 951, 698, 938, 710, 950)(670, 910, 703, 943, 685, 925, 702, 942)(671, 911, 701, 941, 684, 924, 704, 944)(672, 912, 715, 955, 693, 933, 714, 954)(673, 913, 707, 947, 688, 928, 706, 946)(674, 914, 705, 945, 687, 927, 708, 948)(675, 915, 697, 937, 678, 918, 694, 934)(676, 916, 695, 935, 677, 917, 696, 936)(679, 919, 692, 932, 682, 922, 689, 929)(680, 920, 690, 930, 681, 921, 691, 931)(683, 923, 709, 949, 699, 939, 712, 952)(686, 926, 713, 953, 700, 940, 716, 956)
	L = (1, 482)(2, 481)(3, 487)(4, 489)(5, 490)(6, 492)(7, 483)(8, 495)(9, 484)(10, 485)(11, 500)(12, 486)(13, 503)(14, 505)(15, 488)(16, 508)(17, 510)(18, 511)(19, 513)(20, 491)(21, 516)(22, 518)(23, 493)(24, 515)(25, 494)(26, 517)(27, 512)(28, 496)(29, 514)(30, 497)(31, 498)(32, 507)(33, 499)(34, 509)(35, 504)(36, 501)(37, 506)(38, 502)(39, 529)(40, 530)(41, 531)(42, 532)(43, 528)(44, 533)(45, 534)(46, 535)(47, 536)(48, 523)(49, 519)(50, 520)(51, 521)(52, 522)(53, 524)(54, 525)(55, 526)(56, 527)(57, 545)(58, 546)(59, 547)(60, 548)(61, 549)(62, 550)(63, 551)(64, 552)(65, 537)(66, 538)(67, 539)(68, 540)(69, 541)(70, 542)(71, 543)(72, 544)(73, 583)(74, 566)(75, 568)(76, 586)(77, 613)(78, 616)(79, 618)(80, 617)(81, 615)(82, 614)(83, 608)(84, 627)(85, 606)(86, 554)(87, 630)(88, 555)(89, 620)(90, 619)(91, 637)(92, 622)(93, 621)(94, 624)(95, 623)(96, 642)(97, 626)(98, 625)(99, 605)(100, 629)(101, 628)(102, 607)(103, 553)(104, 632)(105, 631)(106, 556)(107, 634)(108, 633)(109, 636)(110, 635)(111, 644)(112, 639)(113, 638)(114, 641)(115, 640)(116, 643)(117, 646)(118, 645)(119, 648)(120, 647)(121, 650)(122, 649)(123, 652)(124, 651)(125, 579)(126, 565)(127, 582)(128, 563)(129, 654)(130, 653)(131, 656)(132, 655)(133, 557)(134, 562)(135, 561)(136, 558)(137, 560)(138, 559)(139, 570)(140, 569)(141, 573)(142, 572)(143, 575)(144, 574)(145, 578)(146, 577)(147, 564)(148, 581)(149, 580)(150, 567)(151, 585)(152, 584)(153, 588)(154, 587)(155, 590)(156, 589)(157, 571)(158, 593)(159, 592)(160, 595)(161, 594)(162, 576)(163, 596)(164, 591)(165, 598)(166, 597)(167, 600)(168, 599)(169, 602)(170, 601)(171, 604)(172, 603)(173, 610)(174, 609)(175, 612)(176, 611)(177, 664)(178, 661)(179, 663)(180, 662)(181, 658)(182, 660)(183, 659)(184, 657)(185, 693)(186, 700)(187, 686)(188, 672)(189, 719)(190, 710)(191, 711)(192, 668)(193, 714)(194, 715)(195, 708)(196, 705)(197, 706)(198, 707)(199, 704)(200, 701)(201, 702)(202, 703)(203, 720)(204, 712)(205, 709)(206, 667)(207, 716)(208, 713)(209, 696)(210, 695)(211, 694)(212, 697)(213, 665)(214, 691)(215, 690)(216, 689)(217, 692)(218, 717)(219, 718)(220, 666)(221, 680)(222, 681)(223, 682)(224, 679)(225, 676)(226, 677)(227, 678)(228, 675)(229, 685)(230, 670)(231, 671)(232, 684)(233, 688)(234, 673)(235, 674)(236, 687)(237, 698)(238, 699)(239, 669)(240, 683)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 60, 2, 60 ), ( 2, 60, 2, 60, 2, 60, 2, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2328
Graph:: bipartite
	v = 180 e = 480 f = 248
	degree seq :: [ 4^120, 8^60 ]

E27.2326 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y2^2 * Y1^-1)^2, Y2^30 ]
Map::
	R = (1, 241, 2, 242, 6, 246, 4, 244)(3, 243, 9, 249, 21, 261, 11, 251)(5, 245, 13, 253, 18, 258, 7, 247)(8, 248, 19, 259, 31, 271, 15, 255)(10, 250, 23, 263, 37, 277, 20, 260)(12, 252, 16, 256, 32, 272, 27, 267)(14, 254, 26, 266, 44, 284, 28, 268)(17, 257, 34, 274, 51, 291, 33, 273)(22, 262, 30, 270, 48, 288, 39, 279)(24, 264, 38, 278, 49, 289, 41, 281)(25, 265, 40, 280, 50, 290, 36, 276)(29, 269, 35, 275, 52, 292, 45, 285)(42, 282, 57, 297, 65, 305, 55, 295)(43, 283, 58, 298, 73, 313, 59, 299)(46, 286, 61, 301, 67, 307, 53, 293)(47, 287, 63, 303, 69, 309, 54, 294)(56, 296, 71, 311, 81, 321, 66, 306)(60, 300, 75, 315, 87, 327, 72, 312)(62, 302, 68, 308, 83, 323, 77, 317)(64, 304, 78, 318, 93, 333, 79, 319)(70, 310, 85, 325, 99, 339, 84, 324)(74, 314, 82, 322, 97, 337, 89, 329)(76, 316, 88, 328, 98, 338, 90, 330)(80, 320, 86, 326, 100, 340, 94, 334)(91, 331, 105, 345, 113, 353, 103, 343)(92, 332, 106, 346, 121, 361, 107, 347)(95, 335, 109, 349, 115, 355, 101, 341)(96, 336, 111, 351, 117, 357, 102, 342)(104, 344, 119, 359, 129, 369, 114, 354)(108, 348, 123, 363, 135, 375, 120, 360)(110, 350, 116, 356, 131, 371, 125, 365)(112, 352, 126, 366, 141, 381, 127, 367)(118, 358, 133, 373, 147, 387, 132, 372)(122, 362, 130, 370, 145, 385, 137, 377)(124, 364, 136, 376, 146, 386, 138, 378)(128, 368, 134, 374, 148, 388, 142, 382)(139, 379, 153, 393, 161, 401, 151, 391)(140, 380, 154, 394, 169, 409, 155, 395)(143, 383, 157, 397, 163, 403, 149, 389)(144, 384, 159, 399, 165, 405, 150, 390)(152, 392, 167, 407, 177, 417, 162, 402)(156, 396, 171, 411, 183, 423, 168, 408)(158, 398, 164, 404, 179, 419, 173, 413)(160, 400, 174, 414, 189, 429, 175, 415)(166, 406, 181, 421, 195, 435, 180, 420)(170, 410, 178, 418, 193, 433, 185, 425)(172, 412, 184, 424, 194, 434, 186, 426)(176, 416, 182, 422, 196, 436, 190, 430)(187, 427, 201, 441, 209, 449, 199, 439)(188, 428, 202, 442, 217, 457, 203, 443)(191, 431, 205, 445, 211, 451, 197, 437)(192, 432, 207, 447, 213, 453, 198, 438)(200, 440, 215, 455, 224, 464, 210, 450)(204, 444, 219, 459, 230, 470, 216, 456)(206, 446, 212, 452, 226, 466, 221, 461)(208, 448, 222, 462, 234, 474, 223, 463)(214, 454, 228, 468, 237, 477, 227, 467)(218, 458, 225, 465, 235, 475, 231, 471)(220, 460, 229, 469, 236, 476, 232, 472)(233, 473, 239, 479, 240, 480, 238, 478)(481, 721, 483, 723, 490, 730, 504, 744, 523, 763, 540, 780, 556, 796, 572, 812, 588, 828, 604, 844, 620, 860, 636, 876, 652, 892, 668, 908, 684, 924, 700, 940, 688, 928, 672, 912, 656, 896, 640, 880, 624, 864, 608, 848, 592, 832, 576, 816, 560, 800, 544, 784, 527, 767, 509, 749, 494, 734, 485, 725)(482, 722, 487, 727, 497, 737, 515, 755, 534, 774, 550, 790, 566, 806, 582, 822, 598, 838, 614, 854, 630, 870, 646, 886, 662, 902, 678, 918, 694, 934, 709, 949, 696, 936, 680, 920, 664, 904, 648, 888, 632, 872, 616, 856, 600, 840, 584, 824, 568, 808, 552, 792, 536, 776, 518, 758, 500, 740, 488, 728)(484, 724, 492, 732, 506, 746, 525, 765, 542, 782, 558, 798, 574, 814, 590, 830, 606, 846, 622, 862, 638, 878, 654, 894, 670, 910, 686, 926, 702, 942, 712, 952, 698, 938, 682, 922, 666, 906, 650, 890, 634, 874, 618, 858, 602, 842, 586, 826, 570, 810, 554, 794, 538, 778, 521, 761, 502, 742, 489, 729)(486, 726, 495, 735, 510, 750, 529, 769, 546, 786, 562, 802, 578, 818, 594, 834, 610, 850, 626, 866, 642, 882, 658, 898, 674, 914, 690, 930, 705, 945, 716, 956, 707, 947, 692, 932, 676, 916, 660, 900, 644, 884, 628, 868, 612, 852, 596, 836, 580, 820, 564, 804, 548, 788, 532, 772, 513, 753, 496, 736)(491, 731, 505, 745, 493, 733, 508, 748, 526, 766, 543, 783, 559, 799, 575, 815, 591, 831, 607, 847, 623, 863, 639, 879, 655, 895, 671, 911, 687, 927, 703, 943, 713, 953, 699, 939, 683, 923, 667, 907, 651, 891, 635, 875, 619, 859, 603, 843, 587, 827, 571, 811, 555, 795, 539, 779, 522, 762, 503, 743)(498, 738, 516, 756, 499, 739, 517, 757, 535, 775, 551, 791, 567, 807, 583, 823, 599, 839, 615, 855, 631, 871, 647, 887, 663, 903, 679, 919, 695, 935, 710, 950, 718, 958, 708, 948, 693, 933, 677, 917, 661, 901, 645, 885, 629, 869, 613, 853, 597, 837, 581, 821, 565, 805, 549, 789, 533, 773, 514, 754)(501, 741, 519, 759, 537, 777, 553, 793, 569, 809, 585, 825, 601, 841, 617, 857, 633, 873, 649, 889, 665, 905, 681, 921, 697, 937, 711, 951, 719, 959, 714, 954, 701, 941, 685, 925, 669, 909, 653, 893, 637, 877, 621, 861, 605, 845, 589, 829, 573, 813, 557, 797, 541, 781, 524, 764, 507, 747, 520, 760)(511, 751, 530, 770, 512, 752, 531, 771, 547, 787, 563, 803, 579, 819, 595, 835, 611, 851, 627, 867, 643, 883, 659, 899, 675, 915, 691, 931, 706, 946, 717, 957, 720, 960, 715, 955, 704, 944, 689, 929, 673, 913, 657, 897, 641, 881, 625, 865, 609, 849, 593, 833, 577, 817, 561, 801, 545, 785, 528, 768)
	L = (1, 483)(2, 487)(3, 490)(4, 492)(5, 481)(6, 495)(7, 497)(8, 482)(9, 484)(10, 504)(11, 505)(12, 506)(13, 508)(14, 485)(15, 510)(16, 486)(17, 515)(18, 516)(19, 517)(20, 488)(21, 519)(22, 489)(23, 491)(24, 523)(25, 493)(26, 525)(27, 520)(28, 526)(29, 494)(30, 529)(31, 530)(32, 531)(33, 496)(34, 498)(35, 534)(36, 499)(37, 535)(38, 500)(39, 537)(40, 501)(41, 502)(42, 503)(43, 540)(44, 507)(45, 542)(46, 543)(47, 509)(48, 511)(49, 546)(50, 512)(51, 547)(52, 513)(53, 514)(54, 550)(55, 551)(56, 518)(57, 553)(58, 521)(59, 522)(60, 556)(61, 524)(62, 558)(63, 559)(64, 527)(65, 528)(66, 562)(67, 563)(68, 532)(69, 533)(70, 566)(71, 567)(72, 536)(73, 569)(74, 538)(75, 539)(76, 572)(77, 541)(78, 574)(79, 575)(80, 544)(81, 545)(82, 578)(83, 579)(84, 548)(85, 549)(86, 582)(87, 583)(88, 552)(89, 585)(90, 554)(91, 555)(92, 588)(93, 557)(94, 590)(95, 591)(96, 560)(97, 561)(98, 594)(99, 595)(100, 564)(101, 565)(102, 598)(103, 599)(104, 568)(105, 601)(106, 570)(107, 571)(108, 604)(109, 573)(110, 606)(111, 607)(112, 576)(113, 577)(114, 610)(115, 611)(116, 580)(117, 581)(118, 614)(119, 615)(120, 584)(121, 617)(122, 586)(123, 587)(124, 620)(125, 589)(126, 622)(127, 623)(128, 592)(129, 593)(130, 626)(131, 627)(132, 596)(133, 597)(134, 630)(135, 631)(136, 600)(137, 633)(138, 602)(139, 603)(140, 636)(141, 605)(142, 638)(143, 639)(144, 608)(145, 609)(146, 642)(147, 643)(148, 612)(149, 613)(150, 646)(151, 647)(152, 616)(153, 649)(154, 618)(155, 619)(156, 652)(157, 621)(158, 654)(159, 655)(160, 624)(161, 625)(162, 658)(163, 659)(164, 628)(165, 629)(166, 662)(167, 663)(168, 632)(169, 665)(170, 634)(171, 635)(172, 668)(173, 637)(174, 670)(175, 671)(176, 640)(177, 641)(178, 674)(179, 675)(180, 644)(181, 645)(182, 678)(183, 679)(184, 648)(185, 681)(186, 650)(187, 651)(188, 684)(189, 653)(190, 686)(191, 687)(192, 656)(193, 657)(194, 690)(195, 691)(196, 660)(197, 661)(198, 694)(199, 695)(200, 664)(201, 697)(202, 666)(203, 667)(204, 700)(205, 669)(206, 702)(207, 703)(208, 672)(209, 673)(210, 705)(211, 706)(212, 676)(213, 677)(214, 709)(215, 710)(216, 680)(217, 711)(218, 682)(219, 683)(220, 688)(221, 685)(222, 712)(223, 713)(224, 689)(225, 716)(226, 717)(227, 692)(228, 693)(229, 696)(230, 718)(231, 719)(232, 698)(233, 699)(234, 701)(235, 704)(236, 707)(237, 720)(238, 708)(239, 714)(240, 715)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E27.2327
Graph:: bipartite
	v = 68 e = 480 f = 360
	degree seq :: [ 8^60, 60^8 ]

E27.2327 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3^-1 * Y2 * Y3^-2)^2, Y3^12 * Y2 * Y3^-18 * Y2, (Y3^-1 * Y1^-1)^30 ]
Map:: polytopal
	R = (1, 241)(2, 242)(3, 243)(4, 244)(5, 245)(6, 246)(7, 247)(8, 248)(9, 249)(10, 250)(11, 251)(12, 252)(13, 253)(14, 254)(15, 255)(16, 256)(17, 257)(18, 258)(19, 259)(20, 260)(21, 261)(22, 262)(23, 263)(24, 264)(25, 265)(26, 266)(27, 267)(28, 268)(29, 269)(30, 270)(31, 271)(32, 272)(33, 273)(34, 274)(35, 275)(36, 276)(37, 277)(38, 278)(39, 279)(40, 280)(41, 281)(42, 282)(43, 283)(44, 284)(45, 285)(46, 286)(47, 287)(48, 288)(49, 289)(50, 290)(51, 291)(52, 292)(53, 293)(54, 294)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 300)(61, 301)(62, 302)(63, 303)(64, 304)(65, 305)(66, 306)(67, 307)(68, 308)(69, 309)(70, 310)(71, 311)(72, 312)(73, 313)(74, 314)(75, 315)(76, 316)(77, 317)(78, 318)(79, 319)(80, 320)(81, 321)(82, 322)(83, 323)(84, 324)(85, 325)(86, 326)(87, 327)(88, 328)(89, 329)(90, 330)(91, 331)(92, 332)(93, 333)(94, 334)(95, 335)(96, 336)(97, 337)(98, 338)(99, 339)(100, 340)(101, 341)(102, 342)(103, 343)(104, 344)(105, 345)(106, 346)(107, 347)(108, 348)(109, 349)(110, 350)(111, 351)(112, 352)(113, 353)(114, 354)(115, 355)(116, 356)(117, 357)(118, 358)(119, 359)(120, 360)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)(481, 721, 482, 722)(483, 723, 487, 727)(484, 724, 489, 729)(485, 725, 491, 731)(486, 726, 493, 733)(488, 728, 497, 737)(490, 730, 501, 741)(492, 732, 505, 745)(494, 734, 509, 749)(495, 735, 508, 748)(496, 736, 512, 752)(498, 738, 510, 750)(499, 739, 517, 757)(500, 740, 503, 743)(502, 742, 506, 746)(504, 744, 522, 762)(507, 747, 527, 767)(511, 751, 531, 771)(513, 753, 528, 768)(514, 754, 533, 773)(515, 755, 529, 769)(516, 756, 534, 774)(518, 758, 523, 763)(519, 759, 525, 765)(520, 760, 538, 778)(521, 761, 541, 781)(524, 764, 543, 783)(526, 766, 544, 784)(530, 770, 548, 788)(532, 772, 547, 787)(535, 775, 552, 792)(536, 776, 554, 794)(537, 777, 542, 782)(539, 779, 556, 796)(540, 780, 558, 798)(545, 785, 561, 801)(546, 786, 563, 803)(549, 789, 565, 805)(550, 790, 567, 807)(551, 791, 560, 800)(553, 793, 569, 809)(555, 795, 568, 808)(557, 797, 573, 813)(559, 799, 564, 804)(562, 802, 577, 817)(566, 806, 581, 821)(570, 810, 582, 822)(571, 811, 583, 823)(572, 812, 586, 826)(574, 814, 578, 818)(575, 815, 579, 819)(576, 816, 590, 830)(580, 820, 594, 834)(584, 824, 598, 838)(585, 825, 597, 837)(587, 827, 601, 841)(588, 828, 603, 843)(589, 829, 593, 833)(591, 831, 605, 845)(592, 832, 607, 847)(595, 835, 609, 849)(596, 836, 611, 851)(599, 839, 613, 853)(600, 840, 615, 855)(602, 842, 617, 857)(604, 844, 616, 856)(606, 846, 621, 861)(608, 848, 612, 852)(610, 850, 625, 865)(614, 854, 629, 869)(618, 858, 630, 870)(619, 859, 631, 871)(620, 860, 634, 874)(622, 862, 626, 866)(623, 863, 627, 867)(624, 864, 638, 878)(628, 868, 642, 882)(632, 872, 646, 886)(633, 873, 645, 885)(635, 875, 649, 889)(636, 876, 651, 891)(637, 877, 641, 881)(639, 879, 653, 893)(640, 880, 655, 895)(643, 883, 657, 897)(644, 884, 659, 899)(647, 887, 661, 901)(648, 888, 663, 903)(650, 890, 665, 905)(652, 892, 664, 904)(654, 894, 669, 909)(656, 896, 660, 900)(658, 898, 673, 913)(662, 902, 677, 917)(666, 906, 678, 918)(667, 907, 679, 919)(668, 908, 682, 922)(670, 910, 674, 914)(671, 911, 675, 915)(672, 912, 686, 926)(676, 916, 690, 930)(680, 920, 694, 934)(681, 921, 693, 933)(683, 923, 697, 937)(684, 924, 699, 939)(685, 925, 689, 929)(687, 927, 701, 941)(688, 928, 703, 943)(691, 931, 704, 944)(692, 932, 706, 946)(695, 935, 708, 948)(696, 936, 710, 950)(698, 938, 711, 951)(700, 940, 707, 947)(702, 942, 714, 954)(705, 945, 715, 955)(709, 949, 718, 958)(712, 952, 717, 957)(713, 953, 716, 956)(719, 959, 720, 960)
	L = (1, 483)(2, 485)(3, 488)(4, 481)(5, 492)(6, 482)(7, 495)(8, 498)(9, 499)(10, 484)(11, 503)(12, 506)(13, 507)(14, 486)(15, 511)(16, 487)(17, 514)(18, 516)(19, 518)(20, 489)(21, 519)(22, 490)(23, 521)(24, 491)(25, 524)(26, 526)(27, 528)(28, 493)(29, 529)(30, 494)(31, 501)(32, 532)(33, 496)(34, 500)(35, 497)(36, 536)(37, 531)(38, 538)(39, 539)(40, 502)(41, 509)(42, 542)(43, 504)(44, 508)(45, 505)(46, 546)(47, 541)(48, 548)(49, 549)(50, 510)(51, 551)(52, 552)(53, 512)(54, 513)(55, 515)(56, 555)(57, 517)(58, 557)(59, 558)(60, 520)(61, 560)(62, 561)(63, 522)(64, 523)(65, 525)(66, 564)(67, 527)(68, 566)(69, 567)(70, 530)(71, 533)(72, 569)(73, 534)(74, 535)(75, 572)(76, 537)(77, 574)(78, 575)(79, 540)(80, 543)(81, 577)(82, 544)(83, 545)(84, 580)(85, 547)(86, 582)(87, 583)(88, 550)(89, 585)(90, 553)(91, 554)(92, 588)(93, 556)(94, 590)(95, 591)(96, 559)(97, 593)(98, 562)(99, 563)(100, 596)(101, 565)(102, 598)(103, 599)(104, 568)(105, 601)(106, 570)(107, 571)(108, 604)(109, 573)(110, 606)(111, 607)(112, 576)(113, 609)(114, 578)(115, 579)(116, 612)(117, 581)(118, 614)(119, 615)(120, 584)(121, 617)(122, 586)(123, 587)(124, 620)(125, 589)(126, 622)(127, 623)(128, 592)(129, 625)(130, 594)(131, 595)(132, 628)(133, 597)(134, 630)(135, 631)(136, 600)(137, 633)(138, 602)(139, 603)(140, 636)(141, 605)(142, 638)(143, 639)(144, 608)(145, 641)(146, 610)(147, 611)(148, 644)(149, 613)(150, 646)(151, 647)(152, 616)(153, 649)(154, 618)(155, 619)(156, 652)(157, 621)(158, 654)(159, 655)(160, 624)(161, 657)(162, 626)(163, 627)(164, 660)(165, 629)(166, 662)(167, 663)(168, 632)(169, 665)(170, 634)(171, 635)(172, 668)(173, 637)(174, 670)(175, 671)(176, 640)(177, 673)(178, 642)(179, 643)(180, 676)(181, 645)(182, 678)(183, 679)(184, 648)(185, 681)(186, 650)(187, 651)(188, 684)(189, 653)(190, 686)(191, 687)(192, 656)(193, 689)(194, 658)(195, 659)(196, 692)(197, 661)(198, 694)(199, 695)(200, 664)(201, 697)(202, 666)(203, 667)(204, 700)(205, 669)(206, 702)(207, 703)(208, 672)(209, 704)(210, 674)(211, 675)(212, 707)(213, 677)(214, 709)(215, 710)(216, 680)(217, 711)(218, 682)(219, 683)(220, 688)(221, 685)(222, 713)(223, 712)(224, 715)(225, 690)(226, 691)(227, 696)(228, 693)(229, 717)(230, 716)(231, 719)(232, 698)(233, 699)(234, 701)(235, 720)(236, 705)(237, 706)(238, 708)(239, 714)(240, 718)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 8, 60 ), ( 8, 60, 8, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2326
Graph:: simple bipartite
	v = 360 e = 480 f = 68
	degree seq :: [ 2^240, 4^120 ]

E27.2328 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y1^30 ]
Map:: polytopal
	R = (1, 241, 2, 242, 5, 245, 11, 251, 23, 263, 41, 281, 61, 301, 80, 320, 97, 337, 113, 353, 129, 369, 145, 385, 161, 401, 177, 417, 193, 433, 209, 449, 208, 448, 192, 432, 176, 416, 160, 400, 144, 384, 128, 368, 112, 352, 96, 336, 79, 319, 60, 300, 40, 280, 22, 262, 10, 250, 4, 244)(3, 243, 7, 247, 15, 255, 31, 271, 51, 291, 71, 311, 89, 329, 105, 345, 121, 361, 137, 377, 153, 393, 169, 409, 185, 425, 201, 441, 217, 457, 224, 464, 213, 453, 195, 435, 178, 418, 165, 405, 147, 387, 130, 370, 117, 357, 99, 339, 81, 321, 65, 305, 43, 283, 24, 264, 18, 258, 8, 248)(6, 246, 13, 253, 27, 267, 21, 261, 39, 279, 59, 299, 78, 318, 95, 335, 111, 351, 127, 367, 143, 383, 159, 399, 175, 415, 191, 431, 207, 447, 223, 463, 227, 467, 211, 451, 194, 434, 181, 421, 163, 403, 146, 386, 133, 373, 115, 355, 98, 338, 84, 324, 63, 303, 42, 282, 30, 270, 14, 254)(9, 249, 19, 259, 37, 277, 57, 297, 76, 316, 93, 333, 109, 349, 125, 365, 141, 381, 157, 397, 173, 413, 189, 429, 205, 445, 221, 461, 225, 465, 210, 450, 197, 437, 179, 419, 162, 402, 149, 389, 131, 371, 114, 354, 101, 341, 82, 322, 62, 302, 46, 286, 26, 266, 12, 252, 25, 265, 20, 260)(16, 256, 33, 273, 53, 293, 36, 276, 45, 285, 67, 307, 86, 326, 100, 340, 118, 358, 135, 375, 148, 388, 166, 406, 183, 423, 196, 436, 214, 454, 229, 469, 235, 475, 232, 472, 218, 458, 204, 444, 187, 427, 170, 410, 156, 396, 139, 379, 122, 362, 108, 348, 91, 331, 72, 312, 55, 295, 34, 274)(17, 257, 35, 275, 50, 290, 64, 304, 85, 325, 103, 343, 116, 356, 134, 374, 151, 391, 164, 404, 182, 422, 199, 439, 212, 452, 228, 468, 237, 477, 231, 471, 219, 459, 202, 442, 186, 426, 171, 411, 154, 394, 138, 378, 123, 363, 106, 346, 90, 330, 73, 313, 52, 292, 32, 272, 48, 288, 28, 268)(29, 269, 49, 289, 68, 308, 83, 323, 102, 342, 119, 359, 132, 372, 150, 390, 167, 407, 180, 420, 198, 438, 215, 455, 226, 466, 236, 476, 234, 474, 222, 462, 206, 446, 190, 430, 174, 414, 158, 398, 142, 382, 126, 366, 110, 350, 94, 334, 77, 317, 58, 298, 38, 278, 47, 287, 66, 306, 44, 284)(54, 294, 75, 315, 92, 332, 107, 347, 124, 364, 140, 380, 155, 395, 172, 412, 188, 428, 203, 443, 220, 460, 233, 473, 239, 479, 240, 480, 238, 478, 230, 470, 216, 456, 200, 440, 184, 424, 168, 408, 152, 392, 136, 376, 120, 360, 104, 344, 88, 328, 70, 310, 56, 296, 74, 314, 87, 327, 69, 309)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960)
	L = (1, 483)(2, 486)(3, 481)(4, 489)(5, 492)(6, 482)(7, 496)(8, 497)(9, 484)(10, 501)(11, 504)(12, 485)(13, 508)(14, 509)(15, 512)(16, 487)(17, 488)(18, 516)(19, 518)(20, 513)(21, 490)(22, 511)(23, 522)(24, 491)(25, 524)(26, 525)(27, 527)(28, 493)(29, 494)(30, 530)(31, 502)(32, 495)(33, 500)(34, 534)(35, 536)(36, 498)(37, 535)(38, 499)(39, 532)(40, 537)(41, 542)(42, 503)(43, 544)(44, 505)(45, 506)(46, 548)(47, 507)(48, 549)(49, 550)(50, 510)(51, 552)(52, 519)(53, 554)(54, 514)(55, 517)(56, 515)(57, 520)(58, 555)(59, 557)(60, 558)(61, 561)(62, 521)(63, 563)(64, 523)(65, 566)(66, 567)(67, 568)(68, 526)(69, 528)(70, 529)(71, 570)(72, 531)(73, 572)(74, 533)(75, 538)(76, 574)(77, 539)(78, 540)(79, 569)(80, 578)(81, 541)(82, 580)(83, 543)(84, 583)(85, 584)(86, 545)(87, 546)(88, 547)(89, 559)(90, 551)(91, 587)(92, 553)(93, 588)(94, 556)(95, 586)(96, 589)(97, 594)(98, 560)(99, 596)(100, 562)(101, 599)(102, 600)(103, 564)(104, 565)(105, 602)(106, 575)(107, 571)(108, 573)(109, 576)(110, 604)(111, 606)(112, 607)(113, 610)(114, 577)(115, 612)(116, 579)(117, 615)(118, 616)(119, 581)(120, 582)(121, 618)(122, 585)(123, 620)(124, 590)(125, 622)(126, 591)(127, 592)(128, 617)(129, 626)(130, 593)(131, 628)(132, 595)(133, 631)(134, 632)(135, 597)(136, 598)(137, 608)(138, 601)(139, 635)(140, 603)(141, 636)(142, 605)(143, 634)(144, 637)(145, 642)(146, 609)(147, 644)(148, 611)(149, 647)(150, 648)(151, 613)(152, 614)(153, 650)(154, 623)(155, 619)(156, 621)(157, 624)(158, 652)(159, 654)(160, 655)(161, 658)(162, 625)(163, 660)(164, 627)(165, 663)(166, 664)(167, 629)(168, 630)(169, 666)(170, 633)(171, 668)(172, 638)(173, 670)(174, 639)(175, 640)(176, 665)(177, 674)(178, 641)(179, 676)(180, 643)(181, 679)(182, 680)(183, 645)(184, 646)(185, 656)(186, 649)(187, 683)(188, 651)(189, 684)(190, 653)(191, 682)(192, 685)(193, 690)(194, 657)(195, 692)(196, 659)(197, 695)(198, 696)(199, 661)(200, 662)(201, 698)(202, 671)(203, 667)(204, 669)(205, 672)(206, 700)(207, 702)(208, 703)(209, 704)(210, 673)(211, 706)(212, 675)(213, 709)(214, 710)(215, 677)(216, 678)(217, 711)(218, 681)(219, 713)(220, 686)(221, 714)(222, 687)(223, 688)(224, 689)(225, 715)(226, 691)(227, 717)(228, 718)(229, 693)(230, 694)(231, 697)(232, 719)(233, 699)(234, 701)(235, 705)(236, 720)(237, 707)(238, 708)(239, 712)(240, 716)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2325
Graph:: simple bipartite
	v = 248 e = 480 f = 180
	degree seq :: [ 2^240, 60^8 ]

E27.2329 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, (Y2^-2 * Y1 * Y2^-1)^2, Y2^30 ]
Map::
	R = (1, 241, 2, 242)(3, 243, 7, 247)(4, 244, 9, 249)(5, 245, 11, 251)(6, 246, 13, 253)(8, 248, 17, 257)(10, 250, 21, 261)(12, 252, 25, 265)(14, 254, 29, 269)(15, 255, 28, 268)(16, 256, 32, 272)(18, 258, 30, 270)(19, 259, 37, 277)(20, 260, 23, 263)(22, 262, 26, 266)(24, 264, 42, 282)(27, 267, 47, 287)(31, 271, 51, 291)(33, 273, 48, 288)(34, 274, 53, 293)(35, 275, 49, 289)(36, 276, 54, 294)(38, 278, 43, 283)(39, 279, 45, 285)(40, 280, 58, 298)(41, 281, 61, 301)(44, 284, 63, 303)(46, 286, 64, 304)(50, 290, 68, 308)(52, 292, 67, 307)(55, 295, 72, 312)(56, 296, 74, 314)(57, 297, 62, 302)(59, 299, 76, 316)(60, 300, 78, 318)(65, 305, 81, 321)(66, 306, 83, 323)(69, 309, 85, 325)(70, 310, 87, 327)(71, 311, 80, 320)(73, 313, 89, 329)(75, 315, 88, 328)(77, 317, 93, 333)(79, 319, 84, 324)(82, 322, 97, 337)(86, 326, 101, 341)(90, 330, 102, 342)(91, 331, 103, 343)(92, 332, 106, 346)(94, 334, 98, 338)(95, 335, 99, 339)(96, 336, 110, 350)(100, 340, 114, 354)(104, 344, 118, 358)(105, 345, 117, 357)(107, 347, 121, 361)(108, 348, 123, 363)(109, 349, 113, 353)(111, 351, 125, 365)(112, 352, 127, 367)(115, 355, 129, 369)(116, 356, 131, 371)(119, 359, 133, 373)(120, 360, 135, 375)(122, 362, 137, 377)(124, 364, 136, 376)(126, 366, 141, 381)(128, 368, 132, 372)(130, 370, 145, 385)(134, 374, 149, 389)(138, 378, 150, 390)(139, 379, 151, 391)(140, 380, 154, 394)(142, 382, 146, 386)(143, 383, 147, 387)(144, 384, 158, 398)(148, 388, 162, 402)(152, 392, 166, 406)(153, 393, 165, 405)(155, 395, 169, 409)(156, 396, 171, 411)(157, 397, 161, 401)(159, 399, 173, 413)(160, 400, 175, 415)(163, 403, 177, 417)(164, 404, 179, 419)(167, 407, 181, 421)(168, 408, 183, 423)(170, 410, 185, 425)(172, 412, 184, 424)(174, 414, 189, 429)(176, 416, 180, 420)(178, 418, 193, 433)(182, 422, 197, 437)(186, 426, 198, 438)(187, 427, 199, 439)(188, 428, 202, 442)(190, 430, 194, 434)(191, 431, 195, 435)(192, 432, 206, 446)(196, 436, 210, 450)(200, 440, 214, 454)(201, 441, 213, 453)(203, 443, 217, 457)(204, 444, 219, 459)(205, 445, 209, 449)(207, 447, 221, 461)(208, 448, 223, 463)(211, 451, 224, 464)(212, 452, 226, 466)(215, 455, 228, 468)(216, 456, 230, 470)(218, 458, 231, 471)(220, 460, 227, 467)(222, 462, 234, 474)(225, 465, 235, 475)(229, 469, 238, 478)(232, 472, 237, 477)(233, 473, 236, 476)(239, 479, 240, 480)(481, 721, 483, 723, 488, 728, 498, 738, 516, 756, 536, 776, 555, 795, 572, 812, 588, 828, 604, 844, 620, 860, 636, 876, 652, 892, 668, 908, 684, 924, 700, 940, 688, 928, 672, 912, 656, 896, 640, 880, 624, 864, 608, 848, 592, 832, 576, 816, 559, 799, 540, 780, 520, 760, 502, 742, 490, 730, 484, 724)(482, 722, 485, 725, 492, 732, 506, 746, 526, 766, 546, 786, 564, 804, 580, 820, 596, 836, 612, 852, 628, 868, 644, 884, 660, 900, 676, 916, 692, 932, 707, 947, 696, 936, 680, 920, 664, 904, 648, 888, 632, 872, 616, 856, 600, 840, 584, 824, 568, 808, 550, 790, 530, 770, 510, 750, 494, 734, 486, 726)(487, 727, 495, 735, 511, 751, 501, 741, 519, 759, 539, 779, 558, 798, 575, 815, 591, 831, 607, 847, 623, 863, 639, 879, 655, 895, 671, 911, 687, 927, 703, 943, 712, 952, 698, 938, 682, 922, 666, 906, 650, 890, 634, 874, 618, 858, 602, 842, 586, 826, 570, 810, 553, 793, 534, 774, 513, 753, 496, 736)(489, 729, 499, 739, 518, 758, 538, 778, 557, 797, 574, 814, 590, 830, 606, 846, 622, 862, 638, 878, 654, 894, 670, 910, 686, 926, 702, 942, 713, 953, 699, 939, 683, 923, 667, 907, 651, 891, 635, 875, 619, 859, 603, 843, 587, 827, 571, 811, 554, 794, 535, 775, 515, 755, 497, 737, 514, 754, 500, 740)(491, 731, 503, 743, 521, 761, 509, 749, 529, 769, 549, 789, 567, 807, 583, 823, 599, 839, 615, 855, 631, 871, 647, 887, 663, 903, 679, 919, 695, 935, 710, 950, 716, 956, 705, 945, 690, 930, 674, 914, 658, 898, 642, 882, 626, 866, 610, 850, 594, 834, 578, 818, 562, 802, 544, 784, 523, 763, 504, 744)(493, 733, 507, 747, 528, 768, 548, 788, 566, 806, 582, 822, 598, 838, 614, 854, 630, 870, 646, 886, 662, 902, 678, 918, 694, 934, 709, 949, 717, 957, 706, 946, 691, 931, 675, 915, 659, 899, 643, 883, 627, 867, 611, 851, 595, 835, 579, 819, 563, 803, 545, 785, 525, 765, 505, 745, 524, 764, 508, 748)(512, 752, 532, 772, 552, 792, 569, 809, 585, 825, 601, 841, 617, 857, 633, 873, 649, 889, 665, 905, 681, 921, 697, 937, 711, 951, 719, 959, 714, 954, 701, 941, 685, 925, 669, 909, 653, 893, 637, 877, 621, 861, 605, 845, 589, 829, 573, 813, 556, 796, 537, 777, 517, 757, 531, 771, 551, 791, 533, 773)(522, 762, 542, 782, 561, 801, 577, 817, 593, 833, 609, 849, 625, 865, 641, 881, 657, 897, 673, 913, 689, 929, 704, 944, 715, 955, 720, 960, 718, 958, 708, 948, 693, 933, 677, 917, 661, 901, 645, 885, 629, 869, 613, 853, 597, 837, 581, 821, 565, 805, 547, 787, 527, 767, 541, 781, 560, 800, 543, 783)
	L = (1, 482)(2, 481)(3, 487)(4, 489)(5, 491)(6, 493)(7, 483)(8, 497)(9, 484)(10, 501)(11, 485)(12, 505)(13, 486)(14, 509)(15, 508)(16, 512)(17, 488)(18, 510)(19, 517)(20, 503)(21, 490)(22, 506)(23, 500)(24, 522)(25, 492)(26, 502)(27, 527)(28, 495)(29, 494)(30, 498)(31, 531)(32, 496)(33, 528)(34, 533)(35, 529)(36, 534)(37, 499)(38, 523)(39, 525)(40, 538)(41, 541)(42, 504)(43, 518)(44, 543)(45, 519)(46, 544)(47, 507)(48, 513)(49, 515)(50, 548)(51, 511)(52, 547)(53, 514)(54, 516)(55, 552)(56, 554)(57, 542)(58, 520)(59, 556)(60, 558)(61, 521)(62, 537)(63, 524)(64, 526)(65, 561)(66, 563)(67, 532)(68, 530)(69, 565)(70, 567)(71, 560)(72, 535)(73, 569)(74, 536)(75, 568)(76, 539)(77, 573)(78, 540)(79, 564)(80, 551)(81, 545)(82, 577)(83, 546)(84, 559)(85, 549)(86, 581)(87, 550)(88, 555)(89, 553)(90, 582)(91, 583)(92, 586)(93, 557)(94, 578)(95, 579)(96, 590)(97, 562)(98, 574)(99, 575)(100, 594)(101, 566)(102, 570)(103, 571)(104, 598)(105, 597)(106, 572)(107, 601)(108, 603)(109, 593)(110, 576)(111, 605)(112, 607)(113, 589)(114, 580)(115, 609)(116, 611)(117, 585)(118, 584)(119, 613)(120, 615)(121, 587)(122, 617)(123, 588)(124, 616)(125, 591)(126, 621)(127, 592)(128, 612)(129, 595)(130, 625)(131, 596)(132, 608)(133, 599)(134, 629)(135, 600)(136, 604)(137, 602)(138, 630)(139, 631)(140, 634)(141, 606)(142, 626)(143, 627)(144, 638)(145, 610)(146, 622)(147, 623)(148, 642)(149, 614)(150, 618)(151, 619)(152, 646)(153, 645)(154, 620)(155, 649)(156, 651)(157, 641)(158, 624)(159, 653)(160, 655)(161, 637)(162, 628)(163, 657)(164, 659)(165, 633)(166, 632)(167, 661)(168, 663)(169, 635)(170, 665)(171, 636)(172, 664)(173, 639)(174, 669)(175, 640)(176, 660)(177, 643)(178, 673)(179, 644)(180, 656)(181, 647)(182, 677)(183, 648)(184, 652)(185, 650)(186, 678)(187, 679)(188, 682)(189, 654)(190, 674)(191, 675)(192, 686)(193, 658)(194, 670)(195, 671)(196, 690)(197, 662)(198, 666)(199, 667)(200, 694)(201, 693)(202, 668)(203, 697)(204, 699)(205, 689)(206, 672)(207, 701)(208, 703)(209, 685)(210, 676)(211, 704)(212, 706)(213, 681)(214, 680)(215, 708)(216, 710)(217, 683)(218, 711)(219, 684)(220, 707)(221, 687)(222, 714)(223, 688)(224, 691)(225, 715)(226, 692)(227, 700)(228, 695)(229, 718)(230, 696)(231, 698)(232, 717)(233, 716)(234, 702)(235, 705)(236, 713)(237, 712)(238, 709)(239, 720)(240, 719)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E27.2330
Graph:: bipartite
	v = 128 e = 480 f = 300
	degree seq :: [ 4^120, 60^8 ]

E27.2330 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 30})
Quotient :: dipole
Aut^+ = C2 x ((C5 x A4) : C2) (small group id <240, 197>)
Aut   = $<480, 1199>$ (small group id <480, 1199>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y1^-1)^2, (Y3 * Y2^-1)^30 ]
Map:: polytopal
	R = (1, 241, 2, 242, 6, 246, 4, 244)(3, 243, 9, 249, 21, 261, 11, 251)(5, 245, 13, 253, 18, 258, 7, 247)(8, 248, 19, 259, 31, 271, 15, 255)(10, 250, 23, 263, 37, 277, 20, 260)(12, 252, 16, 256, 32, 272, 27, 267)(14, 254, 26, 266, 44, 284, 28, 268)(17, 257, 34, 274, 51, 291, 33, 273)(22, 262, 30, 270, 48, 288, 39, 279)(24, 264, 38, 278, 49, 289, 41, 281)(25, 265, 40, 280, 50, 290, 36, 276)(29, 269, 35, 275, 52, 292, 45, 285)(42, 282, 57, 297, 65, 305, 55, 295)(43, 283, 58, 298, 73, 313, 59, 299)(46, 286, 61, 301, 67, 307, 53, 293)(47, 287, 63, 303, 69, 309, 54, 294)(56, 296, 71, 311, 81, 321, 66, 306)(60, 300, 75, 315, 87, 327, 72, 312)(62, 302, 68, 308, 83, 323, 77, 317)(64, 304, 78, 318, 93, 333, 79, 319)(70, 310, 85, 325, 99, 339, 84, 324)(74, 314, 82, 322, 97, 337, 89, 329)(76, 316, 88, 328, 98, 338, 90, 330)(80, 320, 86, 326, 100, 340, 94, 334)(91, 331, 105, 345, 113, 353, 103, 343)(92, 332, 106, 346, 121, 361, 107, 347)(95, 335, 109, 349, 115, 355, 101, 341)(96, 336, 111, 351, 117, 357, 102, 342)(104, 344, 119, 359, 129, 369, 114, 354)(108, 348, 123, 363, 135, 375, 120, 360)(110, 350, 116, 356, 131, 371, 125, 365)(112, 352, 126, 366, 141, 381, 127, 367)(118, 358, 133, 373, 147, 387, 132, 372)(122, 362, 130, 370, 145, 385, 137, 377)(124, 364, 136, 376, 146, 386, 138, 378)(128, 368, 134, 374, 148, 388, 142, 382)(139, 379, 153, 393, 161, 401, 151, 391)(140, 380, 154, 394, 169, 409, 155, 395)(143, 383, 157, 397, 163, 403, 149, 389)(144, 384, 159, 399, 165, 405, 150, 390)(152, 392, 167, 407, 177, 417, 162, 402)(156, 396, 171, 411, 183, 423, 168, 408)(158, 398, 164, 404, 179, 419, 173, 413)(160, 400, 174, 414, 189, 429, 175, 415)(166, 406, 181, 421, 195, 435, 180, 420)(170, 410, 178, 418, 193, 433, 185, 425)(172, 412, 184, 424, 194, 434, 186, 426)(176, 416, 182, 422, 196, 436, 190, 430)(187, 427, 201, 441, 209, 449, 199, 439)(188, 428, 202, 442, 217, 457, 203, 443)(191, 431, 205, 445, 211, 451, 197, 437)(192, 432, 207, 447, 213, 453, 198, 438)(200, 440, 215, 455, 224, 464, 210, 450)(204, 444, 219, 459, 230, 470, 216, 456)(206, 446, 212, 452, 226, 466, 221, 461)(208, 448, 222, 462, 234, 474, 223, 463)(214, 454, 228, 468, 237, 477, 227, 467)(218, 458, 225, 465, 235, 475, 231, 471)(220, 460, 229, 469, 236, 476, 232, 472)(233, 473, 239, 479, 240, 480, 238, 478)(481, 721)(482, 722)(483, 723)(484, 724)(485, 725)(486, 726)(487, 727)(488, 728)(489, 729)(490, 730)(491, 731)(492, 732)(493, 733)(494, 734)(495, 735)(496, 736)(497, 737)(498, 738)(499, 739)(500, 740)(501, 741)(502, 742)(503, 743)(504, 744)(505, 745)(506, 746)(507, 747)(508, 748)(509, 749)(510, 750)(511, 751)(512, 752)(513, 753)(514, 754)(515, 755)(516, 756)(517, 757)(518, 758)(519, 759)(520, 760)(521, 761)(522, 762)(523, 763)(524, 764)(525, 765)(526, 766)(527, 767)(528, 768)(529, 769)(530, 770)(531, 771)(532, 772)(533, 773)(534, 774)(535, 775)(536, 776)(537, 777)(538, 778)(539, 779)(540, 780)(541, 781)(542, 782)(543, 783)(544, 784)(545, 785)(546, 786)(547, 787)(548, 788)(549, 789)(550, 790)(551, 791)(552, 792)(553, 793)(554, 794)(555, 795)(556, 796)(557, 797)(558, 798)(559, 799)(560, 800)(561, 801)(562, 802)(563, 803)(564, 804)(565, 805)(566, 806)(567, 807)(568, 808)(569, 809)(570, 810)(571, 811)(572, 812)(573, 813)(574, 814)(575, 815)(576, 816)(577, 817)(578, 818)(579, 819)(580, 820)(581, 821)(582, 822)(583, 823)(584, 824)(585, 825)(586, 826)(587, 827)(588, 828)(589, 829)(590, 830)(591, 831)(592, 832)(593, 833)(594, 834)(595, 835)(596, 836)(597, 837)(598, 838)(599, 839)(600, 840)(601, 841)(602, 842)(603, 843)(604, 844)(605, 845)(606, 846)(607, 847)(608, 848)(609, 849)(610, 850)(611, 851)(612, 852)(613, 853)(614, 854)(615, 855)(616, 856)(617, 857)(618, 858)(619, 859)(620, 860)(621, 861)(622, 862)(623, 863)(624, 864)(625, 865)(626, 866)(627, 867)(628, 868)(629, 869)(630, 870)(631, 871)(632, 872)(633, 873)(634, 874)(635, 875)(636, 876)(637, 877)(638, 878)(639, 879)(640, 880)(641, 881)(642, 882)(643, 883)(644, 884)(645, 885)(646, 886)(647, 887)(648, 888)(649, 889)(650, 890)(651, 891)(652, 892)(653, 893)(654, 894)(655, 895)(656, 896)(657, 897)(658, 898)(659, 899)(660, 900)(661, 901)(662, 902)(663, 903)(664, 904)(665, 905)(666, 906)(667, 907)(668, 908)(669, 909)(670, 910)(671, 911)(672, 912)(673, 913)(674, 914)(675, 915)(676, 916)(677, 917)(678, 918)(679, 919)(680, 920)(681, 921)(682, 922)(683, 923)(684, 924)(685, 925)(686, 926)(687, 927)(688, 928)(689, 929)(690, 930)(691, 931)(692, 932)(693, 933)(694, 934)(695, 935)(696, 936)(697, 937)(698, 938)(699, 939)(700, 940)(701, 941)(702, 942)(703, 943)(704, 944)(705, 945)(706, 946)(707, 947)(708, 948)(709, 949)(710, 950)(711, 951)(712, 952)(713, 953)(714, 954)(715, 955)(716, 956)(717, 957)(718, 958)(719, 959)(720, 960)
	L = (1, 483)(2, 487)(3, 490)(4, 492)(5, 481)(6, 495)(7, 497)(8, 482)(9, 484)(10, 504)(11, 505)(12, 506)(13, 508)(14, 485)(15, 510)(16, 486)(17, 515)(18, 516)(19, 517)(20, 488)(21, 519)(22, 489)(23, 491)(24, 523)(25, 493)(26, 525)(27, 520)(28, 526)(29, 494)(30, 529)(31, 530)(32, 531)(33, 496)(34, 498)(35, 534)(36, 499)(37, 535)(38, 500)(39, 537)(40, 501)(41, 502)(42, 503)(43, 540)(44, 507)(45, 542)(46, 543)(47, 509)(48, 511)(49, 546)(50, 512)(51, 547)(52, 513)(53, 514)(54, 550)(55, 551)(56, 518)(57, 553)(58, 521)(59, 522)(60, 556)(61, 524)(62, 558)(63, 559)(64, 527)(65, 528)(66, 562)(67, 563)(68, 532)(69, 533)(70, 566)(71, 567)(72, 536)(73, 569)(74, 538)(75, 539)(76, 572)(77, 541)(78, 574)(79, 575)(80, 544)(81, 545)(82, 578)(83, 579)(84, 548)(85, 549)(86, 582)(87, 583)(88, 552)(89, 585)(90, 554)(91, 555)(92, 588)(93, 557)(94, 590)(95, 591)(96, 560)(97, 561)(98, 594)(99, 595)(100, 564)(101, 565)(102, 598)(103, 599)(104, 568)(105, 601)(106, 570)(107, 571)(108, 604)(109, 573)(110, 606)(111, 607)(112, 576)(113, 577)(114, 610)(115, 611)(116, 580)(117, 581)(118, 614)(119, 615)(120, 584)(121, 617)(122, 586)(123, 587)(124, 620)(125, 589)(126, 622)(127, 623)(128, 592)(129, 593)(130, 626)(131, 627)(132, 596)(133, 597)(134, 630)(135, 631)(136, 600)(137, 633)(138, 602)(139, 603)(140, 636)(141, 605)(142, 638)(143, 639)(144, 608)(145, 609)(146, 642)(147, 643)(148, 612)(149, 613)(150, 646)(151, 647)(152, 616)(153, 649)(154, 618)(155, 619)(156, 652)(157, 621)(158, 654)(159, 655)(160, 624)(161, 625)(162, 658)(163, 659)(164, 628)(165, 629)(166, 662)(167, 663)(168, 632)(169, 665)(170, 634)(171, 635)(172, 668)(173, 637)(174, 670)(175, 671)(176, 640)(177, 641)(178, 674)(179, 675)(180, 644)(181, 645)(182, 678)(183, 679)(184, 648)(185, 681)(186, 650)(187, 651)(188, 684)(189, 653)(190, 686)(191, 687)(192, 656)(193, 657)(194, 690)(195, 691)(196, 660)(197, 661)(198, 694)(199, 695)(200, 664)(201, 697)(202, 666)(203, 667)(204, 700)(205, 669)(206, 702)(207, 703)(208, 672)(209, 673)(210, 705)(211, 706)(212, 676)(213, 677)(214, 709)(215, 710)(216, 680)(217, 711)(218, 682)(219, 683)(220, 688)(221, 685)(222, 712)(223, 713)(224, 689)(225, 716)(226, 717)(227, 692)(228, 693)(229, 696)(230, 718)(231, 719)(232, 698)(233, 699)(234, 701)(235, 704)(236, 707)(237, 720)(238, 708)(239, 714)(240, 715)(241, 721)(242, 722)(243, 723)(244, 724)(245, 725)(246, 726)(247, 727)(248, 728)(249, 729)(250, 730)(251, 731)(252, 732)(253, 733)(254, 734)(255, 735)(256, 736)(257, 737)(258, 738)(259, 739)(260, 740)(261, 741)(262, 742)(263, 743)(264, 744)(265, 745)(266, 746)(267, 747)(268, 748)(269, 749)(270, 750)(271, 751)(272, 752)(273, 753)(274, 754)(275, 755)(276, 756)(277, 757)(278, 758)(279, 759)(280, 760)(281, 761)(282, 762)(283, 763)(284, 764)(285, 765)(286, 766)(287, 767)(288, 768)(289, 769)(290, 770)(291, 771)(292, 772)(293, 773)(294, 774)(295, 775)(296, 776)(297, 777)(298, 778)(299, 779)(300, 780)(301, 781)(302, 782)(303, 783)(304, 784)(305, 785)(306, 786)(307, 787)(308, 788)(309, 789)(310, 790)(311, 791)(312, 792)(313, 793)(314, 794)(315, 795)(316, 796)(317, 797)(318, 798)(319, 799)(320, 800)(321, 801)(322, 802)(323, 803)(324, 804)(325, 805)(326, 806)(327, 807)(328, 808)(329, 809)(330, 810)(331, 811)(332, 812)(333, 813)(334, 814)(335, 815)(336, 816)(337, 817)(338, 818)(339, 819)(340, 820)(341, 821)(342, 822)(343, 823)(344, 824)(345, 825)(346, 826)(347, 827)(348, 828)(349, 829)(350, 830)(351, 831)(352, 832)(353, 833)(354, 834)(355, 835)(356, 836)(357, 837)(358, 838)(359, 839)(360, 840)(361, 841)(362, 842)(363, 843)(364, 844)(365, 845)(366, 846)(367, 847)(368, 848)(369, 849)(370, 850)(371, 851)(372, 852)(373, 853)(374, 854)(375, 855)(376, 856)(377, 857)(378, 858)(379, 859)(380, 860)(381, 861)(382, 862)(383, 863)(384, 864)(385, 865)(386, 866)(387, 867)(388, 868)(389, 869)(390, 870)(391, 871)(392, 872)(393, 873)(394, 874)(395, 875)(396, 876)(397, 877)(398, 878)(399, 879)(400, 880)(401, 881)(402, 882)(403, 883)(404, 884)(405, 885)(406, 886)(407, 887)(408, 888)(409, 889)(410, 890)(411, 891)(412, 892)(413, 893)(414, 894)(415, 895)(416, 896)(417, 897)(418, 898)(419, 899)(420, 900)(421, 901)(422, 902)(423, 903)(424, 904)(425, 905)(426, 906)(427, 907)(428, 908)(429, 909)(430, 910)(431, 911)(432, 912)(433, 913)(434, 914)(435, 915)(436, 916)(437, 917)(438, 918)(439, 919)(440, 920)(441, 921)(442, 922)(443, 923)(444, 924)(445, 925)(446, 926)(447, 927)(448, 928)(449, 929)(450, 930)(451, 931)(452, 932)(453, 933)(454, 934)(455, 935)(456, 936)(457, 937)(458, 938)(459, 939)(460, 940)(461, 941)(462, 942)(463, 943)(464, 944)(465, 945)(466, 946)(467, 947)(468, 948)(469, 949)(470, 950)(471, 951)(472, 952)(473, 953)(474, 954)(475, 955)(476, 956)(477, 957)(478, 958)(479, 959)(480, 960)
	local type(s) :: { ( 4, 60 ), ( 4, 60, 4, 60, 4, 60, 4, 60 ) }
Outer automorphisms :: reflexible
Dual of E27.2329
Graph:: simple bipartite
	v = 300 e = 480 f = 128
	degree seq :: [ 2^240, 8^60 ]

E27.2331 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 3, 6})
Quotient :: edge
Aut^+ = (C13 x Q8) : C3 (small group id <312, 26>)
Aut   = (C13 x Q8) : C3 (small group id <312, 26>)
|r| :: 1
Presentation :: [ X1^3, (X2 * X1)^3, X2^6, X2^-1 * X1 * X2^-3 * X1^-1 * X2^-2, X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 29, 31)(12, 32, 22)(15, 37, 38)(17, 40, 42)(21, 48, 49)(23, 51, 52)(25, 41, 56)(27, 57, 59)(28, 60, 54)(30, 63, 53)(33, 68, 69)(34, 58, 70)(35, 71, 72)(36, 73, 74)(39, 75, 76)(43, 79, 81)(44, 82, 77)(45, 80, 84)(46, 85, 86)(47, 87, 88)(50, 89, 90)(55, 94, 95)(61, 101, 102)(62, 103, 104)(64, 107, 109)(65, 110, 105)(66, 108, 112)(67, 113, 114)(78, 124, 125)(83, 122, 130)(91, 106, 140)(92, 141, 142)(93, 143, 144)(96, 147, 148)(97, 149, 151)(98, 152, 115)(99, 150, 154)(100, 155, 117)(111, 138, 161)(116, 166, 145)(118, 167, 168)(119, 169, 170)(120, 171, 172)(121, 173, 174)(123, 175, 176)(126, 179, 181)(127, 182, 131)(128, 180, 184)(129, 185, 133)(132, 186, 177)(134, 187, 188)(135, 189, 190)(136, 191, 192)(137, 193, 194)(139, 195, 196)(146, 205, 206)(153, 204, 212)(156, 217, 218)(157, 219, 221)(158, 222, 162)(159, 220, 224)(160, 225, 164)(163, 226, 197)(165, 227, 199)(178, 239, 240)(183, 238, 245)(198, 261, 259)(200, 243, 262)(201, 241, 263)(202, 264, 265)(203, 266, 267)(207, 270, 271)(208, 272, 256)(209, 254, 213)(210, 273, 255)(211, 253, 215)(214, 275, 228)(216, 276, 268)(223, 278, 283)(229, 292, 230)(231, 286, 282)(232, 284, 280)(233, 281, 293)(234, 279, 294)(235, 295, 296)(236, 297, 298)(237, 299, 300)(242, 260, 246)(244, 291, 248)(247, 302, 250)(249, 303, 301)(251, 304, 252)(257, 274, 305)(258, 306, 307)(269, 288, 285)(277, 309, 311)(287, 312, 308)(289, 310, 290)(313, 315, 321, 337, 327, 317)(314, 318, 329, 353, 333, 319)(316, 323, 342, 368, 345, 324)(320, 334, 362, 349, 365, 335)(322, 339, 370, 350, 373, 340)(325, 346, 367, 336, 366, 347)(326, 348, 360, 338, 351, 328)(330, 355, 392, 361, 395, 356)(331, 357, 390, 352, 389, 358)(332, 359, 380, 354, 374, 341)(343, 376, 420, 381, 423, 377)(344, 378, 418, 375, 417, 379)(363, 403, 451, 401, 426, 404)(364, 405, 413, 402, 408, 369)(371, 409, 462, 414, 465, 410)(372, 411, 428, 382, 427, 412)(383, 429, 458, 406, 457, 430)(384, 431, 387, 407, 432, 385)(386, 433, 391, 388, 435, 434)(393, 438, 492, 442, 495, 439)(394, 440, 444, 396, 443, 441)(397, 445, 490, 436, 489, 446)(398, 447, 415, 437, 448, 399)(400, 449, 419, 416, 468, 450)(421, 469, 532, 473, 535, 470)(422, 471, 475, 424, 474, 472)(425, 476, 510, 452, 509, 477)(453, 511, 572, 507, 571, 512)(454, 513, 459, 508, 514, 455)(456, 515, 461, 460, 519, 516)(463, 520, 585, 524, 586, 521)(464, 522, 526, 466, 525, 523)(467, 527, 541, 478, 540, 528)(479, 542, 581, 517, 580, 543)(480, 544, 483, 518, 545, 481)(482, 546, 485, 484, 547, 487)(486, 548, 550, 488, 549, 491)(493, 553, 574, 557, 576, 554)(494, 555, 559, 496, 558, 556)(497, 560, 563, 498, 562, 561)(499, 564, 587, 551, 613, 565)(500, 566, 503, 552, 567, 501)(502, 568, 505, 504, 569, 529)(506, 570, 590, 530, 589, 531)(533, 591, 605, 595, 607, 592)(534, 593, 597, 536, 596, 594)(537, 598, 601, 538, 600, 599)(539, 602, 614, 573, 620, 603)(575, 612, 578, 577, 610, 582)(579, 621, 617, 583, 618, 584)(588, 616, 624, 604, 615, 622)(606, 623, 611, 608, 619, 609)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 6^3 ), ( 6^6 ) }
Outer automorphisms :: chiral
Dual of E27.2332
Transitivity :: ET+
Graph:: simple bipartite
	v = 156 e = 312 f = 104
	degree seq :: [ 3^104, 6^52 ]

E27.2332 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 3, 6})
Quotient :: loop
Aut^+ = (C13 x Q8) : C3 (small group id <312, 26>)
Aut   = (C13 x Q8) : C3 (small group id <312, 26>)
|r| :: 1
Presentation :: [ X1^3, X2^3, X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1, (X2^-1 * X1^-1)^6, X1 * X2^-1 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 313, 2, 314, 4, 316)(3, 315, 8, 320, 9, 321)(5, 317, 12, 324, 13, 325)(6, 318, 14, 326, 15, 327)(7, 319, 16, 328, 17, 329)(10, 322, 22, 334, 23, 335)(11, 323, 24, 336, 25, 337)(18, 330, 38, 350, 39, 351)(19, 331, 40, 352, 41, 353)(20, 332, 42, 354, 43, 355)(21, 333, 44, 356, 45, 357)(26, 338, 54, 366, 55, 367)(27, 339, 56, 368, 57, 369)(28, 340, 58, 370, 59, 371)(29, 341, 60, 372, 61, 373)(30, 342, 62, 374, 63, 375)(31, 343, 64, 376, 65, 377)(32, 344, 66, 378, 67, 379)(33, 345, 68, 380, 69, 381)(34, 346, 70, 382, 71, 383)(35, 347, 72, 384, 73, 385)(36, 348, 74, 386, 75, 387)(37, 349, 76, 388, 77, 389)(46, 358, 92, 404, 93, 405)(47, 359, 94, 406, 95, 407)(48, 360, 96, 408, 97, 409)(49, 361, 98, 410, 79, 391)(50, 362, 99, 411, 100, 412)(51, 363, 101, 413, 81, 393)(52, 364, 102, 414, 85, 397)(53, 365, 103, 415, 104, 416)(78, 390, 116, 428, 115, 427)(80, 392, 133, 445, 134, 446)(82, 394, 135, 447, 136, 448)(83, 395, 137, 449, 138, 450)(84, 396, 139, 451, 105, 417)(86, 398, 140, 452, 141, 453)(87, 399, 142, 454, 143, 455)(88, 400, 144, 456, 106, 418)(89, 401, 145, 457, 146, 458)(90, 402, 147, 459, 108, 420)(91, 403, 148, 460, 111, 423)(107, 419, 160, 472, 161, 473)(109, 421, 162, 474, 163, 475)(110, 422, 164, 476, 165, 477)(112, 424, 166, 478, 167, 479)(113, 425, 168, 480, 169, 481)(114, 426, 118, 430, 170, 482)(117, 429, 171, 483, 172, 484)(119, 431, 173, 485, 174, 486)(120, 432, 175, 487, 124, 436)(121, 433, 176, 488, 177, 489)(122, 434, 178, 490, 126, 438)(123, 435, 179, 491, 129, 441)(125, 437, 180, 492, 181, 493)(127, 439, 182, 494, 183, 495)(128, 440, 184, 496, 185, 497)(130, 442, 186, 498, 187, 499)(131, 443, 188, 500, 189, 501)(132, 444, 150, 462, 190, 502)(149, 461, 211, 523, 212, 524)(151, 463, 213, 525, 214, 526)(152, 464, 215, 527, 155, 467)(153, 465, 216, 528, 217, 529)(154, 466, 218, 530, 157, 469)(156, 468, 219, 531, 191, 503)(158, 470, 220, 532, 221, 533)(159, 471, 222, 534, 196, 508)(192, 504, 257, 569, 193, 505)(194, 506, 238, 550, 258, 570)(195, 507, 236, 548, 259, 571)(197, 509, 260, 572, 261, 573)(198, 510, 262, 574, 263, 575)(199, 511, 201, 513, 264, 576)(200, 512, 265, 577, 266, 578)(202, 514, 267, 579, 252, 564)(203, 515, 249, 561, 206, 518)(204, 516, 268, 580, 251, 563)(205, 517, 248, 560, 208, 520)(207, 519, 269, 581, 223, 535)(209, 521, 270, 582, 271, 583)(210, 522, 272, 584, 228, 540)(224, 536, 287, 599, 225, 537)(226, 538, 280, 592, 277, 589)(227, 539, 278, 590, 275, 587)(229, 541, 276, 588, 288, 600)(230, 542, 274, 586, 289, 601)(231, 543, 290, 602, 291, 603)(232, 544, 292, 604, 293, 605)(233, 545, 294, 606, 234, 546)(235, 547, 295, 607, 296, 608)(237, 549, 286, 598, 240, 552)(239, 551, 285, 597, 242, 554)(241, 553, 297, 609, 245, 557)(243, 555, 298, 610, 299, 611)(244, 556, 300, 612, 250, 562)(246, 558, 301, 613, 247, 559)(253, 565, 302, 614, 303, 615)(254, 566, 304, 616, 305, 617)(255, 567, 306, 618, 256, 568)(273, 585, 308, 620, 311, 623)(279, 591, 310, 622, 282, 594)(281, 593, 309, 621, 307, 619)(283, 595, 312, 624, 284, 596)
	L = (1, 315)(2, 318)(3, 317)(4, 322)(5, 313)(6, 319)(7, 314)(8, 330)(9, 332)(10, 323)(11, 316)(12, 338)(13, 340)(14, 342)(15, 344)(16, 346)(17, 348)(18, 331)(19, 320)(20, 333)(21, 321)(22, 358)(23, 360)(24, 362)(25, 364)(26, 339)(27, 324)(28, 341)(29, 325)(30, 343)(31, 326)(32, 345)(33, 327)(34, 347)(35, 328)(36, 349)(37, 329)(38, 390)(39, 391)(40, 393)(41, 395)(42, 397)(43, 399)(44, 401)(45, 403)(46, 359)(47, 334)(48, 361)(49, 335)(50, 363)(51, 336)(52, 365)(53, 337)(54, 415)(55, 418)(56, 420)(57, 422)(58, 423)(59, 425)(60, 426)(61, 404)(62, 428)(63, 357)(64, 369)(65, 429)(66, 371)(67, 431)(68, 433)(69, 435)(70, 372)(71, 436)(72, 438)(73, 440)(74, 441)(75, 443)(76, 444)(77, 350)(78, 389)(79, 392)(80, 351)(81, 394)(82, 352)(83, 396)(84, 353)(85, 398)(86, 354)(87, 400)(88, 355)(89, 402)(90, 356)(91, 375)(92, 427)(93, 381)(94, 385)(95, 461)(96, 387)(97, 463)(98, 465)(99, 388)(100, 467)(101, 469)(102, 446)(103, 417)(104, 374)(105, 366)(106, 419)(107, 367)(108, 421)(109, 368)(110, 376)(111, 424)(112, 370)(113, 378)(114, 382)(115, 373)(116, 416)(117, 430)(118, 377)(119, 432)(120, 379)(121, 434)(122, 380)(123, 405)(124, 437)(125, 383)(126, 439)(127, 384)(128, 406)(129, 442)(130, 386)(131, 408)(132, 411)(133, 503)(134, 471)(135, 505)(136, 507)(137, 508)(138, 510)(139, 511)(140, 448)(141, 512)(142, 450)(143, 514)(144, 516)(145, 451)(146, 518)(147, 520)(148, 473)(149, 462)(150, 407)(151, 464)(152, 409)(153, 466)(154, 410)(155, 468)(156, 412)(157, 470)(158, 413)(159, 414)(160, 535)(161, 522)(162, 537)(163, 539)(164, 540)(165, 542)(166, 475)(167, 543)(168, 477)(169, 544)(170, 546)(171, 479)(172, 547)(173, 484)(174, 548)(175, 550)(176, 482)(177, 552)(178, 554)(179, 493)(180, 557)(181, 556)(182, 559)(183, 561)(184, 562)(185, 564)(186, 495)(187, 565)(188, 497)(189, 566)(190, 568)(191, 504)(192, 445)(193, 506)(194, 447)(195, 452)(196, 509)(197, 449)(198, 454)(199, 457)(200, 513)(201, 453)(202, 515)(203, 455)(204, 517)(205, 456)(206, 519)(207, 458)(208, 521)(209, 459)(210, 460)(211, 499)(212, 585)(213, 524)(214, 586)(215, 588)(216, 502)(217, 590)(218, 592)(219, 594)(220, 596)(221, 598)(222, 533)(223, 536)(224, 472)(225, 538)(226, 474)(227, 478)(228, 541)(229, 476)(230, 480)(231, 483)(232, 545)(233, 481)(234, 488)(235, 485)(236, 549)(237, 486)(238, 551)(239, 487)(240, 553)(241, 489)(242, 555)(243, 490)(244, 491)(245, 558)(246, 492)(247, 560)(248, 494)(249, 498)(250, 563)(251, 496)(252, 500)(253, 523)(254, 567)(255, 501)(256, 528)(257, 619)(258, 606)(259, 605)(260, 570)(261, 608)(262, 571)(263, 616)(264, 614)(265, 573)(266, 620)(267, 578)(268, 576)(269, 612)(270, 610)(271, 622)(272, 583)(273, 525)(274, 587)(275, 526)(276, 589)(277, 527)(278, 591)(279, 529)(280, 593)(281, 530)(282, 595)(283, 531)(284, 597)(285, 532)(286, 534)(287, 613)(288, 618)(289, 617)(290, 600)(291, 623)(292, 603)(293, 574)(294, 572)(295, 601)(296, 577)(297, 569)(298, 621)(299, 581)(300, 611)(301, 624)(302, 580)(303, 575)(304, 615)(305, 607)(306, 602)(307, 609)(308, 579)(309, 582)(310, 584)(311, 604)(312, 599)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: chiral
Dual of E27.2331
Transitivity :: ET+ VT+
Graph:: simple
	v = 104 e = 312 f = 156
	degree seq :: [ 6^104 ]

E27.2333 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 12})
Quotient :: halfedge
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1^-1)^4, (X1^3 * X2 * X1)^2, (X1^2 * X2 * X1^2)^2, X1^12, X1^-2 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^-2 * X2 * X1^-1 * X2 * X1 * X2, X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^2 * X2 * X1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 45, 80, 79, 44, 22, 10, 4)(3, 7, 15, 31, 59, 101, 132, 82, 46, 37, 18, 8)(6, 13, 27, 53, 43, 78, 128, 130, 81, 58, 30, 14)(9, 19, 38, 71, 117, 136, 85, 48, 24, 47, 40, 20)(12, 25, 49, 42, 21, 41, 76, 125, 129, 90, 52, 26)(16, 33, 63, 107, 70, 84, 134, 196, 157, 111, 65, 34)(17, 35, 66, 100, 131, 193, 158, 102, 60, 95, 55, 28)(29, 56, 96, 145, 192, 190, 127, 77, 91, 140, 87, 50)(32, 61, 103, 69, 36, 68, 115, 175, 194, 163, 106, 62)(39, 73, 120, 133, 83, 51, 88, 141, 200, 184, 122, 74)(54, 92, 146, 99, 57, 98, 155, 224, 191, 216, 149, 93)(64, 109, 167, 233, 253, 243, 177, 116, 164, 230, 160, 104)(67, 113, 172, 219, 151, 105, 161, 231, 251, 240, 174, 114)(72, 118, 178, 124, 75, 123, 185, 199, 135, 198, 180, 119)(86, 137, 201, 144, 89, 143, 210, 188, 126, 187, 204, 138)(94, 150, 217, 266, 227, 274, 226, 156, 112, 171, 213, 147)(97, 153, 221, 260, 206, 148, 214, 265, 250, 272, 223, 154)(108, 165, 225, 170, 110, 169, 212, 255, 197, 254, 215, 166)(121, 182, 245, 256, 207, 261, 247, 186, 195, 252, 244, 179)(139, 205, 258, 248, 189, 249, 263, 211, 152, 220, 257, 202)(142, 208, 162, 232, 181, 203, 176, 241, 183, 228, 159, 209)(168, 236, 273, 301, 276, 234, 267, 297, 285, 290, 264, 237)(173, 239, 282, 302, 277, 291, 269, 218, 268, 295, 281, 238)(222, 271, 300, 288, 296, 287, 293, 259, 292, 286, 299, 270)(229, 275, 246, 283, 242, 284, 289, 278, 235, 279, 294, 262)(280, 305, 311, 307, 309, 298, 310, 303, 312, 306, 308, 304)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 60)(34, 64)(35, 67)(37, 70)(38, 72)(40, 75)(41, 77)(42, 73)(44, 59)(45, 81)(47, 83)(48, 84)(49, 86)(52, 89)(53, 91)(55, 94)(56, 97)(58, 100)(61, 104)(62, 105)(63, 108)(65, 110)(66, 112)(68, 116)(69, 113)(71, 111)(74, 121)(76, 126)(78, 102)(79, 117)(80, 129)(82, 131)(85, 135)(87, 139)(88, 142)(90, 145)(92, 147)(93, 148)(95, 151)(96, 152)(98, 156)(99, 153)(101, 157)(103, 159)(106, 162)(107, 164)(109, 168)(114, 173)(115, 176)(118, 179)(119, 169)(120, 181)(122, 183)(123, 186)(124, 165)(125, 184)(127, 189)(128, 191)(130, 192)(132, 194)(133, 195)(134, 197)(136, 200)(137, 202)(138, 203)(140, 206)(141, 207)(143, 211)(144, 208)(146, 212)(149, 215)(150, 218)(154, 222)(155, 225)(158, 227)(160, 229)(161, 201)(163, 233)(166, 234)(167, 235)(170, 236)(171, 238)(172, 210)(174, 204)(175, 240)(177, 242)(178, 223)(180, 221)(182, 246)(185, 214)(187, 248)(188, 228)(190, 250)(193, 251)(196, 253)(198, 256)(199, 254)(205, 259)(209, 262)(213, 264)(216, 266)(217, 267)(219, 268)(220, 270)(224, 272)(226, 273)(230, 276)(231, 277)(232, 278)(237, 280)(239, 258)(241, 283)(243, 285)(244, 271)(245, 286)(247, 287)(249, 288)(252, 289)(255, 290)(257, 291)(260, 292)(261, 294)(263, 295)(265, 296)(269, 298)(274, 302)(275, 303)(279, 304)(281, 305)(282, 306)(284, 307)(293, 308)(297, 309)(299, 310)(300, 311)(301, 312)
	local type(s) :: { ( 4^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 26 e = 156 f = 78
	degree seq :: [ 12^26 ]

E27.2334 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 12})
Quotient :: halfedge
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X2^2, X1^4, (X2 * X1^-1 * X2 * X1^-1 * X2 * X1^2)^2, X2 * X1^-1 * X2 * X1^2 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1, (X1^-1 * X2)^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 41, 25)(15, 26, 44, 27)(21, 35, 59, 36)(22, 37, 62, 38)(23, 39, 65, 40)(29, 48, 80, 49)(30, 50, 83, 51)(32, 53, 88, 54)(33, 55, 91, 56)(34, 57, 94, 58)(42, 69, 93, 70)(43, 71, 115, 72)(45, 74, 119, 75)(46, 76, 89, 77)(47, 78, 124, 79)(52, 86, 131, 87)(60, 98, 85, 99)(61, 100, 146, 101)(63, 103, 150, 104)(64, 105, 81, 106)(66, 108, 157, 109)(67, 110, 143, 97)(68, 111, 160, 112)(73, 118, 141, 95)(82, 127, 180, 128)(84, 129, 183, 130)(90, 135, 190, 136)(92, 138, 194, 139)(96, 142, 189, 134)(102, 149, 187, 132)(107, 155, 217, 156)(113, 162, 123, 163)(114, 164, 206, 165)(116, 167, 224, 168)(117, 169, 120, 170)(121, 173, 228, 174)(122, 175, 231, 176)(125, 137, 193, 178)(126, 133, 188, 179)(140, 197, 249, 198)(144, 202, 154, 203)(145, 204, 242, 205)(147, 207, 255, 208)(148, 209, 151, 210)(152, 213, 172, 214)(153, 215, 166, 216)(158, 195, 244, 192)(159, 191, 243, 219)(161, 220, 262, 218)(171, 201, 251, 227)(177, 232, 273, 230)(181, 235, 250, 200)(182, 199, 184, 236)(185, 237, 246, 238)(186, 239, 280, 240)(196, 247, 212, 248)(211, 241, 281, 258)(221, 265, 226, 266)(222, 267, 283, 268)(223, 269, 225, 270)(229, 272, 285, 264)(233, 274, 282, 275)(234, 276, 284, 245)(252, 289, 257, 290)(253, 291, 278, 292)(254, 293, 256, 294)(259, 296, 279, 288)(260, 297, 277, 298)(261, 299, 310, 300)(263, 287, 271, 295)(286, 307, 303, 308)(301, 311, 304, 306)(302, 312, 305, 309)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 42)(25, 43)(26, 45)(27, 46)(28, 47)(31, 52)(35, 60)(36, 61)(37, 63)(38, 64)(39, 66)(40, 67)(41, 68)(44, 73)(48, 81)(49, 82)(50, 84)(51, 85)(53, 89)(54, 90)(55, 92)(56, 93)(57, 95)(58, 96)(59, 97)(62, 102)(65, 107)(69, 113)(70, 114)(71, 116)(72, 117)(74, 120)(75, 121)(76, 122)(77, 123)(78, 125)(79, 111)(80, 126)(83, 108)(86, 132)(87, 133)(88, 134)(91, 137)(94, 140)(98, 144)(99, 145)(100, 147)(101, 148)(103, 151)(104, 152)(105, 153)(106, 154)(109, 158)(110, 159)(112, 161)(115, 166)(118, 171)(119, 172)(124, 177)(127, 181)(128, 182)(129, 184)(130, 185)(131, 186)(135, 191)(136, 192)(138, 195)(139, 196)(141, 199)(142, 200)(143, 201)(146, 206)(149, 211)(150, 212)(155, 215)(156, 214)(157, 218)(160, 208)(162, 221)(163, 222)(164, 197)(165, 223)(167, 225)(168, 188)(169, 187)(170, 226)(173, 229)(174, 230)(175, 232)(176, 233)(178, 209)(179, 234)(180, 231)(183, 228)(189, 241)(190, 242)(193, 245)(194, 246)(198, 248)(202, 252)(203, 253)(204, 239)(205, 254)(207, 256)(210, 257)(213, 259)(216, 260)(217, 261)(219, 263)(220, 264)(224, 271)(227, 269)(235, 277)(236, 278)(237, 279)(238, 240)(243, 282)(244, 283)(247, 285)(249, 286)(250, 287)(251, 288)(255, 295)(258, 293)(262, 297)(265, 301)(266, 302)(267, 299)(268, 303)(270, 304)(272, 281)(273, 305)(274, 284)(275, 300)(276, 296)(280, 306)(289, 309)(290, 310)(291, 307)(292, 311)(294, 312)(298, 308)
	local type(s) :: { ( 12^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 78 e = 156 f = 26
	degree seq :: [ 4^78 ]

E27.2335 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 12})
Quotient :: edge
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X1^2, X2^4, (X1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1)^2, X1 * X2^-1 * X1 * X2^2 * X1 * X2^2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2, (X2 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1)^2, (X2 * X1)^12 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 9)(5, 10)(6, 12)(8, 15)(11, 20)(13, 23)(14, 25)(16, 28)(17, 30)(18, 31)(19, 33)(21, 36)(22, 38)(24, 41)(26, 44)(27, 46)(29, 49)(32, 54)(34, 57)(35, 59)(37, 62)(39, 65)(40, 67)(42, 70)(43, 72)(45, 75)(47, 78)(48, 80)(50, 83)(51, 85)(52, 86)(53, 88)(55, 91)(56, 93)(58, 96)(60, 99)(61, 101)(63, 104)(64, 106)(66, 98)(68, 103)(69, 112)(71, 115)(73, 105)(74, 119)(76, 122)(77, 87)(79, 124)(81, 127)(82, 89)(84, 94)(90, 136)(92, 139)(95, 143)(97, 146)(100, 148)(102, 151)(107, 155)(108, 156)(109, 157)(110, 159)(111, 160)(113, 163)(114, 165)(116, 168)(117, 169)(118, 162)(120, 167)(121, 173)(123, 176)(125, 178)(126, 180)(128, 182)(129, 183)(130, 185)(131, 186)(132, 187)(133, 188)(134, 190)(135, 191)(137, 194)(138, 196)(140, 199)(141, 200)(142, 193)(144, 198)(145, 204)(147, 207)(149, 209)(150, 211)(152, 213)(153, 214)(154, 216)(158, 189)(161, 225)(164, 227)(166, 228)(170, 205)(171, 202)(172, 230)(174, 201)(175, 232)(177, 234)(179, 215)(181, 222)(184, 210)(192, 247)(195, 249)(197, 250)(203, 252)(206, 254)(208, 256)(212, 244)(217, 261)(218, 262)(219, 263)(220, 265)(221, 266)(223, 267)(224, 268)(226, 270)(229, 264)(231, 274)(233, 275)(235, 277)(236, 278)(237, 279)(238, 273)(239, 280)(240, 281)(241, 282)(242, 284)(243, 285)(245, 286)(246, 287)(248, 289)(251, 283)(253, 293)(255, 294)(257, 296)(258, 297)(259, 298)(260, 292)(269, 290)(271, 288)(272, 304)(276, 295)(291, 311)(299, 309)(300, 310)(301, 312)(302, 306)(303, 307)(305, 308)(313, 315, 320, 316)(314, 317, 323, 318)(319, 325, 336, 326)(321, 328, 341, 329)(322, 330, 344, 331)(324, 333, 349, 334)(327, 338, 357, 339)(332, 346, 370, 347)(335, 351, 378, 352)(337, 354, 383, 355)(340, 359, 391, 360)(342, 362, 396, 363)(343, 364, 399, 365)(345, 367, 404, 368)(348, 372, 412, 373)(350, 375, 417, 376)(353, 380, 423, 381)(356, 385, 430, 386)(358, 388, 435, 389)(361, 393, 440, 394)(366, 401, 447, 402)(369, 406, 454, 407)(371, 409, 459, 410)(374, 414, 464, 415)(377, 419, 397, 420)(379, 421, 470, 422)(382, 425, 476, 426)(384, 428, 390, 429)(387, 432, 484, 433)(392, 437, 491, 438)(395, 441, 496, 442)(398, 443, 418, 444)(400, 445, 501, 446)(403, 449, 507, 450)(405, 452, 411, 453)(408, 456, 515, 457)(413, 461, 522, 462)(416, 465, 527, 466)(424, 473, 538, 474)(427, 478, 511, 479)(431, 482, 541, 483)(434, 486, 543, 487)(436, 485, 508, 489)(439, 488, 545, 493)(448, 504, 560, 505)(451, 509, 480, 510)(455, 513, 563, 514)(458, 517, 565, 518)(460, 516, 477, 520)(463, 519, 567, 524)(467, 529, 481, 530)(468, 531, 576, 532)(469, 533, 558, 503)(471, 534, 475, 535)(472, 500, 555, 536)(490, 547, 581, 537)(492, 525, 495, 548)(494, 526, 570, 523)(497, 549, 586, 550)(498, 551, 512, 552)(499, 553, 595, 554)(502, 556, 506, 557)(521, 569, 600, 559)(528, 571, 605, 572)(539, 580, 544, 583)(540, 582, 608, 584)(542, 575, 615, 585)(546, 588, 610, 587)(561, 599, 566, 602)(562, 601, 589, 603)(564, 594, 622, 604)(568, 607, 591, 606)(573, 611, 579, 612)(574, 613, 590, 614)(577, 616, 578, 617)(592, 618, 598, 619)(593, 620, 609, 621)(596, 623, 597, 624)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 24, 24 ), ( 24^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 234 e = 312 f = 26
	degree seq :: [ 2^156, 4^78 ]

E27.2336 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 12})
Quotient :: edge
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X1^4, (X2^-1 * X1^-1)^2, (X2^2 * X1^-1 * X2)^2, (X2^-3 * X1)^2, X2^12, X2^-1 * X1 * X2^2 * X1^2 * X2^2 * X1^-1 * X2 * X1^-1 * X2^2 * X1, X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1 * X2 * X1^-1, X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2 * X1^-1 * X2^-2 * X1^-1 * X2 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 21, 11)(5, 13, 18, 7)(8, 19, 34, 15)(10, 23, 49, 25)(12, 16, 35, 28)(14, 31, 61, 29)(17, 37, 73, 39)(20, 43, 81, 41)(22, 47, 86, 45)(24, 51, 83, 44)(26, 46, 87, 55)(27, 56, 102, 58)(30, 62, 79, 40)(32, 57, 104, 63)(33, 65, 113, 67)(36, 71, 121, 69)(38, 75, 123, 72)(42, 82, 119, 68)(48, 66, 115, 89)(50, 94, 152, 92)(52, 84, 116, 91)(53, 93, 153, 98)(54, 99, 162, 100)(59, 70, 122, 106)(60, 107, 171, 109)(64, 76, 124, 105)(74, 127, 196, 125)(77, 126, 197, 131)(78, 132, 206, 133)(80, 135, 209, 137)(85, 141, 217, 143)(88, 147, 222, 145)(90, 149, 221, 144)(95, 142, 205, 155)(96, 158, 216, 139)(97, 150, 219, 157)(101, 146, 203, 164)(103, 166, 239, 165)(108, 173, 199, 128)(110, 176, 208, 134)(111, 168, 213, 178)(112, 174, 201, 130)(114, 181, 246, 179)(117, 180, 247, 185)(118, 186, 253, 187)(120, 189, 256, 191)(129, 202, 260, 193)(136, 211, 249, 182)(138, 214, 255, 188)(140, 212, 251, 184)(148, 183, 175, 224)(151, 227, 280, 229)(154, 233, 284, 231)(156, 195, 261, 230)(159, 228, 170, 192)(160, 234, 282, 235)(161, 232, 167, 190)(163, 210, 269, 236)(169, 194, 258, 240)(172, 241, 277, 225)(177, 244, 287, 242)(198, 264, 300, 263)(200, 245, 288, 262)(204, 265, 237, 266)(207, 257, 295, 267)(215, 272, 302, 270)(218, 273, 293, 254)(220, 275, 305, 276)(223, 278, 303, 274)(226, 279, 294, 271)(238, 286, 289, 250)(243, 252, 292, 268)(248, 291, 310, 290)(259, 297, 312, 296)(281, 299, 308, 306)(283, 298, 309, 307)(285, 301, 311, 304)(313, 315, 322, 336, 364, 409, 472, 424, 376, 344, 326, 317)(314, 319, 329, 350, 388, 442, 516, 452, 396, 356, 332, 320)(316, 324, 339, 369, 417, 481, 538, 462, 403, 360, 334, 321)(318, 327, 345, 378, 428, 496, 564, 506, 436, 384, 348, 328)(323, 338, 366, 343, 375, 423, 489, 546, 469, 407, 362, 335)(325, 341, 372, 420, 486, 547, 471, 408, 363, 337, 365, 342)(330, 352, 390, 355, 395, 451, 527, 577, 513, 440, 386, 349)(331, 353, 392, 448, 524, 578, 515, 441, 387, 351, 389, 354)(333, 357, 397, 454, 531, 583, 526, 480, 416, 370, 400, 358)(340, 371, 402, 359, 401, 460, 535, 591, 552, 479, 415, 368)(346, 380, 430, 383, 435, 505, 571, 604, 563, 494, 426, 377)(347, 381, 432, 502, 570, 555, 488, 495, 427, 379, 429, 382)(361, 404, 463, 540, 594, 554, 484, 419, 373, 412, 466, 405)(367, 413, 468, 406, 467, 509, 575, 556, 490, 521, 475, 411)(374, 410, 473, 503, 470, 504, 434, 497, 485, 421, 487, 422)(385, 437, 507, 476, 549, 582, 522, 447, 393, 445, 510, 438)(391, 446, 512, 439, 511, 559, 602, 584, 528, 568, 519, 444)(394, 443, 517, 455, 514, 458, 399, 457, 523, 449, 525, 450)(398, 456, 532, 459, 414, 477, 550, 567, 606, 586, 530, 453)(418, 482, 541, 478, 544, 465, 543, 590, 536, 483, 537, 461)(425, 491, 557, 520, 580, 608, 569, 501, 433, 499, 560, 492)(431, 500, 562, 493, 561, 534, 588, 609, 572, 529, 566, 498)(464, 542, 595, 545, 474, 548, 597, 553, 599, 612, 593, 539)(508, 574, 611, 576, 518, 579, 613, 581, 614, 622, 610, 573)(533, 589, 616, 585, 615, 596, 619, 598, 551, 592, 618, 587)(558, 601, 621, 603, 565, 605, 623, 607, 624, 617, 620, 600)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 4^4 ), ( 4^12 ) }
Outer automorphisms :: chiral
Dual of E27.2338
Transitivity :: ET+
Graph:: simple bipartite
	v = 104 e = 312 f = 156
	degree seq :: [ 4^78, 12^26 ]

E27.2337 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 12})
Quotient :: edge
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1^-1)^4, (X1^3 * X2 * X1)^2, X1^12, (X2 * X1^-1 * X2 * X1^2 * X2 * X1^-1)^2, X2 * X1^2 * X2 * X1^2 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 ]
Map:: polytopal
	R = (1, 2, 5, 11, 23, 45, 80, 79, 44, 22, 10, 4)(3, 7, 15, 31, 59, 101, 132, 82, 46, 37, 18, 8)(6, 13, 27, 53, 43, 78, 128, 130, 81, 58, 30, 14)(9, 19, 38, 71, 117, 136, 85, 48, 24, 47, 40, 20)(12, 25, 49, 42, 21, 41, 76, 125, 129, 90, 52, 26)(16, 33, 63, 107, 70, 84, 134, 196, 157, 111, 65, 34)(17, 35, 66, 100, 131, 193, 158, 102, 60, 95, 55, 28)(29, 56, 96, 145, 192, 190, 127, 77, 91, 140, 87, 50)(32, 61, 103, 69, 36, 68, 115, 175, 194, 163, 106, 62)(39, 73, 120, 133, 83, 51, 88, 141, 200, 184, 122, 74)(54, 92, 146, 99, 57, 98, 155, 224, 191, 216, 149, 93)(64, 109, 167, 233, 253, 243, 177, 116, 164, 230, 160, 104)(67, 113, 172, 219, 151, 105, 161, 231, 251, 240, 174, 114)(72, 118, 178, 124, 75, 123, 185, 199, 135, 198, 180, 119)(86, 137, 201, 144, 89, 143, 210, 188, 126, 187, 204, 138)(94, 150, 217, 266, 227, 274, 226, 156, 112, 171, 213, 147)(97, 153, 221, 260, 206, 148, 214, 265, 250, 272, 223, 154)(108, 165, 225, 170, 110, 169, 212, 255, 197, 254, 215, 166)(121, 182, 245, 256, 207, 261, 247, 186, 195, 252, 244, 179)(139, 205, 258, 248, 189, 249, 263, 211, 152, 220, 257, 202)(142, 208, 162, 232, 181, 203, 176, 241, 183, 228, 159, 209)(168, 236, 273, 301, 276, 234, 267, 297, 285, 290, 264, 237)(173, 239, 282, 302, 277, 291, 269, 218, 268, 295, 281, 238)(222, 271, 300, 288, 296, 287, 293, 259, 292, 286, 299, 270)(229, 275, 246, 283, 242, 284, 289, 278, 235, 279, 294, 262)(280, 305, 311, 307, 309, 298, 310, 303, 312, 306, 308, 304)(313, 315)(314, 318)(316, 321)(317, 324)(319, 328)(320, 329)(322, 333)(323, 336)(325, 340)(326, 341)(327, 344)(330, 348)(331, 351)(332, 345)(334, 355)(335, 358)(337, 362)(338, 363)(339, 366)(342, 369)(343, 372)(346, 376)(347, 379)(349, 382)(350, 384)(352, 387)(353, 389)(354, 385)(356, 371)(357, 393)(359, 395)(360, 396)(361, 398)(364, 401)(365, 403)(367, 406)(368, 409)(370, 412)(373, 416)(374, 417)(375, 420)(377, 422)(378, 424)(380, 428)(381, 425)(383, 423)(386, 433)(388, 438)(390, 414)(391, 429)(392, 441)(394, 443)(397, 447)(399, 451)(400, 454)(402, 457)(404, 459)(405, 460)(407, 463)(408, 464)(410, 468)(411, 465)(413, 469)(415, 471)(418, 474)(419, 476)(421, 480)(426, 485)(427, 488)(430, 491)(431, 481)(432, 493)(434, 495)(435, 498)(436, 477)(437, 496)(439, 501)(440, 503)(442, 504)(444, 506)(445, 507)(446, 509)(448, 512)(449, 514)(450, 515)(452, 518)(453, 519)(455, 523)(456, 520)(458, 524)(461, 527)(462, 530)(466, 534)(467, 537)(470, 539)(472, 541)(473, 513)(475, 545)(478, 546)(479, 547)(482, 548)(483, 550)(484, 522)(486, 516)(487, 552)(489, 554)(490, 535)(492, 533)(494, 558)(497, 526)(499, 560)(500, 540)(502, 562)(505, 563)(508, 565)(510, 568)(511, 566)(517, 571)(521, 574)(525, 576)(528, 578)(529, 579)(531, 580)(532, 582)(536, 584)(538, 585)(542, 588)(543, 589)(544, 590)(549, 592)(551, 570)(553, 595)(555, 597)(556, 583)(557, 598)(559, 599)(561, 600)(564, 601)(567, 602)(569, 603)(572, 604)(573, 606)(575, 607)(577, 608)(581, 610)(586, 614)(587, 615)(591, 616)(593, 617)(594, 618)(596, 619)(605, 620)(609, 621)(611, 622)(612, 623)(613, 624)
	L = (1, 313)(2, 314)(3, 315)(4, 316)(5, 317)(6, 318)(7, 319)(8, 320)(9, 321)(10, 322)(11, 323)(12, 324)(13, 325)(14, 326)(15, 327)(16, 328)(17, 329)(18, 330)(19, 331)(20, 332)(21, 333)(22, 334)(23, 335)(24, 336)(25, 337)(26, 338)(27, 339)(28, 340)(29, 341)(30, 342)(31, 343)(32, 344)(33, 345)(34, 346)(35, 347)(36, 348)(37, 349)(38, 350)(39, 351)(40, 352)(41, 353)(42, 354)(43, 355)(44, 356)(45, 357)(46, 358)(47, 359)(48, 360)(49, 361)(50, 362)(51, 363)(52, 364)(53, 365)(54, 366)(55, 367)(56, 368)(57, 369)(58, 370)(59, 371)(60, 372)(61, 373)(62, 374)(63, 375)(64, 376)(65, 377)(66, 378)(67, 379)(68, 380)(69, 381)(70, 382)(71, 383)(72, 384)(73, 385)(74, 386)(75, 387)(76, 388)(77, 389)(78, 390)(79, 391)(80, 392)(81, 393)(82, 394)(83, 395)(84, 396)(85, 397)(86, 398)(87, 399)(88, 400)(89, 401)(90, 402)(91, 403)(92, 404)(93, 405)(94, 406)(95, 407)(96, 408)(97, 409)(98, 410)(99, 411)(100, 412)(101, 413)(102, 414)(103, 415)(104, 416)(105, 417)(106, 418)(107, 419)(108, 420)(109, 421)(110, 422)(111, 423)(112, 424)(113, 425)(114, 426)(115, 427)(116, 428)(117, 429)(118, 430)(119, 431)(120, 432)(121, 433)(122, 434)(123, 435)(124, 436)(125, 437)(126, 438)(127, 439)(128, 440)(129, 441)(130, 442)(131, 443)(132, 444)(133, 445)(134, 446)(135, 447)(136, 448)(137, 449)(138, 450)(139, 451)(140, 452)(141, 453)(142, 454)(143, 455)(144, 456)(145, 457)(146, 458)(147, 459)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 466)(155, 467)(156, 468)(157, 469)(158, 470)(159, 471)(160, 472)(161, 473)(162, 474)(163, 475)(164, 476)(165, 477)(166, 478)(167, 479)(168, 480)(169, 481)(170, 482)(171, 483)(172, 484)(173, 485)(174, 486)(175, 487)(176, 488)(177, 489)(178, 490)(179, 491)(180, 492)(181, 493)(182, 494)(183, 495)(184, 496)(185, 497)(186, 498)(187, 499)(188, 500)(189, 501)(190, 502)(191, 503)(192, 504)(193, 505)(194, 506)(195, 507)(196, 508)(197, 509)(198, 510)(199, 511)(200, 512)(201, 513)(202, 514)(203, 515)(204, 516)(205, 517)(206, 518)(207, 519)(208, 520)(209, 521)(210, 522)(211, 523)(212, 524)(213, 525)(214, 526)(215, 527)(216, 528)(217, 529)(218, 530)(219, 531)(220, 532)(221, 533)(222, 534)(223, 535)(224, 536)(225, 537)(226, 538)(227, 539)(228, 540)(229, 541)(230, 542)(231, 543)(232, 544)(233, 545)(234, 546)(235, 547)(236, 548)(237, 549)(238, 550)(239, 551)(240, 552)(241, 553)(242, 554)(243, 555)(244, 556)(245, 557)(246, 558)(247, 559)(248, 560)(249, 561)(250, 562)(251, 563)(252, 564)(253, 565)(254, 566)(255, 567)(256, 568)(257, 569)(258, 570)(259, 571)(260, 572)(261, 573)(262, 574)(263, 575)(264, 576)(265, 577)(266, 578)(267, 579)(268, 580)(269, 581)(270, 582)(271, 583)(272, 584)(273, 585)(274, 586)(275, 587)(276, 588)(277, 589)(278, 590)(279, 591)(280, 592)(281, 593)(282, 594)(283, 595)(284, 596)(285, 597)(286, 598)(287, 599)(288, 600)(289, 601)(290, 602)(291, 603)(292, 604)(293, 605)(294, 606)(295, 607)(296, 608)(297, 609)(298, 610)(299, 611)(300, 612)(301, 613)(302, 614)(303, 615)(304, 616)(305, 617)(306, 618)(307, 619)(308, 620)(309, 621)(310, 622)(311, 623)(312, 624)
	local type(s) :: { ( 8, 8 ), ( 8^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 182 e = 312 f = 78
	degree seq :: [ 2^156, 12^26 ]

E27.2338 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 12})
Quotient :: loop
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X1^2, X2^4, (X1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1)^2, X1 * X2^-1 * X1 * X2^2 * X1 * X2^2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1 * X2, (X2 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1)^2, (X2 * X1)^12 ]
Map:: polytopal non-degenerate
	R = (1, 313, 2, 314)(3, 315, 7, 319)(4, 316, 9, 321)(5, 317, 10, 322)(6, 318, 12, 324)(8, 320, 15, 327)(11, 323, 20, 332)(13, 325, 23, 335)(14, 326, 25, 337)(16, 328, 28, 340)(17, 329, 30, 342)(18, 330, 31, 343)(19, 331, 33, 345)(21, 333, 36, 348)(22, 334, 38, 350)(24, 336, 41, 353)(26, 338, 44, 356)(27, 339, 46, 358)(29, 341, 49, 361)(32, 344, 54, 366)(34, 346, 57, 369)(35, 347, 59, 371)(37, 349, 62, 374)(39, 351, 65, 377)(40, 352, 67, 379)(42, 354, 70, 382)(43, 355, 72, 384)(45, 357, 75, 387)(47, 359, 78, 390)(48, 360, 80, 392)(50, 362, 83, 395)(51, 363, 85, 397)(52, 364, 86, 398)(53, 365, 88, 400)(55, 367, 91, 403)(56, 368, 93, 405)(58, 370, 96, 408)(60, 372, 99, 411)(61, 373, 101, 413)(63, 375, 104, 416)(64, 376, 106, 418)(66, 378, 98, 410)(68, 380, 103, 415)(69, 381, 112, 424)(71, 383, 115, 427)(73, 385, 105, 417)(74, 386, 119, 431)(76, 388, 122, 434)(77, 389, 87, 399)(79, 391, 124, 436)(81, 393, 127, 439)(82, 394, 89, 401)(84, 396, 94, 406)(90, 402, 136, 448)(92, 404, 139, 451)(95, 407, 143, 455)(97, 409, 146, 458)(100, 412, 148, 460)(102, 414, 151, 463)(107, 419, 155, 467)(108, 420, 156, 468)(109, 421, 157, 469)(110, 422, 159, 471)(111, 423, 160, 472)(113, 425, 163, 475)(114, 426, 165, 477)(116, 428, 168, 480)(117, 429, 169, 481)(118, 430, 162, 474)(120, 432, 167, 479)(121, 433, 173, 485)(123, 435, 176, 488)(125, 437, 178, 490)(126, 438, 180, 492)(128, 440, 182, 494)(129, 441, 183, 495)(130, 442, 185, 497)(131, 443, 186, 498)(132, 444, 187, 499)(133, 445, 188, 500)(134, 446, 190, 502)(135, 447, 191, 503)(137, 449, 194, 506)(138, 450, 196, 508)(140, 452, 199, 511)(141, 453, 200, 512)(142, 454, 193, 505)(144, 456, 198, 510)(145, 457, 204, 516)(147, 459, 207, 519)(149, 461, 209, 521)(150, 462, 211, 523)(152, 464, 213, 525)(153, 465, 214, 526)(154, 466, 216, 528)(158, 470, 189, 501)(161, 473, 225, 537)(164, 476, 227, 539)(166, 478, 228, 540)(170, 482, 205, 517)(171, 483, 202, 514)(172, 484, 230, 542)(174, 486, 201, 513)(175, 487, 232, 544)(177, 489, 234, 546)(179, 491, 215, 527)(181, 493, 222, 534)(184, 496, 210, 522)(192, 504, 247, 559)(195, 507, 249, 561)(197, 509, 250, 562)(203, 515, 252, 564)(206, 518, 254, 566)(208, 520, 256, 568)(212, 524, 244, 556)(217, 529, 261, 573)(218, 530, 262, 574)(219, 531, 263, 575)(220, 532, 265, 577)(221, 533, 266, 578)(223, 535, 267, 579)(224, 536, 268, 580)(226, 538, 270, 582)(229, 541, 264, 576)(231, 543, 274, 586)(233, 545, 275, 587)(235, 547, 277, 589)(236, 548, 278, 590)(237, 549, 279, 591)(238, 550, 273, 585)(239, 551, 280, 592)(240, 552, 281, 593)(241, 553, 282, 594)(242, 554, 284, 596)(243, 555, 285, 597)(245, 557, 286, 598)(246, 558, 287, 599)(248, 560, 289, 601)(251, 563, 283, 595)(253, 565, 293, 605)(255, 567, 294, 606)(257, 569, 296, 608)(258, 570, 297, 609)(259, 571, 298, 610)(260, 572, 292, 604)(269, 581, 290, 602)(271, 583, 288, 600)(272, 584, 304, 616)(276, 588, 295, 607)(291, 603, 311, 623)(299, 611, 309, 621)(300, 612, 310, 622)(301, 613, 312, 624)(302, 614, 306, 618)(303, 615, 307, 619)(305, 617, 308, 620)
	L = (1, 315)(2, 317)(3, 320)(4, 313)(5, 323)(6, 314)(7, 325)(8, 316)(9, 328)(10, 330)(11, 318)(12, 333)(13, 336)(14, 319)(15, 338)(16, 341)(17, 321)(18, 344)(19, 322)(20, 346)(21, 349)(22, 324)(23, 351)(24, 326)(25, 354)(26, 357)(27, 327)(28, 359)(29, 329)(30, 362)(31, 364)(32, 331)(33, 367)(34, 370)(35, 332)(36, 372)(37, 334)(38, 375)(39, 378)(40, 335)(41, 380)(42, 383)(43, 337)(44, 385)(45, 339)(46, 388)(47, 391)(48, 340)(49, 393)(50, 396)(51, 342)(52, 399)(53, 343)(54, 401)(55, 404)(56, 345)(57, 406)(58, 347)(59, 409)(60, 412)(61, 348)(62, 414)(63, 417)(64, 350)(65, 419)(66, 352)(67, 421)(68, 423)(69, 353)(70, 425)(71, 355)(72, 428)(73, 430)(74, 356)(75, 432)(76, 435)(77, 358)(78, 429)(79, 360)(80, 437)(81, 440)(82, 361)(83, 441)(84, 363)(85, 420)(86, 443)(87, 365)(88, 445)(89, 447)(90, 366)(91, 449)(92, 368)(93, 452)(94, 454)(95, 369)(96, 456)(97, 459)(98, 371)(99, 453)(100, 373)(101, 461)(102, 464)(103, 374)(104, 465)(105, 376)(106, 444)(107, 397)(108, 377)(109, 470)(110, 379)(111, 381)(112, 473)(113, 476)(114, 382)(115, 478)(116, 390)(117, 384)(118, 386)(119, 482)(120, 484)(121, 387)(122, 486)(123, 389)(124, 485)(125, 491)(126, 392)(127, 488)(128, 394)(129, 496)(130, 395)(131, 418)(132, 398)(133, 501)(134, 400)(135, 402)(136, 504)(137, 507)(138, 403)(139, 509)(140, 411)(141, 405)(142, 407)(143, 513)(144, 515)(145, 408)(146, 517)(147, 410)(148, 516)(149, 522)(150, 413)(151, 519)(152, 415)(153, 527)(154, 416)(155, 529)(156, 531)(157, 533)(158, 422)(159, 534)(160, 500)(161, 538)(162, 424)(163, 535)(164, 426)(165, 520)(166, 511)(167, 427)(168, 510)(169, 530)(170, 541)(171, 431)(172, 433)(173, 508)(174, 543)(175, 434)(176, 545)(177, 436)(178, 547)(179, 438)(180, 525)(181, 439)(182, 526)(183, 548)(184, 442)(185, 549)(186, 551)(187, 553)(188, 555)(189, 446)(190, 556)(191, 469)(192, 560)(193, 448)(194, 557)(195, 450)(196, 489)(197, 480)(198, 451)(199, 479)(200, 552)(201, 563)(202, 455)(203, 457)(204, 477)(205, 565)(206, 458)(207, 567)(208, 460)(209, 569)(210, 462)(211, 494)(212, 463)(213, 495)(214, 570)(215, 466)(216, 571)(217, 481)(218, 467)(219, 576)(220, 468)(221, 558)(222, 475)(223, 471)(224, 472)(225, 490)(226, 474)(227, 580)(228, 582)(229, 483)(230, 575)(231, 487)(232, 583)(233, 493)(234, 588)(235, 581)(236, 492)(237, 586)(238, 497)(239, 512)(240, 498)(241, 595)(242, 499)(243, 536)(244, 506)(245, 502)(246, 503)(247, 521)(248, 505)(249, 599)(250, 601)(251, 514)(252, 594)(253, 518)(254, 602)(255, 524)(256, 607)(257, 600)(258, 523)(259, 605)(260, 528)(261, 611)(262, 613)(263, 615)(264, 532)(265, 616)(266, 617)(267, 612)(268, 544)(269, 537)(270, 608)(271, 539)(272, 540)(273, 542)(274, 550)(275, 546)(276, 610)(277, 603)(278, 614)(279, 606)(280, 618)(281, 620)(282, 622)(283, 554)(284, 623)(285, 624)(286, 619)(287, 566)(288, 559)(289, 589)(290, 561)(291, 562)(292, 564)(293, 572)(294, 568)(295, 591)(296, 584)(297, 621)(298, 587)(299, 579)(300, 573)(301, 590)(302, 574)(303, 585)(304, 578)(305, 577)(306, 598)(307, 592)(308, 609)(309, 593)(310, 604)(311, 597)(312, 596)
	local type(s) :: { ( 4, 12, 4, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2336
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 156 e = 312 f = 104
	degree seq :: [ 4^156 ]

E27.2339 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 12})
Quotient :: loop
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X1^4, (X2^-1 * X1^-1)^2, (X2^2 * X1^-1 * X2)^2, (X2^-3 * X1)^2, X2^12, X2^-1 * X1 * X2^2 * X1^2 * X2^2 * X1^-1 * X2 * X1^-1 * X2^2 * X1, X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2^2 * X1^-1 * X2^-3 * X1^-1 * X2 * X1^-1, X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2 * X1^-1 * X2^-2 * X1^-1 * X2 * X1^-1 ]
Map::
	R = (1, 313, 2, 314, 6, 318, 4, 316)(3, 315, 9, 321, 21, 333, 11, 323)(5, 317, 13, 325, 18, 330, 7, 319)(8, 320, 19, 331, 34, 346, 15, 327)(10, 322, 23, 335, 49, 361, 25, 337)(12, 324, 16, 328, 35, 347, 28, 340)(14, 326, 31, 343, 61, 373, 29, 341)(17, 329, 37, 349, 73, 385, 39, 351)(20, 332, 43, 355, 81, 393, 41, 353)(22, 334, 47, 359, 86, 398, 45, 357)(24, 336, 51, 363, 83, 395, 44, 356)(26, 338, 46, 358, 87, 399, 55, 367)(27, 339, 56, 368, 102, 414, 58, 370)(30, 342, 62, 374, 79, 391, 40, 352)(32, 344, 57, 369, 104, 416, 63, 375)(33, 345, 65, 377, 113, 425, 67, 379)(36, 348, 71, 383, 121, 433, 69, 381)(38, 350, 75, 387, 123, 435, 72, 384)(42, 354, 82, 394, 119, 431, 68, 380)(48, 360, 66, 378, 115, 427, 89, 401)(50, 362, 94, 406, 152, 464, 92, 404)(52, 364, 84, 396, 116, 428, 91, 403)(53, 365, 93, 405, 153, 465, 98, 410)(54, 366, 99, 411, 162, 474, 100, 412)(59, 371, 70, 382, 122, 434, 106, 418)(60, 372, 107, 419, 171, 483, 109, 421)(64, 376, 76, 388, 124, 436, 105, 417)(74, 386, 127, 439, 196, 508, 125, 437)(77, 389, 126, 438, 197, 509, 131, 443)(78, 390, 132, 444, 206, 518, 133, 445)(80, 392, 135, 447, 209, 521, 137, 449)(85, 397, 141, 453, 217, 529, 143, 455)(88, 400, 147, 459, 222, 534, 145, 457)(90, 402, 149, 461, 221, 533, 144, 456)(95, 407, 142, 454, 205, 517, 155, 467)(96, 408, 158, 470, 216, 528, 139, 451)(97, 409, 150, 462, 219, 531, 157, 469)(101, 413, 146, 458, 203, 515, 164, 476)(103, 415, 166, 478, 239, 551, 165, 477)(108, 420, 173, 485, 199, 511, 128, 440)(110, 422, 176, 488, 208, 520, 134, 446)(111, 423, 168, 480, 213, 525, 178, 490)(112, 424, 174, 486, 201, 513, 130, 442)(114, 426, 181, 493, 246, 558, 179, 491)(117, 429, 180, 492, 247, 559, 185, 497)(118, 430, 186, 498, 253, 565, 187, 499)(120, 432, 189, 501, 256, 568, 191, 503)(129, 441, 202, 514, 260, 572, 193, 505)(136, 448, 211, 523, 249, 561, 182, 494)(138, 450, 214, 526, 255, 567, 188, 500)(140, 452, 212, 524, 251, 563, 184, 496)(148, 460, 183, 495, 175, 487, 224, 536)(151, 463, 227, 539, 280, 592, 229, 541)(154, 466, 233, 545, 284, 596, 231, 543)(156, 468, 195, 507, 261, 573, 230, 542)(159, 471, 228, 540, 170, 482, 192, 504)(160, 472, 234, 546, 282, 594, 235, 547)(161, 473, 232, 544, 167, 479, 190, 502)(163, 475, 210, 522, 269, 581, 236, 548)(169, 481, 194, 506, 258, 570, 240, 552)(172, 484, 241, 553, 277, 589, 225, 537)(177, 489, 244, 556, 287, 599, 242, 554)(198, 510, 264, 576, 300, 612, 263, 575)(200, 512, 245, 557, 288, 600, 262, 574)(204, 516, 265, 577, 237, 549, 266, 578)(207, 519, 257, 569, 295, 607, 267, 579)(215, 527, 272, 584, 302, 614, 270, 582)(218, 530, 273, 585, 293, 605, 254, 566)(220, 532, 275, 587, 305, 617, 276, 588)(223, 535, 278, 590, 303, 615, 274, 586)(226, 538, 279, 591, 294, 606, 271, 583)(238, 550, 286, 598, 289, 601, 250, 562)(243, 555, 252, 564, 292, 604, 268, 580)(248, 560, 291, 603, 310, 622, 290, 602)(259, 571, 297, 609, 312, 624, 296, 608)(281, 593, 299, 611, 308, 620, 306, 618)(283, 595, 298, 610, 309, 621, 307, 619)(285, 597, 301, 613, 311, 623, 304, 616)
	L = (1, 315)(2, 319)(3, 322)(4, 324)(5, 313)(6, 327)(7, 329)(8, 314)(9, 316)(10, 336)(11, 338)(12, 339)(13, 341)(14, 317)(15, 345)(16, 318)(17, 350)(18, 352)(19, 353)(20, 320)(21, 357)(22, 321)(23, 323)(24, 364)(25, 365)(26, 366)(27, 369)(28, 371)(29, 372)(30, 325)(31, 375)(32, 326)(33, 378)(34, 380)(35, 381)(36, 328)(37, 330)(38, 388)(39, 389)(40, 390)(41, 392)(42, 331)(43, 395)(44, 332)(45, 397)(46, 333)(47, 401)(48, 334)(49, 404)(50, 335)(51, 337)(52, 409)(53, 342)(54, 343)(55, 413)(56, 340)(57, 417)(58, 400)(59, 402)(60, 420)(61, 412)(62, 410)(63, 423)(64, 344)(65, 346)(66, 428)(67, 429)(68, 430)(69, 432)(70, 347)(71, 435)(72, 348)(73, 437)(74, 349)(75, 351)(76, 442)(77, 354)(78, 355)(79, 446)(80, 448)(81, 445)(82, 443)(83, 451)(84, 356)(85, 454)(86, 456)(87, 457)(88, 358)(89, 460)(90, 359)(91, 360)(92, 463)(93, 361)(94, 467)(95, 362)(96, 363)(97, 472)(98, 473)(99, 367)(100, 466)(101, 468)(102, 477)(103, 368)(104, 370)(105, 481)(106, 482)(107, 373)(108, 486)(109, 487)(110, 374)(111, 489)(112, 376)(113, 491)(114, 377)(115, 379)(116, 496)(117, 382)(118, 383)(119, 500)(120, 502)(121, 499)(122, 497)(123, 505)(124, 384)(125, 507)(126, 385)(127, 511)(128, 386)(129, 387)(130, 516)(131, 517)(132, 391)(133, 510)(134, 512)(135, 393)(136, 524)(137, 525)(138, 394)(139, 527)(140, 396)(141, 398)(142, 531)(143, 514)(144, 532)(145, 523)(146, 399)(147, 414)(148, 535)(149, 418)(150, 403)(151, 540)(152, 542)(153, 543)(154, 405)(155, 509)(156, 406)(157, 407)(158, 504)(159, 408)(160, 424)(161, 503)(162, 548)(163, 411)(164, 549)(165, 550)(166, 544)(167, 415)(168, 416)(169, 538)(170, 541)(171, 537)(172, 419)(173, 421)(174, 547)(175, 422)(176, 495)(177, 546)(178, 521)(179, 557)(180, 425)(181, 561)(182, 426)(183, 427)(184, 564)(185, 485)(186, 431)(187, 560)(188, 562)(189, 433)(190, 570)(191, 470)(192, 434)(193, 571)(194, 436)(195, 476)(196, 574)(197, 575)(198, 438)(199, 559)(200, 439)(201, 440)(202, 458)(203, 441)(204, 452)(205, 455)(206, 579)(207, 444)(208, 580)(209, 475)(210, 447)(211, 449)(212, 578)(213, 450)(214, 480)(215, 577)(216, 568)(217, 566)(218, 453)(219, 583)(220, 459)(221, 589)(222, 588)(223, 591)(224, 483)(225, 461)(226, 462)(227, 464)(228, 594)(229, 478)(230, 595)(231, 590)(232, 465)(233, 474)(234, 469)(235, 471)(236, 597)(237, 582)(238, 567)(239, 592)(240, 479)(241, 599)(242, 484)(243, 488)(244, 490)(245, 520)(246, 601)(247, 602)(248, 492)(249, 534)(250, 493)(251, 494)(252, 506)(253, 605)(254, 498)(255, 606)(256, 519)(257, 501)(258, 555)(259, 604)(260, 529)(261, 508)(262, 611)(263, 556)(264, 518)(265, 513)(266, 515)(267, 613)(268, 608)(269, 614)(270, 522)(271, 526)(272, 528)(273, 615)(274, 530)(275, 533)(276, 609)(277, 616)(278, 536)(279, 552)(280, 618)(281, 539)(282, 554)(283, 545)(284, 619)(285, 553)(286, 551)(287, 612)(288, 558)(289, 621)(290, 584)(291, 565)(292, 563)(293, 623)(294, 586)(295, 624)(296, 569)(297, 572)(298, 573)(299, 576)(300, 593)(301, 581)(302, 622)(303, 596)(304, 585)(305, 620)(306, 587)(307, 598)(308, 600)(309, 603)(310, 610)(311, 607)(312, 617)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 78 e = 312 f = 182
	degree seq :: [ 8^78 ]

E27.2340 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 12})
Quotient :: loop
Aut^+ = S3 x (C13 : C4) (small group id <312, 46>)
Aut   = S3 x (C13 : C4) (small group id <312, 46>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1^-1)^4, (X1^3 * X2 * X1)^2, X1^12, (X2 * X1^-1 * X2 * X1^2 * X2 * X1^-1)^2, X2 * X1^2 * X2 * X1^2 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 ]
Map::
	R = (1, 313, 2, 314, 5, 317, 11, 323, 23, 335, 45, 357, 80, 392, 79, 391, 44, 356, 22, 334, 10, 322, 4, 316)(3, 315, 7, 319, 15, 327, 31, 343, 59, 371, 101, 413, 132, 444, 82, 394, 46, 358, 37, 349, 18, 330, 8, 320)(6, 318, 13, 325, 27, 339, 53, 365, 43, 355, 78, 390, 128, 440, 130, 442, 81, 393, 58, 370, 30, 342, 14, 326)(9, 321, 19, 331, 38, 350, 71, 383, 117, 429, 136, 448, 85, 397, 48, 360, 24, 336, 47, 359, 40, 352, 20, 332)(12, 324, 25, 337, 49, 361, 42, 354, 21, 333, 41, 353, 76, 388, 125, 437, 129, 441, 90, 402, 52, 364, 26, 338)(16, 328, 33, 345, 63, 375, 107, 419, 70, 382, 84, 396, 134, 446, 196, 508, 157, 469, 111, 423, 65, 377, 34, 346)(17, 329, 35, 347, 66, 378, 100, 412, 131, 443, 193, 505, 158, 470, 102, 414, 60, 372, 95, 407, 55, 367, 28, 340)(29, 341, 56, 368, 96, 408, 145, 457, 192, 504, 190, 502, 127, 439, 77, 389, 91, 403, 140, 452, 87, 399, 50, 362)(32, 344, 61, 373, 103, 415, 69, 381, 36, 348, 68, 380, 115, 427, 175, 487, 194, 506, 163, 475, 106, 418, 62, 374)(39, 351, 73, 385, 120, 432, 133, 445, 83, 395, 51, 363, 88, 400, 141, 453, 200, 512, 184, 496, 122, 434, 74, 386)(54, 366, 92, 404, 146, 458, 99, 411, 57, 369, 98, 410, 155, 467, 224, 536, 191, 503, 216, 528, 149, 461, 93, 405)(64, 376, 109, 421, 167, 479, 233, 545, 253, 565, 243, 555, 177, 489, 116, 428, 164, 476, 230, 542, 160, 472, 104, 416)(67, 379, 113, 425, 172, 484, 219, 531, 151, 463, 105, 417, 161, 473, 231, 543, 251, 563, 240, 552, 174, 486, 114, 426)(72, 384, 118, 430, 178, 490, 124, 436, 75, 387, 123, 435, 185, 497, 199, 511, 135, 447, 198, 510, 180, 492, 119, 431)(86, 398, 137, 449, 201, 513, 144, 456, 89, 401, 143, 455, 210, 522, 188, 500, 126, 438, 187, 499, 204, 516, 138, 450)(94, 406, 150, 462, 217, 529, 266, 578, 227, 539, 274, 586, 226, 538, 156, 468, 112, 424, 171, 483, 213, 525, 147, 459)(97, 409, 153, 465, 221, 533, 260, 572, 206, 518, 148, 460, 214, 526, 265, 577, 250, 562, 272, 584, 223, 535, 154, 466)(108, 420, 165, 477, 225, 537, 170, 482, 110, 422, 169, 481, 212, 524, 255, 567, 197, 509, 254, 566, 215, 527, 166, 478)(121, 433, 182, 494, 245, 557, 256, 568, 207, 519, 261, 573, 247, 559, 186, 498, 195, 507, 252, 564, 244, 556, 179, 491)(139, 451, 205, 517, 258, 570, 248, 560, 189, 501, 249, 561, 263, 575, 211, 523, 152, 464, 220, 532, 257, 569, 202, 514)(142, 454, 208, 520, 162, 474, 232, 544, 181, 493, 203, 515, 176, 488, 241, 553, 183, 495, 228, 540, 159, 471, 209, 521)(168, 480, 236, 548, 273, 585, 301, 613, 276, 588, 234, 546, 267, 579, 297, 609, 285, 597, 290, 602, 264, 576, 237, 549)(173, 485, 239, 551, 282, 594, 302, 614, 277, 589, 291, 603, 269, 581, 218, 530, 268, 580, 295, 607, 281, 593, 238, 550)(222, 534, 271, 583, 300, 612, 288, 600, 296, 608, 287, 599, 293, 605, 259, 571, 292, 604, 286, 598, 299, 611, 270, 582)(229, 541, 275, 587, 246, 558, 283, 595, 242, 554, 284, 596, 289, 601, 278, 590, 235, 547, 279, 591, 294, 606, 262, 574)(280, 592, 305, 617, 311, 623, 307, 619, 309, 621, 298, 610, 310, 622, 303, 615, 312, 624, 306, 618, 308, 620, 304, 616)
	L = (1, 315)(2, 318)(3, 313)(4, 321)(5, 324)(6, 314)(7, 328)(8, 329)(9, 316)(10, 333)(11, 336)(12, 317)(13, 340)(14, 341)(15, 344)(16, 319)(17, 320)(18, 348)(19, 351)(20, 345)(21, 322)(22, 355)(23, 358)(24, 323)(25, 362)(26, 363)(27, 366)(28, 325)(29, 326)(30, 369)(31, 372)(32, 327)(33, 332)(34, 376)(35, 379)(36, 330)(37, 382)(38, 384)(39, 331)(40, 387)(41, 389)(42, 385)(43, 334)(44, 371)(45, 393)(46, 335)(47, 395)(48, 396)(49, 398)(50, 337)(51, 338)(52, 401)(53, 403)(54, 339)(55, 406)(56, 409)(57, 342)(58, 412)(59, 356)(60, 343)(61, 416)(62, 417)(63, 420)(64, 346)(65, 422)(66, 424)(67, 347)(68, 428)(69, 425)(70, 349)(71, 423)(72, 350)(73, 354)(74, 433)(75, 352)(76, 438)(77, 353)(78, 414)(79, 429)(80, 441)(81, 357)(82, 443)(83, 359)(84, 360)(85, 447)(86, 361)(87, 451)(88, 454)(89, 364)(90, 457)(91, 365)(92, 459)(93, 460)(94, 367)(95, 463)(96, 464)(97, 368)(98, 468)(99, 465)(100, 370)(101, 469)(102, 390)(103, 471)(104, 373)(105, 374)(106, 474)(107, 476)(108, 375)(109, 480)(110, 377)(111, 383)(112, 378)(113, 381)(114, 485)(115, 488)(116, 380)(117, 391)(118, 491)(119, 481)(120, 493)(121, 386)(122, 495)(123, 498)(124, 477)(125, 496)(126, 388)(127, 501)(128, 503)(129, 392)(130, 504)(131, 394)(132, 506)(133, 507)(134, 509)(135, 397)(136, 512)(137, 514)(138, 515)(139, 399)(140, 518)(141, 519)(142, 400)(143, 523)(144, 520)(145, 402)(146, 524)(147, 404)(148, 405)(149, 527)(150, 530)(151, 407)(152, 408)(153, 411)(154, 534)(155, 537)(156, 410)(157, 413)(158, 539)(159, 415)(160, 541)(161, 513)(162, 418)(163, 545)(164, 419)(165, 436)(166, 546)(167, 547)(168, 421)(169, 431)(170, 548)(171, 550)(172, 522)(173, 426)(174, 516)(175, 552)(176, 427)(177, 554)(178, 535)(179, 430)(180, 533)(181, 432)(182, 558)(183, 434)(184, 437)(185, 526)(186, 435)(187, 560)(188, 540)(189, 439)(190, 562)(191, 440)(192, 442)(193, 563)(194, 444)(195, 445)(196, 565)(197, 446)(198, 568)(199, 566)(200, 448)(201, 473)(202, 449)(203, 450)(204, 486)(205, 571)(206, 452)(207, 453)(208, 456)(209, 574)(210, 484)(211, 455)(212, 458)(213, 576)(214, 497)(215, 461)(216, 578)(217, 579)(218, 462)(219, 580)(220, 582)(221, 492)(222, 466)(223, 490)(224, 584)(225, 467)(226, 585)(227, 470)(228, 500)(229, 472)(230, 588)(231, 589)(232, 590)(233, 475)(234, 478)(235, 479)(236, 482)(237, 592)(238, 483)(239, 570)(240, 487)(241, 595)(242, 489)(243, 597)(244, 583)(245, 598)(246, 494)(247, 599)(248, 499)(249, 600)(250, 502)(251, 505)(252, 601)(253, 508)(254, 511)(255, 602)(256, 510)(257, 603)(258, 551)(259, 517)(260, 604)(261, 606)(262, 521)(263, 607)(264, 525)(265, 608)(266, 528)(267, 529)(268, 531)(269, 610)(270, 532)(271, 556)(272, 536)(273, 538)(274, 614)(275, 615)(276, 542)(277, 543)(278, 544)(279, 616)(280, 549)(281, 617)(282, 618)(283, 553)(284, 619)(285, 555)(286, 557)(287, 559)(288, 561)(289, 564)(290, 567)(291, 569)(292, 572)(293, 620)(294, 573)(295, 575)(296, 577)(297, 621)(298, 581)(299, 622)(300, 623)(301, 624)(302, 586)(303, 587)(304, 591)(305, 593)(306, 594)(307, 596)(308, 605)(309, 609)(310, 611)(311, 612)(312, 613)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 26 e = 312 f = 234
	degree seq :: [ 24^26 ]

E27.2341 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 8})
Quotient :: halfedge
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^-3 * X2 * X1^-1)^2, (X1^-1 * X2 * X1 * X2 * X1^-2)^2, (X1^2 * X2 * X1^-1 * X2 * X1)^2, (X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 44, 37, 18, 8)(6, 13, 27, 51, 43, 56, 30, 14)(9, 19, 38, 46, 24, 45, 40, 20)(12, 25, 47, 42, 21, 41, 50, 26)(16, 33, 60, 93, 67, 74, 62, 34)(17, 35, 63, 88, 57, 83, 53, 28)(29, 54, 84, 72, 79, 111, 76, 48)(32, 58, 89, 66, 36, 65, 92, 59)(39, 69, 103, 107, 73, 49, 77, 70)(52, 80, 115, 87, 55, 86, 118, 81)(61, 95, 132, 100, 129, 168, 126, 90)(64, 98, 137, 161, 120, 91, 127, 99)(68, 101, 139, 106, 71, 105, 141, 102)(75, 108, 146, 114, 78, 113, 149, 109)(82, 119, 159, 124, 97, 136, 156, 116)(85, 122, 163, 194, 151, 117, 157, 123)(94, 130, 172, 135, 96, 134, 174, 131)(104, 143, 185, 144, 145, 187, 182, 140)(110, 150, 192, 154, 121, 162, 189, 147)(112, 152, 195, 184, 142, 148, 190, 153)(125, 165, 209, 171, 128, 170, 212, 166)(133, 176, 222, 267, 214, 173, 219, 177)(138, 180, 205, 160, 204, 256, 224, 178)(155, 197, 247, 202, 158, 201, 250, 198)(164, 208, 244, 193, 243, 299, 258, 206)(167, 213, 265, 217, 175, 221, 262, 210)(169, 215, 268, 225, 179, 211, 263, 216)(181, 227, 281, 231, 183, 230, 283, 228)(186, 196, 246, 289, 235, 232, 286, 234)(188, 236, 290, 241, 191, 240, 293, 237)(199, 251, 307, 254, 203, 255, 304, 248)(200, 252, 309, 259, 207, 249, 305, 253)(218, 270, 328, 274, 220, 273, 329, 271)(223, 277, 325, 266, 324, 358, 331, 275)(226, 269, 327, 350, 312, 279, 302, 280)(229, 284, 336, 285, 233, 287, 334, 282)(238, 294, 344, 297, 242, 298, 341, 291)(239, 295, 346, 301, 245, 292, 342, 296)(257, 313, 357, 308, 278, 332, 359, 311)(260, 310, 272, 330, 348, 315, 276, 316)(261, 317, 361, 322, 264, 321, 364, 318)(288, 320, 366, 337, 339, 326, 363, 338)(300, 349, 381, 345, 314, 360, 382, 347)(303, 351, 383, 355, 306, 354, 385, 352)(319, 365, 392, 367, 323, 368, 390, 362)(333, 369, 393, 373, 335, 372, 395, 370)(340, 375, 397, 379, 343, 378, 399, 376)(353, 386, 404, 387, 356, 388, 403, 384)(371, 391, 407, 396, 374, 389, 405, 394)(377, 400, 410, 401, 380, 402, 409, 398)(406, 411, 415, 414, 408, 412, 416, 413)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 44)(25, 48)(26, 49)(27, 52)(30, 55)(31, 57)(34, 61)(35, 64)(37, 67)(38, 68)(40, 71)(41, 72)(42, 69)(45, 73)(46, 74)(47, 75)(50, 78)(51, 79)(53, 82)(54, 85)(56, 88)(58, 90)(59, 91)(60, 94)(62, 96)(63, 97)(65, 100)(66, 98)(70, 104)(76, 110)(77, 112)(80, 116)(81, 117)(83, 120)(84, 121)(86, 124)(87, 122)(89, 125)(92, 128)(93, 129)(95, 133)(99, 138)(101, 140)(102, 134)(103, 142)(105, 144)(106, 130)(107, 145)(108, 147)(109, 148)(111, 151)(113, 154)(114, 152)(115, 155)(118, 158)(119, 160)(123, 164)(126, 167)(127, 169)(131, 173)(132, 175)(135, 176)(136, 178)(137, 179)(139, 181)(141, 183)(143, 186)(146, 188)(149, 191)(150, 193)(153, 196)(156, 199)(157, 200)(159, 203)(161, 204)(162, 206)(163, 207)(165, 210)(166, 211)(168, 214)(170, 217)(171, 215)(172, 218)(174, 220)(177, 223)(180, 226)(182, 229)(184, 232)(185, 233)(187, 235)(189, 238)(190, 239)(192, 242)(194, 243)(195, 245)(197, 248)(198, 249)(201, 254)(202, 252)(205, 257)(208, 260)(209, 261)(212, 264)(213, 266)(216, 269)(219, 272)(221, 275)(222, 276)(224, 278)(225, 279)(227, 282)(228, 270)(230, 285)(231, 273)(234, 288)(236, 291)(237, 292)(240, 297)(241, 295)(244, 300)(246, 302)(247, 303)(250, 306)(251, 308)(253, 310)(255, 311)(256, 312)(258, 314)(259, 315)(262, 319)(263, 320)(265, 323)(267, 324)(268, 326)(271, 316)(274, 330)(277, 305)(280, 296)(281, 333)(283, 335)(284, 337)(286, 327)(287, 338)(289, 339)(290, 340)(293, 343)(294, 345)(298, 347)(299, 348)(301, 350)(304, 353)(307, 356)(309, 358)(313, 342)(317, 362)(318, 363)(321, 367)(322, 366)(325, 355)(328, 360)(329, 349)(331, 352)(332, 346)(334, 371)(336, 374)(341, 377)(344, 380)(351, 384)(354, 387)(357, 379)(359, 376)(361, 389)(364, 391)(365, 385)(368, 383)(369, 394)(370, 381)(372, 396)(373, 382)(375, 398)(378, 401)(386, 399)(388, 397)(390, 406)(392, 408)(393, 400)(395, 402)(403, 411)(404, 412)(405, 413)(407, 414)(409, 415)(410, 416)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2342 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 8})
Quotient :: halfedge
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X2^2, X1^4, X2 * X1^-1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2 * X2 * X1^-1, (X1 * X2 * X1^-2 * X2 * X1 * X2)^2, (X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1)^2, (X1^-1 * X2)^8, (X2 * X1 * X2 * X1^-1 * X2 * X1^-2 * X2 * X1^-1 * X2 * X1^-1)^2, X1 * X2 * X1^-1 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1 * X2 * X1^-1 * X2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 41, 25)(15, 26, 44, 27)(21, 35, 59, 36)(22, 37, 62, 38)(23, 39, 65, 40)(29, 48, 80, 49)(30, 50, 83, 51)(32, 53, 88, 54)(33, 55, 91, 56)(34, 57, 94, 58)(42, 69, 93, 70)(43, 71, 115, 72)(45, 74, 119, 75)(46, 76, 89, 77)(47, 78, 124, 79)(52, 86, 131, 87)(60, 98, 85, 99)(61, 100, 146, 101)(63, 103, 150, 104)(64, 105, 81, 106)(66, 108, 157, 109)(67, 110, 143, 97)(68, 111, 160, 112)(73, 118, 141, 95)(82, 127, 174, 128)(84, 129, 176, 130)(90, 135, 181, 136)(92, 138, 185, 139)(96, 142, 180, 134)(102, 149, 178, 132)(107, 155, 199, 156)(113, 144, 123, 154)(114, 162, 209, 163)(116, 165, 211, 166)(117, 167, 120, 145)(121, 170, 194, 147)(122, 148, 195, 151)(125, 137, 184, 172)(126, 133, 179, 173)(140, 188, 235, 189)(152, 198, 230, 182)(153, 183, 231, 186)(158, 203, 253, 204)(159, 205, 256, 206)(161, 208, 252, 202)(164, 210, 250, 200)(168, 192, 242, 214)(169, 201, 251, 215)(171, 217, 269, 218)(175, 187, 234, 222)(177, 224, 278, 225)(190, 238, 295, 239)(191, 240, 298, 241)(193, 243, 293, 236)(196, 228, 285, 246)(197, 237, 294, 247)(207, 259, 315, 260)(212, 265, 287, 254)(213, 255, 312, 257)(216, 258, 314, 268)(219, 272, 327, 273)(220, 274, 289, 232)(221, 275, 324, 270)(223, 271, 326, 277)(226, 281, 332, 282)(227, 283, 334, 284)(229, 286, 330, 279)(233, 280, 331, 290)(244, 303, 276, 296)(245, 297, 346, 299)(248, 300, 348, 306)(249, 307, 351, 308)(261, 318, 361, 319)(262, 320, 359, 316)(263, 310, 338, 304)(264, 317, 360, 321)(266, 322, 339, 302)(267, 323, 349, 301)(288, 333, 368, 335)(291, 336, 370, 341)(292, 342, 372, 343)(305, 350, 311, 337)(309, 353, 380, 354)(313, 352, 379, 356)(325, 362, 383, 363)(328, 340, 371, 345)(329, 365, 390, 366)(344, 374, 398, 375)(347, 373, 397, 377)(355, 378, 400, 381)(357, 382, 403, 384)(358, 385, 404, 386)(364, 388, 406, 389)(367, 392, 408, 393)(369, 391, 407, 395)(376, 396, 410, 399)(387, 405, 409, 394)(401, 412, 415, 413)(402, 411, 416, 414)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 42)(25, 43)(26, 45)(27, 46)(28, 47)(31, 52)(35, 60)(36, 61)(37, 63)(38, 64)(39, 66)(40, 67)(41, 68)(44, 73)(48, 81)(49, 82)(50, 84)(51, 85)(53, 89)(54, 90)(55, 92)(56, 93)(57, 95)(58, 96)(59, 97)(62, 102)(65, 107)(69, 113)(70, 114)(71, 116)(72, 117)(74, 120)(75, 121)(76, 122)(77, 123)(78, 125)(79, 111)(80, 126)(83, 108)(86, 132)(87, 133)(88, 134)(91, 137)(94, 140)(98, 144)(99, 145)(100, 147)(101, 148)(103, 151)(104, 152)(105, 153)(106, 154)(109, 158)(110, 159)(112, 161)(115, 164)(118, 168)(119, 169)(124, 171)(127, 175)(128, 162)(129, 163)(130, 165)(131, 177)(135, 182)(136, 183)(138, 186)(139, 187)(141, 190)(142, 191)(143, 192)(146, 193)(149, 196)(150, 197)(155, 200)(156, 201)(157, 202)(160, 207)(166, 212)(167, 213)(170, 216)(172, 219)(173, 220)(174, 221)(176, 223)(178, 226)(179, 227)(180, 228)(181, 229)(184, 232)(185, 233)(188, 236)(189, 237)(194, 244)(195, 245)(198, 248)(199, 249)(203, 254)(204, 255)(205, 257)(206, 258)(208, 261)(209, 262)(210, 263)(211, 264)(214, 266)(215, 267)(217, 270)(218, 271)(222, 276)(224, 279)(225, 280)(230, 287)(231, 288)(234, 291)(235, 292)(238, 296)(239, 297)(240, 299)(241, 300)(242, 301)(243, 302)(246, 304)(247, 305)(250, 306)(251, 309)(252, 310)(253, 311)(256, 313)(259, 316)(260, 317)(265, 281)(268, 324)(269, 325)(272, 303)(273, 320)(274, 328)(275, 322)(277, 318)(278, 329)(282, 333)(283, 335)(284, 336)(285, 337)(286, 338)(289, 339)(290, 340)(293, 341)(294, 344)(295, 345)(298, 347)(307, 350)(308, 352)(312, 355)(314, 357)(315, 358)(319, 332)(321, 330)(323, 362)(326, 364)(327, 349)(331, 367)(334, 369)(342, 371)(343, 373)(346, 376)(348, 378)(351, 377)(353, 381)(354, 382)(356, 383)(359, 384)(360, 387)(361, 365)(363, 385)(366, 391)(368, 394)(370, 396)(372, 395)(374, 399)(375, 400)(379, 401)(380, 402)(386, 390)(388, 403)(389, 405)(392, 409)(393, 410)(397, 411)(398, 412)(404, 414)(406, 413)(407, 415)(408, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2343 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X1^2, X2^4, (X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1)^2, (X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1)^2, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, (X2 * X1)^8, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, X2 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 9)(5, 10)(6, 12)(8, 15)(11, 20)(13, 23)(14, 25)(16, 28)(17, 30)(18, 31)(19, 33)(21, 36)(22, 38)(24, 41)(26, 44)(27, 46)(29, 49)(32, 54)(34, 57)(35, 59)(37, 62)(39, 65)(40, 67)(42, 70)(43, 72)(45, 75)(47, 78)(48, 80)(50, 83)(51, 85)(52, 86)(53, 88)(55, 91)(56, 93)(58, 96)(60, 99)(61, 101)(63, 104)(64, 106)(66, 98)(68, 103)(69, 112)(71, 115)(73, 105)(74, 119)(76, 122)(77, 87)(79, 124)(81, 127)(82, 89)(84, 94)(90, 136)(92, 139)(95, 143)(97, 146)(100, 148)(102, 151)(107, 131)(108, 141)(109, 150)(110, 153)(111, 156)(113, 154)(114, 160)(116, 163)(117, 132)(118, 158)(120, 162)(121, 167)(123, 170)(125, 172)(126, 133)(128, 175)(129, 134)(130, 137)(135, 178)(138, 182)(140, 185)(142, 180)(144, 184)(145, 189)(147, 192)(149, 194)(152, 197)(155, 199)(157, 202)(159, 204)(161, 207)(164, 206)(165, 209)(166, 212)(168, 210)(169, 215)(171, 217)(173, 219)(174, 220)(176, 223)(177, 224)(179, 227)(181, 229)(183, 232)(186, 231)(187, 234)(188, 237)(190, 235)(191, 240)(193, 242)(195, 244)(196, 245)(198, 248)(200, 250)(201, 252)(203, 255)(205, 257)(208, 260)(211, 262)(213, 265)(214, 266)(216, 268)(218, 270)(221, 272)(222, 276)(225, 279)(226, 281)(228, 284)(230, 286)(233, 289)(236, 291)(238, 294)(239, 295)(241, 297)(243, 299)(246, 301)(247, 305)(249, 303)(251, 308)(253, 306)(254, 311)(256, 313)(258, 287)(259, 288)(261, 315)(263, 317)(264, 319)(267, 323)(269, 325)(271, 302)(273, 300)(274, 278)(275, 327)(277, 282)(280, 330)(283, 333)(285, 335)(290, 337)(292, 339)(293, 341)(296, 345)(298, 347)(304, 349)(307, 351)(309, 354)(310, 355)(312, 338)(314, 356)(316, 334)(318, 358)(320, 357)(321, 361)(322, 362)(324, 348)(326, 346)(328, 364)(329, 365)(331, 368)(332, 369)(336, 370)(340, 372)(342, 371)(343, 375)(344, 376)(350, 378)(352, 377)(353, 381)(359, 386)(360, 387)(363, 366)(367, 392)(373, 397)(374, 398)(379, 399)(380, 401)(382, 400)(383, 395)(384, 394)(385, 403)(388, 390)(389, 393)(391, 407)(396, 409)(402, 410)(404, 408)(405, 412)(406, 411)(413, 416)(414, 415)(417, 419, 424, 420)(418, 421, 427, 422)(423, 429, 440, 430)(425, 432, 445, 433)(426, 434, 448, 435)(428, 437, 453, 438)(431, 442, 461, 443)(436, 450, 474, 451)(439, 455, 482, 456)(441, 458, 487, 459)(444, 463, 495, 464)(446, 466, 500, 467)(447, 468, 503, 469)(449, 471, 508, 472)(452, 476, 516, 477)(454, 479, 521, 480)(457, 484, 527, 485)(460, 489, 534, 490)(462, 492, 539, 493)(465, 497, 544, 498)(470, 505, 551, 506)(473, 510, 558, 511)(475, 513, 563, 514)(478, 518, 568, 519)(481, 523, 501, 524)(483, 525, 571, 526)(486, 529, 575, 530)(488, 532, 494, 533)(491, 536, 582, 537)(496, 541, 589, 542)(499, 545, 592, 546)(502, 547, 522, 548)(504, 549, 593, 550)(507, 553, 597, 554)(509, 556, 515, 557)(512, 560, 604, 561)(517, 565, 611, 566)(520, 569, 614, 570)(528, 573, 619, 574)(531, 577, 624, 578)(535, 580, 627, 581)(538, 584, 630, 585)(540, 583, 629, 587)(543, 586, 632, 590)(552, 595, 644, 596)(555, 599, 649, 600)(559, 602, 652, 603)(562, 606, 655, 607)(564, 605, 654, 609)(567, 608, 657, 612)(572, 616, 667, 617)(576, 621, 674, 622)(579, 625, 677, 626)(588, 631, 683, 634)(591, 637, 691, 638)(594, 641, 696, 642)(598, 646, 703, 647)(601, 650, 706, 651)(610, 656, 712, 659)(613, 662, 720, 663)(615, 665, 723, 666)(618, 669, 726, 670)(620, 668, 725, 672)(623, 671, 728, 675)(628, 679, 734, 680)(633, 685, 740, 684)(635, 687, 715, 688)(636, 689, 742, 690)(639, 692, 744, 693)(640, 694, 745, 695)(643, 698, 748, 699)(645, 697, 747, 701)(648, 700, 750, 704)(653, 708, 756, 709)(658, 714, 762, 713)(660, 716, 686, 717)(661, 718, 764, 719)(664, 721, 766, 722)(673, 727, 752, 705)(676, 702, 749, 730)(678, 732, 751, 733)(681, 736, 776, 737)(682, 735, 775, 738)(707, 754, 729, 755)(710, 758, 790, 759)(711, 757, 789, 760)(724, 768, 796, 769)(731, 772, 800, 773)(739, 777, 795, 767)(741, 778, 793, 765)(743, 763, 792, 779)(746, 782, 807, 783)(753, 786, 811, 787)(761, 791, 806, 781)(770, 798, 818, 799)(771, 797, 812, 788)(774, 785, 808, 801)(780, 804, 822, 805)(784, 809, 824, 810)(794, 815, 828, 816)(802, 820, 830, 821)(803, 819, 829, 817)(813, 826, 832, 827)(814, 825, 831, 823)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 16, 16 ), ( 16^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 312 e = 416 f = 52
	degree seq :: [ 2^208, 4^104 ]

E27.2344 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ (X1^-1 * X2^-1)^2, X1^4, X1^-1 * X2^-1 * X1^3 * X2^-1, (X2 * X1^-1 * X2^2)^2, X2^8, X2^-1 * X1 * X2^2 * X1^2 * X2^-4 * X1^-1 * X2 * X1^-2 * X2^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1, X1^-1 * X2^-1 * X1 * X2^2 * X1^2 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-1 * X2 * X1^-1, X2 * X1^-1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1 * X1^2 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1^-2, X2 * X1^-1 * X2^-1 * X1 * X2^2 * X1^2 * X2^-1 * X1 * X2^2 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 21, 11)(5, 13, 18, 7)(8, 19, 34, 15)(10, 23, 49, 25)(12, 16, 35, 28)(14, 31, 61, 29)(17, 37, 72, 39)(20, 43, 80, 41)(22, 47, 84, 45)(24, 51, 82, 44)(26, 46, 85, 55)(27, 56, 99, 58)(30, 62, 78, 40)(32, 57, 101, 63)(33, 64, 106, 66)(36, 70, 114, 68)(38, 74, 116, 71)(42, 81, 112, 67)(48, 65, 108, 87)(50, 92, 139, 90)(52, 75, 109, 89)(53, 91, 140, 95)(54, 96, 146, 97)(59, 69, 115, 102)(60, 103, 152, 104)(73, 119, 168, 117)(76, 118, 169, 122)(77, 123, 175, 124)(79, 126, 178, 127)(83, 129, 181, 131)(86, 135, 188, 133)(88, 137, 186, 132)(93, 130, 183, 142)(94, 144, 171, 120)(98, 134, 189, 148)(100, 150, 205, 149)(105, 154, 177, 125)(107, 157, 212, 155)(110, 156, 213, 160)(111, 161, 219, 162)(113, 164, 222, 165)(121, 173, 215, 158)(128, 180, 221, 163)(136, 159, 217, 190)(138, 192, 254, 193)(141, 197, 260, 195)(143, 199, 258, 194)(145, 196, 261, 201)(147, 203, 266, 202)(151, 166, 224, 207)(153, 208, 272, 209)(167, 225, 291, 226)(170, 230, 297, 228)(172, 232, 295, 227)(174, 229, 298, 234)(176, 236, 303, 235)(179, 238, 306, 239)(182, 243, 310, 241)(184, 242, 311, 245)(185, 246, 316, 247)(187, 249, 319, 250)(191, 253, 318, 248)(198, 244, 314, 262)(200, 264, 299, 231)(204, 251, 321, 268)(206, 270, 341, 269)(210, 274, 305, 237)(211, 275, 347, 276)(214, 280, 353, 278)(216, 282, 351, 277)(218, 279, 354, 284)(220, 286, 359, 285)(223, 288, 362, 289)(233, 301, 355, 281)(240, 308, 361, 287)(252, 283, 357, 322)(255, 326, 363, 324)(256, 325, 349, 327)(257, 328, 358, 329)(259, 331, 352, 332)(263, 335, 389, 330)(265, 333, 350, 337)(267, 339, 393, 338)(271, 290, 364, 343)(273, 344, 348, 345)(292, 367, 315, 365)(293, 366, 309, 368)(294, 369, 320, 370)(296, 372, 312, 373)(300, 376, 404, 371)(302, 374, 317, 378)(304, 380, 340, 379)(307, 382, 313, 383)(323, 387, 402, 384)(334, 385, 403, 390)(336, 392, 405, 375)(342, 396, 412, 395)(346, 360, 401, 381)(356, 399, 413, 397)(377, 407, 414, 398)(386, 400, 388, 409)(391, 408, 415, 410)(394, 406, 416, 411)(417, 419, 426, 440, 468, 448, 430, 421)(418, 423, 433, 454, 491, 460, 436, 424)(420, 428, 443, 473, 505, 464, 438, 425)(422, 431, 449, 481, 525, 487, 452, 432)(427, 442, 470, 447, 479, 509, 466, 439)(429, 445, 476, 510, 467, 441, 469, 446)(434, 456, 493, 459, 498, 536, 489, 453)(435, 457, 495, 537, 490, 455, 492, 458)(437, 461, 499, 546, 517, 474, 502, 462)(444, 475, 504, 463, 503, 552, 516, 472)(450, 483, 527, 486, 532, 574, 523, 480)(451, 484, 529, 575, 524, 482, 526, 485)(465, 506, 554, 519, 477, 513, 557, 507)(471, 514, 559, 508, 558, 614, 563, 512)(478, 511, 561, 616, 560, 520, 569, 521)(488, 533, 583, 542, 496, 540, 586, 534)(494, 541, 588, 535, 587, 647, 592, 539)(497, 538, 590, 649, 589, 543, 595, 544)(500, 548, 601, 551, 515, 565, 598, 545)(501, 549, 603, 660, 599, 547, 600, 550)(518, 567, 622, 566, 606, 668, 607, 553)(522, 571, 627, 580, 530, 578, 630, 572)(528, 579, 632, 573, 631, 697, 636, 577)(531, 576, 634, 699, 633, 581, 639, 582)(555, 610, 673, 613, 562, 618, 671, 608)(556, 611, 675, 624, 568, 609, 672, 612)(564, 620, 683, 619, 678, 750, 679, 615)(570, 625, 689, 752, 680, 617, 681, 626)(584, 643, 710, 646, 591, 651, 708, 641)(585, 644, 712, 654, 594, 642, 709, 645)(593, 653, 720, 652, 715, 791, 716, 648)(596, 655, 723, 793, 717, 650, 718, 656)(597, 657, 725, 665, 604, 663, 728, 658)(602, 664, 729, 659, 621, 685, 733, 662)(605, 661, 731, 801, 730, 666, 736, 667)(623, 687, 739, 669, 738, 802, 758, 686)(628, 693, 766, 696, 635, 701, 764, 691)(629, 694, 768, 704, 638, 692, 765, 695)(637, 703, 776, 702, 771, 814, 772, 698)(640, 705, 779, 816, 773, 700, 774, 706)(670, 740, 778, 747, 676, 745, 770, 741)(674, 746, 804, 742, 682, 754, 780, 744)(677, 743, 763, 760, 688, 748, 769, 749)(684, 756, 807, 751, 806, 820, 810, 755)(690, 753, 767, 813, 808, 761, 775, 762)(707, 781, 727, 788, 713, 786, 735, 782)(711, 787, 819, 783, 719, 795, 737, 785)(714, 784, 726, 798, 722, 789, 732, 790)(721, 797, 822, 792, 821, 829, 824, 796)(724, 794, 757, 811, 823, 799, 734, 800)(759, 809, 827, 812, 825, 805, 826, 803)(777, 818, 831, 815, 830, 828, 832, 817)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: chiral
Dual of E27.2346
Transitivity :: ET+
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2345 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^2 * X2 * X1^2)^2, X1^3 * X2 * X1^-4 * X2 * X1, X1^-1 * X2 * X1^3 * X2 * X1^-1 * X2 * X1 * X2 * X1^-4 * X2 * X1^-2 * X2, X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ]
Map:: polytopal
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 44, 37, 18, 8)(6, 13, 27, 51, 43, 56, 30, 14)(9, 19, 38, 46, 24, 45, 40, 20)(12, 25, 47, 42, 21, 41, 50, 26)(16, 33, 60, 93, 67, 74, 62, 34)(17, 35, 63, 88, 57, 83, 53, 28)(29, 54, 84, 72, 79, 111, 76, 48)(32, 58, 89, 66, 36, 65, 92, 59)(39, 69, 103, 107, 73, 49, 77, 70)(52, 80, 115, 87, 55, 86, 118, 81)(61, 95, 132, 100, 129, 168, 126, 90)(64, 98, 137, 161, 120, 91, 127, 99)(68, 101, 139, 106, 71, 105, 141, 102)(75, 108, 146, 114, 78, 113, 149, 109)(82, 119, 159, 124, 97, 136, 156, 116)(85, 122, 163, 194, 151, 117, 157, 123)(94, 130, 172, 135, 96, 134, 174, 131)(104, 143, 185, 144, 145, 187, 182, 140)(110, 150, 192, 154, 121, 162, 189, 147)(112, 152, 195, 184, 142, 148, 190, 153)(125, 165, 209, 171, 128, 170, 212, 166)(133, 176, 222, 267, 214, 173, 219, 177)(138, 180, 205, 160, 204, 256, 224, 178)(155, 197, 247, 202, 158, 201, 250, 198)(164, 208, 244, 193, 243, 299, 258, 206)(167, 213, 265, 217, 175, 221, 262, 210)(169, 215, 268, 225, 179, 211, 263, 216)(181, 227, 281, 231, 183, 230, 283, 228)(186, 196, 246, 289, 235, 232, 286, 234)(188, 236, 290, 241, 191, 240, 293, 237)(199, 251, 307, 254, 203, 255, 304, 248)(200, 252, 309, 259, 207, 249, 305, 253)(218, 270, 328, 274, 220, 273, 329, 271)(223, 277, 325, 266, 324, 358, 331, 275)(226, 269, 327, 350, 312, 279, 302, 280)(229, 284, 336, 285, 233, 287, 334, 282)(238, 294, 344, 297, 242, 298, 341, 291)(239, 295, 346, 301, 245, 292, 342, 296)(257, 313, 357, 308, 278, 332, 359, 311)(260, 310, 272, 330, 348, 315, 276, 316)(261, 317, 361, 322, 264, 321, 364, 318)(288, 320, 366, 337, 339, 326, 363, 338)(300, 349, 381, 345, 314, 360, 382, 347)(303, 351, 383, 355, 306, 354, 385, 352)(319, 365, 392, 367, 323, 368, 390, 362)(333, 369, 393, 373, 335, 372, 395, 370)(340, 375, 397, 379, 343, 378, 399, 376)(353, 386, 404, 387, 356, 388, 403, 384)(371, 391, 407, 396, 374, 389, 405, 394)(377, 400, 410, 401, 380, 402, 409, 398)(406, 411, 415, 414, 408, 412, 416, 413)(417, 419)(418, 422)(420, 425)(421, 428)(423, 432)(424, 433)(426, 437)(427, 440)(429, 444)(430, 445)(431, 448)(434, 452)(435, 455)(436, 449)(438, 459)(439, 460)(441, 464)(442, 465)(443, 468)(446, 471)(447, 473)(450, 477)(451, 480)(453, 483)(454, 484)(456, 487)(457, 488)(458, 485)(461, 489)(462, 490)(463, 491)(466, 494)(467, 495)(469, 498)(470, 501)(472, 504)(474, 506)(475, 507)(476, 510)(478, 512)(479, 513)(481, 516)(482, 514)(486, 520)(492, 526)(493, 528)(496, 532)(497, 533)(499, 536)(500, 537)(502, 540)(503, 538)(505, 541)(508, 544)(509, 545)(511, 549)(515, 554)(517, 556)(518, 550)(519, 558)(521, 560)(522, 546)(523, 561)(524, 563)(525, 564)(527, 567)(529, 570)(530, 568)(531, 571)(534, 574)(535, 576)(539, 580)(542, 583)(543, 585)(547, 589)(548, 591)(551, 592)(552, 594)(553, 595)(555, 597)(557, 599)(559, 602)(562, 604)(565, 607)(566, 609)(569, 612)(572, 615)(573, 616)(575, 619)(577, 620)(578, 622)(579, 623)(581, 626)(582, 627)(584, 630)(586, 633)(587, 631)(588, 634)(590, 636)(593, 639)(596, 642)(598, 645)(600, 648)(601, 649)(603, 651)(605, 654)(606, 655)(608, 658)(610, 659)(611, 661)(613, 664)(614, 665)(617, 670)(618, 668)(621, 673)(624, 676)(625, 677)(628, 680)(629, 682)(632, 685)(635, 688)(637, 691)(638, 692)(640, 694)(641, 695)(643, 698)(644, 686)(646, 701)(647, 689)(650, 704)(652, 707)(653, 708)(656, 713)(657, 711)(660, 716)(662, 718)(663, 719)(666, 722)(667, 724)(669, 726)(671, 727)(672, 728)(674, 730)(675, 731)(678, 735)(679, 736)(681, 739)(683, 740)(684, 742)(687, 732)(690, 746)(693, 721)(696, 712)(697, 749)(699, 751)(700, 753)(702, 743)(703, 754)(705, 755)(706, 756)(709, 759)(710, 761)(714, 763)(715, 764)(717, 766)(720, 769)(723, 772)(725, 774)(729, 758)(733, 778)(734, 779)(737, 783)(738, 782)(741, 771)(744, 776)(745, 765)(747, 768)(748, 762)(750, 787)(752, 790)(757, 793)(760, 796)(767, 800)(770, 803)(773, 795)(775, 792)(777, 805)(780, 807)(781, 801)(784, 799)(785, 810)(786, 797)(788, 812)(789, 798)(791, 814)(794, 817)(802, 815)(804, 813)(806, 822)(808, 824)(809, 816)(811, 818)(819, 827)(820, 828)(821, 829)(823, 830)(825, 831)(826, 832)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 8, 8 ), ( 8^8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 260 e = 416 f = 104
	degree seq :: [ 2^208, 8^52 ]

E27.2346 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X1^2, X2^4, (X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1)^2, (X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1)^2, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, (X2 * X1)^8, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, X2 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 ]
Map:: polytopal non-degenerate
	R = (1, 417, 2, 418)(3, 419, 7, 423)(4, 420, 9, 425)(5, 421, 10, 426)(6, 422, 12, 428)(8, 424, 15, 431)(11, 427, 20, 436)(13, 429, 23, 439)(14, 430, 25, 441)(16, 432, 28, 444)(17, 433, 30, 446)(18, 434, 31, 447)(19, 435, 33, 449)(21, 437, 36, 452)(22, 438, 38, 454)(24, 440, 41, 457)(26, 442, 44, 460)(27, 443, 46, 462)(29, 445, 49, 465)(32, 448, 54, 470)(34, 450, 57, 473)(35, 451, 59, 475)(37, 453, 62, 478)(39, 455, 65, 481)(40, 456, 67, 483)(42, 458, 70, 486)(43, 459, 72, 488)(45, 461, 75, 491)(47, 463, 78, 494)(48, 464, 80, 496)(50, 466, 83, 499)(51, 467, 85, 501)(52, 468, 86, 502)(53, 469, 88, 504)(55, 471, 91, 507)(56, 472, 93, 509)(58, 474, 96, 512)(60, 476, 99, 515)(61, 477, 101, 517)(63, 479, 104, 520)(64, 480, 106, 522)(66, 482, 98, 514)(68, 484, 103, 519)(69, 485, 112, 528)(71, 487, 115, 531)(73, 489, 105, 521)(74, 490, 119, 535)(76, 492, 122, 538)(77, 493, 87, 503)(79, 495, 124, 540)(81, 497, 127, 543)(82, 498, 89, 505)(84, 500, 94, 510)(90, 506, 136, 552)(92, 508, 139, 555)(95, 511, 143, 559)(97, 513, 146, 562)(100, 516, 148, 564)(102, 518, 151, 567)(107, 523, 131, 547)(108, 524, 141, 557)(109, 525, 150, 566)(110, 526, 153, 569)(111, 527, 156, 572)(113, 529, 154, 570)(114, 530, 160, 576)(116, 532, 163, 579)(117, 533, 132, 548)(118, 534, 158, 574)(120, 536, 162, 578)(121, 537, 167, 583)(123, 539, 170, 586)(125, 541, 172, 588)(126, 542, 133, 549)(128, 544, 175, 591)(129, 545, 134, 550)(130, 546, 137, 553)(135, 551, 178, 594)(138, 554, 182, 598)(140, 556, 185, 601)(142, 558, 180, 596)(144, 560, 184, 600)(145, 561, 189, 605)(147, 563, 192, 608)(149, 565, 194, 610)(152, 568, 197, 613)(155, 571, 199, 615)(157, 573, 202, 618)(159, 575, 204, 620)(161, 577, 207, 623)(164, 580, 206, 622)(165, 581, 209, 625)(166, 582, 212, 628)(168, 584, 210, 626)(169, 585, 215, 631)(171, 587, 217, 633)(173, 589, 219, 635)(174, 590, 220, 636)(176, 592, 223, 639)(177, 593, 224, 640)(179, 595, 227, 643)(181, 597, 229, 645)(183, 599, 232, 648)(186, 602, 231, 647)(187, 603, 234, 650)(188, 604, 237, 653)(190, 606, 235, 651)(191, 607, 240, 656)(193, 609, 242, 658)(195, 611, 244, 660)(196, 612, 245, 661)(198, 614, 248, 664)(200, 616, 250, 666)(201, 617, 252, 668)(203, 619, 255, 671)(205, 621, 257, 673)(208, 624, 260, 676)(211, 627, 262, 678)(213, 629, 265, 681)(214, 630, 266, 682)(216, 632, 268, 684)(218, 634, 270, 686)(221, 637, 272, 688)(222, 638, 276, 692)(225, 641, 279, 695)(226, 642, 281, 697)(228, 644, 284, 700)(230, 646, 286, 702)(233, 649, 289, 705)(236, 652, 291, 707)(238, 654, 294, 710)(239, 655, 295, 711)(241, 657, 297, 713)(243, 659, 299, 715)(246, 662, 301, 717)(247, 663, 305, 721)(249, 665, 303, 719)(251, 667, 308, 724)(253, 669, 306, 722)(254, 670, 311, 727)(256, 672, 313, 729)(258, 674, 287, 703)(259, 675, 288, 704)(261, 677, 315, 731)(263, 679, 317, 733)(264, 680, 319, 735)(267, 683, 323, 739)(269, 685, 325, 741)(271, 687, 302, 718)(273, 689, 300, 716)(274, 690, 278, 694)(275, 691, 327, 743)(277, 693, 282, 698)(280, 696, 330, 746)(283, 699, 333, 749)(285, 701, 335, 751)(290, 706, 337, 753)(292, 708, 339, 755)(293, 709, 341, 757)(296, 712, 345, 761)(298, 714, 347, 763)(304, 720, 349, 765)(307, 723, 351, 767)(309, 725, 354, 770)(310, 726, 355, 771)(312, 728, 338, 754)(314, 730, 356, 772)(316, 732, 334, 750)(318, 734, 358, 774)(320, 736, 357, 773)(321, 737, 361, 777)(322, 738, 362, 778)(324, 740, 348, 764)(326, 742, 346, 762)(328, 744, 364, 780)(329, 745, 365, 781)(331, 747, 368, 784)(332, 748, 369, 785)(336, 752, 370, 786)(340, 756, 372, 788)(342, 758, 371, 787)(343, 759, 375, 791)(344, 760, 376, 792)(350, 766, 378, 794)(352, 768, 377, 793)(353, 769, 381, 797)(359, 775, 386, 802)(360, 776, 387, 803)(363, 779, 366, 782)(367, 783, 392, 808)(373, 789, 397, 813)(374, 790, 398, 814)(379, 795, 399, 815)(380, 796, 401, 817)(382, 798, 400, 816)(383, 799, 395, 811)(384, 800, 394, 810)(385, 801, 403, 819)(388, 804, 390, 806)(389, 805, 393, 809)(391, 807, 407, 823)(396, 812, 409, 825)(402, 818, 410, 826)(404, 820, 408, 824)(405, 821, 412, 828)(406, 822, 411, 827)(413, 829, 416, 832)(414, 830, 415, 831)
	L = (1, 419)(2, 421)(3, 424)(4, 417)(5, 427)(6, 418)(7, 429)(8, 420)(9, 432)(10, 434)(11, 422)(12, 437)(13, 440)(14, 423)(15, 442)(16, 445)(17, 425)(18, 448)(19, 426)(20, 450)(21, 453)(22, 428)(23, 455)(24, 430)(25, 458)(26, 461)(27, 431)(28, 463)(29, 433)(30, 466)(31, 468)(32, 435)(33, 471)(34, 474)(35, 436)(36, 476)(37, 438)(38, 479)(39, 482)(40, 439)(41, 484)(42, 487)(43, 441)(44, 489)(45, 443)(46, 492)(47, 495)(48, 444)(49, 497)(50, 500)(51, 446)(52, 503)(53, 447)(54, 505)(55, 508)(56, 449)(57, 510)(58, 451)(59, 513)(60, 516)(61, 452)(62, 518)(63, 521)(64, 454)(65, 523)(66, 456)(67, 525)(68, 527)(69, 457)(70, 529)(71, 459)(72, 532)(73, 534)(74, 460)(75, 536)(76, 539)(77, 462)(78, 533)(79, 464)(80, 541)(81, 544)(82, 465)(83, 545)(84, 467)(85, 524)(86, 547)(87, 469)(88, 549)(89, 551)(90, 470)(91, 553)(92, 472)(93, 556)(94, 558)(95, 473)(96, 560)(97, 563)(98, 475)(99, 557)(100, 477)(101, 565)(102, 568)(103, 478)(104, 569)(105, 480)(106, 548)(107, 501)(108, 481)(109, 571)(110, 483)(111, 485)(112, 573)(113, 575)(114, 486)(115, 577)(116, 494)(117, 488)(118, 490)(119, 580)(120, 582)(121, 491)(122, 584)(123, 493)(124, 583)(125, 589)(126, 496)(127, 586)(128, 498)(129, 592)(130, 499)(131, 522)(132, 502)(133, 593)(134, 504)(135, 506)(136, 595)(137, 597)(138, 507)(139, 599)(140, 515)(141, 509)(142, 511)(143, 602)(144, 604)(145, 512)(146, 606)(147, 514)(148, 605)(149, 611)(150, 517)(151, 608)(152, 519)(153, 614)(154, 520)(155, 526)(156, 616)(157, 619)(158, 528)(159, 530)(160, 621)(161, 624)(162, 531)(163, 625)(164, 627)(165, 535)(166, 537)(167, 629)(168, 630)(169, 538)(170, 632)(171, 540)(172, 631)(173, 542)(174, 543)(175, 637)(176, 546)(177, 550)(178, 641)(179, 644)(180, 552)(181, 554)(182, 646)(183, 649)(184, 555)(185, 650)(186, 652)(187, 559)(188, 561)(189, 654)(190, 655)(191, 562)(192, 657)(193, 564)(194, 656)(195, 566)(196, 567)(197, 662)(198, 570)(199, 665)(200, 667)(201, 572)(202, 669)(203, 574)(204, 668)(205, 674)(206, 576)(207, 671)(208, 578)(209, 677)(210, 579)(211, 581)(212, 679)(213, 587)(214, 585)(215, 683)(216, 590)(217, 685)(218, 588)(219, 687)(220, 689)(221, 691)(222, 591)(223, 692)(224, 694)(225, 696)(226, 594)(227, 698)(228, 596)(229, 697)(230, 703)(231, 598)(232, 700)(233, 600)(234, 706)(235, 601)(236, 603)(237, 708)(238, 609)(239, 607)(240, 712)(241, 612)(242, 714)(243, 610)(244, 716)(245, 718)(246, 720)(247, 613)(248, 721)(249, 723)(250, 615)(251, 617)(252, 725)(253, 726)(254, 618)(255, 728)(256, 620)(257, 727)(258, 622)(259, 623)(260, 702)(261, 626)(262, 732)(263, 734)(264, 628)(265, 736)(266, 735)(267, 634)(268, 633)(269, 740)(270, 717)(271, 715)(272, 635)(273, 742)(274, 636)(275, 638)(276, 744)(277, 639)(278, 745)(279, 640)(280, 642)(281, 747)(282, 748)(283, 643)(284, 750)(285, 645)(286, 749)(287, 647)(288, 648)(289, 673)(290, 651)(291, 754)(292, 756)(293, 653)(294, 758)(295, 757)(296, 659)(297, 658)(298, 762)(299, 688)(300, 686)(301, 660)(302, 764)(303, 661)(304, 663)(305, 766)(306, 664)(307, 666)(308, 768)(309, 672)(310, 670)(311, 752)(312, 675)(313, 755)(314, 676)(315, 772)(316, 751)(317, 678)(318, 680)(319, 775)(320, 776)(321, 681)(322, 682)(323, 777)(324, 684)(325, 778)(326, 690)(327, 763)(328, 693)(329, 695)(330, 782)(331, 701)(332, 699)(333, 730)(334, 704)(335, 733)(336, 705)(337, 786)(338, 729)(339, 707)(340, 709)(341, 789)(342, 790)(343, 710)(344, 711)(345, 791)(346, 713)(347, 792)(348, 719)(349, 741)(350, 722)(351, 739)(352, 796)(353, 724)(354, 798)(355, 797)(356, 800)(357, 731)(358, 785)(359, 738)(360, 737)(361, 795)(362, 793)(363, 743)(364, 804)(365, 761)(366, 807)(367, 746)(368, 809)(369, 808)(370, 811)(371, 753)(372, 771)(373, 760)(374, 759)(375, 806)(376, 779)(377, 765)(378, 815)(379, 767)(380, 769)(381, 812)(382, 818)(383, 770)(384, 773)(385, 774)(386, 820)(387, 819)(388, 822)(389, 780)(390, 781)(391, 783)(392, 801)(393, 824)(394, 784)(395, 787)(396, 788)(397, 826)(398, 825)(399, 828)(400, 794)(401, 803)(402, 799)(403, 829)(404, 830)(405, 802)(406, 805)(407, 814)(408, 810)(409, 831)(410, 832)(411, 813)(412, 816)(413, 817)(414, 821)(415, 823)(416, 827)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: chiral
Dual of E27.2344
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2347 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ (X1^-1 * X2^-1)^2, X1^4, X1^-1 * X2^-1 * X1^3 * X2^-1, (X2 * X1^-1 * X2^2)^2, X2^8, X2^-1 * X1 * X2^2 * X1^2 * X2^-4 * X1^-1 * X2 * X1^-2 * X2^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1, X1^-1 * X2^-1 * X1 * X2^2 * X1^2 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-1 * X2 * X1^-1, X2 * X1^-1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1 * X1^2 * X2^-1 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1^-2, X2 * X1^-1 * X2^-1 * X1 * X2^2 * X1^2 * X2^-1 * X1 * X2^2 * X1^-1 * X2 * X1^-2 * X2^-2 * X1^-2 ]
Map::
	R = (1, 417, 2, 418, 6, 422, 4, 420)(3, 419, 9, 425, 21, 437, 11, 427)(5, 421, 13, 429, 18, 434, 7, 423)(8, 424, 19, 435, 34, 450, 15, 431)(10, 426, 23, 439, 49, 465, 25, 441)(12, 428, 16, 432, 35, 451, 28, 444)(14, 430, 31, 447, 61, 477, 29, 445)(17, 433, 37, 453, 72, 488, 39, 455)(20, 436, 43, 459, 80, 496, 41, 457)(22, 438, 47, 463, 84, 500, 45, 461)(24, 440, 51, 467, 82, 498, 44, 460)(26, 442, 46, 462, 85, 501, 55, 471)(27, 443, 56, 472, 99, 515, 58, 474)(30, 446, 62, 478, 78, 494, 40, 456)(32, 448, 57, 473, 101, 517, 63, 479)(33, 449, 64, 480, 106, 522, 66, 482)(36, 452, 70, 486, 114, 530, 68, 484)(38, 454, 74, 490, 116, 532, 71, 487)(42, 458, 81, 497, 112, 528, 67, 483)(48, 464, 65, 481, 108, 524, 87, 503)(50, 466, 92, 508, 139, 555, 90, 506)(52, 468, 75, 491, 109, 525, 89, 505)(53, 469, 91, 507, 140, 556, 95, 511)(54, 470, 96, 512, 146, 562, 97, 513)(59, 475, 69, 485, 115, 531, 102, 518)(60, 476, 103, 519, 152, 568, 104, 520)(73, 489, 119, 535, 168, 584, 117, 533)(76, 492, 118, 534, 169, 585, 122, 538)(77, 493, 123, 539, 175, 591, 124, 540)(79, 495, 126, 542, 178, 594, 127, 543)(83, 499, 129, 545, 181, 597, 131, 547)(86, 502, 135, 551, 188, 604, 133, 549)(88, 504, 137, 553, 186, 602, 132, 548)(93, 509, 130, 546, 183, 599, 142, 558)(94, 510, 144, 560, 171, 587, 120, 536)(98, 514, 134, 550, 189, 605, 148, 564)(100, 516, 150, 566, 205, 621, 149, 565)(105, 521, 154, 570, 177, 593, 125, 541)(107, 523, 157, 573, 212, 628, 155, 571)(110, 526, 156, 572, 213, 629, 160, 576)(111, 527, 161, 577, 219, 635, 162, 578)(113, 529, 164, 580, 222, 638, 165, 581)(121, 537, 173, 589, 215, 631, 158, 574)(128, 544, 180, 596, 221, 637, 163, 579)(136, 552, 159, 575, 217, 633, 190, 606)(138, 554, 192, 608, 254, 670, 193, 609)(141, 557, 197, 613, 260, 676, 195, 611)(143, 559, 199, 615, 258, 674, 194, 610)(145, 561, 196, 612, 261, 677, 201, 617)(147, 563, 203, 619, 266, 682, 202, 618)(151, 567, 166, 582, 224, 640, 207, 623)(153, 569, 208, 624, 272, 688, 209, 625)(167, 583, 225, 641, 291, 707, 226, 642)(170, 586, 230, 646, 297, 713, 228, 644)(172, 588, 232, 648, 295, 711, 227, 643)(174, 590, 229, 645, 298, 714, 234, 650)(176, 592, 236, 652, 303, 719, 235, 651)(179, 595, 238, 654, 306, 722, 239, 655)(182, 598, 243, 659, 310, 726, 241, 657)(184, 600, 242, 658, 311, 727, 245, 661)(185, 601, 246, 662, 316, 732, 247, 663)(187, 603, 249, 665, 319, 735, 250, 666)(191, 607, 253, 669, 318, 734, 248, 664)(198, 614, 244, 660, 314, 730, 262, 678)(200, 616, 264, 680, 299, 715, 231, 647)(204, 620, 251, 667, 321, 737, 268, 684)(206, 622, 270, 686, 341, 757, 269, 685)(210, 626, 274, 690, 305, 721, 237, 653)(211, 627, 275, 691, 347, 763, 276, 692)(214, 630, 280, 696, 353, 769, 278, 694)(216, 632, 282, 698, 351, 767, 277, 693)(218, 634, 279, 695, 354, 770, 284, 700)(220, 636, 286, 702, 359, 775, 285, 701)(223, 639, 288, 704, 362, 778, 289, 705)(233, 649, 301, 717, 355, 771, 281, 697)(240, 656, 308, 724, 361, 777, 287, 703)(252, 668, 283, 699, 357, 773, 322, 738)(255, 671, 326, 742, 363, 779, 324, 740)(256, 672, 325, 741, 349, 765, 327, 743)(257, 673, 328, 744, 358, 774, 329, 745)(259, 675, 331, 747, 352, 768, 332, 748)(263, 679, 335, 751, 389, 805, 330, 746)(265, 681, 333, 749, 350, 766, 337, 753)(267, 683, 339, 755, 393, 809, 338, 754)(271, 687, 290, 706, 364, 780, 343, 759)(273, 689, 344, 760, 348, 764, 345, 761)(292, 708, 367, 783, 315, 731, 365, 781)(293, 709, 366, 782, 309, 725, 368, 784)(294, 710, 369, 785, 320, 736, 370, 786)(296, 712, 372, 788, 312, 728, 373, 789)(300, 716, 376, 792, 404, 820, 371, 787)(302, 718, 374, 790, 317, 733, 378, 794)(304, 720, 380, 796, 340, 756, 379, 795)(307, 723, 382, 798, 313, 729, 383, 799)(323, 739, 387, 803, 402, 818, 384, 800)(334, 750, 385, 801, 403, 819, 390, 806)(336, 752, 392, 808, 405, 821, 375, 791)(342, 758, 396, 812, 412, 828, 395, 811)(346, 762, 360, 776, 401, 817, 381, 797)(356, 772, 399, 815, 413, 829, 397, 813)(377, 793, 407, 823, 414, 830, 398, 814)(386, 802, 400, 816, 388, 804, 409, 825)(391, 807, 408, 824, 415, 831, 410, 826)(394, 810, 406, 822, 416, 832, 411, 827)
	L = (1, 419)(2, 423)(3, 426)(4, 428)(5, 417)(6, 431)(7, 433)(8, 418)(9, 420)(10, 440)(11, 442)(12, 443)(13, 445)(14, 421)(15, 449)(16, 422)(17, 454)(18, 456)(19, 457)(20, 424)(21, 461)(22, 425)(23, 427)(24, 468)(25, 469)(26, 470)(27, 473)(28, 475)(29, 476)(30, 429)(31, 479)(32, 430)(33, 481)(34, 483)(35, 484)(36, 432)(37, 434)(38, 491)(39, 492)(40, 493)(41, 495)(42, 435)(43, 498)(44, 436)(45, 499)(46, 437)(47, 503)(48, 438)(49, 506)(50, 439)(51, 441)(52, 448)(53, 446)(54, 447)(55, 514)(56, 444)(57, 505)(58, 502)(59, 504)(60, 510)(61, 513)(62, 511)(63, 509)(64, 450)(65, 525)(66, 526)(67, 527)(68, 529)(69, 451)(70, 532)(71, 452)(72, 533)(73, 453)(74, 455)(75, 460)(76, 458)(77, 459)(78, 541)(79, 537)(80, 540)(81, 538)(82, 536)(83, 546)(84, 548)(85, 549)(86, 462)(87, 552)(88, 463)(89, 464)(90, 554)(91, 465)(92, 558)(93, 466)(94, 467)(95, 561)(96, 471)(97, 557)(98, 559)(99, 565)(100, 472)(101, 474)(102, 567)(103, 477)(104, 569)(105, 478)(106, 571)(107, 480)(108, 482)(109, 487)(110, 485)(111, 486)(112, 579)(113, 575)(114, 578)(115, 576)(116, 574)(117, 583)(118, 488)(119, 587)(120, 489)(121, 490)(122, 590)(123, 494)(124, 586)(125, 588)(126, 496)(127, 595)(128, 497)(129, 500)(130, 517)(131, 600)(132, 601)(133, 603)(134, 501)(135, 515)(136, 516)(137, 518)(138, 519)(139, 610)(140, 611)(141, 507)(142, 614)(143, 508)(144, 520)(145, 616)(146, 618)(147, 512)(148, 620)(149, 598)(150, 606)(151, 622)(152, 609)(153, 521)(154, 625)(155, 627)(156, 522)(157, 631)(158, 523)(159, 524)(160, 634)(161, 528)(162, 630)(163, 632)(164, 530)(165, 639)(166, 531)(167, 542)(168, 643)(169, 644)(170, 534)(171, 647)(172, 535)(173, 543)(174, 649)(175, 651)(176, 539)(177, 653)(178, 642)(179, 544)(180, 655)(181, 657)(182, 545)(183, 547)(184, 550)(185, 551)(186, 664)(187, 660)(188, 663)(189, 661)(190, 668)(191, 553)(192, 555)(193, 672)(194, 673)(195, 675)(196, 556)(197, 562)(198, 563)(199, 564)(200, 560)(201, 681)(202, 671)(203, 678)(204, 683)(205, 685)(206, 566)(207, 687)(208, 568)(209, 689)(210, 570)(211, 580)(212, 693)(213, 694)(214, 572)(215, 697)(216, 573)(217, 581)(218, 699)(219, 701)(220, 577)(221, 703)(222, 692)(223, 582)(224, 705)(225, 584)(226, 709)(227, 710)(228, 712)(229, 585)(230, 591)(231, 592)(232, 593)(233, 589)(234, 718)(235, 708)(236, 715)(237, 720)(238, 594)(239, 723)(240, 596)(241, 725)(242, 597)(243, 621)(244, 599)(245, 731)(246, 602)(247, 728)(248, 729)(249, 604)(250, 736)(251, 605)(252, 607)(253, 738)(254, 740)(255, 608)(256, 612)(257, 613)(258, 746)(259, 624)(260, 745)(261, 743)(262, 750)(263, 615)(264, 617)(265, 626)(266, 754)(267, 619)(268, 756)(269, 733)(270, 623)(271, 739)(272, 748)(273, 752)(274, 753)(275, 628)(276, 765)(277, 766)(278, 768)(279, 629)(280, 635)(281, 636)(282, 637)(283, 633)(284, 774)(285, 764)(286, 771)(287, 776)(288, 638)(289, 779)(290, 640)(291, 781)(292, 641)(293, 645)(294, 646)(295, 787)(296, 654)(297, 786)(298, 784)(299, 791)(300, 648)(301, 650)(302, 656)(303, 795)(304, 652)(305, 797)(306, 789)(307, 793)(308, 794)(309, 665)(310, 798)(311, 788)(312, 658)(313, 659)(314, 666)(315, 801)(316, 790)(317, 662)(318, 800)(319, 782)(320, 667)(321, 785)(322, 802)(323, 669)(324, 778)(325, 670)(326, 682)(327, 763)(328, 674)(329, 770)(330, 804)(331, 676)(332, 769)(333, 677)(334, 679)(335, 806)(336, 680)(337, 767)(338, 780)(339, 684)(340, 807)(341, 811)(342, 686)(343, 809)(344, 688)(345, 775)(346, 690)(347, 760)(348, 691)(349, 695)(350, 696)(351, 813)(352, 704)(353, 749)(354, 741)(355, 814)(356, 698)(357, 700)(358, 706)(359, 762)(360, 702)(361, 818)(362, 747)(363, 816)(364, 744)(365, 727)(366, 707)(367, 719)(368, 726)(369, 711)(370, 735)(371, 819)(372, 713)(373, 732)(374, 714)(375, 716)(376, 821)(377, 717)(378, 757)(379, 737)(380, 721)(381, 822)(382, 722)(383, 734)(384, 724)(385, 730)(386, 758)(387, 759)(388, 742)(389, 826)(390, 820)(391, 751)(392, 761)(393, 827)(394, 755)(395, 823)(396, 825)(397, 808)(398, 772)(399, 830)(400, 773)(401, 777)(402, 831)(403, 783)(404, 810)(405, 829)(406, 792)(407, 799)(408, 796)(409, 805)(410, 803)(411, 812)(412, 832)(413, 824)(414, 828)(415, 815)(416, 817)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 104 e = 416 f = 260
	degree seq :: [ 8^104 ]

E27.2348 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C52 : C4) : C2 (small group id <416, 82>)
Aut   = (C52 : C4) : C2 (small group id <416, 82>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^2 * X2 * X1^2)^2, X1^3 * X2 * X1^-4 * X2 * X1, X1^-1 * X2 * X1^3 * X2 * X1^-1 * X2 * X1 * X2 * X1^-4 * X2 * X1^-2 * X2, X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ]
Map::
	R = (1, 417, 2, 418, 5, 421, 11, 427, 23, 439, 22, 438, 10, 426, 4, 420)(3, 419, 7, 423, 15, 431, 31, 447, 44, 460, 37, 453, 18, 434, 8, 424)(6, 422, 13, 429, 27, 443, 51, 467, 43, 459, 56, 472, 30, 446, 14, 430)(9, 425, 19, 435, 38, 454, 46, 462, 24, 440, 45, 461, 40, 456, 20, 436)(12, 428, 25, 441, 47, 463, 42, 458, 21, 437, 41, 457, 50, 466, 26, 442)(16, 432, 33, 449, 60, 476, 93, 509, 67, 483, 74, 490, 62, 478, 34, 450)(17, 433, 35, 451, 63, 479, 88, 504, 57, 473, 83, 499, 53, 469, 28, 444)(29, 445, 54, 470, 84, 500, 72, 488, 79, 495, 111, 527, 76, 492, 48, 464)(32, 448, 58, 474, 89, 505, 66, 482, 36, 452, 65, 481, 92, 508, 59, 475)(39, 455, 69, 485, 103, 519, 107, 523, 73, 489, 49, 465, 77, 493, 70, 486)(52, 468, 80, 496, 115, 531, 87, 503, 55, 471, 86, 502, 118, 534, 81, 497)(61, 477, 95, 511, 132, 548, 100, 516, 129, 545, 168, 584, 126, 542, 90, 506)(64, 480, 98, 514, 137, 553, 161, 577, 120, 536, 91, 507, 127, 543, 99, 515)(68, 484, 101, 517, 139, 555, 106, 522, 71, 487, 105, 521, 141, 557, 102, 518)(75, 491, 108, 524, 146, 562, 114, 530, 78, 494, 113, 529, 149, 565, 109, 525)(82, 498, 119, 535, 159, 575, 124, 540, 97, 513, 136, 552, 156, 572, 116, 532)(85, 501, 122, 538, 163, 579, 194, 610, 151, 567, 117, 533, 157, 573, 123, 539)(94, 510, 130, 546, 172, 588, 135, 551, 96, 512, 134, 550, 174, 590, 131, 547)(104, 520, 143, 559, 185, 601, 144, 560, 145, 561, 187, 603, 182, 598, 140, 556)(110, 526, 150, 566, 192, 608, 154, 570, 121, 537, 162, 578, 189, 605, 147, 563)(112, 528, 152, 568, 195, 611, 184, 600, 142, 558, 148, 564, 190, 606, 153, 569)(125, 541, 165, 581, 209, 625, 171, 587, 128, 544, 170, 586, 212, 628, 166, 582)(133, 549, 176, 592, 222, 638, 267, 683, 214, 630, 173, 589, 219, 635, 177, 593)(138, 554, 180, 596, 205, 621, 160, 576, 204, 620, 256, 672, 224, 640, 178, 594)(155, 571, 197, 613, 247, 663, 202, 618, 158, 574, 201, 617, 250, 666, 198, 614)(164, 580, 208, 624, 244, 660, 193, 609, 243, 659, 299, 715, 258, 674, 206, 622)(167, 583, 213, 629, 265, 681, 217, 633, 175, 591, 221, 637, 262, 678, 210, 626)(169, 585, 215, 631, 268, 684, 225, 641, 179, 595, 211, 627, 263, 679, 216, 632)(181, 597, 227, 643, 281, 697, 231, 647, 183, 599, 230, 646, 283, 699, 228, 644)(186, 602, 196, 612, 246, 662, 289, 705, 235, 651, 232, 648, 286, 702, 234, 650)(188, 604, 236, 652, 290, 706, 241, 657, 191, 607, 240, 656, 293, 709, 237, 653)(199, 615, 251, 667, 307, 723, 254, 670, 203, 619, 255, 671, 304, 720, 248, 664)(200, 616, 252, 668, 309, 725, 259, 675, 207, 623, 249, 665, 305, 721, 253, 669)(218, 634, 270, 686, 328, 744, 274, 690, 220, 636, 273, 689, 329, 745, 271, 687)(223, 639, 277, 693, 325, 741, 266, 682, 324, 740, 358, 774, 331, 747, 275, 691)(226, 642, 269, 685, 327, 743, 350, 766, 312, 728, 279, 695, 302, 718, 280, 696)(229, 645, 284, 700, 336, 752, 285, 701, 233, 649, 287, 703, 334, 750, 282, 698)(238, 654, 294, 710, 344, 760, 297, 713, 242, 658, 298, 714, 341, 757, 291, 707)(239, 655, 295, 711, 346, 762, 301, 717, 245, 661, 292, 708, 342, 758, 296, 712)(257, 673, 313, 729, 357, 773, 308, 724, 278, 694, 332, 748, 359, 775, 311, 727)(260, 676, 310, 726, 272, 688, 330, 746, 348, 764, 315, 731, 276, 692, 316, 732)(261, 677, 317, 733, 361, 777, 322, 738, 264, 680, 321, 737, 364, 780, 318, 734)(288, 704, 320, 736, 366, 782, 337, 753, 339, 755, 326, 742, 363, 779, 338, 754)(300, 716, 349, 765, 381, 797, 345, 761, 314, 730, 360, 776, 382, 798, 347, 763)(303, 719, 351, 767, 383, 799, 355, 771, 306, 722, 354, 770, 385, 801, 352, 768)(319, 735, 365, 781, 392, 808, 367, 783, 323, 739, 368, 784, 390, 806, 362, 778)(333, 749, 369, 785, 393, 809, 373, 789, 335, 751, 372, 788, 395, 811, 370, 786)(340, 756, 375, 791, 397, 813, 379, 795, 343, 759, 378, 794, 399, 815, 376, 792)(353, 769, 386, 802, 404, 820, 387, 803, 356, 772, 388, 804, 403, 819, 384, 800)(371, 787, 391, 807, 407, 823, 396, 812, 374, 790, 389, 805, 405, 821, 394, 810)(377, 793, 400, 816, 410, 826, 401, 817, 380, 796, 402, 818, 409, 825, 398, 814)(406, 822, 411, 827, 415, 831, 414, 830, 408, 824, 412, 828, 416, 832, 413, 829)
	L = (1, 419)(2, 422)(3, 417)(4, 425)(5, 428)(6, 418)(7, 432)(8, 433)(9, 420)(10, 437)(11, 440)(12, 421)(13, 444)(14, 445)(15, 448)(16, 423)(17, 424)(18, 452)(19, 455)(20, 449)(21, 426)(22, 459)(23, 460)(24, 427)(25, 464)(26, 465)(27, 468)(28, 429)(29, 430)(30, 471)(31, 473)(32, 431)(33, 436)(34, 477)(35, 480)(36, 434)(37, 483)(38, 484)(39, 435)(40, 487)(41, 488)(42, 485)(43, 438)(44, 439)(45, 489)(46, 490)(47, 491)(48, 441)(49, 442)(50, 494)(51, 495)(52, 443)(53, 498)(54, 501)(55, 446)(56, 504)(57, 447)(58, 506)(59, 507)(60, 510)(61, 450)(62, 512)(63, 513)(64, 451)(65, 516)(66, 514)(67, 453)(68, 454)(69, 458)(70, 520)(71, 456)(72, 457)(73, 461)(74, 462)(75, 463)(76, 526)(77, 528)(78, 466)(79, 467)(80, 532)(81, 533)(82, 469)(83, 536)(84, 537)(85, 470)(86, 540)(87, 538)(88, 472)(89, 541)(90, 474)(91, 475)(92, 544)(93, 545)(94, 476)(95, 549)(96, 478)(97, 479)(98, 482)(99, 554)(100, 481)(101, 556)(102, 550)(103, 558)(104, 486)(105, 560)(106, 546)(107, 561)(108, 563)(109, 564)(110, 492)(111, 567)(112, 493)(113, 570)(114, 568)(115, 571)(116, 496)(117, 497)(118, 574)(119, 576)(120, 499)(121, 500)(122, 503)(123, 580)(124, 502)(125, 505)(126, 583)(127, 585)(128, 508)(129, 509)(130, 522)(131, 589)(132, 591)(133, 511)(134, 518)(135, 592)(136, 594)(137, 595)(138, 515)(139, 597)(140, 517)(141, 599)(142, 519)(143, 602)(144, 521)(145, 523)(146, 604)(147, 524)(148, 525)(149, 607)(150, 609)(151, 527)(152, 530)(153, 612)(154, 529)(155, 531)(156, 615)(157, 616)(158, 534)(159, 619)(160, 535)(161, 620)(162, 622)(163, 623)(164, 539)(165, 626)(166, 627)(167, 542)(168, 630)(169, 543)(170, 633)(171, 631)(172, 634)(173, 547)(174, 636)(175, 548)(176, 551)(177, 639)(178, 552)(179, 553)(180, 642)(181, 555)(182, 645)(183, 557)(184, 648)(185, 649)(186, 559)(187, 651)(188, 562)(189, 654)(190, 655)(191, 565)(192, 658)(193, 566)(194, 659)(195, 661)(196, 569)(197, 664)(198, 665)(199, 572)(200, 573)(201, 670)(202, 668)(203, 575)(204, 577)(205, 673)(206, 578)(207, 579)(208, 676)(209, 677)(210, 581)(211, 582)(212, 680)(213, 682)(214, 584)(215, 587)(216, 685)(217, 586)(218, 588)(219, 688)(220, 590)(221, 691)(222, 692)(223, 593)(224, 694)(225, 695)(226, 596)(227, 698)(228, 686)(229, 598)(230, 701)(231, 689)(232, 600)(233, 601)(234, 704)(235, 603)(236, 707)(237, 708)(238, 605)(239, 606)(240, 713)(241, 711)(242, 608)(243, 610)(244, 716)(245, 611)(246, 718)(247, 719)(248, 613)(249, 614)(250, 722)(251, 724)(252, 618)(253, 726)(254, 617)(255, 727)(256, 728)(257, 621)(258, 730)(259, 731)(260, 624)(261, 625)(262, 735)(263, 736)(264, 628)(265, 739)(266, 629)(267, 740)(268, 742)(269, 632)(270, 644)(271, 732)(272, 635)(273, 647)(274, 746)(275, 637)(276, 638)(277, 721)(278, 640)(279, 641)(280, 712)(281, 749)(282, 643)(283, 751)(284, 753)(285, 646)(286, 743)(287, 754)(288, 650)(289, 755)(290, 756)(291, 652)(292, 653)(293, 759)(294, 761)(295, 657)(296, 696)(297, 656)(298, 763)(299, 764)(300, 660)(301, 766)(302, 662)(303, 663)(304, 769)(305, 693)(306, 666)(307, 772)(308, 667)(309, 774)(310, 669)(311, 671)(312, 672)(313, 758)(314, 674)(315, 675)(316, 687)(317, 778)(318, 779)(319, 678)(320, 679)(321, 783)(322, 782)(323, 681)(324, 683)(325, 771)(326, 684)(327, 702)(328, 776)(329, 765)(330, 690)(331, 768)(332, 762)(333, 697)(334, 787)(335, 699)(336, 790)(337, 700)(338, 703)(339, 705)(340, 706)(341, 793)(342, 729)(343, 709)(344, 796)(345, 710)(346, 748)(347, 714)(348, 715)(349, 745)(350, 717)(351, 800)(352, 747)(353, 720)(354, 803)(355, 741)(356, 723)(357, 795)(358, 725)(359, 792)(360, 744)(361, 805)(362, 733)(363, 734)(364, 807)(365, 801)(366, 738)(367, 737)(368, 799)(369, 810)(370, 797)(371, 750)(372, 812)(373, 798)(374, 752)(375, 814)(376, 775)(377, 757)(378, 817)(379, 773)(380, 760)(381, 786)(382, 789)(383, 784)(384, 767)(385, 781)(386, 815)(387, 770)(388, 813)(389, 777)(390, 822)(391, 780)(392, 824)(393, 816)(394, 785)(395, 818)(396, 788)(397, 804)(398, 791)(399, 802)(400, 809)(401, 794)(402, 811)(403, 827)(404, 828)(405, 829)(406, 806)(407, 830)(408, 808)(409, 831)(410, 832)(411, 819)(412, 820)(413, 821)(414, 823)(415, 825)(416, 826)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 52 e = 416 f = 312
	degree seq :: [ 16^52 ]

E27.2349 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 8})
Quotient :: halfedge
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^-2 * X2 * X1^-2)^2, X1^2 * X2 * X1^-4 * X2 * X1^2, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 44, 37, 18, 8)(6, 13, 27, 51, 43, 56, 30, 14)(9, 19, 38, 46, 24, 45, 40, 20)(12, 25, 47, 42, 21, 41, 50, 26)(16, 33, 60, 93, 67, 74, 62, 34)(17, 35, 63, 88, 57, 83, 53, 28)(29, 54, 84, 72, 79, 111, 76, 48)(32, 58, 89, 66, 36, 65, 92, 59)(39, 69, 103, 107, 73, 49, 77, 70)(52, 80, 115, 87, 55, 86, 118, 81)(61, 95, 132, 100, 129, 168, 126, 90)(64, 98, 137, 161, 120, 91, 127, 99)(68, 101, 139, 106, 71, 105, 141, 102)(75, 108, 146, 114, 78, 113, 149, 109)(82, 119, 159, 124, 97, 136, 156, 116)(85, 122, 163, 194, 151, 117, 157, 123)(94, 130, 172, 135, 96, 134, 174, 131)(104, 143, 185, 144, 145, 187, 182, 140)(110, 150, 192, 154, 121, 162, 189, 147)(112, 152, 195, 184, 142, 148, 190, 153)(125, 165, 209, 171, 128, 170, 212, 166)(133, 176, 222, 267, 214, 173, 219, 177)(138, 180, 205, 160, 204, 256, 224, 178)(155, 197, 247, 202, 158, 201, 250, 198)(164, 208, 244, 193, 243, 299, 258, 206)(167, 213, 265, 217, 175, 221, 262, 210)(169, 215, 268, 225, 179, 211, 263, 216)(181, 227, 281, 231, 183, 230, 283, 228)(186, 196, 246, 289, 235, 232, 286, 234)(188, 236, 290, 241, 191, 240, 293, 237)(199, 251, 307, 254, 203, 255, 304, 248)(200, 252, 309, 259, 207, 249, 305, 253)(218, 270, 326, 274, 220, 273, 328, 271)(223, 277, 300, 266, 323, 345, 314, 275)(226, 269, 325, 359, 312, 279, 333, 280)(229, 284, 334, 285, 233, 287, 336, 282)(238, 294, 344, 297, 242, 298, 341, 291)(239, 295, 346, 301, 245, 292, 342, 296)(257, 313, 339, 308, 278, 332, 288, 311)(260, 310, 358, 319, 348, 315, 360, 316)(261, 317, 361, 322, 264, 321, 363, 318)(272, 329, 371, 331, 276, 327, 369, 330)(302, 347, 381, 353, 338, 349, 382, 350)(303, 351, 383, 356, 306, 355, 385, 352)(320, 364, 390, 366, 324, 362, 389, 365)(335, 367, 391, 374, 337, 372, 392, 373)(340, 375, 397, 379, 343, 378, 399, 376)(354, 386, 404, 388, 357, 384, 403, 387)(368, 393, 407, 396, 370, 395, 408, 394)(377, 400, 410, 402, 380, 398, 409, 401)(405, 412, 415, 414, 406, 411, 416, 413)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 44)(25, 48)(26, 49)(27, 52)(30, 55)(31, 57)(34, 61)(35, 64)(37, 67)(38, 68)(40, 71)(41, 72)(42, 69)(45, 73)(46, 74)(47, 75)(50, 78)(51, 79)(53, 82)(54, 85)(56, 88)(58, 90)(59, 91)(60, 94)(62, 96)(63, 97)(65, 100)(66, 98)(70, 104)(76, 110)(77, 112)(80, 116)(81, 117)(83, 120)(84, 121)(86, 124)(87, 122)(89, 125)(92, 128)(93, 129)(95, 133)(99, 138)(101, 140)(102, 134)(103, 142)(105, 144)(106, 130)(107, 145)(108, 147)(109, 148)(111, 151)(113, 154)(114, 152)(115, 155)(118, 158)(119, 160)(123, 164)(126, 167)(127, 169)(131, 173)(132, 175)(135, 176)(136, 178)(137, 179)(139, 181)(141, 183)(143, 186)(146, 188)(149, 191)(150, 193)(153, 196)(156, 199)(157, 200)(159, 203)(161, 204)(162, 206)(163, 207)(165, 210)(166, 211)(168, 214)(170, 217)(171, 215)(172, 218)(174, 220)(177, 223)(180, 226)(182, 229)(184, 232)(185, 233)(187, 235)(189, 238)(190, 239)(192, 242)(194, 243)(195, 245)(197, 248)(198, 249)(201, 254)(202, 252)(205, 257)(208, 260)(209, 261)(212, 264)(213, 266)(216, 269)(219, 272)(221, 275)(222, 276)(224, 278)(225, 279)(227, 282)(228, 270)(230, 285)(231, 273)(234, 288)(236, 291)(237, 292)(240, 297)(241, 295)(244, 300)(246, 302)(247, 303)(250, 306)(251, 308)(253, 310)(255, 311)(256, 312)(258, 314)(259, 315)(262, 319)(263, 320)(265, 316)(267, 323)(268, 324)(271, 327)(274, 329)(277, 298)(280, 334)(281, 335)(283, 337)(284, 313)(286, 338)(287, 332)(289, 339)(290, 340)(293, 343)(294, 345)(296, 347)(299, 348)(301, 349)(304, 353)(305, 354)(307, 350)(309, 357)(317, 358)(318, 362)(321, 360)(322, 364)(325, 367)(326, 368)(328, 370)(330, 341)(331, 344)(333, 372)(336, 359)(342, 377)(346, 380)(351, 381)(352, 384)(355, 382)(356, 386)(361, 387)(363, 388)(365, 391)(366, 392)(369, 375)(371, 378)(373, 395)(374, 393)(376, 398)(379, 400)(383, 401)(385, 402)(389, 405)(390, 406)(394, 399)(396, 397)(403, 411)(404, 412)(407, 413)(408, 414)(409, 415)(410, 416)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 52 e = 208 f = 104
	degree seq :: [ 8^52 ]

E27.2350 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 4, 8})
Quotient :: halfedge
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X2^2, X1^4, (X2 * X1 * X2 * X1^-2 * X2 * X1)^2, (X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1)^2, (X1^-1 * X2)^8, X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 41, 25)(15, 26, 44, 27)(21, 35, 59, 36)(22, 37, 62, 38)(23, 39, 65, 40)(29, 48, 80, 49)(30, 50, 83, 51)(32, 53, 88, 54)(33, 55, 91, 56)(34, 57, 94, 58)(42, 69, 93, 70)(43, 71, 115, 72)(45, 74, 119, 75)(46, 76, 89, 77)(47, 78, 124, 79)(52, 86, 131, 87)(60, 98, 85, 99)(61, 100, 146, 101)(63, 103, 150, 104)(64, 105, 81, 106)(66, 108, 157, 109)(67, 110, 143, 97)(68, 111, 160, 112)(73, 118, 141, 95)(82, 127, 174, 128)(84, 129, 176, 130)(90, 135, 181, 136)(92, 138, 185, 139)(96, 142, 180, 134)(102, 149, 178, 132)(107, 155, 199, 156)(113, 144, 123, 154)(114, 162, 209, 163)(116, 165, 211, 166)(117, 167, 120, 145)(121, 170, 194, 147)(122, 148, 195, 151)(125, 137, 184, 172)(126, 133, 179, 173)(140, 188, 235, 189)(152, 198, 230, 182)(153, 183, 231, 186)(158, 203, 253, 204)(159, 205, 256, 206)(161, 208, 252, 202)(164, 210, 250, 200)(168, 192, 242, 214)(169, 201, 251, 215)(171, 217, 269, 218)(175, 187, 234, 222)(177, 224, 278, 225)(190, 238, 295, 239)(191, 240, 298, 241)(193, 243, 293, 236)(196, 228, 285, 246)(197, 237, 294, 247)(207, 259, 317, 260)(212, 265, 313, 254)(213, 255, 314, 257)(216, 258, 316, 268)(219, 272, 326, 273)(220, 274, 289, 232)(221, 275, 324, 270)(223, 271, 325, 277)(226, 281, 332, 282)(227, 283, 335, 284)(229, 286, 330, 279)(233, 280, 331, 290)(244, 303, 347, 296)(245, 297, 348, 299)(248, 300, 261, 306)(249, 307, 351, 308)(262, 320, 359, 318)(263, 311, 345, 321)(264, 319, 338, 305)(266, 322, 349, 302)(267, 291, 337, 301)(276, 315, 353, 327)(287, 340, 369, 333)(288, 334, 370, 336)(292, 342, 372, 343)(304, 350, 371, 339)(309, 354, 381, 355)(310, 356, 328, 341)(312, 357, 380, 352)(323, 361, 386, 362)(329, 365, 390, 366)(344, 374, 398, 375)(346, 376, 397, 373)(358, 382, 404, 383)(360, 377, 399, 384)(363, 379, 401, 388)(364, 389, 406, 387)(367, 392, 408, 393)(368, 394, 407, 391)(378, 395, 409, 400)(385, 405, 410, 396)(402, 411, 415, 414)(403, 412, 416, 413)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 42)(25, 43)(26, 45)(27, 46)(28, 47)(31, 52)(35, 60)(36, 61)(37, 63)(38, 64)(39, 66)(40, 67)(41, 68)(44, 73)(48, 81)(49, 82)(50, 84)(51, 85)(53, 89)(54, 90)(55, 92)(56, 93)(57, 95)(58, 96)(59, 97)(62, 102)(65, 107)(69, 113)(70, 114)(71, 116)(72, 117)(74, 120)(75, 121)(76, 122)(77, 123)(78, 125)(79, 111)(80, 126)(83, 108)(86, 132)(87, 133)(88, 134)(91, 137)(94, 140)(98, 144)(99, 145)(100, 147)(101, 148)(103, 151)(104, 152)(105, 153)(106, 154)(109, 158)(110, 159)(112, 161)(115, 164)(118, 168)(119, 169)(124, 171)(127, 175)(128, 162)(129, 163)(130, 165)(131, 177)(135, 182)(136, 183)(138, 186)(139, 187)(141, 190)(142, 191)(143, 192)(146, 193)(149, 196)(150, 197)(155, 200)(156, 201)(157, 202)(160, 207)(166, 212)(167, 213)(170, 216)(172, 219)(173, 220)(174, 221)(176, 223)(178, 226)(179, 227)(180, 228)(181, 229)(184, 232)(185, 233)(188, 236)(189, 237)(194, 244)(195, 245)(198, 248)(199, 249)(203, 254)(204, 255)(205, 257)(206, 258)(208, 261)(209, 262)(210, 263)(211, 264)(214, 266)(215, 267)(217, 270)(218, 271)(222, 276)(224, 279)(225, 280)(230, 287)(231, 288)(234, 291)(235, 292)(238, 296)(239, 297)(240, 299)(241, 300)(242, 301)(243, 302)(246, 304)(247, 305)(250, 309)(251, 310)(252, 311)(253, 312)(256, 315)(259, 318)(260, 319)(265, 298)(268, 290)(269, 323)(272, 327)(273, 320)(274, 316)(275, 328)(277, 306)(278, 329)(281, 333)(282, 334)(283, 336)(284, 337)(285, 338)(286, 339)(289, 341)(293, 344)(294, 345)(295, 346)(303, 335)(307, 352)(308, 353)(313, 343)(314, 358)(317, 340)(321, 360)(322, 331)(324, 363)(325, 350)(326, 364)(330, 367)(332, 368)(342, 373)(347, 366)(348, 377)(349, 378)(351, 379)(354, 372)(355, 382)(356, 383)(357, 384)(359, 385)(361, 387)(362, 369)(365, 391)(370, 395)(371, 396)(374, 390)(375, 399)(376, 400)(380, 402)(381, 403)(386, 392)(388, 405)(389, 404)(393, 409)(394, 410)(397, 411)(398, 412)(401, 413)(406, 414)(407, 415)(408, 416)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 104 e = 208 f = 52
	degree seq :: [ 4^104 ]

E27.2351 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X1^2, X2^4, X1 * X2^2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1, (X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1)^2, (X2 * X1)^8, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, X1 * X2 * X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 9)(5, 10)(6, 12)(8, 15)(11, 20)(13, 23)(14, 25)(16, 28)(17, 30)(18, 31)(19, 33)(21, 36)(22, 38)(24, 41)(26, 44)(27, 46)(29, 49)(32, 54)(34, 57)(35, 59)(37, 62)(39, 65)(40, 67)(42, 70)(43, 72)(45, 75)(47, 78)(48, 80)(50, 83)(51, 85)(52, 86)(53, 88)(55, 91)(56, 93)(58, 96)(60, 99)(61, 101)(63, 104)(64, 106)(66, 98)(68, 103)(69, 112)(71, 115)(73, 105)(74, 119)(76, 122)(77, 87)(79, 124)(81, 127)(82, 89)(84, 94)(90, 136)(92, 139)(95, 143)(97, 146)(100, 148)(102, 151)(107, 131)(108, 141)(109, 150)(110, 153)(111, 156)(113, 154)(114, 160)(116, 163)(117, 132)(118, 158)(120, 162)(121, 167)(123, 170)(125, 172)(126, 133)(128, 175)(129, 134)(130, 137)(135, 178)(138, 182)(140, 185)(142, 180)(144, 184)(145, 189)(147, 192)(149, 194)(152, 197)(155, 199)(157, 202)(159, 204)(161, 207)(164, 206)(165, 209)(166, 212)(168, 210)(169, 215)(171, 217)(173, 219)(174, 220)(176, 223)(177, 224)(179, 227)(181, 229)(183, 232)(186, 231)(187, 234)(188, 237)(190, 235)(191, 240)(193, 242)(195, 244)(196, 245)(198, 248)(200, 250)(201, 252)(203, 255)(205, 257)(208, 260)(211, 262)(213, 265)(214, 266)(216, 268)(218, 270)(221, 272)(222, 276)(225, 279)(226, 281)(228, 284)(230, 286)(233, 289)(236, 291)(238, 294)(239, 295)(241, 297)(243, 299)(246, 301)(247, 305)(249, 303)(251, 308)(253, 306)(254, 283)(256, 285)(258, 311)(259, 312)(261, 315)(263, 317)(264, 319)(267, 298)(269, 296)(271, 324)(273, 323)(274, 278)(275, 327)(277, 282)(280, 330)(287, 333)(288, 334)(290, 337)(292, 339)(293, 341)(300, 346)(302, 345)(304, 349)(307, 351)(309, 332)(310, 331)(313, 353)(314, 357)(316, 355)(318, 360)(320, 358)(321, 344)(322, 343)(325, 361)(326, 362)(328, 354)(329, 365)(335, 367)(336, 371)(338, 369)(340, 374)(342, 372)(347, 375)(348, 376)(350, 368)(352, 378)(356, 382)(359, 384)(363, 388)(364, 366)(370, 393)(373, 395)(377, 399)(379, 397)(380, 392)(381, 391)(383, 398)(385, 403)(386, 390)(387, 394)(389, 404)(396, 409)(400, 410)(401, 408)(402, 407)(405, 412)(406, 411)(413, 416)(414, 415)(417, 419, 424, 420)(418, 421, 427, 422)(423, 429, 440, 430)(425, 432, 445, 433)(426, 434, 448, 435)(428, 437, 453, 438)(431, 442, 461, 443)(436, 450, 474, 451)(439, 455, 482, 456)(441, 458, 487, 459)(444, 463, 495, 464)(446, 466, 500, 467)(447, 468, 503, 469)(449, 471, 508, 472)(452, 476, 516, 477)(454, 479, 521, 480)(457, 484, 527, 485)(460, 489, 534, 490)(462, 492, 539, 493)(465, 497, 544, 498)(470, 505, 551, 506)(473, 510, 558, 511)(475, 513, 563, 514)(478, 518, 568, 519)(481, 523, 501, 524)(483, 525, 571, 526)(486, 529, 575, 530)(488, 532, 494, 533)(491, 536, 582, 537)(496, 541, 589, 542)(499, 545, 592, 546)(502, 547, 522, 548)(504, 549, 593, 550)(507, 553, 597, 554)(509, 556, 515, 557)(512, 560, 604, 561)(517, 565, 611, 566)(520, 569, 614, 570)(528, 573, 619, 574)(531, 577, 624, 578)(535, 580, 627, 581)(538, 584, 630, 585)(540, 583, 629, 587)(543, 586, 632, 590)(552, 595, 644, 596)(555, 599, 649, 600)(559, 602, 652, 603)(562, 606, 655, 607)(564, 605, 654, 609)(567, 608, 657, 612)(572, 616, 667, 617)(576, 621, 674, 622)(579, 625, 677, 626)(588, 631, 683, 634)(591, 637, 691, 638)(594, 641, 696, 642)(598, 646, 703, 647)(601, 650, 706, 651)(610, 656, 712, 659)(613, 662, 720, 663)(615, 665, 723, 666)(618, 669, 702, 670)(620, 668, 725, 672)(623, 671, 726, 675)(628, 679, 734, 680)(633, 685, 738, 684)(635, 687, 741, 688)(636, 689, 742, 690)(639, 692, 744, 693)(640, 694, 745, 695)(643, 698, 673, 699)(645, 697, 747, 701)(648, 700, 748, 704)(653, 708, 756, 709)(658, 714, 760, 713)(660, 716, 763, 717)(661, 718, 764, 719)(664, 721, 766, 722)(676, 729, 772, 730)(678, 732, 775, 733)(681, 736, 762, 737)(682, 735, 761, 715)(686, 711, 757, 739)(705, 751, 786, 752)(707, 754, 789, 755)(710, 758, 740, 759)(724, 768, 783, 749)(727, 746, 782, 769)(728, 770, 797, 771)(731, 773, 799, 774)(743, 779, 805, 780)(750, 784, 808, 785)(753, 787, 810, 788)(765, 793, 816, 794)(767, 795, 817, 796)(776, 801, 813, 791)(777, 790, 812, 802)(778, 803, 822, 804)(781, 806, 823, 807)(792, 814, 828, 815)(798, 818, 829, 819)(800, 820, 830, 821)(809, 824, 831, 825)(811, 826, 832, 827)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 16, 16 ), ( 16^4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 312 e = 416 f = 52
	degree seq :: [ 2^208, 4^104 ]

E27.2352 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ (X1 * X2)^2, X1^4, (X2^-1 * X1 * X2^-2)^2, X2^8, X2^-1 * X1^-1 * X2^4 * X1 * X2^-3, (X2 * X1^-1 * X2^-2 * X1^-1 * X2)^2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^2 * X1^-2 * X2 * X1^-1 * X2^2 * X1^-1, X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^2 * X2^-2 * X1^-1 * X2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1^-1, X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-2 * X1^-2 * X2^-2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-2 * X2^-2 * X1^-2 * X2^-2 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 21, 11)(5, 13, 18, 7)(8, 19, 34, 15)(10, 23, 49, 25)(12, 16, 35, 28)(14, 31, 61, 29)(17, 37, 72, 39)(20, 43, 80, 41)(22, 47, 84, 45)(24, 51, 82, 44)(26, 46, 85, 55)(27, 56, 99, 58)(30, 62, 78, 40)(32, 57, 101, 63)(33, 64, 106, 66)(36, 70, 114, 68)(38, 74, 116, 71)(42, 81, 112, 67)(48, 65, 108, 87)(50, 92, 139, 90)(52, 75, 109, 89)(53, 91, 140, 95)(54, 96, 146, 97)(59, 69, 115, 102)(60, 103, 152, 104)(73, 119, 168, 117)(76, 118, 169, 122)(77, 123, 175, 124)(79, 126, 178, 127)(83, 129, 181, 131)(86, 135, 188, 133)(88, 137, 186, 132)(93, 130, 183, 142)(94, 144, 171, 120)(98, 134, 189, 148)(100, 150, 205, 149)(105, 154, 177, 125)(107, 157, 212, 155)(110, 156, 213, 160)(111, 161, 219, 162)(113, 164, 222, 165)(121, 173, 215, 158)(128, 180, 221, 163)(136, 159, 217, 190)(138, 192, 254, 193)(141, 197, 260, 195)(143, 199, 258, 194)(145, 196, 261, 201)(147, 203, 266, 202)(151, 166, 224, 207)(153, 208, 272, 209)(167, 225, 291, 226)(170, 230, 297, 228)(172, 232, 295, 227)(174, 229, 298, 234)(176, 236, 303, 235)(179, 238, 306, 239)(182, 243, 310, 241)(184, 242, 311, 245)(185, 246, 316, 247)(187, 249, 319, 250)(191, 253, 318, 248)(198, 244, 314, 262)(200, 264, 299, 231)(204, 251, 321, 268)(206, 270, 341, 269)(210, 274, 305, 237)(211, 275, 347, 276)(214, 280, 353, 278)(216, 282, 351, 277)(218, 279, 354, 284)(220, 286, 359, 285)(223, 288, 362, 289)(233, 301, 355, 281)(240, 308, 361, 287)(252, 283, 357, 322)(255, 326, 350, 324)(256, 325, 360, 327)(257, 328, 348, 329)(259, 331, 356, 332)(263, 335, 352, 330)(265, 333, 392, 337)(267, 339, 349, 338)(271, 290, 364, 343)(273, 344, 384, 345)(292, 367, 317, 365)(293, 366, 323, 368)(294, 369, 313, 370)(296, 372, 342, 373)(300, 376, 312, 371)(302, 374, 404, 378)(304, 380, 309, 379)(307, 382, 402, 383)(315, 381, 346, 386)(320, 387, 411, 388)(334, 385, 409, 393)(336, 394, 405, 375)(340, 389, 401, 363)(358, 397, 413, 400)(377, 406, 391, 398)(390, 399, 414, 403)(395, 407, 415, 412)(396, 408, 416, 410)(417, 419, 426, 440, 468, 448, 430, 421)(418, 423, 433, 454, 491, 460, 436, 424)(420, 428, 443, 473, 505, 464, 438, 425)(422, 431, 449, 481, 525, 487, 452, 432)(427, 442, 470, 447, 479, 509, 466, 439)(429, 445, 476, 510, 467, 441, 469, 446)(434, 456, 493, 459, 498, 536, 489, 453)(435, 457, 495, 537, 490, 455, 492, 458)(437, 461, 499, 546, 517, 474, 502, 462)(444, 475, 504, 463, 503, 552, 516, 472)(450, 483, 527, 486, 532, 574, 523, 480)(451, 484, 529, 575, 524, 482, 526, 485)(465, 506, 554, 519, 477, 513, 557, 507)(471, 514, 559, 508, 558, 614, 563, 512)(478, 511, 561, 616, 560, 520, 569, 521)(488, 533, 583, 542, 496, 540, 586, 534)(494, 541, 588, 535, 587, 647, 592, 539)(497, 538, 590, 649, 589, 543, 595, 544)(500, 548, 601, 551, 515, 565, 598, 545)(501, 549, 603, 660, 599, 547, 600, 550)(518, 567, 622, 566, 606, 668, 607, 553)(522, 571, 627, 580, 530, 578, 630, 572)(528, 579, 632, 573, 631, 697, 636, 577)(531, 576, 634, 699, 633, 581, 639, 582)(555, 610, 673, 613, 562, 618, 671, 608)(556, 611, 675, 624, 568, 609, 672, 612)(564, 620, 683, 619, 678, 750, 679, 615)(570, 625, 689, 752, 680, 617, 681, 626)(584, 643, 710, 646, 591, 651, 708, 641)(585, 644, 712, 654, 594, 642, 709, 645)(593, 653, 720, 652, 715, 791, 716, 648)(596, 655, 723, 793, 717, 650, 718, 656)(597, 657, 725, 665, 604, 663, 728, 658)(602, 664, 729, 659, 621, 685, 733, 662)(605, 661, 731, 801, 730, 666, 736, 667)(623, 687, 739, 669, 738, 806, 758, 686)(628, 693, 766, 696, 635, 701, 764, 691)(629, 694, 768, 704, 638, 692, 765, 695)(637, 703, 776, 702, 771, 814, 772, 698)(640, 705, 779, 815, 773, 700, 774, 706)(670, 740, 767, 747, 676, 745, 775, 741)(674, 746, 769, 742, 682, 754, 763, 744)(677, 743, 777, 760, 688, 748, 807, 749)(684, 756, 778, 751, 809, 813, 770, 755)(690, 753, 811, 827, 810, 761, 812, 762)(707, 781, 757, 788, 713, 786, 734, 782)(711, 787, 732, 783, 719, 795, 726, 785)(714, 784, 759, 798, 722, 789, 819, 790)(721, 797, 727, 792, 821, 803, 735, 796)(724, 794, 823, 808, 822, 799, 824, 800)(737, 804, 828, 829, 825, 802, 826, 805)(780, 816, 831, 820, 830, 817, 832, 818)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: chiral
Dual of E27.2354
Transitivity :: ET+
Graph:: simple bipartite
	v = 156 e = 416 f = 208
	degree seq :: [ 4^104, 8^52 ]

E27.2353 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 4, 8})
Quotient :: edge
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^-2 * X2 * X1^-2)^2, X1^2 * X2 * X1^-4 * X2 * X1^2, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ]
Map:: polytopal
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 31, 44, 37, 18, 8)(6, 13, 27, 51, 43, 56, 30, 14)(9, 19, 38, 46, 24, 45, 40, 20)(12, 25, 47, 42, 21, 41, 50, 26)(16, 33, 60, 93, 67, 74, 62, 34)(17, 35, 63, 88, 57, 83, 53, 28)(29, 54, 84, 72, 79, 111, 76, 48)(32, 58, 89, 66, 36, 65, 92, 59)(39, 69, 103, 107, 73, 49, 77, 70)(52, 80, 115, 87, 55, 86, 118, 81)(61, 95, 132, 100, 129, 168, 126, 90)(64, 98, 137, 161, 120, 91, 127, 99)(68, 101, 139, 106, 71, 105, 141, 102)(75, 108, 146, 114, 78, 113, 149, 109)(82, 119, 159, 124, 97, 136, 156, 116)(85, 122, 163, 194, 151, 117, 157, 123)(94, 130, 172, 135, 96, 134, 174, 131)(104, 143, 185, 144, 145, 187, 182, 140)(110, 150, 192, 154, 121, 162, 189, 147)(112, 152, 195, 184, 142, 148, 190, 153)(125, 165, 209, 171, 128, 170, 212, 166)(133, 176, 222, 267, 214, 173, 219, 177)(138, 180, 205, 160, 204, 256, 224, 178)(155, 197, 247, 202, 158, 201, 250, 198)(164, 208, 244, 193, 243, 299, 258, 206)(167, 213, 265, 217, 175, 221, 262, 210)(169, 215, 268, 225, 179, 211, 263, 216)(181, 227, 281, 231, 183, 230, 283, 228)(186, 196, 246, 289, 235, 232, 286, 234)(188, 236, 290, 241, 191, 240, 293, 237)(199, 251, 307, 254, 203, 255, 304, 248)(200, 252, 309, 259, 207, 249, 305, 253)(218, 270, 326, 274, 220, 273, 328, 271)(223, 277, 300, 266, 323, 345, 314, 275)(226, 269, 325, 359, 312, 279, 333, 280)(229, 284, 334, 285, 233, 287, 336, 282)(238, 294, 344, 297, 242, 298, 341, 291)(239, 295, 346, 301, 245, 292, 342, 296)(257, 313, 339, 308, 278, 332, 288, 311)(260, 310, 358, 319, 348, 315, 360, 316)(261, 317, 361, 322, 264, 321, 363, 318)(272, 329, 371, 331, 276, 327, 369, 330)(302, 347, 381, 353, 338, 349, 382, 350)(303, 351, 383, 356, 306, 355, 385, 352)(320, 364, 390, 366, 324, 362, 389, 365)(335, 367, 391, 374, 337, 372, 392, 373)(340, 375, 397, 379, 343, 378, 399, 376)(354, 386, 404, 388, 357, 384, 403, 387)(368, 393, 407, 396, 370, 395, 408, 394)(377, 400, 410, 402, 380, 398, 409, 401)(405, 412, 415, 414, 406, 411, 416, 413)(417, 419)(418, 422)(420, 425)(421, 428)(423, 432)(424, 433)(426, 437)(427, 440)(429, 444)(430, 445)(431, 448)(434, 452)(435, 455)(436, 449)(438, 459)(439, 460)(441, 464)(442, 465)(443, 468)(446, 471)(447, 473)(450, 477)(451, 480)(453, 483)(454, 484)(456, 487)(457, 488)(458, 485)(461, 489)(462, 490)(463, 491)(466, 494)(467, 495)(469, 498)(470, 501)(472, 504)(474, 506)(475, 507)(476, 510)(478, 512)(479, 513)(481, 516)(482, 514)(486, 520)(492, 526)(493, 528)(496, 532)(497, 533)(499, 536)(500, 537)(502, 540)(503, 538)(505, 541)(508, 544)(509, 545)(511, 549)(515, 554)(517, 556)(518, 550)(519, 558)(521, 560)(522, 546)(523, 561)(524, 563)(525, 564)(527, 567)(529, 570)(530, 568)(531, 571)(534, 574)(535, 576)(539, 580)(542, 583)(543, 585)(547, 589)(548, 591)(551, 592)(552, 594)(553, 595)(555, 597)(557, 599)(559, 602)(562, 604)(565, 607)(566, 609)(569, 612)(572, 615)(573, 616)(575, 619)(577, 620)(578, 622)(579, 623)(581, 626)(582, 627)(584, 630)(586, 633)(587, 631)(588, 634)(590, 636)(593, 639)(596, 642)(598, 645)(600, 648)(601, 649)(603, 651)(605, 654)(606, 655)(608, 658)(610, 659)(611, 661)(613, 664)(614, 665)(617, 670)(618, 668)(621, 673)(624, 676)(625, 677)(628, 680)(629, 682)(632, 685)(635, 688)(637, 691)(638, 692)(640, 694)(641, 695)(643, 698)(644, 686)(646, 701)(647, 689)(650, 704)(652, 707)(653, 708)(656, 713)(657, 711)(660, 716)(662, 718)(663, 719)(666, 722)(667, 724)(669, 726)(671, 727)(672, 728)(674, 730)(675, 731)(678, 735)(679, 736)(681, 732)(683, 739)(684, 740)(687, 743)(690, 745)(693, 714)(696, 750)(697, 751)(699, 753)(700, 729)(702, 754)(703, 748)(705, 755)(706, 756)(709, 759)(710, 761)(712, 763)(715, 764)(717, 765)(720, 769)(721, 770)(723, 766)(725, 773)(733, 774)(734, 778)(737, 776)(738, 780)(741, 783)(742, 784)(744, 786)(746, 757)(747, 760)(749, 788)(752, 775)(758, 793)(762, 796)(767, 797)(768, 800)(771, 798)(772, 802)(777, 803)(779, 804)(781, 807)(782, 808)(785, 791)(787, 794)(789, 811)(790, 809)(792, 814)(795, 816)(799, 817)(801, 818)(805, 821)(806, 822)(810, 815)(812, 813)(819, 827)(820, 828)(823, 829)(824, 830)(825, 831)(826, 832)
	L = (1, 417)(2, 418)(3, 419)(4, 420)(5, 421)(6, 422)(7, 423)(8, 424)(9, 425)(10, 426)(11, 427)(12, 428)(13, 429)(14, 430)(15, 431)(16, 432)(17, 433)(18, 434)(19, 435)(20, 436)(21, 437)(22, 438)(23, 439)(24, 440)(25, 441)(26, 442)(27, 443)(28, 444)(29, 445)(30, 446)(31, 447)(32, 448)(33, 449)(34, 450)(35, 451)(36, 452)(37, 453)(38, 454)(39, 455)(40, 456)(41, 457)(42, 458)(43, 459)(44, 460)(45, 461)(46, 462)(47, 463)(48, 464)(49, 465)(50, 466)(51, 467)(52, 468)(53, 469)(54, 470)(55, 471)(56, 472)(57, 473)(58, 474)(59, 475)(60, 476)(61, 477)(62, 478)(63, 479)(64, 480)(65, 481)(66, 482)(67, 483)(68, 484)(69, 485)(70, 486)(71, 487)(72, 488)(73, 489)(74, 490)(75, 491)(76, 492)(77, 493)(78, 494)(79, 495)(80, 496)(81, 497)(82, 498)(83, 499)(84, 500)(85, 501)(86, 502)(87, 503)(88, 504)(89, 505)(90, 506)(91, 507)(92, 508)(93, 509)(94, 510)(95, 511)(96, 512)(97, 513)(98, 514)(99, 515)(100, 516)(101, 517)(102, 518)(103, 519)(104, 520)(105, 521)(106, 522)(107, 523)(108, 524)(109, 525)(110, 526)(111, 527)(112, 528)(113, 529)(114, 530)(115, 531)(116, 532)(117, 533)(118, 534)(119, 535)(120, 536)(121, 537)(122, 538)(123, 539)(124, 540)(125, 541)(126, 542)(127, 543)(128, 544)(129, 545)(130, 546)(131, 547)(132, 548)(133, 549)(134, 550)(135, 551)(136, 552)(137, 553)(138, 554)(139, 555)(140, 556)(141, 557)(142, 558)(143, 559)(144, 560)(145, 561)(146, 562)(147, 563)(148, 564)(149, 565)(150, 566)(151, 567)(152, 568)(153, 569)(154, 570)(155, 571)(156, 572)(157, 573)(158, 574)(159, 575)(160, 576)(161, 577)(162, 578)(163, 579)(164, 580)(165, 581)(166, 582)(167, 583)(168, 584)(169, 585)(170, 586)(171, 587)(172, 588)(173, 589)(174, 590)(175, 591)(176, 592)(177, 593)(178, 594)(179, 595)(180, 596)(181, 597)(182, 598)(183, 599)(184, 600)(185, 601)(186, 602)(187, 603)(188, 604)(189, 605)(190, 606)(191, 607)(192, 608)(193, 609)(194, 610)(195, 611)(196, 612)(197, 613)(198, 614)(199, 615)(200, 616)(201, 617)(202, 618)(203, 619)(204, 620)(205, 621)(206, 622)(207, 623)(208, 624)(209, 625)(210, 626)(211, 627)(212, 628)(213, 629)(214, 630)(215, 631)(216, 632)(217, 633)(218, 634)(219, 635)(220, 636)(221, 637)(222, 638)(223, 639)(224, 640)(225, 641)(226, 642)(227, 643)(228, 644)(229, 645)(230, 646)(231, 647)(232, 648)(233, 649)(234, 650)(235, 651)(236, 652)(237, 653)(238, 654)(239, 655)(240, 656)(241, 657)(242, 658)(243, 659)(244, 660)(245, 661)(246, 662)(247, 663)(248, 664)(249, 665)(250, 666)(251, 667)(252, 668)(253, 669)(254, 670)(255, 671)(256, 672)(257, 673)(258, 674)(259, 675)(260, 676)(261, 677)(262, 678)(263, 679)(264, 680)(265, 681)(266, 682)(267, 683)(268, 684)(269, 685)(270, 686)(271, 687)(272, 688)(273, 689)(274, 690)(275, 691)(276, 692)(277, 693)(278, 694)(279, 695)(280, 696)(281, 697)(282, 698)(283, 699)(284, 700)(285, 701)(286, 702)(287, 703)(288, 704)(289, 705)(290, 706)(291, 707)(292, 708)(293, 709)(294, 710)(295, 711)(296, 712)(297, 713)(298, 714)(299, 715)(300, 716)(301, 717)(302, 718)(303, 719)(304, 720)(305, 721)(306, 722)(307, 723)(308, 724)(309, 725)(310, 726)(311, 727)(312, 728)(313, 729)(314, 730)(315, 731)(316, 732)(317, 733)(318, 734)(319, 735)(320, 736)(321, 737)(322, 738)(323, 739)(324, 740)(325, 741)(326, 742)(327, 743)(328, 744)(329, 745)(330, 746)(331, 747)(332, 748)(333, 749)(334, 750)(335, 751)(336, 752)(337, 753)(338, 754)(339, 755)(340, 756)(341, 757)(342, 758)(343, 759)(344, 760)(345, 761)(346, 762)(347, 763)(348, 764)(349, 765)(350, 766)(351, 767)(352, 768)(353, 769)(354, 770)(355, 771)(356, 772)(357, 773)(358, 774)(359, 775)(360, 776)(361, 777)(362, 778)(363, 779)(364, 780)(365, 781)(366, 782)(367, 783)(368, 784)(369, 785)(370, 786)(371, 787)(372, 788)(373, 789)(374, 790)(375, 791)(376, 792)(377, 793)(378, 794)(379, 795)(380, 796)(381, 797)(382, 798)(383, 799)(384, 800)(385, 801)(386, 802)(387, 803)(388, 804)(389, 805)(390, 806)(391, 807)(392, 808)(393, 809)(394, 810)(395, 811)(396, 812)(397, 813)(398, 814)(399, 815)(400, 816)(401, 817)(402, 818)(403, 819)(404, 820)(405, 821)(406, 822)(407, 823)(408, 824)(409, 825)(410, 826)(411, 827)(412, 828)(413, 829)(414, 830)(415, 831)(416, 832)
	local type(s) :: { ( 8, 8 ), ( 8^8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 260 e = 416 f = 104
	degree seq :: [ 2^208, 8^52 ]

E27.2354 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X1^2, X2^4, X1 * X2^2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1, (X1 * X2^-2 * X1 * X2^-1 * X1 * X2^-1)^2, (X2 * X1)^8, (X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2)^2, X1 * X2 * X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 417, 2, 418)(3, 419, 7, 423)(4, 420, 9, 425)(5, 421, 10, 426)(6, 422, 12, 428)(8, 424, 15, 431)(11, 427, 20, 436)(13, 429, 23, 439)(14, 430, 25, 441)(16, 432, 28, 444)(17, 433, 30, 446)(18, 434, 31, 447)(19, 435, 33, 449)(21, 437, 36, 452)(22, 438, 38, 454)(24, 440, 41, 457)(26, 442, 44, 460)(27, 443, 46, 462)(29, 445, 49, 465)(32, 448, 54, 470)(34, 450, 57, 473)(35, 451, 59, 475)(37, 453, 62, 478)(39, 455, 65, 481)(40, 456, 67, 483)(42, 458, 70, 486)(43, 459, 72, 488)(45, 461, 75, 491)(47, 463, 78, 494)(48, 464, 80, 496)(50, 466, 83, 499)(51, 467, 85, 501)(52, 468, 86, 502)(53, 469, 88, 504)(55, 471, 91, 507)(56, 472, 93, 509)(58, 474, 96, 512)(60, 476, 99, 515)(61, 477, 101, 517)(63, 479, 104, 520)(64, 480, 106, 522)(66, 482, 98, 514)(68, 484, 103, 519)(69, 485, 112, 528)(71, 487, 115, 531)(73, 489, 105, 521)(74, 490, 119, 535)(76, 492, 122, 538)(77, 493, 87, 503)(79, 495, 124, 540)(81, 497, 127, 543)(82, 498, 89, 505)(84, 500, 94, 510)(90, 506, 136, 552)(92, 508, 139, 555)(95, 511, 143, 559)(97, 513, 146, 562)(100, 516, 148, 564)(102, 518, 151, 567)(107, 523, 131, 547)(108, 524, 141, 557)(109, 525, 150, 566)(110, 526, 153, 569)(111, 527, 156, 572)(113, 529, 154, 570)(114, 530, 160, 576)(116, 532, 163, 579)(117, 533, 132, 548)(118, 534, 158, 574)(120, 536, 162, 578)(121, 537, 167, 583)(123, 539, 170, 586)(125, 541, 172, 588)(126, 542, 133, 549)(128, 544, 175, 591)(129, 545, 134, 550)(130, 546, 137, 553)(135, 551, 178, 594)(138, 554, 182, 598)(140, 556, 185, 601)(142, 558, 180, 596)(144, 560, 184, 600)(145, 561, 189, 605)(147, 563, 192, 608)(149, 565, 194, 610)(152, 568, 197, 613)(155, 571, 199, 615)(157, 573, 202, 618)(159, 575, 204, 620)(161, 577, 207, 623)(164, 580, 206, 622)(165, 581, 209, 625)(166, 582, 212, 628)(168, 584, 210, 626)(169, 585, 215, 631)(171, 587, 217, 633)(173, 589, 219, 635)(174, 590, 220, 636)(176, 592, 223, 639)(177, 593, 224, 640)(179, 595, 227, 643)(181, 597, 229, 645)(183, 599, 232, 648)(186, 602, 231, 647)(187, 603, 234, 650)(188, 604, 237, 653)(190, 606, 235, 651)(191, 607, 240, 656)(193, 609, 242, 658)(195, 611, 244, 660)(196, 612, 245, 661)(198, 614, 248, 664)(200, 616, 250, 666)(201, 617, 252, 668)(203, 619, 255, 671)(205, 621, 257, 673)(208, 624, 260, 676)(211, 627, 262, 678)(213, 629, 265, 681)(214, 630, 266, 682)(216, 632, 268, 684)(218, 634, 270, 686)(221, 637, 272, 688)(222, 638, 276, 692)(225, 641, 279, 695)(226, 642, 281, 697)(228, 644, 284, 700)(230, 646, 286, 702)(233, 649, 289, 705)(236, 652, 291, 707)(238, 654, 294, 710)(239, 655, 295, 711)(241, 657, 297, 713)(243, 659, 299, 715)(246, 662, 301, 717)(247, 663, 305, 721)(249, 665, 303, 719)(251, 667, 308, 724)(253, 669, 306, 722)(254, 670, 283, 699)(256, 672, 285, 701)(258, 674, 311, 727)(259, 675, 312, 728)(261, 677, 315, 731)(263, 679, 317, 733)(264, 680, 319, 735)(267, 683, 298, 714)(269, 685, 296, 712)(271, 687, 324, 740)(273, 689, 323, 739)(274, 690, 278, 694)(275, 691, 327, 743)(277, 693, 282, 698)(280, 696, 330, 746)(287, 703, 333, 749)(288, 704, 334, 750)(290, 706, 337, 753)(292, 708, 339, 755)(293, 709, 341, 757)(300, 716, 346, 762)(302, 718, 345, 761)(304, 720, 349, 765)(307, 723, 351, 767)(309, 725, 332, 748)(310, 726, 331, 747)(313, 729, 353, 769)(314, 730, 357, 773)(316, 732, 355, 771)(318, 734, 360, 776)(320, 736, 358, 774)(321, 737, 344, 760)(322, 738, 343, 759)(325, 741, 361, 777)(326, 742, 362, 778)(328, 744, 354, 770)(329, 745, 365, 781)(335, 751, 367, 783)(336, 752, 371, 787)(338, 754, 369, 785)(340, 756, 374, 790)(342, 758, 372, 788)(347, 763, 375, 791)(348, 764, 376, 792)(350, 766, 368, 784)(352, 768, 378, 794)(356, 772, 382, 798)(359, 775, 384, 800)(363, 779, 388, 804)(364, 780, 366, 782)(370, 786, 393, 809)(373, 789, 395, 811)(377, 793, 399, 815)(379, 795, 397, 813)(380, 796, 392, 808)(381, 797, 391, 807)(383, 799, 398, 814)(385, 801, 403, 819)(386, 802, 390, 806)(387, 803, 394, 810)(389, 805, 404, 820)(396, 812, 409, 825)(400, 816, 410, 826)(401, 817, 408, 824)(402, 818, 407, 823)(405, 821, 412, 828)(406, 822, 411, 827)(413, 829, 416, 832)(414, 830, 415, 831)
	L = (1, 419)(2, 421)(3, 424)(4, 417)(5, 427)(6, 418)(7, 429)(8, 420)(9, 432)(10, 434)(11, 422)(12, 437)(13, 440)(14, 423)(15, 442)(16, 445)(17, 425)(18, 448)(19, 426)(20, 450)(21, 453)(22, 428)(23, 455)(24, 430)(25, 458)(26, 461)(27, 431)(28, 463)(29, 433)(30, 466)(31, 468)(32, 435)(33, 471)(34, 474)(35, 436)(36, 476)(37, 438)(38, 479)(39, 482)(40, 439)(41, 484)(42, 487)(43, 441)(44, 489)(45, 443)(46, 492)(47, 495)(48, 444)(49, 497)(50, 500)(51, 446)(52, 503)(53, 447)(54, 505)(55, 508)(56, 449)(57, 510)(58, 451)(59, 513)(60, 516)(61, 452)(62, 518)(63, 521)(64, 454)(65, 523)(66, 456)(67, 525)(68, 527)(69, 457)(70, 529)(71, 459)(72, 532)(73, 534)(74, 460)(75, 536)(76, 539)(77, 462)(78, 533)(79, 464)(80, 541)(81, 544)(82, 465)(83, 545)(84, 467)(85, 524)(86, 547)(87, 469)(88, 549)(89, 551)(90, 470)(91, 553)(92, 472)(93, 556)(94, 558)(95, 473)(96, 560)(97, 563)(98, 475)(99, 557)(100, 477)(101, 565)(102, 568)(103, 478)(104, 569)(105, 480)(106, 548)(107, 501)(108, 481)(109, 571)(110, 483)(111, 485)(112, 573)(113, 575)(114, 486)(115, 577)(116, 494)(117, 488)(118, 490)(119, 580)(120, 582)(121, 491)(122, 584)(123, 493)(124, 583)(125, 589)(126, 496)(127, 586)(128, 498)(129, 592)(130, 499)(131, 522)(132, 502)(133, 593)(134, 504)(135, 506)(136, 595)(137, 597)(138, 507)(139, 599)(140, 515)(141, 509)(142, 511)(143, 602)(144, 604)(145, 512)(146, 606)(147, 514)(148, 605)(149, 611)(150, 517)(151, 608)(152, 519)(153, 614)(154, 520)(155, 526)(156, 616)(157, 619)(158, 528)(159, 530)(160, 621)(161, 624)(162, 531)(163, 625)(164, 627)(165, 535)(166, 537)(167, 629)(168, 630)(169, 538)(170, 632)(171, 540)(172, 631)(173, 542)(174, 543)(175, 637)(176, 546)(177, 550)(178, 641)(179, 644)(180, 552)(181, 554)(182, 646)(183, 649)(184, 555)(185, 650)(186, 652)(187, 559)(188, 561)(189, 654)(190, 655)(191, 562)(192, 657)(193, 564)(194, 656)(195, 566)(196, 567)(197, 662)(198, 570)(199, 665)(200, 667)(201, 572)(202, 669)(203, 574)(204, 668)(205, 674)(206, 576)(207, 671)(208, 578)(209, 677)(210, 579)(211, 581)(212, 679)(213, 587)(214, 585)(215, 683)(216, 590)(217, 685)(218, 588)(219, 687)(220, 689)(221, 691)(222, 591)(223, 692)(224, 694)(225, 696)(226, 594)(227, 698)(228, 596)(229, 697)(230, 703)(231, 598)(232, 700)(233, 600)(234, 706)(235, 601)(236, 603)(237, 708)(238, 609)(239, 607)(240, 712)(241, 612)(242, 714)(243, 610)(244, 716)(245, 718)(246, 720)(247, 613)(248, 721)(249, 723)(250, 615)(251, 617)(252, 725)(253, 702)(254, 618)(255, 726)(256, 620)(257, 699)(258, 622)(259, 623)(260, 729)(261, 626)(262, 732)(263, 734)(264, 628)(265, 736)(266, 735)(267, 634)(268, 633)(269, 738)(270, 711)(271, 741)(272, 635)(273, 742)(274, 636)(275, 638)(276, 744)(277, 639)(278, 745)(279, 640)(280, 642)(281, 747)(282, 673)(283, 643)(284, 748)(285, 645)(286, 670)(287, 647)(288, 648)(289, 751)(290, 651)(291, 754)(292, 756)(293, 653)(294, 758)(295, 757)(296, 659)(297, 658)(298, 760)(299, 682)(300, 763)(301, 660)(302, 764)(303, 661)(304, 663)(305, 766)(306, 664)(307, 666)(308, 768)(309, 672)(310, 675)(311, 746)(312, 770)(313, 772)(314, 676)(315, 773)(316, 775)(317, 678)(318, 680)(319, 761)(320, 762)(321, 681)(322, 684)(323, 686)(324, 759)(325, 688)(326, 690)(327, 779)(328, 693)(329, 695)(330, 782)(331, 701)(332, 704)(333, 724)(334, 784)(335, 786)(336, 705)(337, 787)(338, 789)(339, 707)(340, 709)(341, 739)(342, 740)(343, 710)(344, 713)(345, 715)(346, 737)(347, 717)(348, 719)(349, 793)(350, 722)(351, 795)(352, 783)(353, 727)(354, 797)(355, 728)(356, 730)(357, 799)(358, 731)(359, 733)(360, 801)(361, 790)(362, 803)(363, 805)(364, 743)(365, 806)(366, 769)(367, 749)(368, 808)(369, 750)(370, 752)(371, 810)(372, 753)(373, 755)(374, 812)(375, 776)(376, 814)(377, 816)(378, 765)(379, 817)(380, 767)(381, 771)(382, 818)(383, 774)(384, 820)(385, 813)(386, 777)(387, 822)(388, 778)(389, 780)(390, 823)(391, 781)(392, 785)(393, 824)(394, 788)(395, 826)(396, 802)(397, 791)(398, 828)(399, 792)(400, 794)(401, 796)(402, 829)(403, 798)(404, 830)(405, 800)(406, 804)(407, 807)(408, 831)(409, 809)(410, 832)(411, 811)(412, 815)(413, 819)(414, 821)(415, 825)(416, 827)
	local type(s) :: { ( 4, 8, 4, 8 ) }
Outer automorphisms :: chiral
Dual of E27.2352
Transitivity :: ET+ VT+
Graph:: simple bipartite
	v = 208 e = 416 f = 156
	degree seq :: [ 4^208 ]

E27.2355 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ (X1 * X2)^2, X1^4, (X2^-1 * X1 * X2^-2)^2, X2^8, X2^-1 * X1^-1 * X2^4 * X1 * X2^-3, (X2 * X1^-1 * X2^-2 * X1^-1 * X2)^2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^2 * X1^-2 * X2 * X1^-1 * X2^2 * X1^-1, X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1 * X2 * X1^2 * X2^-2 * X1^-1 * X2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1^-1, X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2^-2 * X1^-2 * X2^-2 * X1^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-2 * X2^-2 * X1^-2 * X2^-2 * X1^-1 ]
Map::
	R = (1, 417, 2, 418, 6, 422, 4, 420)(3, 419, 9, 425, 21, 437, 11, 427)(5, 421, 13, 429, 18, 434, 7, 423)(8, 424, 19, 435, 34, 450, 15, 431)(10, 426, 23, 439, 49, 465, 25, 441)(12, 428, 16, 432, 35, 451, 28, 444)(14, 430, 31, 447, 61, 477, 29, 445)(17, 433, 37, 453, 72, 488, 39, 455)(20, 436, 43, 459, 80, 496, 41, 457)(22, 438, 47, 463, 84, 500, 45, 461)(24, 440, 51, 467, 82, 498, 44, 460)(26, 442, 46, 462, 85, 501, 55, 471)(27, 443, 56, 472, 99, 515, 58, 474)(30, 446, 62, 478, 78, 494, 40, 456)(32, 448, 57, 473, 101, 517, 63, 479)(33, 449, 64, 480, 106, 522, 66, 482)(36, 452, 70, 486, 114, 530, 68, 484)(38, 454, 74, 490, 116, 532, 71, 487)(42, 458, 81, 497, 112, 528, 67, 483)(48, 464, 65, 481, 108, 524, 87, 503)(50, 466, 92, 508, 139, 555, 90, 506)(52, 468, 75, 491, 109, 525, 89, 505)(53, 469, 91, 507, 140, 556, 95, 511)(54, 470, 96, 512, 146, 562, 97, 513)(59, 475, 69, 485, 115, 531, 102, 518)(60, 476, 103, 519, 152, 568, 104, 520)(73, 489, 119, 535, 168, 584, 117, 533)(76, 492, 118, 534, 169, 585, 122, 538)(77, 493, 123, 539, 175, 591, 124, 540)(79, 495, 126, 542, 178, 594, 127, 543)(83, 499, 129, 545, 181, 597, 131, 547)(86, 502, 135, 551, 188, 604, 133, 549)(88, 504, 137, 553, 186, 602, 132, 548)(93, 509, 130, 546, 183, 599, 142, 558)(94, 510, 144, 560, 171, 587, 120, 536)(98, 514, 134, 550, 189, 605, 148, 564)(100, 516, 150, 566, 205, 621, 149, 565)(105, 521, 154, 570, 177, 593, 125, 541)(107, 523, 157, 573, 212, 628, 155, 571)(110, 526, 156, 572, 213, 629, 160, 576)(111, 527, 161, 577, 219, 635, 162, 578)(113, 529, 164, 580, 222, 638, 165, 581)(121, 537, 173, 589, 215, 631, 158, 574)(128, 544, 180, 596, 221, 637, 163, 579)(136, 552, 159, 575, 217, 633, 190, 606)(138, 554, 192, 608, 254, 670, 193, 609)(141, 557, 197, 613, 260, 676, 195, 611)(143, 559, 199, 615, 258, 674, 194, 610)(145, 561, 196, 612, 261, 677, 201, 617)(147, 563, 203, 619, 266, 682, 202, 618)(151, 567, 166, 582, 224, 640, 207, 623)(153, 569, 208, 624, 272, 688, 209, 625)(167, 583, 225, 641, 291, 707, 226, 642)(170, 586, 230, 646, 297, 713, 228, 644)(172, 588, 232, 648, 295, 711, 227, 643)(174, 590, 229, 645, 298, 714, 234, 650)(176, 592, 236, 652, 303, 719, 235, 651)(179, 595, 238, 654, 306, 722, 239, 655)(182, 598, 243, 659, 310, 726, 241, 657)(184, 600, 242, 658, 311, 727, 245, 661)(185, 601, 246, 662, 316, 732, 247, 663)(187, 603, 249, 665, 319, 735, 250, 666)(191, 607, 253, 669, 318, 734, 248, 664)(198, 614, 244, 660, 314, 730, 262, 678)(200, 616, 264, 680, 299, 715, 231, 647)(204, 620, 251, 667, 321, 737, 268, 684)(206, 622, 270, 686, 341, 757, 269, 685)(210, 626, 274, 690, 305, 721, 237, 653)(211, 627, 275, 691, 347, 763, 276, 692)(214, 630, 280, 696, 353, 769, 278, 694)(216, 632, 282, 698, 351, 767, 277, 693)(218, 634, 279, 695, 354, 770, 284, 700)(220, 636, 286, 702, 359, 775, 285, 701)(223, 639, 288, 704, 362, 778, 289, 705)(233, 649, 301, 717, 355, 771, 281, 697)(240, 656, 308, 724, 361, 777, 287, 703)(252, 668, 283, 699, 357, 773, 322, 738)(255, 671, 326, 742, 350, 766, 324, 740)(256, 672, 325, 741, 360, 776, 327, 743)(257, 673, 328, 744, 348, 764, 329, 745)(259, 675, 331, 747, 356, 772, 332, 748)(263, 679, 335, 751, 352, 768, 330, 746)(265, 681, 333, 749, 392, 808, 337, 753)(267, 683, 339, 755, 349, 765, 338, 754)(271, 687, 290, 706, 364, 780, 343, 759)(273, 689, 344, 760, 384, 800, 345, 761)(292, 708, 367, 783, 317, 733, 365, 781)(293, 709, 366, 782, 323, 739, 368, 784)(294, 710, 369, 785, 313, 729, 370, 786)(296, 712, 372, 788, 342, 758, 373, 789)(300, 716, 376, 792, 312, 728, 371, 787)(302, 718, 374, 790, 404, 820, 378, 794)(304, 720, 380, 796, 309, 725, 379, 795)(307, 723, 382, 798, 402, 818, 383, 799)(315, 731, 381, 797, 346, 762, 386, 802)(320, 736, 387, 803, 411, 827, 388, 804)(334, 750, 385, 801, 409, 825, 393, 809)(336, 752, 394, 810, 405, 821, 375, 791)(340, 756, 389, 805, 401, 817, 363, 779)(358, 774, 397, 813, 413, 829, 400, 816)(377, 793, 406, 822, 391, 807, 398, 814)(390, 806, 399, 815, 414, 830, 403, 819)(395, 811, 407, 823, 415, 831, 412, 828)(396, 812, 408, 824, 416, 832, 410, 826)
	L = (1, 419)(2, 423)(3, 426)(4, 428)(5, 417)(6, 431)(7, 433)(8, 418)(9, 420)(10, 440)(11, 442)(12, 443)(13, 445)(14, 421)(15, 449)(16, 422)(17, 454)(18, 456)(19, 457)(20, 424)(21, 461)(22, 425)(23, 427)(24, 468)(25, 469)(26, 470)(27, 473)(28, 475)(29, 476)(30, 429)(31, 479)(32, 430)(33, 481)(34, 483)(35, 484)(36, 432)(37, 434)(38, 491)(39, 492)(40, 493)(41, 495)(42, 435)(43, 498)(44, 436)(45, 499)(46, 437)(47, 503)(48, 438)(49, 506)(50, 439)(51, 441)(52, 448)(53, 446)(54, 447)(55, 514)(56, 444)(57, 505)(58, 502)(59, 504)(60, 510)(61, 513)(62, 511)(63, 509)(64, 450)(65, 525)(66, 526)(67, 527)(68, 529)(69, 451)(70, 532)(71, 452)(72, 533)(73, 453)(74, 455)(75, 460)(76, 458)(77, 459)(78, 541)(79, 537)(80, 540)(81, 538)(82, 536)(83, 546)(84, 548)(85, 549)(86, 462)(87, 552)(88, 463)(89, 464)(90, 554)(91, 465)(92, 558)(93, 466)(94, 467)(95, 561)(96, 471)(97, 557)(98, 559)(99, 565)(100, 472)(101, 474)(102, 567)(103, 477)(104, 569)(105, 478)(106, 571)(107, 480)(108, 482)(109, 487)(110, 485)(111, 486)(112, 579)(113, 575)(114, 578)(115, 576)(116, 574)(117, 583)(118, 488)(119, 587)(120, 489)(121, 490)(122, 590)(123, 494)(124, 586)(125, 588)(126, 496)(127, 595)(128, 497)(129, 500)(130, 517)(131, 600)(132, 601)(133, 603)(134, 501)(135, 515)(136, 516)(137, 518)(138, 519)(139, 610)(140, 611)(141, 507)(142, 614)(143, 508)(144, 520)(145, 616)(146, 618)(147, 512)(148, 620)(149, 598)(150, 606)(151, 622)(152, 609)(153, 521)(154, 625)(155, 627)(156, 522)(157, 631)(158, 523)(159, 524)(160, 634)(161, 528)(162, 630)(163, 632)(164, 530)(165, 639)(166, 531)(167, 542)(168, 643)(169, 644)(170, 534)(171, 647)(172, 535)(173, 543)(174, 649)(175, 651)(176, 539)(177, 653)(178, 642)(179, 544)(180, 655)(181, 657)(182, 545)(183, 547)(184, 550)(185, 551)(186, 664)(187, 660)(188, 663)(189, 661)(190, 668)(191, 553)(192, 555)(193, 672)(194, 673)(195, 675)(196, 556)(197, 562)(198, 563)(199, 564)(200, 560)(201, 681)(202, 671)(203, 678)(204, 683)(205, 685)(206, 566)(207, 687)(208, 568)(209, 689)(210, 570)(211, 580)(212, 693)(213, 694)(214, 572)(215, 697)(216, 573)(217, 581)(218, 699)(219, 701)(220, 577)(221, 703)(222, 692)(223, 582)(224, 705)(225, 584)(226, 709)(227, 710)(228, 712)(229, 585)(230, 591)(231, 592)(232, 593)(233, 589)(234, 718)(235, 708)(236, 715)(237, 720)(238, 594)(239, 723)(240, 596)(241, 725)(242, 597)(243, 621)(244, 599)(245, 731)(246, 602)(247, 728)(248, 729)(249, 604)(250, 736)(251, 605)(252, 607)(253, 738)(254, 740)(255, 608)(256, 612)(257, 613)(258, 746)(259, 624)(260, 745)(261, 743)(262, 750)(263, 615)(264, 617)(265, 626)(266, 754)(267, 619)(268, 756)(269, 733)(270, 623)(271, 739)(272, 748)(273, 752)(274, 753)(275, 628)(276, 765)(277, 766)(278, 768)(279, 629)(280, 635)(281, 636)(282, 637)(283, 633)(284, 774)(285, 764)(286, 771)(287, 776)(288, 638)(289, 779)(290, 640)(291, 781)(292, 641)(293, 645)(294, 646)(295, 787)(296, 654)(297, 786)(298, 784)(299, 791)(300, 648)(301, 650)(302, 656)(303, 795)(304, 652)(305, 797)(306, 789)(307, 793)(308, 794)(309, 665)(310, 785)(311, 792)(312, 658)(313, 659)(314, 666)(315, 801)(316, 783)(317, 662)(318, 782)(319, 796)(320, 667)(321, 804)(322, 806)(323, 669)(324, 767)(325, 670)(326, 682)(327, 777)(328, 674)(329, 775)(330, 769)(331, 676)(332, 807)(333, 677)(334, 679)(335, 809)(336, 680)(337, 811)(338, 763)(339, 684)(340, 778)(341, 788)(342, 686)(343, 798)(344, 688)(345, 812)(346, 690)(347, 744)(348, 691)(349, 695)(350, 696)(351, 747)(352, 704)(353, 742)(354, 755)(355, 814)(356, 698)(357, 700)(358, 706)(359, 741)(360, 702)(361, 760)(362, 751)(363, 815)(364, 816)(365, 757)(366, 707)(367, 719)(368, 759)(369, 711)(370, 734)(371, 732)(372, 713)(373, 819)(374, 714)(375, 716)(376, 821)(377, 717)(378, 823)(379, 726)(380, 721)(381, 727)(382, 722)(383, 824)(384, 724)(385, 730)(386, 826)(387, 735)(388, 828)(389, 737)(390, 758)(391, 749)(392, 822)(393, 813)(394, 761)(395, 827)(396, 762)(397, 770)(398, 772)(399, 773)(400, 831)(401, 832)(402, 780)(403, 790)(404, 830)(405, 803)(406, 799)(407, 808)(408, 800)(409, 802)(410, 805)(411, 810)(412, 829)(413, 825)(414, 817)(415, 820)(416, 818)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 104 e = 416 f = 260
	degree seq :: [ 8^104 ]

E27.2356 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 4, 8})
Quotient :: loop
Aut^+ = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
Aut   = (C4 x (C13 : C4)) : C2 (small group id <416, 85>)
|r| :: 1
Presentation :: [ X2^2, X1^8, (X2 * X1^-1)^4, (X1^-2 * X2 * X1^-2)^2, X1^2 * X2 * X1^-4 * X2 * X1^2, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 ]
Map::
	R = (1, 417, 2, 418, 5, 421, 11, 427, 23, 439, 22, 438, 10, 426, 4, 420)(3, 419, 7, 423, 15, 431, 31, 447, 44, 460, 37, 453, 18, 434, 8, 424)(6, 422, 13, 429, 27, 443, 51, 467, 43, 459, 56, 472, 30, 446, 14, 430)(9, 425, 19, 435, 38, 454, 46, 462, 24, 440, 45, 461, 40, 456, 20, 436)(12, 428, 25, 441, 47, 463, 42, 458, 21, 437, 41, 457, 50, 466, 26, 442)(16, 432, 33, 449, 60, 476, 93, 509, 67, 483, 74, 490, 62, 478, 34, 450)(17, 433, 35, 451, 63, 479, 88, 504, 57, 473, 83, 499, 53, 469, 28, 444)(29, 445, 54, 470, 84, 500, 72, 488, 79, 495, 111, 527, 76, 492, 48, 464)(32, 448, 58, 474, 89, 505, 66, 482, 36, 452, 65, 481, 92, 508, 59, 475)(39, 455, 69, 485, 103, 519, 107, 523, 73, 489, 49, 465, 77, 493, 70, 486)(52, 468, 80, 496, 115, 531, 87, 503, 55, 471, 86, 502, 118, 534, 81, 497)(61, 477, 95, 511, 132, 548, 100, 516, 129, 545, 168, 584, 126, 542, 90, 506)(64, 480, 98, 514, 137, 553, 161, 577, 120, 536, 91, 507, 127, 543, 99, 515)(68, 484, 101, 517, 139, 555, 106, 522, 71, 487, 105, 521, 141, 557, 102, 518)(75, 491, 108, 524, 146, 562, 114, 530, 78, 494, 113, 529, 149, 565, 109, 525)(82, 498, 119, 535, 159, 575, 124, 540, 97, 513, 136, 552, 156, 572, 116, 532)(85, 501, 122, 538, 163, 579, 194, 610, 151, 567, 117, 533, 157, 573, 123, 539)(94, 510, 130, 546, 172, 588, 135, 551, 96, 512, 134, 550, 174, 590, 131, 547)(104, 520, 143, 559, 185, 601, 144, 560, 145, 561, 187, 603, 182, 598, 140, 556)(110, 526, 150, 566, 192, 608, 154, 570, 121, 537, 162, 578, 189, 605, 147, 563)(112, 528, 152, 568, 195, 611, 184, 600, 142, 558, 148, 564, 190, 606, 153, 569)(125, 541, 165, 581, 209, 625, 171, 587, 128, 544, 170, 586, 212, 628, 166, 582)(133, 549, 176, 592, 222, 638, 267, 683, 214, 630, 173, 589, 219, 635, 177, 593)(138, 554, 180, 596, 205, 621, 160, 576, 204, 620, 256, 672, 224, 640, 178, 594)(155, 571, 197, 613, 247, 663, 202, 618, 158, 574, 201, 617, 250, 666, 198, 614)(164, 580, 208, 624, 244, 660, 193, 609, 243, 659, 299, 715, 258, 674, 206, 622)(167, 583, 213, 629, 265, 681, 217, 633, 175, 591, 221, 637, 262, 678, 210, 626)(169, 585, 215, 631, 268, 684, 225, 641, 179, 595, 211, 627, 263, 679, 216, 632)(181, 597, 227, 643, 281, 697, 231, 647, 183, 599, 230, 646, 283, 699, 228, 644)(186, 602, 196, 612, 246, 662, 289, 705, 235, 651, 232, 648, 286, 702, 234, 650)(188, 604, 236, 652, 290, 706, 241, 657, 191, 607, 240, 656, 293, 709, 237, 653)(199, 615, 251, 667, 307, 723, 254, 670, 203, 619, 255, 671, 304, 720, 248, 664)(200, 616, 252, 668, 309, 725, 259, 675, 207, 623, 249, 665, 305, 721, 253, 669)(218, 634, 270, 686, 326, 742, 274, 690, 220, 636, 273, 689, 328, 744, 271, 687)(223, 639, 277, 693, 300, 716, 266, 682, 323, 739, 345, 761, 314, 730, 275, 691)(226, 642, 269, 685, 325, 741, 359, 775, 312, 728, 279, 695, 333, 749, 280, 696)(229, 645, 284, 700, 334, 750, 285, 701, 233, 649, 287, 703, 336, 752, 282, 698)(238, 654, 294, 710, 344, 760, 297, 713, 242, 658, 298, 714, 341, 757, 291, 707)(239, 655, 295, 711, 346, 762, 301, 717, 245, 661, 292, 708, 342, 758, 296, 712)(257, 673, 313, 729, 339, 755, 308, 724, 278, 694, 332, 748, 288, 704, 311, 727)(260, 676, 310, 726, 358, 774, 319, 735, 348, 764, 315, 731, 360, 776, 316, 732)(261, 677, 317, 733, 361, 777, 322, 738, 264, 680, 321, 737, 363, 779, 318, 734)(272, 688, 329, 745, 371, 787, 331, 747, 276, 692, 327, 743, 369, 785, 330, 746)(302, 718, 347, 763, 381, 797, 353, 769, 338, 754, 349, 765, 382, 798, 350, 766)(303, 719, 351, 767, 383, 799, 356, 772, 306, 722, 355, 771, 385, 801, 352, 768)(320, 736, 364, 780, 390, 806, 366, 782, 324, 740, 362, 778, 389, 805, 365, 781)(335, 751, 367, 783, 391, 807, 374, 790, 337, 753, 372, 788, 392, 808, 373, 789)(340, 756, 375, 791, 397, 813, 379, 795, 343, 759, 378, 794, 399, 815, 376, 792)(354, 770, 386, 802, 404, 820, 388, 804, 357, 773, 384, 800, 403, 819, 387, 803)(368, 784, 393, 809, 407, 823, 396, 812, 370, 786, 395, 811, 408, 824, 394, 810)(377, 793, 400, 816, 410, 826, 402, 818, 380, 796, 398, 814, 409, 825, 401, 817)(405, 821, 412, 828, 415, 831, 414, 830, 406, 822, 411, 827, 416, 832, 413, 829)
	L = (1, 419)(2, 422)(3, 417)(4, 425)(5, 428)(6, 418)(7, 432)(8, 433)(9, 420)(10, 437)(11, 440)(12, 421)(13, 444)(14, 445)(15, 448)(16, 423)(17, 424)(18, 452)(19, 455)(20, 449)(21, 426)(22, 459)(23, 460)(24, 427)(25, 464)(26, 465)(27, 468)(28, 429)(29, 430)(30, 471)(31, 473)(32, 431)(33, 436)(34, 477)(35, 480)(36, 434)(37, 483)(38, 484)(39, 435)(40, 487)(41, 488)(42, 485)(43, 438)(44, 439)(45, 489)(46, 490)(47, 491)(48, 441)(49, 442)(50, 494)(51, 495)(52, 443)(53, 498)(54, 501)(55, 446)(56, 504)(57, 447)(58, 506)(59, 507)(60, 510)(61, 450)(62, 512)(63, 513)(64, 451)(65, 516)(66, 514)(67, 453)(68, 454)(69, 458)(70, 520)(71, 456)(72, 457)(73, 461)(74, 462)(75, 463)(76, 526)(77, 528)(78, 466)(79, 467)(80, 532)(81, 533)(82, 469)(83, 536)(84, 537)(85, 470)(86, 540)(87, 538)(88, 472)(89, 541)(90, 474)(91, 475)(92, 544)(93, 545)(94, 476)(95, 549)(96, 478)(97, 479)(98, 482)(99, 554)(100, 481)(101, 556)(102, 550)(103, 558)(104, 486)(105, 560)(106, 546)(107, 561)(108, 563)(109, 564)(110, 492)(111, 567)(112, 493)(113, 570)(114, 568)(115, 571)(116, 496)(117, 497)(118, 574)(119, 576)(120, 499)(121, 500)(122, 503)(123, 580)(124, 502)(125, 505)(126, 583)(127, 585)(128, 508)(129, 509)(130, 522)(131, 589)(132, 591)(133, 511)(134, 518)(135, 592)(136, 594)(137, 595)(138, 515)(139, 597)(140, 517)(141, 599)(142, 519)(143, 602)(144, 521)(145, 523)(146, 604)(147, 524)(148, 525)(149, 607)(150, 609)(151, 527)(152, 530)(153, 612)(154, 529)(155, 531)(156, 615)(157, 616)(158, 534)(159, 619)(160, 535)(161, 620)(162, 622)(163, 623)(164, 539)(165, 626)(166, 627)(167, 542)(168, 630)(169, 543)(170, 633)(171, 631)(172, 634)(173, 547)(174, 636)(175, 548)(176, 551)(177, 639)(178, 552)(179, 553)(180, 642)(181, 555)(182, 645)(183, 557)(184, 648)(185, 649)(186, 559)(187, 651)(188, 562)(189, 654)(190, 655)(191, 565)(192, 658)(193, 566)(194, 659)(195, 661)(196, 569)(197, 664)(198, 665)(199, 572)(200, 573)(201, 670)(202, 668)(203, 575)(204, 577)(205, 673)(206, 578)(207, 579)(208, 676)(209, 677)(210, 581)(211, 582)(212, 680)(213, 682)(214, 584)(215, 587)(216, 685)(217, 586)(218, 588)(219, 688)(220, 590)(221, 691)(222, 692)(223, 593)(224, 694)(225, 695)(226, 596)(227, 698)(228, 686)(229, 598)(230, 701)(231, 689)(232, 600)(233, 601)(234, 704)(235, 603)(236, 707)(237, 708)(238, 605)(239, 606)(240, 713)(241, 711)(242, 608)(243, 610)(244, 716)(245, 611)(246, 718)(247, 719)(248, 613)(249, 614)(250, 722)(251, 724)(252, 618)(253, 726)(254, 617)(255, 727)(256, 728)(257, 621)(258, 730)(259, 731)(260, 624)(261, 625)(262, 735)(263, 736)(264, 628)(265, 732)(266, 629)(267, 739)(268, 740)(269, 632)(270, 644)(271, 743)(272, 635)(273, 647)(274, 745)(275, 637)(276, 638)(277, 714)(278, 640)(279, 641)(280, 750)(281, 751)(282, 643)(283, 753)(284, 729)(285, 646)(286, 754)(287, 748)(288, 650)(289, 755)(290, 756)(291, 652)(292, 653)(293, 759)(294, 761)(295, 657)(296, 763)(297, 656)(298, 693)(299, 764)(300, 660)(301, 765)(302, 662)(303, 663)(304, 769)(305, 770)(306, 666)(307, 766)(308, 667)(309, 773)(310, 669)(311, 671)(312, 672)(313, 700)(314, 674)(315, 675)(316, 681)(317, 774)(318, 778)(319, 678)(320, 679)(321, 776)(322, 780)(323, 683)(324, 684)(325, 783)(326, 784)(327, 687)(328, 786)(329, 690)(330, 757)(331, 760)(332, 703)(333, 788)(334, 696)(335, 697)(336, 775)(337, 699)(338, 702)(339, 705)(340, 706)(341, 746)(342, 793)(343, 709)(344, 747)(345, 710)(346, 796)(347, 712)(348, 715)(349, 717)(350, 723)(351, 797)(352, 800)(353, 720)(354, 721)(355, 798)(356, 802)(357, 725)(358, 733)(359, 752)(360, 737)(361, 803)(362, 734)(363, 804)(364, 738)(365, 807)(366, 808)(367, 741)(368, 742)(369, 791)(370, 744)(371, 794)(372, 749)(373, 811)(374, 809)(375, 785)(376, 814)(377, 758)(378, 787)(379, 816)(380, 762)(381, 767)(382, 771)(383, 817)(384, 768)(385, 818)(386, 772)(387, 777)(388, 779)(389, 821)(390, 822)(391, 781)(392, 782)(393, 790)(394, 815)(395, 789)(396, 813)(397, 812)(398, 792)(399, 810)(400, 795)(401, 799)(402, 801)(403, 827)(404, 828)(405, 805)(406, 806)(407, 829)(408, 830)(409, 831)(410, 832)(411, 819)(412, 820)(413, 823)(414, 824)(415, 825)(416, 826)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 52 e = 416 f = 312
	degree seq :: [ 16^52 ]

E27.2357 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 3, 12})
Quotient :: halfedge
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1)^3, X1^12, (X1^2 * X2 * X1^-1 * X2 * X1^2)^2, (X1^-3 * X2 * X1^2 * X2 * X1^-2)^2, X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-3 * X2 * X1^-3, X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-3 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^2 * X2 * X1^-2 * X2 * X1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 21, 37, 63, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 104, 91, 54, 31, 17, 8)(6, 13, 25, 43, 73, 119, 103, 128, 78, 46, 26, 14)(9, 18, 32, 55, 92, 106, 64, 105, 86, 51, 29, 16)(12, 23, 41, 69, 113, 101, 61, 102, 118, 72, 42, 24)(19, 34, 58, 97, 108, 66, 38, 65, 107, 96, 57, 33)(22, 39, 67, 109, 99, 59, 35, 60, 100, 112, 68, 40)(28, 49, 83, 132, 181, 142, 90, 143, 186, 135, 84, 50)(30, 52, 87, 138, 176, 127, 80, 129, 171, 123, 75, 44)(45, 76, 124, 172, 222, 166, 120, 167, 217, 162, 115, 70)(48, 81, 130, 177, 140, 88, 53, 89, 141, 180, 131, 82)(56, 94, 146, 195, 246, 188, 137, 154, 206, 198, 147, 95)(71, 116, 163, 218, 204, 152, 159, 213, 265, 209, 156, 110)(74, 121, 168, 223, 174, 125, 77, 126, 175, 226, 169, 122)(85, 136, 187, 244, 194, 145, 93, 144, 193, 240, 183, 133)(98, 150, 202, 259, 261, 205, 153, 111, 157, 210, 203, 151)(114, 160, 214, 269, 220, 164, 117, 165, 221, 272, 215, 161)(134, 184, 241, 299, 250, 192, 237, 295, 356, 291, 234, 178)(139, 190, 248, 307, 349, 284, 228, 179, 235, 292, 249, 191)(148, 199, 256, 316, 258, 201, 149, 200, 257, 312, 253, 196)(155, 207, 262, 322, 267, 211, 158, 212, 268, 325, 263, 208)(170, 227, 283, 347, 288, 232, 189, 247, 306, 343, 280, 224)(173, 230, 286, 351, 405, 336, 274, 225, 281, 344, 287, 231)(182, 238, 296, 360, 301, 242, 185, 243, 302, 363, 297, 239)(197, 254, 313, 371, 305, 245, 304, 370, 440, 375, 309, 251)(216, 273, 335, 403, 340, 278, 229, 285, 350, 399, 332, 270)(219, 276, 338, 407, 468, 393, 327, 271, 333, 400, 339, 277)(233, 289, 353, 421, 358, 293, 236, 294, 359, 424, 354, 290)(252, 310, 376, 446, 380, 314, 255, 315, 381, 449, 377, 311)(260, 320, 386, 455, 383, 317, 321, 387, 459, 456, 384, 318)(264, 326, 392, 466, 396, 330, 275, 337, 406, 462, 389, 323)(266, 328, 394, 469, 457, 385, 319, 324, 390, 463, 395, 329)(279, 341, 409, 483, 413, 345, 282, 346, 414, 486, 410, 342)(298, 364, 434, 512, 438, 368, 303, 369, 439, 508, 431, 361)(300, 366, 436, 515, 579, 502, 426, 362, 432, 509, 437, 367)(308, 374, 444, 493, 417, 348, 416, 492, 572, 520, 442, 372)(331, 397, 471, 549, 475, 401, 334, 402, 476, 552, 472, 398)(352, 420, 496, 559, 479, 404, 478, 558, 609, 574, 494, 418)(355, 425, 501, 540, 505, 429, 365, 435, 514, 544, 498, 422)(357, 427, 503, 580, 521, 443, 373, 423, 499, 577, 504, 428)(378, 450, 528, 573, 531, 453, 382, 454, 532, 588, 525, 447)(379, 451, 529, 595, 605, 587, 518, 448, 526, 593, 530, 452)(388, 460, 538, 598, 542, 464, 391, 465, 543, 516, 539, 461)(408, 482, 562, 497, 546, 467, 545, 602, 578, 500, 560, 480)(411, 487, 567, 533, 570, 490, 415, 491, 571, 534, 564, 484)(412, 488, 568, 613, 575, 495, 419, 485, 565, 611, 569, 489)(430, 506, 582, 616, 585, 510, 433, 511, 576, 614, 583, 507)(441, 519, 556, 477, 557, 513, 445, 523, 550, 473, 553, 517)(458, 470, 548, 604, 563, 597, 537, 535, 596, 612, 566, 536)(474, 554, 607, 624, 610, 561, 481, 551, 606, 623, 608, 555)(522, 581, 617, 592, 524, 591, 615, 589, 620, 594, 527, 590)(541, 600, 586, 618, 622, 603, 547, 599, 584, 619, 621, 601)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 64)(40, 65)(41, 70)(42, 71)(43, 74)(46, 77)(47, 80)(50, 81)(51, 85)(52, 88)(54, 90)(55, 93)(57, 94)(58, 98)(60, 101)(62, 103)(63, 104)(66, 105)(67, 110)(68, 111)(69, 114)(72, 117)(73, 120)(75, 121)(76, 125)(78, 127)(79, 128)(82, 129)(83, 133)(84, 134)(86, 137)(87, 139)(89, 142)(91, 106)(92, 143)(95, 144)(96, 148)(97, 149)(99, 150)(100, 152)(102, 119)(107, 153)(108, 154)(109, 155)(112, 158)(113, 159)(115, 160)(116, 164)(118, 166)(122, 167)(123, 170)(124, 173)(126, 176)(130, 178)(131, 179)(132, 182)(135, 185)(136, 188)(138, 189)(140, 190)(141, 192)(145, 186)(146, 196)(147, 197)(151, 200)(156, 207)(157, 211)(161, 213)(162, 216)(163, 219)(165, 222)(168, 224)(169, 225)(171, 228)(172, 229)(174, 230)(175, 232)(177, 233)(180, 236)(181, 237)(183, 238)(184, 242)(187, 245)(191, 247)(193, 251)(194, 243)(195, 252)(198, 255)(199, 205)(201, 206)(202, 208)(203, 260)(204, 212)(209, 264)(210, 266)(214, 270)(215, 271)(217, 274)(218, 275)(220, 276)(221, 278)(223, 279)(226, 282)(227, 284)(231, 285)(234, 289)(235, 293)(239, 295)(240, 298)(241, 300)(244, 303)(246, 304)(248, 290)(249, 308)(250, 294)(253, 310)(254, 314)(256, 317)(257, 318)(258, 315)(259, 319)(261, 321)(262, 323)(263, 324)(265, 327)(267, 328)(268, 330)(269, 331)(272, 334)(273, 336)(277, 337)(280, 341)(281, 345)(283, 348)(286, 342)(287, 352)(288, 346)(291, 355)(292, 357)(296, 361)(297, 362)(299, 365)(301, 366)(302, 368)(305, 369)(306, 372)(307, 373)(309, 364)(311, 370)(312, 378)(313, 379)(316, 382)(320, 329)(322, 388)(325, 391)(326, 393)(332, 397)(333, 401)(335, 404)(338, 398)(339, 408)(340, 402)(343, 411)(344, 412)(347, 415)(349, 416)(350, 418)(351, 419)(353, 422)(354, 423)(356, 426)(358, 427)(359, 429)(360, 430)(363, 433)(367, 435)(371, 441)(374, 428)(375, 445)(376, 447)(377, 448)(380, 451)(381, 453)(383, 454)(384, 450)(385, 387)(386, 458)(389, 460)(390, 464)(392, 467)(394, 461)(395, 470)(396, 465)(399, 473)(400, 474)(403, 477)(405, 478)(406, 480)(407, 481)(409, 484)(410, 485)(413, 488)(414, 490)(417, 491)(420, 489)(421, 497)(424, 500)(425, 502)(431, 506)(432, 510)(434, 513)(436, 507)(437, 516)(438, 511)(439, 517)(440, 518)(442, 487)(443, 492)(444, 522)(446, 524)(449, 527)(452, 519)(455, 533)(456, 534)(457, 535)(459, 537)(462, 540)(463, 541)(466, 544)(468, 545)(469, 547)(471, 550)(472, 551)(475, 554)(476, 556)(479, 557)(482, 555)(483, 563)(486, 566)(493, 573)(494, 553)(495, 558)(496, 576)(498, 546)(499, 578)(501, 538)(503, 562)(504, 581)(505, 560)(508, 574)(509, 584)(512, 559)(514, 543)(515, 586)(520, 588)(521, 589)(523, 587)(525, 591)(526, 594)(528, 571)(529, 592)(530, 552)(531, 590)(532, 567)(536, 570)(539, 599)(542, 600)(548, 601)(549, 605)(561, 602)(564, 597)(565, 612)(568, 604)(569, 614)(572, 615)(575, 616)(577, 610)(579, 598)(580, 608)(582, 609)(583, 618)(585, 619)(593, 606)(595, 607)(596, 603)(611, 622)(613, 621)(617, 624)(620, 623)
	local type(s) :: { ( 3^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 52 e = 312 f = 208
	degree seq :: [ 12^52 ]

E27.2358 :: Family: { 2Pex } :: Oriented family(ies): { E1a }
Signature :: (0; {2, 3, 12})
Quotient :: halfedge
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X2^2, X1^3, (X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1)^2, (X1^-1 * X2)^12, X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 67, 68)(48, 69, 70)(49, 71, 72)(50, 73, 74)(59, 83, 84)(60, 85, 86)(61, 87, 88)(62, 89, 90)(63, 91, 92)(64, 93, 94)(65, 95, 96)(66, 97, 98)(75, 107, 108)(76, 109, 110)(77, 111, 112)(78, 113, 114)(79, 115, 116)(80, 117, 118)(81, 119, 120)(82, 121, 122)(99, 139, 140)(100, 141, 142)(101, 143, 144)(102, 145, 146)(103, 147, 148)(104, 149, 150)(105, 151, 152)(106, 153, 154)(123, 171, 170)(124, 172, 173)(125, 174, 175)(126, 176, 177)(127, 178, 179)(128, 180, 181)(129, 182, 183)(130, 184, 156)(131, 185, 186)(132, 187, 188)(133, 189, 190)(134, 191, 157)(135, 192, 193)(136, 194, 159)(137, 195, 163)(138, 196, 197)(155, 282, 208)(158, 296, 346)(160, 295, 527)(161, 232, 416)(162, 298, 198)(164, 226, 397)(165, 300, 552)(166, 302, 199)(167, 215, 361)(168, 301, 201)(169, 304, 204)(200, 340, 348)(202, 339, 461)(203, 239, 436)(205, 233, 418)(206, 278, 518)(207, 212, 351)(209, 344, 322)(210, 345, 337)(211, 347, 350)(213, 353, 356)(214, 357, 360)(216, 363, 366)(217, 367, 370)(218, 371, 317)(219, 373, 376)(220, 377, 379)(221, 380, 382)(222, 383, 386)(223, 387, 390)(224, 391, 393)(225, 394, 309)(227, 400, 402)(228, 403, 395)(229, 405, 408)(230, 409, 412)(231, 413, 415)(234, 421, 423)(235, 424, 374)(236, 426, 429)(237, 430, 316)(238, 433, 435)(240, 438, 312)(241, 425, 333)(242, 250, 265)(243, 442, 444)(244, 445, 384)(245, 329, 449)(246, 450, 453)(247, 454, 456)(248, 457, 335)(249, 446, 389)(251, 460, 419)(252, 462, 364)(253, 463, 466)(254, 467, 274)(255, 470, 472)(256, 473, 330)(257, 475, 477)(258, 478, 406)(259, 286, 482)(260, 483, 327)(261, 484, 487)(262, 488, 490)(263, 491, 494)(264, 404, 369)(266, 496, 324)(267, 497, 354)(268, 498, 501)(269, 469, 291)(270, 502, 503)(271, 504, 506)(272, 465, 507)(273, 508, 427)(275, 510, 511)(276, 512, 514)(277, 515, 517)(279, 479, 411)(280, 521, 524)(281, 381, 359)(283, 526, 398)(284, 528, 358)(285, 529, 531)(287, 486, 533)(288, 534, 307)(289, 500, 537)(290, 481, 447)(292, 539, 519)(293, 540, 542)(294, 543, 314)(297, 308, 432)(299, 548, 551)(303, 392, 365)(305, 555, 352)(306, 556, 559)(310, 550, 560)(311, 561, 563)(313, 428, 538)(315, 545, 464)(318, 567, 544)(319, 568, 570)(320, 571, 332)(321, 572, 574)(323, 576, 439)(325, 578, 368)(326, 579, 581)(328, 577, 422)(331, 452, 341)(334, 558, 586)(336, 448, 480)(338, 589, 458)(342, 591, 594)(343, 372, 355)(349, 587, 362)(375, 565, 414)(378, 399, 616)(385, 564, 434)(388, 420, 613)(396, 617, 455)(401, 440, 619)(407, 509, 471)(410, 441, 610)(417, 620, 489)(431, 459, 580)(437, 621, 516)(443, 493, 618)(451, 495, 609)(468, 520, 530)(474, 623, 573)(476, 523, 622)(485, 525, 604)(492, 554, 615)(499, 532, 590)(505, 569, 566)(513, 553, 562)(522, 575, 612)(535, 582, 557)(536, 593, 624)(541, 595, 601)(546, 608, 614)(547, 600, 605)(549, 588, 607)(583, 602, 599)(584, 592, 585)(596, 603, 611)(597, 606, 598)
	L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(139, 196)(140, 198)(141, 199)(142, 200)(143, 201)(144, 202)(145, 203)(146, 172)(147, 204)(148, 205)(149, 206)(150, 174)(151, 207)(152, 178)(153, 185)(154, 208)(171, 250)(173, 305)(175, 307)(176, 309)(177, 209)(179, 312)(180, 314)(181, 266)(182, 317)(183, 260)(184, 320)(186, 322)(187, 324)(188, 267)(189, 327)(190, 328)(191, 330)(192, 332)(193, 333)(194, 335)(195, 337)(197, 242)(210, 346)(211, 348)(212, 352)(213, 354)(214, 358)(215, 362)(216, 364)(217, 368)(218, 372)(219, 374)(220, 378)(221, 381)(222, 384)(223, 388)(224, 392)(225, 395)(226, 398)(227, 401)(228, 404)(229, 406)(230, 410)(231, 414)(232, 382)(233, 419)(234, 422)(235, 425)(236, 427)(237, 431)(238, 434)(239, 393)(240, 439)(241, 423)(243, 443)(244, 446)(245, 447)(246, 451)(247, 455)(248, 458)(249, 444)(251, 461)(252, 418)(253, 464)(254, 468)(255, 471)(256, 415)(257, 476)(258, 479)(259, 480)(261, 485)(262, 489)(263, 492)(264, 402)(265, 282)(268, 499)(269, 315)(270, 313)(271, 435)(272, 310)(273, 308)(274, 509)(275, 416)(276, 513)(277, 516)(278, 519)(279, 477)(280, 522)(281, 379)(283, 527)(284, 397)(285, 530)(286, 532)(287, 336)(288, 456)(289, 536)(290, 331)(291, 538)(292, 436)(293, 541)(294, 544)(295, 490)(296, 376)(297, 507)(298, 349)(299, 549)(300, 511)(301, 494)(302, 506)(303, 390)(304, 350)(306, 557)(311, 472)(316, 564)(318, 394)(319, 569)(321, 573)(323, 534)(325, 438)(326, 580)(329, 535)(334, 585)(338, 473)(339, 517)(340, 386)(341, 537)(342, 592)(343, 370)(344, 355)(345, 359)(347, 365)(351, 369)(353, 375)(356, 571)(357, 385)(360, 587)(361, 389)(363, 396)(366, 555)(367, 407)(371, 411)(373, 417)(377, 428)(380, 432)(383, 437)(387, 448)(391, 452)(399, 457)(400, 465)(403, 469)(405, 474)(408, 497)(409, 481)(412, 565)(413, 486)(420, 491)(421, 500)(424, 482)(426, 505)(429, 528)(430, 478)(433, 470)(440, 518)(441, 521)(442, 475)(445, 467)(449, 462)(450, 508)(453, 617)(454, 502)(459, 548)(460, 558)(463, 562)(466, 578)(483, 524)(484, 545)(487, 620)(488, 550)(493, 552)(495, 591)(496, 563)(498, 601)(501, 616)(503, 600)(504, 554)(510, 551)(512, 590)(514, 621)(515, 593)(520, 540)(523, 543)(525, 602)(526, 547)(529, 604)(531, 613)(533, 586)(539, 594)(542, 567)(546, 566)(553, 596)(556, 607)(559, 619)(560, 606)(561, 575)(568, 582)(570, 623)(572, 584)(574, 577)(576, 597)(579, 609)(581, 610)(583, 624)(588, 605)(589, 599)(595, 598)(603, 615)(608, 612)(611, 622)(614, 618)
	local type(s) :: { ( 12^3 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 208 e = 312 f = 52
	degree seq :: [ 3^208 ]

E27.2359 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X1^2, X2^3, (X2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1)^2, (X2^-1 * X1)^12, X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 ]
Map:: polytopal
	R = (1, 2)(3, 7)(4, 8)(5, 9)(6, 10)(11, 19)(12, 20)(13, 21)(14, 22)(15, 23)(16, 24)(17, 25)(18, 26)(27, 43)(28, 44)(29, 45)(30, 46)(31, 47)(32, 48)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(59, 91)(60, 92)(61, 93)(62, 94)(63, 95)(64, 96)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(123, 187)(124, 170)(125, 178)(126, 188)(127, 182)(128, 189)(129, 190)(130, 191)(131, 184)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 156)(139, 185)(140, 198)(141, 199)(142, 200)(143, 201)(144, 202)(145, 203)(146, 157)(147, 204)(148, 205)(149, 206)(150, 159)(151, 207)(152, 163)(153, 171)(154, 208)(155, 315)(158, 318)(160, 320)(161, 322)(162, 292)(164, 326)(165, 328)(166, 234)(167, 330)(168, 331)(169, 333)(172, 337)(173, 338)(174, 339)(175, 341)(176, 342)(177, 344)(179, 347)(180, 348)(181, 350)(183, 352)(186, 355)(209, 382)(210, 384)(211, 386)(212, 388)(213, 390)(214, 392)(215, 394)(216, 396)(217, 398)(218, 400)(219, 402)(220, 405)(221, 407)(222, 409)(223, 411)(224, 413)(225, 414)(226, 416)(227, 418)(228, 421)(229, 423)(230, 426)(231, 428)(232, 431)(233, 433)(235, 436)(236, 438)(237, 439)(238, 441)(239, 442)(240, 443)(241, 446)(242, 448)(243, 362)(244, 452)(245, 453)(246, 454)(247, 378)(248, 458)(249, 460)(250, 461)(251, 463)(252, 465)(253, 455)(254, 468)(255, 469)(256, 471)(257, 473)(258, 475)(259, 477)(260, 478)(261, 480)(262, 482)(263, 444)(264, 485)(265, 486)(266, 488)(267, 490)(268, 493)(269, 376)(270, 497)(271, 498)(272, 499)(273, 287)(274, 502)(275, 285)(276, 505)(277, 506)(278, 507)(279, 364)(280, 510)(281, 512)(282, 514)(283, 515)(284, 495)(286, 518)(288, 374)(289, 520)(290, 521)(291, 425)(293, 467)(294, 526)(295, 321)(296, 319)(297, 529)(298, 531)(299, 532)(300, 415)(301, 535)(302, 349)(303, 343)(304, 537)(305, 430)(306, 345)(307, 334)(308, 340)(309, 543)(310, 332)(311, 546)(312, 547)(313, 548)(314, 550)(316, 484)(317, 556)(323, 540)(324, 561)(325, 562)(327, 410)(329, 565)(335, 568)(336, 420)(346, 575)(351, 577)(353, 578)(354, 579)(356, 545)(357, 553)(358, 585)(359, 587)(360, 379)(361, 504)(363, 522)(365, 523)(366, 589)(367, 391)(368, 591)(369, 404)(370, 558)(371, 592)(372, 583)(373, 595)(375, 450)(377, 598)(380, 572)(381, 593)(383, 600)(385, 601)(387, 573)(389, 541)(393, 604)(395, 566)(397, 590)(399, 479)(401, 528)(403, 462)(406, 559)(408, 602)(412, 560)(417, 530)(419, 470)(422, 574)(424, 434)(427, 610)(429, 487)(432, 542)(435, 509)(437, 611)(440, 476)(445, 527)(447, 481)(449, 619)(451, 459)(456, 557)(457, 464)(466, 496)(472, 501)(474, 617)(483, 513)(489, 517)(491, 613)(492, 623)(494, 622)(500, 599)(503, 576)(508, 524)(511, 621)(516, 614)(519, 544)(525, 594)(533, 569)(534, 584)(536, 567)(538, 615)(539, 563)(549, 597)(551, 608)(552, 570)(554, 609)(555, 603)(564, 624)(571, 581)(580, 620)(582, 606)(586, 618)(588, 607)(596, 612)(605, 616)(625, 627, 628)(626, 629, 630)(631, 635, 636)(632, 637, 638)(633, 639, 640)(634, 641, 642)(643, 651, 652)(644, 653, 654)(645, 655, 656)(646, 657, 658)(647, 659, 660)(648, 661, 662)(649, 663, 664)(650, 665, 666)(667, 683, 684)(668, 685, 686)(669, 687, 688)(670, 689, 690)(671, 691, 692)(672, 693, 694)(673, 695, 696)(674, 697, 698)(675, 699, 700)(676, 701, 702)(677, 703, 704)(678, 705, 706)(679, 707, 708)(680, 709, 710)(681, 711, 712)(682, 713, 714)(715, 747, 748)(716, 749, 750)(717, 751, 752)(718, 753, 754)(719, 755, 756)(720, 757, 758)(721, 759, 760)(722, 761, 762)(723, 763, 764)(724, 765, 766)(725, 767, 768)(726, 769, 770)(727, 771, 772)(728, 773, 774)(729, 775, 776)(730, 777, 778)(731, 779, 780)(732, 781, 782)(733, 783, 784)(734, 785, 786)(735, 787, 788)(736, 789, 790)(737, 791, 792)(738, 793, 794)(739, 795, 796)(740, 797, 798)(741, 799, 800)(742, 801, 802)(743, 803, 804)(744, 805, 806)(745, 807, 808)(746, 809, 810)(811, 981, 832)(812, 983, 1180)(813, 984, 1087)(814, 917, 1149)(815, 987, 822)(816, 840, 1021)(817, 835, 1011)(818, 989, 823)(819, 882, 1100)(820, 991, 825)(821, 923, 828)(824, 996, 1217)(826, 998, 1095)(827, 929, 1164)(829, 846, 1034)(830, 833, 1007)(831, 918, 1151)(834, 1009, 974)(836, 1013, 952)(837, 953, 1015)(838, 1017, 950)(839, 925, 1019)(841, 1023, 1003)(842, 1025, 912)(843, 1027, 1028)(844, 1030, 900)(845, 935, 1032)(847, 888, 1036)(848, 975, 990)(849, 1039, 972)(850, 878, 1041)(851, 1043, 1044)(852, 1046, 868)(853, 1048, 1049)(854, 1051, 894)(855, 1053, 1054)(856, 1056, 862)(857, 1058, 988)(858, 1059, 962)(859, 1061, 906)(860, 997, 1004)(861, 956, 1064)(863, 907, 913)(864, 1068, 1069)(865, 873, 1071)(866, 1073, 1074)(867, 926, 1075)(869, 895, 901)(870, 1079, 1080)(871, 883, 1081)(872, 1083, 954)(874, 1086, 1002)(875, 1088, 1020)(876, 948, 970)(877, 1090, 1091)(879, 1094, 911)(880, 1096, 1033)(881, 1098, 995)(884, 1103, 1070)(885, 1105, 1016)(886, 922, 933)(887, 1107, 1108)(889, 1111, 899)(890, 1113, 1038)(891, 1115, 1116)(892, 1118, 1119)(893, 936, 1120)(896, 1052, 1124)(897, 919, 1125)(898, 1127, 1128)(902, 1082, 1132)(903, 930, 1133)(904, 1135, 1123)(905, 977, 1137)(908, 1042, 1140)(909, 943, 1141)(910, 1143, 994)(914, 1099, 1146)(915, 964, 1147)(916, 1148, 961)(920, 1152, 1040)(921, 1154, 1008)(924, 1157, 1158)(927, 1160, 1063)(928, 1162, 1163)(931, 1165, 1065)(932, 1166, 1014)(934, 1168, 1169)(937, 1173, 1067)(938, 1175, 1176)(939, 1177, 979)(940, 1179, 946)(941, 1181, 976)(942, 992, 1150)(944, 993, 1104)(945, 1183, 1035)(947, 1184, 1006)(949, 971, 957)(951, 1187, 1188)(955, 1190, 965)(958, 1191, 986)(959, 1001, 1193)(960, 1153, 968)(963, 1194, 1195)(966, 1129, 1112)(967, 1197, 1076)(969, 1198, 1018)(973, 1200, 1174)(978, 1204, 1078)(980, 1206, 1207)(982, 1210, 1131)(985, 1047, 1212)(999, 1026, 1220)(1000, 1102, 1221)(1005, 1223, 1156)(1010, 1218, 1226)(1012, 1227, 1213)(1022, 1229, 1196)(1024, 1230, 1144)(1029, 1232, 1130)(1031, 1101, 1234)(1037, 1084, 1235)(1045, 1237, 1077)(1050, 1239, 1122)(1055, 1241, 1066)(1057, 1242, 1182)(1060, 1222, 1139)(1062, 1092, 1185)(1072, 1109, 1155)(1085, 1244, 1136)(1089, 1142, 1201)(1093, 1245, 1192)(1097, 1202, 1219)(1106, 1126, 1170)(1110, 1246, 1161)(1114, 1171, 1243)(1117, 1159, 1167)(1121, 1172, 1224)(1134, 1189, 1199)(1138, 1203, 1225)(1145, 1178, 1231)(1186, 1205, 1238)(1208, 1240, 1211)(1209, 1228, 1216)(1214, 1247, 1233)(1215, 1248, 1236)
	L = (1, 625)(2, 626)(3, 627)(4, 628)(5, 629)(6, 630)(7, 631)(8, 632)(9, 633)(10, 634)(11, 635)(12, 636)(13, 637)(14, 638)(15, 639)(16, 640)(17, 641)(18, 642)(19, 643)(20, 644)(21, 645)(22, 646)(23, 647)(24, 648)(25, 649)(26, 650)(27, 651)(28, 652)(29, 653)(30, 654)(31, 655)(32, 656)(33, 657)(34, 658)(35, 659)(36, 660)(37, 661)(38, 662)(39, 663)(40, 664)(41, 665)(42, 666)(43, 667)(44, 668)(45, 669)(46, 670)(47, 671)(48, 672)(49, 673)(50, 674)(51, 675)(52, 676)(53, 677)(54, 678)(55, 679)(56, 680)(57, 681)(58, 682)(59, 683)(60, 684)(61, 685)(62, 686)(63, 687)(64, 688)(65, 689)(66, 690)(67, 691)(68, 692)(69, 693)(70, 694)(71, 695)(72, 696)(73, 697)(74, 698)(75, 699)(76, 700)(77, 701)(78, 702)(79, 703)(80, 704)(81, 705)(82, 706)(83, 707)(84, 708)(85, 709)(86, 710)(87, 711)(88, 712)(89, 713)(90, 714)(91, 715)(92, 716)(93, 717)(94, 718)(95, 719)(96, 720)(97, 721)(98, 722)(99, 723)(100, 724)(101, 725)(102, 726)(103, 727)(104, 728)(105, 729)(106, 730)(107, 731)(108, 732)(109, 733)(110, 734)(111, 735)(112, 736)(113, 737)(114, 738)(115, 739)(116, 740)(117, 741)(118, 742)(119, 743)(120, 744)(121, 745)(122, 746)(123, 747)(124, 748)(125, 749)(126, 750)(127, 751)(128, 752)(129, 753)(130, 754)(131, 755)(132, 756)(133, 757)(134, 758)(135, 759)(136, 760)(137, 761)(138, 762)(139, 763)(140, 764)(141, 765)(142, 766)(143, 767)(144, 768)(145, 769)(146, 770)(147, 771)(148, 772)(149, 773)(150, 774)(151, 775)(152, 776)(153, 777)(154, 778)(155, 779)(156, 780)(157, 781)(158, 782)(159, 783)(160, 784)(161, 785)(162, 786)(163, 787)(164, 788)(165, 789)(166, 790)(167, 791)(168, 792)(169, 793)(170, 794)(171, 795)(172, 796)(173, 797)(174, 798)(175, 799)(176, 800)(177, 801)(178, 802)(179, 803)(180, 804)(181, 805)(182, 806)(183, 807)(184, 808)(185, 809)(186, 810)(187, 811)(188, 812)(189, 813)(190, 814)(191, 815)(192, 816)(193, 817)(194, 818)(195, 819)(196, 820)(197, 821)(198, 822)(199, 823)(200, 824)(201, 825)(202, 826)(203, 827)(204, 828)(205, 829)(206, 830)(207, 831)(208, 832)(209, 833)(210, 834)(211, 835)(212, 836)(213, 837)(214, 838)(215, 839)(216, 840)(217, 841)(218, 842)(219, 843)(220, 844)(221, 845)(222, 846)(223, 847)(224, 848)(225, 849)(226, 850)(227, 851)(228, 852)(229, 853)(230, 854)(231, 855)(232, 856)(233, 857)(234, 858)(235, 859)(236, 860)(237, 861)(238, 862)(239, 863)(240, 864)(241, 865)(242, 866)(243, 867)(244, 868)(245, 869)(246, 870)(247, 871)(248, 872)(249, 873)(250, 874)(251, 875)(252, 876)(253, 877)(254, 878)(255, 879)(256, 880)(257, 881)(258, 882)(259, 883)(260, 884)(261, 885)(262, 886)(263, 887)(264, 888)(265, 889)(266, 890)(267, 891)(268, 892)(269, 893)(270, 894)(271, 895)(272, 896)(273, 897)(274, 898)(275, 899)(276, 900)(277, 901)(278, 902)(279, 903)(280, 904)(281, 905)(282, 906)(283, 907)(284, 908)(285, 909)(286, 910)(287, 911)(288, 912)(289, 913)(290, 914)(291, 915)(292, 916)(293, 917)(294, 918)(295, 919)(296, 920)(297, 921)(298, 922)(299, 923)(300, 924)(301, 925)(302, 926)(303, 927)(304, 928)(305, 929)(306, 930)(307, 931)(308, 932)(309, 933)(310, 934)(311, 935)(312, 936)(313, 937)(314, 938)(315, 939)(316, 940)(317, 941)(318, 942)(319, 943)(320, 944)(321, 945)(322, 946)(323, 947)(324, 948)(325, 949)(326, 950)(327, 951)(328, 952)(329, 953)(330, 954)(331, 955)(332, 956)(333, 957)(334, 958)(335, 959)(336, 960)(337, 961)(338, 962)(339, 963)(340, 964)(341, 965)(342, 966)(343, 967)(344, 968)(345, 969)(346, 970)(347, 971)(348, 972)(349, 973)(350, 974)(351, 975)(352, 976)(353, 977)(354, 978)(355, 979)(356, 980)(357, 981)(358, 982)(359, 983)(360, 984)(361, 985)(362, 986)(363, 987)(364, 988)(365, 989)(366, 990)(367, 991)(368, 992)(369, 993)(370, 994)(371, 995)(372, 996)(373, 997)(374, 998)(375, 999)(376, 1000)(377, 1001)(378, 1002)(379, 1003)(380, 1004)(381, 1005)(382, 1006)(383, 1007)(384, 1008)(385, 1009)(386, 1010)(387, 1011)(388, 1012)(389, 1013)(390, 1014)(391, 1015)(392, 1016)(393, 1017)(394, 1018)(395, 1019)(396, 1020)(397, 1021)(398, 1022)(399, 1023)(400, 1024)(401, 1025)(402, 1026)(403, 1027)(404, 1028)(405, 1029)(406, 1030)(407, 1031)(408, 1032)(409, 1033)(410, 1034)(411, 1035)(412, 1036)(413, 1037)(414, 1038)(415, 1039)(416, 1040)(417, 1041)(418, 1042)(419, 1043)(420, 1044)(421, 1045)(422, 1046)(423, 1047)(424, 1048)(425, 1049)(426, 1050)(427, 1051)(428, 1052)(429, 1053)(430, 1054)(431, 1055)(432, 1056)(433, 1057)(434, 1058)(435, 1059)(436, 1060)(437, 1061)(438, 1062)(439, 1063)(440, 1064)(441, 1065)(442, 1066)(443, 1067)(444, 1068)(445, 1069)(446, 1070)(447, 1071)(448, 1072)(449, 1073)(450, 1074)(451, 1075)(452, 1076)(453, 1077)(454, 1078)(455, 1079)(456, 1080)(457, 1081)(458, 1082)(459, 1083)(460, 1084)(461, 1085)(462, 1086)(463, 1087)(464, 1088)(465, 1089)(466, 1090)(467, 1091)(468, 1092)(469, 1093)(470, 1094)(471, 1095)(472, 1096)(473, 1097)(474, 1098)(475, 1099)(476, 1100)(477, 1101)(478, 1102)(479, 1103)(480, 1104)(481, 1105)(482, 1106)(483, 1107)(484, 1108)(485, 1109)(486, 1110)(487, 1111)(488, 1112)(489, 1113)(490, 1114)(491, 1115)(492, 1116)(493, 1117)(494, 1118)(495, 1119)(496, 1120)(497, 1121)(498, 1122)(499, 1123)(500, 1124)(501, 1125)(502, 1126)(503, 1127)(504, 1128)(505, 1129)(506, 1130)(507, 1131)(508, 1132)(509, 1133)(510, 1134)(511, 1135)(512, 1136)(513, 1137)(514, 1138)(515, 1139)(516, 1140)(517, 1141)(518, 1142)(519, 1143)(520, 1144)(521, 1145)(522, 1146)(523, 1147)(524, 1148)(525, 1149)(526, 1150)(527, 1151)(528, 1152)(529, 1153)(530, 1154)(531, 1155)(532, 1156)(533, 1157)(534, 1158)(535, 1159)(536, 1160)(537, 1161)(538, 1162)(539, 1163)(540, 1164)(541, 1165)(542, 1166)(543, 1167)(544, 1168)(545, 1169)(546, 1170)(547, 1171)(548, 1172)(549, 1173)(550, 1174)(551, 1175)(552, 1176)(553, 1177)(554, 1178)(555, 1179)(556, 1180)(557, 1181)(558, 1182)(559, 1183)(560, 1184)(561, 1185)(562, 1186)(563, 1187)(564, 1188)(565, 1189)(566, 1190)(567, 1191)(568, 1192)(569, 1193)(570, 1194)(571, 1195)(572, 1196)(573, 1197)(574, 1198)(575, 1199)(576, 1200)(577, 1201)(578, 1202)(579, 1203)(580, 1204)(581, 1205)(582, 1206)(583, 1207)(584, 1208)(585, 1209)(586, 1210)(587, 1211)(588, 1212)(589, 1213)(590, 1214)(591, 1215)(592, 1216)(593, 1217)(594, 1218)(595, 1219)(596, 1220)(597, 1221)(598, 1222)(599, 1223)(600, 1224)(601, 1225)(602, 1226)(603, 1227)(604, 1228)(605, 1229)(606, 1230)(607, 1231)(608, 1232)(609, 1233)(610, 1234)(611, 1235)(612, 1236)(613, 1237)(614, 1238)(615, 1239)(616, 1240)(617, 1241)(618, 1242)(619, 1243)(620, 1244)(621, 1245)(622, 1246)(623, 1247)(624, 1248)
	local type(s) :: { ( 24, 24 ), ( 24^3 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 520 e = 624 f = 52
	degree seq :: [ 2^312, 3^208 ]

E27.2360 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X1^3, (X2 * X1)^2, (X2^2 * X1^-1 * X2^3)^2, X2^12, (X2^2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1)^2, X2 * X1^-1 * X2^-3 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^2 * X1 * X2^-2 * X1 * X2^-2 * X1^-1 * X2 * X1, X2^2 * X1^-1 * X2^2 * X1^-1 * X2^-3 * X1 * X2^-2 * X1 * X2^-2 * X1^-1 * X2 * X1^-1 * X2^3 * X1 * X2^-1 * X1, X1 * X2^-2 * X1^-1 * X2^2 * X1 * X2^-1 * X1 * X2^-3 * X1^-1 * X2 * X1^-1 * X2^2 * X1^-1 * X2^2 * X1^-1 * X2 * X1^-1 * X2^-2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 12, 6)(7, 15, 11)(9, 18, 20)(13, 25, 23)(14, 24, 28)(16, 31, 29)(17, 33, 21)(19, 36, 38)(22, 30, 42)(26, 47, 45)(27, 49, 51)(32, 57, 55)(34, 61, 59)(35, 63, 39)(37, 66, 68)(40, 60, 72)(41, 73, 75)(43, 46, 78)(44, 79, 52)(48, 85, 83)(50, 88, 90)(53, 56, 94)(54, 95, 76)(58, 101, 99)(62, 107, 105)(64, 111, 109)(65, 113, 69)(67, 116, 102)(70, 110, 121)(71, 122, 124)(74, 127, 129)(77, 132, 134)(80, 138, 136)(81, 84, 140)(82, 141, 135)(86, 128, 143)(87, 144, 91)(89, 147, 108)(92, 137, 152)(93, 153, 155)(96, 159, 157)(97, 100, 161)(98, 162, 156)(103, 106, 165)(104, 166, 125)(112, 175, 173)(114, 178, 176)(115, 180, 118)(117, 148, 170)(119, 177, 182)(120, 183, 184)(123, 187, 142)(126, 190, 130)(131, 158, 192)(133, 194, 163)(139, 200, 201)(145, 205, 203)(146, 207, 149)(150, 204, 209)(151, 210, 211)(154, 214, 168)(160, 220, 221)(164, 223, 225)(167, 229, 227)(169, 231, 226)(171, 174, 233)(172, 234, 185)(179, 242, 240)(181, 244, 243)(186, 249, 188)(189, 228, 251)(191, 253, 252)(193, 255, 195)(196, 202, 260)(197, 199, 262)(198, 263, 212)(206, 257, 269)(208, 272, 271)(213, 277, 215)(216, 222, 282)(217, 219, 284)(218, 285, 254)(224, 290, 236)(230, 279, 296)(232, 298, 300)(235, 304, 302)(237, 306, 301)(238, 241, 308)(239, 309, 245)(246, 316, 247)(248, 303, 318)(250, 320, 319)(256, 327, 325)(258, 326, 329)(259, 330, 331)(261, 333, 334)(264, 336, 265)(266, 338, 332)(267, 270, 340)(268, 341, 273)(274, 348, 275)(276, 335, 350)(278, 353, 351)(280, 352, 355)(281, 356, 357)(283, 359, 360)(286, 362, 287)(288, 364, 358)(289, 365, 291)(292, 297, 370)(293, 295, 372)(294, 373, 321)(299, 377, 311)(305, 367, 383)(307, 385, 386)(310, 390, 388)(312, 392, 387)(313, 314, 393)(315, 389, 395)(317, 397, 396)(322, 323, 402)(324, 361, 404)(328, 408, 343)(337, 416, 417)(339, 419, 420)(342, 424, 422)(344, 426, 421)(345, 346, 427)(347, 423, 429)(349, 431, 430)(354, 436, 374)(363, 444, 445)(366, 449, 447)(368, 448, 451)(369, 452, 453)(371, 455, 456)(375, 459, 454)(376, 460, 378)(379, 384, 465)(380, 382, 467)(381, 468, 398)(391, 462, 477)(394, 480, 479)(399, 400, 485)(401, 457, 487)(403, 489, 488)(405, 407, 492)(406, 493, 409)(410, 498, 411)(412, 418, 500)(413, 501, 414)(415, 503, 432)(425, 496, 513)(428, 516, 515)(433, 435, 522)(434, 523, 437)(438, 528, 439)(440, 446, 530)(441, 531, 442)(443, 533, 490)(450, 540, 469)(458, 526, 548)(461, 552, 550)(463, 551, 554)(464, 520, 555)(466, 556, 557)(470, 518, 519)(471, 560, 472)(473, 478, 525)(474, 476, 536)(475, 564, 481)(482, 483, 529)(484, 558, 524)(486, 509, 514)(491, 572, 573)(494, 571, 574)(495, 569, 570)(497, 575, 577)(499, 544, 549)(502, 578, 579)(504, 580, 505)(506, 543, 542)(507, 582, 508)(510, 512, 547)(511, 586, 517)(521, 591, 592)(527, 593, 595)(532, 596, 597)(534, 598, 535)(537, 539, 601)(538, 602, 541)(545, 607, 546)(553, 612, 565)(559, 605, 583)(561, 588, 589)(562, 599, 616)(563, 590, 617)(566, 567, 604)(568, 618, 603)(576, 610, 587)(581, 622, 600)(584, 606, 623)(585, 608, 624)(594, 619, 609)(611, 621, 613)(614, 620, 615)(625, 627, 633, 643, 661, 691, 741, 710, 672, 650, 637, 629)(626, 630, 638, 651, 674, 713, 772, 726, 682, 656, 640, 631)(628, 635, 646, 665, 698, 752, 794, 732, 686, 658, 641, 632)(634, 645, 664, 695, 747, 709, 767, 753, 736, 688, 659, 642)(636, 647, 667, 701, 757, 725, 740, 692, 742, 704, 668, 648)(639, 653, 677, 717, 778, 731, 771, 714, 773, 720, 678, 654)(644, 663, 694, 744, 708, 671, 707, 766, 803, 738, 689, 660)(649, 669, 705, 763, 805, 739, 690, 662, 693, 743, 706, 670)(652, 676, 716, 775, 724, 681, 723, 787, 830, 769, 711, 673)(655, 679, 721, 784, 832, 770, 712, 675, 715, 774, 722, 680)(657, 683, 727, 788, 848, 799, 751, 699, 754, 791, 728, 684)(666, 700, 755, 793, 730, 685, 729, 792, 854, 815, 750, 697)(687, 733, 795, 856, 923, 866, 811, 748, 812, 859, 796, 734)(696, 749, 813, 861, 798, 735, 797, 860, 929, 874, 810, 746)(702, 759, 820, 883, 823, 762, 804, 867, 937, 880, 817, 756)(703, 760, 821, 885, 952, 881, 818, 758, 819, 882, 822, 761)(718, 780, 840, 905, 843, 783, 831, 895, 969, 902, 837, 777)(719, 781, 841, 907, 978, 903, 838, 779, 839, 904, 842, 782)(737, 800, 862, 931, 888, 824, 764, 808, 871, 934, 863, 801)(745, 809, 872, 936, 865, 802, 864, 935, 1015, 941, 870, 807)(765, 806, 869, 939, 1018, 938, 868, 825, 889, 961, 890, 826)(768, 827, 891, 963, 910, 844, 785, 835, 899, 966, 892, 828)(776, 836, 900, 968, 894, 829, 893, 967, 1049, 973, 898, 834)(786, 833, 897, 971, 1052, 970, 896, 845, 911, 987, 912, 846)(789, 850, 916, 993, 919, 853, 814, 876, 946, 990, 913, 847)(790, 851, 917, 995, 1074, 991, 914, 849, 915, 992, 918, 852)(816, 878, 948, 1027, 947, 877, 920, 998, 1082, 999, 921, 855)(857, 925, 1003, 1088, 1006, 928, 873, 943, 1023, 1085, 1000, 922)(858, 926, 1004, 1090, 1177, 1086, 1001, 924, 1002, 1087, 1005, 927)(875, 945, 1025, 1110, 1024, 944, 1007, 1093, 1183, 1094, 1008, 930)(879, 949, 1029, 1115, 1037, 957, 886, 955, 1035, 1118, 1030, 950)(884, 956, 1036, 1119, 1031, 951, 1017, 1103, 1190, 1123, 1034, 954)(887, 953, 1033, 1121, 1200, 1120, 1032, 958, 1038, 1126, 1039, 959)(901, 975, 1057, 1145, 1065, 983, 908, 981, 1063, 1148, 1058, 976)(906, 982, 1064, 1149, 1059, 977, 1051, 1139, 1212, 1153, 1062, 980)(909, 979, 1061, 1151, 1218, 1150, 1060, 984, 1066, 1156, 1067, 985)(932, 1011, 1097, 1154, 1100, 1014, 940, 1020, 1106, 1185, 1095, 1009)(933, 1012, 1098, 1187, 1128, 1040, 960, 1010, 1096, 1186, 1099, 1013)(942, 1022, 1108, 1152, 1107, 1021, 1101, 1189, 1215, 1146, 1102, 1016)(962, 1041, 1129, 1205, 1225, 1191, 1104, 1019, 1105, 1192, 1130, 1042)(964, 1045, 1133, 1111, 1136, 1048, 972, 1054, 1142, 1207, 1131, 1043)(965, 1046, 1134, 1209, 1158, 1068, 986, 1044, 1132, 1208, 1135, 1047)(974, 1056, 1144, 1089, 1143, 1055, 1137, 1211, 1176, 1109, 1138, 1050)(988, 1069, 1159, 1223, 1184, 1213, 1140, 1053, 1141, 1214, 1160, 1070)(989, 1071, 1161, 1224, 1169, 1079, 996, 1077, 1167, 1227, 1162, 1072)(994, 1078, 1168, 1228, 1163, 1073, 1026, 1112, 1193, 1124, 1166, 1076)(997, 1075, 1165, 1230, 1206, 1229, 1164, 1080, 1170, 1232, 1171, 1081)(1028, 1114, 1195, 1122, 1173, 1083, 1172, 1233, 1196, 1116, 1194, 1113)(1084, 1174, 1234, 1201, 1238, 1180, 1091, 1179, 1127, 1203, 1235, 1175)(1092, 1178, 1237, 1220, 1155, 1216, 1236, 1181, 1239, 1217, 1147, 1182)(1117, 1198, 1157, 1221, 1245, 1202, 1125, 1197, 1243, 1219, 1244, 1199)(1188, 1240, 1222, 1248, 1231, 1246, 1204, 1241, 1210, 1247, 1226, 1242)
	L = (1, 625)(2, 626)(3, 627)(4, 628)(5, 629)(6, 630)(7, 631)(8, 632)(9, 633)(10, 634)(11, 635)(12, 636)(13, 637)(14, 638)(15, 639)(16, 640)(17, 641)(18, 642)(19, 643)(20, 644)(21, 645)(22, 646)(23, 647)(24, 648)(25, 649)(26, 650)(27, 651)(28, 652)(29, 653)(30, 654)(31, 655)(32, 656)(33, 657)(34, 658)(35, 659)(36, 660)(37, 661)(38, 662)(39, 663)(40, 664)(41, 665)(42, 666)(43, 667)(44, 668)(45, 669)(46, 670)(47, 671)(48, 672)(49, 673)(50, 674)(51, 675)(52, 676)(53, 677)(54, 678)(55, 679)(56, 680)(57, 681)(58, 682)(59, 683)(60, 684)(61, 685)(62, 686)(63, 687)(64, 688)(65, 689)(66, 690)(67, 691)(68, 692)(69, 693)(70, 694)(71, 695)(72, 696)(73, 697)(74, 698)(75, 699)(76, 700)(77, 701)(78, 702)(79, 703)(80, 704)(81, 705)(82, 706)(83, 707)(84, 708)(85, 709)(86, 710)(87, 711)(88, 712)(89, 713)(90, 714)(91, 715)(92, 716)(93, 717)(94, 718)(95, 719)(96, 720)(97, 721)(98, 722)(99, 723)(100, 724)(101, 725)(102, 726)(103, 727)(104, 728)(105, 729)(106, 730)(107, 731)(108, 732)(109, 733)(110, 734)(111, 735)(112, 736)(113, 737)(114, 738)(115, 739)(116, 740)(117, 741)(118, 742)(119, 743)(120, 744)(121, 745)(122, 746)(123, 747)(124, 748)(125, 749)(126, 750)(127, 751)(128, 752)(129, 753)(130, 754)(131, 755)(132, 756)(133, 757)(134, 758)(135, 759)(136, 760)(137, 761)(138, 762)(139, 763)(140, 764)(141, 765)(142, 766)(143, 767)(144, 768)(145, 769)(146, 770)(147, 771)(148, 772)(149, 773)(150, 774)(151, 775)(152, 776)(153, 777)(154, 778)(155, 779)(156, 780)(157, 781)(158, 782)(159, 783)(160, 784)(161, 785)(162, 786)(163, 787)(164, 788)(165, 789)(166, 790)(167, 791)(168, 792)(169, 793)(170, 794)(171, 795)(172, 796)(173, 797)(174, 798)(175, 799)(176, 800)(177, 801)(178, 802)(179, 803)(180, 804)(181, 805)(182, 806)(183, 807)(184, 808)(185, 809)(186, 810)(187, 811)(188, 812)(189, 813)(190, 814)(191, 815)(192, 816)(193, 817)(194, 818)(195, 819)(196, 820)(197, 821)(198, 822)(199, 823)(200, 824)(201, 825)(202, 826)(203, 827)(204, 828)(205, 829)(206, 830)(207, 831)(208, 832)(209, 833)(210, 834)(211, 835)(212, 836)(213, 837)(214, 838)(215, 839)(216, 840)(217, 841)(218, 842)(219, 843)(220, 844)(221, 845)(222, 846)(223, 847)(224, 848)(225, 849)(226, 850)(227, 851)(228, 852)(229, 853)(230, 854)(231, 855)(232, 856)(233, 857)(234, 858)(235, 859)(236, 860)(237, 861)(238, 862)(239, 863)(240, 864)(241, 865)(242, 866)(243, 867)(244, 868)(245, 869)(246, 870)(247, 871)(248, 872)(249, 873)(250, 874)(251, 875)(252, 876)(253, 877)(254, 878)(255, 879)(256, 880)(257, 881)(258, 882)(259, 883)(260, 884)(261, 885)(262, 886)(263, 887)(264, 888)(265, 889)(266, 890)(267, 891)(268, 892)(269, 893)(270, 894)(271, 895)(272, 896)(273, 897)(274, 898)(275, 899)(276, 900)(277, 901)(278, 902)(279, 903)(280, 904)(281, 905)(282, 906)(283, 907)(284, 908)(285, 909)(286, 910)(287, 911)(288, 912)(289, 913)(290, 914)(291, 915)(292, 916)(293, 917)(294, 918)(295, 919)(296, 920)(297, 921)(298, 922)(299, 923)(300, 924)(301, 925)(302, 926)(303, 927)(304, 928)(305, 929)(306, 930)(307, 931)(308, 932)(309, 933)(310, 934)(311, 935)(312, 936)(313, 937)(314, 938)(315, 939)(316, 940)(317, 941)(318, 942)(319, 943)(320, 944)(321, 945)(322, 946)(323, 947)(324, 948)(325, 949)(326, 950)(327, 951)(328, 952)(329, 953)(330, 954)(331, 955)(332, 956)(333, 957)(334, 958)(335, 959)(336, 960)(337, 961)(338, 962)(339, 963)(340, 964)(341, 965)(342, 966)(343, 967)(344, 968)(345, 969)(346, 970)(347, 971)(348, 972)(349, 973)(350, 974)(351, 975)(352, 976)(353, 977)(354, 978)(355, 979)(356, 980)(357, 981)(358, 982)(359, 983)(360, 984)(361, 985)(362, 986)(363, 987)(364, 988)(365, 989)(366, 990)(367, 991)(368, 992)(369, 993)(370, 994)(371, 995)(372, 996)(373, 997)(374, 998)(375, 999)(376, 1000)(377, 1001)(378, 1002)(379, 1003)(380, 1004)(381, 1005)(382, 1006)(383, 1007)(384, 1008)(385, 1009)(386, 1010)(387, 1011)(388, 1012)(389, 1013)(390, 1014)(391, 1015)(392, 1016)(393, 1017)(394, 1018)(395, 1019)(396, 1020)(397, 1021)(398, 1022)(399, 1023)(400, 1024)(401, 1025)(402, 1026)(403, 1027)(404, 1028)(405, 1029)(406, 1030)(407, 1031)(408, 1032)(409, 1033)(410, 1034)(411, 1035)(412, 1036)(413, 1037)(414, 1038)(415, 1039)(416, 1040)(417, 1041)(418, 1042)(419, 1043)(420, 1044)(421, 1045)(422, 1046)(423, 1047)(424, 1048)(425, 1049)(426, 1050)(427, 1051)(428, 1052)(429, 1053)(430, 1054)(431, 1055)(432, 1056)(433, 1057)(434, 1058)(435, 1059)(436, 1060)(437, 1061)(438, 1062)(439, 1063)(440, 1064)(441, 1065)(442, 1066)(443, 1067)(444, 1068)(445, 1069)(446, 1070)(447, 1071)(448, 1072)(449, 1073)(450, 1074)(451, 1075)(452, 1076)(453, 1077)(454, 1078)(455, 1079)(456, 1080)(457, 1081)(458, 1082)(459, 1083)(460, 1084)(461, 1085)(462, 1086)(463, 1087)(464, 1088)(465, 1089)(466, 1090)(467, 1091)(468, 1092)(469, 1093)(470, 1094)(471, 1095)(472, 1096)(473, 1097)(474, 1098)(475, 1099)(476, 1100)(477, 1101)(478, 1102)(479, 1103)(480, 1104)(481, 1105)(482, 1106)(483, 1107)(484, 1108)(485, 1109)(486, 1110)(487, 1111)(488, 1112)(489, 1113)(490, 1114)(491, 1115)(492, 1116)(493, 1117)(494, 1118)(495, 1119)(496, 1120)(497, 1121)(498, 1122)(499, 1123)(500, 1124)(501, 1125)(502, 1126)(503, 1127)(504, 1128)(505, 1129)(506, 1130)(507, 1131)(508, 1132)(509, 1133)(510, 1134)(511, 1135)(512, 1136)(513, 1137)(514, 1138)(515, 1139)(516, 1140)(517, 1141)(518, 1142)(519, 1143)(520, 1144)(521, 1145)(522, 1146)(523, 1147)(524, 1148)(525, 1149)(526, 1150)(527, 1151)(528, 1152)(529, 1153)(530, 1154)(531, 1155)(532, 1156)(533, 1157)(534, 1158)(535, 1159)(536, 1160)(537, 1161)(538, 1162)(539, 1163)(540, 1164)(541, 1165)(542, 1166)(543, 1167)(544, 1168)(545, 1169)(546, 1170)(547, 1171)(548, 1172)(549, 1173)(550, 1174)(551, 1175)(552, 1176)(553, 1177)(554, 1178)(555, 1179)(556, 1180)(557, 1181)(558, 1182)(559, 1183)(560, 1184)(561, 1185)(562, 1186)(563, 1187)(564, 1188)(565, 1189)(566, 1190)(567, 1191)(568, 1192)(569, 1193)(570, 1194)(571, 1195)(572, 1196)(573, 1197)(574, 1198)(575, 1199)(576, 1200)(577, 1201)(578, 1202)(579, 1203)(580, 1204)(581, 1205)(582, 1206)(583, 1207)(584, 1208)(585, 1209)(586, 1210)(587, 1211)(588, 1212)(589, 1213)(590, 1214)(591, 1215)(592, 1216)(593, 1217)(594, 1218)(595, 1219)(596, 1220)(597, 1221)(598, 1222)(599, 1223)(600, 1224)(601, 1225)(602, 1226)(603, 1227)(604, 1228)(605, 1229)(606, 1230)(607, 1231)(608, 1232)(609, 1233)(610, 1234)(611, 1235)(612, 1236)(613, 1237)(614, 1238)(615, 1239)(616, 1240)(617, 1241)(618, 1242)(619, 1243)(620, 1244)(621, 1245)(622, 1246)(623, 1247)(624, 1248)
	local type(s) :: { ( 4^3 ), ( 4^12 ) }
Outer automorphisms :: chiral
Dual of E27.2362
Transitivity :: ET+
Graph:: simple bipartite
	v = 260 e = 624 f = 312
	degree seq :: [ 3^208, 12^52 ]

E27.2361 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1^-1)^3, X1^12, (X1^-2 * X2 * X1^-4)^2, (X1^-4 * X2 * X1 * X2)^2, (X1^2 * X2 * X1^-2 * X2 * X1^3)^2, X2 * X1^-2 * X2 * X1 * X2 * X1^-2 * X2 * X1^3 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^3 * X2 * X1^2 * X2 * X1^-2 ]
Map:: polytopal
	R = (1, 2, 5, 11, 21, 37, 63, 62, 36, 20, 10, 4)(3, 7, 15, 27, 47, 79, 104, 91, 54, 31, 17, 8)(6, 13, 25, 43, 73, 119, 103, 128, 78, 46, 26, 14)(9, 18, 32, 55, 92, 106, 64, 105, 86, 51, 29, 16)(12, 23, 41, 69, 113, 101, 61, 102, 118, 72, 42, 24)(19, 34, 58, 97, 108, 66, 38, 65, 107, 96, 57, 33)(22, 39, 67, 109, 99, 59, 35, 60, 100, 112, 68, 40)(28, 49, 83, 132, 181, 142, 90, 143, 186, 135, 84, 50)(30, 52, 87, 138, 176, 127, 80, 129, 171, 123, 75, 44)(45, 76, 124, 172, 222, 166, 120, 167, 217, 162, 115, 70)(48, 81, 130, 177, 140, 88, 53, 89, 141, 180, 131, 82)(56, 94, 146, 195, 246, 188, 137, 154, 206, 198, 147, 95)(71, 116, 163, 218, 204, 152, 159, 213, 265, 209, 156, 110)(74, 121, 168, 223, 174, 125, 77, 126, 175, 226, 169, 122)(85, 136, 187, 244, 194, 145, 93, 144, 193, 240, 183, 133)(98, 150, 202, 259, 261, 205, 153, 111, 157, 210, 203, 151)(114, 160, 214, 269, 220, 164, 117, 165, 221, 272, 215, 161)(134, 184, 241, 299, 250, 192, 237, 295, 356, 291, 234, 178)(139, 190, 248, 307, 349, 284, 228, 179, 235, 292, 249, 191)(148, 199, 256, 316, 258, 201, 149, 200, 257, 312, 253, 196)(155, 207, 262, 322, 267, 211, 158, 212, 268, 325, 263, 208)(170, 227, 283, 347, 288, 232, 189, 247, 306, 343, 280, 224)(173, 230, 286, 351, 405, 336, 274, 225, 281, 344, 287, 231)(182, 238, 296, 360, 301, 242, 185, 243, 302, 363, 297, 239)(197, 254, 313, 371, 305, 245, 304, 370, 440, 375, 309, 251)(216, 273, 335, 403, 340, 278, 229, 285, 350, 399, 332, 270)(219, 276, 338, 407, 468, 393, 327, 271, 333, 400, 339, 277)(233, 289, 353, 421, 358, 293, 236, 294, 359, 424, 354, 290)(252, 310, 376, 446, 380, 314, 255, 315, 381, 449, 377, 311)(260, 320, 386, 455, 383, 317, 321, 387, 459, 456, 384, 318)(264, 326, 392, 466, 396, 330, 275, 337, 406, 462, 389, 323)(266, 328, 394, 469, 457, 385, 319, 324, 390, 463, 395, 329)(279, 341, 409, 483, 413, 345, 282, 346, 414, 486, 410, 342)(298, 364, 434, 512, 438, 368, 303, 369, 439, 508, 431, 361)(300, 366, 436, 515, 579, 502, 426, 362, 432, 509, 437, 367)(308, 374, 444, 493, 417, 348, 416, 492, 572, 520, 442, 372)(331, 397, 471, 549, 475, 401, 334, 402, 476, 552, 472, 398)(352, 420, 496, 559, 479, 404, 478, 558, 609, 574, 494, 418)(355, 425, 501, 540, 505, 429, 365, 435, 514, 544, 498, 422)(357, 427, 503, 580, 521, 443, 373, 423, 499, 577, 504, 428)(378, 450, 528, 573, 531, 453, 382, 454, 532, 588, 525, 447)(379, 451, 529, 595, 605, 587, 518, 448, 526, 593, 530, 452)(388, 460, 538, 598, 542, 464, 391, 465, 543, 516, 539, 461)(408, 482, 562, 497, 546, 467, 545, 602, 578, 500, 560, 480)(411, 487, 567, 533, 570, 490, 415, 491, 571, 534, 564, 484)(412, 488, 568, 613, 575, 495, 419, 485, 565, 611, 569, 489)(430, 506, 582, 616, 585, 510, 433, 511, 576, 614, 583, 507)(441, 519, 556, 477, 557, 513, 445, 523, 550, 473, 553, 517)(458, 470, 548, 604, 563, 597, 537, 535, 596, 612, 566, 536)(474, 554, 607, 624, 610, 561, 481, 551, 606, 623, 608, 555)(522, 581, 617, 592, 524, 591, 615, 589, 620, 594, 527, 590)(541, 600, 586, 618, 622, 603, 547, 599, 584, 619, 621, 601)(625, 627)(626, 630)(628, 633)(629, 636)(631, 640)(632, 637)(634, 643)(635, 646)(638, 647)(639, 652)(641, 654)(642, 657)(644, 659)(645, 662)(648, 663)(649, 668)(650, 669)(651, 672)(653, 673)(655, 677)(656, 680)(658, 683)(660, 685)(661, 688)(664, 689)(665, 694)(666, 695)(667, 698)(670, 701)(671, 704)(674, 705)(675, 709)(676, 712)(678, 714)(679, 717)(681, 718)(682, 722)(684, 725)(686, 727)(687, 728)(690, 729)(691, 734)(692, 735)(693, 738)(696, 741)(697, 744)(699, 745)(700, 749)(702, 751)(703, 752)(706, 753)(707, 757)(708, 758)(710, 761)(711, 763)(713, 766)(715, 730)(716, 767)(719, 768)(720, 772)(721, 773)(723, 774)(724, 776)(726, 743)(731, 777)(732, 778)(733, 779)(736, 782)(737, 783)(739, 784)(740, 788)(742, 790)(746, 791)(747, 794)(748, 797)(750, 800)(754, 802)(755, 803)(756, 806)(759, 809)(760, 812)(762, 813)(764, 814)(765, 816)(769, 810)(770, 820)(771, 821)(775, 824)(780, 831)(781, 835)(785, 837)(786, 840)(787, 843)(789, 846)(792, 848)(793, 849)(795, 852)(796, 853)(798, 854)(799, 856)(801, 857)(804, 860)(805, 861)(807, 862)(808, 866)(811, 869)(815, 871)(817, 875)(818, 867)(819, 876)(822, 879)(823, 829)(825, 830)(826, 832)(827, 884)(828, 836)(833, 888)(834, 890)(838, 894)(839, 895)(841, 898)(842, 899)(844, 900)(845, 902)(847, 903)(850, 906)(851, 908)(855, 909)(858, 913)(859, 917)(863, 919)(864, 922)(865, 924)(868, 927)(870, 928)(872, 914)(873, 932)(874, 918)(877, 934)(878, 938)(880, 941)(881, 942)(882, 939)(883, 943)(885, 945)(886, 947)(887, 948)(889, 951)(891, 952)(892, 954)(893, 955)(896, 958)(897, 960)(901, 961)(904, 965)(905, 969)(907, 972)(910, 966)(911, 976)(912, 970)(915, 979)(916, 981)(920, 985)(921, 986)(923, 989)(925, 990)(926, 992)(929, 993)(930, 996)(931, 997)(933, 988)(935, 994)(936, 1002)(937, 1003)(940, 1006)(944, 953)(946, 1012)(949, 1015)(950, 1017)(956, 1021)(957, 1025)(959, 1028)(962, 1022)(963, 1032)(964, 1026)(967, 1035)(968, 1036)(971, 1039)(973, 1040)(974, 1042)(975, 1043)(977, 1046)(978, 1047)(980, 1050)(982, 1051)(983, 1053)(984, 1054)(987, 1057)(991, 1059)(995, 1065)(998, 1052)(999, 1069)(1000, 1071)(1001, 1072)(1004, 1075)(1005, 1077)(1007, 1078)(1008, 1074)(1009, 1011)(1010, 1082)(1013, 1084)(1014, 1088)(1016, 1091)(1018, 1085)(1019, 1094)(1020, 1089)(1023, 1097)(1024, 1098)(1027, 1101)(1029, 1102)(1030, 1104)(1031, 1105)(1033, 1108)(1034, 1109)(1037, 1112)(1038, 1114)(1041, 1115)(1044, 1113)(1045, 1121)(1048, 1124)(1049, 1126)(1055, 1130)(1056, 1134)(1058, 1137)(1060, 1131)(1061, 1140)(1062, 1135)(1063, 1141)(1064, 1142)(1066, 1111)(1067, 1116)(1068, 1146)(1070, 1148)(1073, 1151)(1076, 1143)(1079, 1157)(1080, 1158)(1081, 1159)(1083, 1161)(1086, 1164)(1087, 1165)(1090, 1168)(1092, 1169)(1093, 1171)(1095, 1174)(1096, 1175)(1099, 1178)(1100, 1180)(1103, 1181)(1106, 1179)(1107, 1187)(1110, 1190)(1117, 1197)(1118, 1177)(1119, 1182)(1120, 1200)(1122, 1170)(1123, 1202)(1125, 1162)(1127, 1186)(1128, 1205)(1129, 1184)(1132, 1198)(1133, 1208)(1136, 1183)(1138, 1167)(1139, 1210)(1144, 1212)(1145, 1213)(1147, 1211)(1149, 1215)(1150, 1218)(1152, 1195)(1153, 1216)(1154, 1176)(1155, 1214)(1156, 1191)(1160, 1194)(1163, 1223)(1166, 1224)(1172, 1225)(1173, 1229)(1185, 1226)(1188, 1221)(1189, 1236)(1192, 1228)(1193, 1238)(1196, 1239)(1199, 1240)(1201, 1234)(1203, 1222)(1204, 1232)(1206, 1233)(1207, 1242)(1209, 1243)(1217, 1230)(1219, 1231)(1220, 1227)(1235, 1246)(1237, 1245)(1241, 1248)(1244, 1247)
	L = (1, 625)(2, 626)(3, 627)(4, 628)(5, 629)(6, 630)(7, 631)(8, 632)(9, 633)(10, 634)(11, 635)(12, 636)(13, 637)(14, 638)(15, 639)(16, 640)(17, 641)(18, 642)(19, 643)(20, 644)(21, 645)(22, 646)(23, 647)(24, 648)(25, 649)(26, 650)(27, 651)(28, 652)(29, 653)(30, 654)(31, 655)(32, 656)(33, 657)(34, 658)(35, 659)(36, 660)(37, 661)(38, 662)(39, 663)(40, 664)(41, 665)(42, 666)(43, 667)(44, 668)(45, 669)(46, 670)(47, 671)(48, 672)(49, 673)(50, 674)(51, 675)(52, 676)(53, 677)(54, 678)(55, 679)(56, 680)(57, 681)(58, 682)(59, 683)(60, 684)(61, 685)(62, 686)(63, 687)(64, 688)(65, 689)(66, 690)(67, 691)(68, 692)(69, 693)(70, 694)(71, 695)(72, 696)(73, 697)(74, 698)(75, 699)(76, 700)(77, 701)(78, 702)(79, 703)(80, 704)(81, 705)(82, 706)(83, 707)(84, 708)(85, 709)(86, 710)(87, 711)(88, 712)(89, 713)(90, 714)(91, 715)(92, 716)(93, 717)(94, 718)(95, 719)(96, 720)(97, 721)(98, 722)(99, 723)(100, 724)(101, 725)(102, 726)(103, 727)(104, 728)(105, 729)(106, 730)(107, 731)(108, 732)(109, 733)(110, 734)(111, 735)(112, 736)(113, 737)(114, 738)(115, 739)(116, 740)(117, 741)(118, 742)(119, 743)(120, 744)(121, 745)(122, 746)(123, 747)(124, 748)(125, 749)(126, 750)(127, 751)(128, 752)(129, 753)(130, 754)(131, 755)(132, 756)(133, 757)(134, 758)(135, 759)(136, 760)(137, 761)(138, 762)(139, 763)(140, 764)(141, 765)(142, 766)(143, 767)(144, 768)(145, 769)(146, 770)(147, 771)(148, 772)(149, 773)(150, 774)(151, 775)(152, 776)(153, 777)(154, 778)(155, 779)(156, 780)(157, 781)(158, 782)(159, 783)(160, 784)(161, 785)(162, 786)(163, 787)(164, 788)(165, 789)(166, 790)(167, 791)(168, 792)(169, 793)(170, 794)(171, 795)(172, 796)(173, 797)(174, 798)(175, 799)(176, 800)(177, 801)(178, 802)(179, 803)(180, 804)(181, 805)(182, 806)(183, 807)(184, 808)(185, 809)(186, 810)(187, 811)(188, 812)(189, 813)(190, 814)(191, 815)(192, 816)(193, 817)(194, 818)(195, 819)(196, 820)(197, 821)(198, 822)(199, 823)(200, 824)(201, 825)(202, 826)(203, 827)(204, 828)(205, 829)(206, 830)(207, 831)(208, 832)(209, 833)(210, 834)(211, 835)(212, 836)(213, 837)(214, 838)(215, 839)(216, 840)(217, 841)(218, 842)(219, 843)(220, 844)(221, 845)(222, 846)(223, 847)(224, 848)(225, 849)(226, 850)(227, 851)(228, 852)(229, 853)(230, 854)(231, 855)(232, 856)(233, 857)(234, 858)(235, 859)(236, 860)(237, 861)(238, 862)(239, 863)(240, 864)(241, 865)(242, 866)(243, 867)(244, 868)(245, 869)(246, 870)(247, 871)(248, 872)(249, 873)(250, 874)(251, 875)(252, 876)(253, 877)(254, 878)(255, 879)(256, 880)(257, 881)(258, 882)(259, 883)(260, 884)(261, 885)(262, 886)(263, 887)(264, 888)(265, 889)(266, 890)(267, 891)(268, 892)(269, 893)(270, 894)(271, 895)(272, 896)(273, 897)(274, 898)(275, 899)(276, 900)(277, 901)(278, 902)(279, 903)(280, 904)(281, 905)(282, 906)(283, 907)(284, 908)(285, 909)(286, 910)(287, 911)(288, 912)(289, 913)(290, 914)(291, 915)(292, 916)(293, 917)(294, 918)(295, 919)(296, 920)(297, 921)(298, 922)(299, 923)(300, 924)(301, 925)(302, 926)(303, 927)(304, 928)(305, 929)(306, 930)(307, 931)(308, 932)(309, 933)(310, 934)(311, 935)(312, 936)(313, 937)(314, 938)(315, 939)(316, 940)(317, 941)(318, 942)(319, 943)(320, 944)(321, 945)(322, 946)(323, 947)(324, 948)(325, 949)(326, 950)(327, 951)(328, 952)(329, 953)(330, 954)(331, 955)(332, 956)(333, 957)(334, 958)(335, 959)(336, 960)(337, 961)(338, 962)(339, 963)(340, 964)(341, 965)(342, 966)(343, 967)(344, 968)(345, 969)(346, 970)(347, 971)(348, 972)(349, 973)(350, 974)(351, 975)(352, 976)(353, 977)(354, 978)(355, 979)(356, 980)(357, 981)(358, 982)(359, 983)(360, 984)(361, 985)(362, 986)(363, 987)(364, 988)(365, 989)(366, 990)(367, 991)(368, 992)(369, 993)(370, 994)(371, 995)(372, 996)(373, 997)(374, 998)(375, 999)(376, 1000)(377, 1001)(378, 1002)(379, 1003)(380, 1004)(381, 1005)(382, 1006)(383, 1007)(384, 1008)(385, 1009)(386, 1010)(387, 1011)(388, 1012)(389, 1013)(390, 1014)(391, 1015)(392, 1016)(393, 1017)(394, 1018)(395, 1019)(396, 1020)(397, 1021)(398, 1022)(399, 1023)(400, 1024)(401, 1025)(402, 1026)(403, 1027)(404, 1028)(405, 1029)(406, 1030)(407, 1031)(408, 1032)(409, 1033)(410, 1034)(411, 1035)(412, 1036)(413, 1037)(414, 1038)(415, 1039)(416, 1040)(417, 1041)(418, 1042)(419, 1043)(420, 1044)(421, 1045)(422, 1046)(423, 1047)(424, 1048)(425, 1049)(426, 1050)(427, 1051)(428, 1052)(429, 1053)(430, 1054)(431, 1055)(432, 1056)(433, 1057)(434, 1058)(435, 1059)(436, 1060)(437, 1061)(438, 1062)(439, 1063)(440, 1064)(441, 1065)(442, 1066)(443, 1067)(444, 1068)(445, 1069)(446, 1070)(447, 1071)(448, 1072)(449, 1073)(450, 1074)(451, 1075)(452, 1076)(453, 1077)(454, 1078)(455, 1079)(456, 1080)(457, 1081)(458, 1082)(459, 1083)(460, 1084)(461, 1085)(462, 1086)(463, 1087)(464, 1088)(465, 1089)(466, 1090)(467, 1091)(468, 1092)(469, 1093)(470, 1094)(471, 1095)(472, 1096)(473, 1097)(474, 1098)(475, 1099)(476, 1100)(477, 1101)(478, 1102)(479, 1103)(480, 1104)(481, 1105)(482, 1106)(483, 1107)(484, 1108)(485, 1109)(486, 1110)(487, 1111)(488, 1112)(489, 1113)(490, 1114)(491, 1115)(492, 1116)(493, 1117)(494, 1118)(495, 1119)(496, 1120)(497, 1121)(498, 1122)(499, 1123)(500, 1124)(501, 1125)(502, 1126)(503, 1127)(504, 1128)(505, 1129)(506, 1130)(507, 1131)(508, 1132)(509, 1133)(510, 1134)(511, 1135)(512, 1136)(513, 1137)(514, 1138)(515, 1139)(516, 1140)(517, 1141)(518, 1142)(519, 1143)(520, 1144)(521, 1145)(522, 1146)(523, 1147)(524, 1148)(525, 1149)(526, 1150)(527, 1151)(528, 1152)(529, 1153)(530, 1154)(531, 1155)(532, 1156)(533, 1157)(534, 1158)(535, 1159)(536, 1160)(537, 1161)(538, 1162)(539, 1163)(540, 1164)(541, 1165)(542, 1166)(543, 1167)(544, 1168)(545, 1169)(546, 1170)(547, 1171)(548, 1172)(549, 1173)(550, 1174)(551, 1175)(552, 1176)(553, 1177)(554, 1178)(555, 1179)(556, 1180)(557, 1181)(558, 1182)(559, 1183)(560, 1184)(561, 1185)(562, 1186)(563, 1187)(564, 1188)(565, 1189)(566, 1190)(567, 1191)(568, 1192)(569, 1193)(570, 1194)(571, 1195)(572, 1196)(573, 1197)(574, 1198)(575, 1199)(576, 1200)(577, 1201)(578, 1202)(579, 1203)(580, 1204)(581, 1205)(582, 1206)(583, 1207)(584, 1208)(585, 1209)(586, 1210)(587, 1211)(588, 1212)(589, 1213)(590, 1214)(591, 1215)(592, 1216)(593, 1217)(594, 1218)(595, 1219)(596, 1220)(597, 1221)(598, 1222)(599, 1223)(600, 1224)(601, 1225)(602, 1226)(603, 1227)(604, 1228)(605, 1229)(606, 1230)(607, 1231)(608, 1232)(609, 1233)(610, 1234)(611, 1235)(612, 1236)(613, 1237)(614, 1238)(615, 1239)(616, 1240)(617, 1241)(618, 1242)(619, 1243)(620, 1244)(621, 1245)(622, 1246)(623, 1247)(624, 1248)
	local type(s) :: { ( 6, 6 ), ( 6^12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 364 e = 624 f = 208
	degree seq :: [ 2^312, 12^52 ]

E27.2362 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X1^2, X2^3, (X2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1)^2, (X2^-1 * X1)^12, X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2 * X1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 625, 2, 626)(3, 627, 7, 631)(4, 628, 8, 632)(5, 629, 9, 633)(6, 630, 10, 634)(11, 635, 19, 643)(12, 636, 20, 644)(13, 637, 21, 645)(14, 638, 22, 646)(15, 639, 23, 647)(16, 640, 24, 648)(17, 641, 25, 649)(18, 642, 26, 650)(27, 651, 43, 667)(28, 652, 44, 668)(29, 653, 45, 669)(30, 654, 46, 670)(31, 655, 47, 671)(32, 656, 48, 672)(33, 657, 49, 673)(34, 658, 50, 674)(35, 659, 51, 675)(36, 660, 52, 676)(37, 661, 53, 677)(38, 662, 54, 678)(39, 663, 55, 679)(40, 664, 56, 680)(41, 665, 57, 681)(42, 666, 58, 682)(59, 683, 91, 715)(60, 684, 92, 716)(61, 685, 93, 717)(62, 686, 94, 718)(63, 687, 95, 719)(64, 688, 96, 720)(65, 689, 97, 721)(66, 690, 98, 722)(67, 691, 99, 723)(68, 692, 100, 724)(69, 693, 101, 725)(70, 694, 102, 726)(71, 695, 103, 727)(72, 696, 104, 728)(73, 697, 105, 729)(74, 698, 106, 730)(75, 699, 107, 731)(76, 700, 108, 732)(77, 701, 109, 733)(78, 702, 110, 734)(79, 703, 111, 735)(80, 704, 112, 736)(81, 705, 113, 737)(82, 706, 114, 738)(83, 707, 115, 739)(84, 708, 116, 740)(85, 709, 117, 741)(86, 710, 118, 742)(87, 711, 119, 743)(88, 712, 120, 744)(89, 713, 121, 745)(90, 714, 122, 746)(123, 747, 187, 811)(124, 748, 170, 794)(125, 749, 178, 802)(126, 750, 188, 812)(127, 751, 182, 806)(128, 752, 189, 813)(129, 753, 190, 814)(130, 754, 191, 815)(131, 755, 184, 808)(132, 756, 192, 816)(133, 757, 193, 817)(134, 758, 194, 818)(135, 759, 195, 819)(136, 760, 196, 820)(137, 761, 197, 821)(138, 762, 156, 780)(139, 763, 185, 809)(140, 764, 198, 822)(141, 765, 199, 823)(142, 766, 200, 824)(143, 767, 201, 825)(144, 768, 202, 826)(145, 769, 203, 827)(146, 770, 157, 781)(147, 771, 204, 828)(148, 772, 205, 829)(149, 773, 206, 830)(150, 774, 159, 783)(151, 775, 207, 831)(152, 776, 163, 787)(153, 777, 171, 795)(154, 778, 208, 832)(155, 779, 319, 943)(158, 782, 310, 934)(160, 784, 211, 835)(161, 785, 218, 842)(162, 786, 324, 948)(164, 788, 269, 893)(165, 789, 327, 951)(166, 790, 328, 952)(167, 791, 330, 954)(168, 792, 261, 885)(169, 793, 260, 884)(172, 796, 302, 926)(173, 797, 334, 958)(174, 798, 317, 941)(175, 799, 336, 960)(176, 800, 217, 841)(177, 801, 212, 836)(179, 803, 339, 963)(180, 804, 341, 965)(181, 805, 277, 901)(183, 807, 312, 936)(186, 810, 343, 967)(209, 833, 289, 913)(210, 834, 274, 898)(213, 837, 282, 906)(214, 838, 248, 872)(215, 839, 296, 920)(216, 840, 240, 864)(219, 843, 361, 985)(220, 844, 224, 848)(221, 845, 326, 950)(222, 846, 236, 860)(223, 847, 407, 1031)(225, 849, 305, 929)(226, 850, 244, 868)(227, 851, 290, 914)(228, 852, 346, 970)(229, 853, 350, 974)(230, 854, 366, 990)(231, 855, 275, 899)(232, 856, 428, 1052)(233, 857, 397, 1021)(234, 858, 433, 1057)(235, 859, 436, 1060)(237, 861, 315, 939)(238, 862, 270, 894)(239, 863, 443, 1067)(241, 865, 265, 889)(242, 866, 278, 902)(243, 867, 360, 984)(245, 869, 340, 964)(246, 870, 285, 909)(247, 871, 458, 1082)(249, 873, 255, 879)(250, 874, 292, 916)(251, 875, 283, 907)(252, 876, 469, 1093)(253, 877, 419, 1043)(254, 878, 473, 1097)(256, 880, 478, 1102)(257, 881, 424, 1048)(258, 882, 482, 1106)(259, 883, 297, 921)(262, 886, 362, 986)(263, 887, 430, 1054)(264, 888, 480, 1104)(266, 890, 495, 1119)(267, 891, 435, 1059)(268, 892, 367, 991)(271, 895, 502, 1126)(272, 896, 332, 956)(273, 897, 507, 1131)(276, 900, 354, 978)(279, 903, 514, 1138)(280, 904, 364, 988)(281, 905, 518, 1142)(284, 908, 372, 996)(286, 910, 528, 1152)(287, 911, 308, 932)(288, 912, 511, 1135)(291, 915, 420, 1044)(293, 917, 534, 1158)(294, 918, 509, 1133)(295, 919, 538, 1162)(298, 922, 488, 1112)(299, 923, 363, 987)(300, 924, 351, 975)(301, 925, 438, 1062)(303, 927, 446, 1070)(304, 928, 431, 1055)(306, 930, 556, 1180)(307, 931, 475, 1099)(309, 933, 333, 957)(311, 935, 445, 1069)(313, 937, 409, 1033)(314, 938, 471, 1095)(316, 940, 544, 1168)(318, 942, 347, 971)(320, 944, 486, 1110)(321, 945, 550, 1174)(322, 946, 398, 1022)(323, 947, 460, 1084)(325, 949, 421, 1045)(329, 953, 585, 1209)(331, 955, 492, 1116)(335, 959, 385, 1009)(337, 961, 400, 1024)(338, 962, 489, 1113)(342, 966, 525, 1149)(344, 968, 562, 1186)(345, 969, 573, 1197)(348, 972, 523, 1147)(349, 973, 603, 1227)(352, 976, 425, 1049)(353, 977, 521, 1145)(355, 979, 549, 1173)(356, 980, 606, 1230)(357, 981, 520, 1144)(358, 982, 503, 1127)(359, 983, 610, 1234)(365, 989, 551, 1175)(368, 992, 465, 1089)(369, 993, 463, 1087)(370, 994, 614, 1238)(371, 995, 461, 1085)(373, 997, 563, 1187)(374, 998, 580, 1204)(375, 999, 515, 1139)(376, 1000, 584, 1208)(377, 1001, 565, 1189)(378, 1002, 589, 1213)(379, 1003, 583, 1207)(380, 1004, 560, 1184)(381, 1005, 555, 1179)(382, 1006, 542, 1166)(383, 1007, 541, 1165)(384, 1008, 612, 1236)(386, 1010, 484, 1108)(387, 1011, 569, 1193)(388, 1012, 546, 1170)(389, 1013, 494, 1118)(390, 1014, 467, 1091)(391, 1015, 595, 1219)(392, 1016, 574, 1198)(393, 1017, 477, 1101)(394, 1018, 449, 1073)(395, 1019, 448, 1072)(396, 1020, 601, 1225)(399, 1023, 476, 1100)(401, 1025, 618, 1242)(402, 1026, 427, 1051)(403, 1027, 426, 1050)(404, 1028, 605, 1229)(405, 1029, 598, 1222)(406, 1030, 468, 1092)(408, 1032, 493, 1117)(410, 1034, 619, 1243)(411, 1035, 417, 1041)(412, 1036, 416, 1040)(413, 1037, 620, 1244)(414, 1038, 571, 1195)(415, 1039, 485, 1109)(418, 1042, 587, 1211)(422, 1046, 439, 1063)(423, 1047, 530, 1154)(429, 1053, 557, 1181)(432, 1056, 454, 1078)(434, 1058, 505, 1129)(437, 1061, 554, 1178)(440, 1064, 621, 1245)(441, 1065, 498, 1122)(442, 1066, 547, 1171)(444, 1068, 568, 1192)(447, 1071, 596, 1220)(450, 1074, 623, 1247)(451, 1075, 558, 1182)(452, 1076, 561, 1185)(453, 1077, 582, 1206)(455, 1079, 608, 1232)(456, 1080, 483, 1107)(457, 1081, 575, 1199)(459, 1083, 594, 1218)(462, 1086, 611, 1235)(464, 1088, 604, 1228)(466, 1090, 590, 1214)(470, 1094, 570, 1194)(472, 1096, 501, 1125)(474, 1098, 516, 1140)(479, 1103, 497, 1121)(481, 1105, 496, 1120)(487, 1111, 607, 1231)(490, 1114, 527, 1151)(491, 1115, 536, 1160)(499, 1123, 609, 1233)(500, 1124, 540, 1164)(504, 1128, 578, 1202)(506, 1130, 581, 1205)(508, 1132, 592, 1216)(510, 1134, 577, 1201)(512, 1136, 543, 1167)(513, 1137, 591, 1215)(517, 1141, 599, 1223)(519, 1143, 622, 1246)(522, 1146, 539, 1163)(524, 1148, 533, 1157)(526, 1150, 613, 1237)(529, 1153, 586, 1210)(531, 1155, 553, 1177)(532, 1156, 566, 1190)(535, 1159, 564, 1188)(537, 1161, 572, 1196)(545, 1169, 616, 1240)(548, 1172, 600, 1224)(552, 1176, 588, 1212)(559, 1183, 579, 1203)(567, 1191, 602, 1226)(576, 1200, 624, 1248)(593, 1217, 617, 1241)(597, 1221, 615, 1239)
	L = (1, 627)(2, 629)(3, 628)(4, 625)(5, 630)(6, 626)(7, 635)(8, 637)(9, 639)(10, 641)(11, 636)(12, 631)(13, 638)(14, 632)(15, 640)(16, 633)(17, 642)(18, 634)(19, 651)(20, 653)(21, 655)(22, 657)(23, 659)(24, 661)(25, 663)(26, 665)(27, 652)(28, 643)(29, 654)(30, 644)(31, 656)(32, 645)(33, 658)(34, 646)(35, 660)(36, 647)(37, 662)(38, 648)(39, 664)(40, 649)(41, 666)(42, 650)(43, 683)(44, 685)(45, 687)(46, 689)(47, 691)(48, 693)(49, 695)(50, 697)(51, 699)(52, 701)(53, 703)(54, 705)(55, 707)(56, 709)(57, 711)(58, 713)(59, 684)(60, 667)(61, 686)(62, 668)(63, 688)(64, 669)(65, 690)(66, 670)(67, 692)(68, 671)(69, 694)(70, 672)(71, 696)(72, 673)(73, 698)(74, 674)(75, 700)(76, 675)(77, 702)(78, 676)(79, 704)(80, 677)(81, 706)(82, 678)(83, 708)(84, 679)(85, 710)(86, 680)(87, 712)(88, 681)(89, 714)(90, 682)(91, 747)(92, 749)(93, 751)(94, 753)(95, 755)(96, 757)(97, 759)(98, 761)(99, 763)(100, 765)(101, 767)(102, 769)(103, 771)(104, 773)(105, 775)(106, 777)(107, 779)(108, 781)(109, 783)(110, 785)(111, 787)(112, 789)(113, 791)(114, 793)(115, 795)(116, 797)(117, 799)(118, 801)(119, 803)(120, 805)(121, 807)(122, 809)(123, 748)(124, 715)(125, 750)(126, 716)(127, 752)(128, 717)(129, 754)(130, 718)(131, 756)(132, 719)(133, 758)(134, 720)(135, 760)(136, 721)(137, 762)(138, 722)(139, 764)(140, 723)(141, 766)(142, 724)(143, 768)(144, 725)(145, 770)(146, 726)(147, 772)(148, 727)(149, 774)(150, 728)(151, 776)(152, 729)(153, 778)(154, 730)(155, 780)(156, 731)(157, 782)(158, 732)(159, 784)(160, 733)(161, 786)(162, 734)(163, 788)(164, 735)(165, 790)(166, 736)(167, 792)(168, 737)(169, 794)(170, 738)(171, 796)(172, 739)(173, 798)(174, 740)(175, 800)(176, 741)(177, 802)(178, 742)(179, 804)(180, 743)(181, 806)(182, 744)(183, 808)(184, 745)(185, 810)(186, 746)(187, 969)(188, 970)(189, 972)(190, 973)(191, 975)(192, 977)(193, 979)(194, 913)(195, 982)(196, 984)(197, 986)(198, 815)(199, 818)(200, 990)(201, 820)(202, 993)(203, 994)(204, 821)(205, 995)(206, 997)(207, 999)(208, 811)(209, 1002)(210, 1004)(211, 1006)(212, 1008)(213, 1010)(214, 1012)(215, 1014)(216, 1016)(217, 1018)(218, 1020)(219, 1023)(220, 1025)(221, 1027)(222, 1029)(223, 1032)(224, 1034)(225, 1036)(226, 1038)(227, 1040)(228, 1042)(229, 1045)(230, 1047)(231, 1050)(232, 1053)(233, 1055)(234, 1058)(235, 1061)(236, 953)(237, 949)(238, 1065)(239, 1068)(240, 1071)(241, 1073)(242, 1075)(243, 1077)(244, 930)(245, 928)(246, 1080)(247, 1083)(248, 1085)(249, 1087)(250, 1089)(251, 1091)(252, 1094)(253, 1095)(254, 1098)(255, 1100)(256, 1103)(257, 1104)(258, 1107)(259, 1108)(260, 1093)(261, 1060)(262, 1111)(263, 1113)(264, 1115)(265, 1117)(266, 1120)(267, 1097)(268, 1122)(269, 1124)(270, 940)(271, 938)(272, 1129)(273, 1132)(274, 958)(275, 951)(276, 1135)(277, 1137)(278, 890)(279, 888)(280, 1140)(281, 1143)(282, 1145)(283, 1147)(284, 1149)(285, 966)(286, 962)(287, 1154)(288, 1156)(289, 823)(290, 817)(291, 1131)(292, 880)(293, 878)(294, 1160)(295, 983)(296, 1164)(297, 1166)(298, 1168)(299, 1170)(300, 1102)(301, 1067)(302, 948)(303, 1175)(304, 1079)(305, 1178)(306, 1078)(307, 1106)(308, 1182)(309, 1184)(310, 1052)(311, 1031)(312, 1188)(313, 1152)(314, 1128)(315, 1192)(316, 1125)(317, 1057)(318, 1195)(319, 1197)(320, 1198)(321, 1119)(322, 1082)(323, 1202)(324, 1174)(325, 1064)(326, 1206)(327, 1134)(328, 898)(329, 1063)(330, 1210)(331, 991)(332, 992)(333, 1213)(334, 952)(335, 985)(336, 885)(337, 1126)(338, 989)(339, 884)(340, 1218)(341, 1220)(342, 1151)(343, 943)(344, 1222)(345, 832)(346, 1159)(347, 1225)(348, 1163)(349, 1062)(350, 830)(351, 822)(352, 1142)(353, 1059)(354, 856)(355, 914)(356, 882)(357, 1232)(358, 1200)(359, 1000)(360, 825)(361, 1215)(362, 828)(363, 1236)(364, 912)(365, 910)(366, 1231)(367, 1211)(368, 1212)(369, 1235)(370, 1069)(371, 1099)(372, 876)(373, 974)(374, 858)(375, 1239)(376, 919)(377, 1180)(378, 1003)(379, 833)(380, 1005)(381, 834)(382, 1007)(383, 835)(384, 1009)(385, 836)(386, 1011)(387, 837)(388, 1013)(389, 838)(390, 1015)(391, 839)(392, 1017)(393, 840)(394, 1019)(395, 841)(396, 1022)(397, 901)(398, 842)(399, 1024)(400, 843)(401, 1026)(402, 844)(403, 1028)(404, 845)(405, 1030)(406, 846)(407, 1187)(408, 1033)(409, 847)(410, 1035)(411, 848)(412, 1037)(413, 849)(414, 1039)(415, 850)(416, 1041)(417, 851)(418, 1044)(419, 867)(420, 852)(421, 1046)(422, 853)(423, 1049)(424, 893)(425, 854)(426, 1051)(427, 855)(428, 1139)(429, 978)(430, 859)(431, 1056)(432, 857)(433, 1194)(434, 998)(435, 816)(436, 960)(437, 1054)(438, 814)(439, 860)(440, 861)(441, 1066)(442, 862)(443, 1173)(444, 1070)(445, 827)(446, 863)(447, 1072)(448, 864)(449, 1074)(450, 865)(451, 1076)(452, 866)(453, 1043)(454, 868)(455, 869)(456, 1081)(457, 870)(458, 1201)(459, 1084)(460, 871)(461, 1086)(462, 872)(463, 1088)(464, 873)(465, 1090)(466, 874)(467, 1092)(468, 875)(469, 963)(470, 996)(471, 1096)(472, 877)(473, 1121)(474, 917)(475, 829)(476, 1101)(477, 879)(478, 1127)(479, 916)(480, 1105)(481, 881)(482, 1181)(483, 980)(484, 1109)(485, 883)(486, 1238)(487, 1112)(488, 886)(489, 1114)(490, 887)(491, 903)(492, 965)(493, 1118)(494, 889)(495, 1153)(496, 902)(497, 891)(498, 1123)(499, 892)(500, 1048)(501, 894)(502, 1216)(503, 924)(504, 895)(505, 1130)(506, 896)(507, 1157)(508, 1133)(509, 897)(510, 899)(511, 1136)(512, 900)(513, 1021)(514, 1246)(515, 934)(516, 1141)(517, 904)(518, 1228)(519, 1144)(520, 905)(521, 1146)(522, 906)(523, 1148)(524, 907)(525, 1150)(526, 908)(527, 909)(528, 1190)(529, 945)(530, 1155)(531, 911)(532, 988)(533, 915)(534, 1234)(535, 812)(536, 1161)(537, 918)(538, 1247)(539, 813)(540, 1165)(541, 920)(542, 1167)(543, 921)(544, 1169)(545, 922)(546, 1171)(547, 923)(548, 954)(549, 925)(550, 926)(551, 1176)(552, 927)(553, 1248)(554, 1179)(555, 929)(556, 1217)(557, 931)(558, 1183)(559, 932)(560, 1185)(561, 933)(562, 1227)(563, 935)(564, 1189)(565, 936)(566, 937)(567, 1221)(568, 1193)(569, 939)(570, 941)(571, 1196)(572, 942)(573, 967)(574, 1199)(575, 944)(576, 819)(577, 946)(578, 1203)(579, 947)(580, 1162)(581, 1224)(582, 1207)(583, 950)(584, 1245)(585, 1191)(586, 1172)(587, 955)(588, 956)(589, 1214)(590, 957)(591, 959)(592, 961)(593, 1001)(594, 1219)(595, 964)(596, 1116)(597, 1209)(598, 1223)(599, 968)(600, 1242)(601, 1226)(602, 971)(603, 1241)(604, 976)(605, 1138)(606, 1208)(607, 824)(608, 1233)(609, 981)(610, 1244)(611, 826)(612, 1237)(613, 987)(614, 1240)(615, 831)(616, 1110)(617, 1186)(618, 1205)(619, 1177)(620, 1158)(621, 1230)(622, 1229)(623, 1204)(624, 1243)
	local type(s) :: { ( 3, 12, 3, 12 ) }
Outer automorphisms :: chiral
Dual of E27.2360
Transitivity :: ET+ VT+
Graph:: simple
	v = 312 e = 624 f = 260
	degree seq :: [ 4^312 ]

E27.2363 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X1^3, (X2 * X1)^2, (X2^2 * X1^-1 * X2^3)^2, X2^12, (X2^2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-1)^2, X2 * X1^-1 * X2^-3 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^2 * X1 * X2^-2 * X1 * X2^-2 * X1^-1 * X2 * X1, X2^2 * X1^-1 * X2^2 * X1^-1 * X2^-3 * X1 * X2^-2 * X1 * X2^-2 * X1^-1 * X2 * X1^-1 * X2^3 * X1 * X2^-1 * X1, X1 * X2^-2 * X1^-1 * X2^2 * X1 * X2^-1 * X1 * X2^-3 * X1^-1 * X2 * X1^-1 * X2^2 * X1^-1 * X2^2 * X1^-1 * X2 * X1^-1 * X2^-2 ]
Map::
	R = (1, 625, 2, 626, 4, 628)(3, 627, 8, 632, 10, 634)(5, 629, 12, 636, 6, 630)(7, 631, 15, 639, 11, 635)(9, 633, 18, 642, 20, 644)(13, 637, 25, 649, 23, 647)(14, 638, 24, 648, 28, 652)(16, 640, 31, 655, 29, 653)(17, 641, 33, 657, 21, 645)(19, 643, 36, 660, 38, 662)(22, 646, 30, 654, 42, 666)(26, 650, 47, 671, 45, 669)(27, 651, 49, 673, 51, 675)(32, 656, 57, 681, 55, 679)(34, 658, 61, 685, 59, 683)(35, 659, 63, 687, 39, 663)(37, 661, 66, 690, 68, 692)(40, 664, 60, 684, 72, 696)(41, 665, 73, 697, 75, 699)(43, 667, 46, 670, 78, 702)(44, 668, 79, 703, 52, 676)(48, 672, 85, 709, 83, 707)(50, 674, 88, 712, 90, 714)(53, 677, 56, 680, 94, 718)(54, 678, 95, 719, 76, 700)(58, 682, 101, 725, 99, 723)(62, 686, 107, 731, 105, 729)(64, 688, 111, 735, 109, 733)(65, 689, 113, 737, 69, 693)(67, 691, 116, 740, 102, 726)(70, 694, 110, 734, 121, 745)(71, 695, 122, 746, 124, 748)(74, 698, 127, 751, 129, 753)(77, 701, 132, 756, 134, 758)(80, 704, 138, 762, 136, 760)(81, 705, 84, 708, 140, 764)(82, 706, 141, 765, 135, 759)(86, 710, 128, 752, 143, 767)(87, 711, 144, 768, 91, 715)(89, 713, 147, 771, 108, 732)(92, 716, 137, 761, 152, 776)(93, 717, 153, 777, 155, 779)(96, 720, 159, 783, 157, 781)(97, 721, 100, 724, 161, 785)(98, 722, 162, 786, 156, 780)(103, 727, 106, 730, 165, 789)(104, 728, 166, 790, 125, 749)(112, 736, 175, 799, 173, 797)(114, 738, 178, 802, 176, 800)(115, 739, 180, 804, 118, 742)(117, 741, 148, 772, 170, 794)(119, 743, 177, 801, 182, 806)(120, 744, 183, 807, 184, 808)(123, 747, 187, 811, 142, 766)(126, 750, 190, 814, 130, 754)(131, 755, 158, 782, 192, 816)(133, 757, 194, 818, 163, 787)(139, 763, 200, 824, 201, 825)(145, 769, 205, 829, 203, 827)(146, 770, 207, 831, 149, 773)(150, 774, 204, 828, 209, 833)(151, 775, 210, 834, 211, 835)(154, 778, 214, 838, 168, 792)(160, 784, 220, 844, 221, 845)(164, 788, 223, 847, 225, 849)(167, 791, 229, 853, 227, 851)(169, 793, 231, 855, 226, 850)(171, 795, 174, 798, 233, 857)(172, 796, 234, 858, 185, 809)(179, 803, 242, 866, 240, 864)(181, 805, 244, 868, 243, 867)(186, 810, 249, 873, 188, 812)(189, 813, 228, 852, 251, 875)(191, 815, 253, 877, 252, 876)(193, 817, 255, 879, 195, 819)(196, 820, 202, 826, 260, 884)(197, 821, 199, 823, 262, 886)(198, 822, 263, 887, 212, 836)(206, 830, 257, 881, 269, 893)(208, 832, 272, 896, 271, 895)(213, 837, 277, 901, 215, 839)(216, 840, 222, 846, 282, 906)(217, 841, 219, 843, 284, 908)(218, 842, 285, 909, 254, 878)(224, 848, 290, 914, 236, 860)(230, 854, 279, 903, 296, 920)(232, 856, 298, 922, 300, 924)(235, 859, 304, 928, 302, 926)(237, 861, 306, 930, 301, 925)(238, 862, 241, 865, 308, 932)(239, 863, 309, 933, 245, 869)(246, 870, 316, 940, 247, 871)(248, 872, 303, 927, 318, 942)(250, 874, 320, 944, 319, 943)(256, 880, 327, 951, 325, 949)(258, 882, 326, 950, 329, 953)(259, 883, 330, 954, 331, 955)(261, 885, 333, 957, 334, 958)(264, 888, 336, 960, 265, 889)(266, 890, 338, 962, 332, 956)(267, 891, 270, 894, 340, 964)(268, 892, 341, 965, 273, 897)(274, 898, 348, 972, 275, 899)(276, 900, 335, 959, 350, 974)(278, 902, 353, 977, 351, 975)(280, 904, 352, 976, 355, 979)(281, 905, 356, 980, 357, 981)(283, 907, 359, 983, 360, 984)(286, 910, 362, 986, 287, 911)(288, 912, 364, 988, 358, 982)(289, 913, 365, 989, 291, 915)(292, 916, 297, 921, 370, 994)(293, 917, 295, 919, 372, 996)(294, 918, 373, 997, 321, 945)(299, 923, 377, 1001, 311, 935)(305, 929, 367, 991, 383, 1007)(307, 931, 385, 1009, 386, 1010)(310, 934, 390, 1014, 388, 1012)(312, 936, 392, 1016, 387, 1011)(313, 937, 314, 938, 393, 1017)(315, 939, 389, 1013, 395, 1019)(317, 941, 397, 1021, 396, 1020)(322, 946, 323, 947, 402, 1026)(324, 948, 361, 985, 404, 1028)(328, 952, 408, 1032, 343, 967)(337, 961, 416, 1040, 417, 1041)(339, 963, 419, 1043, 420, 1044)(342, 966, 424, 1048, 422, 1046)(344, 968, 426, 1050, 421, 1045)(345, 969, 346, 970, 427, 1051)(347, 971, 423, 1047, 429, 1053)(349, 973, 431, 1055, 430, 1054)(354, 978, 436, 1060, 374, 998)(363, 987, 444, 1068, 445, 1069)(366, 990, 449, 1073, 447, 1071)(368, 992, 448, 1072, 451, 1075)(369, 993, 452, 1076, 453, 1077)(371, 995, 455, 1079, 456, 1080)(375, 999, 459, 1083, 454, 1078)(376, 1000, 460, 1084, 378, 1002)(379, 1003, 384, 1008, 465, 1089)(380, 1004, 382, 1006, 467, 1091)(381, 1005, 468, 1092, 398, 1022)(391, 1015, 462, 1086, 477, 1101)(394, 1018, 480, 1104, 479, 1103)(399, 1023, 400, 1024, 485, 1109)(401, 1025, 457, 1081, 487, 1111)(403, 1027, 489, 1113, 488, 1112)(405, 1029, 407, 1031, 492, 1116)(406, 1030, 493, 1117, 409, 1033)(410, 1034, 498, 1122, 411, 1035)(412, 1036, 418, 1042, 500, 1124)(413, 1037, 501, 1125, 414, 1038)(415, 1039, 503, 1127, 432, 1056)(425, 1049, 496, 1120, 513, 1137)(428, 1052, 516, 1140, 515, 1139)(433, 1057, 435, 1059, 522, 1146)(434, 1058, 523, 1147, 437, 1061)(438, 1062, 528, 1152, 439, 1063)(440, 1064, 446, 1070, 530, 1154)(441, 1065, 531, 1155, 442, 1066)(443, 1067, 533, 1157, 490, 1114)(450, 1074, 540, 1164, 469, 1093)(458, 1082, 526, 1150, 548, 1172)(461, 1085, 552, 1176, 550, 1174)(463, 1087, 551, 1175, 554, 1178)(464, 1088, 520, 1144, 555, 1179)(466, 1090, 556, 1180, 557, 1181)(470, 1094, 518, 1142, 519, 1143)(471, 1095, 560, 1184, 472, 1096)(473, 1097, 478, 1102, 525, 1149)(474, 1098, 476, 1100, 536, 1160)(475, 1099, 564, 1188, 481, 1105)(482, 1106, 483, 1107, 529, 1153)(484, 1108, 558, 1182, 524, 1148)(486, 1110, 509, 1133, 514, 1138)(491, 1115, 572, 1196, 573, 1197)(494, 1118, 571, 1195, 574, 1198)(495, 1119, 569, 1193, 570, 1194)(497, 1121, 575, 1199, 577, 1201)(499, 1123, 544, 1168, 549, 1173)(502, 1126, 578, 1202, 579, 1203)(504, 1128, 580, 1204, 505, 1129)(506, 1130, 543, 1167, 542, 1166)(507, 1131, 582, 1206, 508, 1132)(510, 1134, 512, 1136, 547, 1171)(511, 1135, 586, 1210, 517, 1141)(521, 1145, 591, 1215, 592, 1216)(527, 1151, 593, 1217, 595, 1219)(532, 1156, 596, 1220, 597, 1221)(534, 1158, 598, 1222, 535, 1159)(537, 1161, 539, 1163, 601, 1225)(538, 1162, 602, 1226, 541, 1165)(545, 1169, 607, 1231, 546, 1170)(553, 1177, 612, 1236, 565, 1189)(559, 1183, 605, 1229, 583, 1207)(561, 1185, 588, 1212, 589, 1213)(562, 1186, 599, 1223, 616, 1240)(563, 1187, 590, 1214, 617, 1241)(566, 1190, 567, 1191, 604, 1228)(568, 1192, 618, 1242, 603, 1227)(576, 1200, 610, 1234, 587, 1211)(581, 1205, 622, 1246, 600, 1224)(584, 1208, 606, 1230, 623, 1247)(585, 1209, 608, 1232, 624, 1248)(594, 1218, 619, 1243, 609, 1233)(611, 1235, 621, 1245, 613, 1237)(614, 1238, 620, 1244, 615, 1239)
	L = (1, 627)(2, 630)(3, 633)(4, 635)(5, 625)(6, 638)(7, 626)(8, 628)(9, 643)(10, 645)(11, 646)(12, 647)(13, 629)(14, 651)(15, 653)(16, 631)(17, 632)(18, 634)(19, 661)(20, 663)(21, 664)(22, 665)(23, 667)(24, 636)(25, 669)(26, 637)(27, 674)(28, 676)(29, 677)(30, 639)(31, 679)(32, 640)(33, 683)(34, 641)(35, 642)(36, 644)(37, 691)(38, 693)(39, 694)(40, 695)(41, 698)(42, 700)(43, 701)(44, 648)(45, 705)(46, 649)(47, 707)(48, 650)(49, 652)(50, 713)(51, 715)(52, 716)(53, 717)(54, 654)(55, 721)(56, 655)(57, 723)(58, 656)(59, 727)(60, 657)(61, 729)(62, 658)(63, 733)(64, 659)(65, 660)(66, 662)(67, 741)(68, 742)(69, 743)(70, 744)(71, 747)(72, 749)(73, 666)(74, 752)(75, 754)(76, 755)(77, 757)(78, 759)(79, 760)(80, 668)(81, 763)(82, 670)(83, 766)(84, 671)(85, 767)(86, 672)(87, 673)(88, 675)(89, 772)(90, 773)(91, 774)(92, 775)(93, 778)(94, 780)(95, 781)(96, 678)(97, 784)(98, 680)(99, 787)(100, 681)(101, 740)(102, 682)(103, 788)(104, 684)(105, 792)(106, 685)(107, 771)(108, 686)(109, 795)(110, 687)(111, 797)(112, 688)(113, 800)(114, 689)(115, 690)(116, 692)(117, 710)(118, 704)(119, 706)(120, 708)(121, 809)(122, 696)(123, 709)(124, 812)(125, 813)(126, 697)(127, 699)(128, 794)(129, 736)(130, 791)(131, 793)(132, 702)(133, 725)(134, 819)(135, 820)(136, 821)(137, 703)(138, 804)(139, 805)(140, 808)(141, 806)(142, 803)(143, 753)(144, 827)(145, 711)(146, 712)(147, 714)(148, 726)(149, 720)(150, 722)(151, 724)(152, 836)(153, 718)(154, 731)(155, 839)(156, 840)(157, 841)(158, 719)(159, 831)(160, 832)(161, 835)(162, 833)(163, 830)(164, 848)(165, 850)(166, 851)(167, 728)(168, 854)(169, 730)(170, 732)(171, 856)(172, 734)(173, 860)(174, 735)(175, 751)(176, 862)(177, 737)(178, 864)(179, 738)(180, 867)(181, 739)(182, 869)(183, 745)(184, 871)(185, 872)(186, 746)(187, 748)(188, 859)(189, 861)(190, 876)(191, 750)(192, 878)(193, 756)(194, 758)(195, 882)(196, 883)(197, 885)(198, 761)(199, 762)(200, 764)(201, 889)(202, 765)(203, 891)(204, 768)(205, 893)(206, 769)(207, 895)(208, 770)(209, 897)(210, 776)(211, 899)(212, 900)(213, 777)(214, 779)(215, 904)(216, 905)(217, 907)(218, 782)(219, 783)(220, 785)(221, 911)(222, 786)(223, 789)(224, 799)(225, 915)(226, 916)(227, 917)(228, 790)(229, 814)(230, 815)(231, 816)(232, 923)(233, 925)(234, 926)(235, 796)(236, 929)(237, 798)(238, 931)(239, 801)(240, 935)(241, 802)(242, 811)(243, 937)(244, 825)(245, 939)(246, 807)(247, 934)(248, 936)(249, 943)(250, 810)(251, 945)(252, 946)(253, 920)(254, 948)(255, 949)(256, 817)(257, 818)(258, 822)(259, 823)(260, 956)(261, 952)(262, 955)(263, 953)(264, 824)(265, 961)(266, 826)(267, 963)(268, 828)(269, 967)(270, 829)(271, 969)(272, 845)(273, 971)(274, 834)(275, 966)(276, 968)(277, 975)(278, 837)(279, 838)(280, 842)(281, 843)(282, 982)(283, 978)(284, 981)(285, 979)(286, 844)(287, 987)(288, 846)(289, 847)(290, 849)(291, 992)(292, 993)(293, 995)(294, 852)(295, 853)(296, 998)(297, 855)(298, 857)(299, 866)(300, 1002)(301, 1003)(302, 1004)(303, 858)(304, 873)(305, 874)(306, 875)(307, 888)(308, 1011)(309, 1012)(310, 863)(311, 1015)(312, 865)(313, 880)(314, 868)(315, 1018)(316, 1020)(317, 870)(318, 1022)(319, 1023)(320, 1007)(321, 1025)(322, 990)(323, 877)(324, 1027)(325, 1029)(326, 879)(327, 1017)(328, 881)(329, 1033)(330, 884)(331, 1035)(332, 1036)(333, 886)(334, 1038)(335, 887)(336, 1010)(337, 890)(338, 1041)(339, 910)(340, 1045)(341, 1046)(342, 892)(343, 1049)(344, 894)(345, 902)(346, 896)(347, 1052)(348, 1054)(349, 898)(350, 1056)(351, 1057)(352, 901)(353, 1051)(354, 903)(355, 1061)(356, 906)(357, 1063)(358, 1064)(359, 908)(360, 1066)(361, 909)(362, 1044)(363, 912)(364, 1069)(365, 1071)(366, 913)(367, 914)(368, 918)(369, 919)(370, 1078)(371, 1074)(372, 1077)(373, 1075)(374, 1082)(375, 921)(376, 922)(377, 924)(378, 1087)(379, 1088)(380, 1090)(381, 927)(382, 928)(383, 1093)(384, 930)(385, 932)(386, 1096)(387, 1097)(388, 1098)(389, 933)(390, 940)(391, 941)(392, 942)(393, 1103)(394, 938)(395, 1105)(396, 1106)(397, 1101)(398, 1108)(399, 1085)(400, 944)(401, 1110)(402, 1112)(403, 947)(404, 1114)(405, 1115)(406, 950)(407, 951)(408, 958)(409, 1121)(410, 954)(411, 1118)(412, 1119)(413, 957)(414, 1126)(415, 959)(416, 960)(417, 1129)(418, 962)(419, 964)(420, 1132)(421, 1133)(422, 1134)(423, 965)(424, 972)(425, 973)(426, 974)(427, 1139)(428, 970)(429, 1141)(430, 1142)(431, 1137)(432, 1144)(433, 1145)(434, 976)(435, 977)(436, 984)(437, 1151)(438, 980)(439, 1148)(440, 1149)(441, 983)(442, 1156)(443, 985)(444, 986)(445, 1159)(446, 988)(447, 1161)(448, 989)(449, 1026)(450, 991)(451, 1165)(452, 994)(453, 1167)(454, 1168)(455, 996)(456, 1170)(457, 997)(458, 999)(459, 1172)(460, 1174)(461, 1000)(462, 1001)(463, 1005)(464, 1006)(465, 1143)(466, 1177)(467, 1179)(468, 1178)(469, 1183)(470, 1008)(471, 1009)(472, 1186)(473, 1154)(474, 1187)(475, 1013)(476, 1014)(477, 1189)(478, 1016)(479, 1190)(480, 1019)(481, 1192)(482, 1185)(483, 1021)(484, 1152)(485, 1138)(486, 1024)(487, 1136)(488, 1193)(489, 1028)(490, 1195)(491, 1037)(492, 1194)(493, 1198)(494, 1030)(495, 1031)(496, 1032)(497, 1200)(498, 1173)(499, 1034)(500, 1166)(501, 1197)(502, 1039)(503, 1203)(504, 1040)(505, 1205)(506, 1042)(507, 1043)(508, 1208)(509, 1111)(510, 1209)(511, 1047)(512, 1048)(513, 1211)(514, 1050)(515, 1212)(516, 1053)(517, 1214)(518, 1207)(519, 1055)(520, 1089)(521, 1065)(522, 1102)(523, 1182)(524, 1058)(525, 1059)(526, 1060)(527, 1218)(528, 1107)(529, 1062)(530, 1100)(531, 1216)(532, 1067)(533, 1221)(534, 1068)(535, 1223)(536, 1070)(537, 1224)(538, 1072)(539, 1073)(540, 1080)(541, 1230)(542, 1076)(543, 1227)(544, 1228)(545, 1079)(546, 1232)(547, 1081)(548, 1233)(549, 1083)(550, 1234)(551, 1084)(552, 1109)(553, 1086)(554, 1237)(555, 1127)(556, 1091)(557, 1239)(558, 1092)(559, 1094)(560, 1213)(561, 1095)(562, 1099)(563, 1128)(564, 1240)(565, 1215)(566, 1123)(567, 1104)(568, 1130)(569, 1124)(570, 1113)(571, 1122)(572, 1116)(573, 1243)(574, 1157)(575, 1117)(576, 1120)(577, 1238)(578, 1125)(579, 1235)(580, 1241)(581, 1225)(582, 1229)(583, 1131)(584, 1135)(585, 1158)(586, 1247)(587, 1176)(588, 1153)(589, 1140)(590, 1160)(591, 1146)(592, 1236)(593, 1147)(594, 1150)(595, 1244)(596, 1155)(597, 1245)(598, 1248)(599, 1184)(600, 1169)(601, 1191)(602, 1242)(603, 1162)(604, 1163)(605, 1164)(606, 1206)(607, 1246)(608, 1171)(609, 1196)(610, 1201)(611, 1175)(612, 1181)(613, 1220)(614, 1180)(615, 1217)(616, 1222)(617, 1210)(618, 1188)(619, 1219)(620, 1199)(621, 1202)(622, 1204)(623, 1226)(624, 1231)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 208 e = 624 f = 364
	degree seq :: [ 6^208 ]

E27.2364 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = $<624, 150>$ (small group id <624, 150>)
Aut   = $<624, 150>$ (small group id <624, 150>)
|r| :: 1
Presentation :: [ X2^2, (X2 * X1^-1)^3, X1^12, (X1^-2 * X2 * X1^-4)^2, (X1^-4 * X2 * X1 * X2)^2, (X1^2 * X2 * X1^-2 * X2 * X1^3)^2, X2 * X1^-2 * X2 * X1 * X2 * X1^-2 * X2 * X1^3 * X2 * X1^2 * X2 * X1^-2 * X2 * X1^3 * X2 * X1^2 * X2 * X1^-2 ]
Map::
	R = (1, 625, 2, 626, 5, 629, 11, 635, 21, 645, 37, 661, 63, 687, 62, 686, 36, 660, 20, 644, 10, 634, 4, 628)(3, 627, 7, 631, 15, 639, 27, 651, 47, 671, 79, 703, 104, 728, 91, 715, 54, 678, 31, 655, 17, 641, 8, 632)(6, 630, 13, 637, 25, 649, 43, 667, 73, 697, 119, 743, 103, 727, 128, 752, 78, 702, 46, 670, 26, 650, 14, 638)(9, 633, 18, 642, 32, 656, 55, 679, 92, 716, 106, 730, 64, 688, 105, 729, 86, 710, 51, 675, 29, 653, 16, 640)(12, 636, 23, 647, 41, 665, 69, 693, 113, 737, 101, 725, 61, 685, 102, 726, 118, 742, 72, 696, 42, 666, 24, 648)(19, 643, 34, 658, 58, 682, 97, 721, 108, 732, 66, 690, 38, 662, 65, 689, 107, 731, 96, 720, 57, 681, 33, 657)(22, 646, 39, 663, 67, 691, 109, 733, 99, 723, 59, 683, 35, 659, 60, 684, 100, 724, 112, 736, 68, 692, 40, 664)(28, 652, 49, 673, 83, 707, 132, 756, 181, 805, 142, 766, 90, 714, 143, 767, 186, 810, 135, 759, 84, 708, 50, 674)(30, 654, 52, 676, 87, 711, 138, 762, 176, 800, 127, 751, 80, 704, 129, 753, 171, 795, 123, 747, 75, 699, 44, 668)(45, 669, 76, 700, 124, 748, 172, 796, 222, 846, 166, 790, 120, 744, 167, 791, 217, 841, 162, 786, 115, 739, 70, 694)(48, 672, 81, 705, 130, 754, 177, 801, 140, 764, 88, 712, 53, 677, 89, 713, 141, 765, 180, 804, 131, 755, 82, 706)(56, 680, 94, 718, 146, 770, 195, 819, 246, 870, 188, 812, 137, 761, 154, 778, 206, 830, 198, 822, 147, 771, 95, 719)(71, 695, 116, 740, 163, 787, 218, 842, 204, 828, 152, 776, 159, 783, 213, 837, 265, 889, 209, 833, 156, 780, 110, 734)(74, 698, 121, 745, 168, 792, 223, 847, 174, 798, 125, 749, 77, 701, 126, 750, 175, 799, 226, 850, 169, 793, 122, 746)(85, 709, 136, 760, 187, 811, 244, 868, 194, 818, 145, 769, 93, 717, 144, 768, 193, 817, 240, 864, 183, 807, 133, 757)(98, 722, 150, 774, 202, 826, 259, 883, 261, 885, 205, 829, 153, 777, 111, 735, 157, 781, 210, 834, 203, 827, 151, 775)(114, 738, 160, 784, 214, 838, 269, 893, 220, 844, 164, 788, 117, 741, 165, 789, 221, 845, 272, 896, 215, 839, 161, 785)(134, 758, 184, 808, 241, 865, 299, 923, 250, 874, 192, 816, 237, 861, 295, 919, 356, 980, 291, 915, 234, 858, 178, 802)(139, 763, 190, 814, 248, 872, 307, 931, 349, 973, 284, 908, 228, 852, 179, 803, 235, 859, 292, 916, 249, 873, 191, 815)(148, 772, 199, 823, 256, 880, 316, 940, 258, 882, 201, 825, 149, 773, 200, 824, 257, 881, 312, 936, 253, 877, 196, 820)(155, 779, 207, 831, 262, 886, 322, 946, 267, 891, 211, 835, 158, 782, 212, 836, 268, 892, 325, 949, 263, 887, 208, 832)(170, 794, 227, 851, 283, 907, 347, 971, 288, 912, 232, 856, 189, 813, 247, 871, 306, 930, 343, 967, 280, 904, 224, 848)(173, 797, 230, 854, 286, 910, 351, 975, 405, 1029, 336, 960, 274, 898, 225, 849, 281, 905, 344, 968, 287, 911, 231, 855)(182, 806, 238, 862, 296, 920, 360, 984, 301, 925, 242, 866, 185, 809, 243, 867, 302, 926, 363, 987, 297, 921, 239, 863)(197, 821, 254, 878, 313, 937, 371, 995, 305, 929, 245, 869, 304, 928, 370, 994, 440, 1064, 375, 999, 309, 933, 251, 875)(216, 840, 273, 897, 335, 959, 403, 1027, 340, 964, 278, 902, 229, 853, 285, 909, 350, 974, 399, 1023, 332, 956, 270, 894)(219, 843, 276, 900, 338, 962, 407, 1031, 468, 1092, 393, 1017, 327, 951, 271, 895, 333, 957, 400, 1024, 339, 963, 277, 901)(233, 857, 289, 913, 353, 977, 421, 1045, 358, 982, 293, 917, 236, 860, 294, 918, 359, 983, 424, 1048, 354, 978, 290, 914)(252, 876, 310, 934, 376, 1000, 446, 1070, 380, 1004, 314, 938, 255, 879, 315, 939, 381, 1005, 449, 1073, 377, 1001, 311, 935)(260, 884, 320, 944, 386, 1010, 455, 1079, 383, 1007, 317, 941, 321, 945, 387, 1011, 459, 1083, 456, 1080, 384, 1008, 318, 942)(264, 888, 326, 950, 392, 1016, 466, 1090, 396, 1020, 330, 954, 275, 899, 337, 961, 406, 1030, 462, 1086, 389, 1013, 323, 947)(266, 890, 328, 952, 394, 1018, 469, 1093, 457, 1081, 385, 1009, 319, 943, 324, 948, 390, 1014, 463, 1087, 395, 1019, 329, 953)(279, 903, 341, 965, 409, 1033, 483, 1107, 413, 1037, 345, 969, 282, 906, 346, 970, 414, 1038, 486, 1110, 410, 1034, 342, 966)(298, 922, 364, 988, 434, 1058, 512, 1136, 438, 1062, 368, 992, 303, 927, 369, 993, 439, 1063, 508, 1132, 431, 1055, 361, 985)(300, 924, 366, 990, 436, 1060, 515, 1139, 579, 1203, 502, 1126, 426, 1050, 362, 986, 432, 1056, 509, 1133, 437, 1061, 367, 991)(308, 932, 374, 998, 444, 1068, 493, 1117, 417, 1041, 348, 972, 416, 1040, 492, 1116, 572, 1196, 520, 1144, 442, 1066, 372, 996)(331, 955, 397, 1021, 471, 1095, 549, 1173, 475, 1099, 401, 1025, 334, 958, 402, 1026, 476, 1100, 552, 1176, 472, 1096, 398, 1022)(352, 976, 420, 1044, 496, 1120, 559, 1183, 479, 1103, 404, 1028, 478, 1102, 558, 1182, 609, 1233, 574, 1198, 494, 1118, 418, 1042)(355, 979, 425, 1049, 501, 1125, 540, 1164, 505, 1129, 429, 1053, 365, 989, 435, 1059, 514, 1138, 544, 1168, 498, 1122, 422, 1046)(357, 981, 427, 1051, 503, 1127, 580, 1204, 521, 1145, 443, 1067, 373, 997, 423, 1047, 499, 1123, 577, 1201, 504, 1128, 428, 1052)(378, 1002, 450, 1074, 528, 1152, 573, 1197, 531, 1155, 453, 1077, 382, 1006, 454, 1078, 532, 1156, 588, 1212, 525, 1149, 447, 1071)(379, 1003, 451, 1075, 529, 1153, 595, 1219, 605, 1229, 587, 1211, 518, 1142, 448, 1072, 526, 1150, 593, 1217, 530, 1154, 452, 1076)(388, 1012, 460, 1084, 538, 1162, 598, 1222, 542, 1166, 464, 1088, 391, 1015, 465, 1089, 543, 1167, 516, 1140, 539, 1163, 461, 1085)(408, 1032, 482, 1106, 562, 1186, 497, 1121, 546, 1170, 467, 1091, 545, 1169, 602, 1226, 578, 1202, 500, 1124, 560, 1184, 480, 1104)(411, 1035, 487, 1111, 567, 1191, 533, 1157, 570, 1194, 490, 1114, 415, 1039, 491, 1115, 571, 1195, 534, 1158, 564, 1188, 484, 1108)(412, 1036, 488, 1112, 568, 1192, 613, 1237, 575, 1199, 495, 1119, 419, 1043, 485, 1109, 565, 1189, 611, 1235, 569, 1193, 489, 1113)(430, 1054, 506, 1130, 582, 1206, 616, 1240, 585, 1209, 510, 1134, 433, 1057, 511, 1135, 576, 1200, 614, 1238, 583, 1207, 507, 1131)(441, 1065, 519, 1143, 556, 1180, 477, 1101, 557, 1181, 513, 1137, 445, 1069, 523, 1147, 550, 1174, 473, 1097, 553, 1177, 517, 1141)(458, 1082, 470, 1094, 548, 1172, 604, 1228, 563, 1187, 597, 1221, 537, 1161, 535, 1159, 596, 1220, 612, 1236, 566, 1190, 536, 1160)(474, 1098, 554, 1178, 607, 1231, 624, 1248, 610, 1234, 561, 1185, 481, 1105, 551, 1175, 606, 1230, 623, 1247, 608, 1232, 555, 1179)(522, 1146, 581, 1205, 617, 1241, 592, 1216, 524, 1148, 591, 1215, 615, 1239, 589, 1213, 620, 1244, 594, 1218, 527, 1151, 590, 1214)(541, 1165, 600, 1224, 586, 1210, 618, 1242, 622, 1246, 603, 1227, 547, 1171, 599, 1223, 584, 1208, 619, 1243, 621, 1245, 601, 1225)
	L = (1, 627)(2, 630)(3, 625)(4, 633)(5, 636)(6, 626)(7, 640)(8, 637)(9, 628)(10, 643)(11, 646)(12, 629)(13, 632)(14, 647)(15, 652)(16, 631)(17, 654)(18, 657)(19, 634)(20, 659)(21, 662)(22, 635)(23, 638)(24, 663)(25, 668)(26, 669)(27, 672)(28, 639)(29, 673)(30, 641)(31, 677)(32, 680)(33, 642)(34, 683)(35, 644)(36, 685)(37, 688)(38, 645)(39, 648)(40, 689)(41, 694)(42, 695)(43, 698)(44, 649)(45, 650)(46, 701)(47, 704)(48, 651)(49, 653)(50, 705)(51, 709)(52, 712)(53, 655)(54, 714)(55, 717)(56, 656)(57, 718)(58, 722)(59, 658)(60, 725)(61, 660)(62, 727)(63, 728)(64, 661)(65, 664)(66, 729)(67, 734)(68, 735)(69, 738)(70, 665)(71, 666)(72, 741)(73, 744)(74, 667)(75, 745)(76, 749)(77, 670)(78, 751)(79, 752)(80, 671)(81, 674)(82, 753)(83, 757)(84, 758)(85, 675)(86, 761)(87, 763)(88, 676)(89, 766)(90, 678)(91, 730)(92, 767)(93, 679)(94, 681)(95, 768)(96, 772)(97, 773)(98, 682)(99, 774)(100, 776)(101, 684)(102, 743)(103, 686)(104, 687)(105, 690)(106, 715)(107, 777)(108, 778)(109, 779)(110, 691)(111, 692)(112, 782)(113, 783)(114, 693)(115, 784)(116, 788)(117, 696)(118, 790)(119, 726)(120, 697)(121, 699)(122, 791)(123, 794)(124, 797)(125, 700)(126, 800)(127, 702)(128, 703)(129, 706)(130, 802)(131, 803)(132, 806)(133, 707)(134, 708)(135, 809)(136, 812)(137, 710)(138, 813)(139, 711)(140, 814)(141, 816)(142, 713)(143, 716)(144, 719)(145, 810)(146, 820)(147, 821)(148, 720)(149, 721)(150, 723)(151, 824)(152, 724)(153, 731)(154, 732)(155, 733)(156, 831)(157, 835)(158, 736)(159, 737)(160, 739)(161, 837)(162, 840)(163, 843)(164, 740)(165, 846)(166, 742)(167, 746)(168, 848)(169, 849)(170, 747)(171, 852)(172, 853)(173, 748)(174, 854)(175, 856)(176, 750)(177, 857)(178, 754)(179, 755)(180, 860)(181, 861)(182, 756)(183, 862)(184, 866)(185, 759)(186, 769)(187, 869)(188, 760)(189, 762)(190, 764)(191, 871)(192, 765)(193, 875)(194, 867)(195, 876)(196, 770)(197, 771)(198, 879)(199, 829)(200, 775)(201, 830)(202, 832)(203, 884)(204, 836)(205, 823)(206, 825)(207, 780)(208, 826)(209, 888)(210, 890)(211, 781)(212, 828)(213, 785)(214, 894)(215, 895)(216, 786)(217, 898)(218, 899)(219, 787)(220, 900)(221, 902)(222, 789)(223, 903)(224, 792)(225, 793)(226, 906)(227, 908)(228, 795)(229, 796)(230, 798)(231, 909)(232, 799)(233, 801)(234, 913)(235, 917)(236, 804)(237, 805)(238, 807)(239, 919)(240, 922)(241, 924)(242, 808)(243, 818)(244, 927)(245, 811)(246, 928)(247, 815)(248, 914)(249, 932)(250, 918)(251, 817)(252, 819)(253, 934)(254, 938)(255, 822)(256, 941)(257, 942)(258, 939)(259, 943)(260, 827)(261, 945)(262, 947)(263, 948)(264, 833)(265, 951)(266, 834)(267, 952)(268, 954)(269, 955)(270, 838)(271, 839)(272, 958)(273, 960)(274, 841)(275, 842)(276, 844)(277, 961)(278, 845)(279, 847)(280, 965)(281, 969)(282, 850)(283, 972)(284, 851)(285, 855)(286, 966)(287, 976)(288, 970)(289, 858)(290, 872)(291, 979)(292, 981)(293, 859)(294, 874)(295, 863)(296, 985)(297, 986)(298, 864)(299, 989)(300, 865)(301, 990)(302, 992)(303, 868)(304, 870)(305, 993)(306, 996)(307, 997)(308, 873)(309, 988)(310, 877)(311, 994)(312, 1002)(313, 1003)(314, 878)(315, 882)(316, 1006)(317, 880)(318, 881)(319, 883)(320, 953)(321, 885)(322, 1012)(323, 886)(324, 887)(325, 1015)(326, 1017)(327, 889)(328, 891)(329, 944)(330, 892)(331, 893)(332, 1021)(333, 1025)(334, 896)(335, 1028)(336, 897)(337, 901)(338, 1022)(339, 1032)(340, 1026)(341, 904)(342, 910)(343, 1035)(344, 1036)(345, 905)(346, 912)(347, 1039)(348, 907)(349, 1040)(350, 1042)(351, 1043)(352, 911)(353, 1046)(354, 1047)(355, 915)(356, 1050)(357, 916)(358, 1051)(359, 1053)(360, 1054)(361, 920)(362, 921)(363, 1057)(364, 933)(365, 923)(366, 925)(367, 1059)(368, 926)(369, 929)(370, 935)(371, 1065)(372, 930)(373, 931)(374, 1052)(375, 1069)(376, 1071)(377, 1072)(378, 936)(379, 937)(380, 1075)(381, 1077)(382, 940)(383, 1078)(384, 1074)(385, 1011)(386, 1082)(387, 1009)(388, 946)(389, 1084)(390, 1088)(391, 949)(392, 1091)(393, 950)(394, 1085)(395, 1094)(396, 1089)(397, 956)(398, 962)(399, 1097)(400, 1098)(401, 957)(402, 964)(403, 1101)(404, 959)(405, 1102)(406, 1104)(407, 1105)(408, 963)(409, 1108)(410, 1109)(411, 967)(412, 968)(413, 1112)(414, 1114)(415, 971)(416, 973)(417, 1115)(418, 974)(419, 975)(420, 1113)(421, 1121)(422, 977)(423, 978)(424, 1124)(425, 1126)(426, 980)(427, 982)(428, 998)(429, 983)(430, 984)(431, 1130)(432, 1134)(433, 987)(434, 1137)(435, 991)(436, 1131)(437, 1140)(438, 1135)(439, 1141)(440, 1142)(441, 995)(442, 1111)(443, 1116)(444, 1146)(445, 999)(446, 1148)(447, 1000)(448, 1001)(449, 1151)(450, 1008)(451, 1004)(452, 1143)(453, 1005)(454, 1007)(455, 1157)(456, 1158)(457, 1159)(458, 1010)(459, 1161)(460, 1013)(461, 1018)(462, 1164)(463, 1165)(464, 1014)(465, 1020)(466, 1168)(467, 1016)(468, 1169)(469, 1171)(470, 1019)(471, 1174)(472, 1175)(473, 1023)(474, 1024)(475, 1178)(476, 1180)(477, 1027)(478, 1029)(479, 1181)(480, 1030)(481, 1031)(482, 1179)(483, 1187)(484, 1033)(485, 1034)(486, 1190)(487, 1066)(488, 1037)(489, 1044)(490, 1038)(491, 1041)(492, 1067)(493, 1197)(494, 1177)(495, 1182)(496, 1200)(497, 1045)(498, 1170)(499, 1202)(500, 1048)(501, 1162)(502, 1049)(503, 1186)(504, 1205)(505, 1184)(506, 1055)(507, 1060)(508, 1198)(509, 1208)(510, 1056)(511, 1062)(512, 1183)(513, 1058)(514, 1167)(515, 1210)(516, 1061)(517, 1063)(518, 1064)(519, 1076)(520, 1212)(521, 1213)(522, 1068)(523, 1211)(524, 1070)(525, 1215)(526, 1218)(527, 1073)(528, 1195)(529, 1216)(530, 1176)(531, 1214)(532, 1191)(533, 1079)(534, 1080)(535, 1081)(536, 1194)(537, 1083)(538, 1125)(539, 1223)(540, 1086)(541, 1087)(542, 1224)(543, 1138)(544, 1090)(545, 1092)(546, 1122)(547, 1093)(548, 1225)(549, 1229)(550, 1095)(551, 1096)(552, 1154)(553, 1118)(554, 1099)(555, 1106)(556, 1100)(557, 1103)(558, 1119)(559, 1136)(560, 1129)(561, 1226)(562, 1127)(563, 1107)(564, 1221)(565, 1236)(566, 1110)(567, 1156)(568, 1228)(569, 1238)(570, 1160)(571, 1152)(572, 1239)(573, 1117)(574, 1132)(575, 1240)(576, 1120)(577, 1234)(578, 1123)(579, 1222)(580, 1232)(581, 1128)(582, 1233)(583, 1242)(584, 1133)(585, 1243)(586, 1139)(587, 1147)(588, 1144)(589, 1145)(590, 1155)(591, 1149)(592, 1153)(593, 1230)(594, 1150)(595, 1231)(596, 1227)(597, 1188)(598, 1203)(599, 1163)(600, 1166)(601, 1172)(602, 1185)(603, 1220)(604, 1192)(605, 1173)(606, 1217)(607, 1219)(608, 1204)(609, 1206)(610, 1201)(611, 1246)(612, 1189)(613, 1245)(614, 1193)(615, 1196)(616, 1199)(617, 1248)(618, 1207)(619, 1209)(620, 1247)(621, 1237)(622, 1235)(623, 1244)(624, 1241)
	local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph::
	v = 52 e = 624 f = 520
	degree seq :: [ 24^52 ]

## Checksum: 2364 records.
## Written on: Sat Jan 25 08:49:59 CET 2020